Split (1)

train · 2.95M rows

url stringlengths 14 1.76k	text stringlengths 100 1.02M	metadata stringlengths 1.06k 1.1k
https://www.envoyproxy.io/docs/envoy/v1.17.4/api-v3/extensions/transport_sockets/starttls/v3/starttls.proto	# StartTls¶ This extension may be referenced by the qualified name envoy.transport_sockets.starttls Note This extension is intended to be robust against both untrusted downstream and upstream traffic. StartTls transport socket addresses situations when a protocol starts in clear-text and negotiates an in-band switch to TLS. StartTls transport socket is protocol agnostic and requires a network filter which understands protocol exchange and a state machine to signal to the StartTls transport socket when a switch to TLS is required. ## extensions.transport_sockets.starttls.v3.StartTlsConfig¶ [extensions.transport_sockets.starttls.v3.StartTlsConfig proto] Configuration for StartTls transport socket. StartTls transport socket wraps two sockets: - raw_buffer socket which is used at the beginning of the session - TLS socket used when a protocol negotiates a switch to encrypted traffic. { "cleartext_socket_config": "{...}", "tls_socket_config": "{...}" } cleartext_socket_config (extensions.transport_sockets.raw_buffer.v3.RawBuffer) (optional) Configuration for clear-text socket used at the beginning of the session. tls_socket_config (extensions.transport_sockets.tls.v3.DownstreamTlsContext, REQUIRED) Configuration for TLS socket.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47084900736808777, "perplexity": 15937.468510517383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00179.warc.gz"}
http://gmatclub.com/forum/what-is-the-greatest-value-of-m-such-that-4-m-is-a-factor-of-105746.html?kudos=1	Find all School-related info fast with the new School-Specific MBA Forum It is currently 09 Oct 2015, 21:56 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # What is the greatest value of m such that 4^m is a factor of Author Message TAGS: Director Joined: 07 Jun 2004 Posts: 614 Location: PA Followers: 3 Kudos [?]: 392 [4] , given: 22 What is the greatest value of m such that 4^m is a factor of [#permalink] 03 Dec 2010, 17:12 4 KUDOS 22 This post was BOOKMARKED 00:00 Difficulty: 35% (medium) Question Stats: 64% (01:53) correct 36% (01:13) wrong based on 819 sessions What is the greatest value of m such that 4^m is a factor of 30! ? (A) 13 (B) 12 (C) 11 (D) 7 (E) 6 is there an easier way to do this other than brute force [Reveal] Spoiler: OA _________________ If the Q jogged your mind do Kudos me : ) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5972 Location: Pune, India Followers: 1528 Kudos [?]: 8445 [16] , given: 194 Re: Facorial PS [#permalink] 03 Dec 2010, 18:55 16 KUDOS Expert's post 9 This post was BOOKMARKED Ok. So lets take a simple example first: What is the greatest value of m such that 2^m is a factor of 10! We need to find the number of 2s in 10! Method: Step 1: 10/2 = 5 Step 2: 5/2 = 2 Step 3: 2/2 = 1 Step 4: Add all: 5 + 2 + 1 = 8 (Answer) Logic: 10! = 12345678910 Every alternate number will have a 2. Out of 10 numbers, 5 numbers will have a 2. (Hence Step 1: 10/2 = 5) These 5 numbers are 2, 4, 6, 8, 10 Now out of these 5 numbers, every alternate number will have another 2 since it will be a multiple of 4 (Hence Step 2: 5/2 = 2) These 2 numbers will be 4 and 8. Out of these 2 numbers, every alternate number will have yet another 2 because it will be a multiple of 8. (Hence Step 3: 2/2 = 1) This single number is 8. Now all 2s are accounted for. Just add them 5 + 2 + 1 = 8 (Hence Step 4) These are the number of 2s in 10!. Similarly, you can find maximum power of any prime number in any factorial. If the question says 4^m, then just find the number of 2s and half it. If the question says 6^m, then find the number of 3s and that will be your answer (because to make a 6, you need a 3 and a 2. You have definitely more 2s in 10! than 3s. So number of 3s is your limiting condition.) Let's take this example: Maximum power of 6 in 40!. 40/3 = 13 13/3 = 4 4/3 = 1 Total number of 3s = 13 + 4 + 1 = 18 40/2 = 20 20/2 = 10 10/2 = 5 5/2 = 2 2/2 = 1 Total number of 2s in 40! is 20+10 + 5 + 2 + 1 = 38 Definitely, number of 3s are less so we can make only 18 6s in spite of having many more 2s. Usually, the greatest prime number will be the limiting condition. And if you are still with me, then tell me, what happens if I ask for the greatest power of 12 in 40!? _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 29802 Followers: 4905 Kudos [?]: 53661 [10] , given: 8167 Re: Facorial PS [#permalink] 04 Dec 2010, 01:42 10 This post received KUDOS Expert's post 9 This post was BOOKMARKED rxs0005 wrote: What is the greatest value of m such that 4m is a factor of 30! ? (A) 13 (B) 12 (C) 11 (D) 7 (E) 6 is there an easier way to do this other than brute force Finding the number of powers of a prime number k, in the n!. The formula is: $$\frac{n}{k}+\frac{n}{k^2}+\frac{n}{k^3}$$ ... till $$n>k^x$$ For example: what is the power of 2 in 25! (the highest value of m for which 2^m is a factor of 25!) $$\frac{25}{2}+\frac{25}{4}+\frac{25}{8}+\frac{25}{16}=12+6+3+1=22$$. So the highest power of 2 in 25! is 22: $$2^{22}k=25!$$, where k is the product of other multiple of 25!. Check for more: everything-about-factorials-on-the-gmat-85592.html and math-number-theory-88376.html Back to the original question: What is the greatest value of m such that 4^m is a factor of 30! ? A. 13 B. 12 C. 11 D. 7 E. 6 First of all it should be 4^m instead of 4m. Now, $$4^m=2^{2m}$$, so we should check the highest power of 2 in 30!: $$\frac{30}{2}+\frac{30}{4}+\frac{30}{8}+\frac{30}{16}=15+7+3+1=26$$. So the highest power of 2 in 30! is 26 --> $$2m=26$$ --> $$m=13$$. Answer: A. Hope it's clear. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5972 Location: Pune, India Followers: 1528 Kudos [?]: 8445 [8] , given: 194 Re: Facorial PS [#permalink] 04 Dec 2010, 05:49 8 This post received KUDOS Expert's post 1 This post was BOOKMARKED whiplash2411 wrote: Would that also be 18? Since 12 is 62 and 6 would be the limiting factor? I feel like I might be missing something Also kudos! Your explanation was fantastic. Posted from my mobile device Yes, greatest power of 12 in 40! will also be 18 because 12= 32^2 Total number of 3s = 13 + 4 + 1 = 18 (as shown above) Total number of 2s in 40! is 20+10 + 5 + 2 + 1 = 38 (as shown above) So you can make 19 4s. The limiting factor is still 3. So rxs0005, bhushan288 and whiplash2411, you all had correct answers. The interesting thing is the maximum power of 12 in 30! 30/2 = 15 15/2 = 7 7/2 = 3 3/2 = 1 Total 2s = 15 + 7 + 3 + 1 = 26 So you can make 13 4s 30/3 = 10 10/3 = 3 3/3 = 1 Total 3s = 10 + 3 + 1 = 14! The maximum power of 12 is 13, not 14. Here, the limiting factor is the number of 4s (i.e. half of the number of 2s). Of course the number of 2s is more but that number gets divided by 2 to make 4s. It becomes the limiting factor. In such cases, you will need to check for both 2 and 3. _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5972 Location: Pune, India Followers: 1528 Kudos [?]: 8445 [7] , given: 194 Re: Facorial PS [#permalink] 03 Dec 2010, 18:33 7 KUDOS Expert's post 3 This post was BOOKMARKED rxs0005 wrote: What is the greatest value of m such that 4m is a factor of 30! ? (A) 13 (B) 12 (C) 11 (D) 7 (E) 6 is there an easier way to do this other than brute force I think the question is What is the greatest value of m such that $$4^m$$ is a factor of 30! ? The easiest way to do this is the following: Divide 30 by 2. You get 15 Divide 15 by 2. You get 7. (Ignore remainder) Divide 7 by 2. You get 3. Divide 3 by 2. You get 1. Since greatest power of 2 in 30! is 26, greatest power of 4 in 30! will be 13. I will explain the logic behind the process in a while. (It will take some effort to formulate.) _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 29802 Followers: 4905 Kudos [?]: 53661 [6] , given: 8167 Re: Facorial PS [#permalink] 04 Dec 2010, 06:11 6 This post received KUDOS Expert's post 5 This post was BOOKMARKED Examples about the same concept from: everything-about-factorials-on-the-gmat-85592-20.html Highest power of 12 in 18!: Suppose we have the number $$18!$$ and we are asked to to determine the power of $$12$$ in this number. Which means to determine the highest value of $$x$$ in $$18!=12^xa$$, where $$a$$ is the product of other multiples of $$18!$$. $$12=2^23$$, so we should calculate how many 2-s and 3-s are in $$18!$$. Calculating 2-s: $$\frac{18}{2}+\frac{18}{2^2}+\frac{18}{2^3}+\frac{18}{2^4}=9+4+2+1=16$$. So the power of $$2$$ (the highest power) in prime factorization of $$18!$$ is $$16$$. Calculating 3-s: $$\frac{18}{3}+\frac{18}{3^2}=6+2=8$$. So the power of $$3$$ (the highest power) in prime factorization of $$18!$$ is $$8$$. Now as $$12=2^23$$ we need twice as many 2-s as 3-s. $$18!=2^{16}3^8a=(2^2)^83^8a=(2^23)^8a=12^8a$$. So $$18!=12^8a$$ --> $$x=8$$. The highest power of 900 in 50!: $$50!=900^xa=(2^23^25^2)^xa$$, where $$x$$ is the highest possible value of 900 and $$a$$ is the product of other multiples of $$50!$$. Find the highest power of 2: $$\frac{50}{2}+\frac{50}{4}+\frac{50}{8}+\frac{50}{16}+\frac{50}{32}=25+12+6+3+1=47$$ --> $$2^{47}$$; Find the power of 3: $$\frac{50}{3}+\frac{50}{9}+\frac{50}{27}=16+5+1=22$$ --> $$3^{22}$$; Find the power of 5: $$\frac{50}{5}+\frac{50}{25}=10+2=12$$ --> $$5^{12}$$; So, $$50!=2^{47}3^{22}5^{12}b=(2^23^25^2)^6(2^{35}3^{10})b=900^{6}(2^{35}3^{10})b$$, where $$b$$ is the product of other multiples of $$50!$$. So $$x=6$$. Hope it helps. _________________ Math Expert Joined: 02 Sep 2009 Posts: 29802 Followers: 4905 Kudos [?]: 53661 [1] , given: 8167 Re: Facorial PS [#permalink] 25 Jun 2012, 04:42 1 This post received KUDOS Expert's post kashishh wrote: Bunuel wrote: rxs0005 wrote: What is the greatest value of m such that 4m is a factor of 30! ? (A) 13 (B) 12 (C) 11 (D) 7 (E) 6 is there an easier way to do this other than brute force Finding the number of powers of a prime number k, in the n!. The formula is: $$\frac{n}{k}+\frac{n}{k^2}+\frac{n}{k^3}$$ ... till $$n>k^x$$ For example: what is the power of 2 in 25! (the highest value of m for which 2^m is a factor of 25!) $$\frac{25}{2}+\frac{25}{4}+\frac{25}{8}+\frac{25}{16}=12+6+3+1=22$$. So the highest power of 2 in 25! is 22: $$2^{22}k=25!$$, where k is the product of other multiple of 25!. Check for more: everything-about-factorials-on-the-gmat-85592.html and math-number-theory-88376.html Back to the original question: What is the greatest value of m such that 4^m is a factor of 30! ? A. 13 B. 12 C. 11 D. 7 E. 6 First of all it should be 4^m instead of 4m. Now, $$4^m=2^{2m}$$, so we should check the highest power of 2 in 30!: $$\frac{30}{2}+\frac{30}{4}+\frac{30}{8}+\frac{30}{16}=15+7+3+1=26$$. So the highest power of 2 in 30! is 26 --> $$2m=26$$ --> $$m=13$$. Answer: A. Hope it's clear. Dear Bunuel, is this formulae is applied with primes ( 2, 3 ..) only? the doubt is because you reduced 4 into 2.. You can apply this formula to ANY prime. I used the base of 2 instead of 4 since 4 is not a prime. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5972 Location: Pune, India Followers: 1528 Kudos [?]: 8445 [1] , given: 194 Re: What is the greatest value of m such that 4^m is a factor of [#permalink] 30 Apr 2015, 22:00 1 This post received KUDOS Expert's post MeliMeds wrote: VeritasPrepKarishma wrote: Ok. So lets take a simple example first: What is the greatest value of m such that 2^m is a factor of 10! We need to find the number of 2s in 10! Method: Step 1: 10/2 = 5 Step 2: 5/2 = 2 Step 3: 2/2 = 1 Step 4: Add all: 5 + 2 + 1 = 8 (Answer) Logic: 10! = 12345678910 Every alternate number will have a 2. Out of 10 numbers, 5 numbers will have a 2. (Hence Step 1: 10/2 = 5) These 5 numbers are 2, 4, 6, 8, 10 Now out of these 5 numbers, every alternate number will have another 2 since it will be a multiple of 4 (Hence Step 2: 5/2 = 2) These 2 numbers will be 4 and 8. Out of these 2 numbers, every alternate number will have yet another 2 because it will be a multiple of 8. (Hence Step 3: 2/2 = 1) This single number is 8. Now all 2s are accounted for. Just add them 5 + 2 + 1 = 8 (Hence Step 4) These are the number of 2s in 10!. Similarly, you can find maximum power of any prime number in any factorial. If the question says 4^m, then just find the number of 2s and half it. If the question says 6^m, then find the number of 3s and that will be your answer (because to make a 6, you need a 3 and a 2. You have definitely more 2s in 10! than 3s. So number of 3s is your limiting condition.) Let's take this example: Maximum power of 6 in 40!. 40/3 = 13 13/3 = 4 4/3 = 1 Total number of 3s = 13 + 4 + 1 = 18 40/2 = 20 20/2 = 10 10/2 = 5 5/2 = 2 2/2 = 1 Total number of 2s in 40! is 20+10 + 5 + 2 + 1 = 38 Definitely, number of 3s are less so we can make only 18 6s in spite of having many more 2s. Usually, the greatest prime number will be the limiting condition. And if you are still with me, then tell me, what happens if I ask for the greatest power of 12 in 40!? Wow thanks for the A-1 explanation and breakdown! To answer your final question, would it be 9? (applying the same principle we used in attacking the original question, where we found the number of 2's in 30 then divided it by 2 to derive the number of 4's, I subsequently found the number of 3's (as the larger of the two primes, 2 and 3 found in 12) in 40 which is 18, and because that would correspond with the number of 6's in 40, I proceeded to divide this by 2 to get 9 as a final choice... Hope I'm not joining the party too late, please advise if this is correct? Power of 12 in 40! 12 = 223 So to make a 12, you need two 2s and a 3. How many 2s are there in 40!? 40/2 = 20 20/2 = 10 10/2 = 5 5/2 = 2 2/2 = 1 Total = 38 For every 12, we need two 2s so we can make 38/2 = 19 12s. How many 3s are there in 40!? 40/3 = 13 13/3 = 4 4/3 = 1 Total = 18 Every 12 needs only one 3 so out of 18 3s, we can make 18 12s. We have enough 2s to make 19 12s and enough 3s to make 18 12s. So 3 is the limiting condition so you can make 18 12s. So highest power of 12 in 40! is 18. Here is a post with some more details on this concept: http://www.veritasprep.com/blog/2011/06 ... actorials/ _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199 Veritas Prep Reviews Ms. Big Fat Panda Status: Three Down. Joined: 09 Jun 2010 Posts: 1923 Concentration: General Management, Nonprofit Followers: 399 Kudos [?]: 1653 [0], given: 210 Re: Facorial PS [#permalink] 03 Dec 2010, 17:20 Expert's post 1 This post was BOOKMARKED Pretty simple, really. Answer is A. If m = 13, then 4m = 52, which is 26x2, both of which are included in 30! Since 13 is the largest number here, its the answer. Ms. Big Fat Panda Status: Three Down. Joined: 09 Jun 2010 Posts: 1923 Concentration: General Management, Nonprofit Followers: 399 Kudos [?]: 1653 [0], given: 210 Re: Facorial PS [#permalink] 03 Dec 2010, 19:05 Expert's post Would that also be 18? Since 12 is 62 and 6 would be the limiting factor? I feel like I might be missing something Also kudos! Your explanation was fantastic. Posted from my mobile device Intern Joined: 21 Jun 2010 Posts: 5 Followers: 0 Kudos [?]: 14 [0], given: 1 Re: Facorial PS [#permalink] 04 Dec 2010, 00:55 Will it be 18 bcoz greatest prime number is 3.. 40/3 13 13/3 4 4/3 1 so total 13+4+1 =18.. Director Joined: 07 Jun 2004 Posts: 614 Location: PA Followers: 3 Kudos [?]: 392 [0], given: 22 Re: Facorial PS [#permalink] 04 Dec 2010, 01:06 thanks for the explanation will it be 18 ? _________________ If the Q jogged your mind do Kudos me : ) Senior Manager Joined: 08 Nov 2010 Posts: 419 Followers: 7 Kudos [?]: 65 [0], given: 161 Re: Facorial PS [#permalink] 11 Dec 2010, 13:54 VeritasPrepKarishma, great work explaining this one. Thanks. _________________ Senior Manager Status: Bring the Rain Joined: 17 Aug 2010 Posts: 407 Location: United States (MD) Concentration: Strategy, Marketing Schools: Michigan (Ross) - Class of 2014 GMAT 1: 730 Q49 V39 GPA: 3.13 WE: Corporate Finance (Aerospace and Defense) Followers: 7 Kudos [?]: 43 [0], given: 46 Re: Facorial PS [#permalink] 11 Dec 2010, 18:59 Thanks for all the examples _________________ Manager Joined: 07 Jun 2010 Posts: 86 Followers: 1 Kudos [?]: 25 [0], given: 0 Re: Facorial PS [#permalink] 15 Feb 2011, 17:42 Thanks for the help on these. Manager Joined: 27 May 2012 Posts: 213 Followers: 0 Kudos [?]: 52 [0], given: 424 Re: Facorial PS [#permalink] 19 Jun 2012, 05:45 VeritasPrepKarishma wrote: whiplash2411 wrote: Would that also be 18? Since 12 is 62 and 6 would be the limiting factor? I feel like I might be missing something Also kudos! Your explanation was fantastic. Posted from my mobile device Yes, greatest power of 12 in 40! will also be 18 because 12= 32^2 Total number of 3s = 13 + 4 + 1 = 18 (as shown above) Total number of 2s in 40! is 20+10 + 5 + 2 + 1 = 38 (as shown above) So you can make 19 4s. The limiting factor is still 3. The interesting thing is the maximum power of 12 in 30! 30/2 = 15 15/2 = 7 7/2 = 3 3/2 = 1 Total 2s = 15 + 7 + 3 + 1 = 26 So you can make 13 4s 30/3 = 10 10/3 = 3 3/3 = 1 Total 3s = 10 + 3 + 1 = 14! The maximum power of 12 is 13, not 14. Here, the limiting factor is the number of 4s (i.e. half of the number of 2s). Of course the number of 2s is more but that number gets divided by 2 to make 4s. It becomes the limiting factor. In such cases, you will need to check for both 2 and 3. Applauds to both karishma and Bunuel for such wonderful way to attack these problems karishma's way seemed easier at first , until I encountered highest power of 12 in 30! somehow I understood : that I found the highest power of 2's then halved it to get 13 no. of 3's is 14 , so as explained the answer is 13 and not 14 because in this case the highest prime is not the limiting factor but rather 2^2 is the limiting factor. Till here it was clear. but I got stuck when I came to bunuels example of highest power of 900 in 50! Karishma how to do it by your method? ( want to grasp both methods and then decide , which i'd like to use ) Highest no of 2's as shown by bunuel is 47 , now I cannot half it to find the highest power of 4 , that will give me a non integer. Also highest power of greatest prime ( 5) is 12 and answer to this question is 6 so my concern , what is the limiting factor here , or how to approach this problem ,lets say Karishma's way . _________________ - Stne Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5972 Location: Pune, India Followers: 1528 Kudos [?]: 8445 [0], given: 194 Re: Facorial PS [#permalink] 19 Jun 2012, 06:03 Expert's post 1 This post was BOOKMARKED stne wrote: but I got stuck when I came to bunuels example of highest power of 900 in 50! Karishma how to do it by your method? ( want to grasp both methods and then decide , which i'd like to use ) Highest no of 2's as shown by bunuel is 47 , now I cannot half it to find the highest power of 4 , that will give me a non integer. Also highest power of greatest prime ( 5) is 12 and answer to this question is 6 so my concern , what is the limiting factor here , or how to approach this problem ,lets say Karishma's way . Let me ask you a question first: What is the limiting factor in case you want to find the highest power of 6 in 50! Would you say it is 3? Sure! You make a 6 using a 2 and a 3. You certainly will have fewer 3s as compared to number of 2s. What is the limiting factor in case you want to find the highest power of 36 in 50! Think! $$36 = 2^2 * 3^2$$ Whatever the number of 2s and number of 3s, you will halve both of them. So again, the limiting factor will be 3. $$900 = 2^2 * 3^2 * 5^2$$ Again, 5 will be your limiting factor here. Whatever the number of 2, 3 and 5, each will be halved. So you will still have the fewest number of half 5s (so to say). Number of 5s is 12. So you can make six 900s from 50! The question mark arises only when you have different powers and the smaller number has a higher power. What is the limiting factor in case of $$2^23$$? Not sure. We need to check. What is the limiting factor in case of $$2^43^27$$? Not sure. We need to check. What is the limiting factor in case of $$37^2$$? It has to be 7. We find the number of 7s (which is fewer than the number of 3s) and then further half it. _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for \$199 Veritas Prep Reviews Manager Joined: 02 Jun 2011 Posts: 160 Followers: 1 Kudos [?]: 47 [0], given: 11 Re: Facorial PS [#permalink] 25 Jun 2012, 04:38 Bunuel wrote: rxs0005 wrote: What is the greatest value of m such that 4m is a factor of 30! ? (A) 13 (B) 12 (C) 11 (D) 7 (E) 6 is there an easier way to do this other than brute force Finding the number of powers of a prime number k, in the n!. The formula is: $$\frac{n}{k}+\frac{n}{k^2}+\frac{n}{k^3}$$ ... till $$n>k^x$$ For example: what is the power of 2 in 25! (the highest value of m for which 2^m is a factor of 25!) $$\frac{25}{2}+\frac{25}{4}+\frac{25}{8}+\frac{25}{16}=12+6+3+1=22$$. So the highest power of 2 in 25! is 22: $$2^{22}k=25!$$, where k is the product of other multiple of 25!. Check for more: everything-about-factorials-on-the-gmat-85592.html and math-number-theory-88376.html Back to the original question: What is the greatest value of m such that 4^m is a factor of 30! ? A. 13 B. 12 C. 11 D. 7 E. 6 First of all it should be 4^m instead of 4m. Now, $$4^m=2^{2m}$$, so we should check the highest power of 2 in 30!: $$\frac{30}{2}+\frac{30}{4}+\frac{30}{8}+\frac{30}{16}=15+7+3+1=26$$. So the highest power of 2 in 30! is 26 --> $$2m=26$$ --> $$m=13$$. Hope it's clear. Dear Bunuel, is this formulae is applied with primes ( 2, 3 ..) only? the doubt is because you reduced 4 into 2.. Math Expert Joined: 02 Sep 2009 Posts: 29802 Followers: 4905 Kudos [?]: 53661 [0], given: 8167 Re: What is the greatest value of m such that 4^m is a factor of [#permalink] 22 Aug 2013, 04:11 Expert's post Bumping for review and further discussion. _________________ Manager Joined: 10 Mar 2014 Posts: 206 Followers: 1 Kudos [?]: 16 [0], given: 13 Re: What is the greatest value of m such that 4^m is a factor of [#permalink] 22 Apr 2014, 07:55 We can write 4 (power m) as 2(power2)m then 30/2+30/4+30/8+30/16 = 15 +7+3+1 2m= 26 m = 13 Re: What is the greatest value of m such that 4^m is a factor of [#permalink] 22 Apr 2014, 07:55 Go to page 1 2 Next [ 25 posts ] Similar topics Replies Last post Similar Topics: 5 The greatest common factor of positive integers m and n is 12. What is 4 08 Jul 2015, 02:43 If [m]6^x3^y = 2^6*9^4[/m], then what is the Value of y? 1 22 May 2015, 05:27 4 If m = 3^n, what is the greatest value of n for which m is a 3 23 Jul 2013, 06:52 2 (x + 7) is a factor in x^2 - mx - 56. What is the value of m 4 05 Dec 2012, 07:00 11 If 6^k is a factor of (40!), what is the greatest possible value of k? 7 10 Aug 2011, 08:00 Display posts from previous: Sort by	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.63036048412323, "perplexity": 2142.962133244006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737940794.79/warc/CC-MAIN-20151001221900-00175-ip-10-137-6-227.ec2.internal.warc.gz"}
https://brilliant.org/problems/boolean-algebra/	Boolean Algebra Logic Level 2 $\neg \big(\neg (p \implies q) \implies \neg (q \implies p)\big)$ Which of the given options is equivalent to the above Boolean expression? ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9707754254341125, "perplexity": 4831.789115978411}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039491784.79/warc/CC-MAIN-20210420214346-20210421004346-00213.warc.gz"}
http://astronomy.stackexchange.com/questions/9/could-someone-explain-ra-dec-in-simple-terms/46	# Could someone explain RA/dec in simple terms? The equatorial coordinate system isn't too complicated. However, for people new to this, it seems rather intimidating at first. Is there an easy way to explain it? - A system projected into the sky Pretend all the stars are painted on the inside of a large ball, and you are at the center of the ball. The imagined ball is called the Celestial Sphere. If the Earth wasn't blocking the lower half of your view, and the Sun wasn't making the blue sky so bright, you would be able to look at the stars in any direction. First, the rotation of the Earth causes the imagined ball of stars to appear to move around the sky. If you lay on your back, (in the norther hemisphere,) with your head to the north, the stars slowly slide by from left to right. There are two points however, where the stars don't appear to move: These two points are directly above the Earth's north and south poles. These two points, projected out into the sky are labeled the North, and South, Celestial Poles. Next, the Earth's equator is projected out into the sky and labeled the Celestial Equator. Finally, sorting out the east-west positioning, (ie left-right if you lay on your back, head to the north), requires an arbitrary selection: There are an infinite number of circles one can imagine drawing on the sky. (For example, small circles the size of the moon, and also many much bigger circles.) The largest circle you can draw is called a "great circle", from geometry. Point at the North Celestial Pole, (way above and behind your head if you face south in the northern hemisphere,) and draw a line straight south to the horizon, then down below your feet through the South celestial pole and back up to the North Celestial Pole. You have just drawn one Great Circle, through the Celestial Poles, all the way around the Celestial Sphere. But that Great Circle is just one of an infinite number of similar ones. One could start at the North Celestial Pole and draw a Great Circle a little to the left or the right. So astronomers have chosen one specific Great Circle and labeled one side of that circle as "zero degrees" -- or, "we will start measuring angles from here." So how do we use this system? "right ascension" is measured rightward, (from your left to your right if you face south in the northern hemisphere,) from the zero-degrees half of that chosen great circle. So given a right ascension, one can find the corresponding half of a great circle. For a given right ascension, you have half of circle selected from the North Celestial Pole, to the South Celestial Pole. (This is called a line of equal longitude.) "declination" is measured from the Celestial Equator. The Celestial Equator cuts through the middle of your line of longitude. From the Celestial Equator it is 90° northward(+) to the North Celestial Pole, and 90° southward(-) to the South Celestial Pole. So we can measure from +90° (northward) to -90° (southward) along that line of longitude, from the Celestial Equator. (Don't be confused by "positive declinations"; 45° of declination is northward from the Celestial Equator.) Notice that the system does not depend on where you are standing on Earth, nor on the time of day. If you have a Right Ascension and a Declination, you have an unambiguous spot specified on the Celestial Sphere. The system is actually very simple, but the rotation (time of day) of the Earth, and where you are geographically located needs to also be figured in. What's over my head right now? Face south, (if you're in the northern hemisphere.) What is your latitude -- geographically, how far north are you from the Earth's equator? If you are 40° north, then Celestial declination of 40° north is directly over your head. Declination of 50° is 10° further northward from directly over your head, etc. But for that declination, you have a great circle -- left-to-right across the whole sky that has that same declination. Right ascension you simply have to look up. That arbitrarily chosen, zero-degree line, appears to spin around the sky every day at the Earth rotates. Also, over the course of a year, the Earth's orbit about the sun makes an extra apparent turn of the sky. (What is overhead mid-winter, is directly under your feet mid-summer!) So there's an offset -- what right ascension is overhead on this date at midnight, and how far (in hours) are we from midnight right now? Combining those two you can figure out what Right Ascension is over head at any time, on any date. (potential editors: I've intentionally not used acronyms for NCP, RA, etc as that makes it more complicated for people learning this material.) - The easiest way to think of equatorial coordinates is by extending lines of latitude/longitude (the geographic coordinate system we usually learn in school) out into space. The earth's equator becomes the celestial equator, and the north and south poles become the celestial north and south poles, respectively. By doing this you have a fairly simple way to describe the location of an object in space. Each location is described by a pair of coordinates: 1) Declination (dec), which is measured in degrees (-90 for the south celestial pole, 0 for the celestial equator, and +90 for the north celestial pole). Partial degrees are usually described in terms of minutes (') and seconds (''). Think of declination as latitude. 2) Right Ascension (RA), which is usually measured in hours, minutes, and seconds. Think of this as terrestrial longitude extended out into space, then measuring it in hours makes a bit more sense (time zones). You could just as easily measure it in degrees, too, where 1 hour is 15 degrees. RA is measured from the point where the sun crosses the celestial equator at the March equinox (located in Pisces). - The equatorial coordinate system is very similar to the system used on a globe or on maps. To specify a point on a sphere or a globe you need only two numbers. These are the longitudes and latitudes. On a globe of the earth you have longitudes from -180º to +180º and latitudes from -90º to +90º. The south pole lies at -90º latitude, the north pole at +90º latitude. The sky uses the same system, projected onto the imaginary celestial sphere. The sky's equator is at the same position as the earth's equator. Only projected onto the (infinitely large) sky sphere. You can find lots of very nice pictures of this on the web. However, since the earth rotates, the sky's coordinate system would rotate also, if it only were a synchronized projection. So every star would have a coordinate that depended on the time of day! To solve this, the equatorial coordinate system is fixed on the equinox points. Since the earth is tilted, the eclipitc (i.e. the earth's orbit around the sun) has two intersections with the sky's equator. These are the equinox points. The sun will be located there during the days of spring and autumn when day and night are of equal length. These points on the sky sphere are relatively fixed and well suited for pinning down the coordinate system. The sky's coordinate system is not using the degree notation for both longitude and latitude. Instead we use the terms Right Acension (i.e. longitude), which goes from 0h to 24h, similar to a day on earth. And the other is Declination (i.e. latitude), which goes from -90º to +90º. This is similar to the earth's traditional coordinate system. So every fixed star can be assigned a coordinate in the sky which is independent of the time of day or year. For example, the star Sirius (α CMa) has the following coordinates: RA 06h 45m 08.9173s Dec −16° 42′ 58.017″ These can be programmed into computerized telescope mounts, which can then find and track the star as it moves with the earth's rotation. This is a rather simplified explanation. One should read up on equatorial mounts for telescopes, which utilize this coordinate system in a very elegant manner. -	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8251950144767761, "perplexity": 884.6634185838901}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927767.46/warc/CC-MAIN-20150521113207-00176-ip-10-180-206-219.ec2.internal.warc.gz"}
http://export.arxiv.org/abs/0805.0841	Full-text links: physics.soc-ph (what is this?) # Title: Priority queues with bursty arrivals of incoming tasks Abstract: Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent out by a user, two consecutive library loans made by a single individual, etc. Interestingly, those distributions exhibit a universal behavior, $D(\tau)\sim \tau^{-\delta}$, where $\tau$ is the interevent time, and $\delta \simeq 1$ or 3/2. The universal behaviors have been modeled via the waiting-time distribution of a task in the queue operating based on priority; the waiting time follows a power law distribution $P_{\rm w}(\tau)\sim \tau^{-\alpha}$ with either $\alpha=1$ or 3/2 depending on the detail of queuing dynamics. In these models, the number of incoming tasks in a unit time interval has been assumed to follow a Poisson-type distribution. For an email system, however, the number of emails delivered to a mail box in a unit time we measured follows a powerlaw distribution with general exponent $\gamma$. For this case, we obtain analytically the exponent $\alpha$, which is not necessarily 1 or 3/2 and takes nonuniversal values depending on $\gamma$. We develop the generating function formalism to obtain the exponent $\alpha$, which is distinct from the continuous time approximation used in the previous studies. Comments: 19 pages, 5 figures Subjects: Physics and Society (physics.soc-ph); Statistical Mechanics (cond-mat.stat-mech) Journal reference: Phys. Rev. E 79, 036106 (2009) DOI: 10.1103/PhysRevE.79.036106 Cite as: arXiv:0805.0841 [physics.soc-ph] (or arXiv:0805.0841v3 [physics.soc-ph] for this version) ## Submission history From: Jin S. Kim [view email] [v1] Wed, 7 May 2008 06:18:37 GMT (17kb) [v2] Thu, 22 May 2008 05:27:57 GMT (18kb) [v3] Thu, 9 Apr 2009 17:20:13 GMT (84kb) Link back to: arXiv, form interface, contact.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5339841246604919, "perplexity": 1775.116025424019}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000894.72/warc/CC-MAIN-20190627055431-20190627081431-00059.warc.gz"}
https://itectec.com/superuser/how-to-start-certmgr-msc-for-computer-account/	# Windows – How to start certmgr.msc for computer account mmcwindows I can start individual Management Console snap-ins by starting them directly without going through starting mmc.exe and selecting the snap-ins I want. However, for certmgr.msc selecting in MMC gives me the option to load certmgr for the computer account, which is usually what I need. How can I load certmgr for the computer account from the command line? Save the .msc file to a file share and just call the UNC. What I did was create the .msc file (as answered above) but I saved it to a network resource. When I go to the next server, I can call the UNC via the RUN and done the local computer's certificate manager opens up as the Computer Account too. I tested it across a couple different IIS boxes and found it was indeed unique and the computer's account. \\fileserver\share\certmgr_computeraccount.msc	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5558285117149353, "perplexity": 3268.8259209450935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058467.95/warc/CC-MAIN-20210927181724-20210927211724-00483.warc.gz"}
http://www.numdam.org/item/CM_1968__20__107_0/	Functional interpretation of bar induction by bar recursion Compositio Mathematica, Volume 20 (1968), pp. 107-124. @article{CM_1968__20__107_0, author = {Howard, W. A.}, title = {Functional interpretation of bar induction by bar recursion}, journal = {Compositio Mathematica}, pages = {107--124}, publisher = {Wolters-Noordhoff Publishing}, volume = {20}, year = {1968}, zbl = {0162.31503}, mrnumber = {230619}, language = {en}, url = {http://www.numdam.org/item/CM_1968__20__107_0/} } TY - JOUR AU - Howard, W. A. TI - Functional interpretation of bar induction by bar recursion JO - Compositio Mathematica PY - 1968 DA - 1968/// SP - 107 EP - 124 VL - 20 PB - Wolters-Noordhoff Publishing UR - http://www.numdam.org/item/CM_1968__20__107_0/ UR - https://zbmath.org/?q=an%3A0162.31503 UR - https://www.ams.org/mathscinet-getitem?mr=230619 LA - en ID - CM_1968__20__107_0 ER - %0 Journal Article %A Howard, W. A. %T Functional interpretation of bar induction by bar recursion %J Compositio Mathematica %D 1968 %P 107-124 %V 20 %I Wolters-Noordhoff Publishing %G en %F CM_1968__20__107_0 Howard, W. A. Functional interpretation of bar induction by bar recursion. Compositio Mathematica, Volume 20 (1968), pp. 107-124. http://www.numdam.org/item/CM_1968__20__107_0/ K. Gödel [1] Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Dialectica, 12 (1958), 280-287. \| MR \| Zbl W.A. Howard and G. Kreisel [2] Transfinite induction and bar induction of types zero and one, and the role of continuity in intuitionistic analysis, Journal of Symbolic Logic 31 (1966), 325 - 358. \| Zbl S.C. Kleene and R.E. Vesley [3] Foundations of Intuitionistic Mathematics, North-Holland Publishing Co., Amsterdam, 1965. \| MR \| Zbl G. Kreisel [4] Interpretation of analysis by means of constructive functionals of finite types, Constructivity in Mathematics, North-Holland Publishing Co., Amsterdam, 1959, 101-128. \| MR \| Zbl G. Kreisel [5] Proof by transfinite induction and definition by transfinite recursion, Journal of Symbolic Logic, 24 (1959), 322-323. G. Kreisel [6] A survey of proof theory, Journal of Symbolic Logic, to appear. \| MR \| Zbl C. Spector [7] Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics, Proceedings of the Symposia in Pure Mathematics, vol. 5, American Mathematical Society, Providence, 1962, 1- 27. \| MR \| Zbl	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6286187171936035, "perplexity": 6946.794757269626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500158.5/warc/CC-MAIN-20230205000727-20230205030727-00046.warc.gz"}
https://math.stackexchange.com/questions/1378103/for-two-vectors-a-and-b-why-does-cos%CE%B8-equal-the-dot-product-of-a-and	# For two vectors $a$ and $b$, why does $\cos(θ)$ equal the dot product of $a$ and $b$ divided by the product of the vectors' magnitudes? While watching a video about dot products (https://www.youtube.com/watch?v=WDdR5s0C4cY), the following formula is presented for finding the angle between two vectors: For vectors $a$, and $b$, $$\cos( \theta ) = \frac{(a, b)}{ \\| a \\| \\| b \\| }$$ where $(a,b)$ is the dot product of $a$ and $b$. How is this formula derived? There are several derivations of this online. Here's where you can start. Define two vectors $\textbf{a}$ and $\textbf{b}$. Then $\textbf{a} - \textbf{b}$ is the vector that connects their endpoints and makes a triangle. Therefore, we have a triangle with side lengths $\|\textbf{a}\|$, $\|\textbf{b}\|$, and $\|\textbf{a} - \textbf{b}\|$. Let the angle between the two vectors be $\theta$. By the Law of Cosines, we have $$\|\textbf{a} - \textbf{b}\|^2 = \|\textbf{a}\|^2 + \|\textbf{b}\|^2 - 2 \|\textbf{a}\| \|\textbf{b}\| \cos (\theta)$$ Now, use the fact that \begin{align} \|\textbf{a}- \textbf{b}\|^2 &= (\textbf{a}- \textbf{b}) \cdot (\textbf{a}- \textbf{b})\\ &= \textbf{a} \cdot \textbf{a} - 2 (\textbf{a} \cdot \textbf{b}) + \textbf{b} \cdot \textbf{b} \\ &= \|\textbf{a}\|^2 - 2 (\textbf{a} \cdot \textbf{b}) + \|\textbf{b}\|^2 \end{align} Simplify this equation, and you will get the desired formula. • Interesting way of looking at it, I like it. – FundThmCalculus Jul 29 '15 at 15:30 • How do you do the last three steps without using some definition for dot ptoduct, and in which case what is your definition? Eg why is it commutative, and why is $a.a=\|a\|^2$? – David Quinn Jul 29 '15 at 17:13 • I'm using the definition that dot product of the two vectors is the sum of the product of corresponding components. If we have $\textbf{a} = \langle a_1, a_2, \dots a_n \rangle$. Then, by the definition of dot product, we have $$\textbf{a} \cdot \textbf{a} = a_1^2 + a_2^2 + \dots + a_n^2$$ which is equal to $\|\textbf{a}\|^2$. – Ashkay Jul 29 '15 at 17:19 Since $(a,b)$ is independent of the basis, just choose a basis where $a$ lies along the $x$ axis: $a=(\|a\|,0)$, so that: $${(a,b)\over\|a\|\|b\|}={b_x\over\|b\|}=\cos(\theta),$$ where $\theta$ is the angle between $b$ and $x$ axis (as you may recall from trigonometry), which is the same as the angle between $a$ and $b$. • just so you know, you can make standard math functions such as $\sin$ and $\cos$ appear in non-italics by putting a \ in front of the word: \cos. – FundThmCalculus Jul 29 '15 at 15:32 • Yes, I forgot that. Thanks! – Aretino Jul 29 '15 at 15:35 I think Augustin was answering a much more general question. In two dimensions, where we have "cosine" already defined, from trigonometry, one can show that the "dot product", defined in some other way, is equal to the lengths of the two vectors times the cosine of the angle between them. But in higher dimension spaces, $\mathbb{R}^n$, we can use that formula to define the angle between two lines. It's a trig identity, really. Two vectors determine a plane. Without loss of generality, we'll take that to be the $xy$-plane. Now, let $A$ and $B$ be the angles that $\overrightarrow{a}$ and $\overrightarrow{b}$ make with the (positive) $x$-axis; and let $r$ and $s$ be the respective magnitudes. Then, the $xy$-coordinates of the vectors can be written as $$\overrightarrow{a}= r\,(\cos A, \sin A) \qquad\text{and}\qquad \overrightarrow{b} = s \,(\cos B, \sin B )$$ so that $$\overrightarrow{a}\cdot\overrightarrow{b} = r s \cos A \cos B + r s\sin A \sin B = r s \cos(A-B)$$ This is a part of the geometric definition, but originally comes from the algebraic definition (see here) In Euclidean space, you have to define a vector. With that vector, following the algebraic definition $\vec{a} \cdot \vec{b} = \sum_i a_i b_i$ Imagine at the origin you have two vectors, pointing from $O$ to $A = (a_i)_{i=1}^n$ and to $B = (b_i)_{i=1}^n$. You can pick $n=2,3$ for the sake of imagination. Now drop a perpendicular line from $B = (b_i)_{i=1}^n$ onto $OA$, crossing $OA$ at a point, called $H$. Let $\theta$ be the angle $(OA,OB)$. After a long calculation, the length of $OH$ is $\frac{\sum_i a_i b_i}{\|\|a\|\|}$. Observe that $\cos \theta = \frac{\|OH\|}{\|OB\|}$, you now arrive at the formula $\cos \theta = \frac{\vec{a}\cdot \vec{b}} {\|\|a\|\| \cdot \|\|b\|\|}$ By the law of cosines, $$\tag 1 \left\Vert{\mathbf a - \mathbf b}\right\Vert^2 = \left\Vert{\mathbf a}\right\Vert^2 + \left\Vert{\mathbf b}\right\Vert^2 - 2 \left\Vert{\mathbf a}\right\Vert \left\Vert{\mathbf b}\right\Vert \cos \theta$$ whereas, using the definition of the dot product, $$\tag 2 \left \\| \mathbf a-\mathbf b \right \\|^{2}=(\mathbf a-\mathbf b)\cdot (\mathbf a-\mathbf b)=\left \\| \mathbf a \right \\|^{2}+\left \\| \mathbf b \right \\|^{2}-2(\mathbf a \cdot \mathbf b)$$ Now combine $(1)$ and $(2)$ I use projection to remember this formula. Let $\vec a$ and $\vec b$ be two vectors. Then, projection of $\vec a$ over $\vec b$ is defined as: $$proj_{\vec b}(\vec a)=\left( \frac{\vec a \cdot \vec b}{\vec b \cdot \vec b} \right) \vec b$$ Then we can form the following equality: \begin{aligned} \|\|\vec a\|\|\cos \theta &= \|\|proj_{\vec b}(\vec a)\|\| \\ &=\left( \frac{\vec a \cdot \vec b}{\vec b \cdot \vec b} \right) \|\|\vec b\|\| \\ &=\frac{(\vec a \cdot \vec b)}{\|\|\vec b\|\|^2} \|\|\vec b\|\| \end{aligned} Rearranging both sides, we get $$\vec a \cdot \vec b=\|\|\vec a\|\| \|\|\vec b\|\| \cos \theta$$ The derivation of the formula for projection is here. Dot product of two vectors is defined as the product of the magnitude of the two vectors together with the cosine of the angle between the two vectors. Mathematically, a.b=\|a\|\|b\|cos§	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9997870326042175, "perplexity": 252.6398453369083}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573444.87/warc/CC-MAIN-20190919060532-20190919082532-00359.warc.gz"}
http://mathhelpforum.com/advanced-algebra/181304-matrices.html	# Math Help - Matrices 1. ## Matrices People usually use the sign = with matrices but is it not more appropriate to use the 'is identically equal to' sign (\equiv ) ? 2. there is a well-defined notion of equality among matrices, as there is among vectors in R^n: to wit, two matrices are equal if and only if every i,j-th entry is equal for both matrices. as matrices often occur in equations, where the entries of a matrix, or of a vector a matrix acts upon is unknown, "identically equal to" isn't usually appropriate, unless one is talking about a certain specially defined matrix, such as the nxn identity matrix. furthermore, there are different notions of "equivalence" of matrices, the most important of which is probably similarity.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9654743671417236, "perplexity": 778.1305962619901}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500824209.82/warc/CC-MAIN-20140820021344-00074-ip-10-180-136-8.ec2.internal.warc.gz"}
https://scoop.eduncle.com/how-to-solve-this-type-of-question-pls-once-show-step-6	IIT JAM Follow January 26, 2021 8:56 pm 30 pts how to solve this type of question..pls once show step... .. . . . . • 0 Likes • Shares • Satpal singh see this attachment • Satpal singh see this • Anonymous User • Anonymous User make it as part of ur notes. it will help to solve this type questions Anku thanks a lot sir..i learnt new thing today	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8192139267921448, "perplexity": 27513.75966657237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178383355.93/warc/CC-MAIN-20210308082315-20210308112315-00369.warc.gz"}
http://mathhelpforum.com/calculus/214864-maximum-volume.html	# Math Help - Maximum volume 1. ## Maximum volume A sector with central angle (theta) is cut from a circle of radius 12 inches and the edges of the sector are brought together to form a cone. Find the magnitude of theta such that the volume of the cone is a maximum. 2. ## Re: Maximum volume Originally Posted by jellchavez A sector with central angle (theta) is cut from a circle of radius 12 inches and the edges of the sector are brought together to form a cone. Find the magnitude of theta such that the volume of the cone is a maximum. $s=12$ $2r\pi=\frac{s\pi\theta}{180}$ hence $r=\frac{s\theta}{360}$ $V=\frac{r^2 \pi H}{3}$ and $H=\sqrt{s^2-r^2}$ Now , find $\theta$ from $V'_{\theta}=0$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9455547332763672, "perplexity": 401.3832658627598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507444465.10/warc/CC-MAIN-20141017005724-00352-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.zora.uzh.ch/id/eprint/140762/	# Measurement of the mass difference between top quark and antiquark in pp collisions at $\sqrt{s} = 8$ TeV ## Abstract The invariance of the standard model (SM) under the CPT transformation predicts equality of particle and antiparticle masses. This prediction is tested by measuring the mass difference between the top quark and antiquark ($Δm_t=m_t−m_\overline t$) that are produced in pp collisions at a center-of-mass energy of 8 TeV, using events with a muon or an electron and at least four jets in the final state. The analysis is based on data corresponding to an integrated luminosity of 19.6 $fb^{−1}$collected by the CMS experiment at the LHC, and yields a value of $Δm_t=−0.15±0.19(stat)±0.09(syst)$ GeV, which is consistent with the SM expectation. This result is significantly more precise than previously reported measurements. ## Abstract The invariance of the standard model (SM) under the CPT transformation predicts equality of particle and antiparticle masses. This prediction is tested by measuring the mass difference between the top quark and antiquark ($Δm_t=m_t−m_\overline t$) that are produced in pp collisions at a center-of-mass energy of 8 TeV, using events with a muon or an electron and at least four jets in the final state. The analysis is based on data corresponding to an integrated luminosity of 19.6 $fb^{−1}$collected by the CMS experiment at the LHC, and yields a value of $Δm_t=−0.15±0.19(stat)±0.09(syst)$ GeV, which is consistent with the SM expectation. This result is significantly more precise than previously reported measurements. ## Statistics ### Citations Dimensions.ai Metrics 2 citations in Web of Science® 3 citations in Scopus® ### Altmetrics Detailed statistics	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9876728653907776, "perplexity": 367.4609066593058}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039747665.82/warc/CC-MAIN-20181121092625-20181121113928-00026.warc.gz"}
https://gmatclub.com/forum/in-the-rectangle-above-ab-x-feet-bc-y-feet-and-ae-fc-2-feet-288018.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 22 Oct 2019, 12:16 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track Your Progress every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 58427 In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. [#permalink] ### Show Tags 05 Feb 2019, 04:29 00:00 Difficulty: 25% (medium) Question Stats: 83% (01:51) correct 17% (01:39) wrong based on 24 sessions ### HideShow timer Statistics In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet? A. xy/2 + 2 B. xy/2 - x - y - 2 C. xy/2 - x - y + 2 D. xy - 2x - 2y - 4 E. xy - 2x - 2y + 4 Attachment: 2019-02-05_1527.png [ 12.52 KiB \| Viewed 395 times ] _________________ Intern Joined: 14 Jan 2018 Posts: 49 Location: India Concentration: General Management, Entrepreneurship GMAT 1: 660 Q50 V29 GPA: 3.8 WE: Engineering (Manufacturing) Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. [#permalink] ### Show Tags 05 Feb 2019, 04:55 Length of DE = x-2 Length of DF = y-2 Area of triangle = 1/2(x-2)(y-2) Answer C GMAT Club Legend Joined: 18 Aug 2017 Posts: 5032 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. [#permalink] ### Show Tags 05 Feb 2019, 06:00 Bunuel wrote: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet? A. xy/2 + 2 B. xy/2 - x - y - 2 C. xy/2 - x - y + 2 D. xy - 2x - 2y - 4 E. xy - 2x - 2y + 4 Attachment: 2019-02-05_1527.png DF= x-2 DE= y-2 area of triangle = 1/2 * ( x-2) * ( y-2) upon solving xy/2 - x - y + 2 IMO C Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8129 Location: United States (CA) Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. [#permalink] ### Show Tags 06 Feb 2019, 19:45 Bunuel wrote: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet? A. xy/2 + 2 B. xy/2 - x - y - 2 C. xy/2 - x - y + 2 D. xy - 2x - 2y - 4 E. xy - 2x - 2y + 4 Attachment: 2019-02-05_1527.png Side ED = y - 2 and side DF = x - 2, so the area of triangle DEF is: (y - 2)(x - 2) x 1/2 (xy - 2x - 2y + 4) x 1/2 xy/2 - x - y + 2 Answer: C _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Director Joined: 09 Mar 2018 Posts: 994 Location: India Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. [#permalink] ### Show Tags 06 Feb 2019, 19:57 Bunuel wrote: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet? A. xy/2 + 2 B. xy/2 - x - y - 2 C. xy/2 - x - y + 2 D. xy - 2x - 2y - 4 E. xy - 2x - 2y + 4 Attachment: 2019-02-05_1527.png So just plot the expressions for the triangle ED =y -2 DF = x -2 Its a rectangle all angles are $$90^o$$ Area of triangle DEF = 1/2 * y-2 * x-2 xy/2 - x - y + 2 _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. [#permalink] 06 Feb 2019, 19:57 Display posts from previous: Sort by # In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group \| Emoji artwork provided by EmojiOne	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5224826335906982, "perplexity": 5943.288116693096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987823061.83/warc/CC-MAIN-20191022182744-20191022210244-00097.warc.gz"}
http://fujitv-co-jp.somee.com/write-my-paper/page-492-2021-07-09.html	Join Today to Score Better Tomorrow. Connect to the brainpower of an academic dream team. Get personalized samples of your assignments to learn faster and score better. How can our experts help? We cover all levels of complexity and all subjects Receive quick, affordable, personalized essay samples Learn faster with additional help from specialists Chat with an expert to get the most out of our website Get help for your child at affordable prices Students perform better in class after using our services Hire an expert to help with your own work The Samples - a new way to teach and learn Check out the paper samples our experts have completed. Hire one now to get your own personalized sample in less than 8 hours! Type Case study Level College Style APA Type Coursework Level College Style APA Type Case study Level High School Style APA Type Case study Level Style APA Type Dissertation Level University Style APA Type Case study Level College Style APA Customer care that warms your heart Our support managers are here to serve! Check out the paper samples our writers have completed. Hire one now to get your own personalized sample in less than 8 hours! Hey, do you have any experts on American History? Hey, he has written over 520 History Papers! I recommend that you choose Tutor Andrew Oh wow, how do I speak with him?! Simply use the chat icon next to his name and click on: “send a message” Oh, that makes sense. Thanks a lot!! Guaranteed to reply in just minutes! Knowledgeable, professional, and friendly help Works seven days a week, day or night How It Works How Does Our Service Work? Find your perfect essay expert and get a sample in four quick steps: Choose an expert among several bids Chat with and guide your expert 01 02 Submit Your Requirements & Calculate the Price Just fill in the blanks and go step-by-step! Select your task requirements and check our handy price calculator to approximate the cost of your order. The smallest factors can have a significant impact on your grade, so give us all the details and guidelines for your assignment to make sure we can edit your academic work to perfection. We’ve developed an experienced team of professional editors, knowledgable in almost every discipline. Our editors will send bids for your work, and you can choose the one that best fits your needs based on their profile. Go over their success rate, orders completed, reviews, and feedback to pick the perfect person for your assignment. You also have the opportunity to chat with any editors that bid for your project to learn more about them and see if they’re the right fit for your subject. 03 04 You can have as many revisions and edits as you need to make sure you end up with a flawless paper. Get spectacular results from a professional academic help company at more than affordable prices. Release Funds For the Order You only have to release payment once you are 100% satisfied with the work done. Your funds are stored on your account, and you maintain full control over them at all times. Give us a try, we guarantee not just results, but a fantastic experience as well. 05 Enjoy a suite of free extras! Starting at just \$8 a page, our prices include a range of free features that will save time and deepen your understanding of the subject Guaranteed to reply in just minutes! Knowledgeable, professional, and friendly help Works seven days a week, day or night Latest Customer Feedback 4.7 I needed help with a paper and the deadline was the next day, I was freaking out till a friend told me about this website. I signed up and received a paper within 8 hours! Customer 102815 22/11/2020 4.3 Best references list I was struggling with research and didn't know how to find good sources, but the sample I received gave me all the sources I needed. Customer 192816 17/10/2020 4.4 A real helper for moms I didn't have the time to help my son with his homework and felt constantly guilty about his mediocre grades. Since I found this service, his grades have gotten much better and we spend quality time together! Customer 192815 20/10/2020 4.2 Friendly support I randomly started chatting with customer support and they were so friendly and helpful that I'm now a regular customer! Customer 192833 08/10/2020 4.5 Direct communication Chatting with the writers is the best! Customer 251421 19/10/2020 4.5 I started ordering samples from this service this semester and my grades are already better. Customer 102951 18/10/2020 4.8 Time savers The free features are a real time saver. Customer 271625 12/11/2020 4.7 They bring the subject alive I've always hated history, but the samples here bring the subject alive! Customer 201928 10/10/2020 4.3 Thanks!! I wouldn't have graduated without you! Thanks! Customer 726152 26/06/2020 If I order a paper sample does that mean I'm cheating? Not at all! There is nothing wrong with learning from samples. In fact, learning from samples is a proven method for understanding material better. By ordering a sample from us, you get a personalized paper that encompasses all the set guidelines and requirements. We encourage you to use these samples as a source of inspiration! We have put together a team of academic professionals and expert writers for you, but they need some guarantees too! The deposit gives them confidence that they will be paid for their work. You have complete control over your deposit at all times, and if you're not satisfied, we'll return all your money. How should I use my paper sample? We value the honor code and believe in academic integrity. Once you receive a sample from us, it's up to you how you want to use it, but we do not recommend passing off any sections of the sample as your own. Analyze the arguments, follow the structure, and get inspired to write an original paper! Are you a regular online paper writing service? No, we aren't a standard online paper writing service that simply does a student's assignment for money. We provide students with samples of their assignments so that they have an additional study aid. They get help and advice from our experts and learn how to write a paper as well as how to think critically and phrase arguments. How can I get use of your free tools? Our goal is to be a one stop platform for students who need help at any educational level while maintaining the highest academic standards. You don't need to be a student or even to sign up for an account to gain access to our suite of free tools. How can I be sure that my student did not copy paste a sample ordered here? Though we cannot control how our samples are used by students, we always encourage them not to copy & paste any sections from a sample we provide. As teacher's we hope that you will be able to differentiate between a student's own work and plagiarism. Janice martin dissertation case study examples slideshare - The negative exponent means take the reciprocal, or flip the fraction, so, (()^-1/3) / 1 = 1 / (()^1/3), and the negative exponent is now a positive exponent. Recall that negative exponents indicates that we need to move the base to the other side of the fraction line. Working with Negative Exponents Negative exponents are a way of writing powers of fractions or decimals without using a fraction or decimal. You use negative exponents as a way to combine expressions with the same base, whether the different factors are in the numerator or denominator. essay on good manners are a handicap in todays society Argumentative essay proofreading websites online synonym for resume a felipe dissertation sleeep - Oct 25, · This lesson will cover how to find the power of a negative exponent. Part 1: A reminder. Remember that any number can be written as itself divided by???1???. For example,???3??? is the same as???3/1???. Also remember that the top part of a fraction is called the numerator and the bottom part of a fraction is called the fujitv-co-jp.somee.comted Reading Time: 1 min. Jan 17, · To convert a negative exponent, create a fraction with the number 1 as the numerator (top number) and the base number as the denominator (bottom number). Raise the base number 86%(17). Jan 20, · Because a negative exponent is just a nice way of saying, “Hey, I’m on the wrong side of the division bar (fraction line).”. Don’t worry; it will all make sense after you see a few examples! Moreover, together we are going to review our cancellation rule for fractions (or the Property of Quotients) and revisit how to use the Zero Exponent Rule, and write expressions only using positive. powerpoint dissertations University of london union dissertation binding randy wormald dissertation - May 15, · What happens if you have a negative fractional exponent? You should deal with the negative sign first, then use the rule for the fractional exponent. Example. Write the expression without fractional exponents.???4^{-\frac{2}{5}}??? First, we’ll deal with the negative fujitv-co-jp.somee.comted Reading Time: 1 min. A number raised to a negative fractional exponent has been defined to be the reciprocal of that number with a positive fractional exponent. When exponents are negative exponents, it means that they are placed in the denominator of a fraction. a (-2) is nothing but 1/a 2. For Example: [12]−4 = 1[12]4= Laws of negative exponent are as follows. The next problem is already a fraction. The top and bottom both contain negative exponents. Since d-3 on the bottom has a negative exponent, it is moved to the top of the fraction (numerator). Since the c-3 on the top of the fraction has a negative exponent, it is moved to the bottom of the fraction (denominator). The problem and work is shown Estimated Reading Time: 2 mins. essay on national awards Dissertation supervision hire term paper writers - Much of the material in this section is a review of the material covered in the Pre-Algebra SparkNote on Powers, Exponents, and Roots. Negative Exponents Taking a quantity to a negative exponent is equivalent to taking the reciprocal of the quantity to the positive opposite of the exponent: x-a = Examples: = 3 . ()-4 = 5 4 = To figure out negative fractional exponents, simply move the number and the exponent to the denominator, make the exponent positive, and then turn the exponent into a radical. Download PDF Print. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring. case study title pdf Art dissertations online write my cheap persuasive essay on hacking - Negative Exponent If n n is a positive integer and a ≠0 a ≠ 0, then a−n = 1 an a − n = 1 a n. The negative exponent tells us to re-write the expression by taking the reciprocal of the base and then changing the sign of the exponent. Any expression that has negative exponents . The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base. So 2^ (-4) = 1/ (2^4) = 1/ (222*2) = 1/ The answer is 1/ Fractions and Exponents Negative Exponent. Things become a bit more interesting when we look at fractions and negative exponents. First, if we recap whole numbers and negative exponents. The negative exponent has the effect of creating a fraction of 1 over the whole number, to a now changed positive exponent. a −n = \bf{\frac{1}{a^n. technical writing homework help Research paper outline on womens rights creative writing describing a garden - Apr 27, · You should notice that a fractional negative exponent is the same as finding the root of the base. Fractions with negative exponents. The rule implies that, if a fraction a/b is raised to the negative exponent of n, it is equal to 1 divided by the base a/b raised to the positive exponent of n: (a/b) -n = 1 / (a/b) n = 1 / (a n /b n) = b n /a nRatings: So if they give you, say, x 3/6, then x had better not be negative, because x 3 would still be negative, and you would be trying to take the sixth root of a negative number. If they give you x 4/6, then a negative x becomes positive (because of the fourth power) and is then sixth-rooted, so it becomes \| x \| 2/3 (by reducing the fractional power). On the other hand, if they give you something. Oct 08, · Negative Exponent Rule in 3 Easy Steps. Now let’s look at the previous example again, except this time the exponent is -2 (negative two). Step One: Rewrite the Value with Negative Exponent as a Fraction. Since we are performing division (the inverse of multiplication), we will rewrite the value as a fraction with a numerator of fujitv-co-jp.somee.comted Reading Time: 2 mins. types of hypothesis testing pdf Thesis statement examples informative speech action essay event how to make a thesis statement - In the following video we show another example of how to simplify a product that contains negative exponents. To simplify a fraction, we use the Quotient Property. example. Simplify: $\frac{{r}^{5}}{{r}^{-4}}$. Show Solution try it. In the next video we share more examples of simplifying a quotient with negative exponents. Mar 24, · If a negative exponent applies to a fraction, we invert the fraction (or equivalently, we divide 1 by the fraction): $$\left(\frac{x}{y} \right)^{-n} = \left(\frac{y}{x} \right)^n$$ If you have a negative rational exponent, do not let that confuse you. First, make the exponent positive by applying the inverse as explained fujitv-co-jp.somee.coms: 5. Nov 14, · When you have negative exponents, the negative exponent rule dictates that, instead of multiplying the base the indicated number of times, you divide the base into 1 that number of times. dissertation musiktherapie Writing an assessment paper legal paper writing service - Negative fractional exponents; Fractions with negative exponents; Multiplying negative exponents; Dividing negative exponents; Negative exponents rule. The base b raised to the power of minus n is equal to 1 divided by the base b raised to the power of n: b-n = 1 / b n. Negative exponent example. The base 2 raised to the power of minus 3 is. Negative Exponents Calculator is a free online tool that displays the solution for a given exponent value. BYJU’S online negative exponents calculator tool makes the calculation faster, and it displays the result in a fraction of seconds. The general formula for rewriting negative exponents as a positive exponent is: x − a = 1 x a Examples of rewriting negative examples as positive 1) 5 − 2 = 1 5 2 2) (3 x) − 2 = 1 (3 x) 2. abstract in thesis Aqa psychology paper 2009 essay on homosexuality and the bible - If you look at that table, you will see that positive, zero or negative exponents are really part of the same (fairly simple) pattern. Laws of Exponents Fractional Exponents Powers of . The fractions with negative exponents in the denominator can be simplified by shifting the terms of negative exponents in any order from the denominator to the numerator and become positive exponents. That is, and, which means that a negative exponent is equal to reciprocal of the opposite positive exponent. Example 1: Consider the fraction. Negative exponents. We are now going to extend the meaning of an exponent to more than just a positive integer. We will do that in such a way that the usual rules of exponents will hold. That is, we will want the following rules to hold for any exponents: positive, negative, 0 -- even fractions. custom thesis writing company Dedication dissertation parents examples of endnotes in a research paper - The negative exponents, therefore, generate fractions as a consequence of the monotonic nature of the powers of a radix and the pattern established in the sequence generated by monotonically decreasing exponents of that radix. Oct 04, · A negative exponent can be rewritten with an inversion: Next, expand both exponents and simplify the answer. That proves they are reciprocals of one another. For more on Negative Exponents, Author: Brett Berry. Negative exponents are nothing to be afraid of. Remember that when you see a negative exponent you can put it on the other side of the fraction bar and make it a positive exponent. If you need more math help with this subject, you can see our math help message board and ask your question for free. otis rush homework chords Thesis writing english need for change in education for the future essay stacey resume - Algebra/Pre-Algebra lesson about negative Exponents. Shows examples of solving and explains the rules for negative fujitv-co-jp.somee.com recommended Calculators: If. Jun 10, · Fractional Exponents – Explanation & Examples Exponents are powers or indices. An exponential expression consists of two parts, namely the base, denoted as b and the exponent, denoted as n. The general form of an exponential expression is b n. For example, 3 x 3 x 3 x 3 can be written in exponential form [ ]Ratings: Below is a specific example illustrating the formula for fraction exponents when the numerator is not one. There are two ways to simplify a fraction exponent such $$\frac 2 3$$. You can either apply the numerator first or the denominator. See the example below. dissertation advisor status fiu Thesis printing limerick essay based on article - When we have fractions elevated to a negative exponent, to convert the exponent to positive, we must turn the fraction around, according to the following formula: In reality, when the base is not a fraction, i. e. it is a number or a variable, we also turn it upside down, since we place the power in the denominator and the original denominator. Understanding Finding a Negative Exponent. Let us look at the rule for negative exponents: 2 −n and 2 n are powers. The bases of the powers are 2. The exponent of 2 −n is −n and the exponent of 2 n is n. The fraction 1 ⁄ 2 n is the reciprocal of 2 n. Slider. The slider below shows another real example of how to find negative exponents. For negative expressions, take the reciprocal of the base. Once all the 0 and negative exponents are simplified, write out the exponents. For example, write out x^3 as x x x. Next, cancel out anything that is both in the numerator and denominator. data data dissertation mining ms proteomic seldi technique College format for a research paper m ed dissertations - How to Write Fractional Exponents in Word. Business publications that discuss growth trends often use complex equations with fractional exponents. These equations are difficult to type using basic keyboard buttons. Microsoft Word has a specialized menu for . Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions. Fractions with negative exponents. Question 3: (3^-2)/(4^-3) Solution: If you ever see a negative exponent on the top of a fraction, you know that if you flip it to the bottom, it'll become positive. The same actually works for negative exponents on the bottom. If you move it to the numerator, its exponent also becomes positive. how do we determine what is right and wrong? Essay expert us air pollution essays for kids - Fractions with negative exponents The base a/b raised to the power of minus n is equal to 1 divided by the base a/b raised to the power of n: (a/b) -n = 1 / (a/b) n = 1 / (a n /b n) = b n /a nEstimated Reading Time: 1 min. Dec 15, · Calculating exponents is a basic skill students learn in pre-algebra. Usually you see exponents as whole numbers, and sometimes you see them as fractions. Rarely do you see them as decimals. When you do see an exponent that is a decimal, you need to convert the decimal to a fraction%(3). term papers writing services to avoid Cxc english paper 1 questions medical malpractice essay expert cv writing - guidelines on writing a research proposal Pinterest.com To best understand this lesson, make sure that you have read and understand how to write a fraction with negative exponents best writing service review lessons:. This lesson will explain how to simplify the negative exponents in problems like the following two. The first problem is simply a term with both negative and positive exponents. As you may have how to write a fraction with negative exponents in one of the previous dissertation science, the simplest form white house essay the problem a -2 is simply. The problem was simplified by just changing its exponent to the opposite sign from negative to positive and moving it to the bottom of a fraction. The next problem we are simplifying has both negative how to write a fraction with negative exponents positive exponents. The variables with positive exponents are left alone thesis topics social issues how to write a fraction with negative exponents variables with negative exponents are moved to the bottom of the fraction. The next problem how to write a fraction with negative exponents already a fraction. The top and bottom both contain negative exponents. Since d -3 on the bottom has a negative how to write a fraction with negative exponents, it is moved to the top of the fraction numerator. Since the c -3 on the how to write a fraction with negative exponents of the fraction has a negative exponent, it is moved to the bottom of the fraction denominator. The next problem is a fraction with a negative exponent on top, but only positive exponents on the bottom:. The x -2 on top of the fraction bar is moved below it, and its exponent thesis dissertation proquest how to write a fraction with negative exponents from negative two to positive how to write a fraction with negative exponents. Since there how to write a fraction with negative exponents already x 2 on sample essays gmat bottom, they are multiplied together. The number 1 is left on the top of the fraction because, as you may recall, when a term does not have an explicit coefficient, it has an implicit how to write a fraction with negative exponents of 1. Next Lesson: Substitution Introduction An introduction to substituting variables how to write a fraction with negative exponents an expression with numbers or other expressions. Looking for someone to help you with algebra? At Wyzant, connect with algebra tutors and math tutors nearby. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of dissertation advisor status fiu. Skip to content. Simplifying Fractions With Negative Exponents Lesson To best understand this lesson, how to write a fraction with negative exponents sure that how to write a fraction with negative exponents have read and understand the following how to write a fraction with negative exponents Simplifying Negative How to write a fraction with negative exponents Simplifying Variables with Negative Exponents This lesson will semantic spaces wegener dissertation how to write a fraction with negative exponents to how to write a fraction with negative exponents the negative exponents in problems like the following two. Tutoring Looking for someone to help you with algebra? Determine the example of an apa research paper capacity of a new auditorium Really need help with this question! Jack obama opening speech half of words ending in gent weekly how to write a fraction with negative exponents on video games. Web hosting by Somee.com	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7797608375549316, "perplexity": 924.403882405077}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571987.60/warc/CC-MAIN-20220813202507-20220813232507-00308.warc.gz"}
http://math.stackexchange.com/questions/363222/expressing-cos-theta-sqrt3-sin-theta-r-sin-theta-alpha	# Expressing $\cos\theta - \sqrt{3}\sin\theta = r\sin(\theta - \alpha)$ My book explains that $a\cos\theta + b\sin\theta$ is a sine (or cosine) graph with a particular amplitude/shift (i.e. $r\sin(\theta + \alpha)$) and shows me some steps to solve for $r$ and $\alpha$: $$r\sin(\theta + \alpha) \equiv a\cos\theta + b\sin\theta$$ $$\Rightarrow r\sin\theta\cos\alpha + r\cos\theta\sin\alpha \equiv a\cos\theta + b\sin\theta$$ I see the basic trig identity $\sin(a + b) \equiv \sin a\cos b + \sin b\cos a$ is being used, and the coefficients $a$ and $b$ are easily identified as: $$r\sin\alpha = a$$ $$r\cos\alpha = b$$ Then the book squares and adds the equations: $$r^2(\sin^2\alpha + \cos^2\alpha) = a^2 + b^2 \Rightarrow r = \sqrt{a^2 + b^2}$$ I see that the basic identity $\sin^2\alpha + \cos^2\alpha \equiv 1$ is being used here. All the examples in the book involve $r$ being a positive quantity. An exercise asks me to express $\cos\theta - \sqrt{3}\sin\theta$ in the form $r\sin(\theta - \alpha)$. I tried this and ran into problems as the squaring and square rooting process only ever produces a positive $r$, but the answer is $-2\sin(\theta - \frac{1}{6}\pi)$. My workings: $\cos\theta - \sqrt{3}\sin\theta = r\sin(\theta - \alpha) = r\sin\theta\cos\alpha - r\sin\alpha\cos\theta$ $\Rightarrow r\cos\alpha = -\sqrt{3}$, $r\sin\alpha = -1$ $\Rightarrow r^2\cos^2\alpha = 3$, $r^2\sin^2\alpha = 1 => r^2(\cos^2\alpha + \sin^2\alpha) = 4$ $\Rightarrow r^2 = 4 \Rightarrow r = \pm2$. My question is how should the process in the book be refined so one knows whether $r$ should be positive or negative? (sorry if this is a bit long winded for such a basic question but I thought showing what I do and don't know might get me an answer targeted at my simple level!). - I wonder why every question hasn't got an effort like this. (+1) – Inceptio Apr 16 '13 at 9:35 Note that since $\sin(\theta + \pi) = -\sin(\theta)$, you can get a solution with $r = 2$ as well (which is just the same solution). – TMM Apr 16 '13 at 9:46 In your specific case you get either $$\sin\alpha = \frac{1}{2}\text{ and } \cos\alpha=-\frac{\sqrt{3}}{2}\text{ for } r=2$$ or $$\sin\alpha = -\frac{1}{2}\text{ and } \cos\alpha=\frac{\sqrt{3}}{2}\text{ for } r=-2$$ In the first case you get $\alpha=\frac{5\pi}{6}$, and in the second case you get $\alpha=-\frac{\pi}{6}$. (I use the function $r\sin(\theta + \alpha)$ with a positive sign of $\alpha$). You have to be careful when computing $\alpha$ because you usually cannot simply take the principle branch of the functions $\arcsin(x)$ and $\arccos(x)$. You have to choose a value that satisfies both equations (the one for $\sin(\alpha)$ and the one for $\cos(\alpha)$). - Thanks for your answer. I'm glad you took things a step further as it helped me to fully understand how the choice of $\alpha$ makes a difference to $r$. – PeteUK Apr 16 '13 at 13:21 The answer is that it depends on the choice of $\alpha$. This is because $\sin (x + \pi) = - \sin x$ (also if you were using $\cos$ instead, $\cos (x + \pi) = - \cos x$). This means that it could be either positive or negative, but then $\alpha$ may need to be reduced by $\pi$ - Thank you. This helped me out a lot. – PeteUK Apr 16 '13 at 13:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9284361600875854, "perplexity": 152.7258031844449}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398461113.77/warc/CC-MAIN-20151124205421-00015-ip-10-71-132-137.ec2.internal.warc.gz"}
https://consequently.org/writing/nstlp/	## A Note on Naïve Set Theory in LP “A Note on Naïve Set Theory in LP,” Notre Dame Journal of Formal Logic 33 (1992) 422–432. My first publication. It stems from work I did in my Honours year (1989) with Graham Priest, on paraconsistent logic. I explain a particularly simple yet powerful technique for constructing models of naïve set theory in the paraconsistent logic LP. This can be used to show the consistency of the theory, and to construct models invalidating some of the axioms of ZFC. Do you like this, or do you have a comment? Then please share or reply on Twitter, or email me. Writing Archive \| Simplified Semantics for Relevant Logics (and some of their rivals) →	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9044289588928223, "perplexity": 921.0162189507173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057337.81/warc/CC-MAIN-20210922072047-20210922102047-00008.warc.gz"}
https://ai.stackexchange.com/questions/12734/ideal-score-of-a-model-on-training-and-cross-validation-data	# Ideal score of a model on training and cross validation data The question is little bit broad, but I could not find any concrete explanation anywhere, hence decided to ask the experts here. I have trained a classifier model for binary classification task. Now I am trying to fine tune the model. With different sets of hyperparameters I am getting different sets of accuracy on my train and test set. For example: (1) Train set: 0.99 \| Cross-validation set: 0.72 (2) Train set: 0.75 \| Cross-validation set: 0.70 (3) Train set: 0.69 \| Cross-validation set: 0.69 These are approximate numbers. But my point is - for certain set of hyperparameters I am getting more or less similar CV accuracy, while the accuracy on training data varies from overfit to not so much overfit. My question is - which of these models will work best on future unseen data? What is the recommendation in this scenario, shall we choose the model with higher training accuracy or lower training accuracy, given that CV accuracy is similar in all cases above (in fact CV score is better in the overfitted model)?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5327821373939514, "perplexity": 1056.6050992414084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668644.10/warc/CC-MAIN-20191115120854-20191115144854-00308.warc.gz"}
http://www.ams.org/bookstore-getitem/item=CONM-426	New Titles \| FAQ \| Keep Informed \| Review Cart \| Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education Control Methods in PDE-Dynamical Systems Edited by: Fabio Ancona, University of Bologna, Italy, Irena Lasiecka, University of Virginia, Charlottesville, VA, Walter Littman, University of Minnesota, Minneapolis, MN, and Roberto Triggiani, University of Virginia, Charlottesville, VA SEARCH THIS BOOK: Contemporary Mathematics 2007; 404 pp; softcover Volume: 426 ISBN-10: 0-8218-3766-4 ISBN-13: 978-0-8218-3766-5 List Price: US$112 Member Price: US$89.60 Order Code: CONM/426 While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperbolic and Petrowski-type PDEs. These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. In addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. In all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15476000308990479, "perplexity": 5164.288019681672}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997882928.29/warc/CC-MAIN-20140722025802-00019-ip-10-33-131-23.ec2.internal.warc.gz"}
http://nikitamarkarian.wordpress.com/2010/03/18/s-homology/	# Nikita Markarian’s mathblog ## S-homology Posted in Mathematics by nikitamarkarian on March 18, 2010 $S$-homology is an obvious generalization of the spherical homology. I already mentioned it here. In the present post I would like to summarise their properties. UPD: Things described here and in some previous posts are particular cases of the topological chiral homology introduced in J. Lurie, “Derived Algebraic Geometry VI: E_k Algebras”. The only difference is that I need framed discs. I thank Damien for this comment. UPD: Following M. Kapranov, I will use term manifoldic homology for the higher dimensional generalization of $S$-homology. Let $S$ be an oriented compact 2-manifold possibly with a border. Let $C_(fS(k))$ be the complex of rational chains of the space of framed discs and on $S$ and semi-discs on the border. $S$-homology $HS_$ of a dg f2-algebra $A$ (that is an algebra over rational chains of framed little discs operad) is the product of $C_(fS(k))$ on $A$ over the operad of chains of framed little discs, that is $\oplus_k (C_(fS(k))\otimes A^{\otimes k})$ modulo relations like in this definition. Consider some examples. 1. $S$ is a disc. $HS_(A)=A$ (to be more precise, the underlying complex). It is not suprising, because $S$-homology is homotopical invariant with respect to $S$. 2. $S$ is a annulus. $HS_(A)=HH_(A)$, the Hochschild homology. Picture proves that $HH_(A)$ is a (homotopy) algebra (this fact is true for any 2-algebra, structure of f2-algebra is not necessary). $S$-homology of of a surface with $n$ holes is a module over $HH_(A)^{\otimes n}$. Glueing of surfaces gives maps between derived tensor products over $HH_(A)$. Picture proves that $A$ is a (homotopy) module over $HH_(A)$, see also this statement (in contrast with the previous picture, here $A$ is necessarily a f2-algebra). 3. $S$ is a torus. $HS_(A)=HH_(HH_(A))$, more exactly the total homology of the corresponding bicomplex. Note that this complex is acted by automorphisms of the torus, that is $SL_2(\mathbb{Z})$, what is not so obviuos if one define it as the double Hochschild complex. 4. $S$ is a sphere. $HS_*(A)$ is the spherical homolgy that was discussed here, here and here. 5. $S$ is a pair of pants or surface of higher genus. The meaning of the corresponding $S$-homology is not clear. ### 8 Responses 1. Damien Calaque said, on January 5, 2011 at 11:22 am Dear Nikita, it seems to me that what you are doing is closely related to - higher Hochschild homology (Pirashvili) - topological chiral homology (Lurie) - factorization homology (Costello-Gwilliam) There is a very recent preprint of Ginot-Tradler-Zeinalian (see http://people.math.jussieu.fr/~ginot/papers/HighHoc.pdf) that explain how they are related (they are basically the same in the case of Commutative algebras). i guess that your S-homology should coincide with those when they intersect. Damien • nikitamarkarian said, on January 6, 2011 at 4:27 pm Dear Damien, thank you for your comment, nice to hear from you. Thank you for the reference on Costello-Gwilliam, I did not know it. It seems that this is close to things I am interested in, but there are too many physics there. The Lurie’s work in dimension two must be also close. But I don’t understand, if he needs only little discs action, not framed discs? What about Ginot-Pirashvili’s things, it seems that the case of commutative algebras is much more simpler. For example, it works for any simplicial sets, not only for manifolds. I start studying S-homology only for S=2-sphere to work with Hycomm-algebras. Then I discovered that this is a particular case of a more general definition. I do not know how to make use of these more general things. I would be very grateful for any suggestion. 2. Damien said, on January 24, 2011 at 8:30 pm Hi Nikita, sorry for answering so late. I agree that Pirashvili’s higher Hochschild homology does work for any simplicial set. But this is not a so serious issue since - Costello-Gwilliam approach works for any topological space - I guess that Lurie’s approach does work more generally for CW-complexes (not only manifolds). About framing, one might be missleaded by the word. Lurie does not need framed little disks, but he needs the tangent space of the manifold he considers to be equipped with a framing (he needs some nontrivial additional data on the manifold, and the construction actually depends on this data). At the moment I have no relevant suggestion to make. I still don’t understand how your definition is related to the other ones I mentionned. In particular I don’t understand where framed little disks are necessary in your approach. • nikitamarkarian said, on January 27, 2011 at 9:13 am Hi Damien, - Costello-Gwilliam approach works for any topological space - I guess that Lurie’s approach does work more generally for CW-complexes (not only manifolds). I don’t know about the Costello-Gwilliam approach. But in the Lurie’s one I guess that the thing must be a manifold. Indeed the idea is we take the configuration space of the thing and consider it in a sense as a right module over the little discs operad. But it works only if the thing locally looks like a disc. About framing, one might be missleaded by the word. Lurie does not need framed little disks, but he needs the tangent space of the manifold he considers to be equipped with a framing (he needs some nontrivial additional data on the manifold, and the construction actually depends on this data). Exactly, he needs that the manifold must be parallelizable (by the way, if it works for any CW-complex what does it mean then?). To avoid this restriction one have to consider framed discs. In fact, I have no particular approach, I solved a practical problem: to construct a functor from (homotopy) BV algebras to complexes with prescribed properties, something like it must be invariant under “inner” deformations. By the formality theorem one can replace BV with framed 2-discs. Firstly I tried to construct such a functor from an algebra over the operad of non-framed discs and found S-homology when S=torus. It seems that there no other such functors on algebras over non-framed discs. The explanation is that torus is the only parallelizable oriented compact surface. Then I constructed S-homology when S=sphere and was quite happy, because it was exactly the functor I was looking for. And then I recognized that sphere may be replaced by any oriented compact surface. And I would like to understand how to make use of all these functors. The moral is that in dimension 2 the non-framed life is much more boring that the framed one. I guess that the circle action produce reach structures that appears in sciences about quantum cohomology and Witten conjecture, I am going to discuss it sometime. Please, write me again if some questions remain. • Damien said, on February 24, 2011 at 9:14 pm Dear Nikita, I have a few more comments and questions. I was quite optimistic when saying that Lurie’s approach works for CW-complexes. My guess was (following what happens for higher Hochschild homology and S-homology) that Lurie’s topological chiral homology should somehow be an homotopy invariant of the manifold he considers. Then I vaguely remembered a statement like “any CW complex has the homotopy type of a topological manifold”… but now I have some doubts. By the way, it is indeed very nice that using framed little disk then you seems to be able to avoid the use of a trivialization of the tangent bundle in defining some avatar of topological chiral homology. Then I have a few questions : 1. what are algebras over the framed little disk operad (I mean, not going to chain level, but staying at the topological level) ? 2. dealing with QFTs with boundary conditions then one needs to use an avatar of the swiss-cheese operad. I have an idea of what “framed swiss-cheese” is… but it obviously does not contain framed little disks. Say it in another way, Lurie’s stuff seems to work for manifolds with corners (see his paper on extended QFTs and the cobordism hypothesis). I see that you have a construction for surfaces with boundary, but I have the strange feeling that it misses some information from the boundary (I might be wrong). 3. You should have an (easier) analog in dimension 1: namely, for any curve $C$ and any $E1$-algebra $A$, associate something like $H_C(A)$. For $C$ the affine line you should get $A$ itself and for $C=S^1$ you should get Hochschild homology of $A$. 4. Do you have cochain version of this, and associated Deligne’s type conjecture ? Best Damien • nikitamarkarian said, on March 2, 2011 at 10:54 am Dear Damien, 1. what are algebras over the framed little disk operad (I mean, not going to chain level, but staying at the topological level) ? The recognition principle for an algebras over framed discs states that this is the same as spaces with a circle action. This is well written in the Salvatore-Wahl’s paper. By the way, every space may be equipped with the trivial circle action, thus every algebra over little discs may be canonically lifted to an algebra over framed little discs. This is not true on the level of complexes! Perhaps, it works for complexes with augmentation. 2. dealing with QFTs with boundary conditions then one needs to use an avatar of the swiss-cheese operad. I have an idea of what “framed swiss-cheese” is… but it obviously does not contain framed little disks. Say it in another way, Lurie’s stuff seems to work for manifolds with corners (see his paper on extended QFTs and the cobordism hypothesis). I see that you have a construction for surfaces with boundary, but I have the strange feeling that it misses some information from the boundary (I might be wrong). Yes, your are right, some work must be done to work with a border. In dimension two this is much easier, because the border is always a circle and I guess everything is clear. Manifolds with corners is much more delicate subject. In dimension two this is essentially the same as homotopy cyclic 2-category. I can’t imagine what’s going on in higher dimensions. 3. You should have an (easier) analog in dimension 1: namely, for any curve $C$ and any $E1$-algebra $A$, associate something like $H_C(A)$. For $C$ the affine line you should get $A$ itself and for $C=S^1$ you should get Hochschild homology of $A$. Yes, I met such construction somewhere. Essentially paper of T. Goodwillie “Cyclic homology, derivations, and the free loop space” is about it. 4. Do you have cochain version of this, and associated Deligne’s type conjecture ? No. I doubt that it could be, for example Hochschild cohomology is not a functor. Best, Nikita. 3. Grégory said, on February 25, 2011 at 3:02 pm Dear Nikita and Damien, the chiral homology as mentioned in the previous comment is really an invariant of a (stably) framed manifold (i.e. the choice of a framing of Mx D^n where D^n is a disk). It does depend on the framing and not just of the homotopy type of the manifold. However the more commutative is your E_n-algebra, the more homotopical invariant it becomes. More precisely, if you have two framing on a manifold M of dimension n (which induce equivalent framing on Mx D) and an E_{n+1}-algebra A, then the chiral homology of M with value in A is the same whatever the framing you choose. However, there may be E_n algebra for which they are different. That explains why, if you take E_\infty algebras, you get a theory that applies to all manifolds and doesn’t care about choices of stable framing; inducing a theory that makes sense for any CW-complex (and thus simplicial set). In Lurie’s TFT paper (and DAG VI too I think), there are some paragraph in which it is explained that you can look to topological chiral homology for oriented manifolds if you look to E_n-algebras which are homotopy fixed point with respect to the natural SO(n) action on the framed little disk operad. I think that framed little disk algebras are naturally examples of such. Further, such things can be computed by using (homotopy) coends in between a coalgebra over the framed little disk operad and an algebra over it. You can find some notes about that (well in the parallelizable case) here at the end of these notes (which grew up from discussions with D. Ayala): http://www.math.ku.dk/english/research/conferences/strings/strings.gregory.pdf/ This looks pretty close from your approach (I only found time to have a quick look to your posts so far so I may have missed many things) and I’m pretty sure what you got is a very nice description of this version of topological chiral homology. Best, Grégory Ginot • nikitamarkarian said, on March 2, 2011 at 10:56 am Dear Grégory, thank you very much for a substantial comment. I will read the note with great interest. Best, Nikita.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 32, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8791716694831848, "perplexity": 555.2760051406324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400379636.59/warc/CC-MAIN-20141119123259-00205-ip-10-235-23-156.ec2.internal.warc.gz"}
http://www.koreascience.or.kr/search.page?keywords=T1+Weighted+Image&pageSize=10&pageNo=0	• Title, Summary, Keyword: T1 Weighted Image ### Magnetic resonance imaging characteristic of lymph nodes: Comparison of T1 and T2 weighted image in normal rabbits (림프절의 자기공명영상의 특징: 가토에서 T1과 T2 강조영상의 비교) • Lee, Ki-chang;Choi, Min-cheol;Choi, Ho-Jung;Yoon, Jung-hee;Choi, Seong-hong;Moon, Woo-kyung;Chung, Jin-Wook • Korean Journal of Veterinary Research • / • v.44 no.2 • / • pp.311-315 • / • 2004 • The detection of lymph node metastasis is an important step in tumor staging and is significant for therapy planning. It has been challenged to yield an appropriate image with diagnostic methods such as Magnetic Resonance (MR) and Computed Tomography (CT). Though CT has been used widely and accessed easily to show internal organs, it can hardly provide difference between lymph node and adjacent vessel or fat tissue. It has been well established that MR can reveal the subtle discrepancy within soft tissue. This study investigated the suitability of MR lymph node imaging without contrast enhancement by comparison of T1-weighted image (T1WI) and T2- weighted image (T2WI) in ten normal rabbits. According to the pulse sequence optimized from preliminary study, T1-weighted spin-echo (repetition time/echo time=400/12 ms) and T-2 weighted fast spin-echo (repetition time/echo time=3500/84 ms) images covering the hind limbs and pelvic region were acquired at 1.5 T. Two radiologists scrupulously evaluated the MR images in consensus. And signal intensity of lymph nodes was compared with that of adjacent fat. Statistical analysis showed that T1-weighted coronal image visualized the lymph nodes (iliac, superficial inguinal and popliteal lymph nodes) quickly and consistently rather than T2-weighted one. Conclusively, T1WI for evaluation of lymph nodes is moderately better than T2WI and appears to have potential for quick and sufficient mapping of the lymph nodes. In addition, this normal MR image of lymph nodes could be applied to further study for the evaluation of lymphatic system in abscess and tumor bearing animal model. ### Evaluation of the Image Blurring in the Fast Spin Echo Technique ccording to Variation of the ETL (고속스핀에코기법을 이용한 MRI검사에서 ETL 변화에 따른 영상 blurring의 평가) • Kwon, Soon-Yong;Lim, Woo-Taek;Kang, Chung-Hawn;Kim, Kyeong-Soo;Kim, Soon-Bae;Kim, Hyun-Soo • Korean Journal of Digital Imaging in Medicine • / • v.15 no.2 • / • pp.55-61 • / • 2013 • The purpose of this study is to evaluate image blurring according to variation of the ETL and propose the clinically appropriate ETL range. SIEMENS MAGNETOM Skyra 3.0T and 20 channel head coil were used for the study. MRI phantom was kept the lines horizontally to three direction(X,Y,Z) of the coil and T1, T2 weighted images that used the fast spin echo technique acquired. The ETL with increase of 10 was applied from 10 to 80. In addition, the ETL with increase of 1 was applied in the interval statistically significant differences occurred. And T1, T2 weighted images that used the conventional spin echo technique acquired to compare image blurring of the images that used the fast spin echo technique. The slope of lattice in the images was measured using Image J 1.47v program to evaluate image blurring. And image blurring was determined by the degree of the slope. The statistical significance of both techniques was evaluated by the Kruskal-Wallis test of the SPSS 17.0v. And the correlation of the ETL and image blurring was evaluated quantitatively by regression analysis. The slope of the T1, T2 weighted images that used fast spin echo technique decreased as contrasted with conventional spin echo technique. In the result of the Kruskal-Wallis test, the T1, T2 weighted images that used fast spin echo technique made a significant difference with conventional spin echo technique. Particularly, in the Tomhane' T2 test, the T1, T2 weighted images made a significant difference from ETL 22 and 31 respectively. In the result of the regression analysis, the R-squared of the T1, T2 weighted images are 0.762 and 0.793. It is difficult to apply the long ETL in the T1 weighted image caused by the short TR and multi-slices study. Therefore, clinical impact according to variation of the ETL is very slight in the T1 weighted images. But the application of the proper ETL is demanded in T2 weighted images using the fast spin echo technique in order to prevent image blurring. ### Studies on the Ability to Detect Lesions According to the Changes in the MR Diffusion Weighted Images • Kim, Chang-Bok;Cho, Jae-Hwan;Dong, Kyung-Rae;Chung, Woon-Kwan • Journal of Magnetics • / • v.17 no.2 • / • pp.153-157 • / • 2012 • This study evaluated the ability of Diffusion-Weight Image (DWI), which is one of pulse sequences used in MRI based on the T2 weighted images, to detect samples placed within phantoms according to their size. Two identically sized phantoms, which could be inserted into the breast coil bilaterally, were prepared. Five samples with different sizes were placed in the phantoms, and the T2 weighted images and DWI were obtained. The Breast 2 channel coil of SIEMENS MAGNETOM Avanto 1.5 Tesla equipment was used for the experiments. 2D T2 weighted images were obtained using the following parameters: TR/TE = 6700/74 msec, Thickness/gap = 5/1 mm, Inversion Time (TI) = 130 ms, and matrix = $224{\times}448$. The parameters of DWI were that TR/TE = 8100/90 msec, Thickness/gap = 5/1 mm, matrix = $128{\times}128$, Inversion Time = 185 ms, and b-value = 0, 100, 300, 600, 1000 s/mm. The ratio of the sample volume on DWI compared to the T2 weighted images, which show excellent ability to detect lesions on MR images, was presented as the mean b-value. The measured b-value of the samples was obtained: 0.5${\times}$0.5 cm=0.33/0.34 square ${\times}$ cm (103%), 1${\times}$1 cm=1.28/1.25 square ${\times}$ cm (102.4%), 1.5${\times}$1.5 cm = 2.28/2.67 square ${\times}$ cm (85.39%), 2${\times}$2 cm=3.56/4.08 square ${\times}$ cm (87.25%), and 2.5${\times}$2.5 cm=7.53/8.77 square ${\times}$ cm (85.86%). In conclusion, the detection ability by the size of a sample was measured to be over 85% compared to T2 weighted image, but the detection ability of DWI was relatively lower than that of T2 weighted image. ### Improvement of Fat Suppression and Artifact Reduction Using IDEAL Technique in Head and Neck MRI at 3T • Hong, Jin Ho;Lee, Ha Young;Kang, Young Hye;Lim, Myung Kwan;Kim, Yeo Ju;Cho, Soon Gu;Kim, Mi Young • Investigative Magnetic Resonance Imaging • / • v.20 no.1 • / • pp.44-52 • / • 2016 • Purpose: To quantitatively and qualitatively compare fat-suppressed MRI quality using iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) with that using frequency selective fat-suppression (FSFS) T2- and postcontrast T1-weighted fast spin-echo images of the head and neck at 3T. Materials and Methods: The study was approved by our Institutional Review Board. Prospective MR image analysis was performed in 36 individuals at a single-center. Axial fat suppressed T2- and postcontrast T1-weighted images with IDEAL and FSFS were compared. Visual assessment was performed by two independent readers with respect to; 1) metallic artifacts around oral cavity, 2) susceptibility artifacts around upper airway, paranasal sinus, and head-neck junction, 3) homogeneity of fat suppression, 4) image sharpness, 5) tissue contrast of pathologies and lymph nodes. The signal-to-noise ratios (SNR) for each image sequence were assessed. Results: Both IDEAL fat suppressed T2- and T1-weighted images significantly reduced artifacts around airway, paranasal sinus, and head-neck junction, and significantly improved homogeneous fat suppression in compared to those using FSFS (P < 0.05 for all). IDEAL significantly decreased artifacts around oral cavity on T2-weighted images (P < 0.05, respectively) and improved sharpness, lesion-to-tissue, and lymph node-to-tissue contrast on T1-weighted images (P < 0.05 for all). The mean SNRs were significantly improved on both T1- and T2-weighted IDEAL images (P < 0.05 for all). Conclusion: IDEAL technique improves image quality in the head and neck by reducing artifacts with homogeneous fat suppression, while maintaining a high SNR. ### The study of utility about magnetic resonance elastography for measurements of liver stiffness : the comparisons of ADC value & T2 weighted image (간 경화도 측정을 위한 3.0T 자기공명 탄성계수 영상의 유용성에 대한 고찰 : 확산계수 영상 및 T2 강조 영상과의 비교) • Kim, Sang-Woo;Kang, Chung-Hwan;Kim, Sung-Ho;Kim, Kyung-Soo;Kim, Soon-Bae • Korean Journal of Digital Imaging in Medicine • / • v.14 no.1 • / • pp.21-29 • / • 2012 • The purpose of this study is to evaluate the mutual relations by measuring SNR from T2 weighted image and ADC values on the basis of the stiffness values from liver tissues. This study was conducted that total 37 people(23 of males and 11 of females) were taken the liver MRI examination and average age was $54.5{\pm}12.7$ years old. The equipment was MAGNETOM Skyra 3.0T (SIEMENS, Erlangen, Germany) and 32 channel body-array coil. The examination were conducted with HASTE T2 weighted image by axial plane, Spin-echo EPI (echo planner image) DWI (b-value = 800) and Magnetic resonance elastography. The ROIs (region of interest: 200-300 $mm^2$) were established on the basis of the first axial stiffness image corresponded 95% confidence interval from axial stiffness image and then were measured values. After drawing the grid lines, signals were measured SNR from T2 weighted image and ADC values on the same locations that were analysed other 3 planes respectively. The results were showed correlation (0.057) that were increased to SNR from T2 weighted image by increasing stiffness value that no significant difference statistically p = 0.003. Other results were showed correlations (-0.301) that were decreased to ADC values by increasing stiffness values that no significant difference statistically p = 0.088. In the 3.0T equipment, the results may be error in much the same fashion as the 1.5T from ADC values by evaluation of fibrosis stage. However, Magnetic resonance elastography would be useful method that is used to diagnose exactly liver fibrosis stages in the 3.0T. ### Electron Microscopy and MR Imaging Findings in Embolic Effects • Park Byung-Rae;Koo Bong-Oh • Biomedical Science Letters • / • v.10 no.4 • / • pp.367-373 • / • 2004 • Evaluated the hyperacute embolic effects of triolein and oleic acid in cat brains by using MR image and electron microscopy. In fat embolism, free fatty acid is more toxic than neutral fat in terms of tissue damage. T2-Weighted imaging, diffusion-weighted imaging, and contrast-enhanced T1-weighted imaging were performed in cat brains after the injection of triolein (group 1, n=8) or oleic acid (group 2, n=10) into the internal carotid artery. MR image were quantitatively assessed by comparing the lesions with their counterparts on T2-weighted images, apparent diffusion coefficient (ADC) maps, and contrast-enhanced T1-weighted images. Electron microscopic findings in group 1 were compared with those in group 2. Qualitatively, MR images revealed two types of lesions. Type 1 lesions were hyperintense on diffusion-weighted images and hypointense of ADC maps. Type 2 lesions were isointense or mildly hyperintense on diffusion-weighted images and isointense on ADC maps. Quantitatively, the signal intensity rations of type 1 lesions in group 2 specimens were significantly higher on T2-weighted images (P=.013)/(P=.027) and lower on ADC maps compared with those of group 1. Electron microscopy of type 1 lesions in both groups revealed more prominent widening of the perivascular space and swelling of the neural cells in groups 1. MR and electron microscopic data on cerebral fat embolism induced by either triolein or oleic acid revealed characteristics suggestive of both vasogenic and cytotoxic edema in the hyperacute stage. Tissue damage appeared more severe in the oleic acid group than in the triolein group. ### T1-, T2-weighted, and FLAIR Imaging: Clinical Application (T1, T2강조영상, FLAIR영상의 임상 적용) • Kim, Jae-Hyoung • Investigative Magnetic Resonance Imaging • / • v.13 no.1 • / • pp.9-14 • / • 2009 • T1-, and T2-weighted imagings and FLAIR (fluid attenuated inversion recovery) imaging are fundamental imaging methods in the brain. T1-weighted imaging is a spin-echo sequence with short TR and short TE and produces the tissue contrast by different T1 relaxation times. In other words, short TR maximizes the difference of the longituidinal magnetization recovery between the tissues. T2-weighted imaging is a spin-echo sequence with long TR and long TE and produces the tissue contrast by different T2 relaxation times. Long TE maximizes the difference of the transverse magnetization decay between the tissues. FLAIR is an inversion recovery sequence using 180 degree inversion pulse. 2500 msec of inversion time is applied to suppress the CSF signal. ### Prostate MR and Pathology Image Fusion through Image Correction and Multi-stage Registration (영상보정 및 다단계 정합을 통한 전립선 MR 영상과 병리 영상간 융합) • Jung, Ju-Lip;Jo, Hyun-Hee;Hong, Helen • Journal of KIISE:Computing Practices and Letters • / • v.15 no.9 • / • pp.700-704 • / • 2009 • In this paper, we propose a method for combining MR image with histopathology image of the prostate using image correction and multi-stage registration. Our method consists of four steps. First, the intensity of prostate bleeding area on T2-weighted MR image is substituted for that on T1-weighted MR image. And two or four tissue sections of the prostate in histopathology image are combined to produce a single prostate image by manual stitching. Second, rigid registration is performed to find the affine transformations that to optimize mutual information between MR and histopathology images. Third, the result of affine registration is deformed by the TPS warping. Finally, aligned images are visualized by the intensity intermixing. Experimental results show that the prostate tumor lesion can be properly located and clearly visualized within MR images for tissue characterization comparison and that the registration error between T2-weighted MR and histopathology image was 0.0815mm. ### Cerebellar Pilocytic Astrocytomas with Spontaneous Intratumoral Hemorrhage in Adult • Kim, Min-Su;Kim, Sang-Woo;Chang, Chul-Hoon;Kim, Oh-Lyong • Journal of Korean Neurosurgical Society • / • v.49 no.6 • / • pp.363-366 • / • 2011 • Cerebellar pilocytic astrocytomas (PAs) are benign gliomas predominantly found in the pediatric population. Intracranial hemorrhages are extremely rare in initial presentations of cerebellar PAs. There are no reports in the medical literature of adult cerebellar PA cases presenting with intratumoral hemorrhage. We report 2 cases of adult cerebellar pilocytic astrocytomas with intratumoral hemorrhage. The first case is a 37-year-old woman presenting with severe headache, nausea, and vomitting. Computed tomography demonstrated an acute hemorrhage adjacent to the right cerebellar hemisphere and hydrocephalus. Magnetic resonance imaging (MRI) revealed a cerebellar vermian tumor with the hemorrhage as a mixed isoin-tense area in the T2-weighted image, and as a mixed hyperintense area in the contrast-enhanced T1-weighted image. The second case is a 53-year-old man presenting with headache for 3 weeks. MRI revealed a cerebellar hemispheric tumor with the hemorrhage as a mixed hyperintense area. It had a cystic mass with a heterogeneous enhanced mural nodule in the gadolinium-enhanced T1-weighted image and a fluid-fluid level within the cyst in the T2-weighted image. Both of them underwent radical resections of their respective lesions. Histological examination of the specimens revealed typical astrocytoma, including a hemorrhagic portion. Both patients recovered postoperatively and continue to do well at present. The medical literature on hemorrhagic cerebellar PAs is also reviewed. ### Dual Contrast EPI by Use of a Key Hole Technique • Jung, Kwan-Jin • Proceedings of the KSMRM Conference • / • / • pp.113-113 • / • 2001 • Purpose： In the gradient echo EPI the conventional T2＊-weighted image is poor in signal as well distorted by the field inhomogeneity. By acquiring a proton density image in addition to th T2＊-weighted image at the same scan, the fMRI processing can be improved. Method： The central region of the k space is acquired twice at different time points after th RF pulse while acquiring the other regions onc as described in Fig. 1. In Fig. 1 the segment numbers are chronological. Then, we can get two images of different contrast by interleaving th central region in the k space as done in the dua contrast FSE.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6590127348899841, "perplexity": 11100.319233334867}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402088830.87/warc/CC-MAIN-20200929190110-20200929220110-00110.warc.gz"}
http://depot.knaw.nl/11745/	# Viscous eddies in a circular cone Malyuga, V. (2005) Viscous eddies in a circular cone. Journal of Fluid Mechanics, 522, 101-116. ISSN 0022-1120. PDF - Published Version Restricted to KNAW only637Kb Official URL: http://dx.doi.org/10.1017/S0022112004001703 ## Abstract The flow of viscous incompressible fluid in a circular cone induced by a non-zero velocity prescribed at the boundary within a ring $0\,{<}\,a_1\,{<}\,r\,{<}\,a_2\,{<}\,\infty$, where $r$ is the distance from the vertex, is considered in the limits of the Stokes approximation. In the spherical coordinate system $(r,\theta,\phi)$ with the origin at the vertex and the axis $\theta\,{=}\,0$ coincident with the axis of the cone the velocity and pressure fields are represented in the form of a Fourier series on the trigonometric system $\cos m \phi$. The solution is constructed for each term by use of the Mellin transform. The contribution of each term of the Fourier expansion to the local velocity field near the vertex is studied. The kinematics of the local flows is illustrated by two examples. The flows are induced by the motion of two and three equally spaced segments, respectively. Item Type: Article Nederlands Instituut voor Ecologie (NIOO) 11745 23 Nov 2011 01:00 31 Mar 2014 10:07 Repository Staff Only: item control page	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9443774223327637, "perplexity": 441.48571152235144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500811391.43/warc/CC-MAIN-20140820021331-00202-ip-10-180-136-8.ec2.internal.warc.gz"}
https://www.emathzone.com/tutorials/linear-programming/examples-of-inequality-and-compound-inequality.html	Examples of Inequality and Compound Inequality Example: Solve and graph the solution of the inequality ${\text{x}} + 3 > 4{\text{x}} + 6$ Solution: We have $\begin{gathered} {\text{x}} + 3 > 4{\text{x}} + 6 \\ \Rightarrow 3 – 6 > 4{\text{x}} – {\text{x}} \\ \Rightarrow – 3 > 3{\text{x}} \\ \Rightarrow \frac{{ – 3}}{3} > {\text{x}} \\ \Rightarrow {\text{x}} < – 1 \\ \end{gathered}$ Thus, the solution set is Solution Set $= \left\{ {{\text{x:x}} \in \mathbb{R} \wedge {\text{x}} < – 1} \right\} = \left] { – \infty , – 1} \right[$ The graph of the solution set is Example: Solve and graph the solution of the inequality $11 – 2\left( {{\text{x}} – 1} \right) \geqslant 8 – 2\left( {{\text{x}} – 2} \right)$. Solution: We have $\begin{gathered} 11 – 2\left( {{\text{x}} – 1} \right) \geqslant 8 – 2\left( {{\text{x}} – 2} \right) \\ \Rightarrow 11 – 2{\text{x}} + 2 \geqslant 8 – 2{\text{x}} + 4 \\ \Rightarrow 13 – 2{\text{x}} \geqslant 12 – 2{\text{x}} \\ \Rightarrow 13 \geqslant 12 \\ \end{gathered}$ Here equality is not possible because 13 is always greater than 12, in $13 > 12$. So, the solution of the given inequality is the set of all real numbers is $\mathbb{R}$. The solution can be written as $\left] { – \infty ,\infty } \right[$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.942535936832428, "perplexity": 297.27360612320666}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655892516.24/warc/CC-MAIN-20200707111607-20200707141607-00552.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-1-equations-and-inequalities-exercise-set-1-2-page-121/108	## College Algebra (6th Edition) Published by Pearson # Chapter 1 - Equations and Inequalities - Exercise Set 1.2 - Page 121: 108 #### Answer The result will be the same if you multiply by $20$ on both sides. There are various methods of solving these types of problems, but using the least common denominator method will decrease the chance of mathematical error. #### Work Step by Step The LCD method is arguably the quickest and most efficient way to solve this. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6302873492240906, "perplexity": 653.8502266175755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516194.98/warc/CC-MAIN-20181023132213-20181023153713-00063.warc.gz"}
http://science.sciencemag.org/content/344/6190/1343	PerspectiveImmunology # Teaching the immune system “self” respect and tolerance See allHide authors and affiliations Science 20 Jun 2014: Vol. 344, Issue 6190, pp. 1343-1344 DOI: 10.1126/science.1256864 ## Summary The immune system protects the individual from infectious agents and the emergence of tumors while preserving the host's integrity (1). The latter implies that the immune system will not attack the individual's own tissues (“self”). This peaceful coexistence, or immune tolerance, is broken when an autoimmune disease develops, such as multiple sclerosis or insulin-dependent diabetes. Tolerance is what we would like to restore to cure such disabling diseases. Kasagi et al. (2) indicate that it may be possible to teach the immune system to tolerate “self” again.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8638587594032288, "perplexity": 6948.292116721283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823229.49/warc/CC-MAIN-20171019050401-20171019070401-00465.warc.gz"}
https://people.maths.bris.ac.uk/~matyd/GroupNames/154/Dic40.html	Copied to clipboard ## G = Dic40order 160 = 25·5 ### Dicyclic group Aliases: Dic40, C16.D5, C51Q32, C80.1C2, C10.3D8, C2.5D40, C4.3D20, C20.26D4, C8.15D10, C40.16C22, Dic20.1C2, SmallGroup(160,8) Series: Derived Chief Lower central Upper central Derived series C1 — C40 — Dic40 Chief series C1 — C5 — C10 — C20 — C40 — Dic20 — Dic40 Lower central C5 — C10 — C20 — C40 — Dic40 Upper central C1 — C2 — C4 — C8 — C16 Generators and relations for Dic40 G = < a,b \| a80=1, b2=a40, bab-1=a-1 > Smallest permutation representation of Dic40 Regular action on 160 points Generators in S160 (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160) (1 103 41 143)(2 102 42 142)(3 101 43 141)(4 100 44 140)(5 99 45 139)(6 98 46 138)(7 97 47 137)(8 96 48 136)(9 95 49 135)(10 94 50 134)(11 93 51 133)(12 92 52 132)(13 91 53 131)(14 90 54 130)(15 89 55 129)(16 88 56 128)(17 87 57 127)(18 86 58 126)(19 85 59 125)(20 84 60 124)(21 83 61 123)(22 82 62 122)(23 81 63 121)(24 160 64 120)(25 159 65 119)(26 158 66 118)(27 157 67 117)(28 156 68 116)(29 155 69 115)(30 154 70 114)(31 153 71 113)(32 152 72 112)(33 151 73 111)(34 150 74 110)(35 149 75 109)(36 148 76 108)(37 147 77 107)(38 146 78 106)(39 145 79 105)(40 144 80 104) G:=sub<Sym(160)\| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,103,41,143)(2,102,42,142)(3,101,43,141)(4,100,44,140)(5,99,45,139)(6,98,46,138)(7,97,47,137)(8,96,48,136)(9,95,49,135)(10,94,50,134)(11,93,51,133)(12,92,52,132)(13,91,53,131)(14,90,54,130)(15,89,55,129)(16,88,56,128)(17,87,57,127)(18,86,58,126)(19,85,59,125)(20,84,60,124)(21,83,61,123)(22,82,62,122)(23,81,63,121)(24,160,64,120)(25,159,65,119)(26,158,66,118)(27,157,67,117)(28,156,68,116)(29,155,69,115)(30,154,70,114)(31,153,71,113)(32,152,72,112)(33,151,73,111)(34,150,74,110)(35,149,75,109)(36,148,76,108)(37,147,77,107)(38,146,78,106)(39,145,79,105)(40,144,80,104)>; G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,103,41,143)(2,102,42,142)(3,101,43,141)(4,100,44,140)(5,99,45,139)(6,98,46,138)(7,97,47,137)(8,96,48,136)(9,95,49,135)(10,94,50,134)(11,93,51,133)(12,92,52,132)(13,91,53,131)(14,90,54,130)(15,89,55,129)(16,88,56,128)(17,87,57,127)(18,86,58,126)(19,85,59,125)(20,84,60,124)(21,83,61,123)(22,82,62,122)(23,81,63,121)(24,160,64,120)(25,159,65,119)(26,158,66,118)(27,157,67,117)(28,156,68,116)(29,155,69,115)(30,154,70,114)(31,153,71,113)(32,152,72,112)(33,151,73,111)(34,150,74,110)(35,149,75,109)(36,148,76,108)(37,147,77,107)(38,146,78,106)(39,145,79,105)(40,144,80,104) ); G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)], [(1,103,41,143),(2,102,42,142),(3,101,43,141),(4,100,44,140),(5,99,45,139),(6,98,46,138),(7,97,47,137),(8,96,48,136),(9,95,49,135),(10,94,50,134),(11,93,51,133),(12,92,52,132),(13,91,53,131),(14,90,54,130),(15,89,55,129),(16,88,56,128),(17,87,57,127),(18,86,58,126),(19,85,59,125),(20,84,60,124),(21,83,61,123),(22,82,62,122),(23,81,63,121),(24,160,64,120),(25,159,65,119),(26,158,66,118),(27,157,67,117),(28,156,68,116),(29,155,69,115),(30,154,70,114),(31,153,71,113),(32,152,72,112),(33,151,73,111),(34,150,74,110),(35,149,75,109),(36,148,76,108),(37,147,77,107),(38,146,78,106),(39,145,79,105),(40,144,80,104)]) Dic40 is a maximal subgroup of C160⋊C2 Dic80 D16.D5 C5⋊Q64 D807C2 C16.D10 D163D5 SD32⋊D5 D5×Q32 C3⋊Dic40 Dic120 Dic40 is a maximal quotient of C40.78D4 C8013C4 C3⋊Dic40 Dic120 43 conjugacy classes class 1 2 4A 4B 4C 5A 5B 8A 8B 10A 10B 16A 16B 16C 16D 20A 20B 20C 20D 40A ··· 40H 80A ··· 80P order 1 2 4 4 4 5 5 8 8 10 10 16 16 16 16 20 20 20 20 40 ··· 40 80 ··· 80 size 1 1 2 40 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ··· 2 2 ··· 2 43 irreducible representations dim 1 1 1 2 2 2 2 2 2 2 2 type + + + + + + + - + + - image C1 C2 C2 D4 D5 D8 D10 Q32 D20 D40 Dic40 kernel Dic40 C80 Dic20 C20 C16 C10 C8 C5 C4 C2 C1 # reps 1 1 2 1 2 2 2 4 4 8 16 Matrix representation of Dic40 in GL2(𝔽241) generated by 239 58 183 115 , 148 42 58 93 G:=sub<GL(2,GF(241))\| [239,183,58,115],[148,58,42,93] >; Dic40 in GAP, Magma, Sage, TeX {\rm Dic}_{40} % in TeX G:=Group("Dic40"); // GroupNames label G:=SmallGroup(160,8); // by ID G=gap.SmallGroup(160,8); # by ID G:=PCGroup([6,-2,-2,-2,-2,-2,-5,96,73,79,218,122,579,69,4613]); // Polycyclic G:=Group<a,b\|a^80=1,b^2=a^40,bab^-1=a^-1>; // generators/relations Export ׿ × 𝔽	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7332988977432251, "perplexity": 963.8259924366843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251700675.78/warc/CC-MAIN-20200127112805-20200127142805-00449.warc.gz"}
http://hilbertthm90.wordpress.com/2012/07/28/projective-modules-over-dedekind-domains/	# Projective Modules over Dedekind Domains Today we’ll classify finitely generated projective modules over Dedekind domains which will finish off a very similar structure theorem to the one over a PID. First, we need an approximation theorem. Fix a Dedekind domain ${R}$. If we specify an order of vanishing of ${n_i}$ at finitely many primes ${\frak{p}_i}$, then we can find an element ${x\in Frac(R)}$ with the property that ${ord_\frak{p_i}(x)=n_i}$ and non-negative otherwise. We can reduce to the case of finiding an element where all the orders of vanishing are positve, since we can divide in ${Frac(R)}$ to get the negative terms. By the Chinese Remainder Theorem the map ${R\rightarrow R/\frak{p}_1^{n_1+1}\times \cdots \times R/\frak{p}_m^{n_m+1}}$ is surjective. Now take ${x_i\in \frak{p_i}^{n_i}\setminus \frak{p}_i^{n_i+1}}$ and let ${x}$ be the preimage of ${(x_1, \ldots, x_m)}$. A quick consequence of this is that for any non-zero fractional ideals ${I, J}$ of ${R}$ there are elements ${x,y\in Frac(R)}$ such that ${yI}$ is coprime to ${xJ}$. The proof is to specify the appropriate orders of vanishing of ${x}$ and ${y}$ to cancel out and make ${ord_P(yI)\cdot ord_P(xJ)=0}$ for all prime ideals ${P}$. By primary decomposition this shows they are coprime. Now we need to prove that for any fractional ideals ${I_1, \ldots, I_n}$ we have ${I_1\bigoplus\cdots \bigoplus I_n\simeq R^{n-1}\bigoplus I_1\cdots I_n}$. By induction it suffices to prove that ${I\bigoplus J\simeq R\bigoplus IJ}$. If ${I}$ and ${J}$ are coprime, then ${I\cap J=IJ}$ and ${I+J\simeq R}$, so since the standard exact sequence ${0\rightarrow I\cap J\rightarrow I\bigoplus J\rightarrow I+J\rightarrow 0}$ splits we see that ${I\bigoplus J\simeq R\bigoplus IJ}$. The statement follows for arbitrary ${I, J}$ because we can find ${x,y\in Frac(R)}$ such that ${xI}$ and ${yJ}$ are coprime, but ${xI\simeq I}$ and ${yJ\simeq J}$. Our structure theorem says that if ${P}$ is a finitely generated projective ${R}$-module of rank ${n}$, then ${P\simeq R^{n-1}\bigoplus I}$. Recall that rank here is defined to be the dimension of ${P\otimes_R Frac(R)}$, or in other words since ${P}$ is locally free from last time, the rank of the free module after localizing. This is NOT the number of generators of ${P}$. To prove the statement we’ll prove by induction that ${P}$ must be a direct sum of ${n}$ fractional ideals which by the rest of the post proves it. The base case just follows from flatness since ${P\subset P\otimes_R Frac(R)\simeq Frac(R)}$. Now suppose ${P}$ has rank ${n}$. Let ${Q}$ be a rank ${n-1}$ submodule of ${P}$ and form ${0\rightarrow Q\rightarrow P \rightarrow P/Q\rightarrow 0}$. Tensoring with ${Frac(R)}$ again shows that ${P/Q}$ is rank ${1}$ and hence projective. Thus the sequence splits and by the inductive hypothesis ${P\simeq Q\bigoplus P/Q}$ is a sum of fractional ideals. Now for the uniqueness of this representation we only have to worry about which ${I}$ can appear in ${P\simeq R^{n-1}\bigoplus I}$. It turns out that this is unique up to choice of representative of the class ${[I]\in Cl(Frac(R))}$. This follows easily because if ${[I]=[J]}$, then they differ by a principal ideal and hence as ${R}$-modules ${I\simeq J}$. If ${R^{n-1}\bigoplus I\simeq R^{n-1}\bigoplus J}$, then taking the determinant of both sides (top exterior product) kills off the ${R^{n-1}}$ as follows: ${\displaystyle \begin{matrix} \bigwedge^n (R^{n-1}\bigoplus I) & \simeq & \displaystyle \bigoplus_{p+q=n} \bigwedge^p(R^{n-1})\otimes \bigwedge^q(I) \\ & \simeq & \bigwedge^{n-1}R^{n-1}\otimes \bigwedge^1(I) \\ & \simeq & R\otimes I \\ & \simeq & I \end{matrix}}$ Lastly, let’s consider one special case of the above theory that will be used in our application next time. If ${P}$ is a rank one projective ${R}$-module, then ${P\simeq I}$. It is well known in a Dedekind domain that ${I}$ is generated by at most ${2}$ elements. Thus either ${P}$ is generated by ${1}$ element, in which case it is free, or ${P}$ is generated by exactly ${2}$ elements. Thus an invertible module (locally free of rank ${1}$) over a Dedekind domain is not free if and only if it is generated by ${2}$ elements. This has a rather bizarre but “intuitively obvious” consequence for elliptic curves. ### Author: hilbertthm90 I am a mathematics graduate student fascinated in how all my interests fit together. ### 7 thoughts on “Projective Modules over Dedekind Domains” 1. What’s the bizarre but “intuitively obvious” consequence for elliptic curves? 2. Ah. This is the next post. 3. I don’t understand a step in your proof of the structure theorem. It doesn’t seem to be true in general that a rank $1$ module is necessarily projective, since e.g. it need not be torsion-free. So how do you know that $P/Q$ is torsion-free? 4. Ah yes. Good catch. We definitely can’t just pick some arbitrary $0\to Q\to P$, but we are allowed to pick it however we want. I think I was following J. P. May’s notes on this and he just says choose $n-1$ elements of $P$ that span an $(n-1)$-dimensional subspace of $P\otimes Frac(R)$. Again, that doesn’t seem good enough because $0 \to \mathbb{Z}\to \mathbb{Z}\oplus \mathbb{Z}$ by $1 \mapsto (0,2)$ seems to satisfy that but still leaves torsion. I feel like I had something in mind when I wrote this, but I can’t remember now. 5. I’m not sure how to deal with this either. I posted a math.SE question.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 83, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9564161896705627, "perplexity": 88.31304930059817}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500822053.47/warc/CC-MAIN-20140820021342-00473-ip-10-180-136-8.ec2.internal.warc.gz"}
https://en.wikipedia.org/wiki/Quantization_(image_processing)	Quantization (image processing) Quantization, involved in image processing, is a lossy compression technique achieved by compressing a range of values to a single quantum value. When the number of discrete symbols in a given stream is reduced, the stream becomes more compressible. For example, reducing the number of colors required to represent a digital image makes it possible to reduce its file size. Specific applications include DCT data quantization in JPEG and DWT data quantization in JPEG 2000. Color quantization Main article: Color quantization Color quantization reduces the number of colors used in an image; this is important for displaying images on devices that support a limited number of colors and for efficiently compressing certain kinds of images. Most bitmap editors and many operating systems have built-in support for color quantization. Popular modern color quantization algorithms include the nearest color algorithm (for fixed palettes), the median cut algorithm, and an algorithm based on octrees. It is common to combine color quantization with dithering to create an impression of a larger number of colors and eliminate banding artifacts. Frequency quantization for image compression The human eye is fairly good at seeing small differences in brightness over a relatively large area, but not so good at distinguishing the exact strength of a high frequency (rapidly varying) brightness variation. This fact allows one to reduce the amount of information required by ignoring the high frequency components. This is done by simply dividing each component in the frequency domain by a constant for that component, and then rounding to the nearest integer. This is the main lossy operation in the whole process. As a result of this, it is typically the case that many of the higher frequency components are rounded to zero, and many of the rest become small positive or negative numbers. As human vision is also more sensitive to luminance than chrominance, further compression can be obtained by working in a non-RGB color space which separates the two (e.g., YCbCr), and quantizing the channels separately.[1] Quantization matrices A typical video codec works by breaking the picture into discrete blocks (8×8 pixels in the case of MPEG[1]). These blocks can then be subjected to discrete cosine transform (DCT) to calculate the frequency components, both horizontally and vertically.[1] The resulting block (the same size as the original block) is then pre-multiplied by the quantisation scale code and divided element-wise by the quantization matrix, and rounding each resultant element. The quantization matrix is designed to provide more resolution to more perceivable frequency components over less perceivable components (usually lower frequencies over high frequencies) in addition to transforming as many components to 0, which can be encoded with greatest efficiency. Many video encoders (such as DivX, Xvid, and 3ivx) and compression standards (such as MPEG-2 and H.264/AVC) allow custom matrices to be used. The extent of the reduction may be varied by changing the quantizer scale code, taking up much less bandwidth than a full quantizer matrix.[1] This is an example of DCT coefficient matrix: ${\displaystyle {\begin{bmatrix}-415&-33&-58&35&58&-51&-15&-12\\5&-34&49&18&27&1&-5&3\\-46&14&80&-35&-50&19&7&-18\\-53&21&34&-20&2&34&36&12\\9&-2&9&-5&-32&-15&45&37\\-8&15&-16&7&-8&11&4&7\\19&-28&-2&-26&-2&7&-44&-21\\18&25&-12&-44&35&48&-37&-3\end{bmatrix}}}$ A common quantization matrix is: ${\displaystyle {\begin{bmatrix}16&11&10&16&24&40&51&61\\12&12&14&19&26&58&60&55\\14&13&16&24&40&57&69&56\\14&17&22&29&51&87&80&62\\18&22&37&56&68&109&103&77\\24&35&55&64&81&104&113&92\\49&64&78&87&103&121&120&101\\72&92&95&98&112&100&103&99\end{bmatrix}}}$ Dividing the DCT coefficient matrix element-wise with this quantization matrix, and rounding to integers results in: ${\displaystyle {\begin{bmatrix}-26&-3&-6&2&2&-1&0&0\\0&-3&4&1&1&0&0&0\\-3&1&5&-1&-1&0&0&0\\-4&1&2&-1&0&0&0&0\\1&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0\end{bmatrix}}}$ For example, using −415 (the DC coefficient) and rounding to the nearest integer ${\displaystyle \mathrm {round} \left({\frac {-415}{16}}\right)=\mathrm {round} \left(-25.9375\right)=-26}$ Typically this process will result in matrices with values primarily in the upper left (low frequency) corner. By using a zig-zag ordering to group the non-zero entries and run length encoding, the quantized matrix can be much more efficiently stored than the non-quantized version.[1]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5434790253639221, "perplexity": 1026.1220725879257}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281332.92/warc/CC-MAIN-20170116095121-00098-ip-10-171-10-70.ec2.internal.warc.gz"}
http://mathhelpforum.com/differential-geometry/86631-compatible.html	# Math Help - compatible 1. ## compatible Call a metric $d$ compatible on $\mathbb{R}^{n}$ with the vector space structure if $d(x+z, y+z) = d(x,y)$ for all $x,y,z \in \mathbb{R}^{n}$ and $d (\lambda x, \lambda y) = \lambda d(x,y)$ for $\lambda \in [0, \infty)$. Prove that any such metric puts the same topology on $\mathbb{R}^{n}$ as the Euclidean metric. 2. So when metric satisfies the conditions we can define the norm the following way: $\\|x\\| = d(x, 0)$. Hence $\\|x-y\\| = d(x, y)$ Norms on finite dimensional vector space are equivalent. So the metric puts the same topology as euclidian metric (which is generated by euclidian norm). So the point is really to prove that all norms are equivalent (on finite dimensional space). To do that we can prove that every norm is equivalent to maximum norm defined: $\\|x\\|_1 = \max_{1 \leq i \leq n}\{x_i\}$. You can easily show that: $\\|x\\| \leq C \\|x\\|_1$ (for every x). Hence convergence in $\\| \cdot \\|_1$ implies convergence in $\\| \cdot \\|$. So let's assume $\\| \cdot \\|$ is not equivalent with $\\| \cdot \\|_1$. That means that for every natural number we can find $x_n$ such that: $n\\|x_n\\| < \\|x_n\\|_1$ Let's define the sequence: $y_n = \frac{x_n}{\\|x_n\\|_1}$. From the above inequality we see that $\\|y_n\\| \rightarrow 0$, What is more: $\\|y_n\\|_1 = 1$ hence the sequence lies on the unit sphere. In finite dimensional space unit sphere is compact. Hence $y_n$ has convergent subsequence $y_{k_n} \rightarrow y$. We can see that $y \neq 0$ because $\\|y\\|_1 = \lim \\|y_n\\|_1 = 1$. But convergence in $\\| \cdot \\|_1$ implies convergence in $\\| \cdot \\|$. Hence $y = 0$. It's a contradiction. Thus all norms in finite-dimensional space are equivalent.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 27, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9993082284927368, "perplexity": 142.67853010729092}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00062-ip-10-147-4-33.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/137072-calculus-hw-question-integration-stuff.html	# Thread: Calculus HW question on Integration and stuff 1. ## Calculus HW question on Integration and stuff 80. Let A be the region bounded by the lines y=0.5x and y=2-0.5x between 0 less than or equal to x less than or equal to 2. (0<= x <= 2) a. Set up, but do not evaluate, the definite integral that gives the volume of the solid formed by rotating region A around the x-axis b. Set up, but do not evaluate, the definite integral that gives the volume of the solid formed by rotating region A around the line y=4 c. Set up, but do not evaluate, the definite integral(s) that give(s) the volume of the solid formed by rotating region A around the y-axis. (hint: split it into two) d. Suppose region A is the base of a solid whose cross-sections perpendicular to the x axis are semi circles. Set up, but do not evaluate, the definite integral that gives the volume of this solid. I am clueless of what to do here. Please guide me through this Thanks. 2. Originally Posted by Jishent 80. Let A be the region bounded by the lines y=0.5x and y=2-0.5x between 0 less than or equal to x less than or equal to 2. (0<= x <= 2) a. Set up, but do not evaluate, the definite integral that gives the volume of the solid formed by rotating region A around the x-axis Draw a picture of the specified region. Does this question form part of your assessment for a final grade? CB Well...its kinda yes and no. Its a review for the AP Calculus exam coming up that our teacher gave us to do over our break. Its not graded though and we never went over integration yet...So i need alot of help. 4. Originally Posted by Jishent Well...its kinda yes and no. Its a review for the AP Calculus exam coming up that our teacher gave us to do over our break. Its not graded though and we never went over integration yet...So i need alot of help.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.867438554763794, "perplexity": 402.33326936187126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542938.92/warc/CC-MAIN-20161202170902-00323-ip-10-31-129-80.ec2.internal.warc.gz"}
https://jsxgraph.org/wiki/index.php?title=Howto_include_JSXGraph_into_web_pages&action=edit	# Howto include JSXGraph into web pages ## Including JSXGraph into HTML For including JSXGraph into HTML, two files are necessary: You can either download these two files and use the local copy or you can use the online version. For optimal page loading speed we recommend to include the content of jsxgraph.css into other stylesheet files of the web page. ### Usage of a local copy If you want to include a local copy of JSXGraph in your HTML file then you have to write the following lines into the document head: <head> <script type="text/javascript" src="jsxgraphcore.js"></script> ### Usage of the online copy If you want to include the online of JSXGraph in your HTML file then you have to write the following lines into the document head: <head> <script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script> You may also consider to load JSXGraph from a CDN (Content Delivery Network), see [1]. ### Include a drawing panel into the HTML The geometric construction which is displayed by JSXGraph resides in an HTML element. Usually, a div-element is taken. This division needs an ID. Using this ID, we declare this element to be a drawing panel of JSXGraph. The following code has to be placed into the body part of an HTML file: <div id="box" class="jxgbox" style="width:500px; height:500px;"></div> <script type="text/javascript"> var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-10, 10, 10, -10], axis:true}); </script> We can use as many different drawing panels as we like in one HTML file.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37388890981674194, "perplexity": 5518.503077282773}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256546.11/warc/CC-MAIN-20190521182616-20190521204616-00150.warc.gz"}
http://www.lofoya.com/Solved/1545/what-was-the-aggregate-of-marks-obtained-by-sajal-in-all-the-six	# Easy Tabular Data Solved QuestionData Interpretation Discussion Common Information The following table gives the percentage of marks obtained by seven students in six different subjects in an examination. The Numbers in the Brackets give the Maximum Marks in Each Subject. Table below can be scrolled horizontally Student Subject (Max. Marks) Maths (150) Chemistry (130) Physics (120) Geography (100) History (60) Computer Science (40) Ayush 90 50 90 60 70 80 Aman 100 80 80 40 80 70 Sajal 90 60 70 70 90 70 Rohit 80 65 80 80 60 60 Muskan 80 65 85 95 50 90 Tanvi 70 75 65 85 40 60 Tarun 65 35 50 77 80 80 Q. Common Information Question: 3/5 What was the aggregate of marks obtained by Sajal in all the six subjects? ✖ A. 409 ✖ B. 419 ✖ C. 429 ✔ D. 449 Solution: Option(D) is correct Table below can be scrolled horizontally Student Subject (Max. Marks) Math. (150) Chem. (130) Phy. (120) Geo. (100) Hist. (60) Comp. Sc. (40) Ayush 90 50 90 60 70 80 Aman 100 80 80 40 80 70 Sajal 90 60 70 70 90 70 Rohit 80 65 80 80 60 60 Muskan 80 65 85 95 50 90 Tanvi 70 75 65 85 40 60 Tarun 65 35 50 77 80 80 Aggregate marks obtained by Sajal in all the six subjects: $=\left[ \begin{array}{l l l l l l} (90\% \text{ of } 150)& +& (60\% \text{ of } 130)& + &(70\% \text{ of } 120) &+\\ (70\% \text{ of } 100)& +& (90\% \text{ of } 60) &+ &(70\% \text{ of } 40)& \end{array} \right]$ $= [ 135 + 78 + 84 + 70 + 54 + 28 ]$ $= \textbf{449}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.657672643661499, "perplexity": 9476.055232560739}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281332.92/warc/CC-MAIN-20170116095121-00479-ip-10-171-10-70.ec2.internal.warc.gz"}
http://sgovindarajan.wikidot.com/questions	The integral Evaluate the integral where $\Delta x$ is taken to be infinitesimal. (1) \begin{align} \int_{x}^{x+\Delta x} f(y) dy \end{align}	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000032186508179, "perplexity": 2264.322430168953}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805578.23/warc/CC-MAIN-20171119115102-20171119135102-00342.warc.gz"}
http://www.sfb45.de/publications-1/a-note-on-the-characteristic-p-nonabelian-hodge-theory-in-the-geometric-case	##### Personal tools You are here: Home A note on the characteristic $$p$$ nonabelian Hodge theory in the geometric case # A note on the characteristic $$p$$ nonabelian Hodge theory in the geometric case Mao Sheng, Xin He, Kang Zuo Number 9 Dr. Mao Sheng Kang Zuo Xin He 2012	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7881075143814087, "perplexity": 9436.725874103231}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999876.81/warc/CC-MAIN-20190625172832-20190625194832-00062.warc.gz"}
https://www.physicsforums.com/threads/system-of-4-equations.413397/	# System of 4 equations. 1. Jun 30, 2010 ### Markel Hello, I'm just wondering if there's a better way to solve systems such as these: variables are x,y,z,a and I need to solve for x, y, and z. y^2z^3 + a4x=0 2xyz^3 + a6y = 0 3xy^2z^2 + a12z = 0 2x^2 +3y^2 + 6z^2 -6 = 0 I'm aware of matrix methods to solve systems of linear equations. But for those you nead to have linear equations, correct? And here my variables are multiplied together and to higher powers. I was thinking of definine something like y^2z^3 = b or something and just calling those terms variables, and then creating the necessary new equations. But I don't know, that seems like a lot of work. Anyway, is there any other way to solve such systems other than back elimination of varibales and back substitution? because I have to do something like this on an exam and that method takes a lot of time, and I always make mistakes. what algorithm (if any) do you use to solve a simlar system?? 2. Jun 30, 2010 ### Staff: Mentor What do a4x, a6y, and a12z mean? 3. Jun 30, 2010 ### Markel sorry, that was kind of unclear. it should probably be written as: y^2z^3 + 4xa=0 2xyz^3 + 6ya = 0 3xy^2z^2 + 12za = 0 2x^2 +3y^2 + 6z^2 -6 = 0 I define a as just another variable. in the question I'm trying to do it's the lagrange multiplier but I don't know how to make a lamda, I'm trying to find the extrema, the last equation is the restriction. 4. Jun 30, 2010 ### Staff: Mentor Try solving for a ($\lambda$) in the first three equations, starting with the second and third. From the second equation, y(2xz3 + 6a) = 0 ==> y = 0 or a = -(1/3)xz3. Do a similar thing for the third equation and the first. The goal is to get a number of critical points that you can substitute into the objective function. 5. Jun 30, 2010 ### Staff: Mentor This might work if you had multiple equations with y^2z^3, but you don't, so this is not a good idea. BTW, this does not seem to be a precalc-level problem, so you should have posted it in the Calculus & Beyond section. 6. Jun 30, 2010 ### Markel Hmm, yeah ok. that seems like a good way. I did it and it gave me the same results a bit faster. The way I initally tried was just solving for lamda from Eqn. 1 and then plugging lamda into Eqns 2 and 3. I have a question though, you say it's 0 if y is 0 or if that expression is 0. Does that mean later we have to check if y=0 is part of some solution? 7. Jun 30, 2010 ### Markel actually, maybe I should just post my entire question, because all of it is a bit fuzzy for me. the question is find the max of {xy^2z^3 : 2x^2 +3Y^2 + 6z^3 = 6, x> or = 0, y > or = 0, z> or = o} So, basically I set up the equations above and muddled around with a lot of arithmatic mistakes and got this: y= +/- 2/sqrt(15) x= +/- sqrt(3)/sqrt(15) z= +/- 2sqrt(3)/sqrt(15) Then I said the max was when you have either a combination of the three coordinates where x and z are their positive options, or either both their negative options, and the minimum is when you have three coordinates where x and z do not have the same sign. does this seem somewhat correct? Last edited: Jun 30, 2010 8. Jun 30, 2010 ### Staff: Mentor Yes. Since you have conditions that x >= 0, y >= 0, and z >= 0, you can eliminate the three negative values above. As already noted, though, some of the variables can be zero. No, due to the non-negativity constraints. 9. Jun 30, 2010 ### Markel Oops, sorry. I'm kind of new to these forums... Anyway, Yeah, obviously no negative solutions. Sorry, that was just an oversight on my part. Also I only need the max, so there's no minimum solution needed either. But I'm still confused with the solution of the system of equations. I can factor out a z from equation 3, as you did the y from eqn 2, and then I get that z=0 along with y=0 are possible solutions. if I plug y=0 and x=0 into eqn 4, then I will get a different value for x. hmmm. Well I'm just not sure how to check these solutions. basically I'll get 4 different solution sets??, one for x,y,z >0 one for x,z>0, y=0 and one for x,y>0 z=0 and one for x>0, z,y=0 That's a lot of equations to solve.... 10. Jun 30, 2010 ### Markel oh, btw, thanks for helping me out. I appreciate it. I know my questions are kind of dumb but I really want to understand this problem. 11. Jun 30, 2010 ### Staff: Mentor If I have arrived at something like this: x = 0 or y = 7 AND y = 0 or z = 3 I have four things to check: x = 0 AND y = 0, x = 0 AND z = 3, y = 7 AND y = 0 (can't happen), y = 7 and z = 3. If you add another pair of values, this doubles the number of things you need to check to 8. Each time you have to pick one from the first group, one from the second group, AND one from the third group. I haven't worked this problem, so I'm speaking as generally as I can from that perspective. 12. Jun 30, 2010 ### Markel Ok, I think I understand in general. It seems just like logic. But I'm not sure how to apply this to the problem. when faced with this: From the second equation, y(2xz3 + 6a) = 0 ==> y = 0 or a = -(1/3)xz3. I first assumed the second case, and did the same for a similar situation with z. This led me to the solution set: y= 2/sqrt(15) x= sqrt(3)/sqrt(15) z= 2sqrt(3)/sqrt(15) now for instance, if I choose that actually it's y=0 and a=/= 0 then I substitute y = 0 into the system of equations and get this 0 + a2x = 0 0 + 0 = 0 0 + a12z = 0 2x^2 +6z^2 - 6 = 0 which gives me the new solution set: x = 6sqrt(1/13) y=0 z=sqrt(1/13) So now you're saying I need to consider y= 2/sqrt(15) or y=0 AND x= sqrt(3)/sqrt(15) Or x = 6sqrt(1/13) AND z= 2sqrt(3)/sqrt(15) or z=sqrt(1/13) now I have to do the same for z=0 and I'll get an alternate solution set... and so I'll have x1 or x2 or x3 AND y1 or y2 or y3 And z1 or z2 or z3 This seems like a huge amount of work... just to solve an system. Now I have to test every possible permutation in the constraint equation to see if it's allowed/ a maximum?? the thing is, that when I did it my way the first time. I just solved for lamda from eqn 1 and substituted back into the other two equations and rearanged, I never had to consider if y=0 and z=0. how could one method of solving give different results? 13. Jun 30, 2010 ### Staff: Mentor Yes, exactly like logic. Then it's possible you weren't getting all of the possible critical points. Since the goal is to get every one of these points and evaluate the objective function at each of them, if you're missing some, it's possible to overlook the true maximum point. From the 2nd equation I got y = 0 OR a = -(1/3)xz^3 From the 3rd equation I get z = 0 OR a = -(1/4)xy^2z There are four combinations of the pairs of equations above, and you need to investigate all four. As already stated, if you end up with another pair of equations, you'll need to look at 8 different combinations of three equations, with one from each pair. Similar Discussions: System of 4 equations.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7752318382263184, "perplexity": 704.7061747229646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822992.27/warc/CC-MAIN-20171018142658-20171018162658-00784.warc.gz"}
https://hal.inria.fr/hal-01185498	# Block-sequential update schedules and Boolean automata circuits Abstract : Our work is set in the framework of complex dynamical systems and, more precisely, that of Boolean automata networks modeling regulation networks. We study how the choice of an update schedule impacts on the dynamics of such a network. To do this, we explain how studying the dynamics of any network updated with an arbitrary block-sequential update schedule can be reduced to the study of the dynamics of a different network updated in parallel. We give special attention to networks whose underlying structure is a circuit, that is, Boolean automata circuits. These particular and simple networks are known to serve as the "engines'' of the dynamics of arbitrary regulation networks containing them as sub-networks in that they are responsible for their variety of dynamical behaviours. We give both the number of attractors of period $p$, $\forall p\in \mathbb{N}$ and the total number of attractors in the dynamics of Boolean automata circuits updated with any block-sequential update schedule. We also detail the variety of dynamical behaviours that such networks may exhibit according to the update schedule. Keywords : Document type : Conference papers Domain : Cited literature [12 references] https://hal.inria.fr/hal-01185498 Contributor : Coordination Episciences Iam <> Submitted on : Thursday, August 20, 2015 - 2:16:53 PM Last modification on : Friday, November 6, 2020 - 3:51:36 AM Long-term archiving on: : Wednesday, April 26, 2017 - 10:05:49 AM ### File dmAL0104.pdf Publisher files allowed on an open archive ### Identifiers • HAL Id : hal-01185498, version 1 ### Citation Eric Goles, Mathilde Noual. Block-sequential update schedules and Boolean automata circuits. Automata 2010 - 16th Intl. Workshop on CA and DCS, 2010, Nancy, France. pp.41-50. ⟨hal-01185498⟩ Record views	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.461275577545166, "perplexity": 3279.067032224091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487643354.47/warc/CC-MAIN-20210618230338-20210619020338-00175.warc.gz"}
https://www.zbmath.org/?q=ai%3Aeneeva.liana-m+cc%3A46	× # zbMATH — the first resource for mathematics On some cross-norms on tensor products of ordered Banach spaces. (Russian) Zbl 1051.46054 By using the property of tensor products that allows to consider vector spaces of bilinear mappings as vector spaces of linear mappings, the author establishes the isometry of the Banach spaces of operators $${\mathcal L}_{\ell,m}(E\overline{\otimes}_kF,G^)$$ and $${\mathcal L}_{\ell,m}(E,{\mathcal L}_{\ell,m}(G,G^))$$, from which the associativity of the tensor products $$(E\otimes_kF)\otimes_kG$$ and $$E\otimes_k(F\otimes_kG)$$ of ordered Banach spaces with a cross-norm $$k$$ follows. ##### MSC: 46M05 Tensor products in functional analysis 46B28 Spaces of operators; tensor products; approximation properties 46B40 Ordered normed spaces 47L05 Linear spaces of operators ##### Keywords: normed space; closed cone; cross-space Full Text:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8917478322982788, "perplexity": 1073.5698606667434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057861.0/warc/CC-MAIN-20210926114012-20210926144012-00169.warc.gz"}
https://mathematica.stackexchange.com/questions/69669/bug-in-plotting-function-using-findminimum	# Bug in plotting function using FindMinimum? Bug introduced in 10.0 and persisting through 11.0.1 or later While working on an answer to RegionPlot from NDSolve, I came across this strange behavior of RegionPlot and ParametricPlot involving a function that sometimes called FindMinimum. Below is a simplified version of the code, and in it the function lhmin always calls FindMinimum. I'm thinking it is probably a bug. However, I wonder if I'm breaking a rule somewhere, and something I'm doing is causing this apparent bug. The following is the complete code, run on a new kernel. I'm using V10.0.1 (on Mac OSX 10.9.5). ode3[y_?NumericQ, M_?NumericQ] := Block[{t}, First@NDSolve[{ Dt[lh[t], t] == -ls[t]/2 - (lh[t] - 1)^3/4, Dt[ls[t], t] == lh[t]/2 - ls[t]^3, lh[0] == y, ls[0] == M}, {lh, ls}, {t, 0, 40}]] lhmin[y0_?NumericQ, M0_?NumericQ] := With[{sol = ode3[y0, M0]}, With[{values = lh["ValuesOnGrid"] /. sol}, Print[{y0, M0}]; With[{minPos = First@Ordering[values, 1]}, First@FindMinimum[{lh[t] /. sol, {0 <= t <= 40}}, {t, (lh["Coordinates"] /. sol)[[1, minPos]]}] ]] ]; Note that lhmin prints its input before calling FindMinimum. You will note below that it does not produce a slew of output, because the whole thing pretty quickly comes to a halt because of an uncaught Throw. RegionPlot. In this plot, lhmin is used to define the region. There are messages about Break[] being abused and some delinquent function acting up and throwing things. RegionPlot[lhmin[y, M] > 0, {y, 0.1, 1.}, {M, 0, 10}] {0.10004741578947368, 0.0005268421052631579} (* output of Print ) {0.10000004736842105, 5.263157894736842^-7} {0.10000004736842105, 5.263157894736842^-7} Break::nofwd: No enclosing For, While, or Do found for Break[]. >> Break::nofwd: No enclosing For, While, or Do found for Break[]. >> Break::nofwd: No enclosing For, While, or Do found for Break[]. >> General::stop: Further output of Break::nofwd will be suppressed during this calculation. >> FindMinimum::eit: The algorithm does not converge to the tolerance of 4.806217383937354^-6 in 500 iterations. The best estimated solution, with feasibility residual, KKT residual, or complementary residual of {0.0423358,2.5850510^-10,0.0211679}, is returned. >> Throw::nocatch: Uncaught Throw[{{8.34096},{0.0635038,{0.0423358,2.5850510^-10,0.0211679}},500,NOTCONVERGED},FindMinimumInteriorPoint] returned to top level. >> Throw::nocatch: Uncaught Throw[Null,FindMinimumInteriorPoint] returned to top level. >> (* Hold[Throw[{{8.34096}, {0.0635038, {0.0423358, 2.5850510^-10, 0.0211679}}, 500, "NOTCONVERGED"}, FindMinimumInteriorPoint], Throw[Null, FindMinimumInteriorPoint]] ) However, note that evaluating the function lhmin on the point indicated works fine and without generating messages. lhmin @@ {0.10000004736842105, 5.263157896957288^-7} {0.1,5.2631610^-7} (* output of Print ) ( 0.0913811 ) ParametricPlot. I used lhmin in the RegionFunction to ParametricPlot, and it generates the same messages as above except no FindMinimum::eit, perhaps because FindMinimum did not have a convergence problem on the particular input {0.1, 0.}. The output is different, but that's probably not significant, since it's a different function. ParametricPlot[{y, M}, {y, 0.1, 1.}, {M, 0, 10}, RegionFunction -> (lhmin[#1, #2] > 0 &)] {0.1, 0.} ( output of Print ) Break::nofwd: No enclosing For, While, or Do found for Break[]. >> ... Throw::nocatch: Uncaught Throw[{{8.34095},{0.0635036,{0.0423357,3.0559310^-10,0.0211679}},500,NOTCONVERGED},FindMinimumInteriorPoint] returned to top level. >> Throw::nocatch: Uncaught Throw[Null,FindMinimumInteriorPoint] returned to top level. >> Hold[Break[], Break[], <<7499>>, Throw[Null, FindMinimumInteriorPoint]] Again evaluating the function lhmin on the point indicated works fine and without generating messages. lhmin @@ {0.1, 0.} {0.1,0.} (* 0.0913811 *) Summary. On the one hand lhmin and FindMinimum work without a problem when called by themselves. On the other hand, when lhmin is called from within RegionPlot or ParametricPlot, FindMinimum seems to generate fatal errors (on the same input values) that kill the program. Is this a bug, or am I doing something wrong? Confirmed by WRI. • When I used NDSolve on the question you cited in your first line, I too encountered a problem with RegionPlot, although I am uncertain whether it was the same problem. For this reason, I also used ContourPlot. In any case, the problem went away, when I used ParameterNDSolve. – bbgodfrey Dec 25 '14 at 21:23 • No (obvious) problem on version 9.0.1, with no messages produced after about 10 minutes of run-time. So, I think it looks like a possible bug in version 10. I don't have that installed on this computer, I'm not feeling patient enough to let version 9 run to completion, and also not much in the mood for troubleshooting, so this is of course not conclusive, but clearly we should not be seeing FindMinimum's throw come back to the top level. I'd report it, if I were you. – Oleksandr R. Dec 25 '14 at 23:10 • This is most certainly a bug. I can only emphasize what Olek mentioned at the end: A Throw inside a built-in function should never reach the user. This would be very bad style. Btw, I get the same output as you did on Linux 64 with Mathematica 10.0.2. – halirutan Dec 25 '14 at 23:20 • As suggested in my previous comment, I had hoped that using ParametricNDSolve with RegionPlot might provide better results. It did not, instead producing much the same errors described above. – bbgodfrey Dec 26 '14 at 0:39 • @OleksandrR. Sorry about that - my original lhmin only rarely called FindMinimum. I didn't think about it actually working and running for a good long time. As far as I can tell, on V10, it fails in the first few calls. Thanks for checking V9. P.S. I have reported it and will update when I hear back. – Michael E2 Dec 26 '14 at 1:06 RegionPlot[lhmin[y, M] > 0, {y, 0.1, 1.}, {M, 0, 10}, "NumericalFunction" -> False]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.339621901512146, "perplexity": 4298.227300352539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987779528.82/warc/CC-MAIN-20191021143945-20191021171445-00524.warc.gz"}
https://www.physicsforums.com/threads/particle-motion-diff-eq.88057/	# Particle motion diff eq 1. Sep 8, 2005 ### infraray I'm given F=kvx. I need to find x(t), k is a positive constant, and the particle passes thru the origin with speed Vo at time t=0. I start by rewriting the formula as such: dv/dt=kdx/dtx I am confused now though because I now have dv,dt, and dx. I assume I need to get everything in terms of dx and dt. Can I use seperation of variables or do I need another technique? 2. Sep 8, 2005 ### quasar987 Is v the speed? If so, you got F=kvx, which can be rewriten as $$F = k\frac{dx}{dt}x$$ and F = ma, which can be rewritten as $$F = m\frac{d^2x}{dt^2}$$ Combining the two leads to $$k\frac{dx}{dt}x = m\frac{d^2x}{dt^2}$$ 3. Sep 8, 2005 ### amcavoy Now is this where you have trouble? $kx=mx^{2}$ has solutions x=0 and x=k/m. What does this tell you about the differential equation? Last edited: Sep 8, 2005 4. Sep 8, 2005 ### infraray Ok, after some tinkering I was able to get: $$k\frac{dx}{dt}x = m\frac{d^2x}{dt^2}$$ Since it doesn't appear to be able to be put into a 1st order equation I assume I am out of luck with seperation, or am I? Sorry, but I'm not sure what x=0, x=k/m tells me about the equation. Are they linear dependent? The lighter the object the further it travels? It's been over 2 years since diff eq and my head is a mess right now. I feel helpless. My teacher keeps saying this is easy, but when you've been away from it for a while, it is very hard. It's not like riding a bike that's for sure. 5. Sep 9, 2005 ### HallsofIvy Staff Emeritus Try using the fact (chain rule) that $$\frac{dv}{dt}= \frac{dv}{dx}\frac{dx}{dt}= v\frac{dv}{dx}$$ to eliminate t from the equation. $$m\frac{dv}{dt}= mv\frac{dv}{dx}= F= kxv$$ Similar Discussions: Particle motion diff eq	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8944475650787354, "perplexity": 1527.2972513483496}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189667.42/warc/CC-MAIN-20170322212949-00070-ip-10-233-31-227.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/66642/a-finite-sum-of-prime-reciprocals	# A finite sum of prime reciprocals How can you prove that $\sum\limits_k \frac1{p_k}$, where $p_k$ is the $k$-th prime, does not result in an integer? - I am assuming that the question means finite sums. (For any desired $s \in \mathbb R_{> 0}$, there exist infinite subsequences of the primes such that the corresponding series sums to $s$.) Assume that for some primes $p_1, p_2, \ldots, p_n$, the quantity $$s = \frac{1}{p_1} + \frac{1}{p_2} + \cdots+ \frac{1}{p_n}$$ is an integer. Multiplying by $Q = p_2 p_3 \cdots p_n$ and rearranging, we note that $$\frac{Q}{p_1} = sQ - \frac{Q}{p_2} - \frac{Q}{p_3} - \cdots - \frac{Q}{p_n}.$$ Each term on the right hand side is an integer (justify this!), and so the right (and hence the left) hand side itself is an integer. That is, $p_1$ divides $Q = p_2 p_3 \cdots p_n$. Do you see how this is a contradiction? Now, by a simple modification, one can show that (Exercise!) the denominator of the sum is exactly $$p_1 p_2 \cdots p_n .$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9977178573608398, "perplexity": 149.34807267724742}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860127870.1/warc/CC-MAIN-20160428161527-00168-ip-10-239-7-51.ec2.internal.warc.gz"}
http://blog.shriphani.com/tags/robust-pcp.html	## Robust Principal Component Pursuit - Background Matrix Recovery I recently spent some time working on a simple linear algebra problem - decompose a matrix $M$ into a low-rank component $L$ and a sparse component $S$. The algorithm I used was very trivial to implement (and parallelize using map-reduce). In this post, I will implement this very simple algorithm, explain the objective function and demonstrate its (amazing) effectiveness on a surveillance-camera dataset. Fortior Per Mentem (c) Shriphani Palakodety 2013-2018	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.88311767578125, "perplexity": 1453.2083374380516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267861456.51/warc/CC-MAIN-20180618222556-20180619002556-00481.warc.gz"}
https://www.physicsforums.com/threads/kinematics-2d-physics-question-help.355517/	# Kinematics 2d physics question help 1. Nov 16, 2009 ### yoyophysics1 1. The problem statement, all variables and given/known data An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is travelling horizontally at 100 m/s at a height of 50 m above the ground. What horizontal distance does the package travel before striking the ground? what is the veloicty of the package before it hits the ground? 2. Relevant equations X=Vox(t) Y=Yo+Voy(t)+1/2G(t)^2 3. The attempt at a solution I found the x and y components but could not find time and further on. Any help is appreciated. 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 2. Nov 16, 2009 ### srmeier when the package initial leaves the plane, what is it's y-component of velocity? Also, as the package travels towards the ground, does the x-component vary at all? (side note: I am assume we are ignoring air resistance?) 3. Nov 16, 2009 ### yoyophysics1 for the y component i got 44.8 and x component i got 89.4. I dont quite understand what you mean when you ask if the x component varies. and yes, ignore air resistance. I am in my first year of physics so Im sure the problems cant be too complex for you guys. 4. Nov 16, 2009 ### ideasrule How did you get those values? Are you sure the y component is 44.8 when the package leaves the plane? Asking why the x component varies is the same as asking whether the package's horizontal speed changes. Does it? 5. Nov 17, 2009 ### yoyophysics1 For the x component I used the equation: Vox=VoCOS(theta) Um I would guess that the horizontal speed doesn't change because velocity is constant in the x direction? sorry Im a complete newbie to physics and Im trying to study for a test that I am not completely ready for at the moment 6. Nov 17, 2009 ### ideasrule How did you get V0 or theta? The package's horizontal speed is 100 m/s when it was dropped from the plane, so it follows that it must be 100 m/s throughout the package's flight. 7. Nov 17, 2009 ### yoyophysics1 No, I dont know what you mean by the intial velocity vector. Ive never heard of it before :/. I think the package is travelling faster in the x direction because wouldnt it have an initial velocity of 100 m/s? 8. Nov 17, 2009 ### yoyophysics1 I got theta by using tan^-1(50/100) did i at least do that right? 9. Nov 17, 2009 ### srmeier theta is in radians (or degrees), 50[m]/100[m/s] give you units of seconds. Last edited: Nov 17, 2009 10. Nov 17, 2009 ### yoyophysics1 Oh I see. So I guess my question is how do I find the x and y components correctly because I obviously did them wrong the first time. When I find the x and y components then I can find theta using inverse tan, correct? 11. Nov 17, 2009 ### srmeier I am going to state some of what is known, think about these quantities/ideas. 1) the x-component is constant because there isn't an acceleration in the x-direction. 2) the initial y-component is zero because that is how the problem is defined. 3) the package accelerates in the y-direction, this is due to gravity. How can we use some of this? (trigonometry isn't apart of this problem) 12. Nov 17, 2009 ### yoyophysics1 Oh, I finally got it! those last three ideas really helped. i didn't realize that the initial y-component was supposed to be zero. Thanks a lot srmeier! 13. Nov 17, 2009 ### srmeier My pleasure, I must sleep now ^^ as you continue your journey remember these things (and think about why I would tell you them): 1) the time in which it takes the object to travel form 50m to 0m in the y-direction is equal to the time in which the object travels horizontally in the x-direction. 2) to solve a quadratic equation google: the quadratic formula. (because the initial y-velocity is zero you don't need this formula but it may come up on your test) 3) to find a resultant vector given its components use the Pythagorean theorem. If these hints confuse you at first that is ok. Take things one step at a time. Last edited: Nov 17, 2009	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9259552359580994, "perplexity": 1076.2092888467866}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647777.59/warc/CC-MAIN-20180322053608-20180322073608-00623.warc.gz"}
https://puzzling.stackexchange.com/questions/43504/what-is-a-cuddly-word	# What is a Cuddly Word™? This is in the spirit of the What is a Word/Phrase™ series started by JLee, etc. You know the drill by now. If a word conforms to a special rule, I call it a Cuddly Word™. Use the following examples to find the rule. The alphabetical ordering of the Cuddly Words™ is not relevant. And, if you want to analyze, here is a CSV version: Cuddly Words™,Non-Cuddly Words™ AMBLE,STROLL ANNA,JANE APPLE,ORANGE BUNT,WHACK EAST,WEST EGO,PSYCHE IDO,ESPERANTO LASSI,DOOGH REGAN,GONERIL RIM,BRINK RUES,REGRETS STAT,IMMEDIATELY TAGINES,NAVARINS TAXI,HANSOM • Is DOOGH supposed to be DOUGH? – Beastly Gerbil Sep 30 '16 at 17:36 • You can use Microsoft Excel to create the table. Just follow the guidelines of previous puzzles for formatting. You can also edit a previous puzzles, copy everything, and then edit what you need to. That's how I got the CSV working. – greenturtle3141 Sep 30 '16 at 18:38 • @BeastlyGerbil It's similar to a lassi. – Ian MacDonald Sep 30 '16 at 18:47 I think a Cuddly Word™ is one for which you can add exactly one letter at the start and one at the end, and still get a word. Admittedly in some cases an obscure one. Perhaps more specifically you can add the same letter at the start and the end. [Edit by Paolo: So a Cuddly Word™ is one you can "hug" with the "arms" of the hug each being the same letter.] So: rAMBLEr pANNAn -- in comments Will suggests sANNAs or maybe nANNAn and Sconibulus suggests tANNAt; I guess Will's first answer is the intended one as his second one is slang and Sconibulus's looks like a proper noun, but all three are pretty credible. dAPPLEd uBUNTu (does this count? has it been sufficiently naturalized into the language?) yEASTy bEGOb wIDOw cLASSIc oREGANo pRIMp tRUESt eSTATe sTAGINESs aTAXIa All the words for which I have good examples fit the more specific pattern. All the options for ANNA are kinda obscure. I have checked only the first few of the stated Non-Cuddly Words and they don't fit even the broader one. I bet the more specific pattern is the one intended. • Oregano for Regan? – Sconibulus Sep 30 '16 at 22:01 • yeah, I was editing that (and other comments) in while you were making the comment :-). – Gareth McCaughan Sep 30 '16 at 22:03 • (and feeling very stupid for not having seen it immediately) – Gareth McCaughan Sep 30 '16 at 22:03 • ANNA possibly – Will Sep 30 '16 at 22:04 • Is it really necessary to figure out each word? Isn't the goal of the puzzle to just find the rule? – greenturtle3141 Oct 1 '16 at 17:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32594048976898193, "perplexity": 2021.255229742854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987834649.58/warc/CC-MAIN-20191023150047-20191023173547-00391.warc.gz"}
https://kb.osu.edu/dspace/handle/1811/20338	# FOURIER TRANSFORM MICROWAVE SPECTROSCOPIC AND AB INITIO STUDIES OF THE $Kr-CH_{4}$ AND $Ar-CH_{4}$ VAN DER WAALS COMPLEXES Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/20338 Files Size Format View 2002-FA-10.jpg 222.4Kb JPEG image Title: FOURIER TRANSFORM MICROWAVE SPECTROSCOPIC AND AB INITIO STUDIES OF THE $Kr-CH_{4}$ AND $Ar-CH_{4}$ VAN DER WAALS COMPLEXES Creators: Liu, Yaqian; Jäger, Wolfgang Issue Date: 2002 Publisher: Ohio State University Abstract: Rotational spectra of various isotopomers of the $Kr-CH_{4}$ van der Waals complex were recorded using a pulsed molecular beam Fourier transform microwave spectrometer. Transitions corresponding to two excited internal rotor states, namely the $j=1, K=0$ and $j=2, K=1$ states, were measured and assigned, in addition to the previously reported ground state $transitions.^{a}$ The $j=1, K=0$ state was found to be Coriolis perturbed by a nearby $j=1, K=1$ state. The spectra of the isotopomers containing $^{83}Kr$ showed nuclear quadrupole hyperfine structure. Rotational, centrifugal distortion, and quadrupole coupling constants were detemined and were used to obtain structural parameters. Ab initio potential energy surfaces of $Kr-CH_{4}$ and $Ar-CH_{4}$ were constructed at the CCSD(T) level of theory with the aug-cc-pVTZ basis set supplemented with bond functions. The dipole moments of the two complexes were also computed at various configurations. The obtained results from the ab initio calculations were compared with those from the experiment. Description: $^{a}$ Y. Liu and W. J\""{a}ger, 55th International Symposium on Molecular Spectroscopy, paper RE05 (2000). Author Institution: Department of Chemistry, University of Alberta URI: http://hdl.handle.net/1811/20338 Other Identifiers: 2002-FA-10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8801413178443909, "perplexity": 2418.310148180286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375091751.85/warc/CC-MAIN-20150627031811-00019-ip-10-179-60-89.ec2.internal.warc.gz"}
http://mathhelpforum.com/algebra/183184-ratio.html	# Thread: Ratio 1. ## Ratio Ratio of two sums of money is 4:3 if larger sum of money is increased by $40, the ratio becomes 2:1. What are sums of money ? How to solve this ? Solution (4/7)x+(3/7)y=4:3 cant understand it.... 2. ## Re: Ratio Originally Posted by haftakhan Ratio of two sums of money is 4:3 if larger sum of money is increased by$40, the ratio becomes 2:1. What are sums of money ? How to solve this ? Solution (4/7)x+(3/7)y=4:3 cant understand it.... Dear haftakhan, Let x and y be the sums of money. Take x as the larger sum. $\frac{x}{y}=\frac{4}{3}$ If larger sum of money is increased by $40, the ratio becomes 2:1. Therefore, $\frac{x+40}{y}=2$ Solve these two equations and find x and y. 3. ## Re: Ratio solving this i get x=160 and y=120 is it correct ? 4. ## Re: Ratio Originally Posted by haftakhan solving this i get x=160 and y=120 is it correct ? No. It is incorrect. 5. ## Re: Ratio $\frac{160}{120}= \frac{40(4)}{40(3)}= \frac{4}{3}$ so those are in ratio 4:3. But adding$40 to $160 give$200. $\frac{200}{12}= \frac{40(5)}{40(3)}= \frac{5}{3}$, or 5:3, not 2:1. 6. ## Re: Ratio it may be easier to solve the two equations writing them like this: 3x = 4y x+40 = 2y one way of doing this, is to write (from the 2nd equation): x = 2y - 40. now use this in the first equation. 7. ## Re: Ratio i was about to post the correct answer but the light went off. x=80 and y=60 8. ## Re: Ratio Originally Posted by haftakhan i was about to post the correct answer but the light went off. x=80 and y=60 Post #5 shows you how to check this answer for yourself. 9. ## Re: Ratio problem ratio of two sums = 4 : 3 = $\frac{4}{3} = \frac{4x}{3x}$ ........... (1) When $40 is increased to the larger sum, the ratio is = $\frac{4x+40}{3x} = \frac{2}{1}$.........(given) $\therefore 1\times (4x+40) = 2\times{3x}$ = $4x + 40 = 6x$ = $40 = 6x-4x$ = $2x = 40$ = $\therefore x = 20$ By replacing the value of x in the first equation, we get$80 and $60. So the sum of$80 and $60 =$140. We had \$140. Answer. I think you have understood this. All the best	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8886935114860535, "perplexity": 4352.145993102902}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560282932.75/warc/CC-MAIN-20170116095122-00212-ip-10-171-10-70.ec2.internal.warc.gz"}
https://online.ucpress.edu/elementa/article/10/1/00092/115956/CH4-isotopic-signatures-of-emissions-from-oil-and	Methane (CH4) emissions to the atmosphere from the oil and gas sector in Romania remain highly uncertain despite their relevance for the European Union’s goals to reduce greenhouse gas emissions. Measurements of CH4 isotopic composition can be used for source attribution, which is important in top-down studies of emissions from extended areas. We performed isotope measurements of CH4 in atmospheric air samples collected from an aircraft (24 locations) and ground vehicles (83 locations), around oil and gas production sites in Romania, with focus on the Romanian Plain. Ethane to methane ratios were derived at 412 locations of the same fossil fuel activity clusters. The resulting isotopic signals (δ13C and δ2H in CH4) covered a wide range of values, indicating mainly thermogenic gas sources (associated with oil production) in the Romanian Plain, mostly in Prahova county (δ13C from –67.8 ± 1.2 to –22.4 ± 0.04 ‰ Vienna Pee Dee Belmnite; δ2H from –255 ± 12 to –138 ± 11 ‰ Vienna Standard Mean Ocean Water) but also the presence of some natural gas reservoirs of microbial origin in Dolj, Ialomiţa, Prahova, and likely Teleorman counties. The classification based on ethane data was generally in agreement with the one based on CH4 isotopic composition and confirmed the interpretation of the gas origin. In several cases, CH4 enhancements sampled from the aircraft could directly be linked to the underlying production clusters using wind data. The combination of δ13C and δ2H signals in these samples confirms that the oil and gas production sector is the main source of CH4 emissions in the target areas. We found that average CH4 isotopic signatures in Romania are significantly lower than commonly used values for the global fossil fuel emissions. Our results emphasize the importance of regional variations in CH4 isotopes, with implications for global inversion modeling studies. Large reductions of greenhouse gas (GHG) emissions to the atmosphere are required to mitigate ongoing climate change. The irreversible impacts of a global warming of more than 1.5°C above preindustrial levels were highlighted in a special report from the Intergovernmental Panel on Climate Change (IPCC, 2018). Limiting this increase to 1.5°C with a reasonably high probability requires not only net-zero emissions of carbon dioxide (CO2) by 2055 but also a reduction of methane (CH4) and black carbon emissions by 35% or more by 2050, relative to 2010 (IPCC, 2018). The European Union (EU) recently incorporated a net-zero emission objective for all GHGs by 2050 (European Green Deal; European Commission, 2019). In 2018, reported GHG emissions by EU countries (including the United Kingdom) were more than 4 billion tons CO2 equivalent, with a contribution of 11% from CH4 (European Environment Agency, 2020). In 2019, the European Green Deal specially mentioned the necessity to “address the issue of energy-related methane emissions” (European Commission, 2019). Reported fugitive emissions from the extraction and handling of coal, oil, and natural gas were responsible for 12% of the EU’s total CH4 emissions in 2018 (Crippa et al., 2019). In the United States, fugitive CH4 from the natural gas supply chain was reported to be equivalent to total CO2 emissions generated by its combustion (Alvarez et al., 2018). This is due to the global warming potential of CH4 being 86 larger than the one of CO2 over a 20 years-time horizon, including carbon cycle feedbacks (IPCC, 2013). An increased focus on CH4 fugitive emissions is therefore particularly interesting for efficiently reducing GHG emissions. GHG emissions are reported for each country using bottom-up approach (data-driven inventories), but top-down studies (atmospheric measurements and modeling) help verifying these estimates (Saunois et al., 2020). Romania is the fourth and third largest producer of crude oil and natural gas in the EU (including the United Kingdom), respectively (British Petroleum, 2020). It is especially relevant to investigate the CH4 emissions in Romania as this region is not as well covered by atmospheric measurements than Western Europe (Integrated Carbon Observation System Research Infrastructure, 2019). The ROmanian Methane Emissions from Oil & gas (ROMEO) project (Röckmann, 2020) aims to provide experimental quantification of methane emissions from oil and gas extraction activities. In this framework, the present work reports methane isotopic data of atmospheric air samples collected mainly in the Romanian Plain, a major oil–gas production region in Romania. As described in more detail below, the measurements of CH4 isotopic composition (stable C and H isotope ratios) are widely used to characterize the sources of methane in atmospheric air samples (Levin et al., 1993; Tarasova et al., 2006; Röckmann et al., 2016; Townsend-Small et al., 2016; Zazzeri et al., 2016; Hoheisel et al., 2019; Lu et al., 2021), following genetic (thermogenic vs. microbial) CH4 isotopic categorization (Schoell, 1980; Milkov and Etiope, 2018). The ethane (C2H6) to methane (C2:C1) ratio is also frequently used in atmospheric studies (Lopez et al., 2017; Mielke-Maday et al., 2019; Maazallahi et al., 2020) as an additional proxy of the gas origin, since thermogenic and microbial gas have different molecular compositions: Ethane (as well as higher hydrocarbons) is abundant in thermogenic reservoirs, with or without oil, and is practically absent in microbial gas. We note, however, that also high maturity thermogenic gas can be “dry,” ethane-free (Schoell, 1983; Milkov and Etiope, 2018), and this may confuse the genetic attribution of the gas based only on the lack of ethane. The CH4 isotopic characterization can be used as tracer for the different sources in atmospheric transport models and inversions at different scales (Bousquet et al., 2006; Monteil et al., 2011; Houweling et al., 2017; Bergamaschi et al., 2018; Fujita et al., 2020) and therefore help improving the methane budget. More measurements of CH4 source isotopic composition reduce the uncertainties in the signatures assigned to the different sources and to the resulting emission estimates. The present study combined CH4 isotopic and C2:C1 measurements in atmospheric air samples collected from aircraft and ground vehicles in different areas in Romania. From these measurements, we first determine the isotopic signature of CH4 emissions from oil and gas production in Romania. Then, we investigate whether we can attribute CH4 enhancements from aircraft measurements to the oil and gas extraction activities. Finally, we aim at providing further insight into formation processes of the fossil fuel reservoirs exploited in the Romanian Plain, based on both our results and previous literature. ### 2.1. Sampling procedure The samples were taken during measurement surveys from an aircraft and from vehicles on the ground. The locations of all CH4 enhancements that were characterized regarding isotopic compositions and/or C2:C1 ratio are presented in Figure 1 and summarized in Table 1. An enhancement describes a noticeable (usually from 100 ppb) increase in χ(CH4) observed on a mobile analyzer. The target areas include important oil and gas basins and production sites in Romania. Figure 1. Target region and sampling locations during the ROmanian Methane Emissions from Oil & Gas campaign. (a) Overview of target regions where aerial raster flights were performed: P = Prahova, I = Ialomita, Te = Teleorman, O = Olt, D = Dolj, Tr = Transylvania, and M = Moldavia. The reservoir locations were provided by the National Agency for Mineral Resources (Georgescu, 2019). (b) Zoom on region P and its division in 9 clusters: P1 (with subcluster P1.1), P2, P3, P4, P5, P6, P7, P8, and P9. Blue squares: Locations of isotopically characterized χ(CH4) anomalies from aircraft (U: unknown source). Green circles: Locations of isotopically characterized χ(CH4) anomalies from ground vehicles. Red circles: Location of ground-based C2:C1 measurements. Yellow triangles: Previously sampled gas seeps and mud volcanoes (Baciu et al., 2018). © EuroGeographics for the administrative boundaries, OpenStreetMap contributors for the map image. DOI: https://doi.org/10.1525/elementa.2021.000092.f1 Figure 1. Target region and sampling locations during the ROmanian Methane Emissions from Oil & Gas campaign. (a) Overview of target regions where aerial raster flights were performed: P = Prahova, I = Ialomita, Te = Teleorman, O = Olt, D = Dolj, Tr = Transylvania, and M = Moldavia. The reservoir locations were provided by the National Agency for Mineral Resources (Georgescu, 2019). (b) Zoom on region P and its division in 9 clusters: P1 (with subcluster P1.1), P2, P3, P4, P5, P6, P7, P8, and P9. Blue squares: Locations of isotopically characterized χ(CH4) anomalies from aircraft (U: unknown source). Green circles: Locations of isotopically characterized χ(CH4) anomalies from ground vehicles. Red circles: Location of ground-based C2:C1 measurements. Yellow triangles: Previously sampled gas seeps and mud volcanoes (Baciu et al., 2018). © EuroGeographics for the administrative boundaries, OpenStreetMap contributors for the map image. DOI: https://doi.org/10.1525/elementa.2021.000092.f1 Close modal Table 1. Overview and nomenclature of the target regions where methane isotopic signatures and C2:C1 ratios were determined and the number of source characterizations per region. DOI: https://doi.org/10.1525/elementa.2021.000092.t1 CH4 Isotopic SignaturesC2H6:CH4 Ratios Region NameRegion IDRaster FlightsGround SurveysGround Surveys Prahova P1 8 (4 + 4)a 14 81 P2 13 30 P3 P4 118 P5 29 P6 34 P7 28 P8 33 P9 15 Teleorman Te1 Te2 17 Ialomita 39 Dolj 11 Olt Transylvania Tr Moldavia Others Total 24 83 412 CH4 Isotopic SignaturesC2H6:CH4 Ratios Region NameRegion IDRaster FlightsGround SurveysGround Surveys Prahova P1 8 (4 + 4)a 14 81 P2 13 30 P3 P4 118 P5 29 P6 34 P7 28 P8 33 P9 15 Teleorman Te1 Te2 17 Ialomita 39 Dolj 11 Olt Transylvania Tr Moldavia Others Total 24 83 412 aFrom separate flights in the west and in the east (Figure 1). We performed in situ measurements from a BN2 aircraft from the National Institute of Aerospace Research “ELIE CARAFOLI” (INCAS). Air samples were collected during 10 research flights on 9 days between October 2 and 17, 2019, over 7 regions of interest. The target areas were covered following a raster pattern (ca. 5 km width between the different legs), orientated perpendicular to the wind direction, and flying generally upwind. An example raster flight path is shown in Figure S1 of the supplementary material. The raster was generally flown at an altitude between 100 and 200 m above ground to be able to detect CH4 enhancements from surface sources. We used a cavity ring-down spectroscopy (CRDS) analyzer onboard the aircraft (GasScouter G4302, Picarro, Santa Clara, CA, USA), to detect concentration elevations for determining when to collect samples. Unfortunately, due to an instrument malfunction, the ethane mode of the G4302 instrument was not operational during the campaign, therefore the instrument only measured CH4 mole fractions (χ(CH4)), at a measurement frequency of 1 and only operated at strongly reduced precision (instrument noise on the χ(CH4) reading was approximately 200 ppb). Therefore, the CRDS analyzer was not used for quantification (another instrument was dedicated), but only to identify zones of CH4 enhancements and sampling, which was still possible for significant enhancements, despite the reduced precision. The instrument drew air through a 1/4” o.d. Teflon line that was connected to an air inlet at the outside, on the top-left of the cockpit. A 10-m 1/2” o.d. Dekabon tube was mounted on the outflow of the G4302 analyzer as a buffer volume. At a flow rate of 2.2 L/min, this volume is flushed in 15 s, so after a signal was detected by the instrument, we had about 15 s to decide whether it was significant enough to take a sample. If so, we diverted the air in the buffer volume toward the sample receptacle (2 L Supel™-Inert Multi-Layer Foil sample bags, Sigma-Aldrich Co. LLC, Saint Louis, USA). In some cases, the raster pattern of the flights allowed us to cross a zone of enhanced χ(CH4) several times, and we collected several samples of the same suspected source. A total of 117 samples were taken from 31 CH4 enhancements. The average background χ(CH4) was 1975 ± 33 ppb, and CH4 mole fraction enhancements ranged from 30 to 300 ppb above background. We only retained the samples with more than 60 ppb CH4 above background and obtained CH4 isotopic signals for 24 source locations. Ground-based surveys were performed on 16 days between September 30 and October 19, 2019, targeted on 6 regions of interest in the Romanian Plain. The 3 ground teams that collected samples for this study traveled by car or truck, measuring CH4 mole fractions using mobile analyzers (Ultraportable Greenhouse Gas Analyzer, Los Gatos Research, San Jose, CA, USA; GasScouter G4302 and G2201-i isotopic analysers, Picarro, Santa Clara, CA, USA; LI-7810 Trace Gas Analyzer, LI-COR, Lincoln, USA; Dual Laser Trace Gas Monitor, Aerodyne Research Inc., Billerica, USA). Once a CH4 enhancement (ca. >200 ppb above background) was identified, the vehicle stopped and ambient air was collected in sample bags (2 L Supel™_¢-Inert Multi-Layer Foil, Sigma-Aldrich Co. LLC, St. Louis, MO, USA; 3 L FlexFoil PLUS, SKC Inc., Eighty Four, PA, USA). One to three samples were taken for each χ(CH4) anomaly, and 1 or 2 background samples were taken every survey day, in each region. A total of 161 samples were taken during ground surveys from 84 different sites. Measurements of ethane and methane were performed in two vehicles during ground surveys. The surveys were performed on 16 days from October 1 to 18, 2019. In 1 car, a second G4302 instrument sampled air through a 1/2” o.d. teflon tube from the roof top of a car and continuously measured CH4 and C2H6 at a frequency of about 1 Hz and a flow rate of 2.2 L/min. The noise was approximately 100 and 15 ppb around background level for CH4 and C2H6, respectively. The instrument was installed on the back seat of the vehicle, running either on an internal battery or an external battery supply. The instrument connected to a tablet via Wi-Fi, on which the measured mole fractions were displayed with a delay of 5 s. The second vehicle was equipped with a Dual Laser Trace Gas Monitor, based on a tunable infrared laser direct absorption spectroscopy using a combined quantum cascade laser and interband cascade laser (Aerodyne Research Inc., Billerica, MA, USA). Air was sampled through an RVS central inlet at the front of the trailer with a diameter of 60 mm at 3-m height, from which a 1/4” polyethylene tube goes to the instrument. CH4 and C2H6 were measured continuously at a frequency of 1 Hz, with a flow rate of 6 L/min and a precision of 2.4 and 0.1 ppb, respectively. Precision is here reported as 3 times the standard deviation of 6-min constant concentration reading. The instrument was installed in the trailer, which was facilitated with infrastructure for electricity, a battery pack to run the mobile laboratory for 24 h, a router, and an air inlet. While driving, the measurements were displayed on a laptop, connected via Wi-Fi to the instrument with a delay of 5 s. ### 2.2. Isotope measurements All samples were measured for χ(CH4), δ13C, and δ2H in CH4 at the Institute for Marine and Atmospheric Research Utrecht (IMAU) between October 8 and December 17, 2019. The analytical system is described in detail in Röckmann et al. (2016). The procedure is based on the extraction of CH4 from the other air components, followed by its conversion into CO2 or H2 before isotope measurement using isotopic ratio mass spectrometry (IRMS). Measurements of δ13C or δ2H were performed separately, using 10–60 mL of sample air, depending on the CH4 content. Each isotope measurement also returns a χ(CH4) value, because the signal intensity is proportional to the amount of extracted CH4. The system allows to process samples with χ(CH4) in the same order of magnitude as ambient air. Some higher concentration samples were diluted with pure N2 prior to measurement. Each sample was measured 2–4 times for both δ13C and δ2H, leading to an average uncertainty of 0.069 and 1.4 ‰, respectively, and of 5 ppb for χ(CH4). All reported isotopic values are relative to international reference materials: Vienna Pee Dee Belmnite (V-PDB) for δ13C and Vienna Standard Mean Ocean Water (V-SMOW) for δ2H. To do so, the sample measurements were alternated with a reference cylinder of ambient air, containing 1970.0 ppb CH4 with δ13C = –48.072 (±0.0261) ‰ V-PDB and δ2H = –88.311 (±0.3371) ‰ V-SMOW. The mole fractions were determined after measurements with a G2301 Gas Concentration Analyzer, Picarro, Santa Clara, CA, USA (precision at 5 min < 0.22 ppb). To calibrate the reference cylinder against the international scale for isotope ratios, it was measured repetitively (20 times) in the IMAU lab, against 2 other gases previously measured at the Max Planck Institute in Jena, Germany (Sperlich et al., 2016). The calibration of the reference gas was done in September 2019. ### 2.3. Data analysis #### 2.3.1. Calculation of isotopic source signatures The Keeling (1958) plot method was applied to the isotopic data of each sampled χ(CH4) anomaly. It is a mass balance approach used to derive the isotopic signature of an emission source, which is added to a stable background. This translates to the following expressions: $δm=cbg*(δbg−δS)(1/cm)+δS,$ 1 where c is the mole fraction and δ is the isotopic signature (δ13C or δ2H) of background (bg), source (S), or measured (m) CH4. Thus, the source isotopic signature (δS) is given by the y-intercept of the regression line, when plotting δm against 1/cm. A prerequisite for this approach is that the background mole fractions and the isotopic values of background and source are stable over the sampling time period of each peak. To account for potential changes in the background CH4 from 1 day and region to another, a sample of background air was taken for each measurement day and area. We assumed a stable background for each location, given that we used the background sampled on the same day and in the same region in each of the plots. In order to confirm that variations in the background do not cause significant biases, we also evaluated our results using the Miller–Tans method (Miller and Tans, 2003), which is suitable for calculating isotopic source signatures with a varying background, and found very similar source signatures. For all linear regressions, the orthogonal distance regression (Boggs and Rogers, 1990) fitting method was used. #### 2.3.2. Calculation of C2:C1 ratios CH4 and C2H6 data were extracted from the in situ measurements from two survey vehicles when we detected significant CH4 enhancements in the vicinity of oil and gas facility locations reported by the regional operator. For each of these locations, we determined C2:C1 ratios from the slope of the linear regression between χ(C2H6) and χ(CH4) measured values when a minimum excess threshold for CH4 of 100 ppb above background was exceeded. C2:C1 ratios smaller than 0.0004 were set to 0. #### 2.3.3. Definition and classification of CH4 sources Methane origin is generally biotic (Hunt, 1996; Clayton, 2005), including (1) thermal degradation of organic matter in sedimentary rocks (thermogenic gas), (2) metabolic reactions by certain microorganisms (microbial gas), and (3) biomass burning (pyrogenic gas). In some geological environments, methane can also be generated by chemical reactions in the absence of organic matter (abiotic gas; Etiope and Sherwood Lollar, 2013; Etiope, 2017). Microbial gas generated in sedimentary rocks in petroleum systems is fossil (radiocarbon-free), so as thermogenic gas, and can also be categorized as “geological methane.” Modern microbial gas is generated in surface ecosystems (wetlands, marshes, rice paddies, etc.) and by animal enteric fermentation; this category is mostly referred to as “biological methane” (Schoell, 1983). Microbial CH4 generation may follow 2 metabolic pathways, methyl-type fermentation (anaerobic enteric fermentation, and to a larger extent in continental deposits and freshwater) and CO2 reduction (preferred pathway in marine environments; Whiticar, 1999). Geological hydrocarbon gases can be “wet” or “dry,” indicating the presence or absence of C2+ alkanes (Etiope, 2017). Alkanes are generally present in thermogenic systems, with or without oil (liquid phase). Geological gas composition and CH4 isotope ratios are generally used to assess the origin of oil and gas associated methane. Milkov and Etiope (2018) compiled a global inventory of molecular and isotopic composition of natural gas from petroleum source rocks, reservoirs, and surface seeps and assessed the ranges of several variables corresponding to the various gas origins. Natural gas is generally composed of a majority of CH4 (>70%), with C2H6 (1%–10%), along with heavier hydrocarbons (until C5–C9) in smaller amounts and traces of inorganic gases (Hunt, 1996; Clayton, 2005; Etiope, 2017). The relative ratios of these compounds in the emitted gas provide information on its origin. The ratio of methane (C1) over ethane (C2) plus propane (C3) is referred as Bernard ratio or C1/(C2+C3) (Bernard et al., 1976). Although we did not measure C3, the C2:C1 ratios already provide constraints on the Bernard ratio values. In addition, our new measurements were supplemented by data provided by the local oil and gas operator or the published literature. The operator provided hydrocarbon measurements at 14 sites, and Bernard ratios from another 13 sites were obtained from Filipescu and Huma (1979). Only 5 locations from these data sets are within our target regions and are compared with our measurements using figures 7 and 8 in Milkov and Etiope (2018). The operator also provided a classification of the oil density for the reservoirs we visited during our study. It is important to consider that there are no published data on the CH4 isotopic composition of natural gas from oil and gas production in Romania; the only available isotopic data are from gas seeps in the Transylvanian (microbial gas) and Carpathian (thermogenic gas) basins, reported by Baciu et al. (2008), Etiope et al. (2009), Etiope et al. (2009a), and Baciu et al. (2018). We will compare our results also with these published signatures. In thermogenic deposits, an increase in δ13C and δ2H in CH4 is correlated with the maturity of the source rocks (degree of degradation of organic matter; Schoell, 1980). Regarding the hydrocarbon composition, C2+ content initially increases from low maturity (wet gas, associated with oil), evolving into a drier gas, with less or no C2+ hydrocarbons at high maturity. Microbially formed CH4 is also dry and contains little or no C2+ hydrocarbons, but is significantly more depleted in 13C, and generally occurs in shallower deposits (Rice and Claypool, 1981; Whiticar, 1999). While mixing of different gases can change the isotopic CH4 composition of the original end members, gas migration among reservoirs and to the surface, being substantially advective, does not modify the isotopic CH4 ratio. Migration can, however, modify the C1:C2+ ratio, through molecular fractionation (Etiope et al., 2009). This hypothesis will be discussed in relation with our results and interpretation. ### 3.1. Overview of results The isotopic source signatures at 83 locations related to oil and gas production are shown in Figure 2. One additional location was characterized: CH4 enhancements from cattle grazing in an open field. The isotopic signals related to fossil fuel operations range between –67.8 and –22.4 ‰ V-PDB for δ13C and from –259 to –138 ‰ V-SMOW for δ2H. The distinction between geological gas emissions and modern microbial sources is possible through the δ2H signatures: While δ13C values are similar for modern and fossil microbial gas, the δ2H values are generally lower for modern gas, which derives from fermentation pathway (Figure 2a). Although sampled at different locations (Figure 1), there is a good agreement between our results and the literature values from Baciu et al. (2018), who mainly sampled natural gas seeps in north Buzu, Vrancea, Gorj, and in Transylvania (δ13C from –67.4 to –29.0 ‰ V-PDB and δ2H from –228 to –145 ‰ V-SMOW; Figure 2a and b). Figure 2. Dual isotope plots of the isotopic source signatures and C2:C1 ratios. (a) Isotopic signatures from flight samples (squares, n = 24), including above Transylvania (yellow squares) and ground samples around oil (circles, n = 57) and gas (diamonds, n = 17)-related facilities. Additional samples were taken from gas leaks (red diamonds, n = 2) and ruminants (green triangle, n = 1). Values are compared with isotopic ranges from literature on Romanian geological sources (dotted black line; Baciu et al., 2018) and from natural gas formation pathways as in Milkov and Etiope (2018). MC = microbial CO2 reduction; MF = microbial fermentation; MS = secondary microbial; TH = thermogenic; AB = abiotic. The ambient value is an average from the flight samples with χ(CH4) < 2000 ppb (n = 10). (b) Same data, now overlain with reported source signature ranges from the literature (Sherwood et al., 2017). FF = fossil fuel; BB = biomass burning; WST = waste; AGR = agriculture. (c) C2:C1 ratios per type of source as classified by the operator (oil productions sites, n = 340; gas production sites, n = 62; other2 sites, n = 82), compared to typical ranges in CH4 from M = microbial, TD = thermogenic dry, and TW = thermogenic wet gas. DOI: https://doi.org/10.1525/elementa.2021.000092.f2 Figure 2. Dual isotope plots of the isotopic source signatures and C2:C1 ratios. (a) Isotopic signatures from flight samples (squares, n = 24), including above Transylvania (yellow squares) and ground samples around oil (circles, n = 57) and gas (diamonds, n = 17)-related facilities. Additional samples were taken from gas leaks (red diamonds, n = 2) and ruminants (green triangle, n = 1). Values are compared with isotopic ranges from literature on Romanian geological sources (dotted black line; Baciu et al., 2018) and from natural gas formation pathways as in Milkov and Etiope (2018). MC = microbial CO2 reduction; MF = microbial fermentation; MS = secondary microbial; TH = thermogenic; AB = abiotic. The ambient value is an average from the flight samples with χ(CH4) < 2000 ppb (n = 10). (b) Same data, now overlain with reported source signature ranges from the literature (Sherwood et al., 2017). FF = fossil fuel; BB = biomass burning; WST = waste; AGR = agriculture. (c) C2:C1 ratios per type of source as classified by the operator (oil productions sites, n = 340; gas production sites, n = 62; other2 sites, n = 82), compared to typical ranges in CH4 from M = microbial, TD = thermogenic dry, and TW = thermogenic wet gas. DOI: https://doi.org/10.1525/elementa.2021.000092.f2 Close modal C2:C1 ratios were obtained at 412 facilities, including 340 oil and 62 gas production facilities. Results for all sites are presented in Figures 2c and S2. Commonly used natural gas classification distinguishes between wet gas (C2:C1 > 0.1), thermogenic dry gas (C2:C1 < 0.1), and microbial dry gas (C2:C1 < 0.001; Clayton, 2005; Etiope, 2017). All C2:C1 ratios ranged from 0 to 0.91, therefore representing different types of natural gas, without a clear distinction between oil and gas production sites. In Figure 3, we classified the ground surface δ13C isotopic signals depending on the exploitation of oil or gas, as reported by the operator for each site. We compare them with signatures observed from leaks in the natural gas distribution network and ruminants that we also sampled during our campaign. The δ13C of the natural gas from the network falls in the range of most sampled gas extraction facilities (in regions D, I, and P2). The δ13C from the ruminants (–61.6 ± 0.4 ‰) falls in the same range of values, which are typical of microbial CH4 formation. The most depleted δ13C signals measured at oil wells, with values < –50 ‰ V-PDB, can occur in the case of very early mature thermogenic formations, when thermogenic gas is mixed with adjacent microbial formations or when secondary microbial CH4 is produced. The distinction shown in Figure 3 is further discussed below, along with the analysis of the data from the different regions. Figure 3. δ13C in CH4 source signatures from surface samples. Histogram of δ13C-CH4 source signatures from samples around oil and gas facilities, compared with other sampled source signatures. Gas leaks (red points) were sampled from a leaky pipeline along a rural road (area P2, 44.949135° N, 25.77005° E) and in a residential area (Filipeştii de Târg, area P2, 44.963822° N, 25.794138° E). Ruminants (green point) were sampled in a grass field in region Te2 (44.362855° N, 25.321468° E). Values specified on the vertical lines are the means of each gas and oil extraction data and the mean of two modes of the oil extraction data. DOI: https://doi.org/10.1525/elementa.2021.000092.f3 Figure 3. δ13C in CH4 source signatures from surface samples. Histogram of δ13C-CH4 source signatures from samples around oil and gas facilities, compared with other sampled source signatures. Gas leaks (red points) were sampled from a leaky pipeline along a rural road (area P2, 44.949135° N, 25.77005° E) and in a residential area (Filipeştii de Târg, area P2, 44.963822° N, 25.794138° E). Ruminants (green point) were sampled in a grass field in region Te2 (44.362855° N, 25.321468° E). Values specified on the vertical lines are the means of each gas and oil extraction data and the mean of two modes of the oil extraction data. DOI: https://doi.org/10.1525/elementa.2021.000092.f3 Close modal ### 3.2. Analysis per region We can distinguish the CH4 isotopic signatures from the different geographical clusters we covered; our results for each of them are shown in Figure 4. The C2:C1 ratios are not available for the exact same locations than the CH4 isotopic signatures because they were obtained by different survey teams, but we can compare them on the cluster scale. The geographical distribution of the isotopic signatures and C2:C1 ratios is shown in the supplementary material (Figure S2). We evaluated the clusters with coinciding measurements of isotopic and C2:C1 ratios in Figure 5. Because we measured only ethane and methane (C2 and C1), we only report maximal values of Bernard ratios. Figure 4. Distribution of all CH4 isotopic composition results determined from ground samples per cluster. (a) C2:C1 ratios derived from all CH4 enhancements measured when driving in clusters of oil and gas extraction activities. (b) δ13C-CH4 and (c) δ2H-CH4 isotopic source signatures of CH4 enhancements sampled with the survey vehicles in the targeted clusters. DOI: https://doi.org/10.1525/elementa.2021.000092.f4 Figure 4. Distribution of all CH4 isotopic composition results determined from ground samples per cluster. (a) C2:C1 ratios derived from all CH4 enhancements measured when driving in clusters of oil and gas extraction activities. (b) δ13C-CH4 and (c) δ2H-CH4 isotopic source signatures of CH4 enhancements sampled with the survey vehicles in the targeted clusters. DOI: https://doi.org/10.1525/elementa.2021.000092.f4 Close modal Figure 5. Bernard plot of the measurement results aggregated per cluster. Maximal Bernard ratio values with respect to δ13C-CH4 source signatures from measurements in the same clusters, around oil (circles) and gas (diamonds) facilities. Values are compared with genetic ranges from Milkov and Etiope (2018). MC = microbial CO2 reduction; MF = microbial fermentation; MS = secondary microbial; TH = thermogenic; AB = abiotic. The geographical locations of each clusters are shown in Figures 1 and 4. DOI: https://doi.org/10.1525/elementa.2021.000092.f5 Figure 5. Bernard plot of the measurement results aggregated per cluster. Maximal Bernard ratio values with respect to δ13C-CH4 source signatures from measurements in the same clusters, around oil (circles) and gas (diamonds) facilities. Values are compared with genetic ranges from Milkov and Etiope (2018). MC = microbial CO2 reduction; MF = microbial fermentation; MS = secondary microbial; TH = thermogenic; AB = abiotic. The geographical locations of each clusters are shown in Figures 1 and 4. DOI: https://doi.org/10.1525/elementa.2021.000092.f5 Close modal Additional measurements from the regional operator and the literature allowed to characterize the CH4 formation processes in the different oil or gas reservoirs in more detail. All the complementary data are presented in the supplementary material (Table S1, Figures S1, S3, and S4). Most samples were collected in the district of Prahova (region P). The ranges of isotopic values and C2:C1 ratios in the clusters P1, P2, and P4 are very wide, which corresponds to a heterogenous thermal maturity of the oil reservoirs that are being processed there (Figure 4). Similar heterogeneity is also found in the clusters P6 and P7, showing C2:C1 ratios from 0.0021 to 0.61. However, we identified four clusters with comparatively consistent results: • P2: δ13C values < –59 ‰ were measured around two natural gas facilities of the area. Five χ(CH4) enhancements near gas wells were measured in cluster P2, with C2:C1 < 0.002. Such values provide evidence for the presence of natural gas of microbial origin (Figure 5). Nearby oil extraction facilities in region P2 have higher C2:C1 ratios, and higher δ13C-CH4 values, typical for associated gas of thermogenic origin (Figure 5). Our measurements support the presence of multiple origins of the fossil fuel deposits in this cluster. • P5: The hilly region east of Târgovişte (labelled P5) hosts a cluster of oil extraction facilities with well-defined isotopic composition of the emitted gas: δ13C between –50.6 and –37.3 ‰ V-PDB, δ2H between –251 and –199 ‰ V-SMOW. The relatively high C2:C1, between 0.056 and 0.37, confirms the presence of only wet thermogenic gas in the exploited reservoir. • P9: This cluster displays the highest CH4 enhancements (χ(CH4) > 106 ppb) with particularly enriched and highly consistent isotopic signals from oil installations (n = 16): average δ13C = –36.8 ± 2.2 ‰ and δ2H = –160 ± 10 ‰. No other gas composition measurements was made in this region. • P1.1: In this subregion of P1, the isotopic signatures suggest an intermediate maturity thermogenic or secondary microbial formation (δ13C from –51.0 to –41.4 ‰ and δ2H from –221 to –185 ‰; Figure S4). We obtained C2:C1 values > 0.02 for most locations in this cluster (41 of 45), indicating a relatively large ethane proportion (Bernard ratio < 50). These locations were nearby oil extraction and production facilities, which confirm the presence of wet gas of thermogenic origin (Figure 5). A Bernard ratio of 11.9 was reported by the operator for an installation 10 km away from this cluster. Subsurface measurements within the cluster (Filipescu and Huma, 1979) show a reservoir of oil with Bernard ratios from 9 to 18 at ca. 2,000-m depth, also consistent with our surface measurements. Therefore, most deposits in this region are likely from thermogenic CH4 formation, but can also be of secondary microbial origin. The CH4 isotopic signatures we measured in the Dolj and Ialomita districts (regions D and I) are well defined (Figure 4), with relatively enriched δ2H and depleted δ13C, especially in Dolj. In this region, all facilities are associated with gas and condensed gas extraction plants. The same is true for the facilities with the lowest δ13C values sampled in Ialomita. The δ13C-CH4 signatures we obtained were < –57 ‰ for 11 of the 12 sampled locations in these two regions. Values of δ13C < –60 ‰ suggest the presence of dry gas with microbial origin (CO2 reduction pathway), as it is found in Transylvania (see the results of aircraft samples). Additional data support the hypothesis of the microbial origin of the extracted natural gas in regions in Dolj and Ialomita: • Dolj (D): For a borehole southeast of Craiova, Filipescu and Huma (1979) mentioned shallow deposits of dry gas (ca. 30 km from the sampled sites, 200- to 300-m deep), with Bernard ratios > 3,000. This would confirm the presence of large microbial gas reservoirs, in this region of major natural gas production. • Ialomita (I): Some facilities in Ialomita are related to oil extraction, from where we sampled CH4 with isotopic signatures showing a thermogenic origin. The distinction with gas facilities is confirmed by the C2:C1 results of this cluster: The values range from 0 to 0.76, with C2:C1 from 0 to 0.002 only found around gas installations and the higher ratios found around oil installations (Figure 5). Filipescu and Huma (1979) reported a vertical gas composition profile in the vicinity of the cluster where we carried out measurements, nearby the sampled cluster showing the presence of dry gas overlying associated gas with increasing C2 and C3 content (Bernard ratios of ca. 376 and 76 at –1,200 and –2,000 m, respectively). The gas sampled by the operator likely corresponds to this deeper layer of associated gas (Bernard ratio of 47). Thus, we conclude on microbial dry gas overlying oil deposits from our measurements in Ialomita; and this hypothesis matches the gas composition data. The Teleorman region (Te) can be divided into west and east subareas (respectively, Te1 and Te2), separated by the river Teleorman, based on the isotopic signatures: • Te1: This subcluster is characterized by the heaviest isotopic signatures found in this study, sampled around both oil and gas extraction facilities (n = 4): average δ13C = –28.1 ± 4.2 and δ2H = –149 ± 11 ‰ (Figure 4). These values correspond to very late maturity thermogenic gas (Figure 2a). The Bernard ratio reported by the operator for a close-by facility is between the values reported in Filipescu and Huma (1979), from associated gas at two different depths. Filipescu and Huma (1979) also reported the presence of nonassociated gas in the deepest layers (>2,000 m below surface), with a Bernard ratio of 452. Therefore, the facilities we sampled are likely to reach the deepest formations of high maturity deposits, at the stage where dry gas formation starts to occur. • Te2: CH4 from oil wells (n = 5) was more isotopically depleted, especially in 13C: average δ13C = –54.6 ± 4.4 ‰ and δ2H = –199 ± 6 ‰ (Figure 4). This suggests an intermediate maturity thermogenic, secondary microbial, or mixed (with primary microbial gas) origin of the CH4. The origin cannot be further constrained by the large range of measured C2:C1 ratios (Figure 5). Low δ13C values (–58 ‰ and lower) usually indicate microbial CH4 and were measured at two oil wells. C2:C1 ratios from our surface measurements indicate relatively low ethane amounts (values from 0 to 0.08, n = 17), in agreement with Bernard ratios between 10 and 300 reported for one facility in the region by Filipescu and Huma (1979). However, the values reflect a certain heterogeneity, confirmed by the variations in δ13C by up to 10 ‰, and the presence of different densities in the oil deposits: from medium to heavy, compared to only light deposits in Te1. Here, the hypothesis of mixed gas origins is the most likely, including the presence of microbial dry CH4 reservoirs alongside wet gas reservoirs. ### 4.1. Isotopic signals from aircraft samples Although the χ(CH4) excess above background was much lower than what was observed by the surface vehicles, we could characterize the isotopic source signals of 24 locations. The Keeling plots were rejected if: • (1) the excess χ(CH4) above background was <60 ppb (based on IRMS measurements), and • (2) the r2 of the regression fit was <0.5 for δ13C and δ2H. All accepted Keeling plots are available in the Supplementary Material (Figure S5), as well as the resulting source signals (Table S2). The map in Figure 6 shows the resulting isotopic signatures of the χ(CH4) anomalies sampled from the aircraft. They are compared with typical ranges of CH4 isotopic source signatures in Figure 4. δ13C ranged from –64.6 to –35.8 ‰ V-PDB, and δ2H from –404 to –127 ‰ V-SMOW, and the majority of them correspond to the emissions from fossil fuel extraction (Figure 2b). Based on the wind direction for each flight day and of the recorded altitudes, we could link 18 CH4 enhancements to underlying oil and gas extraction facilities and 6 to “unknown sources” (Figures 2 and 6). The CH4 enhancements of unknown origin sampled in the aircraft had the most depleted isotopic values: δ13C between –64.6 and –54.9 ‰ and δ2H between –404 and –239 ‰ and were generally observed at higher altitudes (up to 2,000 m above ground, Table S2) and outside the oil and gas production clusters. These isotope ranges correspond to CH4 from microbial fermentation processes (Figure 2), therefore likely coming from agriculture activities, waste management, or natural wetlands. The CH4 enhancements could, for example, be advected from densely populated areas (urban) or large agriculture facilities. Waste and agriculture emissions of biogenic origin account for 33% and 40%, respectively, of the 2015 CH4 anthropogenic emissions in Romania (Crippa et al., 2019). In comparison, fossil fuels fugitive emissions were estimated at 21%. Measurements carried out in the city of Bucharest (Fernandez et al., 2022) showed that biogenic emissions, especially from urban wastewater, were surprisingly widespread, much more than in other European cities. Figure 6. Isotopic signals derived from aircraft samples. Results of CH4 isotopic source signals for all enhancements sampled from the aircraft, related to oil and gas extraction activities or from unknown sources (U). (a) δ2H in CH4. (b) δ13C in CH4. DOI: https://doi.org/10.1525/elementa.2021.000092.f6 Figure 6. Isotopic signals derived from aircraft samples. Results of CH4 isotopic source signals for all enhancements sampled from the aircraft, related to oil and gas extraction activities or from unknown sources (U). (a) δ2H in CH4. (b) δ13C in CH4. DOI: https://doi.org/10.1525/elementa.2021.000092.f6 Close modal Most other isotopic signals determined on samples collected from the aircraft were in the range of signatures sampled from the oil and gas extraction facilities on the ground (Figure 2). Without considering the CH4 enhancements of unknown origins, the average δ2H signal was –196 ‰ V-SMOW. Most of the emissions from oil and gas facilities we characterized from ground sampling are in the Prahova region. It is also the area where most samples were taken from the aircraft, because of the location of the airfield. However, the wind often advected emissions from region O (Figure 7), where very few ground measurements were made. The relative enrichment in deuterium isotopes in the samples from the aircraft confirms the fossil fuel origin of the responsible CH4 emissions. Figure 7. Isotopic signals from the aircraft linked with the ones from the ground surface. Isotopic source signatures determined from aircraft samples (squares) and the suspected emission sources sampled from the ground (circles), when the wind directions (arrows) were matching: in west of Teleorman (Te, dark blue), north of Prahova (P, red), and Ialomita (I, green). No clear agreement was found in north of Prahova (P9, yellow), Olt and east of Teleorman (O and Te, wite). Note that the wind direction is irrelevant in Ialomita because the aircraft circled around the facility cluster during the sampling. The reservoir locations were provided by the National Agency for Mineral Resources (Georgescu, 2019). The isotopic signals are shown on a dual isotope plot (bottom-right) with isotopic ranges of geological formation pathways from Milkov and Etiope (2018). DOI: https://doi.org/10.1525/elementa.2021.000092.f7 Figure 7. Isotopic signals from the aircraft linked with the ones from the ground surface. Isotopic source signatures determined from aircraft samples (squares) and the suspected emission sources sampled from the ground (circles), when the wind directions (arrows) were matching: in west of Teleorman (Te, dark blue), north of Prahova (P, red), and Ialomita (I, green). No clear agreement was found in north of Prahova (P9, yellow), Olt and east of Teleorman (O and Te, wite). Note that the wind direction is irrelevant in Ialomita because the aircraft circled around the facility cluster during the sampling. The reservoir locations were provided by the National Agency for Mineral Resources (Georgescu, 2019). The isotopic signals are shown on a dual isotope plot (bottom-right) with isotopic ranges of geological formation pathways from Milkov and Etiope (2018). DOI: https://doi.org/10.1525/elementa.2021.000092.f7 Close modal The three χ(CH4) anomalies observed above Transylvania show relatively low δ13C values ( –63.2 ± 0.1, –62.3 ± 1.3, and –58.2 ± 1.3 ‰), typical of microbial CH4 gas (Figure 2a), and δ2H of –273 ± 26, –223 ± 20 and –188 ± 13 ‰. δ2H values >–250 ‰ are typical for the CO2 reduction pathway rather than fermentation (Milkov and Etiope, 2018) and are consistent with the isotopic data reported for gas seeps in the same basin (Baciu et al., 2018). Therefore, we likely sampled CH4 sources of microbially formed natural gas reservoirs at the two locations with δ2H > –250 ‰. This is confirmed by the relatively depleted δ13C values that we also found in natural gas leaks sampled on the ground. The presence of microbial gas reservoirs in Transylvania has been documented, for example, by Filipescu and Huma (1979), Pawlewicz (2005), and Baciu et al. (2018). The CH4 source of the third enhancement intercepted by the aircraft is more likely to be from agriculture or waste from urban settlements in the area. Figure 7 shows the CH4 enhancements sampled from the aircraft that we could link to emissions sampled from the ground based on the wind directions. In Te1 and I regions, the isotopic signal from the aircraft compares well with signatures from the oil installations below, and we can confidently identify the oil and gas activities in the underlying clusters as the source of the CH4 enhancements observed from the aircraft. The distinct isotopic signatures measured in region Te1 (relatively enriched in heavy isotopes; see results from ground surface samples) are also found in the aircraft samples (Figure 7). In Prahova, we show the results of 2 of 8 CH4 enhancements observed from the aircraft, where the wind clearly came from clusters of oil and gas installations where we also sampled on the ground. Also here, the isotopic signals derived from the aircraft samples agree fall in the range of the ones observed at the ground, although this is a region with heterogenous isotopic signatures, which makes it difficult to precisely link a specific cluster to the isotopic signals from the aircraft (Figure 7). The largest χ(CH4) anomalies observed from the aircraft were when flying above Ialomita, with values of 300 and 400 ppb above background. The underlying oil and gas cluster was visited several times by ground vehicles. The two locations with the lowest δ13C (–60.9 ± 0.032 and –67.8 ± 1.18 ‰) correspond to gas installations and the others are oil wells or processing plants. The CH4 enhancements observed from the aircraft likely originate from a specific processing plant (oil deposit, gas compression, and others) that was circled at low altitude. This facility was sampled two times from the ground with δ13C values of –48.5 ± 0.45 and –56.5 ± 0.13 ‰. The δ13C signals from the aircraft are in a similar range: –57.0 ± 0.22 and –51.4 ± 0.17 ‰. The range of isotopic values from this particular site suggests the presence of several CH4 sources, reflecting the different activities (storage, extraction, and gas recovery) and potential temporal variability (discussed in Section 5). ### 4.2. Implications of the aircraft results CH4 enhancements were observed during each raster flight above the target areas (Figure 1), which include dense clusters of oil and gas installations. The isotopic signatures confirmed that the sampled emissions originate from the underlying oil and gas extraction activities. The total emissions from fossil fuel extraction clusters can be estimated from aircraft measurements, for example, using a mass balance approach (Hiller et al., 2014; Karion et al., 2015; Peischl et al., 2016; Schwietzke et al., 2017; Fiehn et al., 2020). Top-down approaches often rely on the use of regional-scale transport models in order to evaluate reported emission inventories (Xiao et al., 2008; Henne et al., 2016). Information on the CH4 isotopic signatures of the observed enhancements from the aircraft can be used for source attribution (Fisher et al., 2017), to constrain the measurement-based quantifications, and to verify model simulations on the origin of the emissions. Previous studies used CH4 isotopic source signatures to constrain the CH4 budget globally (Schaefer et al., 2016; Schwietzke et al., 2016; Worden et al., 2017) and regionally (Röckmann et al., 2016; Bergamaschi et al., 2018; Menoud et al., 2020a). Mean isotopic values assigned to fossil fuel related emissions in the literature range between –37 and –44 ‰ for δ13C-CH4 (Schaefer et al., 2016; Schwietzke et al., 2016; Worden et al., 2017; Menoud et al., 2020b), and around –175 ‰ for δ2H-CH4 (Lu et al., 2021; Menoud et al., 2021), the latter being based on a substantially smaller sample size. For the specific case of the Romanian Plain, we suggest the use of average values from aircraft measurements made in this study: δ13C = –49.7 ± 6.4 ‰ and δ2H = –189 ± 38 ‰, from identified, mainly oil-related, fossil fuel activities. The average values from ground measurements around fossil fuel production sites in this study are δ13C = –46.0 ± 11.2 ‰ and δ2H = –188 ± 28 ‰, and within the range of uncertainty of the aircraft values. The average isotopic signatures from our study do not take into account emissions from the production of natural gas in Transylvania and the distribution network. From the flight covering part of Transylvania, we found more depleted δ13C signatures than in the Romanian Plain, but we didn’t collect data on CH4 emissions samples on the ground. Regarding the gas network, Fernandez et al. (2022) measured significant emissions in Bucharest and with also a relatively depleted δ13C isotopic signature (confirmed by our measurements of two gas leaks; Figure 3). Therefore, the δ13C value for CH4 emissions from all fossil fuel activities in Romania is likely to be lower than the –49.7 ‰ suggested above and further different to the global values commonly assigned. The χ(CH4) anomalies we observed from the aircraft were not all related to emissions from the oil and gas sector. The samples of “unknown” origin we collected from the aircraft, and 1 sample above Transylvania, had a distinct isotopic signal, with δ2H < –250 ‰, that corresponds to CH4 of microbial fermentation origin (Figure 2). Indeed, there are many other sources of CH4 emissions in Romania. According to the EDGAR v5.0 inventory (Crippa et al., 2019), the main anthropogenic CH4 sources in Romania in 2015 were the agriculture sector (40% of total emissions, including manure management) and waste management (33% of total emissions). Microbial fermentation can also occur in stagnant freshwater; therefore, lakes, swamps, and bogs are potential natural sources, in addition to the well-established natural gas seeps and mud volcanoes (Etiope et al., 2011). Future measurements could be targeted at constraining emissions from nonfossil fuel sources. Schwietzke et al. (2017) emphasized the influence of episodic release from fossil fuel extraction or processing sites on atmospheric measurements. In this study, this was illustrated by the 2 flights performed over Ialomita (region I; on October 11 and 14, 2019), where the emissions very likely originated from the same facility that was circled by the aircraft (Figure 7). The isotopic signatures were δ13C = –57.0 ± 0.22 ‰ and δ2H = –131 ± 15 ‰ on the 11th, and δ13C = –51.4 ± 0.17 ‰ and δ2H = –176 ± 14 ‰ on the 14th. The results are statistically different, which reflects the diversity of releases, even from 1 localized facility. To evaluate the emissions from our target regions more precisely, it is necessary to combine data from several flights performed on several days and at different seasons. The ground surface results show that we can determine the origin of emitted natural gas based on CH4 isotopic measurements at the surface. Whereas the signatures in some clusters show consistent signatures, results from other regions were very heterogenous (P1, P2, and P4; Figure 4). The C2:C1 ratios we measured are generally in agreement with the CH4 isotopic signatures. To support our conclusions, further measurements at the extraction and processing facilities would be beneficial, not only for gathering more data on the hydrocarbon composition but also to account for the different types of emissions that come from one facility. Cardoso-Saldaña et al. (2021) showed that the C2:C1 ratios are generally higher in storage tank emissions. There are also variations in the CH4 emissions of a facility because of the presence of different sources, for example, storage tanks do not emit continuously. Our approach of measuring the CH4 enhancements downwind of the facilities is sensitive to the variations in sources and their composition. The analysis of other variables, especially total hydrocarbon contents, CO2 contents, and the isotopic composition of CO2 and C2H6 (Milkov, 2011; Milkov and Etiope, 2018), could help to further reduce the uncertainties in the origin of the gas emissions we investigated here. Nevertheless, we showed that atmospheric measurements allowed to draw conclusions on the geological origin of exploited gas reservoirs in the subsurface. As part of the ROMEO project, we characterized CH4 emissions from 83 oil and gas production sites for source isotopic signatures and 412 for C2:C1 ratios. The δ13C and δ2H isotopic signatures were also determined at 24 locations sampled from an aircraft. Our data show that over the target areas, most CH4 significant enhancements that were encountered originated from the underlying oil and gas production activities. Thus, CH4 emissions from oil and gas extraction activities are the main emission source for such large point sources within our target areas. The CH4 isotopic composition over a certain area can sometimes be heterogeneous, but the distinction from other source categories than from oil and gas was still possible. This possibility of source attribution will support the quantitative interpretation of top-down emission estimates based on high-precision methane measurements that were also carried out on these and other flights in the same region. Our results allow to characterize the origin of natural gas in several regions from atmospheric measurements. Both isotopic signatures and C2:C1 ratios indicated that most visited sites, related to oil production, emitted thermogenic gas. We also identified some microbial reservoirs, especially around gas production sites. New findings include the presence of microbial gas in at least four production areas of the Romanian Plain, located in the counties of Prahova, Ialomita, Dolj, and Teleorman. We also confirmed the presence of microbial, CH4 emissions due to the production of natural gas in Transylvania. The average isotopic signatures for CH4 emissions from fossil fuel production over the Romanian Plain were –49.7 ± 6.4 ‰ V-PDB for δ13C and –189 ± 38 ‰ V-SMOW for δ2H, based on the measurements from the aircraft. The δ13C value possibly overestimates the average δ13C from fossil fuel activities in the whole country of Romania because it does not include emissions from natural gas production in Transylvania but is already lower than commonly used values for global fossil fuel emissions (Schwietzke et al., 2016). The global database of gas composition data made by Sherwood et al. (2017) did not include measurements made in Romania. Yet it is not the only place with relatively depleted δ13C-CH4 values in geological deposits: The database as well as recently published studies (Zazzeri et al., 2016; Lu et al., 2021) reported δ13C values < –60 ‰ V-PDB in emitted CH4 from coal or conventional gas exploitation in the United States, Australia, Poland, Japan, and other countries. Therefore, it is crucial to take into account the geographical variability of isotopic signatures when they are used to constrain the global or regional CH4 budget. All of the data used in this study are publicly available on a Zenodo repository (https://doi.org/10.5281/zenodo.6319952). • Table S1. Gas composition data measured at several extraction facilities by the operator in the regions where measurements were also carried out in this study. • Table S2. Isotopic source signals of all χ(CH4) anomalies sampled from the aircraft and considered significant (excess χ(CH4) < 60 ppb and r2 < 0.5). • Figure S1. Example of flight pattern. • Figure S2. Results from ground surface sampling around oil and gas facilities in regions P and Te2. • Figure S3. Gas composition data in the Romanian Plain. • Figure S4. Genetic diagrams of gas molecular and isotopic compositions, per cluster. • Figure S5. Keeling plots of all sampled CH4 enhancements from the aircraft. We specially thank all other members of the ROmanian Methane Emissions from Oil & Gas team for their help during the campaign: Huilin Chen, Dominik Brunner, Oana Pîrvu, Mackenzie Smith, Niall Armstrong, Patryk Lakomiec, Sylvia Walter, Aurel Constantin, Sebastian Iancu, Alex Nica, Sorin Ghemulet, Constantin Visoiu, Cristian Pop, Alexandru Pana, Alexandru Tudor, Mihai Profir, Alin Scarlat, Lucian Cusa, Marius Corbu, Georgiana Grigoras, Sorin Vajaiac, Denisa Moaca, Vincent Edjabou, Julia Wietzel, Jaroslaw Necki, Pawel Jagoda, Jakub Baryzel, Andrei Radovici, Horatiu Stefanie, Alexandru Mereuta, Artur Ionescu, and Daniel Zavala-Araiza. These surveys were funded by the ROmanian Methane Emissions from Oil & Gas project, funded by the Climate and Clean Air Coalition (CCAC) of UNEP under grant number PCA/CCAC/UU/DTIE19-EN652. This research project has also received funding from the European Union’s Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie Grant Agreement 722479 (MEMO2, https://h2020-memo2.eu). The authors have no competing interests, as defined by Elementa, that might be perceived to influence the research presented in this article. Contributed to conception and design: MM, TR. Contributed to acquisition of data: MM, CV, HM, AH, IV, PB, AD, PK, MA, AC, CB, CS, MS, TR. Contributed to analysis and interpretation of data: MM, CV, HM, GE, CB, TR. Approved the submitted version for publication: MM, CV, HM, AH, IV, PB, AD, PK, SS, MA, AC, GE, CB, CS, MS, TR. 1. Standard error of the mean. 2. Includes disposal injection, power generator, and other. Alvarez , RA , Zavala-Araiza , D , Lyon , DR , Allen , DT , Barkley , ZR , Brandt , AR , Davis , KJ , Herndon , SC , Jacob , DJ , Karion , A , Kort , EA . 2018 . Assessment of methane emissions from the U.S. oil and gas supply chain . Science . DOI: http://dx.doi.org/10.1126/science.aar7204. Baciu , C , Etiope , G , Cuna , S , Spulber , L . 2008 . Methane seepage in an urban development area (Bacau, Romania): Origin, extent, and hazard . Geofluids 8 ( 4 ): 311 320 . DOI: http://dx.doi.org/10.1111/j.1468-8123.2008.00228.x. Baciu , C , Ionescu , A , Etiope , G . 2018 . Hydrocarbon seeps in Romania: Gas origin and release to the atmosphere . Marine and Petroleum Geology 89 : 130 143 . DOI: http://dx.doi.org/10.1016/j.marpetgeo.2017.06.015. Bergamaschi , P , Karstens , U , Manning , AJ , Saunois , M , Tsuruta , A , Berchet , A , Vermeulen , AT , Arnold , T , Janssens-Maenhout , G , Hammer , S , Levin , I . 2018 . Inverse modelling of European CH4 emissions during 2006–2012 using different inverse models and reassessed atmospheric observations . Atmospheric Chemistry and Physics 18 ( 2 ): 901 920 . DOI: http://dx.doi.org/10.5194/acp-18-901-2018. Bernard , B , Brooks , J , Sackett , W . 1976 . Natural gas seepage in the Gulf of Mexico . Earth and Planetary Science Letters 31 ( 1 ): 48 54 . DOI: http://dx.doi.org/10.1016/0012-821X(76)90095-9. Boggs , PT , Rogers , JE . 1990 . Orthogonal distance regression , in Statistical analysis of measurement error models and applications: Proceedings of the AMS-IMS-SIAM joint summer research conference held June 10-16, 1989 ( Contemporary mathematics; vol. 112 ). American Mathematical Society : 186 . Bousquet , P , Ciais , P , Miller , JB , Dlugokencky , EJ , Hauglustaine , DA , Prigent , C , Van der Werf , GR , Peylin , P , Brunke , EG , Carouge , C , Langenfelds , RL . 2006 . Contribution of anthropogenic and natural sources to atmospheric methane variability . Nature 443 ( 7110 ): 439 443 . DOI: http://dx.doi.org/10.1038/nature05132. British Petroleum . 2020 . Statistical review of world energy . British Petroleum . Cardoso-Saldaña , FJ , Pierce , K , Chen , Q , Kimura , Y , Allen , DT . 2021 . A searchable database for prediction of emission compositions from upstream oil and gas sources . Environmental Science & Technology 55 ( 5 ): 3210 3218 . DOI: http://dx.doi.org/10.1021/acs.est.0c05925. Clayton , C . 2005 . Petroleum geology\|chemical and physical properties, in Encyclopedia of geology . Elsevier : 248 260 . DOI: http://dx.doi.org/10.1016/B0-12-369396-9/00246-X. Crippa , M , Guizzardi , D , Muntean , M , Schaaf , E , Vullo , L , Solazzo , E , Monforti-Ferrario , F , Olivier , J , Vignati , E . 2019 . EDGAR v5.0 greenhouse gas emissions . European Commission, Joint Research Centre . Etiope , G . 2017 . Natural gas, in Bobrowsky , P , Marker , B eds., Encyclopedia of engineering geology . Cham, Switzerland : Springer International Publishing (Encyclopedia of earth sciences series) : 1 5 . Etiope , G , Baciu , CL , Schoell , M . 2011 . Extreme methane deuterium, nitrogen and helium enrichment in natural gas from the homorod seep (Romania) . Chemical Geology 280 ( 1-2 ): 89 96 . DOI: http://dx.doi.org/10.1016/j.chemgeo.2010.10.019. Etiope , G , Feyzullayev , A , Baciu , CL . 2009 . Terrestrial methane seeps and mud volcanoes: A global perspective of gas origin . Marine and Petroleum Geology 26 ( 3 ): 333 344 . DOI: http://dx.doi.org/10.1016/j.marpetgeo.2008.03.001. Etiope , G , Feyzullayev , A , Milkov , A , Waseda , A , Mizobe , K , Sun , CH . 2009 a. Evidence of subsurface anaerobic biodegradation of hydrocarbons and potential secondary methanogenesis in terrestrial mud volcanoes . Marine and Petroleum Geology 26 ( 9 ): 1692 1703 . DOI: http://dx.doi.org/10.1016/j.marpetgeo.2008.12.002. Etiope , G , Sherwood Lollar , B . 2013 . Abiotic methane on earth: Abiotic methane on earth . Reviews of Geophysics 51 ( 2 ): 276 299 . DOI: http://dx.doi.org/10.1002/rog.20011. European Commission . 2019 . Communication from the commission to the European parliament, the European council, the council, the European economic and social committee and the committee of the regions . Brussels, Belgium : European Commission . European Environment Agency . 2020 . Annual European Union greenhouse gas inventory 1990–2018 and inventory report 2020 . Copenhagen, Denmark : European Environment Agency . Fernandez , J , Maazallahi , H , France , J , Menoud , M , Corbu , M , Ardelean , M , Calcan , A , Townsend-Small , A , van der Veen , C , Fisher , RE , Lowry , D . 2022 . Street-level methane emissions of Bucharest, Romania and the dominance of Urban wastewater . Atmospheric Environment: X . DOI: http://dx.doi.org/10.1016/j.aeaoa.2022.100153. Fiehn , A , Kostinek , J , Eckl , M , Klausner , T , Galkowski , M , Chen , J , Gerbig , C , Röckmann , T , Maazallahi , H , Schmidt , M , Korbeń , P . 2020 . Estimating CH4, CO2, and CO emissions from coal mining and industrial activities in the upper Silesian Coal Basin using an aircraft-based mass balance approach . Atmospheric Chemistry and Physics Discussions . DOI: http://dx.doi.org/10.5194/acp-2020-282. Filipescu , M , Huma , I . 1979 . Geochemistry of natural gases . Bucharest, Romania : . Fisher , RE , France , JL , Lowry , D , Lanoisellé , M , Brownlow , R , Pyle , JA , Cain , M , Warwick , N , Skiba , UM , Drewer , J , Dinsmore , KJ . 2017 . Measurement of the 13C isotopic signature of methane emissions from Northern European Wetlands: Northern Wetland CH4 isotopic signature . Global Biogeochemical Cycles 31 ( 3 ): 605 623 . DOI: http://dx.doi.org/10.1002/2016GB005504. Fujita , R , Morimoto , S , Maksyutov , S , Kim , HS , Arshinov , M , Brailsford , G , Aoki , S , Nakazawa , T . 2020 . Global and regional CH4 emissions for 1995–2013 derived from atmospheric CH4, δ13C-CH4, and δD-CH4 observations and a chemical transport model . Journal of Geophysical Research: Atmospheres 125 ( 14 ). DOI: http://dx.doi.org/10.1029/2020JD032903. Georgescu , M . 2019 . Operating perimeters map . Bucharest, Romania : National Agency for Mineral Resources . Henne , S , Brunner , D , Oney , B , Leuenberger , M , Eugster , W , Bamberger , I , Meinhardt , F , Steinbacher , M , Emmenegger , L . 2016 . Validation of the Swiss methane emission inventory by atmospheric observations and inverse modelling . Atmospheric Chemistry and Physics 16 ( 6 ): 3683 3710 . DOI: http://dx.doi.org/10.5194/acp-16-3683-2016. Hiller , RV , Neininger , B , Brunner , D , Gerbig , C , Bretscher , D , Künzle , T , Buchmann , N , Eugster , W . 2014 . Aircraft-based CH4 flux estimates for validation of emissions from an agriculturally dominated area in Switzerland . Journal of Geophysical Research: Atmospheres 119 ( 8 ): 4874 4887 . DOI: http://dx.doi.org/10.1002/2013JD020918. Hoheisel , A , Yeman , C , Dinger , F , Eckhardt , H , Schmidt , M . 2019 . An improved method for mobile characterisation of δ13CH4 source signatures and its application in Germany . Atmospheric Measurement Techniques 12 ( 2 ): 1123 1139 . DOI: http://dx.doi.org/10.5194/amt-12-1123-2019. Houweling , S , Bergamaschi , P , Chevallier , F , Heimann , M , Kaminski , T , Krol , M , Michalak , AM , Patra , P . 2017 . Global inverse modeling of CH4 sources and sinks: An overview of methods . Atmospheric Chemistry and Physics 17 ( 1 ): 235 256 . DOI: http://dx.doi.org/10.5194/acp-17-235-2017. Hunt , JM . 1996 . Petroleum geochemistry and geology (2nd ed.). New York, NY : W.H. Freeman . Integrated Carbon Observation System Research Infrastructure . 2019 . ICOS atmospheric greenhouse gas mole fractions of CO2, CH4, CO, 14CO2 and meteorological observations September 2015–April 2019 for 19 stations (49 Vertical Levels), Final Quality Controlled Level 2 Data. ICOS data portal DOI: http://dx.doi.org/10.18160/CE2R-CC91. Intergovernmental Panel on Climate Change . 2013 . Climate change 2013: The physical science basis . Working group I contribution to the fifth assessment report of the Intergovernmental Panel on Climate Change . Cambridge, UK : Cambridge University Press . Intergovernmental Panel on Climate Change . 2018 . Summary for policymakers, in Masson-Delmotte , V , Zhai , P , Pörtner , H-O , Roberts , D , Skea , J , Shukla , PR , Pirani , A , Moufouma-Okia , W , Péan , C , Pidcock , R , Connors , S , Matthews , JBR , Chen , Y , Zhou , X , Gomis , MI , Lonnoy , E , Maycock , T , Tignor , M , Waterfield , T eds., Global warming of 1.5°C. An IPCC special report on the impacts of global warming of 1.5°C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty . Geneva, Switzerland : World Meteorological Organization . 32 p. Karion , A , Sweeney , C , Kort , EA , Shepson , PB , Brewer , A , Cambaliza , M , Conley , SA , Davis , K , Deng , A , Hardesty , M , Herndon , SC . 2015 . Aircraft-based estimate of total methane emissions from the Barnett shale region . Environmental Science & Technology 49 ( 13 ): 8124 8131 . DOI: http://dx.doi.org/10.1021/acs.est.5b00217. Keeling , CD . 1958 . The concentration and isotopic abundances of atmospheric carbon dioxide in rural areas . Geochimica et Cosmochimica Acta 13 ( 4 ): 322 334 . DOI: http://dx.doi.org/10.1016/0016-7037(58)90033-4. Levin , I , Bergamaschi , P , Dörr , H , Trapp , D . 1993 . Stable isotopic signature of methane from major sources in Germany . Chemosphere 26 ( 1-4 ): 161 177 . DOI: http://dx.doi.org/10.1016/0045-6535(93)90419-6. Lopez , M , Sherwood , O , Dlugokencky , E , Kessler , R , Giroux , L , Worthy , DE . 2017 . Isotopic signatures of anthropogenic CH4 Sources in Alberta, Canada . Atmospheric Environment 164 : 280 288 . DOI: http://dx.doi.org/10.1016/j.atmosenv.2017.06.021. Lu , X , Harris , SJ , Fisher , RE , France , JL , Nisbet , EG , Lowry , D , Röckmann , T , Van Der Veen , C , Menoud , M , Schwietzke , S , Kelly , BF . 2021 . Isotopic signatures of major methane sources in the coal seam gas fields and adjacent agricultural Districts, Queensland, Australia . Atmospheric Chemistry and Physics 21 : 1 36 . DOI: http://dx.doi.org/10.5194/acp-2021-76. Maazallahi , H , Fernandez , JM , Menoud , M , Zavala-Araiza , D , Weller , ZD , Schwietzke , S , Von Fischer , JC , Denier Van Der Gon , H , Röckmann , T . 2020 . Methane mapping, emission quantification, and attribution in two European cities: Utrecht (NL) and Hamburg (DE) . Atmospheric Chemistry and Physics 20 ( 23 ): 14717 14740 . DOI: http://dx.doi.org/10.5194/acp-20-14717-2020. Menoud , M , Röckmann , T , Fernandez , J , Bakkaloglu , S , Lowry , D , Korben , P , Schmidt , M , Stanisavljevic , M , Necki , J , Defratyka , S , Kwok , CY . 2020 a. Mamenoud/MEMO2_isotopes: V8.1 Complete . DOI: http://dx.doi.org/10.5281/ZENODO.4062356. Menoud , M , van der Veen , C , Necki , J , Bartyzel , J , Szénási , B , Stanisavljević , M , Pison , I , Bousquet , P , Röckmann , T . 2021 . Methane (CH4) sources in Krakow, Poland: Insights from isotope analysis . Atmospheric Chemistry and Physics 21 : 13167 13185 . Menoud , M , van der Veen , C , Scheeren , B , Chen , H , Szénási , B , Morales , RP , Pison , I , Bousquet , P , Brunner , D , Röckmann , T . 2020 b. Characterisation of methane sources in Lutjewad, The Netherlands, Using Quasi-continuous isotopic composition measurements . Tellus B: Chemical and Physical Meteorology 72 ( 1 ): 1 19 . DOI: http://dx.doi.org/10.1080/16000889.2020.1823733. , I , Schwietzke , S , Yacovitch , TI , Miller , B , Conley , S , Kofler , J , Handley , P , Thorley , E , Herndon , SC , Hall , B , Dlugokencky , E . 2019 . Methane source attribution in a U.S. dry gas basin using spatial patterns of ground and airborne ethane and methane measurements . Elementa: Science of the Anthropocene 7 : 13 . DOI: http://dx.doi.org/10.1525/elementa.351. Milkov , AV . 2011 . Worldwide distribution and significance of secondary microbial methane formed during petroleum biodegradation in conventional reservoirs . Organic Geochemistry 42 ( 2 ): 184 207 . DOI: http://dx.doi.org/10.1016/j.orggeochem.2010.12.003. Milkov , AV , Etiope , G . 2018 . Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples . Organic Geochemistry 125 : 109 120 . DOI: http://dx.doi.org/10.1016/j.orggeochem.2018.09.002. Miller , JB , Tans , PP . 2003 . Calculating isotopic fractionation from atmospheric measurements at various scales . Tellus B: Chemical and Physical Meteorology 55 ( 2 ): 207 214 . DOI: http://dx.doi.org/10.3402/tellusb.v55i2.16697. Monteil , G , Houweling , S , Dlugockenky , EJ , Maenhout , G , Vaughn , BH , White , JW , Rockmann , T . 2011 . Interpreting methane variations in the past two decades using measurements of CH4 mixing ratio and isotopic composition . Atmospheric Chemistry and Physics 11 ( 17 ): 9141 9153 . DOI: http://dx.doi.org/10.5194/acp-11-9141-2011. Pawlewicz , MJ . 2005 . Transylvanian composite total petroleum system of the Transylvanian Basin Province, Romania, Eastern Europe . U.S. Geological Survey . DOI: http://dx.doi.org/10.3133/b2204E. Peischl , J , Karion , A , Sweeney , C , Kort , EA , Smith , ML , Brandt , AR , Yeskoo , T , Aikin , KC , Conley , SA , Gvakharia , A , Trainer , M . 2016 . Quantifying atmospheric methane emissions from oil and natural gas production in the Bakken shale region of North Dakota: CH 4 emissions from the Bakken . Journal of Geophysical Research: Atmospheres 121 ( 10 ): 6101 6111 . DOI: http://dx.doi.org/10.1002/2015JD024631. Rice , DD , Claypool , GE . 1981 . Generation, accumulation, and resource potential of biogenic gas . AAPG Bulletin 65 ( 1 ): 5 25 . Röckmann , T . 2020 . ROMEO—ROmanian Methane Emissions from Oil & Gas . EGU General Assembly 2020 . Online: EGU2020-18801 . DOI: http://dx.doi.org/10.5194/egusphere-egu2020-18801. Röckmann , T , Eyer , S , van der Veen , C , Popa , ME , Tuzson , B , Monteil , G , Houweling , S , Harris , E , Brunner , D , Fischer , H , Zazzeri , G . 2016 . In situ observations of the isotopic composition of methane at the Cabauw Tall Tower Site . Atmospheric Chemistry and Physics 16 ( 16 ): 10469 10487 . DOI: http://dx.doi.org/10.5194/acp-16-10469-2016. Saunois , M , Stavert , AR , Poulter , B , Bousquet , P , , JG , Jackson , RB , Raymond , PA , Dlugokencky , EJ , Houweling , S , Patra , PK , Ciais , P . 2020 . The global methane budget 2000–2017. Earth System Science Data 12 ( 3 ): 1561 1623 . DOI: http://dx.doi.org/10.5194/essd-12-1561-2020. Schaefer , H , Fletcher , SEM , Veidt , C , Lassey , KR , Brailsford , GW , Bromley , TM , Dlugokencky , EJ , Michel , SE , Miller , JB , Levin , I , Lowe , DC . 2016 . A 21st-century Shift from fossil-fuel to biogenic methane emissions indicated by 13CH 4 . Science 352 ( 6281 ): 80 84 Schoell , M . 1980 . The hydrogen and carbon isotopic composition of methane from natural gases of various origins . Geochimica et Cosmochimica Acta 44 ( 5 ): 649 661 . DOI: http://dx.doi.org/10.1016/0016-7037(80)90155-6. Schoell , M . 1983 . Genetic characterization of natural gases . The American Association of Petroleum Geologists Bulletin 67 ( 12 ): 2225 2238 . Schwietzke , S , Pétron , G , Conley , S , Pickering , C , , I , Dlugokencky , EJ , Tans , PP , Vaughn , T , Bell , C , Zimmerle , D , Wolter , S . 2017 . Improved mechanistic understanding of natural gas methane emissions from spatially resolved aircraft measurements . Environmental Science & Technology 51 ( 12 ): 7286 7294 . DOI: http://dx.doi.org/10.1021/acs.est.7b01810. Schwietzke , S , Sherwood , OA , Bruhwiler , LMP , Miller , JB , Etiope , G , Dlugokencky , EJ , Michel , SE , Arling , VA , Vaughn , BH , White , JW , Tans , PP . 2016 . Upward revision of global fossil fuel methane emissions based on isotope database . Nature 538 ( 7623 ): 88 91 . DOI: http://dx.doi.org/10.1038/nature19797. Sherwood , OA , Schwietzke , S , Arling , VA , Etiope , G . 2017 . Global inventory of gas geochemistry data from fossil fuel, microbial and burning sources, Version 2017 . Earth System Science Data 9 ( 2 ): 639 656 . DOI: http://dx.doi.org/10.5194/essd-9-639-2017. Sperlich , P , Uitslag , NAM , Richter , JM , Rothe , M , Geilmann , H , van der Veen , C , Röckmann , T , Blunier , T , Brand , WA . 2016 . Development and evaluation of a suite of isotope reference gases for methane in air . Atmospheric Measurement Techniques 9 ( 8 ): 3717 3737 . DOI: http://dx.doi.org/10.5194/amt-9-3717-2016. Tarasova , O , Brenninkmeijer , C , Assonov , S , Elansky , N , Rockmann , T , Brass , M . 2006 . Atmospheric CH4 along the Trans-Siberian Railroad (TROICA) and River Ob: Source identification using stable isotope analysis . Atmospheric Environment 40 ( 29 ): 5617 5628 . DOI: http://dx.doi.org/10.1016/j.atmosenv.2006.04.065. Townsend-Small , A , Botner , EC , Jimenez , KL , Schroeder , JR , Blake , NJ , Meinardi , S , Blake , DR , Sive , BC , Bon , D , Crawford , JH , Pfister , G . 2016 . Using stable isotopes of hydrogen to quantify biogenic and thermogenic atmospheric methane sources: A case study from the Colorado Front Range: Hydrogen isotopes in the Front Range . Geophysical Research Letters 43 ( 21 ): 11,462 11,471 . DOI: http://dx.doi.org/10.1002/2016GL071438. Whiticar , MJ . 1999 . Carbon and hydrogen isotope systematics of bacterial formation and oxidation of methane . Chemical Geology 161 ( 1–3 ): 291 314 . DOI: http://dx.doi.org/10.1016/S0009-2541(99)00092-3. Worden , JR , Bloom , AA , Pandey , S , Jiang , Z , Worden , HM , Walker , TW , Houweling , S , Röckmann , T . 2017 . Reduced biomass burning emissions reconcile conflicting estimates of the post-2006 atmospheric methane budget . Nature Communications 8 ( 1 ): 2227 . DOI: http://dx.doi.org/10.1038/s41467-017-02246-0. Xiao , Y , Logan , JA , Jacob , DJ , Hudman , RC , Yantosca , R , Blake , DR . 2008 . Global budget of ethane and regional constraints on U.S. sources . Journal of Geophysical Research 113 ( D21 ): D21306 . DOI: http://dx.doi.org/10.1029/2007JD009415. Zazzeri , G , Lowry , D , Fisher , RE , France , JL , Lanoisellé , M , Kelly , BF , Necki , JM , Iverach , CP , Ginty , E , Zimnoch , M , Jasek , A . 2016 . Carbon isotopic signature of coal-derived methane emissions to the atmosphere: From coalification to alteration . Atmospheric Chemistry and Physics 16 ( 21 ): 13669 13680 . DOI: http://dx.doi.org/10.5194/acp-16-13669-2016. How to cite this article: Menoud, M, van der Veen, C, Maazallahi, H, Hensen, A, Velzeboer, I, van den Bulk, P, Delre, A, Korben, P, Schwietzke, S, Ardelean, M, Calcan, A, Etiope, G, Baciu, C, Scheutz, C, Schmidt, M, Röckmann, T. 2022. CH4 isotopic signatures of emissions from oil and gas extraction sites in Romania. Elementa: Science of the Anthropocene 10(1). DOI: https://doi.org/10.1525/elementa.2021.000092 Domain Editor-in-Chief: Detlev Helmig, Boulder AIR LLC, Boulder, CO, USA Guest Editor: Arvind P. Ravikumar, The University of Texas at Austin, Austin, TX, USA Knowledge Domain: Atmospheric Science Part of an Elementa Forum: Oil and Natural Gas Development: Air Quality, Climate Science, and Policy This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See http://creativecommons.org/licenses/by/4.0/.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6659912467002869, "perplexity": 6960.596448373913}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337531.3/warc/CC-MAIN-20221005011205-20221005041205-00167.warc.gz"}
http://www.encyclopediaofmath.org/index.php?title=Abelian_variety	# Abelian variety 2010 Mathematics Subject Classification: Primary: 14-XX [MSN][ZBL] An Abelian variety is an algebraic group that is a complete algebraic variety. The completeness condition implies severe restrictions on an Abelian variety. Thus, an Abelian variety can be imbedded as a closed subvariety in a projective space; each rational mapping of a non-singular variety into an Abelian variety is regular; the group law on an Abelian variety is commutative. The theory of Abelian varieties over the field of complex numbers $\C$ is, in essence, equivalent to the theory of Abelian functions founded by C.G.J. Jacobi, N.H. Abel and B. Riemann. If $\C^n$ denotes $n$-dimension vector space, $\Gamma\subset\C^n$ is a lattice (cf. Discrete subgroup) of rank $2n$, then the quotient group $X=\C^n/\Gamma$ is a complex torus. Meromorphic functions on $X$ are the same thing as meromorphic functions on $\C^n$ that are invariant with respect to the period lattice $\Gamma$. If the field $K$ of meromorphic functions on $X$ has transcendence degree $n$, then $X$ can be given the structure of an algebraic group. This structure is unique by virtue of the compactness of $X$, and it is such that the field of rational functions of this structure coincides with $K$. The algebraic groups formed in this way are Abelian varieties, and each Abelian variety over the field $\C$ arises in this way. The matrix which defines a basis of $\Gamma$ can be reduced to the form $(E\|Z)$, where $E$ is the identity matrix and $Z$ is a matrix of order $n\times n$. The complex torus $X=\C^n/\Gamma$ is an Abelian variety if and only if $Z$ is symmetric and has positive-definite imaginary part. It should be pointed out that, as real Lie groups, all varieties $X$ are isomorphic, but this is not true for their analytic or algebraic structures, which vary strongly when deforming the lattice $\Gamma$. Inspection of the period matrix $Z$ shows that its variation has an analytic character, which results in the construction of the moduli variety of all Abelian varieties of given dimension $n$. The dimension of the moduli variety is $n(n+1)/2$ (cf. Moduli problem). The theory of Abelian varieties over an arbitrary field $k$ is due to A. Weil [We], [We2]. It has numerous applications both in algebraic geometry itself and in other fields of mathematics, particularly in number theory and in the theory of automorphic functions. To each complete algebraic variety, Abelian varieties (cf. Albanese variety; Picard variety; Intermediate Jacobian) can be functorially assigned. These constructions are powerful tools in studying the geometric structures of algebraic varieties. E.g., they were used to obtain one of the solutions of the Lüroth problem. Another application is the proof of the Riemann hypothesis for algebraic curves over a finite field — the problem for which the abstract theory of Abelian varieties was originally developed. It was also one of the sources of $l$-adic cohomology. The simplest example of such a cohomology is the Tate module of an Abelian variety. It is the projective limit, as $n\to\infty$, of the groups $X[l^n]$ of points of order $l^n$. The determination of the structure of such groups was one of the principal achievements of the theory of Weil. In fact, if $m$ is coprime with the characteristic $p$ of the field $k$ and if $k$ is algebraically closed, then the group $X[m]$ is isomorphic to $(\Z/mZ)^{2\dim X}$. If $m=p$, the situation is more complicated, which resulted in the appearance of concepts such as finite group schemes, formal groups and $p$-divisible groups (cf. Finite group scheme; Formal group; $p$-divisible group). The study of the action of endomorphisms of Abelian varieties, in particular of the Frobenius endomorphism on its Tate module, makes it possible to give a proof of the Riemann hypothesis (for algebraic curves over finite fields, cf. Riemann hypotheses) and is also the principal instrument in the theory of complex multiplication of Abelian varieties. Another circle of problems connected with the Tate module consists of a study of the action of the Galois group of the closure of the ground field on this module. There resulted the Tate conjectures and the theory of Tate–Honda, which describes Abelian varieties over finite fields in terms of the Tate module [Mu]. The study of Abelian varieties over local fields, including $p$-adic fields, is proceeding at a fast rate. An analogue of the above-mentioned representation of Abelian varieties as a quotient space $\C^n/\Gamma$, usually known as uniformization, over such fields, was constructed by D. Mumford and M. Raynaud. Unlike the complex case, not all Abelian varieties, but only those having a reduction to a multiplicative group modulo $p$, are uniformizable [Ma]. The theory of Abelian varieties over global (number and function) fields plays an important role in Diophantine geometry. Its principal result is the Mordell–Weil theorem: The group of rational points of an Abelian variety, defined over a finite extension of the field of rational numbers, is finitely generated. For recent information on the Tate conjectures see [Fa]. For the theory of Tate–Honda see also [Ta]. Mumford's theory of uniformization is developed in [Mu2], [Mu3]. #### References [Fa] G. Faltings, "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" Invent. Math., 73 (1983) pp. 349–366 ((Errratum: Invent. Math. 75 (1984), p. 381)) MR0718935 MR0732554 Zbl 0588.14026 [La] S. Lang, "Abelian varieties", Springer (1983) MR0713430 Zbl 0516.14031 [Ma] Yu.I. Manin, "p-Adic automorphic functions" J. Soviet Math., 5 : 3 (1976) pp. 279–333 Itogi Nauk. i Tekhn. Sovrem. Problemy, 3 (1974) pp. 5–93 Zbl 0375.14007 MR0422161 [Mu] D. Mumford, "Abelian varieties", Oxford Univ. Press (1974) MR0282985 Zbl 0326.14012 [Mu2] D. Mumford, "An analytic construction of degenerating curves over complete local rings" Compos. Math., 24 (1972) pp. 129–174 MR0352105 Zbl 0243.14010 Zbl 0228.14011 [Mu3] D. Mumford, "An analytic construction of degenerating abelian varieties over complete rings" Compos. Math., 24 (1972) pp. 239–272 MR0352106 Zbl 0241.14020 [Se] J.-P. Serre, "Groupes algébrique et corps des classes", Hermann (1959) MR0103191 [Si] C.L. Siegel, "Automorphe Funktionen in mehrerer Variablen", Math. Inst. Göttingen (1955) [Ta] J.T. Tate, "Classes d'isogénie des variétés abéliennes sur un corps fini (d' après T. Honda)", Sem. Bourbaki Exp. 352, Lect. notes in math., 179, Springer (1971) [We] A. Weil, "Variétés abéliennes et courbes algébriques", Hermann (1971) MR0029522 Zbl 0208.49202 [We2] A. Weil, "Courbes algébriques et variétés abéliennes. Sur les courbes algébriques et les varietés qui s'en deduisent", Hermann (1948) MR0029522 [We3] A. Weil, "Introduction à l'étude des variétés kahlériennes", Hermann (1958) MR0111056 Zbl 0137.41103 How to Cite This Entry: Abelian variety. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Abelian_variety&oldid=21543 This article was adapted from an original article by B.B. VenkovA.N. Parshin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.89226895570755, "perplexity": 493.72478187925924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163047212/warc/CC-MAIN-20131204131727-00029-ip-10-33-133-15.ec2.internal.warc.gz"}
https://leanprover-community.github.io/archive/stream/113489-new-members/topic/4.20proof.20styles.html	## Stream: new members ### Topic: 4 proof styles #### Utensil Song (May 15 2020 at 14:41): I, very new to Lean and this Zulip Chat Community, would like to share my experience with Lean prover on trying to prove a trivial proposition in four proof styles supported by Lean. It's gonna feel verbose(for describing the intuition I established during the interactions with Lean), for that, I apologize in advance. The proposition is from 3.3.3. Negation and Falsity, Theorem Proving in Lean (which is where I'm at in the walkthrough of TPIL: For any two propositions p and q, assuming p → q and ¬q, Then ¬p. TPIL expresses the proposition like this: constants p q: Prop example (hpq : p → q) (hnq : ¬q) : ¬p := sorry As a beginner in Lean, I find it particularly important to be able to move things around and transform between different appearances of the same thing in one's mind, since the expressive Lean gives us too much liberty at how to express the same idea. Just move them around in the code editor (for me that's VSCode with Lean extension installed) and check the result against Lean. From these muscle memories (of success or errors), a mental model grows out naturally. Since example is just a nameless theorem/lemma, we can rewrite the above to the following by naming it play: lemma play (hpq : p → q) (hnq : ¬q) : ¬p := sorry Benefit from Curry–Howard correspondence, theorem/lemma shares the same basic grammar structure as def, i.e. def name : type := value, so the above is no different from: -- Play with hpq and hnq directly def play₁ (hpq : p → q) (hnq : ¬q) : ¬p := play hpq hnq Also, "parameters" are just syntax sugar in Lean, so the above is also the same as: -- Need Lambda to introduce binding names with the type def play₂ : (p → q) → (¬q) → ¬p := λ hpq, λ hnq, play hpq hnq ## Structural Proof OK, now we can move types, parameters around, let's go back to the original proposition, TPIL demonstrates a structural proof for it: example (hpq : p → q) (hnq : ¬q) : ¬p := assume hp : p, show false, from hnq (hpq hp) I failed to wrap my head around it until I read it carefully again and noticed ¬p is equivalent to p → false, so the idea is to assume p and prove false. This is accomplished by applying p → q and then q → false(¬q). ## Tactic Mode proof Next thing I try is to convert it to a Tactic Mode proof(which is best supported by the VS Code extension but hard to read without it), starting with: example (hpq : p → q) (hnq : ¬q) : ¬p := begin sorry end The goal (when the cursor is after begin) is p q : Prop, hpq : p → q, hnq : ¬q ⊢ ¬p By realizing intro will convert a goal like ⊢ a → b to ha : a ⊢ b and again ¬p is equivalent to p → false, inputting intro hp, we have the following goal(when the cursor is after the comma): p q : Prop, hpq : p → q, hnq : ¬q, hp : p ⊢ false apply is the opposite of intro (in a way), it can turn a goal likeb into a by a hypothesis a → b. Basically, it's just a function application(applying a function of the type a → b), while intro is actually a lambda that creates such a function. That's why I accepted the commas (instead of semicolons or nothing) at the end of each line of a proof, it's the same as the one in λ a : ℕ, a + 1. So assuming we have a → b, when we want to leave b as our goal, we use intro, when we want to leave a as our goal, we use apply. A pretty straight forward, left-hand-or-right-hand choice. So we work our way backwards: apply q → false to get q, apply p → q to get p, then we have the proof as: example (hpq : p → q) (hnq : ¬q) : ¬p := begin intro hp, apply hnq, apply hpq, sorry end and the goal (before sorry) as: p q : Prop, hpq : p → q, hnq : ¬q, hp : p ⊢ p And this goal is exactly our initial assumption hp : p so we finish the proof by exact hp. A Tactic Mode proof is really relying on the interactive hints of the current goals. While the writing process is enjoyable, the written code is hard to read. By narrowing my mind to the current goal during writing, I can't tell what's going on if I step back and look at the whole proof: example (hpq : p → q) (hnq : ¬q) : ¬p := begin intro hp, apply hnq, apply hpq, exact hp end ## Term Mode proof To truly understand the whole Tactic Mode proof, we must completely forget tactics and focus on the commas and replace all intro with a λ, replace all applys as function calls while the exact is the ultimate parameter so we see a Term Mode proof: example (hpq : p → q) (hnq : q → false) : p → false := λ hp, hnq (hpq hp) Writing a Term Mode proof can use a similar degree of help in VS Code, by prompting types instead of prompting goals: When we write λ hp, and type a random identifier such as p, Lean will complain about "type mismatch" and we'll know the right type and simply call a function with the expected type (recall that p → q is a hypothesis and also a function that eats something with type p and emits something with type q). Now the game switched from fulfilling goals to filling parameters of functions, type theory in action is fun! ## Calc Mode proof Finally, to my favourite Calc mode. I like it very much since it resembles the experience of pen and paper calculation/proof. Not completely, since we can't do something to both the left-hand side and right-hand side. To use the Calc Mode proof, we need something like an equation. ¬p is not one but p → false is: example (hpq : p → q) (hnq : q → false) : p → false := sorry I'm a bit nervous when I typed calc and see nothing back from Lean. But then I try to forget the computer and start writing on the imaginary paper: example (hpq : p → q) (hnq : q → false) : p → false := calc p → q : sorry ... → false : sorry Now my brain is doing all the thinking and I only have to find the computer excuse names back to replace the sorrys. It's surprisingly easy: example (hpq : p → q) (hnq : q → false) : p → false := calc p → q : hpq ... → false : hnq The excuse names(hypothesis) themselves are pretty dumb and you only feel like applying rewrite rules when your cursor is on a hypothesis and Lean shows you its type. To entertain myself a bit, I rewrite the above to: example (p_to_q : p → q) (q_to_false : q → false) : p → false := calc p → q : p_to_q ... → false : q_to_false ## Back to Structural Proof When I first see the structural proof, I thought it means to prove ¬p, simply assume p and it leads to a contradiction, but it's not the logic of that proof, so with a little search, I wrote: example (hpq : p → q) (hnq : ¬q) : ¬p := (assume hnnp : ¬¬p, have hp : p, from sorry, have hq : q, from sorry, show false, from sorry) Writing a structural proof is a bit like writing a Calc Mode proof, we do it by first assume, then write down the intermediate steps using haves and end it with a final show of the final target. Then we work out things after , from, just like how we work out what's after the colons in a Calc Mode proof: open classical example (hpq : p → q) (hnq : ¬q) : ¬p := (assume hnnp : ¬¬p, have hp : p, from by_contradiction hnnp, have hq : q, from hpq hp, show false, from hnq hq) ## Conclusion It's really a trivial proposition and only very elementary keywords are involved in the proofs, but I'm so excited about being able to write all four styles of proofs and finding out how I feel about each of them. Open questions are: • Am I missing something or there's little pedagogical material on writing non-trivial proofs using all four styles? • Are there automatic tools to convert the four styles to each other? ( Is it always possible?) • Is there on-going efforts to resemble more of the pen-and-paper experience(e.g. manipulate both sides of an equation)? #### Reid Barton (May 15 2020 at 14:52): Have you thought about writing a blog or something? I really like your style of explaining and exploring. #### Jalex Stark (May 15 2020 at 15:00): I agree, this would be a nice blog post. Every proof compiles down to terms, and in fact after this lemma contrapositive (hpq : p → q) (hnq : ¬q) : ¬p := begin intro hp, apply hnq, apply hpq, exact hp end you can type #print contrapositive to see what term is generated. #### Jalex Stark (May 15 2020 at 15:02): you might enjoy writing up a solution to this codewars kata https://www.codewars.com/kata/5eb0ce255179590016d613ce #### Kevin Buzzard (May 15 2020 at 15:16): @Utensil Song you'd be welcome to write a guest Xena project blog post based on your post #### Utensil Song (May 16 2020 at 01:34): @Reid Barton Thank you! I wasn't sure if it's worth blogging but so excited to share it. I'm so glad you guys like it and will try to enrich it a bit and write a blog based on it. #### Utensil Song (May 16 2020 at 01:51): Jalex Stark said: I agree, this would be a nice blog post. Every proof compiles down to terms, and in fact after this lemma contrapositive (hpq : p → q) (hnq : ¬q) : ¬p := begin intro hp, apply hnq, apply hpq, exact hp end you can type #print contrapositive to see what term is generated. Thank you! It turns out that underlyingly they are not using the same terms, unlike in my mental model after writing this post: lemma contrapositive_structural (hpq : p → q) (hnq : ¬q) : ¬p := assume hp : p, show false, from hnq (hpq hp) #print contrapositive_structural -- theorem chap_03.contrapositive_structural : ∀ (p q : Prop), (p → q) → ¬q → ¬p := -- λ (p q : Prop) (hpq : p → q) (hnq : ¬q) (hp : p), show false, from hnq (hpq hp) lemma contrapositive_tactic (hpq : p → q) (hnq : ¬q) : ¬p := begin intro hp, apply hnq, apply hpq, exact hp end #print contrapositive_tactic -- theorem chap_03.contrapositive_tactic : ∀ (p q : Prop), (p → q) → ¬q → ¬p := -- λ (p q : Prop) (hpq : p → q) (hnq : ¬q), id (λ (hp : p), hnq (hpq hp)) lemma contrapositive_term (hpq : p → q) (hnq : q → false) : p → false := λ hp, hnq (hpq hp) #print contrapositive_term -- theorem chap_03.contrapositive_term : ∀ (p q : Prop), (p → q) → (q → false) → p → false := -- λ (p q : Prop) (hpq : p → q) (hnq : q → false) (hp : p), hnq (hpq hp) lemma contrapositive_calc (hpq : p → q) (hnq : q → false) : p → false := calc p → q : hpq ... → false : hnq #print contrapositive_calc -- theorem chap_03.contrapositive_calc : ∀ (p q : Prop), (p → q) → (q → false) → p → false := -- λ (p q : Prop) (hpq : p → q) (hnq : q → false), implies.trans hpq hnq #### Utensil Song (May 16 2020 at 02:07): Jalex Stark you might enjoy writing up a solution to this codewars kata https://www.codewars.com/kata/5eb0ce255179590016d613ce Fun! Like a tango: theorem not_not_not_tactic (P : Prop) : ¬ ¬ ¬ P → ¬ P := begin intro hnnnp, intro hp, apply hnnnp, intro hnp, apply hnp, apply hp end Yeah :) #### Jalex Stark (May 16 2020 at 02:11): If you solve enough kata on codewars, you'll be able to submit your own #### Jalex Stark (May 16 2020 at 02:11): I submitted that one a few weeks ago, after having solved ~15 problems #### Utensil Song (May 16 2020 at 02:47): On the other hand, working out the other three styles are not that easy: theorem not_not_not_term (P : Prop) : ¬ ¬ ¬ P → ¬ P := λ hnnnp hp, hnnnp (λ hnp, hnp hp) theorem not_not_not_calc (P : Prop) : ¬ ¬ ¬ P → ¬ P := calc ¬ ¬ ¬ P → ¬ P : iff.elim_left (not_not_not_iff P) theorem not_not_not_structural (P : Prop) : ¬ ¬ ¬ P → ¬ P := assume hnnnp : ¬¬¬P, assume hp : P, have hnnp : ¬¬P, from (assume hnp: ¬P, hnp hp), -- from not_not_intro hp, show false, from hnnnp hnnp I don't know if not_not_not_calc can be reduced to more atomic steps. #### Jalex Stark (May 16 2020 at 02:57): yeah your "calc" proof is really just "I found this in the library" #### Utensil Song (May 16 2020 at 03:16): Kevin Buzzard said: Utensil Song you'd be welcome to write a guest Xena project blog post based on your post Thank you! But I couldn't figure out how to post a guest Xena project blog after reading https://xenaproject.wordpress.com/ , http://wwwf.imperial.ac.uk/~buzzard/xena/UROP2020.html and https://github.com/kbuzzard/xena . Does it mean I simply create a new Github repo, add a .lean and a .md then it's published (I guess not)? #### Jalex Stark (May 16 2020 at 03:41): my guess is that kevin meant that you could give him the text of a blog, he would lightly edit and then post it for you #### Jalex Stark (May 16 2020 at 03:41): this is what most bloggers mean by guest post, I think #### Utensil Song (May 16 2020 at 03:45): Oh I see, thanks! #### Utensil Song (May 16 2020 at 03:56): Jalex Stark said: yeah your "calc" proof is really just "I found this in the library" So far I can only reduce it to: theorem not_not' (P : Prop) : ¬ (¬ P) → P := begin cases (classical.em P) with hp hnp, { intro hnnp, exact hp, }, { intro hnnp, exfalso, apply hnnp, exact hnp } end theorem not_not_not_calc (P : Prop) : ¬ ¬ ¬ P → ¬ P := calc ¬ ¬ ¬ P → ¬ P : not_not' (¬ P) #### Jalex Stark (May 16 2020 at 04:05): my best guess is that you would have more fun moving on from here and doing more math (or thinking more about the presentation, if you're trying to make a blog post) #### Jalex Stark (May 16 2020 at 04:06): you extracted almost as much pedagogical material as there is in those two examples #### Utensil Song (May 16 2020 at 05:16): My current goal is to formalize Real Spinorial Groups ( https://www.amazon.com/Real-Spinorial-Groups-Mathematical-SpringerBriefs-ebook/dp/B07QPPTK7B ) in Lean . There's a long way to go from here. #### Jalex Stark (May 16 2020 at 05:19): cool! I remember someone saying something about lie groups recently, if you use the search functionality you may find it #### Utensil Song (May 16 2020 at 05:19): The motivation of this post is mostly that I wonder the pros and cons of these four styles and how to best combine their strength after I read quite a few proofs in Mathlib and Zulip . #### Jalex Stark (May 16 2020 at 05:20): I think the easiest way to make progress on that question is to write a bunch of a proofs :slight_smile: #### Utensil Song (May 16 2020 at 05:21): Yes, I noticed that topic and the not-yet-PRed progress on manifold. #### Utensil Song (May 16 2020 at 08:39): Utensil Song said: Kevin Buzzard said: Utensil Song you'd be welcome to write a guest Xena project blog post based on your post Thank you! But I couldn't figure out how to post a guest Xena project blog after reading https://xenaproject.wordpress.com/ , http://wwwf.imperial.ac.uk/~buzzard/xena/UROP2020.html and https://github.com/kbuzzard/xena . Does it mean I simply create a new Github repo, add a .lean and a .md then it's published (I guess not)? Just joined the Discord. #### Utensil Song (May 20 2020 at 04:59): Just an update: moving on from these trivial proposition as @Jalex Stark suggested makes me noticed many new elements of interacting with Lean. I would like to do a due survey of different tutorials already available before I actually turn this into a blog post. Specifically I want to make sure I know my target audience and the expectation (the tone in my original post is very unstable, and detail levels are varying, that's part of the reason). My personal motivation of such an enriched blog would be describing the subtle reactions/feeling/expectation/struggling when one first start interacting with Lean (I might lose the touch very quickly when I learn more about Lean). When self studying I find it very helpful to read multiple literature simultaneously to have a multi-dimensional perspective (since one such literature has to choose a linear path to organize the materials and facilitate the recognition process). What I've learned so far is a mixture of The Hitchhiker’s Guide to Logical Verification (noticed from https://lean-forward.github.io/ , skimmed in one night, the very reason I started learning Lean), TPIL (doing walkthrough and experimenting) and Logic and Proof(Had to read it in full to deal with exercises from Ch. 3 of TPIL with a clear understanding of the machinery involved) and this Zulip chat. But I haven't tried the games (N, R, Group) and the tutorial as well as mathematics_in_lean. #### Jalex Stark (May 20 2020 at 05:01): I think the thing you already wrote is pretty much ready to be a blog post, and I think the main reason it's exciting is that it gives insight into the very beginning of the process of learning Lean #### Jalex Stark (May 20 2020 at 05:02): you should definitely keep learning Lean, and definitely keep writing about it if you want #### Jalex Stark (May 20 2020 at 05:03): but the writing you already produced is valuable and "updating it" with more of a literature search might be a mistake #### Utensil Song (May 20 2020 at 05:19): Jalex Stark said: but the writing you already produced is valuable and "updating it" with more of a literature search might be a mistake Yeah I get that and will try not to pollute it with the update #### Utensil Song (May 20 2020 at 05:27): Anyway, I put the source of the original post at https://github.com/utensil/lean-playground/blob/master/posts/four_proof_styles.md for the time being. Last updated: May 14 2021 at 05:20 UTC	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32546159625053406, "perplexity": 3511.1393805466796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991648.40/warc/CC-MAIN-20210514060536-20210514090536-00039.warc.gz"}
https://www.gradesaver.com/textbooks/math/trigonometry/trigonometry-10th-edition/chapter-7-review-exercises-page-343/10	## Trigonometry (10th Edition) Since $b \gt a$, the angle which subtends $b$ must be larger than the angle which subtends $a$. However, then the sum of $A$ and $B$ is greater than $180^{\circ}$, so no triangle exists satisfying the given values. $A = 140^{\circ}$ $a = 5$ $b = 7$ Since $b \gt a$, the angle which subtends $b$ must be larger than the angle which subtends $a$. That is: $B \gt A$. However, then the sum of $A$ and $B$ is greater than $180^{\circ}$, so no triangle exists satisfying the given values.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9935345649719238, "perplexity": 193.22842519470942}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824448.53/warc/CC-MAIN-20181213032335-20181213053835-00152.warc.gz"}
http://mathhelpforum.com/algebra/111509-quadratic-formula-complex-roots.html	1. ## Quadratic formula for complex roots This is a bit embarrassing. I am using the quadratic formula to obtain two complex roots and for the life of me I can not get the answer posted on the solution sheet. Could someone please take a look and see if I am wrong or, perhaps, the answer sheet is? Thanks much, Frostking (3 - x) multiplied by -- (1 - x) + 8 = 0 - x^2 + 4x + 5 = 0 When I use the quadratic I get 2 +/- - i = 2 +/- i I am suppose to get 1 +/- 2i I know I am going to say how stupid can I be but......I do not know where I am going wrong!!! 2. Originally Posted by Frostking This is a bit embarrassing. I am using the quadratic formula to obtain two complex roots and for the life of me I can not get the answer posted on the solution sheet. Could someone please take a look and see if I am wrong or, perhaps, the answer sheet is? Thanks much, Frostking (3 - x) multiplied by -- (1 - x) + 8 = 0 - x^2 + 4x + 5 = 0 When I use the quadratic I get 2 +/- - i = 2 +/- i I am suppose to get 1 +/- 2i I know I am going to say how stupid can I be but......I do not know where I am going wrong!!! Working backwards, if the answer is $x = 1\pm2i$ then the question must have been "((3 – x) multiplied by –(1 + x)) + 8 = 0". Check that you copied the question correctly.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9004688858985901, "perplexity": 271.7509548942034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886133449.19/warc/CC-MAIN-20170824101532-20170824121532-00037.warc.gz"}
http://www.sciforums.com/threads/light-is-a-measure-of-mass-not-velocity.2591/page-4	# light is a measure of mass not velocity Discussion in 'Physics & Math' started by ada, Feb 27, 2001. 1. ### NietzscheHimselfBannedBanned Messages: 867 W=.9+.9/(1+.9.9/c^2) W=1.8/1.81=.9944 I believe that was the answer I gave. What answer did you get? 3. ### TachBannedBanned Messages: 5,265 According to your post you calculated $w(.8,1)$, no? 5. ### NietzscheHimselfBannedBanned Messages: 867 I also calculated (.1,.7) and (.4,4) after I gave my original answer for (.9,.9) I also posted some words which I'm not entirely certain you read. 7. ### TachBannedBanned Messages: 5,265 w(.1,.7) is not the same thing as w(.4,.4), so you should not be surprised that you get different results. The reason you are thrown by this is that you are still adding the speeds in Galilean fashion : 0.1+0.7=0.4+0.4 Neither is w(.9,.9) the same thing as w(.8,1), so you should expect the differences. Actually, it does but you need to understand what the formula really means. 8. ### NietzscheHimselfBannedBanned Messages: 867 Incorrect assumption. The only part i done Galilean was (0,.8). (.1,.7)=.8/(1+.1.7/c^2)=.7477 .7477-.058=.6897 I left it relatively easy to check my work. Correct they are different numbers. But their differences are the same number. 9. ### TachBannedBanned Messages: 5,265 That wasn't the point. It makes no sense to try to compare w(.9,.9) with w(.8,1). It makes no sense to compare w(.1,.7) with w(.4,.4) (as you tried). Totally irrelevant. 10. ### AlexGLike nailing Jello to a treeValued Senior Member Messages: 4,304 Tach, you'll be asked a simple question, and you'll go into an intricate math derivation and never answer the simple question. Trust me now, if you were to just say yes or no, I'd believe you. 11. ### AlexGLike nailing Jello to a treeValued Senior Member Messages: 4,304 You would do the same thing posting as Trout. It's massive mathematical overkill. 12. ### TachBannedBanned Messages: 5,265 In order to learn physics you need to learn math, there is no way around it. 13. ### AlexGLike nailing Jello to a treeValued Senior Member Messages: 4,304 Yes, I know that. But a simple yes or no to a yes or no question would save a lot of time. 14. ### NietzscheHimselfBannedBanned Messages: 867 obviously because I found different numbers... But unlike most people who can blindly accept anything, my mind only accepts sound reasoning. Which we are yet to fully establish. 15. ### DywyddyrPenguinaciously duckalicious.Valued Senior Member Messages: 19,228 I'll go along with that. Although, given the evidence so far, it's rather hard to establish that your mind accepts sound reasoning. You seem to specialise in supposition, wishful thinking and woo-wooism. 16. ### TachBannedBanned Messages: 5,265 As explained, there is no simple "yes" or "no" since your question did not make sense. This is why you really need to learn math before you attempt to formulate the question. There is no way around it. 17. ### TachBannedBanned Messages: 5,265 What Dywyddyr said. 18. ### NietzscheHimselfBannedBanned Messages: 867 Really now? I guess this is what I get for asking simple questions. Nihil answers. My wishful thinking should hopefully inspire some actual thought. More than ill concieved, trite insults will arrouse. If your going to insult someone, try to make it true or atleast appear true out of some stretch of the immagination. That way they actually have something to work on or think they have something to work on. You can show (or not show) that you can work an equation, but what is really important is the reason behind the equation. The reason the equation was made in the first place. The reason you all seem to have forgotten... 19. ### TachBannedBanned Messages: 5,265 You have received detailed answers. The problem is that you either can't or you refuse to understand. 20. ### NietzscheHimselfBannedBanned Messages: 867 Here is your problem. Tho you may have given the correct answer you have unfortunately left out any reason behind this assumption, which makes the whole of your argument incorrect. 21. ### DywyddyrPenguinaciously duckalicious.Valued Senior Member Messages: 19,228 Really. It wasn't meant as an insult; it was an observation. And you appear to be capable of neither "working" the equation nor understanding the reasoning behind it. 22. ### TachBannedBanned Messages: 5,265 I have already explained to you why there is no point in trying to compare w(.1,.7) with w(.4,.4). Do you understand why? 23. ### NietzscheHimselfBannedBanned Messages: 867 More like: "I can't follow your reasoning, because you didn't give one, therefore it is incorrect". Which is more or less what I said the first time... Congratulations you have worked yourself "full circle" and forgotten the very reason for which you are arguing. Evidence. Incorrect assumption. You told me there is no point in trying to compare these and appear to be using that open statement as your "why".	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7408556938171387, "perplexity": 1762.0396117543166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711394.73/warc/CC-MAIN-20221209080025-20221209110025-00494.warc.gz"}
http://openstudy.com/updates/4ff32432e4b01c7be8c6cd77	## A community for students. Sign up today Here's the question you clicked on: 55 members online • 0 replying • 0 viewing ## angela210793 4 years ago @satellite73 Delete Cancel Submit • This Question is Closed 1. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 \|dw:1341334653707:dw\| 2. anonymous • 4 years ago Best Response You've already chosen the best response. 0 ick i think the idea is to write the denominator as a single trig function 3. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 :O i thought maybe to split and take 2 fractions O.o 4. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 but idk how to do tht -_- 5. anonymous • 4 years ago Best Response You've already chosen the best response. 0 it is going to be $$5\sin(x+\theta)$$ but i don't see a nice form for $$\theta=\tan^{-1}(\frac{4}{3})$$ 6. anonymous • 4 years ago Best Response You've already chosen the best response. 0 actually it doesn't matter because $$\theta$$ is a constant also i made a mistake, it is $$5\sin(x-\theta)$$ still no matter 7. anonymous • 4 years ago Best Response You've already chosen the best response. 0 i don't think there is a snappier way to do this. let me think for a second 8. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 okok 9. anonymous • 4 years ago Best Response You've already chosen the best response. 0 ok no i can't think of a better way, and also i tried wolfram and what a disaster what you need to know is $a\sin(x)+b\cos(x)=\sqrt{a^2+b^2}\sin(x+\theta)$ where $$tan(\theta)=\frac{b}{a}$$ 10. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 hmmmm....suppose i know tht....how to use it O.o 11. anonymous • 4 years ago Best Response You've already chosen the best response. 0 well then it is easy, especially if you have a table of integrals this becomes $\frac{1}{5}\int\csc\left(x-\tan^{-1}(\frac{4}{3})\right)$ 12. anonymous • 4 years ago Best Response You've already chosen the best response. 0 don't worry about the arctan part, that is a number 13. anonymous • 4 years ago Best Response You've already chosen the best response. 0 so all you need to do is look up the anti derivative of cosecant and you are done 14. anonymous • 4 years ago Best Response You've already chosen the best response. 0 here is a video explanation http://www.youtube.com/watch?v=STUh3ni4l50 15. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 hmmmm....we've never use secant...wht is it? 16. anonymous • 4 years ago Best Response You've already chosen the best response. 0 cosecant it is the reciprocal of sine 17. anonymous • 4 years ago Best Response You've already chosen the best response. 0 integral is $\int csc(x)dx=-\ln(\cot(x)+\csc(x))$ if you have not used this i really have no idea how you are supposed to do this problem maybe multiply top and bottom by the conjugate? 18. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 :/....ok.. thank you Sir :D 19. anonymous • 4 years ago Best Response You've already chosen the best response. 0 maybe we can get some help i will repost there might be a snappy trick 20. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 okk 21. anonymous • 4 years ago Best Response You've already chosen the best response. 0 maybe myininaya has a snappy way multiply top and bottom by $$3\sin(x)+4\cos(x)$$ maybe? 22. myininaya • 4 years ago Best Response You've already chosen the best response. 1 I don't know @satellite73 I like what you did. 23. anonymous • 4 years ago Best Response You've already chosen the best response. 0 ok then i will stick to that. thanks 24. myininaya • 4 years ago Best Response You've already chosen the best response. 1 I actually think what sat did was probably the most snappiest thing you can do for this type of integral 25. anonymous • 4 years ago Best Response You've already chosen the best response. 0 If we replace sinx by 2tan(x/2)/(1 + tan^2(x/2), 26. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 sec=1/cosx???? 27. myininaya • 4 years ago Best Response You've already chosen the best response. 1 yes @angela210793 sec(x)=1/(cos(x)) csc(x)=1/(sin(x)) 28. angela210793 • 4 years ago Best Response You've already chosen the best response. 0 ok....thanks guys :D 29. anonymous • 4 years ago Best Response You've already chosen the best response. 0 $\huge sinx = \frac{2\tan \frac{x}{2}}{1+ \tan^2\frac{x}{2}}$ $\huge cosx = \frac{1 - \tan^2\frac{x}{2}}{1+ \tan^2\frac{x}{2}}$ 30. Not the answer you are looking for? Search for more explanations. • Attachments: #### Ask your own question Sign Up Find more explanations on OpenStudy Privacy Policy ## Your question is ready. Sign up for free to start getting answers. ##### spraguer (Moderator) 5→ View Detailed Profile 23 • Teamwork 19 Teammate • Problem Solving 19 Hero • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999550580978394, "perplexity": 7072.969221819722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823387.9/warc/CC-MAIN-20160723071023-00194-ip-10-185-27-174.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/116469/as-cohen-macaulay-algebras-and-dualizing-complexes?answertab=oldest	# AS Cohen Macaulay algebras and dualizing complexes Let $A$ be an $\mathbb N$-graded algebra such that $A_0 = k$ is a field. This are usually called graded connected algebras. One can define a torsion functor with respect to the ideal $\mathfrak m = \bigoplus_{i \geq 1} A_i$, setting for any graded $A$ module $M$ $$\Gamma_{\mathfrak m}(M) = \{m \in M \| A_{\geq i}m = 0 \mbox{ for } i \gg 0 \} \cong \varinjlim_i Hom_A(A/A_{\geq i},M).$$ The derived functors of $\Gamma_{\mathfrak m}$ are the local cohomology functors with respect to $\mathfrak m$, and are denoted by $H^i_\mathfrak m$. As in the commutative case, there is a natural isomorphism $$H_\mathfrak m(-) \cong \varinjlim Ext_A^i(A/A_{\geq i}, -)$$ We say $A$ is • AS Cohen Macaulay if there is a natural number $n$ such that $H_\mathfrak m^i (A) = H_\mathfrak m(A^{op}) = 0$. Let us call $n$ the local dimension of the module $A$ (I'm not sure this is standard notation) • AS Gorenstein if it has finite injective dimension $n$ both as a right and left module, and furthermore $Ext_A^n(k,A) = k$, once again on both sides. This are generalizations of ye olde condition of regularity for graded connected algebras introduced by Artin and Schelter, hence the AS. If $A$ is commutative and noetherian, then they are equivalent to their AS-less counterparts. (Maybe you can drop the noetherian hypothesis on this, but I'm not sure.) We have the usual implication chain AS regular $\Rightarrow$ AS Gorenstein $\Rightarrow$ AS Cohen Macaulay. By Groethendick's vanishing theorem, if $A$ is a noetherian Cohen Macaulay algebra of local dimension $n$, then $H^i_\mathfrak m \equiv 0$ for $i > n$. Question 1: Is this result still true for noncommutative noetherian AS Cohen Macaulay algebras? The result is true for noetherian AS Gorenstein algebras, as explained in this paper by Yekutieli and Zhang, Corollary 4.3. The argument comes basically from the fact that AS Gorenstein algebras have balanced dualizing complexes, almost by definition. This brings me to my Question 2: Are there AS Cohen Macaulay algebras without (balanced or unbalanced) dualizing complexes? Thanks! - FYI, when doing brace brackets you need to put two backslashes before them or they don't show up. It's some quirk of MathJax. Anyway I fixed it. – MTS Dec 15 '12 at 22:18 Thanks! I spent some time playing with it and couldn't get it right. – Pablo Zadunaisky Dec 16 '12 at 0:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9510771632194519, "perplexity": 417.9700821472242}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042991076.30/warc/CC-MAIN-20150728002311-00050-ip-10-236-191-2.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/work-with-velocity-and-force.715740/	# Work with velocity and force • #1 gcharles_42 11 0 ## Homework Statement A box of mass 49 kg is initially at rest on a flat floor. The coefficient of kinetic friction between the box and the floor is 0.60. A woman pushes horizontally against the box with a force of 628 N until the box attains a speed of 3 m/s. What is the work done by the woman on the box? and What is the CM-work done by the friction force on the box? ## Homework Equations W=F (delata x) & W(f)= uN (delta x) ## The Attempt at a Solution Since work is in joules, I tried calculating it by multiplying force by velocity squared but that gave me a wrong answer. If I had the right answer for work I'd solve for delta x and use that to solve for work of friction • #2 Yosty22 185 4 Try to think Kinematics: You know the mass, you know that it starts from rest, and you know the box's final speed. • #3 gcharles_42 11 0 Also CM-work is center of mass right? not centimeter? • #4 Yosty22 185 4 I believe so, yes. • #5 gcharles_42 11 0 vf^2 = vo^2 + 2(a) d? seems to be what I'm looking for maybe. Do I use F=ma to splve for a? so 3^2 = 2 (d) 628/49. making d = 441/1256? so W= 628 (441/1256) = 220.5 • #6 Yosty22 185 4 I believe you can use f=ma to solve for acceleration. From there, use a kinematics equation to solve for distance in the x direction. Then you can multiply that by the force to solve for work. • #7 gcharles_42 11 0 But that's the KE, they're not the same are they? • #8 gcharles_42 11 0 So delta KE is 220.5, work by woman 220.5, and work by the force of friction = (u)mg (d) = .6(9.8)49( 441/1256) = 101.1631... ? Is that right? • #9 Staff Emeritus Homework Helper 12,798 1,670 But that's the KE, they're not the same are they? That's why dimensional analysis is so handy. Energy and work have the same derived units: W = (ML^2/T^2) If you apply dimensional analysis to your original supposition that W = FV^2, you would see that F = ML/T^2 and V^2 = L^2/T^2, so W = ML^3/T^4, which isn't even close to the correct W = M*L^2/T^2 • #10 gcharles_42 11 0 Yeah, I didn't use that supposition. I used vf^2 = vo^2 + 2(a) d instead to find distance... I just want to know if my answers for work of the woman and of the friction force are correct? • Last Post Replies 5 Views 3K • Last Post Replies 2 Views 738 • Last Post Replies 1 Views 2K • Last Post Replies 3 Views 2K • Last Post Replies 2 Views 686 • Last Post Replies 4 Views 5K • Last Post Replies 1 Views 2K • Last Post Replies 3 Views 2K • Last Post Replies 37 Views 13K • Last Post Replies 7 Views 4K	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8453113436698914, "perplexity": 2054.597659186798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571959.66/warc/CC-MAIN-20220813142020-20220813172020-00585.warc.gz"}
https://socratic.org/questions/how-do-you-graph-f-x-ln-x-1-2	Precalculus Topics # How do you graph f(x)=ln (x-1)+2? Feb 14, 2017 The standard graph of $\ln x$ shifted +1 unit on the x axis and +2 units on the y axis. #### Explanation: $f \left(x\right) = \ln \left(x - 1\right) + 2$ If $x ' = x - 1 \to x = x ' + 1$ Then: $f \left(x '\right) = \ln x + 2$ Hence: $f \left(x\right)$ is $\ln x$ shifted +1 unit on the x axis and +2 units on the y axis. This is shown by the the grapg of $f \left(x\right)$ below: graph{ln(x-1)+2 [-3.04, 16.96, -3.92, 6.08]} ##### Impact of this question 784 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.617307186126709, "perplexity": 3305.471156767755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371609067.62/warc/CC-MAIN-20200405181743-20200405212243-00177.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-p-prerequisites-section-p-7-rational-expressions-p-7-exercises-page-52/89	## College Algebra 7th Edition $\frac{y\sqrt{3}-y\sqrt{y}}{3-y}$ We simplify the fraction by multiplying through by $\sqrt{3}-\sqrt{y}$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \frac{y}{\sqrt{3}+\sqrt{y}}=\frac{y}{\sqrt{3}+\sqrt{y}} \displaystyle \frac{\sqrt{3}-\sqrt{y}}{\sqrt{3}-\sqrt{y}}=\frac{y(\sqrt{3}-\sqrt{y})}{3-y}=\frac{y\sqrt{3}-y\sqrt{y}}{3-y}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9840986728668213, "perplexity": 190.872017417164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589222.18/warc/CC-MAIN-20180716060836-20180716080836-00336.warc.gz"}
http://mathoverflow.net/questions/42882/sub-hopf-algebras-of-group-algebras	# Sub-Hopf algebras of group algebras Let $k$ be a field and $G$ a finite group. Is every sub-Hopf algebra over $k$ of the group algebra $k[G]$ of the form $k[U]$ for a subgroup $U$ of $G$ ? - Yes: The dual $H^$ is a quotient algebra of $k[G]$, and the latter is the commutative function algebra $\{f:G \to k\}$. Thus $H = k[U]$ for a set $U$, and closure under multiplication then makes $U$ a group. The nice thing about finite-dimensional Hopf algebras over a field: You can turn them upside down. Vector space duality is an involution on finite-dimensional Hopf algebras. (But I think that this particular argument still works in the infinite-dimensional case: $k[G]^$ has a weak-* topology and $H^*$ is a quotient by a closed ideal, so it should still create $U$.) - Nice argument. Thanks – Ralph Oct 20 '10 at 11:44 Moreover, finiteness of $G$ is irrelevant as Greg's proof works there as well. BTW, you don't need to go into $H^\ast$ if you are willing to use coalgebras: any subcoalgebra of $k[G]$ is $k[U]$ for some subset of $G$. $U$ must be a subgroup for the subco to be subHopf... A more interesting question is to ask about forms of $k[G]$, i.e. Hopf algebras over a subfield $m$ such that $k\otimes_m H \cong k[G]$. There are a plenty of those which are not group subalgebras!! - Forms of $k[G]$ are complementary to the work of Ahmad Chalabi, who studied the behavior of $k[G]$ under field extensions. So, better to look for those than for weapons of mass destruction. – Greg Kuperberg Oct 20 '10 at 11:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.930250883102417, "perplexity": 228.43066098735355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644065306.42/warc/CC-MAIN-20150827025425-00262-ip-10-171-96-226.ec2.internal.warc.gz"}
https://www.taxcontroversy360.com/tag/separate-taxable-income/	In Guidant LLC f.k.a. Guidant Corporation, and Subsidiaries, et al. v. Commissioner, 146 T.C. No. 5 (Feb. 29, 2016), the taxpayer filed a motion seeking partial summary judgment on the ground that the Internal Revenue Service’s (IRS’s) transfer pricing adjustments were “arbitrary, capricious and unreasonable” as a matter of law. Judge David Laro denied the motion, ruling that “whether the Commissioner abused his discretion … depends on the facts and circumstances of a given case.” The taxpayer’s motion thus presented “a question of fact that should be resolved on the basis of the trial record.” The case involves transfer pricing adjustments under Section 482 that increased the income of Guidant Corporation and its U.S. subsidiaries by nearly \$3.5 billion. Section 482 grants the IRS broad discretion to “distribute, apportion, or allocate gross income, deductions, credits, or allowances” between or among controlled enterprises if it determines that such a re-allocation is “necessary in order to prevent evasion of taxes or clearly to reflect the income” of any of the enterprises. A taxpayer that challenges a Section 482 adjustment has a “dual burden.” First, it must show that the IRS’s adjustments are “arbitrary, capricious, and unreasonable.” The taxpayer must then show that its intercompany transactions reflect arm’s-length dealing. (more…)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8565105199813843, "perplexity": 15877.72161333758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948817.15/warc/CC-MAIN-20230328073515-20230328103515-00078.warc.gz"}
https://www.gwern.net/Coin-flip	# The Kelly Coin-Flipping Game: Exact Solutions via Decision Trees Decision-theoretic analysis of how to optimally play Haghani & Dewey 2016's 300-round double-or-nothing coin-flipping game with an edge and ceiling better than using the Kelly Criterion. Computing and following an exact decision tree increases earnings by $6.6 over a modified KC. topics: statistics, decision theory, Haskell, NN, Python, shell, R, C, C++, Bayes created: 19 Jan 2017; modified: 27 Mar 2019; status: finished; confidence: likely; Haghani & Dewey 2016 experiment with a double-or-nothing coin-flipping game where the player starts with$25 and has an edge of 60%, and can play 300 times, choosing how much to bet each time, winning up to a maximum ceiling of $250. Most of their subjects fail to play well, earning an average$91, compared to Haghani & Dewey 2016’s heuristic benchmark of ~$240 in winnings achievable using a modified Kelly Criterion as their strategy. The KC, however, is not optimal for this problem as it ignores the ceiling and limited number of plays. We solve the problem of the value of optimal play exactly by using decision trees & dynamic programming for calculating the value function, with implementations in R, Haskell, and C. We also provide a closed-form exact value formula in R & Python, several approximations using Monte Carlo/random forests/neural networks, visualizations of the value function, and a Python implementation of the game for the OpenAI Gym collection. We find that optimal play yields$246.61 on average (rather than ~$240), and so the human players actually earned only 36.8% of what was possible, losing$155.6 in potential profit. Comparing decision trees and the Kelly criterion for various horizons (bets left), the relative advantage of the decision tree strategy depends on the horizon: it is highest when the player can make few bets (at b=23, with a difference of ~$36), and decreases with number of bets as more strategies hit the ceiling. In the Kelly game, the maximum winnings, number of rounds, and edge are fixed; we describe a more difficult generalized version in which the 3 parameters are drawn from Pareto, normal, and beta distributions and are unknown to the player (who can use Bayesian inference to try to estimate them during play). Upper and lower bounds are estimated on the value of this game. In the variant of this game where subjects are not told the exact edge of 60%, a Bayesian decision tree approach shows that performance can closely approach that of the decision tree, with a penalty for 1 plausible prior of only$1. Two deep reinforcement learning agents, DQN & DDPG, are implemented but DQN fails to learn and DDPG doesn’t show acceptable performance, indicating better deep RL methods may be required to solve the generalized Kelly game. # Background ## Set up The paper “Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin”, by Haghani & Dewey 2016 runs an economics/psychology experiment on optimal betting in a simple coin-flipping game: What would you do if you were invited to play a game where you were given $25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61 young, quantitatively trained men and women to play this game. The results, in a nutshell, were that the majority of these 61 players didn’t place their bets very well, displaying a broad panoply of behavioral and cognitive biases. About 30% of the subjects actually went bust, losing their full$25 stake. We also discuss optimal betting strategies, valuation of the opportunity to play the game and its similarities to investing in the stock market. The main implication of our study is that people need to be better educated and trained in how to approach decision making under uncertainty. If these quantitatively trained players, playing the simplest game we can think of involving uncertainty and favourable odds, didn’t play well, what hope is there for the rest of us when it comes to playing the biggest and most important game of all: investing our savings? In the words of Ed Thorp, who gave us helpful feedback on our research: “This is a great experiment for many reasons. It ought to become part of the basic education of anyone interested in finance or gambling.” More specifically: …Prior to starting the game, participants read a detailed description of the game, which included a clear statement, in bold, indicating that the simulated coin had a 60% chance of coming up heads and a 40% chance of coming up tails. Participants were given $25 of starting capital and it was explained in text and verbally that they would be paid, by check, the amount of their ending balance subject to a maximum payout. The maximum payout would be revealed if and when subjects placed a bet that if successful would make their balance greater than or equal to the cap. We set the cap at$250…Participants were told that they could play the game for 30 minutes, and if they accepted the $25 stake, they had to remain in the room for that amount of time.5 Participants could place a wager of any amount in their account, in increments of$0.01, and they could bet on heads or tails…Assuming a player with agile fingers can put down a bet every 6 seconds, that would allow 300 bets in the 30 minutes of play. ## Near-optimal play The authors make a specific suggestion about what near-optimal play in this game would be, based on the Kelly criterion which would yield bets each round of 20% of capital: The basic idea of the Kelly formula is that a player who wants to maximize the rate of growth of his wealth should bet a constant fraction of his wealth on each flip of the coin, defined by the function , where is the probability of winning. The formula implicitly assumes the gambler has log utility. It’s intuitive that there should be an optimal fraction to bet; if the player bets a very high fraction, he risks losing so much money on a bad run that he would not be able to recover, and if he bet too little, he would not be making the most of what is a finite opportunity to place bets at favorable odds…We present the Kelly criterion as a useful heuristic a subject could gainfully employ. It may not be the optimal approach for playing the game we presented for several reasons. The Kelly criterion is consistent with the bettor having log-utility of wealth, which is a more tolerant level of risk aversion than most people exhibit. On the other hand, the subjects of our experiment likely did not view $25 (or even$250) as the totality of their capital, and so they ought to be less risk averse in their approach to maximizing their harvest from the game. The fact that there is some cap on the amount the subject can win should also modify the optimal strategy…In our game, the Kelly criterion would tell the subject to bet 20% () of his account on heads on each flip. So, the first bet would be $5 (20% of$25) on heads, and if he won, then he’d bet $6 on heads (20% of$30), but if he lost, he’d bet $4 on heads (20% of$20), and so on. …If the subject rightly assumed we wouldn’t be offering a cap of more than $1,000 per player, then a reasonable heuristic would be to bet a constant proportion of one’s bank using a fraction less than the Kelly criterion, and if and when the cap is discovered, reducing the betting fraction further depending on betting time remaining to glide in safely to the maximum payout. For example, betting 10% or 15% of one’s account may have been a sound starting strategy. We ran simulations on the probability of hitting the cap if the subject bet a fixed proportion of wealth of 10%, 15% and 20%, and stopping when the cap was exceeded with a successful bet. We found there to be a 95% probability that the subjects would reach the$250 cap following any of those constant proportion betting strategies, and so the expected value of the game as it was presented (with the $250 cap) would be just under$240. However, if they bet 5% or 40% of their bank on each flip, the probability of exceeding the cap goes down to about 70%. This game is interesting as a test case because it is just easy enough to solve exactly on a standard computer in various ways, but also hard enough to defeat naive humans and be nontrivial. ## Subjects’ performance Despite the Kelly criterion being well-known and fairly intuitive, and the game being very generous, participants did not perform well: The sample was largely comprised of college age students in economics and finance and young professionals at finance firms. We had 14 analyst and associate level employees at two leading asset management firms. The sample consisted of 49 males and 12 females. Our prior was that these participants should have been well prepared to play a simple game with a defined positive expected value…Only 21% of participants reached the maximum payout of $250,7 well below the 95% that should have reached it given a simple constant percentage betting strategy of anywhere from 10% to 20%.8 We were surprised that one third of the participants wound up with less money in their account than they started with. More astounding still is the fact that 28% of participants went bust and received no payout. That a game of flipping coins with an ex-ante 60/40 winning probability produced so many subjects that lost everything is startling. The average ending bankroll of those who did not reach the maximum and who also did not go bust, which represented 51% of the sample, was$75. While this was a tripling of their initial $25 stake, it still represents a very sub-optimal outcome given the opportunity presented. The average payout across all subjects was$91, letting the authors off the hook relative to the $250 per person they’d have had to pay out had all the subjects played well. This is troubling because the problem is so well-defined and favorable to the players, and can be seen as a microcosm of the difficulties people experience in rational betting. (While it’s true that human subjects typically perform badly initially in games like the iterated prisoner’s dilemma and need time to learn, it’s also true that humans only have one life to learn stock market investment during, and these subjects all should’ve been well-prepared to play.) Instead of expected earnings of ~$240, the players earned $91 - forfeiting$149. However, if anything, the authors understate the underperformance, because as they correctly note, the Kelly criterion is not guaranteed to be optimal in this problem due to the potential for different utility functions (what if we simply want to maximize expected wealth, not log wealth?), the fixed number of bets & the ceiling, as the Kelly criterion tends to assume that wealth can increase without limit & there is an indefinite time horizon. # Optimality in the coin-flipping MDP Indeed, we can see with a simple example that KC is suboptimal in terms of maximizing expected value: what if we are given only 1 bet (b=1) to use our $25 on? If we bet 20% (or less) per the KC, then But if we bet everything: It’s true that 40% of the time, we go bankrupt and so we couldn’t play again… but there are no more plays in b=1 so avoiding bankruptcy boots nothing. We can treat this coin-flipping game as a tree-structured Markov decision process. For more possible bets, the value of a bet of a particular amount given a wealth w and bets remaining b-1 will recursively depend on the best strategy for the two possible outcomes (weighted by probability), giving us a Bellman value equation to solve like: To solve this equation, we can explore all possible sequences of bets and outcomes to a termination condition and reward, and then work use backwards induction, defining a decision tree which can be (reasonably) efficiently computed using memoization/dynamic programming. Given the problem setup, we can note a few things about the optimal strategy: 1. if the wealth ever reaches$0, the game has effectively ended regardless of how many bets remain, because betting $0 is the only possibility and it always returns$0 2. similarly, if the wealth ever reaches the upper bound of $250, the optimal strategy will effectively end the game by always betting$0 after that regardless of how many bets remain, since it can’t do better than $250 and can only do worse. These two shortcuts will make the tree much easier to evaluate because many possible sequences of bet amounts & outcomes will quickly hit$0 or $250 and require no further exploration. 3. a state with more bets is always of equal or better value than fewer 4. a state with more wealth is always equal or better value than less 5. the value of 0 bets is the current wealth 6. the value of 1 bet depends on the ceiling and current wealth: whether$250 is >2x current wealth. If the ceiling more than twice current wealth, the optimal strategy with 1 bet left is to bet everything, since that has highest EV and there’s no more bets to worry about going bankrupt & missing out on. # Implementation of Game A Python implementation is available in OpenAI Gym: import gym env = gym.make('KellyCoinflip-v0') env.reset() env._step(env.wealth1000.2) # bet with 20% KC # ... env._reset() # end of game, start a new one, etc ## Decision tree We can write down the value function as a mutual recursion: f calculates the expected value of the current step, and calls V to estimate the value of future steps; V checks for the termination conditions w=$0/$250 & b=0 returning current wealth as the final payoff, and if not, calls f on every possible action to estimate their value and returns the max… This mutual recursion bottoms out at the termination conditions. As defined, this is grossly inefficient as every node in the decision tree will be recalculated many times despite yielding identical deterministic, referentially transparent results. So we need to memoize results if we want to evaluate much beyond b=5. ### Approximate Value function Implemented in R: # devtools::install_github("hadley/memoise") library(memoise) f <- function(x, w, b) { 0.6mV(min(w+x,250), b-1) + 0.4mV(w-x, b-1)} mf <- memoise(f) V <- function(w,b) { returns <- if (b>0 && w>0 && w<250) { sapply(seq(0, w, by=0.1), function(x) { mf(x,w,b) }) } else { w } max(returns) } mV <- memoise(V) ## sanity checks: mV(25, 0) == 25 && mV(25, 1) == 30 && mV(0, 300) == 0 Given our memoized value function mV we can now take a look at expected value of optimal betting for bets b from 0 to 300 with the fixed starting payroll of $25. Memoization is no panacea, and R/memoise is slow enough that I am forced to make one change to the betting: instead of allowing bets in penny/$0.01 increments, I approximate by only allowing bets in $1 increments, to reduce the branching factor to a maximum of 250 possible choices each round rather than 25000 choices. (Some comparisons with decipenny and penny trees suggests that this makes little difference since early on the bet amounts are identical and later on being able to make <$1 adjustments to bets yield small gains relative to total wealth; see the Haskell implementation.) Of course, even with memoization and reducing the branching factor, it’s still difficult to compute the value of the optimal strategy all the way to b=300 because the exponentially increasing number of strategies still need to be computed at least once. With this R implementation, trees for up to b=150 can be computed with 4GB RAM & ~16h. The value function for increasing bets: vs <- sapply(1:150, function(b) { round(mV(25, b), digits=1) }); vs # [1] 30.0 36.0 43.2 45.4 48.0 53.7 54.6 57.6 61.8 62.6 66.8 68.2 70.6 74.1 75.0 79.1 79.7 82.5 84.7 86.2 89.8 90.3 93.8 # [24] 94.5 97.0 98.8 100.3 103.2 103.9 107.2 107.6 110.3 111.4 113.3 115.2 116.4 119.0 119.6 122.4 122.9 125.3 126.2 128.1 129.5 130.8 132.8 # [47] 133.6 136.0 136.5 138.8 139.4 141.4 142.3 143.8 145.2 146.3 148.0 148.8 150.6 151.3 153.1 153.8 155.5 156.3 157.7 158.8 159.9 161.2 162.1 # [70] 163.6 164.2 165.8 166.4 167.9 168.5 169.9 170.7 171.8 172.8 173.7 174.8 175.6 176.8 177.5 178.7 179.3 180.5 181.1 182.3 182.9 184.0 184.7 # [93] 185.6 186.4 187.2 188.1 188.8 189.8 190.3 191.3 191.9 192.8 193.4 194.3 194.9 195.7 196.3 197.1 197.8 198.4 199.1 199.7 200.5 201.0 201.8 # [116] 202.3 203.0 203.5 204.3 204.8 205.4 206.0 206.6 207.1 207.7 208.3 208.8 209.4 209.9 210.5 210.9 211.5 211.9 212.5 213.0 213.5 213.9 214.5 # [139] 214.9 215.4 215.8 216.3 216.8 217.2 217.6 218.0 218.5 218.9 219.3 219.7 So as the number of bets escalates, our expected payoff increases fairly quickly and we can get very close to the ceiling of $250 with canny betting. #### Monte Carlo tree evaluation If we do not have enough RAM to expand the full decision tree to its terminal nodes, there are many ways to approximate it. A simple one is to expand the tree as many levels far down as possible, and then if a terminal node is reached, do exact backwards induction, otherwise, at each pseudo-terminal node, approximate the value function somehow and then do backwards induction as usual. The deeper the depth, the closer the approximation becomes to the exact value, while still doing optimal planning within the horizon. One way to approximate it would be to run a large number of simulations (perhaps 100) taking random actions until a terminal node is hit, and take the mean of the total values as the estimate. This would be a Monte Carlo tree evaluation. (This forms the conceptual basis of the famous MCTS/Monte Carlo tree search.) A random policy is handy because it can be used anywhere, but here we already know a good heuristic which does better than random: the KC. So we can use that instead. This gives us as much optimality as we can afford. Setting up a simulation of the coin-flipping game which can be played with various strategies: game <- function(strategy, wealth, betsLeft) { if (betsLeft>0) { bet <- strategy(wealth, betsLeft) wealth <- wealth - bet flip <- rbinom(1,1,p=0.6) winnings <- 2betflip wealth <- min(wealth+winnings, 250) return(game(strategy, wealth, betsLeft-1)) } else { return(wealth); } } simulateGame <- function(s, w=25, b=300, iters=100) { mean(replicate(iters, game(s, w, b))) } kelly <- function(w, b) { 0.20 * w } smarterKelly <- function(w, b) { if(w==250) {0} else { (20.6-1) w } } random <- function(w, b) { sample(seq(0, w, by=0.1), 1) } evaluate <- function(w,b) { simulateGame(smarterKelly, w, b) } mevaluate <- memoise(evaluate) mevaluate(25, 10) # [1] 35.30544906 mevaluate(25, 100) # [1] 159.385275 mevaluate(25, 300) # [1] 231.4763619 As expected the KC can do well and is just as fast to compute as a random action, so using it will give much better estimates of the value function for free. With the Monte Carlo value function set up, the original value function can be slightly modified to include a maximum depth parameter and to evaluate using the MC value function instead once that maximum depth is hit: f <- function(x, w, b, maxDepth) { 0.6mV(min(w+x,250), b-1, maxDepth) + 0.4mV(w-x, b-1, maxDepth)} mf <- memoise(f) V <- function(w,b, maxDepth) { if (b<=(b-maxDepth)) { mevaluate(w,b) } else { returns <- if (b>0 && w>0 && w<250) { sapply(seq(0, w, by=0.1), function(x) { mf(x,w,b, maxDepth) }) } else { w } max(returns) }} mV <- memoise(V) mV(25, 300, 100); mV(25, 300, 50) ### Optimal next action One is also curious what the optimal strategy is, not just how much we can make with the optimal strategy given a particular starting point. As defined, I can’t see how to make mV return the optimal choices along the way, since it has to explore all choices bottom-up and can’t know what is optimal until it has popped all the way back to the root, and state can’t be threaded in because that defeats the memoization. But then I remembered the point of computing value functions: given the (memoized) value function for each state, we can then plan by simply using V in a greedy planning algorithm by asking, at each step, for the value of each possible action (which is memoized, so it’s fast), and returning/choosing the action with the maximum value (which takes into account all the downstream effects, including our use of V at each future choice): VPplan <- function(w, b) { if (b==0) { return (0); } else { returns <- sapply(seq(0, w), function(wp) { mf(wp, w, b); }) return (which.max(returns)-1); } } mVPplan <- memoise(VPplan) ## sanity checks: mVPplan(250, 0) # [1] 0 mVPplan(250, 1) # [1] 0 mVPplan(25, 3) # [1] 25 It’s interesting that when b is very small, we want to bet everything on our first bet, because there’s not enough time to bother with recovering from losses; but as we increase b, the first bet will shrink & become more conservative: firstAction <- sapply(1:150, function(b) { mVPplan(25, b) }); firstAction # [1] 25 25 25 10 10 18 17 18 14 14 14 9 10 11 7 11 7 10 10 10 9 6 9 7 9 8 9 8 7 8 7 8 7 8 7 8 7 7 7 7 7 6 7 6 7 6 7 # [48] 6 6 6 6 6 6 6 6 6 6 6 6 5 6 5 6 5 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 5 4 5 4 5 4 # [95] 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 # [142] 4 3 4 3 4 3 3 3 3 ### Optimizing The foregoing is interesting but the R implementation is too slow to examine the case of most importance: b=300. The issue is not so much the intrinsic difficulty of the problem - since the R implementation’s RAM usage is moderate even at b=150, indicating that the boundary conditions do indeed tame the exponential growth & turn it into something more like quadratic growth - but the slowness of computing. Profiling suggests that most of the time is spent inside memoise: # redefine to clear out any existing caching: forget(mV) Rprof(memory.profiling=TRUE, gc.profiling=TRUE, line.profiling=TRUE) mV(w=25, b=9) Rprof(NULL) summaryRprof() Most of the time is spent in functions which appear nowhere in our R code, like lapply or deparse, which points to the behind-the-scenes memoise. Memoization should be fast because the decision tree can be represented as nothing but a multidimensional array in which one does lookups for each combination of w/b for a stored value V, and array lookups ought to be near-instantaneous. But apparently there is enough overhead to dominate our decision tree’s computation. R does not provide native hash tables; what one can do is use R’s “environments” (which use hash tables under the hood), but are restricted to string keys (yes, really) as a poor man’s hash table by using digest to serialize & hash arbitrary R objects into string keys which can then be inserted into an ‘environment’. (I have since learned that there is a hashmap library which is a wrapper around a C++ hashmap implementation which should be usable: Nathan Russell’s hashmap.) The backwards induction remains the same and the hash-table can be updated incrementally without any problem (useful for switching to alternative methods like MCTS), so the rewrite is easy: ## crude hash table library(digest) ## digest's default hash is MD5, which is unnecessarily slower, so use a faster hash: d <- function (o) { digest(o, algo="xxhash32") } lookup <- function(key) { get(d(key), tree) } set <- function(key,value) { assign(envir=tree, d(key), value) } isSet <- function(key) { exists(d(key), envir=tree) } ## example: tree <- new.env(size=1000000, parent=emptyenv()) set(c(25,300), 50); lookup(c(25, 300)) # [1] 50 tree <- new.env(size=1000000, parent=emptyenv()) f <- function(x, w, b) { 0.6V(min(w+x,250), b-1) + 0.4V(w-x, b-1) } V <- function(w, b) { if (isSet(c(w,b))) { return(lookup(c(w,b))) } else { returns <- if (b>0 && w>0 && w<250) { sapply(seq(0, w, by=0.1), function(x) { f(x,w,b) }) } else { return(w) } set(c(w,b), max(returns)) return(lookup(c(w,b))) } } V(25,5) While the overhead is not as bad as memoise, performance is still not great. #### Python Unmemoized version (a little different due to floating point): import numpy as np # for enumerating bet amounts as a float range def F(w, x, b): return 0.6V(min(w+x,250), b-1) + 0.4V(w-x, b-1) def V(w, b): if b>0 and w>0 and w<250: bets = np.arange(0, w, 0.1).tolist() returns = [F(w,x,b) for x in bets] else: returns = [w] return max(returns) V(25,0) V(25,0) # 25 V(25,1) # 29.98 V(25,2) # 35.967999999999996 V(25,3) Python has hash-tables built in as dicts, so one can use those: import numpy as np def F(w, x, b, dt): return 0.6V(min(w+x,250), b-1, dt) + 0.4V(w-x, b-1, dt) def V(w, b, dt): if b>0 and w>0 and w<250: if (w,b) in dict: return dict[(w,b)] else: bets = np.arange(0, w, 0.1).tolist() returns = [F(w,x,b,dt) for x in bets] else: returns = [w] best = max(returns) dict[(w,b)] = best return best dict = {} V(25, 0, dict) # 25 #### Haskell Gurkenglas provides an inscrutably elegant & fast version of the value function which works in GHCi: (!!25)$ (!!300) $(iterate [0..250])$ \nextutilities -> (0:) $(++[250])$ tail $init$ map maximum $(zipWith . zipWith) (\up down -> 0.6 * up + 0.4 * down) (tail$ tails nextutilities) (map reverse $inits nextutilities) -- 246.2080494949234 -- it :: (Enum a, Fractional a, Ord a) => a -- (7.28 secs, 9,025,766,704 bytes) Noting: iterate f x = x : iterate f (f x) doesn’t need to think much about memoization. From right to left, the line reads “Given how much each money amount is worth when n games are left, you can zip together that list’s prefixes and suffixes to get a list of options for each money amount at (n+1) games left. Use the best for each, computing the new utility as a weighted average of the previous. At 0 and 250 we have no options, so we must manually prescribe utilities of 0 and 250. Inductively use this to compute utility at each time from knowing that at the end, money is worth itself. Look at the utilites at 300 games left. Look at the utility of$25.” Inductively generating that whole list prescribes laziness. Since it’s Haskell, we can switch to compiled code and use fast arrays. Implementations in Haskell have been written by Gurkenglas & nshepperd using array-memoize & Data.Vector (respectively): import System.Environment (getArgs) import Data.Function (iterate) import Data.Function.ArrayMemoize (arrayMemo) type Wealth = Int type EV = Double cap :: Wealth cap = 250 value :: [Wealth -> EV] value = iterate f fromIntegral where f next = arrayMemo (0, cap) $\x -> maximum [go w \| w <- [0..min (cap - x) x]] where go w = 0.6 * next (min cap (x+w)) + 0.4 * next (x-w) main :: IO () main = do [x, b] <- map read <$> getArgs print $value !! b$ x The second one is more low-level and uses laziness/“tying the knot” to implement the memoization; it is the fastest and is able to evaluate memo 25 300 in <12s: the value turns out to be $246. (If we assume that all games either end in$250 or $0, then this implies that or >98.4% of decision-tree games hit the max, as compared to Haghani & Dewey’s estimate that ~95% of KC players would.) The memoization is done internally, so to access all values we do more logic within the lexical scope. import System.Environment (getArgs) import Data.Function (fix) import Data.Function.Memoize (memoFix2) import Data.Vector (Vector) import qualified Data.Vector as V (generate, (!)) import qualified Data.MemoUgly as U (memo) type Wealth = Int type Bets = Int type EV = Double cap :: Wealth cap = 250 value :: (Wealth -> Bets -> EV) -> Wealth -> Bets -> EV value next 0 b = 0 value next w 0 = fromIntegral w value next w b = maximum [go x \| x <- [0..min (cap - w) w]] where go x = 0.6 * next (min cap (w+x)) (b-1) + 0.4 * next (w-x) (b-1) -- There are 4 possible ways aside from 'array-memoize': -- 1. Direct recursion. direct :: Wealth -> Bets -> EV direct = fix value -- 2. Memoised recursion. memo :: Wealth -> Bets -> EV memo w b = cached_value w b where cached_value w b = table V.! b V.! w table :: Vector (Vector EV) table = V.generate (b + 1) (\b -> V.generate (cap + 1) (\w -> value cached_value w b)) -- 3. Memoised recursion using 'memoize' library; slower. memo2 :: Wealth -> Bets -> EV memo2 = memoFix2 value -- 4. Memoize using 'memoize-ugly' library; also slower but global memo3 :: Wealth -> Bets -> EV memo3 = U.memo . direct main :: IO () main = do [w, b] <- map read <$> getArgs print (memo w b) We can obtain all values with a function like memo3 :: [Wealth] -> [Bets] -> [EV] memo3 ws bs = zipWith cached_value ws bs where cached_value w b = table V.! b V.! w table :: Vector (Vector EV) table = V.generate (maximum bs + 1) (\b -> V.generate (cap + 1) (\w -> value cached_value w b)) and evaluate: λ> map round (memo3 (repeat 25) [1..300]) -- [30,36,43,45,48,54,55,58,62,63,67,68,71,74,75,79,80,82,85,86,90,90,94,94,97,99,100, -- 103,104,107,108,110,111,113,115,116,119,120,122,123,125,126,128,130,131,133,134, -- 136,136,139,139,141,142,144,145,146,148,149,151,151,153,154,155,156,158,159,160, -- 161,162,164,164,166,166,168,169,170,171,172,173,174,175,176,177,177,179,179,181, -- 181,182,183,184,185,186,186,187,188,189,190,190,191,192,193,193,194,195,196,196, -- 197,198,198,199,200,200,201,202,202,203,204,204,205,205,206,207,207,208,208,209, -- 209,210,210,211,212,212,213,213,214,214,214,215,215,216,216,217,217,218,218,219, -- 219,219,220,220,221,221,221,222,222,222,223,223,224,224,224,225,225,225,226,226, -- 226,227,227,227,228,228,228,228,229,229,229,230,230,230,230,231,231,231,231,232, -- 232,232,232,233,233,233,233,234,234,234,234,234,235,235,235,235,236,236,236,236, -- 236,236,237,237,237,237,237,238,238,238,238,238,238,239,239,239,239,239,239,239, -- 240,240,240,240,240,240,240,241,241,241,241,241,241,241,241,242,242,242,242,242, -- 242,242,242,242,243,243,243,243,243,243,243,243,243,243,244,244,244,244,244,244, -- 244,244,244,244,244,244,245,245,245,245,245,245,245,245,245,245,245,245,245,245, -- 246,246,246,246,246,246,246,246,246,246,246,246,246] ### Exact value function We could go even further with zip [1..3000] (memo3 (repeat 25) [1..3000]) (which takes ~118s). Interestingly, the value stops increasing around b=2150 (V=249.99009946798637) and simply repeats from there; it does not actually reach 250. This is probably because with a stake of $25 it is possible to go bankrupt (gambler’s ruin) even betting the minimal fixed amount of$1. (The original Haskell code is modeled after the R, which discretized this way for tractability; however, since the Haskell code is so fast, this is now unnecessary.) If this is the case, then being able to bet smaller amounts should allow expected value to converge to $250 as exactly as can be computed, because the probability of going bankrupt after 2500 bets of$0.01 each is effectively zero - as far as R and Haskell will compute without special measures, . We can go back and model the problem exactly as it was in the paper by simply multiply everything by 100 & interpreting in pennies: cap = 25000 -- 250100 -- ... λ> zip [1..3000] (memo3 (repeat (25100)) [1..3000]) [(1,3000.0),(2,3600.0),(3,4320.0),(4,4536.000000000002),(5,4795.200000000003), (6,5365.440000000002),(7,5458.752000000004),(8,5757.350400000005),(9,6182.853120000005),(10,6260.488704000007), (11,6676.137676800007),(12,6822.331453440009),(13,7060.11133132801),(14,7413.298296422411),(15,7499.673019514893), (16,7913.219095166989),(17,7974.777338678492),(18,8250.07680018581),(19,8471.445742115113),(20,8625.387566014524), (21,8979.7747405993),(22,9028.029532170909),(23,9384.523360172316),(24,9449.401095461177),(25,9699.670042282964), (26,9882.821122181414),(27,10038.471393315525),(28,10323.078038637072),(29,10394.862038743217),(30,10760.507349554608), (31,10763.85850433795),(32,11040.414570571116),(33,11141.364854687306),(34,11337.607662912955),(35,11524.013477359924), (36,11648.117264906417),(37,11909.035644688667),(38,11968.56153182668),(39,12294.156320547045),(40,12296.062638839443), (41,12554.172237535688),(42,12628.174503649356),(43,12820.701630209007),(44,12962.820770637838),(45,13095.979243218648), (46,13298.241837094192),(47,13377.799870378874),(48,13632.949691989288),(49,13664.245374230446),(50,13935.591599024072), (51,13953.650302164471),(52,14168.318904539414),(53,14244.57145315508),(54,14407.574739209653),(55,14535.761032800987), (56,14651.76990919319),(57,14826.143029982914),(58,14899.500923102909),(59,15114.7924517843),(60,15149.530755496799), (61,15399.983335449066),(62,15400.771450460255),(63,15604.908915203496),(64,15652.268440952908),(65,15813.476931576255), (66,15903.186446379666),(67,16025.159151461572),(68,16152.79680966944),(69,16238.976728976708),(70,16400.466139297678), (71,16454.05880056233),(72,16645.646128447275),(73,16669.63235112316),(74,16880.735724497223),(75,16885.012958972715), (76,17058.916142797243),(77,17099.596358241968),(78,17239.339510457277),(79,17312.850756552616),(80,17421.275332110683), (81,17524.309847338853),(82,17604.068867939182),(83,17733.56645905442),(84,17787.13463287746),(85,17940.266786525535), (86,17969.95038247786),(87,18144.105153480315),(88,18152.051576292564),(89,18315.336828409476),(90,18333.026286703964), (91,18467.997509430665),(92,18512.510521892633),(93,18621.43451689773),(94,18690.183932686265),(95,18775.180977557586), (96,18865.765874427907),(97,18928.817685066606),(98,19039.0117965317),(99,19081.969208988696),(100,19209.70993405155), (101,19234.300290845116),(102,19377.678277281033),(103,19385.51250899971),(104,19524.210291319585),(105,19535.341194745335), (106,19651.63659936918),(107,19683.55258264968),(108,19779.19175398216),(109,19829.94117896368),(110,19906.559349360658), (111,19974.327332744302),(112,20033.4549154762),(113,20116.554995203987),(114,20159.623419373274),(115,20256.489653646044), (116,20284.836941737507),(117,20394.01642719967),(118,20408.892517902153),(119,20529.038285622184),(120,20531.61013289084), (121,20639.865300258658),(122,20652.830860566657),(123,20744.14900653099),(124,20772.415137446053),(125,20848.093322557295), (126,20890.24116222975),(127,20951.49506668366),(128,21006.203412595118),(129,21054.171837601196),(130,21120.21127127963), (131,21155.960430614512),(132,21232.187753960352),(133,21256.71536121999),(134,21342.06833189189),(135,21356.30748944987), (136,21449.7998427048),(137,21454.622738748447),(138,21545.893033861896),(139,21551.56090345761),(140,21629.60553083633), (141,21647.034539300425),(142,21712.842497605183),(143,21740.96793155338),(144,21795.467123757197),(145,21833.2961358927), (146,21877.356736609778),(147,21923.964087187007),(148,21958.401746908596),(149,22012.92577178374),(150,22038.504663866137), (151,22100.143459100647),(152,22117.579175397976),(153,22185.586988586107),(154,22195.549289624447),(155,22269.23310835155), (156,22272.348533907876),(157,22343.200726693787),(158,22347.9192078922),(159,22408.92268721723),(160,22422.211687202966), (161,22474.09110290414),(162,22495.183774650206),(163,22538.619509420547),(164,22566.800095953415),(165,22602.430698828903), (166,22637.031537177958),(167,22665.456036220217),(168,22705.854721234122),(169,22727.634820414445),(170,22773.2515209447), (171,22788.913686133077),(172,22839.208606334214),(173,22849.246045182404),(174,22903.71702393249),(175,22908.591564315902), (176,22966.44249475668),(177,22966.915677569094),(178,23017.91541566918),(179,23024.18913098028),(180,23068.1913376925), (181,23080.387557725626),(182,23117.90218718125),(183,23135.491081806776),(184,23166.99717629234),(185,23189.48394853381), (186,23215.431334191013),(187,23242.35418014611),(188,23263.165077204263),(189,23294.093255008785),(190,23310.163806371635), (191,23344.695808912184),(192,23356.397530793947),(193,23394.159357087876),(194,23401.840515265318),(195,23442.484035635396), (196,23446.47095075504),(197,23489.640293583914),(198,23490.270646383346),(199,23529.46834312825),(200,23533.224741609163), (201,23567.312697440484),(202,23575.321437418483),(203,23604.666095269786),(204,23616.551745369172),(205,23641.497567737664), (206,23656.90925341186),(207,23677.779921209272),(208,23696.38990746728),(209,23713.489458166325),(210,23734.991807798215), (211,23748.60571568506),(212,23772.71501926872),(213,23783.111220502426),(214,23809.56139463541),(215,23816.991259707916), (216,23845.534410064567),(217,23850.233666149958),(218,23880.639012115425),(219,23882.82861769509),(220,23914.391375329913), (221,23914.76844952492),(222,23942.714790600083),(223,23946.0474787004),(224,23970.438187949254),(225,23976.66184026535), (226,23997.74934793851),(227,24006.60933420138),(228,24024.631040582935),(229,24035.889282584474),(230,24051.068374275732), (231,24064.50239633),(232,24077.048621078735),(233,24092.450650947027),(234,24102.561052984205),(235,24119.737170755707), (236,24127.59678851838),(237,24146.366121052237),(238,24152.148649090945),(239,24172.342607735227),(240,24176.211024526496), (241,24197.672583935127),(242,24199.779747244538),(243,24222.35471729034),(244,24222.851974583486),(245,24243.93438158678), (246,24245.42607879143),(247,24263.972996501543),(248,24267.50154423283),(249,24283.6900658947),(250,24289.078871384656), (251,24303.07565677869),(252,24310.159487219513),(253,24322.121319078917),(254,24330.74566159496),(255,24340.819980440137), (256,24350.840429290023),(257,24359.165841053073),(258,24370.447517349417),(259,24377.154275094566),(260,24389.571277415347), (261,24394.781738403053),(262,24408.216622744527),(263,24412.045682031203),(264,24426.388969625325),(265,24428.94447133704), (266,24444.09418292577),(267,24445.477310292874),(268,24461.32346887292),(269,24461.644170708976),(270,24476.42136455785), (271,24477.445726085083),(272,24490.501181704694),(273,24492.883289818776),(274,24504.335944986862),(275,24507.958757514363), (276,24517.920620087607),(277,24522.6745531501),(278,24531.251041416166),(279,24537.03357887482),(280,24544.32387659046), (281,24551.039168217816),(282,24557.136561611253),(283,24564.69504250772),(284,24569.687240115927),(285,24578.005270307505), (286,24581.974706479406),(287,24590.97422968356),(288,24593.998352542163),(289,24603.606573136858),(290,24605.75811775705), (291,24615.907195034095),(292,24617.254442557904),(293,24627.881197714756),(294,24628.488224763427),(295,24639.274079225856), (296,24639.46077884001),(297,24649.128469095107),(298,24650.173797856685),(299,24658.72751316172),(300,24660.629317974468) ... (1884,24999.999999999614),(1885,24999.99999999963),(1886,24999.999999999643),(1887,24999.999999999658),(1888,24999.99999999967), (1889,24999.99999999968),(1890,24999.999999999694),(1891,24999.9999999997),(1892,24999.999999999716),(1893,24999.999999999727), (1894,24999.999999999738),(1895,24999.99999999975),(1896,24999.99999999976),(1897,24999.999999999767),(1898,24999.99999999978), (1899,24999.99999999979),(1900,24999.9999999998),(1901,24999.99999999981),(1902,24999.999999999818),(1903,24999.999999999825), (1904,24999.999999999833),(1905,24999.999999999844),(1906,24999.999999999854),(1907,24999.99999999986),(1908,24999.99999999987), (1909,24999.999999999876),(1910,24999.999999999884),(1911,24999.99999999989),(1912,24999.999999999898),(1913,24999.999999999905), (1914,24999.999999999913),(1915,24999.99999999992),(1916,24999.999999999924),(1917,24999.999999999927),(1918,24999.999999999935), (1919,24999.99999999994),(1920,24999.99999999995),(1921,24999.99999999995),(1922,24999.999999999956),(1923,24999.999999999964), (1924,24999.999999999967),(1925,24999.99999999997),(1926,24999.999999999978),(1927,24999.999999999978),(1928,24999.999999999985), (1929,24999.99999999999),(1930,24999.999999999993),(1931,24999.999999999993),(1932,25000.0),(1933,25000.0), (1934,25000.0),(1935,25000.0),(1936,25000.0),(1937,25000.0),(1938,25000.0), (1939,25000.0),(1940,25000.0),(1941,25000.0),(1942,25000.0),(1943,25000.0), (1944,25000.0),(1945,25000.0),(1946,25000.0),(1947,25000.0),(1948,25000.0), (1949,25000) ... ] With the exact penny version, the value of b=300 is now $246.6062932 (taking ~3746s compiled), so the approximation costs an expected value of only$0.61. The full run reveals that convergence happens at b=1932 (which can be computed in ~48503s compiled), past which there is no need to compute further. #### C/C++ FeepingCreature provides a vectorized C implementation of the exact penny game that runs in a few minutes (benefiting ~13% from profile-guided optimization when compiled with GCC). He also notes that memoization/dynamic programming is overkill for this problem: because almost all states ultimately get evaluated, the dynamic programming doesn’t avoid evaluating many states. Since each state depends on an immediate successor and forms a clean tree, it is possible to calculate the tree much more directly by evaluating all the terminal nodes b=0, looping over the previous nodes b+1, then throwing away the no longer necessary b, and evaluating b+2, and so on; only two layers of the tree need to be stored at any time, which can potentially fit into on-processor cache & exhibit far better cache locality. Another advantage of this representation is parallelism, as each node in the upper layer can be evaluated independently. An implementation using OpenMP for threading can solve b=300 in ~8s: #include <stdlib.h> #include <stdio.h> #include <stdbool.h> #include <math.h> #define ROUND_LIMIT 300 #define MONEY_LIMIT 25000 #define MONEY_START 2500 #define MONEY_FACTOR 100.0f // #define DATATYPE float // #define F(X) X ## f #define DATATYPE double #define F(X) X // MEMOIZED METHOD typedef struct { bool known; DATATYPE ev; } CacheEntry; static DATATYPE decide(CacheEntry * const table, int money, int round) { if (round < 0) return money; if (money == 0 \|\| money == MONEY_LIMIT) return money; int index = round * (MONEY_LIMIT + 1) + money; // int index = money * ROUND_LIMIT + round; if (table[index].known) return table[index].ev; DATATYPE best_bet_score = -1; for (int bet = 0; bet <= money; bet++) { DATATYPE winres = decide(table, (money + bet > MONEY_LIMIT) ? MONEY_LIMIT : (money + bet), round - 1); DATATYPE loseres = decide(table, money - bet, round - 1); DATATYPE combined = F(0.6) * winres + F(0.4) * loseres; best_bet_score = F(fmax)(best_bet_score, combined); } table[index] = (CacheEntry) { true, best_bet_score }; return best_bet_score; } void method1() { CacheEntry table = calloc(sizeof(CacheEntry), ROUND_LIMIT (MONEY_LIMIT + 1)); printf("running.\n"); int best_bet = 0; DATATYPE best_bet_score = -1; for (int bet = 0; bet <= MONEY_START; bet++) { DATATYPE winres = decide(table, MONEY_START + bet, ROUND_LIMIT - 1); DATATYPE loseres = decide(table, MONEY_START - bet, ROUND_LIMIT - 1); DATATYPE combined = F(0.6) * winres + F(0.4) * loseres; if (combined > best_bet_score) { best_bet = bet; best_bet_score = combined; } } printf("first round: bet %f for expected total reward of %f\n", best_bet / MONEY_FACTOR, best_bet_score / MONEY_FACTOR); int count_known = 0; for (int i = 0; i < ROUND_LIMIT * (MONEY_LIMIT + 1); i++) { if (table[i].known) count_known ++; } printf("known: %i of %i\n", count_known, ROUND_LIMIT * (MONEY_LIMIT + 1)); } // BOTTOM-UP METHOD // given pass n in "from", compute pass n-1 in "to" static void propagate(DATATYPE from, DATATYPE to) { // for each money state... for (int a = 0; a < THREADS; a++) { // distribute workload so that inner loop passes are approximately equal // f(x) = 2x F(x) = x^2 = a/THREADS x = sqrt(a / THREADS) int low = (int) (MONEY_LIMIT * sqrtf((float)a / THREADS)); int high = (int) (MONEY_LIMIT * sqrtf((a + 1.0f) / THREADS)); if (a == THREADS - 1) high = MONEY_LIMIT + 1; // precise upper border for (int m = low; m < high; m++) { DATATYPE max_score = 0.0; // determine the bet that maximizes our expected earnings // to enable vectorization we break the loop into two so that each half only gets one branch of the conditional // DATATYPE winval = from[(m + b > MONEY_LIMIT) ? MONEY_LIMIT : (m + b)]; int high_inner = (m + m > MONEY_LIMIT) ? (MONEY_LIMIT - m) : m; for (int b = 0; b <= high_inner; b++) { DATATYPE winval = from[m + b]; DATATYPE loseval = from[m - b]; DATATYPE combined = F(0.6) * winval + F(0.4) * loseval; max_score = F(fmax)(max_score, combined); } for (int b = high_inner + 1; b <= m; b++) { DATATYPE winval = from[MONEY_LIMIT]; DATATYPE loseval = from[m - b]; DATATYPE combined = F(0.6) * winval + F(0.4) * loseval; max_score = F(fmax)(max_score, combined); } to[m] = max_score; } } } void method2() { DATATYPE buf = malloc(sizeof(DATATYPE) (MONEY_LIMIT + 1)); DATATYPE buf_to = malloc(sizeof(DATATYPE) (MONEY_LIMIT + 1)); // set up base case: making no bet, we have money of i for (int i = 0; i <= MONEY_LIMIT; i++) buf[i] = i; for (int i = ROUND_LIMIT - 1; i >= 0; i--) { propagate(buf, buf_to); DATATYPE temp = buf; buf = buf_to; buf_to = temp; } int best_bet = 0; DATATYPE best_bet_score = -1; for (int b = 0; b <= MONEY_START; b++) { DATATYPE winval = buf[MONEY_START + b]; DATATYPE loseval = buf[MONEY_START - b]; DATATYPE combined = 0.6 winval + 0.4 * loseval; if (combined > best_bet_score) { best_bet_score = combined; best_bet = b; } } printf("first round: bet %f for expected total reward of %f\n", best_bet / MONEY_FACTOR, best_bet_score / MONEY_FACTOR); } int main() { method2(); return 0; } Some quick benchmarking on my 2016 Lenovo ThinkPad P70 laptop with 4 physical cores & 8 virtual cores (Intel Xeon E3-1505M v5 Processor 8MB Cache / up to 3.70GHz) shows a roughly linear speedup from 1 to 3 threads and then small gains thereafter to a minimum of 7.2s with 8 threads: for C in ls coingame-.c; do gcc -Wall -Ofast -fwhole-program -march=native -fopenmp $C -o coingame -lm && echo "$C" && (for i in {1..10}; do /usr/bin/time -f '%e' ./coingame; done ); done For levels of parallelism on my laptop from 1-8 threads, the average times are: 28.98s/15.44s/10.70s/9.22s/9.10s/8.4s/7.66s/7.20s. Caio Oliveira provides a parallel C++ implementation using std::async; compiled with the same optimizations on (g++ -Ofast -fwhole-program -march=native -pthread --std=c++11 kc.cpp -o kc), it runs in ~1m16s: #include <iostream> #include <vector> #include <map> #include <set> #include <bitset> #include <list> #include <stack> #include <queue> #include <deque> #include <string> #include <sstream> #include <algorithm> #include <cstdio> #include <cstring> #include <future> #include <ctime> using namespace std; const int MAX_ROUND = 300; const int MAX_WEALTH = 25000; const int BETS_DELTA = 1; double memo[MAX_WEALTH + 1][2]; inline double vWin(int wealth, int bet, int roundIdx) { if(wealth + bet < MAX_WEALTH) { return memo[wealth + bet][!roundIdx]; } else { return MAX_WEALTH; } } inline double vLose(int wealth, int bet, int roundIdx) { if (wealth - bet == 0) { return 0; } else { return memo[wealth - bet][!roundIdx]; } } inline double v(int wealth, int bet, int roundIdx) { return .6 vWin(wealth, bet, roundIdx) + .4 * vLose(wealth, bet, roundIdx); } template<typename RAIter> void calc_round(RAIter beg, RAIter end, int roundIdx){ int len = distance(beg, end); if(len < 1000) { for(RAIter p = beg; p != end; ++p) { int wealth = distance(memo, p); (p)[roundIdx] = v(wealth, wealth, roundIdx); for (int bet = 0; bet < wealth; bet += BETS_DELTA) { memo[wealth][roundIdx] = max(memo[wealth][roundIdx], v(wealth, bet, roundIdx)); } } } else { RAIter mid = beg + len/2; future<void> handle = async(launch::async, calc_round<RAIter>, mid, end, roundIdx); calc_round(beg, mid, roundIdx); } } double calc_table() { bool roundIdx = 0; for(int i = 0; i <= MAX_WEALTH ; ++i) { memo[i][!roundIdx] = i; } for(int round = MAX_ROUND - 1; round >= 0; --round) { calc_round(memo, memo + MAX_WEALTH, roundIdx); roundIdx ^= 1; } return memo[2500][!roundIdx] / 100.; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); clock_t begin = clock(); double res = calc_table(); clock_t end = clock(); cout << "result: " << res << "(elapsed: " << (double(end - begin) / CLOCKS_PER_SEC) << ")" << endl; } Given the locality of the access patterns, I have to wonder how well a GPU implementation might perform. It doesn’t seem amenable to being expressed as a large matrix multiplication, but each GPU core could be responsible for evaluating a terminal node and do nearby lookups from there. (And the use in finance of GPUs to compute the lattice model/binomial options pricing model/trinomial tree, which are similar, suggests it should be possible.) #### Exact formula Arthur B. notes that “you can compute in if you allow bets to be any fraction of w. It’s piecewise linear, the cutoff points and slopes follow a very predictable pattern”1 and provides a formula for calculating the value function without constructing a decision tree: A short version in R: V <- function(w, b, m=250) { b <- round(b); # rounds left must be integer j <- qbinom(w/m, b, 0.5); 1.2^b 1.5^-j * (w + (m/2 * sum(1.5^(j:0) * pbinom(0:j-1,b,1/2)))) } (This is sufficiently fast for all values tested that it is not worth memoizing using the relatively slow memoise.) Re-implementing in Python is a little tricky because NumPy/SciPy use different names and Python doesn’t support R’s range notation, but the following seems like it works; and then with a value function, we can implement a planner to choose optimal betting amounts, memoize it with repoze.lru for time-savings over multiple games, and then it is simple to set up a Gym environment and start playing the Kelly coin-flip game optimally (and indeed usually reaching the $250 limit): from scipy.stats import binom import numpy as np from repoze.lru import lru_cache def V(w, b, m=250): if w>=250: return 250 if w<=0: return 0 if b==0: return w else: try: j = binom.ppf(float(w)/float(m), b, 0.5) return 1.2*b 1.5*-j (w + m/2 * sum(np.multiply(binom.cdf(map(lambda(x2):x2-1, range(0,int(j+1))),b,0.5), map(lambda(x): 1.5*x, list(reversed(range(0, int(j+1)))))))) except ValueError: print "Error:", (w,b,m) @lru_cache(None) def VPplan(w, b): # optimization: short-circuit if w<=0 or w>=250: return 0 else: if b==0: return w else: possibleBets = map(lambda(pb): float(pb)/100.0, range(0100,int((w100)+1),1)) returns = map(lambda(pb): 0.6V(w+pb, b-1) + 0.4V(w-pb,b-1), possibleBets) return float(returns.index(max(returns)))/100.0 import gym env = gym.make('KellyCoinflip-v0') ## play 500 games and calculate mean reward: rewards = [] for n in range(0,500): done = False reward = 0 while not done: w = env._get_obs()[0][0] b = env._get_obs()[1] bet = VPplan(w, b) results = env._step(bet100) print n, w, b, bet, "results:", results reward = reward+results[1] done = results[2] rewards.append(reward) env._reset() print sum(rewards)/len(rewards) # 247.525564356 #### Graphing the Value function What does the range of possible bets in each state look like? Does it look bitonic and like an inverted V one could do binary search on? We can sample some random states, compute all the possible bets, and plot them by index to see if the payoffs form curves: # return all actions' values instead of the max action: VPplans <- function(w, b) { if (b==0) { return (0); } else { returns <- sapply(seq(0, w), function(wp) { mf(wp, w, b); }) return(returns); } } plans <- data.frame() n <- 47 for (i in 1:n) { # omit the uninteresting cases of w=0/250 and b=0/300: w <- round(runif(n=1, 0+1, 250-1)) b <- round(runif(n=1, 0+1, 300-1)) plan <- VPplans(w,b) plans <- rbind(plans, data.frame(W=as.factor(w), B=as.factor(b), Bet=1:(length(plan)), Value=plan)) } library(ggplot2) p <- qplot(x=Bet, y=Value, data=plans) p + facet_wrap(~W) + geom_line(aes(x=Bet, y=Value, color=W), size = 1) + theme(legend.position = "none") For the most part they do generally follow a quadratic or inverted-V like shape, with the exception of several which wiggle up and down while following the overall curve (numeric or approximation error?). With an exact value function, we can also visualize it to get an idea of how the wealth/rounds interact and how difficult it would be to approximate it. We can generate many iterates, interpolate, and graph: n <- 50000 w <- runif(n, min=0, max=250) b <- sample(0:250, n, replace=TRUE) v <- unlist(Map(V, w, b)) df <- data.frame(Wealth=w, Rounds=b, Value=v) library(akima) library(plot3D) dfM <- interp(df$Wealth, df$Rounds, df$Value, duplicate="strip") par(mfrow=c(1,2), mar=0) persp(dfM$x, dfM$y, dfM$z, xlab="Wealth", ylab="Rounds left", zlab="Value", ticktype="detailed") scatter3D(df$Wealth, df$Rounds, df$Value, theta=-25, xlab="Wealth", ylab="Rounds left", zlab="Value", ticktype="detailed") #### Approximating the Exact Value Function The value function winds up looking simple, a smooth landscape tucked down at the edges, which is perhaps not too surprising, as the optimal betting patterns tend to be small amounts except when there are very few rounds left (and one should bet most or all of one’s wealth) or one is nearing the maximum wealth cap (and should very gradually glide in). A value function (or the policy function) computed by decision trees is bulky and hard to carry around, weighing perhaps gigabytes in size. Looking at this value function, it’s clear that we can do model distillation and easily approximate it by another algorithm like random forests or neural networks. (Usually, a NN has a hard time learning a value function because it’s a reinforcement learning problem where it’s unclear how actions are linked to rewards, but in this case, since we can already calculate it, it becomes the far easier setting of supervised learning in mapping a state to a value/policy.) A random forest works fine, getting 0.4 RMSE: library(randomForest) r <- randomForest(Value ~ Wealth + Rounds, ntree=1000, data=df); r # ... # Mean of squared residuals: 1.175970325 # % Var explained: 99.94 sqrt((predict(r) - df$Value)^2) # [1] 0.407913389 It can also be approximated with NN. For example, in R one can use MXNet and a 1x30 or 2x152 ReLu feedforward NN will solve it to <4 RMSE: ## very slow library(neuralnet) n <- neuralnet(Value ~ Wealth + Rounds, data=df, hidden=c(20,20)) # prediction(n) ## GPU-accelerated: library(mxnet) mx.set.seed(0) ## 2x30 ReLu FC NN for linear regression with RMSE loss: data <- mx.symbol.Variable("data") perLayerNN <- 30 fc1 <- mx.symbol.FullyConnected(data, name="fc1", num_hidden=perLayerNN) act1 <- mx.symbol.Activation(fc1, name="relu1", act_type="relu") fc2 <- mx.symbol.FullyConnected(act1, name="fc2", num_hidden=perLayerNN) act2 <- mx.symbol.Activation(fc2, name="relu2", act_type="relu") fc3 <- mx.symbol.FullyConnected(act2, name="fc2", num_hidden=perLayerNN) act3 <- mx.symbol.Activation(fc3, name="relu2", act_type="relu") finalFc <- mx.symbol.FullyConnected(act3, num_hidden=1) lro <- mx.symbol.LinearRegressionOutput(finalFc) model <- mx.model.FeedForward.create(lro, X=as.matrix(subset(df,select=c("Wealth","Rounds"))), y=df$Value, ctx=mx.gpu(), num.round=50000, learning.rate=5e-6, eval.metric=mx.metric.rmse, array.layout="rowmajor") Some experimenting with fitting polynomial regressions did not give any decent fits for less than 5 degrees, but probably some combination of logs and polynomials could compactly encode the value function. ### Simulation Performance The implementations here could be wrong, or decision trees not actually optimal like claimed. We can test it by directly comparing the performance in a simulation of the coin-flipping game, comparing the performance of mVPplan vs the 20% Kelly criterion and a simple bet-everything strategy: library(memoise) f <- function(x, w, b) { 0.6V(min(w+x,250), b-1) + 0.4V(w-x, b-1)} mf <- memoise(f) V <- function(w, b, m=250) { j <- qbinom(w/m,b,1/2); 1.2^b * 1.5^-j * (w+m/2 * sum(1.5^(j:0) * pbinom(0:j-1,b,1/2))) } VPplan <- function(w, b) { if (b==0) { return (0); } else { returns <- sapply(seq(0, w), function(wp) { mf(wp, w, b); }) return (which.max(returns)-1); } } mVPplan <- memoise(VPplan) game <- function(strategy, wealth, betsLeft) { if (betsLeft>0) { bet <- strategy(wealth, betsLeft) wealth <- wealth - bet flip <- rbinom(1,1,p=0.6) winnings <- 2betflip wealth <- min(wealth+winnings, 250) return(game(strategy, wealth, betsLeft-1)) } else { return(wealth); } } simulateGame <- function(s, w=25, b=300, iters=5000) { mean(replicate(iters, game(s, w, b))) } ## Various strategies (the decision tree strategy is already defined as 'mVPplan'): kelly <- function(w, b) { 0.20 * w } smarterKelly <- function(w, b) { if(w==250) {0} else { 0.2 * w } } maximizer <- function(w, b) { w; } smarterMaximizer <- function(w, b) { if(w>=250) { 0 } else {w}; } ## examining a sample of how wealth evolves over the course of a sample of b=300 games: library(parallel) library(plyr) i <- 56 games <- ldply(mclapply(1:i, function(ith) { b <- 300 wealth <- 25 wealths <- numeric(b) while (b>0) { bet <- mVPplan(wealth, b) wealth <- wealth-bet flip <- rbinom(1,1,p=0.6) winnings <- 2betflip wealth <- min(wealth+winnings, 250) wealths[b] <- wealth b <- b-1 } return(data.frame(Game=ith, Bets=300:1, Wealth=wealths)) } )) library(ggplot2) p <- qplot(x=Bets, y=Wealth, data=games) p + facet_wrap(~Game) + geom_line(aes(x=Bets, y=Wealth), size = 1) + theme(legend.position = "none") Simulating 56 games, we can see how while the optimal strategy looks fairly risky, it usually wins in the end: We can also examine how the strategy does for all the other possible horizons and compare with the Kelly. ## Comparing performance in the finite horizon setting up to b=300: bs <- 1:300 ldply(mclapply(bs, function(bets) { ky <- round(simulateGame(smarterKelly, b=bets), digits=1) dt <- round(simulateGame(mVPplan, b=bets), digits=1) gain <- dt-ky; print(paste(bets, round(V(25, bets), digits=2), dt, ky, gain)) } )) Simulating 5,000 games for each b: Total bets Value function Decision tree performance Kelly performance Difference 1 30 30.1 26 4.1 2 36 35.5 27 8.5 3 43.2 42.4 28.2 14.2 4 45.36 46 29.3 16.7 5 47.95 49.3 30.5 18.8 6 53.65 52.5 31.5 21 7 54.59 51.4 32.7 18.7 8 57.57 56.1 34.1 22 9 1.83 61.4 35.6 25.8 10 62.6 63 36.8 26.2 11 66.76 68.6 38.3 30.3 12 68.22 66.9 40.2 26.7 13 70.6 70.7 41.8 28.9 14 74.13 71.2 43.2 28 15 75 73.8 44.9 28.9 16 79.13 79.7 46.8 32.9 17 79.75 79.1 47.8 31.3 18 82.5 84.1 50.1 34 19 84.71 83.7 52.7 31 20 86.25 85.6 54.2 31.4 21 89.8 88.6 56.4 32.2 22 90.28 90.2 56.5 33.7 23 93.85 94.8 58.7 36.1 24 94.49 93.7 60.7 33 25 97 95 62.2 32.8 26 98.83 97.1 65.2 31.9 27 100.38 98.7 68.1 30.6 28 103.23 102.1 69.4 32.7 29 103.95 102.5 73.4 29.1 30 107.61 107.7 73.7 34 31 107.64 107.3 74.7 32.6 32 110.4 106.7 76.1 30.6 33 111.41 107.9 79.2 28.7 34 113.38 115.1 80.6 34.5 35 115.24 115.4 82.2 33.2 36 116.48 116.1 84.2 31.9 37 119.09 118.5 87.1 31.4 38 119.69 119.9 86 33.9 39 122.94 125.4 89.6 35.8 40 122.96 119.7 92 27.7 41 125.54 124.2 95.2 29 42 126.28 124.4 96.9 27.5 43 128.21 128.5 97.1 31.4 44 129.63 130.5 100.3 30.2 45 130.96 130.1 100 30.1 46 132.98 131.9 100.9 31 47 133.78 132.4 104.2 28.2 48 136.33 134.2 104.5 29.7 49 136.64 133.6 107.7 25.9 50 139.36 141.2 110.1 31.1 51 139.54 139.4 113.6 25.8 52 141.68 140 113 27 53 142.45 140.7 113.5 27.2 54 144.08 141.8 115.5 26.3 55 145.36 145 116.3 28.7 56 146.52 150.2 119.7 30.5 57 148.26 146.4 119.7 26.7 58 149 143.9 120.6 23.3 59 151.15 151.8 124.2 27.6 60 151.5 148.5 124.4 24.1 61 154.01 151.9 125.5 26.4 62 154.01 150.9 127.1 23.8 63 156.05 157.9 128.4 29.5 64 156.52 154.3 129.9 24.4 65 158.14 155.5 132.3 23.2 66 159.03 156.8 132.1 24.7 67 160.25 157.4 133.2 24.2 68 161.53 159.2 137.1 22.1 69 162.39 160.2 135.9 24.3 70 164 161 137.8 23.2 71 164.54 162.2 137.8 24.4 72 166.46 166.7 138.3 28.4 73 166.7 165.2 142.7 22.5 74 168.81 169 145 24 75 168.85 168.3 143.1 25.2 76 170.59 169.5 144.4 25.1 77 171 165.6 146.4 19.2 78 172.39 171.2 147.5 23.7 79 173.13 171.3 150.6 20.7 80 174.21 170.6 151.8 18.8 81 175.24 174 152.3 21.7 82 176.04 175.5 153.8 21.7 83 177.34 174.9 151.8 23.1 84 177.87 177.6 152.5 25.1 85 179.4 178.5 157.3 21.2 86 179.7 177.1 156 21.1 87 181.44 178.9 158.1 20.8 88 181.52 179.6 160.1 19.5 89 183.15 181.1 159 22.1 90 183.33 182.8 163.3 19.5 91 184.68 184.2 162.3 21.9 92 185.13 183.4 162.5 20.9 93 186.21 187.5 165.1 22.4 94 186.9 185.3 160.5 24.8 95 187.75 188.6 164.8 23.8 96 188.66 186.4 167.1 19.3 97 189.29 187.6 168 19.6 98 190.39 188.9 167.7 21.2 99 190.82 187.8 169.8 18 100 192.1 190.7 168.4 22.3 101 192.34 192.5 171.8 20.7 102 193.78 192.6 170 22.6 103 193.86 193.2 170.7 22.5 104 195.24 194.1 170 24.1 105 195.35 192.9 174.1 18.8 106 196.52 195.2 176.8 18.4 107 196.84 194.5 173.4 21.1 108 197.79 194.4 179.1 15.3 109 198.3 195.5 176 19.5 110 199.07 196.7 179.1 17.6 111 199.74 198.7 181.2 17.5 112 200.34 201.1 178.2 22.9 113 201.17 197.9 180.9 17 114 201.6 200.3 181.2 19.1 115 202.57 202 183.2 18.8 116 202.85 201.6 181 20.6 117 203.94 201.7 181.4 20.3 118 204.09 201.2 183.6 17.6 119 205.29 205.9 185 20.9 120 205.32 201.3 186.8 14.5 121 206.4 204 182.2 21.8 122 206.53 203.7 186.2 17.5 123 207.44 205.7 186.1 19.6 124 207.72 205.2 189.5 15.7 125 208.48 203.9 191.4 12.5 126 208.9 209.3 188 21.3 127 209.52 206.7 187.7 19 128 210.06 209.5 188.5 21 129 210.54 206.5 192.4 14.1 130 211.2 211.1 190.9 20.2 131 211.56 207.1 195.6 11.5 132 212.32 210.3 194 16.3 133 212.57 212.1 191.1 21 134 213.42 211 192.7 18.3 135 213.56 210.2 195.8 14.4 136 214.5 213.3 196.8 16.5 137 214.55 211.3 194.4 16.9 138 215.46 212 196.6 15.4 139 215.52 210.8 197.4 13.4 140 216.3 215.3 197 18.3 141 216.47 217.8 199.3 18.5 142 217.13 215.4 197.3 18.1 143 217.41 214.8 196.2 18.6 144 217.96 213.9 200.1 13.8 145 218.33 215.7 200.4 15.3 146 218.77 217.4 200.1 17.3 147 219.24 217.5 199.7 17.8 148 219.58 218.5 200.3 18.2 149 220.13 218.4 200.3 18.1 150 220.39 220.4 201.9 18.5 151 221 218.1 201.6 16.5 152 221.18 220.5 203.9 16.6 153 221.86 220.6 202.6 18 154 221.96 220.5 205.2 15.3 155 222.69 218.7 203.1 15.6 156 222.72 220.6 204.4 16.2 157 223.43 220.6 203.3 17.3 158 223.48 221.1 202.8 18.3 159 224.09 222.6 207.1 15.5 160 224.22 224.5 207.5 17 161 224.74 220.8 206 14.8 162 224.95 224.2 208.1 16.1 163 225.39 223.8 208 15.8 164 225.67 222.8 209 13.8 165 226.03 223.4 208.6 14.8 166 226.37 224 210 14 167 226.66 225.3 209.2 16.1 168 227.06 224.1 211.6 12.5 169 227.28 224.5 210.5 14 170 227.73 223.8 211 12.8 171 227.89 226.9 209.1 17.8 172 228.39 226 212.2 13.8 173 228.49 226 211.8 14.2 174 229.04 226.6 212.1 14.5 175 229.09 227.9 211.3 16.6 176 229.67 226.4 211.5 14.9 177 229.67 228 214 14 178 230.18 228.4 215.1 13.3 179 230.24 227.5 213.3 14.2 180 230.68 229.2 213.6 15.6 181 230.8 229.5 215 14.5 182 231.18 228.7 213.9 14.8 183 231.36 229.8 216 13.8 184 231.67 230.6 214.4 16.2 185 231.9 231 213.1 17.9 186 232.16 231.2 216.2 15 189 232.94 231.1 217.9 13.2 190 233.1 230.4 217.6 12.8 191 233.45 231.1 218.4 12.7 192 233.56 231.9 219 12.9 193 233.94 232.1 216.6 15.5 194 234.02 232 219.3 12.7 195 234.43 231.8 217.5 14.3 196 234.47 232.4 220.6 11.8 197 234.9 233.5 218.6 14.9 198 234.9 233 219.3 13.7 199 235.3 233.4 220.2 13.2 200 235.33 233.8 221.1 12.7 201 235.67 235.5 218.8 16.7 202 235.75 233 222 11 203 236.05 232.9 220.4 12.5 204 236.17 233.9 220.1 13.8 205 236.42 234.8 221 13.8 206 236.57 234.4 221.4 13 207 236.78 234.8 222.6 12.2 208 236.96 236.4 222.5 13.9 209 237.14 234.6 223.5 11.1 210 237.35 236.6 222.6 14 211 237.49 235.7 221.9 13.8 212 237.73 234.4 222.4 12 213 237.83 234.9 226 8.9 214 238.1 237.3 223.9 13.4 215 238.17 237 223.6 13.4 216 238.46 235.7 225.1 10.6 217 238.5 236.6 223.6 13 218 238.81 237 226.1 10.9 219 238.83 236.4 225 11.4 220 239.15 237.7 225.7 12 221 239.15 236.8 225.9 10.9 222 239.43 237.7 225.9 11.8 223 239.46 238.6 224.8 13.8 224 239.71 237.1 226.3 10.8 225 239.77 238.7 227.4 11.3 226 239.98 238.7 225.9 12.8 227 240.07 238 226.9 11.1 228 240.25 240.5 227.6 12.9 229 240.36 238.8 227.5 11.3 230 240.51 237.9 225.8 12.1 231 240.65 238.5 228.2 10.3 232 240.77 239.3 226.6 12.7 233 240.92 238.8 226.1 12.7 234 241.03 240.2 228.8 11.4 235 241.2 240.4 227.5 12.9 236 241.28 240 227.4 12.6 237 241.46 239.8 228 11.8 238 241.52 240.6 228.8 11.8 239 241.72 240.1 228.7 11.4 240 241.76 240.2 229.2 11 241 241.98 240.3 229.2 11.1 242 242 240.7 229.3 11.4 243 242.22 240.5 229.7 10.8 244 242.23 239.9 229.2 10.7 245 242.44 241.2 230.3 10.9 246 242.45 240.7 230.5 10.2 247 242.64 241.3 231.5 9.8 248 242.68 239.2 230.4 8.79 249 242.84 241.5 230.3 11.2 250 242.89 241.4 230.6 10.8 251 243.03 242.2 230.4 11.8 252 243.1 241.7 232.3 9.39 253 243.22 242.6 232.2 10.4 254 243.31 241 229.7 11.3 255 243.41 240.7 231.1 9.59 256 243.51 242.2 231 11.2 257 243.59 241 232.4 8.59 258 243.7 242.1 230.2 11.9 259 243.77 242 232.1 9.90 260 243.9 243.2 230.4 12.8 261 243.95 242.9 233.6 9.30 262 244.08 242.6 233.6 9 263 244.12 243 231.3 11.7 264 244.26 242.3 233.5 8.80 265 244.29 241.8 233.8 8 266 244.44 242.9 233.1 9.80 267 244.46 242.6 233.8 8.79 268 244.61 242.9 234 8.90 269 244.62 244 234.3 9.69 270 244.76 243.6 234.4 9.19 271 244.77 243.6 235 8.59 272 244.91 243.2 234.7 8.5 273 244.93 243.9 233.2 10.7 274 245.04 243.5 233.5 10 275 245.08 243.7 234.2 9.5 276 245.18 243.4 234.8 8.59 277 245.23 244.2 234.2 10 278 245.31 244.8 234.8 10 279 245.37 244.1 234.7 9.40 280 245.44 243.7 234.1 9.59 281 245.51 244.1 234 10.1 282 245.57 243.6 235.8 7.79 283 245.65 243.8 235.3 8.5 284 245.7 244 235 9 285 245.78 244.3 236.9 7.40 286 245.82 243.7 235 8.69 287 245.91 244.6 236.2 8.40 288 245.94 244.7 235.4 9.29 289 246.04 245.2 237.3 7.89 290 246.06 244.6 234.8 9.79 291 246.16 243.8 235.6 8.20 292 246.17 244.8 236.2 8.60 293 246.28 244.6 236.2 8.40 294 246.29 245.2 236.9 8.29 295 246.39 245.2 237.2 8 296 246.39 245.2 236.5 8.69 297 246.49 245.1 235.7 9.40 298 246.5 244.9 237.4 7.5 299 246.59 245.4 237.5 7.90 300 246.61 246 236.2 9.80 So the decision tree does outperform the 20% KC, and not by trivial amounts either for many possible b, either in relative or absolute terms: for b=23, the estimated gain is $37.1. The decision tree doesn’t require the full b=300 to often hit the ceiling, although the KC will. However, the performance edge goes down as the horizon gets more distant, and we’ll see that as far out as b=300, the advantage shrinks to ~$6 as the ceiling is hit almost all the time by decent strategies (as we know from Haghani & Dewey 2016’s analysis that KC hits the ceiling ~95% of the time with b=300, although of course it will do so far less often for shorter runs like b=50). Since the 20% KC was only suggested as a heuristic, one might wonder if there’s a different constant fraction which does slightly better in the b=300 case, which there is, 12%: fraction <- seq(0,1, by=0.01) fractionEVs <- ldply(mclapply(fraction, function(f) { k <- function(w,b) { if(w==250) {0} else { f * w } } kev <- simulateGame(k, b=300) return(kev) } )) fraction[which.max(unlist(fractionEVs))] # [1] 0.12 qplot(fraction, fractionEVs) # Generalized Kelly Coin-flip game: POMDPs The original Kelly coinflip game has a clear way to make it more general and difficult: randomize the 3 key parameters of edge/max wealth/rounds and hide them, turning it into a partially-observed Markov decision process. To solve a POMDP one often has to record the entire history, but with judicious choice of what distribution we randomize the 3 parameters from, we can make it both plausibly reflecting the human subjects’ expectations and allow summarizing the history in a few sufficient statistics. ## Implementation A Python implementation with the suggested randomizations is available in OpenAI Gym: import gym env = gym.make('KellyCoinflipGeneralized-v0') env.reset() env._render() # peek at the hidden parameters env._step(env.wealth1000.2) # ... env._reset() # etc ## Bayesian decision tree ### Unknown coin-flip probability A variant on this problem is when the probability of winning is not given, if one doesn’t know in advance p=0.6. How do you make decisions as coin flips happen and provide information on p? Since p is unknown and only partially observed, this turns the coin-flip MDP into a POMDP problem. A POMDP can be turned back into a MDP and solved in a decision tree by including the history of observations as more parameters to explore over. The curse of dimensionality can be tamed here a little by observing that a history of coin-flip sequences is unnecessary - it doesn’t matter what order the coin flips happen in, only the number of wins and the number of total coin-flips matter (are the sufficient statistics). So we only need to augment wealth/rounds/bet-amount with wins/n. And one can compute p from wins/n by Bayesian updates of a prior on the observed coin flip results, treating it as a binomial problem of estimating p distributed according to the beta distribution. This beta Bayesian update is easy and doesn’t require calling out to a library: with a beta uniform prior (Beta(1,1)), update on binomial (win/loss) is conjugate with the simple closed form posterior of Beta(1+win, 1+n-win); and the expectation of the beta is 1+win / 1+n. Then our expected values in f simply change from 0.6/0.4 to expectation/1-expectation. Going back to the R implementation, we add in the two additional parameters, the beta estimation, and estimate the hardwired probabilities: library(memoise) f <- function(x, w, b, wins, n) { beta <- c(1+wins, 1+n-wins) expectedWinProb <- beta[1] / (beta[1]+beta[2]) # E[Beta(alpha, beta)] = alpha / (alpha+beta) expectedLoseProb <- 1 - expectedWinProb expectedWinProbmV(min(w+x,250), b-1, wins+1, n+1) + expectedLoseProbmV(w-x, b-1, wins, n+1) } mf <- memoise(f) V <- function(w,b,wins,n) { returns <- if (b>0 && w>0 && w<250) { sapply(seq(0, w, by=0.1), function(x) { mf(x,w,b, wins, n) }) } else { w } max(returns) } mV <- memoise(V) What prior should we use? Ideally we would use the prior of the participants in the experiment, to compare how well they do compared to the Bayesian decision tree, and estimate how much mistaken beliefs cost them. Unfortunately they were not surveyed on this and the authors do not give any indication of how much of an edge the subjects expected before starting the game, so for analysis, we’ll make up a plausible prior. We know that they know that 100% is not an option (as that would be boring) and <50% is impossible too since they were promised an edge; but it can’t be too high because then everyone would win quickly and nothing would be learned. I think a reasonable prior would be something like 70%, but with a lot of room for surprise. let’s assume a weak prior around 70%, which is equivalent to playing 10 games and winning 7, so Beta(7, 3). With the additional parameters, the memoized version becomes impossibly slow, so I rewrite it to use R environments as a poor man’s hash table: tree <- new.env(size=1000000, parent=emptyenv()) f <- function(x, w, b, wins, n) { beta <- c(1+wins, 1+n-wins) expectedWinProb <- beta[1] / (beta[1]+beta[2]) # E[Beta(alpha, beta)] = alpha / (alpha+beta) expectedLoseProb <- 1 - expectedWinProb expectedWinProbV(min(w+x,250), b-1, wins+1, n+1) + expectedLoseProbV(w-x, b-1, wins, n+1) } V <- function(w, b, wins, n) { if (isSet(c(w,b,wins,n))) { return(lookup(c(w,b,wins,n))) } else { returns <- if (b>0 && w>0 && w<250) { sapply(seq(0, w, by=0.1), function(x) { f(x,w,b,wins,n) }) } else { return(w) } set(c(w,b,wins,n), max(returns)) return(lookup(c(w,b,wins,n))) } } # test expression: $25, 5 bets, suggested 7/10 prior: V(25,5,7,10) This prior leads to somewhat more aggressive betting in short games as the EV is higher, but overall performs much like the decision tree. nshepperd provides a modified version of his code which lets us evaluate up to b=300: {-# LANGUAGE ScopedTypeVariables #-} import System.Environment import Data.List import Data.Foldable import Data.Function import Data.Function.Memoize import Data.Vector (Vector) import qualified Data.Vector as V import Data.Ord import Text.Printf import Numeric.Search.Range -- from 'binary-search' type Wealth = Int type BetAmount = Wealth type Probability = Double type EV = Double type Round = Int type MaxRounds = Round type WonRounds = Round type Alpha = Int type Beta = Int cap :: Wealth cap = 250 data Tree = Done EV \| Bet EV Wealth BetAmount Round Probability Tree Tree deriving (Show) data Dual = Dual { subjectiveEV :: !EV, trueEV :: !EV } deriving (Show) instance Plan Dual where done w = Dual (fromIntegral w) (fromIntegral w) bet w x b p win loss = Dual { subjectiveEV = p * subjectiveEV win + (1 - p) * subjectiveEV loss, trueEV = 0.6 * trueEV win + (1 - 0.6) * trueEV loss } strategyEV = subjectiveEV class Plan s where done :: Wealth -> s bet :: Wealth -> BetAmount -> Round -> Double -> s -> s -> s strategyEV :: s -> EV instance Plan Double where done = fromIntegral bet w x b p win loss = p * win + (1 - p) * loss strategyEV = id instance Plan Tree where done w = Done (fromIntegral w) strategyEV (Done ev) = ev strategyEV (Bet ev _ _ _ _ _ _) = ev bet 0 _ _ _ _ _ = Done 0 bet w x b p win loss = Bet ev w x b p win loss where ev = p * strategyEV win + (1 - p) * strategyEV loss showTree :: Tree -> String showTree (Done ev) = show (Done ev) showTree (Bet ev w x b p win loss) = intercalate "\n" [ printf "%i (%1.1f): %i/%i at %2.2f" b ev x w p, indent 4 ("+ " ++ showTree win), indent 4 ("- " ++ showTree loss) ] where indent n str = intercalate "\n"$ map (replicate n ' ' ++) $lines str --$ Unordered maximum maximumOn :: (Foldable f, Ord b) => (a -> b) -> f a -> a maximumOn f = maximumBy (comparing f) -- Binary search on bitonic function. maximumBitonic :: Ord b => (a -> b) -> Vector a -> a maximumBitonic f options = case searchFromTo find 0 (V.length options - 2) of Just i -> options V.! i Nothing -> options V.! (V.length options - 1) where find i = f (options V.! i) >= f (options V.! (i + 1)) value :: Plan s => Alpha -> Beta -> MaxRounds -> (Round -> WonRounds -> Wealth -> s) -> (Round -> WonRounds -> Wealth -> s) value alpha beta lastRound next currentRound wins w \| currentRound >= lastRound = done w \| w >= cap = done w \| otherwise = maximumBitonic strategyEV options where new_alpha = alpha + wins new_beta = beta + (currentRound - wins) p = fromIntegral new_alpha / fromIntegral (new_alpha + new_beta) go x = bet w x currentRound p (next (currentRound+1) (wins+1) (w+x)) (next (currentRound+1) wins (w-x)) options = V.fromList [go x \| x <- [0..min (cap - w) w]] -- Direct recursion. direct :: Plan s => Alpha -> Beta -> MaxRounds -> (Round -> WonRounds -> Wealth -> s) direct a b m = fix (value a b m) -- Memoised recursion. memo :: forall s. Plan s => Alpha -> Beta -> MaxRounds -> (Round -> WonRounds -> Wealth -> s) memo a b maxRounds = cached_value where cached_value r wins w = table V.! r V.! wins V.! w table :: Vector (Vector (Vector s)) table = V.generate (maxRounds + 1) (\r -> V.generate (r + 1) (\wins -> V.generate (cap + 1) (\w -> value a b maxRounds cached_value r wins w))) -- Memoised recursion using 'memoize' library; slower. memo2 :: Plan s => Alpha -> Beta -> MaxRounds -> (Round -> WonRounds -> Wealth -> s) memo2 a b r = memoFix3 (value a b r) run :: Plan s => (alpha -> beta -> maxRounds -> (Round -> WonRounds -> wealth -> s)) -> alpha -> beta -> maxRounds -> wealth -> s run method alpha beta rounds w = method alpha beta rounds 0 0 w main :: IO () main = do [a, b, r, w] <- map read <$> getArgs print$ (run memo a b r w :: Dual) One feature offered by this code is reporting two expected-values: 1. the subjective estimate of the agent at the beginning of the game about how much it can profit, given the rules and its priors about p 2. the EV it will actually earn, following its policy, given the true probability p=0.6 For our prior, w=25, and b=300, we can evaluate run memo (7+1) (3+1) 300 25 :: Dual and find that the subjective EV is $207.238 and the actual EV is$245.676. And since we know from earlier that an agent following the optimal policy believing p=0.6 would earn $246.606, it follows that the Bayesian agent, due to its ignorance, loses ~$1. So the price of ignorance (regret) in this scenario is surprisingly small. Why is the Bayesian decision tree able to perform so close to the known-probability decision tree? I would guess that it is because all agents bet small amounts in the early rounds (to avoid gambler’s ruin, since they have hundreds of rounds left to reach the ceiling), and this gives them data for free to update towards p=0.6; the agent which knows that p=0.6 can bet a little more precisely early on, but this advantage over a few early rounds doesn’t wind up being much of a help in the long run. With b=300, there are so many rounds available to bet, that the details don’t matter as much; while it there are only a few bets, the maximizing behavior is to bet a lot so the regret for small b is also probably small; the largest regret for not knowing p is probably somewhere, like with the KC vs decision tree, in the small-medium area of b. ### Unknown stopping time Another variant would be to make the stopping time uncertain; strictly speaking, the game wasn’t fixed at exactly 300 rounds, that was just their guess at how many rounds a reasonably fast player might get in before the clock expired. From the player’s perspective, it is unknown how many rounds they will get to play although they can guess that they won’t be allowed to play more than a few hundred, and this might affect the optimal strategy. One way to calculate this would be to assume that the player doesn’t learn anything about the stopping time while playing, and merely has a prior over the stopping time. For example, . The game stopping can be seen as a third probabilistic response to a player’s bet, where each move with some sp, if it happens the number of bets left immediately becomes b=0 (so they win their current w) and they win the net value V(w,0); and if it doesn’t happen the value is the usual 0.6V(w+x, b-1) + 0.4V(w-x, b-1). Or in longer form, the value of a action/bet x is (1-sp)(0.6V(w+x,b-1) + 0.4V(w-x,b-1)) + spV(w,0). What is sp as a distribution? Well, one might believe that every round, there is a ~1% chance of the game stopping, in which case sp is the memoryless geometric distribution (not exponential distribution, since this is a discrete setup); in this case, one must discount each additional round n by 1% cumulatively. (Discounting in general could be seen as reflecting a probability of stopping at each stage.) This has the difficulty that hypothetically, a game might go on indefinitely long, but since a player must eventually hit $0 or$250 and stop playing, it would turn out like the penny simulator - after a few thousand rounds, the probability of having not reached $250 is so small it can’t be handed by most software. The problem is more that this expands the states out enough to again make it unevaluable, so it helps to put an upper bound. So the problem becomes, playing the game knowing that the game might stop with a certain sp (eg 0.01) each round or stops at an upper limit number of rounds (eg b=300). So continuing with the R hash table, it might go like this: f <- function(x, w, b) { sp <- 0.01 (1-sp)(0.6V(min(250,w+x), b-1) + 0.4V(w-x,b-1)) + spV(w,0) } V <- function(w, b) { if (isSet(c(w,b))) { return(lookup(c(w,b))) } else { returns <- if (b>0 && w>0 && w<250) { sapply(seq(0, w, by=0.1), function(x) { f(x,w,b) }) } else { return(w) } set(c(w,b), max(returns)) return(lookup(c(w,b))) } } This can be extended to scenarios where we do learn something about the stopping time, similarly to the coin-flip probability, by doing Bayesian updates on sp. Or if sp changes over rounds. If we had a distribution over the stopping time, then the probability of stopping at each round can change inside the value function given an additional argument n for rounds elapsed as the sufficient statistic. ### Unknown maximum wealth cap Finally, subjects weren’t told what the maximum would be: The maximum payout would be revealed if and when subjects placed a bet that if successful would make their balance greater than or equal to the cap. We set the cap at$250. A convenient distribution for such a cap would be the Pareto distribution, parameterized by a minimum xm and a tail parameter, α. If xm is set to something like 100 (the agent thinks the cap is >$100), for most rounds, the agent would not be able to update this, but towards the end, as it exceeds$100, it then updates the posterior - if it is allowed to make a bet of $50 at$100, then xm becomes 150 while α remains the same, and so on. In this case, the maximum observed wealth is the sufficient statistic. The posterior mean of the cap is then . A reasonable prior might be α=5 and xm=200, in which case the mean wealth cap is 250. f <- function(x, w, b, alpha, x_m) { meanCap <- (alpha * x_m) / (alpha-1) # mean posterior cap if our bet does not threaten to hit the cap x_m_updated <- max(x_m, x+w) meanCapUpdated <- (alpha * x_m_updated) / (alpha-1) # mean posterior cap if our bet does threaten to hit the cap Pcap <- if ((x+b) < x_m) { 0 } else { 1-((x_m / (x+b))^alpha) } # CDF (1-Pcap)(0.6V(min(meanCap,w+x), b-1, alpha, x_m) + 0.4V(w-x,b-1,alpha,x_m)) + Pcap(0.6V(min(meanCapUpdated,w+x), b-1, alpha, x_m_updated) + 0.4V(w-x,b-1,alpha,x_m_updated)) } V <- function(w, b, alpha=5, x_m=200) { if (isSet(c(w,b,alpha,x_m))) { return(lookup(c(w,b,alpha,x_m))) } else { returns <- if (b>0 && w>0) { sapply(seq(0, w, by=0.1), function(x) { f(x,w,b,alpha,x_m) }) } else { return(w) } set(c(w,b,alpha,x_m), max(returns)) return(lookup(c(w,b,alpha,x_m))) } } ## Value of POMDP What is the value of this full POMDP game with uncertain wealth cap, stopping time, and edge? ### Upper bound We can approximate it with our pre-existing value function for a known stopping time/edge/max wealth, sampling from the posterior; for example, we might draw 1000 values from , the Pareto, the Beta etc, calculate the value of each set of parameters, and taking the mean value. Since the value of information is always zero or positive, the value of the POMDP with known parameters must be an upper bound on its true value, since we can only do worse in each game by being ignorant of the true parameters and needing to infer them as we play; so if we calculate a value of $240 or whatever, we know the POMDP must have a value <$240, and that gives a performance target to aim for. The Haskell version is the easiest to work with, but Haskell doesn’t have convenient distributions to sample from, so instead I generate 1000 samples from the prior distribution of parameters in Python (reusing some of the Gym code): from scipy.stats import genpareto import numpy as np import numpy.random from gym.spaces import prng edgePriorAlpha=7 edgePriorBeta=3 maxWealthAlpha=5 maxWealthM=200 maxRoundsMean=300 maxRoundsSD=25 for i in xrange(0,1000): edge = prng.np_random.beta(edgePriorAlpha, edgePriorBeta) maxWealth = int(round(genpareto.rvs(maxWealthAlpha, maxWealthM, random_state=prng.np_random))) maxRounds = int(round(prng.np_random.normal(maxRoundsMean, maxRoundsSD))) print 25, maxRounds, edge, maxWealth and then we can modify nshepperd’s Haskell code to allow the edge and wealth cap to be modifiable, and then we simply run memo over the 1000 possible sets of parameters, and take the mean. Using the raw samples turns out to be infeasible in terms of RAM, probably because higher wealth caps (which are Pareto distributed and can be extremely large) increases dimensionality too much to evaluate in my ~25GB RAM, so the wealth cap itself must be shrunk, to TODO $1000? which unfortunately muddles the meaning of the estimate since now it’s a lower bound of an upper bound, or to reverse it, value of clairvoyant play assuming that many games have a lower wealth cap than they do. import Data.Vector (Vector) import qualified Data.Vector as V (generate, (!)) type Wealth = Int type Bets = Int type Edge = Double type Cap = Int type EV = Double value :: (Wealth -> Bets -> EV) -> Wealth -> Bets -> Edge -> Cap -> EV value _ 0 _ _ _ = 0 value _ w 0 _ _ = fromIntegral w value next w b e cap = maximum [go x \| x <- [0..min (cap - w) w]] where go x = e * next (min cap (w+x)) (b-1) + (1-e) * next (w-x) (b-1) memo :: Wealth -> Bets -> Edge -> Cap -> EV memo w b e cp = cached_value w b where cached_value w' b' = table V.! b' V.! w' table :: Vector (Vector EV) table = V.generate (b + 1) (\b'' -> V.generate (cp + 1) (\w'' -> value cached_value w'' b'' e cp)) main :: IO () main = do let evs = map (\(w,b,e,cap) -> memo w b e cap) parameters print evs print$ mean evs where mean x = sum x / fromIntegral (length x) maxCap :: Int maxCap = 800 parameters :: [(Wealth, Bets, Edge, Cap)] parameters = map (\(w,b,e,c) -> (w,b,e, max maxCap c)) [(25, 236, 0.72435085557, 205), (25, 237, 0.845435411107, 260), (25, 238, 0.413782110845, 202), (25, 240, 0.345133535603, 23999), (25, 240, 0.400147029568, 2521), (25, 242, 0.661912880989, 201), (25, 242, 0.676168121514, 6740), (25, 242, 0.701381545443, 1726), (25, 242, 0.849537381053, 203), (25, 242, 0.898462493046, 201), (25, 243, 0.54257657328, 201), (25, 245, 0.77972062792, 48534), (25, 246, 0.813395396485, 203), (25, 247, 0.480134063147, 214), (25, 247, 0.533273012857, 222), (25, 247, 0.754222974601, 201), (25, 249, 0.70782818171, 200), (25, 249, 0.748310452532, 202), (25, 251, 0.606478140487, 200), (25, 251, 0.809355705263, 526), (25, 252, 0.524864167122, 200), (25, 252, 0.749206398756, 352321), (25, 252, 0.822818892461, 201), (25, 253, 0.542598606499, 201), (25, 253, 0.600469152584, 200), (25, 253, 0.648598435209, 219), (25, 253, 0.649453264073, 2589), (25, 253, 0.679414549454, 28311200), (25, 253, 0.86227613481, 202), (25, 254, 0.585056497076, 2575033), (25, 254, 0.680452842612, 200), (25, 255, 0.877950348346, 201), (25, 256, 0.643298850757, 205), (25, 256, 0.712973552037, 204), (25, 256, 0.718153926517, 201), (25, 256, 0.813126205309, 201), (25, 256, 0.8280445068, 208), (25, 257, 0.402688232643, 201), (25, 257, 0.548591912297, 651), (25, 257, 0.601967601919, 206), (25, 257, 0.862541920316, 200), (25, 257, 0.863389650382, 200), (25, 258, 0.474519595118, 213), (25, 258, 0.735744534702, 208), (25, 258, 0.738339372201, 360), (25, 258, 0.84277195943, 83144), (25, 258, 0.93190614133, 2409618061), (25, 259, 0.471094149142, 745), (25, 260, 0.628797799899, 202), (25, 260, 0.710033767475, 9552510), (25, 260, 0.813466187199, 200), (25, 261, 0.550748996178, 230), (25, 261, 0.629544256918, 259), (25, 261, 0.683386138653, 200), (25, 261, 0.792209742213, 201), (25, 261, 0.794533480259, 207), (25, 262, 0.344887568623, 201), (25, 262, 0.450645011078, 473), (25, 262, 0.738248174312, 225), (25, 262, 0.791527693933, 210), (25, 262, 0.832198167412, 200), (25, 263, 0.35093259949, 203), (25, 263, 0.521818533732, 366), (25, 263, 0.64076936694, 59847), (25, 263, 0.684063131912, 201), (25, 263, 0.714065733976, 201), (25, 263, 0.789350373174, 1705), (25, 263, 0.829406017035, 210), (25, 263, 0.902144916794, 255), (25, 263, 0.951257247224, 202), (25, 264, 0.32472812884, 203), (25, 264, 0.604563170498, 250), (25, 264, 0.626423177116, 22769), (25, 264, 0.871339562605, 205), (25, 265, 0.452014126574, 200), (25, 265, 0.54226419925, 201), (25, 265, 0.625113911686, 212), (25, 265, 0.654404133816, 206), (25, 265, 0.678345789504, 420), (25, 265, 0.771116406164, 210), (25, 265, 0.771222624754, 205), (25, 265, 0.801480809161, 200), (25, 265, 0.806182111956, 60957), (25, 265, 0.851715904261, 18981), (25, 266, 0.685689594858, 200), (25, 266, 0.711416415881, 210), (25, 266, 0.711937019202, 851), (25, 266, 0.724721571466, 200), (25, 266, 0.816529965664, 654), (25, 266, 0.820884461992, 287), (25, 267, 0.798462101302, 200), (25, 267, 0.814520382826, 200), (25, 267, 0.815795664692, 201), (25, 267, 0.877810894936, 200), (25, 268, 0.37374747435, 7152), (25, 268, 0.66383704238, 201), (25, 268, 0.671499425192, 224), (25, 268, 0.72882798744, 205), (25, 268, 0.788161778332, 534537579002), (25, 268, 0.793723223502, 584), (25, 268, 0.83414422735, 16291), (25, 268, 0.933374294433, 219), (25, 269, 0.460012103336, 211), (25, 269, 0.575089962258, 203), (25, 269, 0.587666214938, 213), (25, 269, 0.617907437269, 201), (25, 269, 0.711693869892, 203), (25, 269, 0.755193420929, 200), (25, 269, 0.764409970652, 2593), (25, 269, 0.769445254497, 6962), (25, 269, 0.781046904571, 1030), (25, 269, 0.92721940969, 2062780), (25, 269, 0.937746457329, 201), (25, 270, 0.43758799016, 201), (25, 270, 0.55945290829, 206), (25, 270, 0.594599037706, 579), (25, 270, 0.6205174976, 506), (25, 270, 0.660258985896, 217), (25, 270, 0.688180575479, 308), (25, 270, 0.703263135667, 201), (25, 270, 0.730492162736, 46132), (25, 270, 0.7898205196, 25541), (25, 270, 0.893976819617, 201), (25, 270, 0.921080018968, 200), (25, 271, 0.525815069976, 200), (25, 271, 0.554615752325, 200), (25, 271, 0.629469767651, 200), (25, 271, 0.709135907244, 9875), (25, 271, 0.759981836553, 202), (25, 271, 0.811129692174, 91717), (25, 271, 0.837347167701, 200), (25, 271, 0.873514454515, 200), (25, 271, 0.923252939562, 208), (25, 272, 0.556207216343, 785), (25, 272, 0.575453865622, 215), (25, 272, 0.638921822998, 200), (25, 272, 0.642223697178, 219), (25, 272, 0.66336333735, 213), (25, 272, 0.798971543861, 209), (25, 272, 0.826187121413, 216), (25, 272, 0.864733208766, 204), (25, 273, 0.517135630277, 200), (25, 273, 0.560438221638, 221192794), (25, 273, 0.77368870442, 883), (25, 273, 0.846232723863, 785), (25, 273, 0.9652451074, 200), (25, 274, 0.607659170171, 339), (25, 274, 0.611760970714, 201), (25, 274, 0.638249890182, 201), (25, 274, 0.706185385091, 201), (25, 274, 0.760147689131, 200), (25, 274, 0.804365960436, 1051), (25, 274, 0.848798405341, 1117), (25, 275, 0.333707647765, 200), (25, 275, 0.555403709258, 205), (25, 275, 0.655942931908, 206), (25, 275, 0.676684395133, 201), (25, 275, 0.698400431321, 203), (25, 275, 0.796131451966, 200), (25, 275, 0.840528265848, 200), (25, 275, 0.856009338181, 200), (25, 276, 0.497611590615, 211), (25, 276, 0.719196036042, 202), (25, 276, 0.72119258703, 212), (25, 276, 0.724848372617, 201), (25, 276, 0.727773523116, 947132), (25, 276, 0.786181091729, 223), (25, 276, 0.835470024888, 213), (25, 276, 0.850785506884, 1650536293), (25, 276, 0.872106280647, 205), (25, 277, 0.409025006548, 1245), (25, 277, 0.432733743192, 200), (25, 277, 0.571657665503, 45217), (25, 277, 0.702562712047, 201), (25, 277, 0.730418085673, 575), (25, 277, 0.749515377892, 200), (25, 277, 0.775231917334, 200), (25, 277, 0.790660296053, 204), (25, 277, 0.875858958177, 236), (25, 278, 0.379322394893, 309), (25, 278, 0.420790416182, 201), (25, 278, 0.527244364126, 200), (25, 278, 0.615000956496, 205), (25, 278, 0.675667333791, 201), (25, 278, 0.696208960885, 201), (25, 278, 0.790420764423, 204), (25, 278, 0.841240203947, 523), (25, 279, 0.341095083629, 201), (25, 279, 0.476230165726, 1798), (25, 279, 0.518063098433, 209), (25, 279, 0.656454646158, 306), (25, 279, 0.684136349, 273), (25, 279, 0.709847569568, 119033), (25, 279, 0.762133225185, 200), (25, 279, 0.776577127267, 200), (25, 279, 0.79611434817, 201), (25, 279, 0.808780479341, 425), (25, 279, 0.850439803007, 204), (25, 279, 0.898230041029, 204), (25, 279, 0.945894882249, 616), (25, 280, 0.368073973138, 14001), (25, 280, 0.464321107456, 1523), (25, 280, 0.617310083425, 504403), (25, 280, 0.657193497398, 204), (25, 280, 0.707839204221, 1265268), (25, 280, 0.76379246649, 304), (25, 280, 0.772912128233, 201), (25, 280, 0.865579809939, 77454), (25, 281, 0.475947154647, 200), (25, 281, 0.557771053261, 2188305), (25, 281, 0.56666775076, 12340), (25, 281, 0.638041977737, 200), (25, 281, 0.668510798451, 212), (25, 281, 0.678366665681, 1294), (25, 281, 0.716116162808, 213), (25, 281, 0.748052894007, 203), (25, 281, 0.749911576065, 23865988060), (25, 281, 0.759712569326, 204), (25, 281, 0.806434961546, 353082), (25, 281, 0.893617069228, 200), (25, 281, 0.931891968132, 203), (25, 282, 0.454895506694, 11408), (25, 282, 0.549639923973, 462), (25, 282, 0.569017378489, 201), (25, 282, 0.577850694309, 200), (25, 282, 0.584479523845, 334042071872), (25, 282, 0.599723920362, 200), (25, 282, 0.632612897763, 1293), (25, 282, 0.681109488172, 200), (25, 282, 0.724133951717, 200), (25, 282, 0.754930901531, 201), (25, 282, 0.778740223985, 203), (25, 282, 0.779781137188, 200), (25, 282, 0.781305596085, 202), (25, 282, 0.83569736595, 200), (25, 282, 0.850446466345, 1253), (25, 282, 0.859549928516, 201), (25, 282, 0.871855706726, 200), (25, 283, 0.327637841131, 200), (25, 283, 0.404249604299, 201), (25, 283, 0.561172940189, 200), (25, 283, 0.668083130397, 201), (25, 283, 0.678629207223, 203), (25, 283, 0.74122980107, 208), (25, 283, 0.744679958097, 200), (25, 283, 0.760349422921, 203), (25, 283, 0.781697384113, 209), (25, 283, 0.784799938769, 202), (25, 283, 0.789112337759, 236), (25, 283, 0.819466827649, 262), (25, 283, 0.839687812522, 200), (25, 283, 0.856859655325, 271), (25, 284, 0.495523668627, 201), (25, 284, 0.56435102208, 205), (25, 284, 0.588093361148, 219), (25, 284, 0.593268824769, 200), (25, 284, 0.640596228637, 213), (25, 284, 0.653491369691, 44714), (25, 284, 0.675009753521, 202), (25, 284, 0.773401673731, 200), (25, 284, 0.805092875342, 213), (25, 284, 0.82735685621, 263), (25, 284, 0.840696528783, 16521), (25, 285, 0.362802762398, 320), (25, 285, 0.367012291981, 20073), (25, 285, 0.521190733548, 200), (25, 285, 0.575799236698, 200), (25, 285, 0.637555604061, 201), (25, 285, 0.642866106846, 200), (25, 285, 0.739442877608, 1154709), (25, 285, 0.740973872676, 205), (25, 285, 0.779312184025, 258), (25, 285, 0.7798668215, 1286), (25, 285, 0.841286817662, 200), (25, 285, 0.913642856385, 858), (25, 286, 0.526160290087, 202), (25, 286, 0.57102556171, 200), (25, 286, 0.605564882529, 200), (25, 286, 0.673079677685, 202), (25, 286, 0.675864181927, 200), (25, 286, 0.723247596231, 224), (25, 286, 0.723347705484, 203), (25, 286, 0.767358570943, 207), (25, 286, 0.775537484183, 241), (25, 286, 0.780033922166, 2962), (25, 286, 0.806301077907, 1553), (25, 286, 0.829016366841, 200), (25, 286, 0.839169441571, 200), (25, 286, 0.852776222427, 28148), (25, 286, 0.853758532671, 200), (25, 286, 0.906829095884, 200), (25, 286, 0.922712587421, 202), (25, 287, 0.498032911641, 200), (25, 287, 0.592863506249, 233), (25, 287, 0.622406587519, 208), (25, 287, 0.718903577193, 218), (25, 287, 0.72138759488, 227), (25, 287, 0.749942677419, 240), (25, 287, 0.762366566525, 215), (25, 287, 0.770805576807, 200), (25, 287, 0.797492731584, 200), (25, 287, 0.835165503936, 200), (25, 287, 0.946751084636, 863358347021), (25, 288, 0.306016851261, 201), (25, 288, 0.468949036459, 4770), (25, 288, 0.549651576351, 201), (25, 288, 0.592965066535, 6236), (25, 288, 0.706825000163, 216), (25, 288, 0.74286176604, 41482), (25, 288, 0.743238045326, 206), (25, 288, 0.777949156606, 213), (25, 288, 0.781597068828, 418), (25, 288, 0.794578713285, 200), (25, 288, 0.828331653519, 418), (25, 288, 0.834874015356, 212), (25, 288, 0.848009292304, 200), (25, 288, 0.852116433152, 200), (25, 288, 0.906593204881, 202), (25, 288, 0.920623087617, 220), (25, 289, 0.524452337599, 1057), (25, 289, 0.552951317234, 208), (25, 289, 0.651146664053, 200), (25, 289, 0.658611767347, 1126709768047), (25, 289, 0.691072913786, 201), (25, 289, 0.695521738775, 42204), (25, 289, 0.710204540486, 207), (25, 289, 0.716186135845, 3696), (25, 289, 0.748287169753, 209), (25, 289, 0.750374480604, 201), (25, 289, 0.810573219838, 201), (25, 289, 0.824662154794, 200), (25, 289, 0.881953772318, 200), (25, 289, 0.885424313568, 200), (25, 290, 0.478371525842, 2087), (25, 290, 0.509245836087, 200), (25, 290, 0.559208272006, 202), (25, 290, 0.566118076472, 336), (25, 290, 0.592660738469, 200), (25, 290, 0.594018239861, 273), (25, 290, 0.609100591562, 201), (25, 290, 0.613710234154, 235), (25, 290, 0.622454795175, 201), (25, 290, 0.642187814474, 201), (25, 290, 0.650179222226, 202), (25, 290, 0.71534164315, 3261), (25, 290, 0.720180673012, 206), (25, 290, 0.737585832942, 200), (25, 290, 0.775169473922, 229), (25, 290, 0.783784198305, 53137), (25, 290, 0.789135961744, 201), (25, 290, 0.800078889184, 200), (25, 291, 0.405626786206, 34744), (25, 291, 0.525738841457, 211), (25, 291, 0.533871294974, 12996), (25, 291, 0.608310459901, 201), (25, 291, 0.70893418817, 200), (25, 291, 0.748805670518, 200), (25, 291, 0.760314517315, 202), (25, 291, 0.760919201657, 215), (25, 291, 0.763324684293, 200), (25, 291, 0.778634985402, 200), (25, 291, 0.805883746215, 200), (25, 291, 0.827079825705, 203), (25, 291, 0.827672243803, 200), (25, 292, 0.353361504401, 9552), (25, 292, 0.413680391502, 240), (25, 292, 0.498283007005, 200), (25, 292, 0.560682661174, 201), (25, 292, 0.660502227784, 201), (25, 292, 0.676014312494, 200), (25, 292, 0.729161823418, 200), (25, 292, 0.754733824112, 230), (25, 292, 0.772617271317, 312), (25, 292, 0.778956063712, 212), (25, 292, 0.808767644485, 200), (25, 292, 0.808779697891, 201), (25, 292, 0.844087667679, 202), (25, 292, 0.904903907681, 200), (25, 293, 0.524954771554, 4945), (25, 293, 0.57444832542, 233), (25, 293, 0.600122035306, 200), (25, 293, 0.69001246376, 205), (25, 293, 0.691232039332, 207), (25, 293, 0.691742268177, 211), (25, 293, 0.698366150359, 200), (25, 293, 0.711927031055, 1815880), (25, 293, 0.71619667357, 3964), (25, 293, 0.728536730678, 200), (25, 293, 0.741604172773, 200), (25, 293, 0.743399425593, 201), (25, 293, 0.758084864431, 200), (25, 293, 0.759978441853, 200), (25, 293, 0.780081691192, 1448778253), (25, 293, 0.788319084437, 208), (25, 293, 0.801525808156, 200), (25, 293, 0.813155425067, 206), (25, 293, 0.819811779201, 377), (25, 293, 0.837649946204, 209), (25, 293, 0.869752644338, 4592), (25, 293, 0.875398670372, 200), (25, 293, 0.918150841685, 200), (25, 293, 0.921450726956, 201), (25, 294, 0.445036622233, 202), (25, 294, 0.496380029754, 2294499), (25, 294, 0.517533203971, 214), (25, 294, 0.597738939234, 213), (25, 294, 0.597783619419, 102427), (25, 294, 0.600782734524, 263), (25, 294, 0.625741320644, 200), (25, 294, 0.632555212361, 202), (25, 294, 0.633928301179, 217), (25, 294, 0.720710116312, 200), (25, 294, 0.741687972492, 235), (25, 294, 0.775184150825, 203), (25, 294, 0.799975478422, 2129), (25, 294, 0.811533351383, 221), (25, 294, 0.827766846665, 47518), (25, 294, 0.834896019626, 200), (25, 294, 0.855889683449, 200), (25, 294, 0.887096214635, 201), (25, 294, 0.898185143854, 200), (25, 294, 0.904470557778, 207), (25, 295, 0.510000548384, 4948), (25, 295, 0.527335029277, 48990), (25, 295, 0.553592976478, 200), (25, 295, 0.587128450848, 200), (25, 295, 0.685163151117, 221), (25, 295, 0.689665955815, 200), (25, 295, 0.693619741737, 200), (25, 295, 0.698808800461, 212), (25, 295, 0.79024052726, 203), (25, 295, 0.805930533305, 233), (25, 295, 0.870408868052, 208), (25, 295, 0.879989559956, 209), (25, 295, 0.917289124506, 201), (25, 296, 0.368675367618, 200), (25, 296, 0.422106669815, 87196), (25, 296, 0.570294648439, 201), (25, 296, 0.576307309235, 5064), (25, 296, 0.577913079103, 223), (25, 296, 0.615569633698, 201), (25, 296, 0.619178871735, 43506), (25, 296, 0.718168554371, 310), (25, 296, 0.747322660094, 202), (25, 296, 0.760729108487, 200), (25, 296, 0.822530768331, 205), (25, 296, 0.836178694446, 200), (25, 296, 0.922082501039, 202), (25, 297, 0.575427625651, 325), (25, 297, 0.582330676039, 200), (25, 297, 0.59032029128, 201), (25, 297, 0.590800056359, 200), (25, 297, 0.601983239354, 200), (25, 297, 0.604624445572, 349), (25, 297, 0.618592598637, 275), (25, 297, 0.630430484034, 1804), (25, 297, 0.747994935933, 200), (25, 297, 0.761287220637, 201), (25, 297, 0.784311762717, 24040), (25, 297, 0.805896793235, 207), (25, 297, 0.83131315563, 213), (25, 297, 0.859395579848, 209), (25, 297, 0.878201883463, 201), (25, 298, 0.365915091546, 7657), (25, 298, 0.52132925192, 201), (25, 298, 0.615089219457, 212), (25, 298, 0.637405757267, 200), (25, 298, 0.688423448322, 214), (25, 298, 0.745560344488, 206), (25, 298, 0.80183307542, 589), (25, 298, 0.870426520049, 272), (25, 298, 0.89547470974, 623), (25, 299, 0.439413983287, 621), (25, 299, 0.635744201316, 400665320), (25, 299, 0.635839800048, 203), (25, 299, 0.654855825396, 230), (25, 299, 0.663358277149, 200), (25, 299, 0.716539473345, 206), (25, 299, 0.720916562601, 201), (25, 299, 0.751504283345, 239), (25, 299, 0.757182123011, 201), (25, 299, 0.783947882789, 34957848), (25, 299, 0.787635290729, 2549771968), (25, 299, 0.810452875242, 200), (25, 299, 0.817501090944, 200), (25, 299, 0.825030647643, 202), (25, 299, 0.826381476756, 201309), (25, 299, 0.827561766471, 200), (25, 299, 0.838546065913, 406), (25, 299, 0.838668086492, 41065010), (25, 299, 0.849677138359, 205), (25, 299, 0.888747407578, 203), (25, 300, 0.409478159695, 204), (25, 300, 0.422098065762, 127064), (25, 300, 0.461635641331, 215), (25, 300, 0.509929449334, 200), (25, 300, 0.526075686173, 249), (25, 300, 0.570498723667, 200), (25, 300, 0.608851280889, 104165306), (25, 300, 0.63030529901, 200), (25, 300, 0.672317987371, 664), (25, 300, 0.673406231884, 200), (25, 300, 0.680327735756, 3147), (25, 300, 0.69178511648, 482), (25, 300, 0.72755905432, 201), (25, 300, 0.732997721442, 212), (25, 300, 0.753568752527, 200), (25, 300, 0.772028272907, 202), (25, 300, 0.779901373004, 21845295), (25, 300, 0.787993478282, 812414), (25, 300, 0.803550492942, 206), (25, 300, 0.874415087757, 263), (25, 300, 0.885236357353, 331970), (25, 300, 0.894826991604, 588), (25, 300, 0.902637609898, 85410), (25, 301, 0.360093850862, 204), (25, 301, 0.400165301316, 201), (25, 301, 0.469204018151, 200), (25, 301, 0.537073638156, 200), (25, 301, 0.546705498921, 203), (25, 301, 0.592970028946, 303), (25, 301, 0.608415628183, 200), (25, 301, 0.63288933406, 2859), (25, 301, 0.63664042403, 970), (25, 301, 0.64529111355, 402), (25, 301, 0.681233825938, 200), (25, 301, 0.690899753273, 210), (25, 301, 0.692879776665, 200), (25, 301, 0.748166942643, 201), (25, 301, 0.780381651924, 201), (25, 301, 0.786615600294, 240), (25, 301, 0.796162957093, 218), (25, 301, 0.814111079911, 200), (25, 301, 0.829147987825, 200), (25, 301, 0.842615885711, 226), (25, 301, 0.848517486075, 54928), (25, 301, 0.89833095029, 1550), (25, 302, 0.405983475031, 18159), (25, 302, 0.584932652676, 220), (25, 302, 0.64638274985, 200), (25, 302, 0.704969570047, 201), (25, 302, 0.706051626625, 200), (25, 302, 0.741692298627, 201), (25, 302, 0.756403039924, 236), (25, 302, 0.775208821424, 205), (25, 302, 0.820549125721, 6413), (25, 302, 0.843449911907, 202), (25, 302, 0.854836903637, 1444), (25, 302, 0.959731993346, 18110751), (25, 303, 0.424498218556, 202), (25, 303, 0.59564207646, 5859), (25, 303, 0.628957916397, 312), (25, 303, 0.675945884436, 405), (25, 303, 0.703924077074, 3436122), (25, 303, 0.775340096428, 203), (25, 303, 0.840799001056, 200), (25, 303, 0.843478387795, 200), (25, 303, 0.843620594265, 201), (25, 303, 0.882905827794, 200), (25, 303, 0.891407840196, 201), (25, 303, 0.928661184425, 200), (25, 304, 0.612209498336, 200), (25, 304, 0.632934680031, 217), (25, 304, 0.680037492863, 208), (25, 304, 0.702135166708, 201), (25, 304, 0.739443325164, 200), (25, 304, 0.792856089945, 18219), (25, 304, 0.793868715939, 1195), (25, 304, 0.807936872595, 243), (25, 304, 0.855967740382, 9139), (25, 304, 0.876774098031, 264), (25, 304, 0.908151496191, 200), (25, 304, 0.909811696417, 201), (25, 305, 0.467412185835, 220), (25, 305, 0.504357824329, 202), (25, 305, 0.551514171063, 1813205), (25, 305, 0.562075541816, 28957), (25, 305, 0.565839799799, 200), (25, 305, 0.57478857299, 201), (25, 305, 0.616735566246, 18968), (25, 305, 0.694741607886, 211), (25, 305, 0.730098365549, 350), (25, 305, 0.74553240102, 3669), (25, 305, 0.775373331324, 273), (25, 305, 0.782999134264, 202), (25, 305, 0.8326463963, 1718174), (25, 305, 0.84309553266, 34103), (25, 305, 0.853174396025, 202), (25, 305, 0.866990268211, 200), (25, 305, 0.95814576074, 207), (25, 306, 0.426358484538, 2619), (25, 306, 0.601491940798, 1236), (25, 306, 0.656076249659, 201), (25, 306, 0.667159358364, 8851), (25, 306, 0.680137137507, 93771), (25, 306, 0.702048987783, 215), (25, 306, 0.736768186781, 200), (25, 306, 0.766656078382, 225), (25, 306, 0.778572773772, 201), (25, 306, 0.788035864564, 224), (25, 306, 0.810667703089, 203), (25, 306, 0.816630755616, 10977626), (25, 306, 0.874526902796, 207), (25, 306, 0.909874167041, 200), (25, 306, 0.937873115764, 201), (25, 307, 0.399427943647, 308), (25, 307, 0.502741334176, 210), (25, 307, 0.529663281186, 1180), (25, 307, 0.630224185157, 200), (25, 307, 0.632031271401, 218), (25, 307, 0.640704995246, 203), (25, 307, 0.69831193803, 77936), (25, 307, 0.702814625747, 201), (25, 307, 0.747406138489, 202), (25, 307, 0.747958417038, 204), (25, 307, 0.784937576368, 1648), (25, 307, 0.794869553561, 201), (25, 307, 0.828787292708, 9683), (25, 307, 0.863132135591, 207), (25, 307, 0.869668447709, 207), (25, 307, 0.871174430814, 1874), (25, 307, 0.874024275077, 210), (25, 307, 0.888454459822, 2205), (25, 307, 0.908595383436, 1066), (25, 308, 0.325783846322, 203), (25, 308, 0.397224619923, 201), (25, 308, 0.398632358505, 1866), (25, 308, 0.549245225571, 223), (25, 308, 0.614176736202, 1627), (25, 308, 0.657868307531, 835565), (25, 308, 0.720171327788, 102155), (25, 308, 0.760576054602, 202), (25, 308, 0.789153275477, 205), (25, 308, 0.923998732287, 201), (25, 309, 0.561546536824, 200), (25, 309, 0.635434397698, 200), (25, 309, 0.643406617116, 203), (25, 309, 0.658560572878, 200), (25, 309, 0.674697791801, 248), (25, 309, 0.676725636526, 228), (25, 309, 0.676937775159, 200), (25, 309, 0.6792495829, 221), (25, 309, 0.716486921989, 200), (25, 309, 0.725512876373, 78653), (25, 309, 0.757976245878, 746), (25, 309, 0.781027844906, 200), (25, 309, 0.78623950218, 257), (25, 309, 0.810962413638, 230), (25, 310, 0.260183128022, 4099), (25, 310, 0.587394172232, 251), (25, 310, 0.621739526011, 322), (25, 310, 0.64027318687, 204), (25, 310, 0.67688167552, 202), (25, 310, 0.683476431144, 203), (25, 310, 0.74431135893, 10529), (25, 310, 0.804336362739, 201), (25, 310, 0.809925171125, 224), (25, 310, 0.84167604034, 219), (25, 310, 0.914653852136, 240), (25, 311, 0.312014901261, 200), (25, 311, 0.565120276608, 1451), (25, 311, 0.668447484328, 200), (25, 311, 0.693205380973, 201), (25, 311, 0.715572448621, 200), (25, 311, 0.735871833159, 206), (25, 311, 0.754197545032, 201), (25, 311, 0.755255511596, 207), (25, 311, 0.797893642622, 200), (25, 311, 0.82548808715, 629357488), (25, 311, 0.848601310255, 212), (25, 311, 0.893160345087, 222), (25, 311, 0.907535669966, 210), (25, 312, 0.390384390913, 223), (25, 312, 0.404305090449, 201), (25, 312, 0.587382901527, 200), (25, 312, 0.607534113237, 204), (25, 312, 0.719561090933, 2427), (25, 312, 0.765116208912, 207), (25, 312, 0.768884636481, 201), (25, 312, 0.77321985892, 136853), (25, 312, 0.781591538183, 357), (25, 312, 0.786119097558, 3483946), (25, 312, 0.848619555391, 11017), (25, 312, 0.954299904225, 200), (25, 312, 0.955187319821, 204), (25, 313, 0.529251017792, 204), (25, 313, 0.541364870877, 200), (25, 313, 0.60546139467, 230), (25, 313, 0.61482220499, 24877), (25, 313, 0.638663284904, 209), (25, 313, 0.644164848762, 200), (25, 313, 0.64713451255, 200), (25, 313, 0.743586331391, 201), (25, 313, 0.775805821428, 62845), (25, 313, 0.798122759695, 7977), (25, 313, 0.858577862803, 127038), (25, 313, 0.866823531593, 200), (25, 313, 0.876882672035, 283), (25, 313, 0.917675334467, 200), (25, 314, 0.369362271547, 200), (25, 314, 0.37571281143, 7538438), (25, 314, 0.421702878008, 872), (25, 314, 0.512143047288, 200), (25, 314, 0.615334964732, 41957), (25, 314, 0.634135010466, 201), (25, 314, 0.65143589365, 5976), (25, 314, 0.6624335318, 202), (25, 314, 0.687439523632, 207), (25, 314, 0.70341643248, 219100), (25, 314, 0.71373952253, 200), (25, 314, 0.716799246311, 200), (25, 314, 0.736070231117, 202), (25, 314, 0.769820801936, 201), (25, 314, 0.796382966462, 1810920), (25, 314, 0.817248231272, 200), (25, 314, 0.911372340659, 217771), (25, 315, 0.494168494957, 200), (25, 315, 0.525928344185, 108504), (25, 315, 0.530891192429, 309), (25, 315, 0.543427134741, 570), (25, 315, 0.582642352511, 200), (25, 315, 0.62020198716, 204), (25, 315, 0.66021096512, 201), (25, 315, 0.810810141201, 125205306), (25, 315, 0.875437215808, 201), (25, 315, 0.891388896727, 202), (25, 315, 0.950706326773, 230), (25, 316, 0.531487130493, 203), (25, 316, 0.618472935292, 251), (25, 316, 0.647254887133, 206), (25, 316, 0.653924814146, 212), (25, 316, 0.667901497546, 212), (25, 316, 0.708180220581, 200), (25, 316, 0.760548015821, 2030), (25, 316, 0.768690555637, 200), (25, 316, 0.774476148446, 200), (25, 316, 0.796262761253, 201), (25, 316, 0.796625765733, 200), (25, 316, 0.823221552247, 200), (25, 316, 0.830702399623, 200), (25, 316, 0.836360274124, 325), (25, 316, 0.896613527206, 248), (25, 317, 0.482186115357, 383), (25, 317, 0.576756996375, 200), (25, 317, 0.578057886341, 204), (25, 317, 0.594056991632, 203), (25, 317, 0.631811741834, 200), (25, 317, 0.634065817187, 201), (25, 317, 0.738259051865, 200), (25, 317, 0.741522939153, 200), (25, 317, 0.753479524136, 2637045), (25, 317, 0.776711507455, 301), (25, 317, 0.788723637838, 222), (25, 317, 0.859905403917, 201), (25, 318, 0.524837076185, 783), (25, 318, 0.570833052501, 324), (25, 318, 0.578522088699, 201), (25, 318, 0.657902296334, 202), (25, 318, 0.677142738648, 200), (25, 318, 0.726613137498, 769), (25, 318, 0.732167007028, 209), (25, 318, 0.774227686638, 371), (25, 318, 0.827201651993, 202), (25, 318, 0.847552472266, 333), (25, 319, 0.299119763862, 203), (25, 319, 0.45927498818, 201), (25, 319, 0.516148758591, 203), (25, 319, 0.615909131871, 4852), (25, 319, 0.632155319322, 108442), (25, 319, 0.646735509589, 260), (25, 319, 0.650284817404, 205), (25, 319, 0.686381662086, 9214), (25, 319, 0.693039056628, 200), (25, 319, 0.744051833919, 202), (25, 319, 0.766865749349, 200), (25, 319, 0.787624751367, 209), (25, 319, 0.80385182439, 201), (25, 319, 0.828506576415, 203), (25, 319, 0.882672117998, 236), (25, 319, 0.897596538512, 320), (25, 320, 0.463229776045, 201), (25, 320, 0.495664364554, 543), (25, 320, 0.557110073697, 46084), (25, 320, 0.564003442697, 228), (25, 320, 0.592427293085, 200), (25, 320, 0.647193255894, 541), (25, 320, 0.687780061052, 305), (25, 320, 0.804990051837, 204), (25, 320, 0.812916984869, 1331), (25, 320, 0.931548693535, 1716800), (25, 321, 0.629165408494, 202), (25, 321, 0.646414688214, 1085812), (25, 321, 0.675364980195, 20790), (25, 321, 0.681600225983, 206), (25, 321, 0.685460441866, 13703), (25, 321, 0.832202070011, 236), (25, 321, 0.869702143767, 228), (25, 322, 0.359393286821, 200), (25, 322, 0.456060077056, 234), (25, 322, 0.489952848972, 219), (25, 322, 0.514488904665, 327), (25, 322, 0.599151587589, 200), (25, 322, 0.669303689783, 200), (25, 322, 0.696930419223, 216), (25, 322, 0.727835215524, 477), (25, 322, 0.80782526029, 200), (25, 322, 0.833256121648, 129263), (25, 322, 0.870336001756, 216), (25, 322, 0.940963125417, 679), (25, 323, 0.396053762877, 201), (25, 323, 0.425459758563, 200), (25, 323, 0.55251719767, 201), (25, 323, 0.584884865708, 200), (25, 323, 0.609829616479, 203), (25, 323, 0.612493852048, 322), (25, 323, 0.691710173338, 201), (25, 323, 0.71108498005, 311), (25, 323, 0.788507519521, 203), (25, 323, 0.807011603621, 200), (25, 323, 0.828169583641, 201), (25, 323, 0.913928205211, 201), (25, 324, 0.45836160144, 200), (25, 324, 0.499107021276, 13215), (25, 324, 0.559870976212, 200), (25, 324, 0.603511924685, 200), (25, 324, 0.623198421134, 210), (25, 324, 0.633639995522, 338), (25, 324, 0.635556007837, 246), (25, 324, 0.683944057834, 364), (25, 324, 0.730240665978, 202), (25, 324, 0.786380149202, 859), (25, 324, 0.798736866984, 263), (25, 324, 0.805943711046, 298), (25, 324, 0.820587885957, 201), (25, 325, 0.231831459255, 200), (25, 325, 0.563362833248, 239), (25, 325, 0.636026944883, 21971), (25, 325, 0.669608327745, 200), (25, 325, 0.716574236797, 200), (25, 325, 0.724404665933, 206), (25, 325, 0.739644789795, 40472), (25, 325, 0.752542864573, 200), (25, 325, 0.824388257792, 6198), (25, 325, 0.915197856113, 202), (25, 326, 0.707329416062, 208), (25, 326, 0.728563259999, 204), (25, 326, 0.752738034251, 201), (25, 326, 0.825564275897, 204), (25, 327, 0.719013790228, 203), (25, 327, 0.72228899991, 200), (25, 327, 0.751466201033, 209), (25, 327, 0.759232117888, 211), (25, 327, 0.767027224929, 1537), (25, 327, 0.778548686629, 203), (25, 327, 0.784075647798, 200), (25, 327, 0.793621518891, 200), (25, 327, 0.806195524296, 229), (25, 327, 0.808608560267, 201), (25, 327, 0.827857910169, 572), (25, 328, 0.393098272591, 203), (25, 328, 0.394325016086, 2993), (25, 328, 0.56951420425, 201), (25, 328, 0.580323359062, 2924475), (25, 328, 0.580905747982, 201), (25, 328, 0.583192577095, 542), (25, 328, 0.597499239304, 213), (25, 328, 0.600613025852, 253), (25, 328, 0.621643431237, 436), (25, 328, 0.701710063929, 200), (25, 328, 0.716681957271, 202), (25, 328, 0.761650010569, 202), (25, 328, 0.772259027715, 206), (25, 328, 0.779616327067, 200), (25, 328, 0.866568305949, 201), (25, 328, 0.898210193557, 515), (25, 329, 0.375129736945, 211), (25, 329, 0.446336810237, 285), (25, 329, 0.642038213561, 1496), (25, 329, 0.645488070638, 205), (25, 329, 0.771011371351, 203), (25, 329, 0.829964202191, 212), (25, 330, 0.511762908051, 201), (25, 330, 0.518705307319, 200), (25, 330, 0.584850797881, 200), (25, 330, 0.730246394391, 135696), (25, 330, 0.751681569544, 2366819428908), (25, 330, 0.92157485973, 200), (25, 331, 0.393252838456, 201), (25, 331, 0.413705536186, 200), (25, 331, 0.541667450199, 200), (25, 331, 0.610163703725, 202), (25, 331, 0.662097234233, 201), (25, 331, 0.711996875688, 557), (25, 331, 0.756070937233, 200), (25, 331, 0.77482801802, 660), (25, 331, 0.785152716014, 202), (25, 331, 0.804310562109, 201), (25, 331, 0.869247778778, 202), (25, 331, 0.900011576777, 206), (25, 332, 0.360501981662, 200), (25, 332, 0.396119173231, 1350), (25, 332, 0.549423865109, 204), (25, 332, 0.572660049768, 12648), (25, 332, 0.626922110118, 200), (25, 332, 0.725028858444, 7829535), (25, 332, 0.770714243024, 200), (25, 332, 0.778895975847, 228), (25, 332, 0.790939903651, 200), (25, 332, 0.845479439223, 204), (25, 333, 0.552595567924, 4737), (25, 333, 0.628912424024, 230), (25, 333, 0.712025685826, 205), (25, 333, 0.745406810596, 201), (25, 333, 0.905976663231, 205), (25, 334, 0.483908768827, 207), (25, 334, 0.60959982508, 200), (25, 334, 0.812519911253, 224), (25, 334, 0.843221977913, 217), (25, 335, 0.60973667496, 201), (25, 335, 0.693600650693, 201), (25, 335, 0.728238441845, 203), (25, 335, 0.75743368108, 210), (25, 335, 0.810360530954, 207), (25, 335, 0.882951536209, 200), (25, 335, 0.893759028105, 208), (25, 336, 0.740623773204, 201), (25, 336, 0.755244695771, 204), (25, 336, 0.831100589453, 200), (25, 337, 0.703493435921, 327), (25, 337, 0.718881873842, 226), (25, 337, 0.81048243721, 206), (25, 337, 0.899330103434, 18637), (25, 338, 0.700633185403, 206), (25, 338, 0.802867938789, 205), (25, 338, 0.805246709953, 4733064), (25, 338, 0.861528612477, 217), (25, 338, 0.875310494507, 201), (25, 339, 0.530202056325, 201), (25, 339, 0.596821460467, 206), (25, 339, 0.637622807415, 201), (25, 339, 0.720319384906, 1063), (25, 339, 0.925562964099, 241), (25, 340, 0.545836200959, 81897), (25, 340, 0.575462739406, 8298), (25, 340, 0.66454554903, 392), (25, 340, 0.665110271015, 200), (25, 340, 0.682396835586, 583), (25, 340, 0.705902758344, 216), (25, 341, 0.485770196306, 202), (25, 341, 0.572928076121, 8075702), (25, 341, 0.584378279664, 200), (25, 341, 0.671131495684, 201), (25, 341, 0.681341791186, 255), (25, 341, 0.729285274999, 56404734), (25, 341, 0.817259802301, 214), (25, 342, 0.7941751354, 201), (25, 342, 0.815001400116, 209), (25, 343, 0.713674285547, 204), (25, 343, 0.776290208985, 210), (25, 344, 0.578809632483, 200), (25, 344, 0.602669599066, 204), (25, 344, 0.640884720483, 201), (25, 344, 0.689617532849, 200), (25, 344, 0.735474986847, 793226), (25, 344, 0.801550588878, 200), (25, 345, 0.511613953266, 200), (25, 345, 0.599632141615, 3606), (25, 345, 0.725633060098, 213), (25, 345, 0.864442340693, 200), (25, 346, 0.629039256263, 519), (25, 346, 0.868847037952, 26139957), (25, 347, 0.383146657028, 505762), (25, 347, 0.793122392817, 887), (25, 348, 0.634239706868, 200), (25, 348, 0.747883842713, 908), (25, 348, 0.751757880877, 206), (25, 349, 0.617658321678, 200), (25, 350, 0.747783531486, 2330), (25, 350, 0.860911393971, 338), (25, 352, 0.686825990299, 10332), (25, 353, 0.683483882694, 227), (25, 353, 0.693201365913, 201), (25, 353, 0.86051685785, 79018), (25, 354, 0.700525525741, 200), (25, 355, 0.81145294361, 2178), (25, 356, 0.595846869158, 200), (25, 356, 0.619201382241, 1819), (25, 358, 0.563881791069, 210), (25, 358, 0.69894141965, 200), (25, 358, 0.743018024778, 325), (25, 358, 0.797592813469, 200), (25, 360, 0.663337283569, 258), (25, 360, 0.788791573196, 376), (25, 361, 0.527838758249, 290), (25, 361, 0.64267249425, 242), (25, 363, 0.487136757184, 200), (25, 365, 0.734633994789, 213), (25, 365, 0.889239450729, 225), (25, 368, 0.664001959486, 201), (25, 370, 0.593215752818, 1180660)] ### Lower bound One baseline would be to simply take our pre-existing exact solution V/VPplan and run it on the generalized Kelly by ignoring observations and assuming 300 rounds. It will probably perform reasonably well since it performs optimally at least one possible setting, and serve as a baseline: import gym env = gym.make('KellyCoinflipGeneralized-v0') rewards = [] for n in range(0,1000): done = False reward = 0 roundsLeft = 300 while not done: w = env._get_obs()[0][0] b = roundsLeft bet = VPplan(w, b) results = env._step(bet100) reward = reward+results[1] print n, w, b, bet, "results:", results roundsLeft = max(0, roundsLeft - 1) done = results[2] rewards.append(reward) env._reset() print sum(rewards)/len(rewards) # 140.642807947 In the general game, it performs poorly because it self-limits to $250 in the many games where the max cap is higher, and it often wipes out to$0 in games where the edge is small or negative. ## Deep RL Since the Bayesian decision tree is too hard to compute in full, we need a different approach. Tabular approaches in general will have difficulty as the full history makes the state-space vastly larger, but also so do just the sufficient statistics of wins/losses + rounds elapsed + maximum observed wealth. One approach which should be able to cope with the complexities would be deep reinforcement learning, whose neural networks let them optimize well in difficult environments; unfortunately, the sparsity of rewards in the Kelly coinflip game (receiving a reward only every ~300 steps) will make solving the game much harder for the agents. To create a deep RL agent for the generalized Kelly coin-flip game, I will use the keras-rl library of agents, which is based on the Keras deep learning framework (backed by TensorFlow); deep learning is often sensitive to choice of hyperparameters, so for hyperparameter optimization, I use the hyperas wrapper around hyperopt (paper). keras-rl offers primarily3 DQN (Mnih et al 2013) and DDPG (Lillicrap et al 2015). DQN is a possibility but for efficiency4 most DQN implementations require/assume a fixed number of actions, which in our case of penny-level betting, implies having 25,000 distinct unordered actions. I tried prototyping DQN for the simple Kelly coin-flip game using the keras-rl DQN example, but after hours, it still had not received any rewards - it repeatedly bet more than its current wealth, equivalent to its current wealth, and busting out, never managing to go 300 rounds to receive any reward and begin learning. (This sort of issue with sparse rewards is a common problem with DQN and deep RL in general, as the most common forms of exploration will flail around at random rather than make deep targeted exploration of particular strategies or try to seek out new regions of state-space which might contain rewards.) One possibility would have been to ‘cheat’ by using the exact value function to provide optimal trajectories for the DQN agent to learn from. DDPG isn’t like tabular learning but is a policy gradient method (Karpathy explains policy gradients). With deep policy gradients, the basic idea is that the ‘actor’ NN repeatedly outputs an action based on the current state, and then at the end of the episode with the final total reward, if the reward is higher than expected, all the neurons who contributed to all the actions get strengthened to be more likely to produce those actions, and if the reward is lower than expected, they are weakened. This is a very indiscriminate error-filled way to train neurons, but it does work if run over enough episodes for the errors to cancel out; the noise can be reduced by training an additional ‘critic’ NN to predict the rewards from actions, based on an experience replay buffer. The NNs are usually fairly small (to avoid overfitting & because of the weak supervision), use RELUs, and the actor NN often has batchnorm added to it. (To prevent them from learning too fast and interfering with each other, a copy is made of each called the ‘target networks’.) For exploration, some random noise is added to the final action; not epsilon-random noise (like in DQN) but a sort of random walk, to make the continuous action consistently lower or higher (and avoid canceling out). A continuous action would have less of an unordered action/curse of dimensionality required switching from DQN to DDPG (example). Unfortunately, DDPG also had initialization problems in overbetting, as its chosen actions would quickly drift to always betting either very large positive or negative numbers, which get converted to betting everything or $0 respectively (which then always result in no rewards via either busting & getting 0 or going 300 rounds & receiving a reward of 0), and it would never return to meaningful bets. To deal with the drift/busting out problem, I decided to add some sort of constraint on the agent: make it choose a continuous action 0-1 (squashed by a final sigmoid activation rather than linear or tanh), and convert it into a valid bet, so all bets would be meaningful and it would have less of a chance to overbet and bust out immediately. (This trick might also be usable in DQN if we discretize 0-1 into, say, 100 percentiles.) My knowledge of Keras is weak, so I was unsure how to convert an action 0-1 to a fraction of the agent’s current wealth, although I did figure out how to multiply it by$250 before passing it in. This resulted in meaningful progress but was sensitive to hyperparameters - for example, the DDPG appeared to train worse with a very large experience replay buffer than with the Lillicrap et al 2015 setting of 10,000. Hyperparameter-wise, Lillicrap et al 2015 used, for the low-dimensional (non-ALE screen) RL problems similar to the general Kelly coin-flip, the settings: • 2 hidden layers of 400 & 300 RELU neurons into a final tanh • an experience replay buffer of 10,000 • Adam SGD optimization algorithm with learning rate: 10-4 • discount/gamma: 0.99 • minibatch size: 64 • an Ornstein-Uhlenbeck process random walk, =0, =0.2, =0.15 For the simple Kelly coin-flip problem, the previous experiment with training based on the exact value function demonstrates that 400/300 neurons would be overkill, and probably a much smaller 3-layer network with <128 neurons would be more than adequate; the discount/gamma being set to 0.99 for Kelly is questionable, as almost no steps result in a reward, and a discount rate of 0.99 would imply for a 300 round game that the final reward from the perspective of the first round would be almost worthless (since ), so a discount rate of 0.999 or even just 1 would make more sense; because the reward is delayed, I expect the gradients to not be so helpful, and perhaps a lower learning rate or larger minibatch size would be required; finally, the exploration noise is probably too small, as the random walk would tend to increase or decrease bet amounts by less than $1, so probably a larger would be better. With these settings, DDPG can achieve an average per-step/round reward of ~0.8 as compared to the optimal average reward of 0.82 ($246 over 300 steps/rounds). For the general Kelly coin-flip problem, the optimal average reward is unknown, but initial tries get ~0.7 (~$210). To try to discover better performance, I set up hyperparameter optimization using hyperas/hyperopt over the following parameters: • number of neurons in each layer in the actor and critic (16-128) • size of the experience replay buffer (0-100000) • exploration noise: • () • (0-1) • () • learning rate: • Adam, main NNs (log uniform -7 to -2; roughly, 0.14 - 0.00…) • Adam, target NNs () • minibatch size (8-2056) Each agent/sample is trained ~8h and is evaluated on mean total reward over 2000 episodes, with 120 samples total. Full source code for the generalized Kelly coin-flip game DDPG: import numpy as np import gym from hyperas.distributions import choice, randint, uniform, normal, loguniform from hyperas import optim from hyperopt import Trials, STATUS_OK, tpe from keras.models import Sequential, Model from keras.layers import Dense, Activation, Flatten, Input, concatenate, Lambda, BatchNormalization from keras.optimizers import Adam from rl.agents import DDPGAgent from rl.memory import SequentialMemory from rl.random import OrnsteinUhlenbeckProcess def model(x_train, y_train, x_test, y_test): ENV_NAME = 'KellyCoinflipGeneralized-v0' gym.undo_logger_setup() # Get the environment and extract the number of actions. env = gym.make(ENV_NAME) numpy.random.seed(123) env.seed(123) nb_actions = 1 # Next, we build a very simple model. actor = Sequential() actor.add(Flatten(input_shape=(1,) + (5,))) actor.add(Dense({{choice([16, 32, 64, 96, 128])}})) actor.add(BatchNormalization()) actor.add(Activation('relu')) actor.add(Dense({{choice([16, 32, 64, 96, 128])}})) actor.add(BatchNormalization()) actor.add(Activation('relu')) actor.add(Dense({{choice([16, 32, 64, 96, 128])}})) actor.add(BatchNormalization()) actor.add(Activation('relu')) # pass into a single sigmoid to force a choice 0-1, corresponding to fraction of total possible wealth. # It would be better to multiply the fraction against one's current wealth to reduce the pseudo-shift # in optimal action with increasing wealth, but how do we set up a multiplication against the first # original input in the Flatten layer? This apparently can't be done as a Sequential... actor.add(Dense(nb_actions)) actor.add(BatchNormalization()) actor.add(Activation('sigmoid')) actor.add(Lambda(lambda x: x*250)) print(actor.summary()) action_input = Input(shape=(nb_actions,), name='action_input') observation_input = Input(shape=(1,) + (5,), name='observation_input') flattened_observation = Flatten()(observation_input) x = concatenate([action_input, flattened_observation]) x = Dense({{choice([16, 32, 64, 96, 128])}})(x) x = Activation('relu')(x) x = Dense({{choice([16, 32, 64, 96, 128])}})(x) x = Activation('relu')(x) x = Dense({{choice([16, 32, 64, 96, 128])}})(x) x = Activation('relu')(x) x = Dense(nb_actions)(x) x = Activation('linear')(x) critic = Model(inputs=[action_input, observation_input], outputs=x) print(critic.summary()) memory = SequentialMemory(limit={{randint(100000)}}, window_length=1) random_process = OrnsteinUhlenbeckProcess(size=nb_actions, theta={{uniform(0,1)}}, mu={{normal(0,5)}}, sigma={{normal(3,3)}}) agent = DDPGAgent(nb_actions=nb_actions, actor=actor, critic=critic, critic_action_input=action_input, memory=memory, nb_steps_warmup_critic=301, nb_steps_warmup_actor=301, random_process=random_process, gamma=1, target_model_update={{loguniform(-7,-2)}}, batch_size={{choice([8,16,32,64,256,512,1024,2056])}}) agent.compile(Adam(lr={{loguniform(-7,-2)}}), metrics=['mae']) # Train; ~120 steps/s, so train for ~8 hours: agent.fit(env, nb_steps=3000000, visualize=False, verbose=1, nb_max_episode_steps=1000) # After training is done, we save the final weights. agent.save_weights('ddpg_{}_weights.h5f', overwrite=True) # Finally, evaluate our algorithm for n episodes. h = agent.test(env, nb_episodes=2000, visualize=False, nb_max_episode_steps=1000) reward = numpy.mean(h.history['episode_reward']) print "Reward: ", reward return {'loss': -reward, 'status': STATUS_OK, 'model': agent} def data(): return [], [], [], [] if __name__ == '__main__': best_run, best_model = optim.minimize(model=model, data=data, algo=tpe.suggest, max_evals=120, # 8h each, 4 per day, 30 days, so 120 trials trials=Trials()) print("Best performing model chosen hyper-parameters:") print(best_run) How could this be improved? 1. fix the output scaling to be a fraction of current wealth rather than a fixed amount of$250; this avoids forcing the NN to learn to change its actions based on current wealth just to keep a constant bet amount, and instead focus on learning deviations from the baseline Kelly small bet of ~12% 2. experiment with batchnorm in the critic as well 3. incorporate the exact value function into the training to see how much benefit the additional supervision provides and how much damage is caused by the RL setting, or pre-populate the experience replay buffer based on samples from the exact value function or the 12% heuristic; it might also be interesting to see how much pretraining on the simple Kelly coin-flip helps with training on the general Kelly coin-flip 4. experiment with additional regularization methods like L2 norm (which Lillicrap et al 2015 also used) 5. try variants on the environment: • scale rewards down to 0-1; deep RL approaches reportedly have trouble with rewards which are not on the unit-scale • instead of underbetting=$0 and overbetting=current wealth, make them illegal bets which terminate an episode 1. That is, the value of the actions/bets 0-w seems like it would be bitonic - increasing linearly to the maximum then linearly decreasing. So one ought to be able to do a binary search over actions or something even better. I assume this is related to Bellman’s proof that finite-horizon MDPs’ value functions are convex and piecewise linear.↩︎ 2. Presumably a 3x5 or smaller NN would also work, but I experienced convergence issues with the SGD optimizer for all 3-layer NNs I experimented with, and as of 29 March 2017, a MXNet bug blocked use of the better optimizers.↩︎ 3. I also tried its CEM implementation, but after trying a variety of settings, CEM never performed better than an average reward of 0.4 or ~$120, inferior to most DDPG runs.↩︎ 4. This follows the original Mnih et al 2013 implementation. The NN is constructed with the screen observation state as the input and a final top layer outputting n reals corresponding to the q-value of the n actions, in that case the fixed number of buttons on the Atari controller. This allows enumeration of all possible actions’ values in a single forward pass of the NN, and picking the maximum.. The alternative would be to input both the screen observation and one possible action, and get out a single q-value for that one action; then to act, the agent would loop over all possible actions in that state, and then finding the maximum actions, which would allow a varying number of possible actions in each state, but at the cost of doing n forward passes (one for each possible action). In the Atari setting, the DQN agent interacts exclusively through the controller which has only a few buttons and a directional pad; and the environments are complex enough that it would be hard to define in advance what are the valid actions for each possible screen, which is something that must be learned, so this fixed-action trick is both necessary and efficient. Thus, it is also used in most implementations or extensions of DQN. In the Kelly coinflip, on the other hand, the discretizing is problematic since the majority of actions will be invalid, using an invalid action is damaging since it leads to overbetting, and we can easily define the range of valid actions in each state (0-w), so the trick is much less compelling.↩︎	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24377226829528809, "perplexity": 10042.21596781609}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232254889.43/warc/CC-MAIN-20190519141556-20190519163556-00195.warc.gz"}
https://stats.stackexchange.com/questions/81975/the-z-test-vs-the-chi2-test-for-comparing-the-odds-of-catching-a-cold-in-2/82556	# The $z$-test vs the $\chi^2$-test for comparing the odds of catching a cold in 2 groups I just read in a rather well-respected (popular) science magazine (the German PM, 02/2013, p.36) about an interesting experiment (without a source, unfortunately). It caught my attention because intuitively I doubted the significance of the result, but the information provided was sufficient for reproducing the statistical testing. The researchers wondered whether getting cold in cold weather increases the odds of catching a cold. So they randomly split a group of 180 students into two groups. One group had to hold their feet into cold water for 20 minutes. The other kept their shoes on. Kind of a funny manipulation, I think, but on the other hand I am not a doctor and maybe doctors think funny. Ethical issues aside. Anyways, after 5 days, 13 of the students in the treatment group had a cold, but only 5 in the group that kept their shoes on. The odds ratio of this experiment thus is 2.87. Given the rather small sample size, I started wondering if this difference may be significant. So I conducted two tests. First a simple test of equality of proportions using the normal approximation. This test has $z=1.988$ with $p=0.0468$. My guess is that this is what the researchers tested. This is truely just significant. However this z-test is only valid in large samples, if I am not mistaken, due to the normal approximation. Furthermore, the prevalence rates are rather small and I wonder whether this may not affect the coverage rate of the confidence interval of the effect. So my second try was a chi-square test of independence, both with Monte-Carlo simulation and standard Pearson Chi-square. Here I find p-values both about $p=.082$. Now that's all not so reassuring about the results. I wondered if there are more options to test this data and what your thoughts on the two tests are (in particular the assumptions of the first, significant, test) • I believe you've performed a continuity correction on the Pearson's chi-squared statistic, which accounts for the discrepancy in p-values. – Scortchi - Reinstate Monica Mar 26 '19 at 17:20 I'd use a permutation test instead of either the Normal approximation or the chi-square. The permutation test is exact and most powerful, conditional upon the data. In this case, we can't calculate all the permutations of the groups, but we can generate a lot of random permutations of the data and get a pretty precise value: group <- c(rep("A",90),rep("B",90)) n_a <- rep(0,100000) for (i in 1:length(n_a)) { temp <- sample(group, size=18) n_a[i] <- sum(temp == "A") } > mean(n_a >= 13) [1] 0.03904 which would indicate a p-value of 0.039. HOWEVER, and this is a big however, I'm guessing that the assumption that the subjects getting colds are independent events is violated. These individuals are students, presumably at the same school. Imagine two of them share a class, or a dorm, or some other activity, or a cafeteria (in a school with multiple cafeterias); the events "#1 gets a cold" and "#2 gets a cold" are not independent. I could imagine that a student would say "let's sign up for this experiment!" to his/her roommate or friends; I could imagine that the students were recruited from classes that the professors taught; I could imagine a lot of ways that the assumption of independence is violated. Perhaps the paper, which I have not read, addresses some of these, but it's hard to see how it could address all of them, and the others that come quickly to mind. • Thanks @jbowman -- in addition you conducted a one sided test, I see. I think this makes more sense then the two sided tests I used. If the normal approximation is done one sided, the p values is .023 above. I like the poit about independence. Probably students also were not isolated when they held their feet into the water, so that's also a way of transmitting a cold. – tomka Jan 12 '14 at 9:54 • (+1) But it's worth noting that you don't need to simulate: the distribution of your test statistic follows a hypergeometric distribution under the null hypothesis (& conditioning on the marginal totals). This is Fisher's Exact Test. – Scortchi - Reinstate Monica Mar 26 '19 at 14:05 @jbowman has given you a good option. I thought I might provide some information regarding your explicit questions about the appropriateness of the $z$-test vs. the $\chi^2$ test. $\boldsymbol z$-test: There are two concerns about the appropriateness of using the $z$-test, both regarding whether the assumed sampling distribution is correct. First, the $z$-test uses the normal distribution instead of the $t$-distribution, implying the standard deviations are known without sampling error. Second, the sampling distribution is continuous, but the data are discrete; since only certain combinations of data are possible, only certain resulting realized test statistic values are possible, which may not well match the theoretical sampling distribution. (I discuss this issue in the context of other tests here: Comparing and contrasting, p-values, significance levels and type I error.) Let's consider the first concern in a different context. If you have two groups with normally distributed data, and you want to see if the means are equivalent, you need to calculate both the means and the standard deviations. Now we know that the means are subject to sampling error, that's why we need to do the test rather than just say these two sample means aren't identical. However, our estimates of the standard deviations also have to be subject to sampling error and we have to take that fact into account somehow. When we do that, it turns out that the test statistic (a kind of scaled mean difference) is distributed as $t$. If we used the normal distribution instead (i.e., the $z$-test), it would mean that we are assuming that our estimates of the standard deviations are without error--perfect. So why could the $z$-test be used in your case? The reason is that your data are binomial (i.e., the number of 'successes' out of a known total of 'trials'), instead of normal. In the binomial distribution, the standard deviation is a function of the mean, so once you have estimated the mean there is no additional uncertainty to have to worry about. Thus, the normal distribution can be used as a model of the sampling distribution of the test statistic. Although using the normal distribution to understand the long-run behavior of the test statistic is technically correct, another issue emerges. The problem is that the normal distribution is continuous, but because your data are discrete, not all values in the theoretical distribution can possibly be found in your dataset. (Again, I discuss this issue in considerably more detail in the above linked answer.) Fortunately, the match between the possible outcomes of your data and the theoretical normal sampling distribution gets better the larger your $N$. In your case, no matter what the true underlying probabilities, you could have as many as all successes or as few as none in each group. That means the number of possible combinations is $91\times 91 = 1,\!729$, which is a lot of possibilities. With a small dataset, you really can run into some of the kinds of problems I discuss in my linked answer, but with $N = 180$, you don't have too much to worry about. I believe the $z$-test was a valid choice for the researchers. $\boldsymbol \chi^2$-test: But what about the $\chi^2$-test? I think that is also a valid choice, but it wouldn't be my first choice. (Let me note in passing that the second concern discussed above--a mismatch between discrete data and a continuous reference distribution--applies just as much to the $\chi^2$-test as it does to the $z$-test, so there is no advantage here.) The problem with the $\chi^2$-test is that it doesn't assume there is anything special about the column totals relative to the row totals; both are treated as though they could have been other possible values. However, this does not accurately reflect the experimental setup. There were 180 people, and 90 were assigned to each group. The only thing that would truly vary across repeated identical studies is the number of people who caught a cold in each group. The $\chi^2$-test incorrectly treats both the number of colds and the number of people in each group as though they could vary, but the $z$-test makes the right assumption. That's why the $z$-test has more power here. For what it's worth, the permutation test suggested by @jbowman also gets this aspect of your design right and doesn't suffer from the discrete-continuous mismatch issue. Thus, it is the best option. But I thought you might like to know a little bit more about how the $z$- and $\chi^2$-tests compare in your situation. • Thank you @gung, I really appreciate your efforts. It makes things clearer. – tomka Jan 17 '14 at 12:18 • @gung i am confused - is chi square and z of proportion the same or not ? stats.stackexchange.com/questions/173415/… – Xavier Bourret Sicotte Nov 13 '18 at 4:14 • @XavierBourretSicotte, the z-test is often implemented under the hood as a chi-squared test, R does that for example. I still often prefer to use the z-test because the information is presented in a way consistent with the understanding that 1 variable is a covariate & the other is the response. – gung - Reinstate Monica Nov 13 '18 at 11:58 • (+1) @XavierBourretSicotte: There are two commonly used z-tests for the difference between two proportions: one is a score test, equivalent to Pearson's chi-squared test (in which the variance in the denominator is calculated under the best-fitting null); the other is a Wald test (in which the variance in the denominator is calculated at the maximum-likelihood estimate of the difference in the two proportions). – Scortchi - Reinstate Monica Mar 26 '19 at 14:14 • @Scortchi thanks for clarifying this! It is the first time i come across such an explicit explanation of the difference - would you be able to link to places where the two approaches are explained? With the corresponding formulae for the variance? – Xavier Bourret Sicotte Mar 26 '19 at 17:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8124528527259827, "perplexity": 485.7872986293506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488253106.51/warc/CC-MAIN-20210620175043-20210620205043-00613.warc.gz"}
https://zz.zabemon.com/blogs/2066/06-06/test-1.html	### Example article testing element rendering In this test article, we test if Markdown elements are rendered correctly. First let us see basic inline elements, such as inline code block lambda x: wrapper(x), URL link, Italic, and bold font. Note that the underscore _ is seen as italic decorator hence, please use \_ in math equation to escape this. Table of contents appears at the place with marker [TOC]. # Section ## Section ### Section #### Section The font size of the first level heading seems a bit big. Also it would be good to have automatic heading numbering. The numbering can in principle be done in css but I prefer it generated by backend. The first paragraph, let's check the line spacing. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer sit amet hendrerit mauris. Quisque sed velit sit amet mi bibendum tempus at et purus. Curabitur eget finibus felis, ac aliquam dui. In in semper urna. Fusce at tellus eu turpis mattis consectetur at ut tortor. Suspendisse est massa, suscipit nec pulvinar vel, efficitur ac lorem. Sed luctus rhoncus magna sit amet cursus. Sed eget blandit lorem, vitae ultricies orci. Donec a nunc malesuada metus ullamcorper vehicula et sed tortor. Suspendisse congue iaculis purus, ut semper sem malesuada non. Donec ac venenatis lectus. Suspendisse ex orci, sagittis id ullamcorper vel, molestie a diam. Nam semper arcu nulla, id scelerisque dui egestas in. Praesent quis nunc ac lorem auctor luctus. Aenean scelerisque, eros at rhoncus convallis, tellus est molestie diam, nec porttitor lacus augue at massa. Aliquam erat volutpat. Nullam risus sem, commodo nec accumsan non, fermentum quis mi. In suscipit nisi tortor, eu suscipit tortor consequat accumsan. Mauris eget molestie arcu. Nunc venenatis leo ut enim tincidunt, eget suscipit tellus dignissim. Nulla sed nunc nec nisi pharetra auctor. Proin porttitor dolor velit, non lacinia nisl fringilla sed. Okay well, they look fine. Next we take a look at displayed code block. This is parsed by Pygments under the default theme. The background colour is the same as in Github. # Python scripts import numpy as np def func(x): return x ** 2 a = np.array([1., 2., 3.]) print(f'Value is: {a:.2f}') Another Rust code block // Rust code fn test<T>(a: T) -> T where T: Mytype { let b = b; // highlight here let c = 'hello'; // hightlight here b + 1 } and another Matlab code block % Matlab code a = [1:1:100]; b = a .^ 2; plot(a, b) We can also have numbered code block. For details, see Python Markdown. 1 2 3 4 5 #!/usr/bin/python # Python codes import matplotlib.pyplot as plt plt.plot([1., 2., 3.]) Add a figure (the max-width of image is set to 90% of the article width, and is auto-centred.) #### Second section Ordered list: 1. Element 1 2. Element 2 3. Element 3 Unordered list: • Elemement 1 • Element 2 Quote block, not sure if its background colour is necessary. Aliquam porttitor fringilla urna, ut mollis metus placerat ac. Morbi convallis suscipit suscipit. Ut accumsan neque et elit consequat eleifend. Integer eros nibh, scelerisque at pharetra quis, tincidunt vitae metus. Suspendisse nunc felis, interdum eu euismod non, gravida posuere augue. Duis malesuada orci quis justo porttitor, ac cursus magna gravida. Nam vehicula turpis quis elementum faucibus. Let's see admonition. Colours are picked from Sphinx website. In principle you could add some icons (e.g., exclamation mark) before these titles, but I do not consider this necessary. If you wish, Google "css ::before icon" for how to so so. Warning This is a warning message. Note This is a note message. Similarly, you could also use this admonition env to define, for example, theorem and lemma, though using quote block could also do the job. Lemma 1 (Kolmogorov--Chentsov). Let $X\colon [0, \infty)\to\mathbb{R}$ be a stochastic process. Suppose that for every $T>0$, there are $\alpha,\beta, C>0$ such that $$$$\mathbb{E}\big[ \abs{X(t) - X(s)}^\alpha \big] \leq C \, \abs{t-s}^{1+\beta},$$$$ for all $s,t\in[0,T]$. Then there is a version $\widetilde{X}$ of $X$ that is Hölder-continuous of every order $\gamma \in (0, \beta \, / \, \alpha)$ 3. Proof. Here shows the proof. However, increasing the top margin of the proof environment (or equivalently increase the bottom margin of the second p child) seems to be non-trivial. Some table. Syntax Description Paragraph Text Here's a sentence with a reference1. The default superscript style is a bit annoying, as I would like to see a number citation. I don't know how to interact with python markdown to add a square bracket around the number, though you could use in markdown to escape parsing them, but result looks a bit aweful. Finally let's test some math. Inline math $f(x) = \sin(x) + \mathbb{E} + \mathbf{A} + \mathcal{F}$, $\R^{N\times 2}, \Q, \N, \T$ and displayed math 2 $$$$\diff X(t) = A \, X(t) \diff t + B \diff W(t), \tag{5} \label{equ:eq}$$$$ The equation above looks fine in Chrome and Firefox, but not in Safari 14.1.2 (16611.3.10.1.6). I think this is a Mathjax problem. I have also pre-defined a few MathJax commands as per the fashion in this .tex. They should be sufficient in many cases. You should edit content/mathjax.html to customise your commands. Note that I am a bit agaist using \left \right to automatically adjust parenthesis height, because these could cause wrong vertal alignment compared to using \big etc. Instead, I prefer to hard-code them, for instance, \mathbb{E}\Big[ #1 \Big]. In the following you could find a few examples. $$$$\begin{split} &\expec{X \cond \FF} \\ &\expecbig{\expp^{\imag X}} \\ &\expecBig{ \big(\expp^{X} - X^2\big)^3 \cond Y}\\ &\cov{X, Y \cond \FF} \\ A\,A^\trans &= A^\trans \, A\\ \norm{A}_2 &\coloneqq \sup_{\norm{u}_2=1} \norm{A \, u}_2\\ &(\jacobian_x\phi)(x)\\ &(\hessian_x\phi)(x)\\ &(A\phi)(x)\\ f_u(v) &= \innerp{u}{v} \\ &\innerpBig{u + z}{\sum^N_{i=1} v_i}\\ \limsup_{N,M\to\infty} X_k &\coloneqq \lim_{N\to\infty} \sup_{M\geq N} X_k \end{split}$$$$ Now I reference Equation \eqref{equ:eq}. At last, let me check the support for Chinese. 測試行. 粗體斜體 # Conclusion Looks like most Markdown elements are rendered properly. There are still some fine tunning to do. # References 1. This is the footnote/reference. Looks like fine but needs some small adjustments. 2. Another reference. 3. Achim Klenke. Probability theory. Springer, 2014.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.9561266899108887, "perplexity": 29846.744720490293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335469.40/warc/CC-MAIN-20220930113830-20220930143830-00358.warc.gz"}
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1176345528	## The Annals of Statistics ### On Nonparametric Measures of Dependence for Random Variables #### Abstract In 1959 A. Renyi proposed a set of axioms for a measure of dependence for pairs of random variables. In the same year A. Sklar introduced the general notion of a copula. This is a function which links an $n$-dimensional distribution function to its one-dimensional margins and is itself a continuous distribution function on the unit $n$-cube, with uniform margins. We show that the copula of a pair of random variables $X, Y$ is invariant under a.s. strictly increasing transformations of $X$ and $Y$, and that any property of the joint distribution function of $X$ and $Y$ which is invariant under such transformations is solely a function of their copula. Exploiting these facts, we use copulas to define several natural nonparametric measures of dependence for pairs of random variables. We show that these measures satisfy reasonable modifications of Renyi's conditions and compare them to various known measures of dependence, e.g., the correlation coefficient and Spearman's $\rho$. #### Article information Source Ann. Statist. Volume 9, Number 4 (1981), 879-885. Dates First available in Project Euclid: 12 April 2007 http://projecteuclid.org/euclid.aos/1176345528 Digital Object Identifier doi:10.1214/aos/1176345528 Mathematical Reviews number (MathSciNet) MR619291 Zentralblatt MATH identifier 0468.62012 JSTOR	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8122373819351196, "perplexity": 615.859659016431}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395621.98/warc/CC-MAIN-20160624154955-00001-ip-10-164-35-72.ec2.internal.warc.gz"}
http://cms.math.ca/10.4153/CMB-2011-153-7	Canadian Mathematical Society www.cms.math.ca location: Publications → journals → CMB Abstract view # Cesàro Operators on the Hardy Spaces of the Half-Plane Read article[PDF: 296KB] Published:2011-08-03 Printed: Jun 2013 • Athanasios G. Arvanitidis, Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece • Aristomenis G. Siskakis, Department of Mathematics, University of Thessaloniki, 54124 Thessaloniki, Greece Format: LaTeX MathJax PDF ## Abstract In this article we study the Cesàro operator $$\mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta,$$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of $\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also discussed. Keywords: Cesàro operators, Hardy spaces, semigroups, composition operators MSC Classifications: 47B38 - Operators on function spaces (general) 30H10 - Hardy spaces 47D03 - Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} © Canadian Mathematical Society, 2015 : https://cms.math.ca/	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8658939003944397, "perplexity": 2443.388785872895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246650671.76/warc/CC-MAIN-20150417045730-00116-ip-10-235-10-82.ec2.internal.warc.gz"}
https://kb.osu.edu/dspace/handle/1811/15290	INFRARED EMISSION AS STUDIED THROUGH THE TEMPERATURE DEPENDENCE OF INTEGRATED INTENSITIES OF A MOLECULAR CRYSTAL. Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/15290 Files Size Format View 1967-N-04.jpg 115.9Kb JPEG image Title: INFRARED EMISSION AS STUDIED THROUGH THE TEMPERATURE DEPENDENCE OF INTEGRATED INTENSITIES OF A MOLECULAR CRYSTAL. Creators: Leles, Byron K.; Neff, Vernon D. Issue Date: 1967 Abstract: The expression for the integrated intensity of an infrared absorption band is normally obtained by neglecting the probability of spontaneous emission. At high temperatures, this factor cannot be neglected, and in fact gives rise to a decrease in intensity with increasing temperature. We have studied this effect experimentally with the molecular crystal, copper phthalocyanine at temperatures up to $600^{\circ}C$. Expressions based on the assumption of a harmonic potential function have been derived for the temperature dependence of the fundamentals and certain overtones and combinations. These expressions compare favorably with the experimental data. URI: http://hdl.handle.net/1811/15290 Other Identifiers: 1967-N-4	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8019199371337891, "perplexity": 1627.40270181918}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011473737/warc/CC-MAIN-20140305092433-00080-ip-10-183-142-35.ec2.internal.warc.gz"}
https://viralfact.in/the-evolution-of-ethereum-ethereum-foundation-blog/	# The Evolution of Ethereum \| Ethereum Foundation Blog Share Many of you know that the Ethereum platform grew out of the realization that blockchains can go far beyond currency, together with a frustration with the limitations of previous projects. The core idea was simple: a blockchain with a built-in Turing-complete programming language, allowing users to build any kind of applications on top. Over time, the vision evolved and expanded. The blockchain remains a crucial centerpiece, but it is ultimately only part of a larger vision of “web 3.0” as described by Gavin Wood here: a more secure, trustworthy and globally accessible internet for agreements, finance, auditing, tracking and simple websites and web applications that use decentralized technology to overcome some of the practical, political and technological inefficiencies of previous approaches. Together with the Ethereum blockchain, we see an entire suite of internally and externally developed, low-level and high-level protocols including Solidity, Whisper, IPFS, zero knowledge proof systems, account management systems, dedicated browsers and much more, all with the goal of providing a coherent vision of the internet as it should be. With such an ambitious vision, come some challenges. Right now, the Ethereum project is in a time of complicated transition. Many of the difficult initial work – myself, Gavin, Jeff, Martin, Lefteris, Felix, Vlad and many others developing four compatible versions of a project that our security auditors have described as having “testing needs … more complex than anything [they’ve] looked at before”, Christoph and Dmitry’s tireless efforts setting up over ten thousand tests, Marian, Taylor and Konstantin’s work on network analysis and emergency response architecture, Christian, Liana and Gavin’s work on getting Solidity off the ground, IMAPP’s work on the JIT EVM, and the many other projects of contributors to the Ethereum platform of which there are too many to mention, all culminating with the successful launch of a blockchain with over $50 million worth of value floating around on it starting from day one, are now behind us. Ethereum now actually exists, and those who were lucky enough to take up Mircea Popescu’s offer to buy ETH from him that he doesn’t have at a price of$ At the same time, however, there are some difficult challenges that remain: some technical, some organizational, and some of almost every kind. The core of the problem is simple. Up until fairly recently, almost all of the work that has been done on the Ethereum project has been done by subsidiaries of the foundation. In the future, however, although the foundation and its subsidiaries are going to continue to take on a strong and leading role, it will be the community that will gradually be the primary driver in making it succeed. This is true for several reasons, some unplanned and some positive. First of all, it is indeed true that the foundation’s finances are limited, and a large part of this was the result of our failure to sell nearly as much of our BTC holdings as we were planning to before the price dropped to $220; as a result, we suffered roughly$ Second, the project’s needs have grown. Over the past twenty months, the project has grown from being a simple attempt to improve on Mastercoin by adding a programming language into an effort to push forward a powerful and expansive vision of “web 3.0” that includes multiple technologies, some built by ourselves and some by others, and a complex software stack that integrates them all with one simple aim: to make it as easy to build secure, globally accessible and trust-minimized decentralized applications as it is to build a website – and hopefully even easier. The foundation and its subsidiaries alone simply do not have the manpower to push the entirety of this vision through to its ultimate completion, including proof-of-stake driven scalable blockchains, seamlessly integrated distributed hash tables, programming languages with formal verification systems backed by state-of-the-art theorem provers and dozens of categories of middleware, all by itself; although the foundation and its subsidiaries can, and will, continue to be the primary driver of technology at the core, a highly community-driven model is necessary and essential, both to help the Ethereum ecosystem maximally grow and flourish and to establish Ethereum as a decentralized project which is ultimately owned by all of humanity, and not any one group. And fortunately, the community has already stepped up. Just to give a few examples, here are a few parts of the Ethereum ecosystem that the Ethereum Foundation and its subsidiaries have had nothing to do with: • Augur: a prediction market that has earned $4.5 million in its recent (and still ongoing) crowdsale • GroupGnosis: another prediction market being developed by Consensys which is already processing bets on the Ethereum block difficulty, sports games, and soon presidential elections • Embark: a NodeJS-based dapp development, testing and deployment framework • Truffle: another dapp development, testing and deployment framework • Ether.camp: a block explorer • etherscan.io: another block explorer • TradeBlock: did I forget to say there’s another ethereum block explorer? • EtherEx: an Ethereum-based asset exchange • The Ether.camp web-based integrated development environment (coming soon) • EthereumWallet.com: an online ether wallet • The Ethereum Java implementation (for which original work was done under the Foundation, but which is now continuing completely independently) • And the Ethereum Haskell implementation, this time with none of our involvement at all! • MyEtherWallet: another ether wallet • Metamask: an ethereum browser-in-a-browser • Andreas Oloffson’s development tutorials • The first data feed contract • Ethereum Alarm Clock, an implementation of one our major planned features for Ethereum 1.1, but as a decentralized middleware service right on the 1.0 Ethereum blockchain! • dapps.ethercasts.com: a webpage listing many of the above, and more (no, I won’t mention the ponzies and gambling sites, except insofar as to credit Martin Holst Swende’s wonderful work in documenting the perils of building a blockchain-based casino with a bad random number generator, and Qian Youcai’s ongoing work on RANDAO to make this situation better). Actually, the Ethereum ecosystem is maturing nicely, and looks unrecognizable from what it was barely a year ago. On the inside, we have Ethereum Foundation subsidiary developers building yet more block explorers and other tools in their spare time, and some developers are already working on implementing Ethereum-based lightning networks, identity and reputation systems, and more. In the near future, there will be several more non-profit and for-profit entities emerging in and around the space, some with the involvement of Ethereum team members, and many with partial involvement from myself. The first of these to announce itself is the Wanxiang blockchain research institute and fund based in Shanghai (yes, this is the “major collaboration” I hinted on recently, and is also my much delayed answer to “how did your China trip go?”), which includes (i) an agreement to purchase 416K ETH, which has already concluded, (ii) an upcoming conference in October, (iii) a non-profit blockchain research institute, and (iv) a$50m blockchain venture-capital fund, all with emphasis on Ethereum development. I fully expect that within six months the Ethereum for-profit ecosystem may well be much more well-capitalized than the Foundation itself. Note that a substantial number of Ethereum foundation subsidiary staff is going to be moving over to the rapidly growing for-profit Ethereum ecosystem over the next half year in order to bring more funds, interest and development effort into Ethereum-land; so far, everyone I have talked to who is leaving the foundation subsidiaries is intending to do this, and they will in many cases simply be continuing, and expanding, the same work that they have started on now either under foundation subsidiary employment or as personal side projects, under a different banner. Ming Chan, who has recently joined the foundation, will be managing the foundation’s administrative matters, helping to develop an updated and more detailed strategic plan, oversee DEVcon 1 setup, and generally make sure that things on the foundation side work smoothly throughout the many simultaneous transitions that are taking place; we have also expanded our advisory board, and the new advisors will be announced soon. Under these circumstances, we must thus ask, what is the Foundation going to do (and not do)? ### Finances Let us start off by providing an overview of the Foundation’s financial situation. Its current holdings are roughly: • 200,000 CHF • 1,800 BTC • 2,700,000 ETH Plus a 490,000 CHF legal fund that will be reserved to cover possible legal defense (it’s like insurance). The foundation’s monthly expenditures are currently ~410,000 CHF and starting Oct 1 are projected to fall to 340,000 CHF; a mid-term goal has been placed of 200,000 – 250,000 CHF as a good target that allows us to deliver on our remaining, but important responsibilities. Assuming that we get there in three months and that ether and bitcoin prices stay the same (heh), we have enough to last until roughly Jun 2016 at the 340,000 rate, and perhaps up to Sep-Dec 2016 given planned transitions; by that point, the intent is for the foundation to secure alternative revenue sources. Possible revenue sources past that point include: • Developer workshops (including extended in-person “courses”) • Third-party donations and grants (whether to the Foundation or to projects that the Foundation would otherwise be spending resources on) Another action that may be taken is, when Ethereum switches to proof of stake, keeping 50% of the old issuance rate active for a year and directing the issuance into some kind of mechanism, perhaps a simple voting scheme or perhaps something more complex incorporating delegated voting, decision markets and potentially other revealed-preference tricks from game theory, in order to pay developers. In any case, our original promise that the issuance rate will not exceed 26.00% per year, and the goal that the eventual final issuance will be much lower (likely 0-3% per year) with proof of stake, will both be kept. We highly welcome community input on whether and how to go down this path; if there is large opposition we will not do this, though the community should understand that NOT doing this comes with a risk of greater reliance on the for-profit ethereum ecosystem. ### Focus Up until perhaps six months ago, the Foundation and its subsidiaries have been doing almost everything in the ecosystem; right now, the foundation and its subsidiaries are still doing much of everything though some community members have stepped up to compete with its own offerings – in some cases, in my own humble opinion, quite excellently. Going forward, the Foundation and its subsidiaries will aim for a more focused approach where it carries out only some of the work in the ecosystem, but does it well. An approximate outline of the Foundation’s activities can be described as follows: • Education • Online documentation and developer resources (new documentation site coming soon!) • Conferences (DEVcon 1 coming in November!) • Hackathons, workshops • Possibly paid in-person development courses • Conferences, events, Meetups co-ordination • Outreach, marketing and evangelism, both to the media/public and to institutions • Compliance and regulatory maintenance • Certifying businesses, individuals, etc (whether ourselves or through a third-party partner) • Highly targeted core development tasks including: • Some core client code • Network observation and coordinating emergency response • Maintaining test suites, certifying clients • Paying for some security audits • Research, including: • Proof of stake (Casper) • Scalability • Abstraction • Formal verification • Zero-knowledge proof integration • Official protocol and sub-protocol specifications Higher-level development tasks will in the medium term be done largely by for-profit entities, volunteers and other members of the community, although the Foundation’s subsidiaries will continue to employ many of the developers in the short term. ### Transparency The Ethereum Foundation would like to express a renewed interest in being maximally transparent in its affairs; to that end, we are publishing the information above, and as an initial trial in going further we are working with Consensys to use their (Ethereum) blockchain-based accounting software Balanc3 to record all expenses relating to Devcon 1. Another important aspect of transparency is more open and inclusive development; to that end, we are making a renewed push to move conversations from Skype to Gitter where they are more publicly visible (eg. you can check out this room right now) and members of the public can more easily participate. We are also evaluating the possibility of introducing a more formal and inclusive process for agreeing on protocol upgrades and welcome input from client developers on this. And there are more announcements both from ourselves and others that will be following soon. In sum, despite the evidence of growing pains, the state of the Ethereum nation is good, its ecosystem is vibrant, and its future is bright. As a Foundation, we will continue to focus on promoting and supporting research, development and education to bring decentralized protocols and tools to the world that empower developers to produce next generation (d)apps, and together build a more globally accessible, more free and more trustworthy Internet. #Evolution #Ethereum #Ethereum #Foundation #Blog	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18226838111877441, "perplexity": 3343.718022381084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500384.17/warc/CC-MAIN-20230207035749-20230207065749-00249.warc.gz"}
https://spec.oneapi.io/versions/latest/elements/oneVPL/source/appendix/VPL_apnds_b.html	# Multiple-segment Encoding¶ Multiple-segment encoding is useful in video editing applications during production, for example when the encoder encodes multiple video clips according to their time line. In general, one can define multiple-segment encoding as dividing an input sequence of frames into segments and encoding them in different encoding sessions with the same or different parameter sets. For example: Segment in Encoding Segment to be Encoded 0s 200s 500s Note Different encoders can also be used. The application must be able to: • Extract encoding parameters from the bitstream of previously encoded segment. • Import these encoding parameters to configure the encoder. Encoding can then continue on the current segment using either the same or similar encoding parameters. Extracting the header that contains the encoding parameter set from the encoded bitstream is usually the task of a format splitter (de-multiplexer). Alternatively, the MFXVideoDECODE_DecodeHeader() function can export the raw header if the application attaches the mfxExtCodingOptionSPSPPS structure as part of the parameters. The encoder can use the mfxExtCodingOptionSPSPPS structure to import the encoding parameters during MFXVideoENCODE_Init(). The encoding parameters are in the encoded bitstream format. Upon a successful import of the header parameters, the encoder will generate bitstreams with a compatible (not necessarily bit-exact) header. The Header Import Functions table shows all functions that can import a header and their error codes if there are unsupported parameters in the header or the encoder is unable to achieve compatibility with the imported header. Function Name Error Code if Import Fails MFXVideoENCODE_Init() MFX_ERR_INCOMPATIBLE_VIDEO_PARAM MFXVideoENCODE_QueryIOSurf() MFX_ERR_INCOMPATIBLE_VIDEO_PARAM MFXVideoENCODE_Reset() MFX_ERR_INCOMPATIBLE_VIDEO_PARAM MFXVideoENCODE_Query() MFX_ERR_UNSUPPORTED The encoder must encode frames to a GOP sequence starting with an IDR frame for H.264 (or I frame for MPEG-2) to ensure that the current segment encoding does not refer to any frames in the previous segment. This ensures that the encoded segment is self-contained, allowing the application to insert the segment anywhere in the final bitstream. After encoding, each encoded segment is HRD compliant. Concatenated segments may not be HRD compliant. The following example shows the encoder initialization procedure that imports H.264 sequence and picture parameter sets: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 mfxStatus init_encoder() { mfxExtCodingOptionSPSPPS option, option_array; / configure mfxExtCodingOptionSPSPPS / memset(&option,0,sizeof(option)); option.Header.BufferId=MFX_EXTBUFF_CODING_OPTION_SPSPPS; option.Header.BufferSz=sizeof(option); option.SPSBuffer=sps_buffer; option.SPSBufSize=sps_buffer_length; option.PPSBuffer=pps_buffer; option.PPSBufSize=pps_buffer_length; / configure mfxVideoParam / mfxVideoParam param; //... param.NumExtParam=1; option_array=&option; param.ExtParam=(mfxExtBuffer)&option_array; / encoder initialization */ mfxStatus status; status=MFXVideoENCODE_Init(session, ¶m); if (status==MFX_ERR_INCOMPATIBLE_VIDEO_PARAM) { printf("Initialization failed.\n"); } else { printf("Initialized.\n"); } return status; }	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6795876026153564, "perplexity": 3696.237020395551}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152112.54/warc/CC-MAIN-20210806020121-20210806050121-00584.warc.gz"}
http://mathhelpforum.com/advanced-algebra/18598-division-algorithm.html	# Math Help - division algorithm 1. ## division algorithm I'm having trouble with a problem, in my abstract algebra class, don't know how to even begin... Let n be a positive integer. Prove that a and c leave the same remainder when divided by n if and only if a - c = nk for some integer k. Now, i understand that the division algorithm basically states a = bq + r. In this case, n would be substituted with b. But, I'm a little confused on how to prove what it's asking for, or if I even understand what it's asking for. Please help! 2. Originally Posted by topsquark If a - c = nk then a = nx + r and c = ny + r for integer x, y, and r. Thus r = c - ny = a - nx c - ny = a - nx a - c = nx - ny = n(x - y) But x - y is an integer, say k. Thus a - c = nk. I did get to that point, but see, my problem is, I'm not sure that would acctually prove what I want, because in the begginig, you are assuming what you are trying to prove... theres no way you could find it any other way in the end, cuz in the begginig it was your starting assumtion.... Now you prove it the other way: Assume a - c = nk and show that this gives a = nx + r and c = ny + s means that r = s. And I've tried this way, but maybe I'm missing something... but, this is what I got by doing it that way... so far.... Since a = nx + r and c = ny + s, than filling it in the equation i want to prove, : nx + r - ny - s = nk but... I still don't know how to isolate the r and the s.... the other integers don't cancel out, I can simplify it a little bit, but I'm not sure how much help it would be to put it in this form: r - s = n(y - x + k) except for the fact that it resembles the first form, (no with integers but with format) I can't see where to go from here.... sighs unless i was able to prove that either n = 0 ( which i didn't think it could be, because it says let n be a positive integer) or I have to prove that y - x + k = 0..... 3. Originally Posted by fruitbodywash I did get to that point, but see, my problem is, I'm not sure that would acctually prove what I want, because in the begginig, you are assuming what you are trying to prove... theres no way you could find it any other way in the end, cuz in the begginig it was your starting assumtion.... And I've tried this way, but maybe I'm missing something... but, this is what I got by doing it that way... so far.... Since a = nx + r and c = ny + s, than filling it in the equation i want to prove, : nx + r - ny - s = nk but... I still don't know how to isolate the r and the s.... the other integers don't cancel out, I can simplify it a little bit, but I'm not sure how much help it would be to put it in this form: r - s = n(y - x + k) except for the fact that it resembles the first form, (no with integers but with format) I can't see where to go from here.... sighs unless i was able to prove that either n = 0 ( which i didn't think it could be, because it says let n be a positive integer) or I have to prove that y - x + k = 0..... You are right, I goofed. Let's try this for the forward proof: Let a - c = nk. We wish to show that both a and c leave the same remainder when divided by n. So a = nx + q c = ny + r where x, y, q, r are unique positive integers (when $0 \leq q,r < n$.) Thus a - c = (nx + q) - (ny + r) = n(x - y) + (q - r) But a - c = nk by hypothesis. Thus nk = n(x - y) + (q - r) Since both q and r are less than n, so is q - r. Thus in order for this equation to be satisfied by integers we must have that k = x - y and 0 = q - r. ie q = r. Thus a = nx + r c = ny + r and they leave the same remainder. -Dan 4. Originally Posted by topsquark Since both q and r are less than n, so is q - r. Thus in order for this equation to be satisfied by integers we must have that k = x - y and 0 = q - r. ie q = r. Thus a = nx + r c = ny + r and they leave the same remainder. -Dan I'm not sure i follow this.... i mean, i understand that q - r will be less than n, but that might not neccisarrily mean that it has to be zero... n could be say... 2 and q - r is 1... and the less than statement would still hold.... I know we want to prove that q - r = 0, but I can't quit seem to understand that step the gets from point A "nk = n(x - y) + (q - r)" to point B "k = (x - y)"... sighs thanks for being patient with me 5. eureka! ok, i think I got it... let me know if this makes sense... Known : a = nx + r c = ny + s 0 < n 0 <= r < n 0 <= s < n r - s < n s - r < n Ok... now for the rearranging.... using a - c = nk a - c = nk ==> (nx + r) - (ny + s) = nk ==> nx + r - ny - s = nk ==> r - s = ny - nx + nk ==> r - s = n(y - x + k) (this next step... is where I'm a little unsure....) ==> (r - s)/n = y - x + k = 0 (because... r - s < n... right?) ==> k = x - y (back to the first equation) a - c = nk ==> (nx + r) - (ny + s) = n(x - y) ==> nx + r - ny + s = nx - ny ==> r - s = 0 ==> r = s ............? is that right? ( I think that that is what you were trying to say up there, but I'm just re-itterating it to you to make sure that I understand it) 6. Originally Posted by fruitbodywash eureka! ok, i think I got it... let me know if this makes sense... Known : a = nx + r c = ny + s 0 < n 0 <= r < n 0 <= s < n r - s < n s - r < n Ok... now for the rearranging.... using a - c = nk a - c = nk ==> (nx + r) - (ny + s) = nk ==> nx + r - ny - s = nk ==> r - s = ny - nx + nk ==> r - s = n(y - x + k) (this next step... is where I'm a little unsure....) ==> (r - s)/n = y - x + k = 0 (because... r - s < n... right?) ==> k = x - y (back to the first equation) a - c = nk ==> (nx + r) - (ny + s) = n(x - y) ==> nx + r - ny + s = nx - ny ==> r - s = 0 ==> r = s ............? is that right? ( I think that that is what you were trying to say up there, but I'm just re-itterating it to you to make sure that I understand it) As far as I know that will work. -Dan 7. Originally Posted by fruitbodywash I'm having trouble with a problem, in my abstract algebra class, don't know how to even begin... No wonder you are having trouble, you have the home work from the elementary number theory class. Let n be a positive integer. Prove that a and c leave the same remainder when divided by n if and only if a - c = nk for some integer k. Now, i understand that the division algorithm basically states a = bq + r. In this case, n would be substituted with b. But, I'm a little confused on how to prove what it's asking for, or if I even understand what it's asking for. Please help! If a and c leave the same remainder when divided by n, then they may be written: a=k1 n + r, c=k2 n + r, so a-c = (k1-k2)n, which proves one half of the if and only if. If a-c=k n, then as we have a=k1 n + r1, c=k2 n + r2 for same k1, k2, 0<=r1<n, 0<=r2<n: a-c = (k1-k2)n + (r1-r2), so r1-r2= k3 n for some k3, so r1 = k3 n + r2, so a= (k1+k3)n + r2, hence r1=r2. Which proves the other half of the if and only if. RonL	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.791970431804657, "perplexity": 573.9979497789487}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928864.16/warc/CC-MAIN-20150521113208-00338-ip-10-180-206-219.ec2.internal.warc.gz"}
http://neoslb.com/vih6o/e3dd2c-pandoc-markdown-to-word	Word documents need to be in the docx format. This is GIT. ↔︎ Emacs Org-Mode Markdown has become the de-facto standard for writing software documentation. Pandoc can convert documents from. pandoc has a nifty feature enabling you to specify a style template when converting a marked-up plaintext file to a word processor format. ← TikiWiki markup So, how do you use that template you just created? Rather than try to convert the rest of the world, just work in Markdown, and convert things to Word before sending to others. Open the template file in LibreOffice Writer, and then press F11 to open LibreOffice Writer's Styles pane. Several different methods of rendering math in HTML are provided, including MathJax and translation to MathML. Pandoc includes a powerful … Pandoc turned it all into a Word document. Pandoc. At my day job, for example, I use several templates—one with a DRAFT watermark, one with a watermark stating FOR INTERNAL USE, and one for a document's final versions. Pandoc understands a number of useful markdown syntax extensions, including document metadata (title, author, date); footnotes; tables; definition lists; superscript and subscript; strikeout; enhanced ordered lists (start number and numbering style are significant); running example lists; delimited code blocks with syntax highlighting; smart quotes, dashes, and ellipses; markdown inside HTML blocks; and inline LaTeX. Add a cover page, which the publisher wanted. These results are serviceable, but a bit bland. I'm a long-time user of free/open source software, and write various things for both fun and profit. You might want to do the same. Next, copy the files into your /home directory. LaTeX math (and even macros) can be used in markdown documents. For more information please refer to the Pandoc User's Guide. And the -o test1.html says to put the output in the file test1.html. Copyright 2006–2020 John MacFarlane. The other way to use your template is to type this set of conversion options at the command line: pandoc -t odt file-name.md --reference-doc=path-to-your-file/reference.odt -o file-name.odt. The document contained links and embedded images. You type pandoc into a terminal, provide it the file you want to convert, then type --output and a name for the output file you want. Use a productive notebook interface to weave together narrative text and code to produce elegantly formatted output. If you're wondering what a converted file looks like with a customized template, here's an example: Many people only need one pandoc template. Pandoc made this easy -- we just added scripts to write out the model inputs as Markdown tables, then embed those tables in a larger writeup, also written in Markdown. Typical examples include converting a Markdown file into a presentation, LaTeX, PDF, or even ePub. Copy. Jul 8th, 2019. You need to generate what pandoc calls a reference template, which is the template it uses when converting text files to word processor documents. Markdown to Word. There are many ways to customize pandoc to fit your needs, including a template system and a powerful system for writing filters. Here's what this article looks like when converted to an ODT file: These results are serviceable, but a bit bland. → Slidy Note, in the case of the PDF, the default is to produce a A4 size page, and therefore the font in the example below is going to look small. With Pandoc you can convert Markdown documents to PDF, HTML, Words DOCX or many other formats. Thanks to the previous work of @dfinke on this extension. Using pandoc is a great way to provide documents in the format that people ask for, without having to give up the command line life. All I needed to do to finish it was: 1. Why. Launch VS Code Quick Open (Ctrl+P), paste the following command, and press enter. For some output formats, pandoc will convert it to an appropriate format stored in the additional variables babel-lang, polyglossia-lang (LaTeX) and context-lang (ConTeXt).Native pandoc Spans and Divs with the lang attribute (value in BCP 47) can be used to switch the language in that range. More Info. Now the generated markdown is very readable and close to what I would write myself. → ZimWiki markup and pandoc will convert it into a properly formatted citation using any of hundreds of CSL styles (including footnote styles, numerical styles, and author-date styles), and add a properly formatted bibliography at the end of the document. The amazing @pdfkungfoo tweeted about a nice feature of Pandoc, the universal document conversion tool: . If strict markdown compatibility is desired, all of these extensions can be turned off. If you have similar needs, start the same way you do for a single template, by creating the file custom-reference.odt. Download new cheat sheet of common Pandoc options and handy syntax for frequently used conversions. See the man page for pandoc or the Pandoc … → OpenDocument XML ↔︎ OpenOffice/LibreOffice ODT 8.1 Custom Word templates. Pandoc can usually auto-detect both formats from their filename extensions and convert from one to the other. In plain English, Pandoc allows you to convert a bunch of files from one markup language into another one. And if you need to create a file for that other word processor (you know the one I mean), replace odt on the command line with docx. Universal markup converter. For alternative ways to install pandoc, see below under the heading for your operating system. Windows. Renders markdown through pandoc. Note: faq.docx is the source Word document and faq_markdown.md is the file name given to the Markdown … And everything looks perfect if you don’t need to make a lot of changes by many employees and keep track of all these changes, discussions and approvals. Let's look at how to add a bit more style to the converted documents. Contribute to jgm/pandoc development by creating an account on GitHub. ↔︎ reStructuredText Using pandoc, you can quickly give people what they want. This post documents my experience using Pandoc to convert Word documents (docx) to markdown. Trivial to do in Word. ↔︎ CSL JSON Converts GitHub-flavored Markdown to a Word document. The filename test1.md tells pandoc which file to convert. . Note that pandoc is also available for a wide variety of operating systems, ranging from two flavors of BSD (NetBSD and FreeBSD) to Chrome OS, MacOS, and Windows. Contribute to jgm/pandoc development by creating an account on GitHub. ↔︎ JATS → S5 Pandoc includes a Haskell library and a standalone command-line program. At its most basic, the pandoc command is among the easiest commands to use. ← BibLaTeX With an increase of students and people using Word for school/college, I found that there was a tool missing for Linux users to quickly write documents (unless you used Libreoffice or paid for Microsoft 360) Here is a tutorial to write pdfs and docx documents using markdown! Lade das Vorlagen-Muster in Word (.dot / .docx -- egal), mache evtl. But we have another powerful tool with an excellent reputation for managing all of this. Pandoc is is a document conversion tool that can be used for exactly this (and a lot of other things). The officeR package allows for opening a Word document, going to named bookmarks within, and replacing the contents. Repeat this process for each template you need. To begin, install pandoc on your computer. Before going through the specifics of the Pandoc markdown syntax and the Pandoc options, I will illustrate a very basic example of Pandoc markdown conversion into a PDF, HTML and DZSlides presentation. Let's look at how to add a bit more style to the converted documents. → Microsoft PowerPoint, ↔︎ MediaWiki markup There is a package installer at pandoc’s download page. You can even put them in the .pandoc folder if you want to. The opinions expressed on this website are those of each author, not of the author's employer or of Red Hat. Rename the resulting file—for example, to custom-reference-draft.odt—then open it in LibreOffice Writer and modify the styles. The simplest way to get the latest pandoc release is to use the installer. Here's an example of a script using the template containing a DRAFT watermark: pandoc -t odt $1.md -o$1.odt --reference-doc=~/Documents/pandoc-templates/custom-reference-draft.odt. → Slideous For example, I run the script todraft.sh to create a word processor document using the template with a DRAFT watermark. LaTeX math is converted (as needed by the output format) to unicode, native Word equation objects, MathML, or roff eqn. ↔︎ Textile Citations work in every output format. I've successfully customized text styles (e.g. markdown, reStructuredText, textile, HTML, DocBook, LaTeX, MediaWiki markup, TWiki markup, OPML, Emacs Org-Mode, Txt2Tags, Microsoft Word docx, EPUB, or Haddock markup; to Pandoc basics. Download the latest installer . You can also customise a theme by writing it to a file (pandoc --print-highlight-style pygments > my.theme), editing the file (my.theme) and then passing it as the argument to --highlight-stylee.g. 2. Pandoc Markdown. → AsciiDoc Overview Version History Q & A Rating & Review. They prefer documents formatted for a certain proprietary application. Get the highlights in your inbox every week. Except where noted, these differences can be suppressed by using the markdown_strict format instead of markdown. pandoc -f docx -t markdown faq.docx -o faq_markdown.md. To select a specific template at conversion time, you'll need to run this command in a terminal: pandoc -t odt file-name.md --reference-doc=path-to-your-file/custom-template.odt -o file-name.odt. ← TWiki markup The good news is that you're not stuck copying and pasting unformatted text into a word processor document. Pandoc includes a powerful system for automatic citations and bibliographies. pandoc test1.md -f markdown -t html -s -o test1.html. Write once, publish twice using Markdown and Pandoc. The bibliographic data may be in BibTeX, BibLaTeX, CSL JSON, or CSL YAML format. Some people, however, need more than one. Copied to clipboard. I don't take myself all that seriously and I do all of my own stunts. I run into this issue frequently, especially at the Day JobTM. Change custom-template.odt to your template file's name. Red Hat and the Red Hat logo are trademarks of Red Hat, Inc., registered in the United States and other countries. Turn your analyses into high quality documents, reports, presentations and dashboards with R Markdown. You can use the program pandoc on the SCF Linux and Mac machines (via the terminal window) to convert from formats such as HTML, LaTeX and Markdown to formats such as HTML, LaTeX, Word, OpenOffice, and PDF, among others. ← txt2tags, ↔︎ DocBook version 4 or 5 pandoc has a nifty feature enabling you to specify a style template when converting a marked-up plaintext file to a word processor format. This command creates a file called custom-reference.odt. Although I've introduced one of the development teams I work with to a Docs Like Code workflow for writing and reviewing release notes, there are a small number of people who have no interest in GitHub or working with Markdown. Pandoc is free software, released under the GPL. What is pandoc? ↔︎ Emacs Muse The vscode-pandoc Visual Studio Code extension lets you quickly render markdown files as a pdf, word document or html file. Pandoc is the swiss-army knife for converting files from one markup format into another: What does Pandoc do? You are responsible for ensuring that you have the necessary permission to reuse any work on this site. If you're using that other word processor, change the references to odt on the command line to docx. I only use Word to write text with simple formatting like lists, italic, bold, and links. You can apply the styles defined in a Word template document to new Word documents generated from R Markdown. Let's take a look at how to convert a document from Markdown to a word processor format in Linux using pandoc. With that on Windows and Ulysses on iOS it looks like a great combo. Dear Community I would like to use Rmarkdown and a reference word.docx to easily apply text, figure & table styles and create an company report. → XWiki markup To follow along, install Pandoc, if you haven’t done so already. Word docx: pandoc -s MANUAL.txt-o example29.docx; LaTeX math to docx: pandoc -s math.tex-o example30.docx; DocBook to markdown: pandoc -f docbook -t markdown -s howto.xml-o example31.text; MediaWiki to html5: pandoc -f mediawiki -t html5 -s haskell.wiki-o example32.html; Custom writer: pandoc -t sample.lua example33.text-o example33.html When it's time to convert a document, pandoc uses this template file. Use multiple languages including R, Python, and SQL. This tool doesn't just work with Markdown, either. See the pandoc site linked earlier for more details. There are two ways to do this. ↔︎ CSL YAML, ↔︎ Microsoft Word docx Although the pandoc manual advises against making other changes to the file, I change the page size and add headers and footers when necessary. Pandoc understands an extended and slightly revised version of John Gruber’s Markdown syntax. This document explains the syntax, noting differences from standard Markdown. If you live your life in plaintext, there invariably comes a time when someone asks for a word processor document. While Markdown is the lingua franca of the development world, the rest of the world still sees Word documents as the de facto way to share text. After installing Pandoc, you can simply run it from command line. Silent update 2019-09-25: added to blog series "Using Org Mode Features". One approach I haven't tried as yet is to use Markdown to output to a Word document then to use Flextable to finalise the tables in the document by replacing placeholders inserted by Markdown or at specific bookmarks. Such a template document is also called a “style reference document.” The key is that you have to create this template document from Pandoc first, and change the style definitions in it later. — Jonathan Mosen (@JonathanMosen) June 12, 2020 I don’t know when was the last time I received a Microsoft Word .docx file. Several different methods of rendering math in HTML are provided, including MathJax and translation to MathML. LaTeX math is converted (as needed by the output format) to unicode, native Word equation objects, MathML, or roff eqn. : Use pandoc --list-highlight-styles to get a list of available styles. Prerequisites → TEI Simple, ← BibTeX However long the streak may have been: it has been broken today. Convert MS Word DOCX Files to Markdown with Images. So far my favourite solution to Markdown on Windows is a tool called Writage. To create this file, type the following in a terminal window: pandoc -o custom-reference.odt --print-default-data-file reference.odt. Microsoft Word is one of the most well-known de facto standards for documentation in many companies. ← Vimwiki markup You can customise the syntax highlighting used for code sections by setting --highlight-style when calling pandoc, e.g. pandoc -s example30.docx --no-wrap --reference-links -t markdown -o example35.md. It is a powerful tool with many features and settings. → via pdflatex, lualatex, xelatex, latexmk, tectonic, wkhtmltopdf, weasyprint, prince, context, or pdfroff. To avoid having to remember a set of options I don't regularly use, I cobbled together some simple, very lame one-line scripts that encapsulate the options for each template. About Visual Studio Code extension lets you render markdown to pdf, word doc or html with pandoc vscode-pandoc. Type this command to create an ODT file (which you can open with a word processor like LibreOffice Writer or AbiWord): pandoc -t odt filename.md -o filename.odt. The first official book authored by the core R Markdown developers that provides a comprehensive and accurate reference to the R Markdown ecosystem. Opensource.com aspires to publish all content under a Creative Commons license but may not be able to do so in all cases. ↔︎ DokuWiki markup Once I ran Pandoc on the mega Markdown file, I had a nicely formatted Word document with automatic references and a bibliography. Converting with style. What I've discussed in this article also allows you to create and convert documents between a wide variety of markup languages. This videos shows how one can create reveal.js html slides from simple markdown documents. If you need to convert files from one markup format into another, pandoc is your swiss-army knife. Note: By default, Pandoc uses LaTeX to generate PDF documents. You can find me at these fine establishments on the web: 6 open source tools for staying organized, Convert files at the command line with this Pandoc cheat sheet, Turn your book into a website and an ePub using Pandoc. See the next section on how to choose from multiple templates if you need more than one. Installation. Word to Markdown using Pandoc. Remember to replace filename with the file's actual name. Pandoc can convert between the following formats: (← = conversion from; → = conversion to; ↔︎ = conversion from and to), ↔︎ Markdown (including CommonMark and GitHub-flavored Markdown) Then, crack open a console terminal window and navigate to the directory containing the file that you want to convert. The easiest way is to drop the template in your /home directory's .pandoc folder—you might have to create the folder first if it doesn't exist. This means that you can write a citation like. → reveal.js ↔︎ Jira wiki markup, → LaTeX Beamer Please do read my "Using Org Mode Features" (UOMF) series page for explanations on articles of this series.. title, heading 1/2, paragraph, ...) and use it in the entire reference document ("update heading 1 to match selection). → DZSlides. Commonly used markup languages include Markdown, ReStructuredText, HTML, LaTex, ePub, and Microsoft Word DOCX. In order to style your documents, you can't just use any template. This can be done in Markdown with Pandoc but it's easier to do in Word, especially since the header syntax in Markdown that uses the #symbol creates actual headers in Word, and Word's table-of-contents generator uses headers to do its thing, which requi… Running pandoc is relatively straightforward for a job like this: pandoc MyWordDoc.docx -f docx -t markdown -o MyWordDoc.md where MyWordDoc.docx is the name of the Word document you want to convert and MyWordDoc.md is the name of the output file (call yours anything you want, but it’s useful to name it with a .md file extension). The -s option says to create a “standalone” file, with a header and footer, not just a fragment. It is used in the develop… Thus, the same toolchain that did the actual work, also drove the final report. For more discussion on open source and the role of the CIO in the enterprise, join us at The EnterprisersProject.com. In this file, you can edit a small number of styles in the document, including those that control the look of paragraphs, headings, captions, titles and subtitles, a basic table, and hyperlinks. It lets you load and save Markdown files in Word which is really cool. Each type of document needs a different template. The library includes separate modules for each input and output format, so adding a new input or output format just requires adding a new module. Add a table of contents. Pandoc User 's Guide with Images even macros ) can be turned off looks. Proprietary application vscode-pandoc Visual Studio Code extension lets you load and save Markdown as... Markdown documents specify a style template when converting a Markdown file into a processor. The next section on how to convert a document, going to named bookmarks within and! I received a Microsoft Word is one of the CIO in the develop… Turn analyses... Math in HTML are provided, including MathJax and translation to MathML needs... It 's time to convert I had a nicely formatted Word document with automatic references and a bibliography for! Epub, and links when calling pandoc, the same toolchain that did actual... Window and navigate to the other those of each author, not of the most well-known de facto standards documentation... Another, pandoc uses LaTeX to generate PDF documents experience using pandoc to fit your needs, start same... My experience using pandoc to convert certain proprietary application a Word template document to new Word need. Logo are trademarks of Red Hat, Inc., registered in the Turn... Have another powerful tool with an excellent reputation for managing all of my own stunts and profit of free/open software! For Code sections by setting -- highlight-style when calling pandoc, you n't... Style to the pandoc … so far my favourite solution to Markdown excellent reputation for managing all my... Pandoc has a nifty feature enabling you to convert files from one to the pandoc command is among the commands... Formats from their filename extensions and convert documents between a wide variety markup... Format in Linux using pandoc ePub, and Microsoft Word DOCX LaTeX to generate PDF documents Word ( /... Of markup languages include Markdown, either follow along, install pandoc, you can apply styles! Great combo 's Guide in Markdown documents to PDF, or CSL YAML format copying and pasting unformatted text a. Languages including R, Python, and replacing the contents of the author 's employer of. Section on pandoc markdown to word to convert it looks like a great combo ” file, type following... Expressed on this extension are many ways to customize pandoc to fit your needs, start same! To follow along, install pandoc, you can simply run it from command line to...., prince pandoc markdown to word context, or CSL YAML format or of Red Hat noted, These can! The -s option says to create this file, type the following in Word. Code extension lets you quickly render Markdown files as a PDF, HTML, Words DOCX many. Software documentation it looks like when converted to an ODT file: These results are serviceable, but a more... Seriously and I do n't take myself all that seriously and I do n't myself. Are trademarks of Red Hat logo are trademarks of Red Hat logo are of... To MathML is your swiss-army knife for converting files from one markup language into another one the! The following command, and SQL in plain English, pandoc uses this template file in LibreOffice Writer and the! Proprietary application more discussion on open source and the role of the CIO in the United States other! Ensuring that you want to powerful … These results are serviceable, but bit. Jgm/Pandoc development by creating the file that you have the necessary permission to reuse work! Open a console terminal window and navigate to the pandoc site linked earlier more! The converted documents create and convert documents between a wide variety of markup languages a time when someone asks a. Ctrl+P ), paste the following in a terminal window: pandoc -o custom-reference.odt -- print-default-data-file reference.odt just use template. List of available styles is that you 're using that other Word processor, change the references ODT... Feature enabling you to create and convert from one to the previous work of @ dfinke on this site PDF! United States and other countries ) can be suppressed by using the template a... More style to the pandoc … so far my favourite solution to Markdown finish it was: 1 a... On articles of this: 1 finish it was: 1 These extensions can be used in Markdown to... Just a fragment document, pandoc is the swiss-army knife prince, context or..., ePub, and SQL Markdown developers that provides a comprehensive and accurate reference to the Markdown! Has a nifty feature enabling you to create a “ standalone ” file, type the following command, replacing! The CIO in the file 's actual name the officeR package allows for opening a Word document! “ standalone ” file, type the following command, and links pandoc 's. Document or HTML file revised version of John Gruber ’ s Markdown syntax 's take a look how! That you want to convert a document, going to named bookmarks within, and Microsoft Word one... S Markdown syntax on open source and the role of the author 's employer or of Red Hat using. Elegantly formatted output ) can be turned off to follow along, install pandoc, the pandoc command among! Uomf ) series page for pandoc or the pandoc User 's Guide template with a header and footer, just... Turned off looks like when converted to an ODT file: These results are serviceable, but a bit...., or CSL YAML format Markdown has become the de-facto standard for writing software documentation copying., how do you use that template you just created lets you load and save Markdown files Word! Source software, and write various things for both fun and profit below the. Pandoc allows you to specify a style template when converting a marked-up plaintext file to Word... When calling pandoc, if you live your life in plaintext, there invariably comes a time when asks! Next section on how to convert note: by default, pandoc is the knife! Just use any template be turned off documents to PDF, Word document or HTML.! Take a look at how to add a bit bland bold, and.. A terminal window: pandoc -o custom-reference.odt -- print-default-data-file reference.odt one to the converted.! N'T just work with Markdown, ReStructuredText, HTML, LaTeX, PDF, HTML,,! Processor document to publish all content under a Creative Commons license but may be. John Gruber ’ s Markdown syntax Word template document to new Word need... Json, or pdfroff quickly give people what they want but we have powerful... Notebook interface to weave together narrative text and Code to produce elegantly formatted output thanks to the containing! Converting a marked-up plaintext file to convert far my favourite solution to Markdown on Windows and on! Word document with automatic references and a standalone command-line program Markdown files as a PDF, HTML, LaTeX PDF. using Org Mode Features '' ( UOMF ) series page for explanations on articles of this to. Including R, Python, and replacing the contents generate PDF documents done so already software, then... To open LibreOffice Writer and modify the styles defined in a terminal window and to! Enterprise, join us at the EnterprisersProject.com style your documents, you can customise the syntax highlighting used for sections. Pandoc you can convert Markdown documents to PDF, HTML, LaTeX ePub. On articles of this series, bold, and Microsoft Word is one of the author employer! All I needed to do to finish it was: 1 this site in LibreOffice,... Writing filters.docx -- egal ), mache evtl window and navigate to the R.. A wide variety of markup languages include Markdown, either pandoc do -f Markdown -t HTML -s test1.html. The develop… Turn your analyses into high quality documents, reports, presentations and dashboards with R Markdown,! By using the template file in LibreOffice Writer, and SQL and.! Hat and the -o test1.html Q & a Rating & Review create convert... Plaintext, there invariably comes a time when someone asks for a certain proprietary application even put them the... People, however, need more than one I only use Word to write text with simple formatting lists. Your swiss-army knife fit your needs, including a template system and a standalone command-line program the amazing pdfkungfoo! Open a console terminal window: pandoc -o custom-reference.odt -- print-default-data-file reference.odt feature! -F pandoc markdown to word -t HTML -s -o test1.html variety of markup languages & Review pandoc free. Enterprise, join us at the Day JobTM F11 to open LibreOffice Writer 's styles.! For a Word document, pandoc is the swiss-army knife for converting files from one markup language another... However, need more than one great combo list-highlight-styles to get the latest pandoc release is to use installer! Own stunts interface to weave together narrative text and Code to produce elegantly formatted output please read. 'S employer or of Red Hat bunch of files from one markup format into another, pandoc uses template... The final report xelatex, latexmk, tectonic, wkhtmltopdf, weasyprint, prince, context or! Formatted for a certain proprietary application more information please refer to the pandoc command is among easiest. Json, or pdfroff been: it has been broken today the previous work of @ on!, also drove the final report this issue frequently, especially at the EnterprisersProject.com says. Processor, change the references to ODT on the mega Markdown file, a! Of this 's employer or of Red Hat the enterprise, join us at the Day JobTM is the knife... History Q & a Rating & Review extended and slightly revised version of John Gruber ’ download... My using Org Mode Features '' ( UOMF ) series page for explanations on of! Newland Homes Customer Care, Career Opportunities In Medical Laboratory Science, Dead Bait For Barramundi, Teacup Cavalier King Charles Spaniel Full Grown, Bacardi Breezer Orange, Tampa City Limits Curfew, Cookie Monster Desktop Wallpaper Hd, Subset Of Deep Learning, Texas Tech Medical School,	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22140662372112274, "perplexity": 6232.832670799659}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487630081.36/warc/CC-MAIN-20210625085140-20210625115140-00445.warc.gz"}
https://hal.archives-ouvertes.fr/hal-00992344	# Vibrating soap lm: origin of the dissipation Abstract : We investigate the complex dispersion relation of a transverse antisymmetric wave on a horizontal soap film. Experimentally, the complex wave number $k$ at a fixed forcing frequency is determined by measuring the vibrating amplitude of the soap film: the wavelength (linked to the real part of $k$) is determined by the spatial variation of the amplitude; the decay length (linked to the imaginary part of $k$) is determined by analyzing the resonance curves of the vibrating wave as a function of the frequency. Theoretically, we compute the complex dispersion relation taking into account the physical properties of the bulk liquid and gas phase, and of the gas-liquid interfaces. The comparison between the computation (developed to the leading order in our experimental conditions) and the experimental results confirms that the phase velocity is fixed by the interplay between surface tension, and liquid and air inertia, as reported in previous studies. Moreover, we show that the attenuation of the transverse antisymmetric wave originates from the viscous dissipation in the gas phase surrounding the liquid film. This result is an important step to understand the propagation of an acoustic wave in a liquid foam, in a bottom-up approach. Keywords : Document type : Preprints, Working Papers, ... Complete list of metadatas Cited literature [3 references] https://hal.archives-ouvertes.fr/hal-00992344 Contributor : Caroline Derec <> Submitted on : Friday, May 16, 2014 - 6:02:12 PM Last modification on : Friday, October 25, 2019 - 11:02:17 AM Long-term archiving on : Saturday, August 16, 2014 - 12:21:17 PM ### File vibrating_soap_film_HAL.pdf Files produced by the author(s) ### Identifiers • HAL Id : hal-00992344, version 1 ### Citation Sébastien Kosgodagan Acharige, Florence Elias, Caroline Derec. Vibrating soap lm: origin of the dissipation. 2014. ⟨hal-00992344⟩ Record views	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8723507523536682, "perplexity": 1534.0392183218787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669755.17/warc/CC-MAIN-20191118104047-20191118132047-00086.warc.gz"}
http://www.cseblog.com/2014/03/value-of-pi-estimation-using-dice.html	# CSE Blog - quant, math, computer science puzzles Quant, Math & Computer Science Puzzles for Interview Preparation & Brain Teasing A collection of ~225 Puzzles with Solutions (classified by difficulty and topic) ## Mar 30, 2014 ### Value of Pi - Estimation using Dice Source: Asked to a friend at Goldman Sachs Quant Interview Problem: Estimate the value of pi using a dice Update: (21 June 2014) Solution posted by Tushar Makkar, 'My first amateur attempt', Satadip, Gaurav Bajaj and me (Pratik) in comments. Thanks 1. Imagine we have a dice and we have to throw in a circle embedded in a 44 square. This circle touches the boundaries of this square. Let’s say out if N trials number of times this dice falls on circle is C and number of times this dice falls on square is N. So the ratio of C/N will represent the ratio of area of circle to the area of square which is [PI(RR) ] /(44). (C/N)=(PI4/16) [ C/N=PI/4 ] => PI=4C/N At this point, we will perform the simulation using N=3000. So, the trick is number of times the dice falls on square is equal to number of trials performed. The range of x and y will vary from -2 and 2. And the condition which is used in simulation to check whether the dice falls inside the circle or not is IF(sqrt(x^2+y^2) <2) then assign cell’s value is 1 and if the condition fails, assign cell’s value as 0 . In the end we can use find out numbers of cells containing 1 to find C/N ratio. Using both the equations we can find approximate value of PI . These kind of problem solving methods are known as Monte Carlo simulation techniques . 1. Correct Solution. Thanks 2. consider a circle inscribed in a square , the probability of a random point from the square also in the circle is pi/4 Now how do we actually pick up a point randomly , this is where the dice will help break the square into 6 by 6 blocks , 2 rolls of dice will give us co-ordinate of the box now if we stop the experiment here give the center of the square as the random point else apply the same experiment to this smaller box . choosing any of the 36 smaller boxes is equally likely so if we do enough trials we can be sure to pick a random point with every point being equally likely. This solution was by my friend Sankeerth(EE , IITB class of 2009) 1. Correct Solution. Thanks 3. I found this link: http://www.monkshouts.org/value-of-pi-using-monte-carlo-simulation/ The die is meant to mislead you. You can simply throw any object randomly in a square and estimate the probability that it lands inside an embedded circle. If the square is of side 2 and the circle of radius 1, then the probability is pi/4. 1. Gowtham, Nope. Its not a trick question. Please check the answer. Interesting aha moment. :-) 4. use monte carlo simulations.... take a square [-3, 3] x [-3, 3] and check a pair of die-rolls(dey give the co-ordinates of point) a large no of times. 1. Yep. Correct. Thanks 5. Here's a little bit neat method. Throw a die six times. Let the values be a, b, c, d, e, f. Define a event X if {(a-1)/6 + (b-1)/36 + (c-1)/216}^2 + {(d-1)/6 + (e-1)/36 + (f-1)/216}^2 <1 and event Y is the otherwise. Calculate {the number of event X} / {(the number of X)+(the number of Y)} This will converges approximately pi. 1. can you please explain how? 2. Details please? Thanks 6. A more accurate solution: divide the square in 6x6 blocks and each square again into 6x6 sub-squares as shown in the image below http://postimg.org/image/xiizzkp2p/ Throw the dice: 1. if the dice points to the square such that it lies in the centre 4x4 square add one to Pi_count variable 2. if the dice points to the 20 squares on the perimeter, throw dice one more time and if the dice points to subsquare which is filled with blue add one to Pi_count. Value of Pi = Pi_count/Num_of_iteration4 The precision improved 6 times with 1.55 times increase in no of dice throws. 1. Yep. Correct. Thanks 7. Generate two such random numbers, x and y, appending digits to each until there are enough digits in both numbers to establish with certainty whether x^2+y^2<1 or x^2+y^2>1. (Equality occurs with probability 0 and can be disregarded.) If x^2+y^2<1, add a tally to the "in" column; otherwise add a tally to the "out" column. After generating a n=in+out such pairs, and so accumulating a total of n tallies, we have π ~ 4in/(in+out). The idea here is that x and y determine a random point in the square [0,1]^2 that is uniformly distributed. The area of the quarter-circular region x^2+y^2<1 is π/4, and so a uniformly selected point in the square will lie in that region with probability π/4. 1. sir do we need to know algorithmic techniques before solving your puzzles....i have jst passed out class 12th	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.835341215133667, "perplexity": 1366.0780719893205}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802768044.102/warc/CC-MAIN-20141217075248-00092-ip-10-231-17-201.ec2.internal.warc.gz"}
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00621060v2	Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises: Harmonic Chains with Bulk Noises Abstract : We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites $1$ and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type. Mots-clés : Document type : Journal articles Domain : Cited literature [12 references] https://hal-ens-lyon.archives-ouvertes.fr/ensl-00621060 Contributor : Cedric Bernardin <> Submitted on : Wednesday, October 26, 2011 - 8:52:06 AM Last modification on : Tuesday, May 26, 2020 - 6:50:52 PM Long-term archiving on: : Friday, January 27, 2012 - 2:24:45 AM Files VFS3.pdf Files produced by the author(s) Identifiers • HAL Id : ensl-00621060, version 2 • ARXIV : 1109.1993 Citation Cedric Bernardin, Venkateshan Kannan, Joel Lebowitz, Jani Lukkarinen. Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises: Harmonic Chains with Bulk Noises. European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2011, 84, pp.685-689. ⟨ensl-00621060v2⟩	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3939623534679413, "perplexity": 6799.31623040077}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402124756.81/warc/CC-MAIN-20201001062039-20201001092039-00571.warc.gz"}
https://www.physicsforums.com/threads/termodynamics-doubt.635391/	Termodynamics doubt 1. Sep 12, 2012 jaumzaum I was solving the question below : "A cylinder have a piston whose mass is insignificant and moves without friction. One mole of an ideal gas is confined into the cylinder. If we expand isotermally the gass at temperature 298K, against a constant external pressure of 0.1 atm, the gas pressure goes from 1atm to 0.1 atm. Calculate the work need for the expansion." I have 2 answers, and I don't know why the second one is wrong: 1) Pressure is constant. W = P(ext)(V2-V1) = P(ext) nRT(1/P2-1/P1) = 0,9.1.8,31.298 = 2.23kJ 2) Gas Pressure is P, so the difference of pressure is P1=(P-0,1). W = ∫P1.dv. V = nRT/P dv = -nRT/P²dP W = ∫-(P-0.1)nRT/P² dP = 2476(ln(P1/P2) - 0.1(P2-P1)) = 2476(2.3+0.09) = 5,91kJ Why the second is wrong, and more important, why the first one is right? What is the definition of work? []'s João 2. Sep 12, 2012 Simon Bridge The Work is the area under the PV diagram. What makes you think (1) is correct and (2) is not? 3. Sep 12, 2012 Andrew Mason In 2. you are using the internal pressure of the gas rather than the external pressure. The thermodynamic work here is the work done by the gas on the external environment (ie. against the external pressure). In effect, the excess internal pressure is not used to do mechanical work. This is a non-reversible expansion because there is a significant difference between the internal gas pressure and the external pressure. This excess pressure causes a very rapid initial outward expansion but does not add to the total work that is done. That work is simply W = Pext(ΔV). AM Similar Discussions: Termodynamics doubt	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9035819172859192, "perplexity": 935.0531392515582}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104636.62/warc/CC-MAIN-20170818121545-20170818141545-00116.warc.gz"}
https://wordpandit.com/data-interpretation-level-1-set-4/	Select Page Direction: The following questions are based on the following bar graph. Read the graph and answer the questions. Blue Bar: Gross traffic receipts Maroon Bar: Total expenditure. Question 1: What is the percentage increase in the gross traffic receipts in 1995-96 as compared to 1993-94? (1) 33.9% (2) 41.5% (3) 20.7% (4) 17% Question 2: If profit = gross traffic receipts— total expenditure, then in 1996-97, what percentage of gross traffic receipts is the profit made? (1) 5.9% (2) 6.4% (3) 7.2% (4) 8% Question 3: In which year was the profit as a percentage of gross traffic receipts the highest? (1) 1997-98 (2) 1996-97 (3) 1995-96 (4) 1994-95 Question 4: In order to make a profit of 10%, what should have been the gross traffic receipts (in Rs. crores) in 1994-95, total expenditure remaining the same? (1) 5,667 (2) 5,876 (3) 6,444 (4) 7,667 Question 5: By what amount (in Rs. crores) has the expenditure increased over the period 1993-94 to 1997-98? (1) 4,100 (2) 3,900 (3) 3,850 (4) 3,700	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8807477951049805, "perplexity": 14457.260875610313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103661137.41/warc/CC-MAIN-20220630031950-20220630061950-00477.warc.gz"}
http://grephysics.net/ans/9277/76	GR 8677927796770177 \| # Login \| Register GR9277 #76 Problem GREPhysics.NET Official Solution Alternate Solutions \prob{76} The configuration of three electrons $1s2p3p$ has which of the following as the value of its maximum possible total angular momentum quantum number? 1. 7/2 2. 3 3. 5/2 4. 2 5. 3/2 Atomic$\Rightarrow$}Orbitals The total angular momentum is given by $j=l+s$ where l is the orbital angular momentum and s is the spin angular momentum. (Note that, to an extent, l and s can be viewed as magnitudes, while $m_l$ and $m_s$ as directions.) The total orbital angular momentum is just $0+1+1$, since one should recall that $(s,p,d,f) \in (0,1,2,3)$. The spin angular momentum is just $1/2+1/2+1/2$ because one has three electrons.(Electrons are fermions that have spin $1/2$.) Thus, the total angular momentum is $j=2+3/2=7/2$, as in choice (A). Alternate Solutions Mall-Saint2016-10-23 00:32:38 We have l=0+1+1=2. Each electron has s=1/2. If we have two electrons, the possible values of s are 0 and 1. Therefore for three electrons, the possible values of s are 1/2 and 3/2. Hence if we have (l=2, s=1/2) the possible j values are 3/2 and 5/2. But if we have (l=2, s=3/2) the possible j values are 1/2, 3/2, 5/2, 7/2. Hence the largest possible j is 7/2.\r\n\r\nAlso note l=2 because m_l = 0 for the 1s state, but m_l = {-1,0,1} for the 2p and 3p states, and so the total m_l can take any value from {-2,-1,0,1,2} -> l=2.Reply to this comment Mall-Saint 2016-10-23 00:32:38 We have l=0+1+1=2. Each electron has s=1/2. If we have two electrons, the possible values of s are 0 and 1. Therefore for three electrons, the possible values of s are 1/2 and 3/2. Hence if we have (l=2, s=1/2) the possible j values are 3/2 and 5/2. But if we have (l=2, s=3/2) the possible j values are 1/2, 3/2, 5/2, 7/2. Hence the largest possible j is 7/2.\r\n\r\nAlso note l=2 because m_l = 0 for the 1s state, but m_l = {-1,0,1} for the 2p and 3p states, and so the total m_l can take any value from {-2,-1,0,1,2} -> l=2. jeffray 2011-11-07 11:19:56 If the state were instead 1s$^2$2s3s, would the calculation change to 0 + 1 + 1 + 1/2 - 1/2 + 1/2 + 1/2? Do the two spins cancel out or do we just add another 1/2? ashowmega 2010-04-02 13:01:05 So, here the electrons are 1s 2p 3p. We know that for s, l=0, for 2p l=-1,0,1, for 3p l=-1,0,1. Hence we have seven values of quantum numbers. And each of them have 1/2 spin angular momentum. Hence, for seven azimutal quantum numbers, the total angular momentum = 7x(1/2) = 7/2 . I guess what I am thinking is right. flyboy6212010-10-22 17:23:43 That's not right. For s states, l=0. For p states, l=1. For spin 1/2 particles (i.e. electrons), s=1/2,m_s=1/2, -1/2. For this problem we are not concerned with any of the m values, only l and s. We have 6 angular momentum quantities to add together: 0, 1, 1, 1/2, 1/2, 1/2 The outcome of adding these together can be any non-negative number you can get by adding or subtracting them. The maximum possible outcome is when they all add together (instead of subtracting). That gives 7/2, which is the answer. Other possible outcomes are 3, 5/2, 2, 3/2, 1, and 1/2. Zero is not possible. coke_man 2008-08-01 12:56:40 I know this is a stupid question, but how is the total orbital angular momentum equal to $0+1+1$. If there is one electron in the $1s$ and one in the $2s$ and one in the $3s$ shouldn't the total angular momentum be $0+1+2$? Could someone please tell me what I'm missing!!! coke_man2008-08-01 13:01:11 Sorry, this should have been categorized under HELP :D note2008-08-23 16:17:19 the s subshell refers to quantum angular momentum number l=0 the p subshell refers to quantum angular momentum number l=1 one electron is in s and two are in p, thus 0+1+1 ebykl2008-10-25 10:18:03 What I can't understand is how can 3electrons can go to third shell. 1s^2 2s^2 2p^6......so the 3electrons must be at must at the 2S shell? segfault2009-09-06 07:43:35 $1s2p3p$ is just a given state. It doesn't necessarily have to be the ground state, $1s^22s$ Moush2010-09-28 18:58:26 I had the same problem as coke_man, and a lot of others did too (only 25% answered correctly) so this is worth mentioning. Whenever I saw $\.l$=1, 2, 3, ... n-1, I incorrectly thought $\.l$ HAS TO BE n-1, but instead $\.l$ can be UP TO n-1. For some reason I never understood that an e- in orbital s has $\.l$=0, and $\.l$=1 for e- in orbital p, etc., REGARDLESS of the principal quantum number shell it's in. All examples I've seen use PQN + orbital combinations that give the same answer with both correct and incorrect assumptions...until ETS. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydcol.html#c2 This comment is best classified as a: (mouseover) Mouseover the respective type above for an explanation of each type. ## Bare Basic LaTeX Rosetta Stone LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces $\alpha^2_0$. type this... to get...$\int_0^\infty$$\int_0^\infty$$\partial$$\partial$$\Rightarrow$$\Rightarrow$$\ddot{x},\dot{x}$$\ddot{x},\dot{x}$$\sqrt{z}$$\sqrt{z}$$\langle my \rangle$$\langle my \rangle$$\left( abacadabra \right)_{me}$$\left( abacadabra \right)_{me}$$\vec{E}$$\vec{E}$$\frac{a}{b}\$ $\frac{a}{b}$ The Sidebar Chatbox... Scroll to see it, or resize your browser to ignore it...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 33, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9685467481613159, "perplexity": 1043.7711559511172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187826210.56/warc/CC-MAIN-20171023164236-20171023184236-00874.warc.gz"}
https://pos.sissa.it/346/121/	Volume 346 - 23rd International Spin Physics Symposium (SPIN2018) - Parallel Session: Low Energy Spin Physics with Lepton, Photon and Hadron Probes (F. Maas and H. Spiesberger) Baryon Electromagnetic Form Factors at BESIII I. Garzia Full text: pdf Pre-published on: 2019 August 19 Published on: 2019 August 23 Abstract Electromagnetic form factors are fundamental observables needed to parametrize the electric and magnetic structure of hadrons and used to probe strong interactions. In this contribution we report on the recent measurements of baryon electromagnetic form factors at the BESIII experiment in Beijing. The BESIII spectrometer is located at the BEPCII collider, a symmetric $e^+e^-$ collider running at the center-of-mass energies between 2.0 and 4.6 GeV. This wide energy range allows direct measurement of electromagnetic form factors both from direct $e^+e^-$ annihilation and from initial-state-radiation processes. Based on the data collected by BESIII at twelve center-of-mass energies between 2.23 and 3.67 GeV, the $e^+e^-\rightarrow p\bar{p}$ cross section and the time-like proton form factors are measured. Preliminary results from the analysis on the initial-state-radiation radiation process $e^+e^-\rightarrow p\bar{p}\gamma$ using a data set of about 7.4 fb$^{-1}$ collected at the center-of-mass energies between 3.773 and 4.6 GeV are also presented. Besides nucleons, all hyperons in the SU(3) spin 1/2 octet and spin 3/2 decuplet are energetically accessible within the BEPCII energy range. Furthermore, a world-leading data sample was collected in 2014-2015 for precision measurements of baryon form factors, which allows the measurement of the relative phase between the electric and magnetic form factors for $\Lambda$ and $\Lambda_c$ hyperons with unprecedented accuracy. The results from the $e^+e^-\rightarrow \Lambda\overline{\Lambda}$ and the $e^+e^-\rightarrow\Lambda_c\overline{\Lambda}_c$ channels are also discussed. DOI: https://doi.org/10.22323/1.346.0121 Open Access	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9543571472167969, "perplexity": 2736.110005952684}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347422065.56/warc/CC-MAIN-20200602002343-20200602032343-00000.warc.gz"}
https://tug.org/pipermail/texhax/2008-February/010080.html	# [texhax] HTML specials with '_' character Michael M. Tung michael.m.tung at gmail.com Sun Feb 17 20:27:54 CET 2008 Reinhard Kotucha [reinhard.kotucha at web.de] wrote: > Michael M. Tung writes: > > Hi! > > > > I have problems with my following macro in plain TeX > > > > \def\mailto#1{ > > \special{html:<a href="mailto:#1">}% > > {\tt #1} > > \special{html:</a>} > > } > > > > which creates a hyperlink for mailing in the final PDF > > file. For standard emails with letters and '@' it works > > fine. However such things as > > > > \mailto{test_user at yahoo.com} > > > > creates an error requiring math mode for '_'. Defining > > > \catcode\_=12 > \def\mailto{\catcode\_=12\relax\@mailto} > > \def\@mailto#1{ > \special{html:<a href="mailto:#1">}% > {\tt #1} > \special{html:</a>} > \catcode\_=8\relax} > \catcode\_=8 > > $$a_1$$ > > \mailto{test_user at yahoo.com} > > $$a_2$$ > \end > > > \mailto changes the catcode and calls \@mailto, which takes the > argument. \@mailto also has to restore the catcode. > > The catcode of _ has be be set to 12 while the macro is read and has > to be restored later. This is not necessary if you replace \_ by the > ASCII character number, for instance \catcode95=12. > > Regards, > Reinhard > Dear Reinhard, many thanks for your speedy reply for the \mailto which now works perfectly! I was trying to use the same logic to add another special macro to my style file, e.g. altogether the code would have \catcode\_=12 \def\mailto{\catcode\_=12\relax\@mailto} \def\@mailto#1{ \special{html:<a href="mailto:#1">}% {\tt #1} \special{html:</a>} \catcode\_=8\relax } \catcode\_=8 \catcode\~=12 \def\href{\catcode\~=12\relax\@href} \def\@href#1#2{ \special{html:<a href="#1">}% {\tt #2} \special{html:</a>} \catcode\~=13\relax } \catcode\~13 For \href the only difference is that I used catcode assignment 13 to mark the '~' active at the end. Unfortunately I get the following error log: ! Use of \@ doesn't match its definition. \mailto ->\catcode \_=12\relax \@m ailto l.12 \mailto {test_user at yahoo.com} What I am doing wrong? I don't see where I redefine '\@'... Best, Mike	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9533417224884033, "perplexity": 26272.449515365617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303709.2/warc/CC-MAIN-20220121192415-20220121222415-00186.warc.gz"}
https://math.stackexchange.com/questions/3546357/is-cofactor-matrix-of-2x2-matrices-unique	# Is cofactor matrix of 2x2 matrices unique? Please consider the 2x2 matrix below: $$\left[\begin{array}{ccc} 1 & 2 \\ 3 & 4 \end{array}\right]$$ According to the definition given here and here, the cofactor matrix becomes: $$\left[\begin{array}{ccc} a_{22} & -a_{12} \\ -a_{21} & a_{11} \end{array}\right] = \left[\begin{array}{ccc} 4 & -2 \\ -3 & 1\end{array}\right]$$ However, when I follow the practice given here and here, I do obtain the following cofactor matrix, which is the transpose of the above: $$\left[\begin{array}{ccc} a_{22} & -a_{21} \\ -a_{12} & a_{11} \end{array}\right] = \left[\begin{array}{ccc} 4 & -3 \\ -2 & 1\end{array}\right]$$ The difference arises from the off-diagonal locations of $$a_{12}$$ and $$a_{21}$$. Are these two cofactors equivalent to each other in some way?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9861225485801697, "perplexity": 189.77928284882094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038069133.25/warc/CC-MAIN-20210412175257-20210412205257-00067.warc.gz"}
https://idswater.com/2020/01/04/what-is-geothermal-energy-being-used-for-today/	# What is geothermal energy being used for today? January 4, 2020 Off By idswater ## What is geothermal energy being used for today? Its current uses include heating buildings (either individually or whole towns), raising plants in greenhouses, drying crops, heating water at fish farms, and several industrial processes, such as pasteurizing milk. ## Why should geothermal be used? There are many advantages of geothermal energy. It can be extracted without burning a fossil fuel such as coal, gas, or oil. Geothermal fields produce only about one-sixth of the carbon dioxide that a relatively clean natural-gas-fueled power plant produces. Binary plants release essentially no emissions. ## What are the 3 main uses of geothermal energy? Geothermal energy can heat, cool, and generate electricity: Geothermal energy can be used in different ways depending on the resource and technology chosen—heating and cooling buildings through geothermal heat pumps, generating electricity through geothermal power plants, and heating structures through direct-use … ## What is the most common geothermal used today? Flash steam plants Flash steam plants are the most common type of geothermal power generation plants in operation today. ## What are 3 disadvantages of geothermal energy? What are the Disadvantages of Geothermal Energy? • Location Restricted. The largest single disadvantage of geothermal energy is that it is location specific. • Environmental Side Effects. • Earthquakes. • High Costs. • Sustainability. ## Why geothermal energy is bad? Geothermal plants can release small amounts of greenhouse gases such as hydrogen sulfide and carbon dioxide. Water that flows through underground reservoirs can pick up trace amounts of toxic elements such as arsenic, mercury, and selenium. ## Does geothermal use a lot of electricity? Geothermal heat pumps don’t generate heat — they just transfer it from the ground into your home. For every 1 unit of energy used to power your geothermal system, on average 4 units of heat energy are supplied. Why geothermal heat pumps use more electricity than furnaces (but less than conventional air conditioners) ## What country is the largest producer of geothermal energy? Top countries producing geothermal power • US. With an installed capacity of 3,639MW in 2018, the US is the leading producer of geothermal energy across the world, producing 16.7 billion kilowatt hours (kWh) of geothermal energy throughout the year. • Indonesia. • Philippines. • Turkey. • New Zealand. • Mexico. • Italy. • Iceland. ## What are some disadvantages of geothermal energy? • Geothermal power plants can only be built at specific sites. • Geothermal facilities have high upfront construction costs. • Geothermal plants can cause earthquakes. ## What is the downside of geothermal energy? This energy source is more environmentally friendly than conventional fuel sources. The largest single disadvantage of geothermal energy is that it is location specific. Geothermal energy runs the risk of triggering earthquakes. A sustainable source of energy as its always available unlike wind and solar. ## Why is geothermal energy important to our future? The Importance Of Geothermal Energy To Our Future. Geothermal energy is 100% reliable, renewable, and green. It’s equally important, if not more so than solar energy. It’s going to contribute significantly to becoming an emission-free world! ## Where does low temperature geothermal energy come from? This heat energy is called low-temperature geothermal energy. Low-temperature geothermal energy is obtained from pockets of heat about 150° C (302° F). Most pockets of low-temperature geothermal energy are found just a few meters below ground. ## What’s the difference between geothermal and nuclear energy? Geothermal energy is the heat left over from eons ago when the Earth is born and supplemented by element decay which is nuclear fission energy. Both are non-renewable in Earth. They only can be used and no replenishment. The element decay is producing less and less energy as the Earth getting older. ## Where was the first geothermal heating system built? The United States opened its first geothermal district heating system in 1892 in Boise, Idaho. This system still provides heat to about 450 homes. Co-produced geothermal energy technology relies on other energy sources. This form of geothermal energy uses water that has been heated as a byproduct in oil and gas wells. ## How is geothermal energy used in the real world? How to Use Geothermal Energy. Geothermal energy is used in three main ways: direct use, power generation, and ground source heating and cooling: Direct Use: The hot water in geothermal reservoirs produces heat and steam, which can be directly used for multiple purposes. ## Where is geothermal energy stored? Geothermal energy is thermal energy stored beneath the earth’s surface. It is clean, renewable, and popular because it can be harnessed from almost anywhere in the world to produce heat and electricity. Historically recognized as hot springs, geothermal energy is commonly used today for residential heating and cooling, and electricity generation. ## What are the pros and cons of geothermal energy? Another disadvantage of geothermal energy is that it causes earthquakes. The geothermal power plants construction can affect the lands’ stability. Hydraulic fracturing is an intrinsic part of building enhanced geothermal system and power plants, but it triggers earthquakes. ## Where are the geothermal power plants in the US? Smaller projects can also be seen in Idaho, Nevada, New Mexico, Oregon, Utah, and Wyoming. California is the state leader with 2,600 MW of geothermal energy currently installed, while Hawaii has one major geothermal power plant that supplies 20% of all energy used on the Big Island.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9080517888069153, "perplexity": 3619.396789727254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00761.warc.gz"}
http://linuxczar.net/blog/2012/01/31/altering-kvm-virtual-disk-images/	I wanted to alter a file that was a disk image for a KVM virtual machine. With a physical machine I use dd fairly often to save and alter the partition table and boot loader. I wanted to do that to a KVM image. The problem being that when you use dd to write to a file, when dd is done it truncates the file. So I would lay down a new partition table and boot loader on my KVM image and find the image was now only a few kilobytes long. It used to be 20 gigabytes in size! To do this we need to use the loop device: # dd if=/dev/zero of=/var/lib/libvirt/images/foo.img bs=1024 count=20971520 # losetup /dev/loop0 /var/lib/libvirt/images/foo.img # dd if=/tmp/bar.img of=/dev/loop0 Now you can use fdisk or other tools to examine the hard disk image on /dev/loop0. When you are done, tear down the loopback. # losetup -d /dev/loop0	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24578912556171417, "perplexity": 4210.414482423009}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221209980.13/warc/CC-MAIN-20180815063517-20180815083517-00554.warc.gz"}
http://www.scstatehouse.gov/sess117_2007-2008/sj08/20080130.htm	South Carolina General Assembly 117th Session, 2007-2008 Journal of the Senate Wednesday, January 30, 2008 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 2:00 P.M., the hour to which it stood adjourned, and was called to order by the PRESIDENT. A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows: Among the opening verses of the book of Joel we read: "What the cutting locust left, the swarming locust has eaten. What the swarming locust left, the hopping locust has eaten, and what the hopping locust left, the destroying locust has eaten." (Joel 1:4) Let us pray: Holy God, as the prophet Joel speaks to us about what had to be an ecological catastrophe in ancient Judah-devastation by a swarm of desert locusts-we are brought up short. We find ourselves thinking about how delicate the balance in our own world is: with our concerns about polluted waterways, about the air we breathe, about the dread of possible ecological disasters. O God, be with all of the leaders of this 117th South Carolina Senate as they strive to be wise and caring stewards of the world around us, for the benefit of ourselves and for our children's children. In Your name we pray, dear Lord. Amen. The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers. MESSAGE FROM THE GOVERNOR The following appointments were transmitted by the Honorable Mark C. Sanford: Statewide Appointments Reappointment, South Carolina Arts Commission, with the term to commence June 30, 2008, and to expire June 30, 2011 At-Large: Sarah L. Hayes, 836 Myrtle Drive, Rock Hill, SC 29730 Referred to the Committee on Education. Reappointment, South Carolina State Ethics Commission, with the term to commence June 30, 2008, and to expire June 30, 2013 3rd Congressional District: E. Kay Biermann Brohl, 48 Cherry Hills Drive, Aiken, SC 29803 Referred to the Committee on Judiciary. Reappointment, South Carolina State Housing, Finance and Development Authority, with the term to commence August 15, 2008, and to expire August 15, 2012 At-Large: John S. Hill, 140 Aspen Trail, Columbia, SC 29206 Referred to the Committee on Labor, Commerce and Industry. Expression of Personal Interest Senator PATTERSON rose for an Expression of Personal Interest. S. 678 (Word version) -- Senator Hutto: A BILL TO AMEND SECTION 20-7-1572, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO GROUNDS FOR TERMINATION OF PARENTAL RIGHTS, SO AS TO PROVIDE THAT THE COURT MAY ORDER TERMINATION OF PARENTAL RIGHTS IF THE INSTITUTIONALIZATION OF A PARENT, INCLUDING INCARCERATION, RENDERS IT IMPROBABLE FOR THE PARENT TO CARE FOR THE CHILD FOR AN EXTENDED PERIOD OF TIME AND IF THE COURT FINDS THAT TERMINATION IS IN THE BEST INTEREST OF THE CHILD. On motion of Senator CLEARY, with unanimous consent, the name of Senator CLEARY was added as a co-sponsor of S. 678. S. 1018 (Word version) -- Senators Martin and Setzler: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 39-5-43 SO AS TO MAKE IT AN UNFAIR TRADE PRACTICE FOR A PERSON WITH AN INTEREST IN A REAL ESTATE TRANSACTION INVOLVING AN APPRAISAL TO COMMIT ANY ACT THAT IMPAIRS THE INDEPENDENT JUDGMENT OF THE APPRAISER IN CARRYING OUT THE APPRAISAL ASSIGNMENT, TO PROVIDE DEFINITIONS, TO PROVIDE FOR A CIVIL CAUSE OF ACTION INCLUDING THE AWARD OF COURT COSTS AND ATTORNEY'S FEES, AND TO PROVIDE FOR REVOCATION OF PROFESSIONAL LICENSES OF OFFENDERS. On motion of Senator CEIPS, with unanimous consent, the names of Senators CEIPS, HAWKINS and LAND were added as co-sponsors of S. 1018. S. 588 (Word version) -- Senators McConnell, Lourie, Rankin, Land and Ritchie: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTIONS 38-71-1345, 38-71-1355, 38-71-1365, AND 38-71-1445 SO AS TO PROVIDE REQUIREMENTS, POWERS, DUTIES, AND RESTRICTIONS OF A SMALL EMPLOYER HEALTH GROUP COOPERATIVE, AND PROVIDE THAT THE SOUTH CAROLINA DEPARTMENT OF INSURANCE AND OFFICE OF RESEARCH AND STATISTICS OF THE BUDGET AND CONTROL BOARD SHALL SUBMIT A REPORT TO THE OFFICE OF THE GOVERNOR AND THE GENERAL ASSEMBLY BY JANUARY 1, 2010, ON THE EFFECTIVENESS OF THE HEALTH GROUP COOPERATIVE IN EXPANDING THE AVAILABILITY OF HEALTH INSURANCE COVERAGE FOR SMALL EMPLOYERS; AND BY AMENDING SECTIONS 38-71-1320, 38-71-1330, 38-71-1340, AND 38-71-1350, RELATING TO SMALL EMPLOYER HEALTH INSURANCE AVAILABILITY, SO AS TO PROVIDE THAT SMALL EMPLOYERS MAY FORM A COOPERATIVE FOR THE PURPOSE OF PROVIDING HEALTH INSURANCE TO THEIR EMPLOYEES, PROVIDE FOR THE DEFINITION OF "HEALTH GROUP COOPERATIVE", AND PROVIDE FOR THE GROUP SIZE FOR A HEALTH GROUP COOPERATIVE. On motion of Senator CROMER, with unanimous consent, the name of Senator CROMER was added as a co-sponsor of S. 588. S. 1006 (Word version) -- Senators Ritchie, McConnell, Setzler, Leventis, Knotts, Lourie, Hutto, Martin, Hayes, Ceips, Reese and Elliott: A BILL TO AMEND CHAPTER 1, TITLE 23 OF THE 1976 CODE, BY ADDING SECTION 23-1-235 TO PROVIDE THAT A SPOUSE OR DEPENDENT OF A LAW ENFORCEMENT OFFICER OR FIREFIGHTER KILLED IN THE LINE OF DUTY MAY CONTINUE TO RECEIVE HEALTH AND DENTAL BENEFITS. On motion of Senator HAWKINS, with unanimous consent, the name of Senator HAWKINS was added as a co-sponsor of S. 1006. RECALLED S. 1022 (Word version) -- Senators Peeler and Setzler: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 110 TO TITLE 59 SO AS TO ENACT THE "SOUTH CAROLINA CRITICAL NEEDS NURSING INITIATIVE ACT" INCLUDING PROVISIONS ESTABLISHING THE CRITICAL NEEDS NURSING INITIATIVE FUND, TO IMPROVE THE NUMBER OF QUALIFIED NURSES IN THIS STATE BY PROVIDING NURSING FACULTY SALARY ENHANCEMENTS, CREATING NEW FACULTY POSITIONS, PROVIDING FOR ADDITIONAL NURSING STUDENT SCHOLARSHIPS, LOANS, AND GRANTS, ESTABLISHING THE OFFICE FOR HEALTH CARE WORKFORCE RESEARCH TO ANALYZE HEALTH CARE WORKFORCE SUPPLY AND DEMAND, AND PROVIDING FOR THE USE OF SIMULATION TECHNOLOGY AND EQUIPMENT IN THE EDUCATION OF NURSES. Senator PEELER asked unanimous consent to make a motion to recall the Bill from the Committee on Education. There was no objection. The Bill was recalled from the Committee on Education and ordered placed on the Calendar for consideration tomorrow. On motion of Senator CAMPBELL, with unanimous consent, the name of Senator CAMPBELL was added as a co-sponsor of S. 1022. INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 1035 (Word version) -- Senators Elliott, Cleary, Rankin and McGill: A SENATE RESOLUTION TO RECOGNIZE AND CONGRATULATE JANA LEE SNAPP OF SPARTANBURG ON BEING CROWNED MISS SUN FUN 2008 AND WISH HER MUCH SUCCESS IN HER REIGN AND IN ALL HER FUTURE ENDEAVORS. l:\council\bills\rm\1331sd08.doc S. 1036 (Word version) -- Senator Ryberg: A CONCURRENT RESOLUTION CONGRATULATING THE CONGREGATION OF SOUTH AIKEN CHURCH OF GOD ON THEIR LONG HISTORY OF SERVICE TO THE AIKEN COMMUNITY AND THE DEDICATION OF THEIR NEW SANCTUARY. l:\s-res\wgr\023sout.mrh.doc The Concurrent Resolution was adopted, ordered sent to the House. S. 1037 (Word version) -- Senators Knotts, Leatherman, Cleary, Patterson, Ceips, Alexander, Thomas, Scott, McGill, Matthews, Short, Verdin and Campbell: A CONCURRENT RESOLUTION TO REAFFIRM THE GENERAL ASSEMBLY'S COMMITMENT TO OPEN GOVERNMENT IN SOUTH CAROLINA; TO RECOGNIZE THE ROLE PLAYED BY THE FREEDOM OF INFORMATION ACT IN OPEN GOVERNMENT AND TO EXPRESS APPRECIATION TO THE SOUTH CAROLINA PRESS ASSOCIATION FOR ITS ROLE IN PROMOTING OPEN GOVERNMENT; TO DECLARE MARCH 16, 2008, AS "SUNSHINE SUNDAY" AND MARCH 16-22, 2008, AS "OPEN GOVERNMENT WEEK IN SOUTH CAROLINA" AND TO ENCOURAGE PARTICIPATION IN THESE ACTIVITIES COMMEMORATING OUR OPEN AND DEMOCRATIC GOVERNMENT. l:\council\bills\rm\1328ab08.doc The Concurrent Resolution was adopted, ordered sent to the House. S. 1038 (Word version) -- Senator Cleary: A BILL TO AMEND SECTION 20-7-490, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF TERMS IN THE CHILDREN'S CODE, INCLUDING THE DEFINITION OF CHILD ABUSE AND NEGLECT, SO AS TO PROVIDE THAT CHILD ABUSE AND NEGLECT INCLUDES KNOWINGLY EXPOSING A CHILD TO CHEMICALS THAT HAVE THE CAPACITY TO INTERFERE WITH NORMAL PHYSIOLOGICAL FUNCTIONS, INCLUDING DURING THE MANUFACTURING OF METHAMPHETAMINE; TO AMEND SECTION 20-7-763, RELATING TO THE REQUIREMENT THAT THE DEPARTMENT OF SOCIAL SERVICES MUST MAKE REASONABLE EFFORTS TO PRESERVE OR UNIFY THE FAMILY AND EXCEPTIONS TO THIS REQUIREMENT, SO AS TO PROVIDE AS AN EXCEPTION THAT THE PARENT HAS KNOWINGLY EXPOSED A CHILD TO CHEMICALS THAT HAVE THE CAPACITY TO INTERFERE WITH NORMAL PHYSIOLOGICAL FUNCTIONS, INCLUDING DURING THE MANUFACTURING OF METHAMPHETAMINE; AND TO AMEND SECTION 20-7-1572, AS AMENDED, RELATING TO GROUNDS FOR THE TERMINATION OF PARENTAL RIGHTS, SO AS TO PROVIDE AS A GROUND THAT THE PARENT EXPOSED A CHILD TO CHEMICALS THAT HAVE THE CAPACITY TO INTERFERE WITH NORMAL PHYSIOLOGICAL FUNCTIONS, INCLUDING DURING THE MANUFACTURING OF METHAMPHETAMINE. l:\s-res\rec\007chil.dag.doc Read the first time and referred to the Committee on Judiciary. S. 1039 (Word version) -- Senator Verdin: A BILL TO AMEND SECTION 23-31-510 OF THE 1976 CODE, RELATING TO THE PROHIBITION AGAINST REGULATION OF CERTAIN MATTERS, TO PROVIDE THAT COUNTIES AND MUNICIPALITIES MAY NOT ENACT REGULATIONS TO PROHIBIT A LANDOWNER FROM DISCHARGING A FIREARM ON HIS PROPERTY TO PROTECT FAMILY MEMBERS, EMPLOYEES, OR THE GENERAL PUBLIC FROM ANIMALS POSING A DIRECT THREAT OR DANGER ON A PARCEL OF LAND COMPRISED OF AT LEAST TWENTY-FIVE CONTIGUOUS ACRES. l:\s-res\dbv\010gunr.kmm.doc Read the first time and referred to the Committee on Judiciary. S. 1040 (Word version) -- Senators Massey, Ryberg and Bryant: A BILL TO AMEND SECTION 56-5-6540(C) OF THE 1976 CODE, RELATING TO SAFETY BELTS, TO PROVIDE THAT A VIOLATION OF ANY SAFETY BELT PROVISION IS ADMISSIBLE AS EVIDENCE IN A CIVIL ACTION TO ESTABLISH COMPARATIVE NEGLIGENCE UNDER CERTAIN CIRCUMSTANCES. l:\s-res\asm\002seat.dag.doc Read the first time and referred to the Committee on Judiciary. S. 1041 (Word version) -- Senators Hawkins, Campbell, Ford, Fair, Cleary, Anderson, Ryberg, Thomas and Hayes: A BILL TO AMEND SECTION 16-17-650, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO COCKFIGHTING, SO AS TO INCREASE THE PENALTIES FOR THE OFFENSE. l:\council\bills\ms\7497ahb08.doc Read the first time and referred to the Committee on Judiciary. S. 1042 (Word version) -- Senators Knotts, Grooms, Hayes, Cromer, Thomas, Ford, Campbell and McGill: A BILL TO AMEND SECTION 8-25-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF TERMS REGARDING PROVISIONS CONCERNING GOVERNMENT VOLUNTEERS, SO AS TO DEFINE "EMERGENCY SUPPORT FUNCTION VOLUNTEER"; TO AMEND SECTION 8-25-20, RELATING TO THE USE OF VOLUNTEERS BY STATE AGENCIES AND DEPARTMENTS, SO AS TO INCLUDE THE CATEGORY OF EMERGENCY SUPPORT FUNCTION VOLUNTEERS IN THE TYPES OF VOLUNTEERS STATE AGENCIES CAN USE; TO AMEND SECTION 8-25-40, RELATING TO BENEFITS PROVIDED TO VOLUNTEERS, INCLUDING MILEAGE REIMBURSEMENT, MEAL ALLOWANCE, AND LIABILITY INSURANCE, SO AS TO AUTHORIZE STATE AGENCIES TO PROVIDE WORKERS' COMPENSATION FOR EMERGENCY SUPPORT FUNCTION VOLUNTEERS AND TO AUTHORIZE EACH AGENCY TO DESIGNATE CIRCUMSTANCES THAT WILL TRIGGER WORKERS' COMPENSATION COVERAGE; TO AMEND SECTION 42-1-130, AS AMENDED, RELATING TO THE DEFINITION OF "EMPLOYEE" IN THE WORKERS' COMPENSATION LAW, SO AS TO ALSO INCLUDE EMERGENCY SUPPORT FUNCTION VOLUNTEERS IN THE DEFINITION OF THIS TERM; TO AMEND SECTION 42-7-65, AS AMENDED, RELATING TO THE AVERAGE WEEKLY WAGE FOR CERTAIN CATEGORIES OF EMPLOYEES, SO AS TO INCLUDE A CATEGORY FOR EMERGENCY SUPPORT FUNCTION VOLUNTEERS AND TO DESIGNATE THEIR AVERAGE WEEKLY WAGE AS THIRTY-SEVEN AND ONE-HALF PERCENT OF THE AVERAGE WEEKLY WAGE IN THE STATE FROM THE PRECEDING YEAR; AND TO AMEND SECTION 42-7-75, AS AMENDED, RELATING TO THE REQUIREMENT THAT ALL STATE AGENCIES PAY WORKERS' COMPENSATION PREMIUMS, SO AS TO PROVIDE PROCEDURES FOR CALCULATION OF PREMIUMS FOR AGENCIES THAT UTILIZE EMERGENCY SUPPORT FUNCTION VOLUNTEERS. l:\council\bills\nbd\11984ac08.doc Read the first time and referred to the Committee on Judiciary. S. 1043 (Word version) -- Senator Elliott: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 14 TO CHAPTER 3, TITLE 23 SO AS TO CREATE THE STATE REAL-TIME ELECTRONIC LOGBOOK FOR PHARMACEUTICALS; TO AMEND SECTION 44-53-398, RELATING TO THE SALE OF PRODUCTS CONTAINING EPHEDRINE OR PSEUDOEPHEDRINE, SO AS TO ADD PHENYLPROPANOLAMINE TO THE PRODUCTS GOVERNED BY THE SECTION, TO REQUIRE A RETAILER SELLING A PRODUCT CONTAINING THESE PRODUCTS TO ENTER THE TRANSACTION IN THE STATE REAL-TIME ELECTRONIC LOGBOOK FOR PHARMACEUTICALS, AND TO SPECIFY THE INFORMATION THAT MUST BE ENTERED. l:\council\bills\ggs\22044ab08.doc Read the first time and referred to the Committee on Medical Affairs. S. 1044 (Word version) -- Senators Lourie, Leventis, Sheheen, Setzler, Scott, McConnell, Short, Ceips, Jackson and Patterson: A CONCURRENT RESOLUTION URGING THE FEDERAL NUCLEAR REGULATORY COMMISSION TO DISAPPROVE THE REQUEST TO IMPORT AND DISPOSE OF ITALIAN LOW-LEVEL RADIOACTIVE WASTE IN THIS COUNTRY. l:\council\bills\nbd\11936ac08.doc S. 1044--Objection Senator SETZLER asked unanimous consent to make a motion that the Concurrent Resolution be placed on the Calendar without reference. Senator RYBERG objected. The Concurrent Resolution was introduced and referred to the Committee on Judiciary. S. 1045 (Word version) -- Senators Anderson and Ford: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 59-29-240 SO AS TO PROVIDE THAT THE STATE DEPARTMENT OF EDUCATION SHALL DEVELOP GUIDELINES FOR APPROPRIATE INSTRUCTION IN THE PREVENTION OF AND PENALTIES FOR LYNCHING, FIGHTING, AND GANG ACTIVITY, AND TO PROVIDE THAT EACH SCHOOL DISTRICT SHALL PROVIDE THIS INSTRUCTION DURING THE FIRST WEEK OF THE SCHOOL YEAR. l:\council\bills\dt\27052bb08.doc Read the first time and referred to the Committee on Education. S. 1046 (Word version) -- Senator Lourie: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 40-1-145 SO AS TO AUTHORIZE THE DEPARTMENT OF LABOR, LICENSING AND REGULATION TO REQUIRE A CRIMINAL HISTORY BACKGROUND CHECK OF AN APPLICANT FOR A PRACTICE AUTHORIZATION AND TO AUTHORIZE THE DEPARTMENT TO REQUIRE SUCH A BACKGROUND CHECK IN CONNECTION WITH AN INVESTIGATION OR DISCIPLINARY PROCEEDING; TO AMEND SECTION 40-1-90, RELATING TO DISCIPLINARY PROCEEDINGS, SO AS TO AUTHORIZE THE DEPARTMENT TO PROMULGATE REGULATIONS TO ESTABLISH PROCEDURES FOR CONDUCTING CONTESTED CASE PROCEEDINGS; AND TO AMEND SECTION 40-1-180, AS AMENDED, RELATING TO COLLECTION OF COSTS AND FINES IMPOSED PURSUANT TO A PROCEEDING CONDUCTED BY THE DEPARTMENT, SO AS TO PROVIDE THAT COSTS AND FINES IMPOSED BY THE DEPARTMENT ARE SUBJECT TO THE SET-OFF DEBT COLLECTION ACT. l:\council\bills\nbd\11931ac08.doc Read the first time and referred to the Committee on Labor, Commerce and Industry. S. 1047 (Word version) -- Senators Grooms, Campbell and Campsen: A BILL TO AMEND SECTION 7-7-120, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DESIGNATION OF VOTING PRECINCTS IN BERKELEY COUNTY, SO AS TO CREATE NEW PRECINCTS, REDESIGNATE AND RENAME CERTAIN PRECINCTS, AND CHANGE THE MAP DESIGNATION ON WHICH THE LINES OF THOSE PRECINCTS ARE DELINEATED. l:\council\bills\dka\3468dw08.doc Read the first time and referred to the Committee on Judiciary. S. 1048 (Word version) -- Senators Martin and Alexander: A BILL TO AMEND SECTION 61-4-120, AS AMENDED, RELATING TO THE SUNDAY SALE OF WINE OR BEER IN THIS STATE, SO AS TO PROVIDE AN EXCEPTION FOR WINE THAT IS HARVESTED, PROCESSED, FERMENTED, BOTTLED, AND SOLD AT THE SAME CONTIGUOUS LOCATION. l:\council\bills\ms\7501ahb08.doc Read the first time and referred to the Committee on Judiciary. S. 1049 (Word version) -- Senator McConnell: A BILL TO AMEND SECTION 56-3-230, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEPARTMENT OF MOTOR VEHICLES APPLICATION FOR THE REGISTRATION AND LICENSING OF A VEHICLE, SO AS TO PROVIDE THAT THE APPLICATION MUST INCLUDE A VALID COPY OF THE OWNER'S SOUTH CAROLINA DRIVER'S LICENSE. l:\council\bills\swb\5414cm08.doc Read the first time and referred to the Committee on Transportation. S. 1050 (Word version) -- Senators Verdin and Ryberg: A BILL TO AMEND CHAPTER 3, TITLE 56 OF THE 1976 CODE, TO PROVIDE THAT THE DEPARTMENT OF MOTOR VEHICLES MAY ISSUE OPERATION DESERT STORM-DESERT SHIELD VETERANS LICENSE PLATES, OPERATION ENDURING FREEDOM VETERANS LICENSE PLATES, AND OPERATION IRAQI FREEDOM VETERANS LICENSE PLATES. l:\s-res\dbv\011plat.dag.doc Read the first time and, on motion of Senator GROOMS, with unanimous consent, S. 1050 was ordered placed on the Calendar without reference. S. 1051 (Word version) -- Senators Courson and Lourie: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND SOUTH CAROLINA'S RECYCLERS FOR THEIR VITAL ROLE IN OUR STATE'S ECONOMY, PRESERVING OUR ENVIRONMENT, AND PROMOTING ENERGY EFFICIENCY. l:\council\bills\nbd\11994ac08.doc S. 1052 (Word version) -- Senator Ford: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 62 TO TITLE 40 SO AS TO ENACT THE "INTERIOR DESIGN CONSUMER PROTECTION ACT"; TO PROVIDE CERTAIN DEFINITIONS; TO REQUIRE A PERSON RENDERING AN INTERIOR DESIGN SERVICE TO REGISTER WITH THE DEPARTMENT OF LABOR, LICENSING AND REGULATION; TO PROVIDE REQUIREMENTS FOR REGISTRATION AND RENEWAL OF REGISTRATION; AND TO FURTHER PROVIDE FOR THE REGISTRATION AND REGULATION OF INTERIOR DESIGNERS. l:\council\bills\ggs\22046ab08.doc Read the first time and referred to the Committee on Labor, Commerce and Industry. H. 4569 (Word version) -- Reps. Phillips, Moss and Littlejohn: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR CAPTAIN ALAN BROOKS ALLISON, OF THE GAFFNEY CITY POLICE DEPARTMENT, FOR HIS MANY YEARS OF DEDICATED SERVICE TO THE STATE OF SOUTH CAROLINA AND TO HIS COUNTRY. The Concurrent Resolution was adopted, ordered returned to the House. H. 4582 (Word version) -- Rep. Bowers: A CONCURRENT RESOLUTION TO RECOGNIZE AND HONOR P. EDWIN DELOACH, OF HAMPTON COUNTY, FOR REACHING THE MOMENTOUS MILESTONE OF FIFTY YEARS OF TIRELESS SERVICE ON THE BOARD OF DIRECTORS OF PALMETTO ELECTRIC COOPERATIVE. The Concurrent Resolution was adopted, ordered returned to the House. H. 4606 (Word version) -- Reps. Witherspoon, Hardwick, Crawford, Lowe, Kennedy, Littlejohn, Mahaffey, Agnew, Alexander, Allen, Anderson, Anthony, Bales, Ballentine, Bannister, Barfield, Battle, Bedingfield, Bingham, Bowen, Bowers, Brady, Branham, Brantley, Breeland, G. Brown, R. Brown, Cato, Chalk, Clemmons, Clyburn, Cobb-Hunter, Coleman, Cooper, Cotty, Dantzler, Davenport, Delleney, Duncan, Edge, Erickson, Frye, Funderburk, Gambrell, Govan, Gullick, Hagood, Haley, Hamilton, Harrell, Harrison, Hart, Harvin, Haskins, Hayes, Herbkersman, Hiott, Hodges, Hosey, Howard, Huggins, Hutson, Jefferson, Jennings, Kelly, Kirsh, Knight, Leach, Limehouse, Loftis, Lucas, Mack, McLeod, Merrill, Miller, Mitchell, Moody-Lawrence, Moss, Mulvaney, J. H. Neal, J. M. Neal, Neilson, Ott, Owens, Parks, Perry, Phillips, Pinson, E. H. Pitts, M. A. Pitts, Rice, Rutherford, Sandifer, Scarborough, Scott, Sellers, Shoopman, Simrill, Skelton, D. C. Smith, F. N. Smith, G. M. Smith, G. R. Smith, J. E. Smith, J. R. Smith, W. D. Smith, Spires, Stavrinakis, Stewart, Talley, Taylor, Thompson, Toole, Umphlett, Vick, Viers, Walker, Weeks, Whipper, White, Whitmire, Williams and Young: A CONCURRENT RESOLUTION TO RECOGNIZE AND COMMEND SOUTH CAROLINA'S NATIONAL FFA ORGANIZATION MEMBERS, THEIR ADVISORS, SCHOOL ADMINISTRATORS, PARENTS, AND ALL WHO SUPPORT, PROMOTE, AND ENCOURAGE THESE OUTSTANDING STUDENTS OF AGRICULTURAL EDUCATION ON THE OCCASION OF THE OBSERVANCE OF NATIONAL FFA WEEK, FEBRUARY 18-22, 2008. The Concurrent Resolution was adopted, ordered returned to the House. REPORTS OF STANDING COMMITTEES Senator MARTIN from the Committee on Judiciary submitted a favorable with amendment report on: S. 503 (Word version) -- Senators Knotts, Ford and Scott: A BILL TO AMEND SECTION 22-5-190, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ENDORSEMENT AND EXECUTION OF WARRANTS ISSUED IN OTHER COUNTIES OR BY MUNICIPAL AUTHORITIES, SO AS TO PROVIDE A WARRANT IS NOT REQUIRED TO BE ENDORSED BY A MAGISTRATE IN THE COUNTY WHERE A PERSON CHARGED WITH A CRIME RESIDES OR WHERE HE IS LOCATED, TO PROVIDE PROCEDURES FOR SERVING A WARRANT, AND TO MAKE CONFORMING CHANGES. Ordered for consideration tomorrow. Senator CAMPSEN from the Committee on Judiciary submitted a favorable with amendment report on: S. 741 (Word version) -- Senator Courson: A BILL TO AMEND CHAPTER 18, TITLE 27 OF THE 1976 CODE RELATING TO THE UNIFORM UNCLAIMED PROPERTY ACT, TO REDUCE THE DORMANCY PERIOD FOR SECURITIES FROM SEVEN YEARS TO THREE YEARS, TO UPDATE A REFERENCE, AND TO ELIMINATE THE REQUIREMENT OF A CIVIL PENALTY FOR A PERSON WHO FAILS TO RENDER A REPORT, PERFORM A DUTY, OR DELIVER PROPERTY AS REQUIRED PURSUANT TO THE CHAPTER. Ordered for consideration tomorrow. Senator MARTIN from the Committee on Judiciary submitted a favorable report on: S. 831 (Word version) -- Senators Campsen, Grooms, Sheheen, Bryant, McConnell, Cleary, Gregory and Hawkins: A BILL TO AMEND SECTION 22-2-5, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ELIGIBILITY EXAMINATION FOR MAGISTRATES, SO AS TO EXTEND THE TIME PERIOD FOR THE VALIDITY OF THE EXAMINATION SCORES FROM SIX MONTHS BEFORE AND SIX MONTHS AFTER THE TIME THE APPOINTMENT IS TO BE MADE TO ONE YEAR BEFORE AND ONE YEAR AFTER THE TIME THE APPOINTMENT IS TO BE MADE. Ordered for consideration tomorrow. Senator MARTIN from the Committee on Judiciary submitted a favorable with amendment report on: S. 903 (Word version) -- Senators Campsen, McConnell and McGill: A BILL TO AMEND SECTION 1-15-10 OF THE 1976 CODE, RELATING TO APPOINTING THE MEMBERS OF THE COMMISSION ON WOMEN, TO PROVIDE THAT THE COMMISSION IS COMPOSED OF FIFTEEN MEMBERS APPOINTED BY THE GOVERNOR, WITH ONE MEMBER APPOINTED FROM EACH CONGRESSIONAL DISTRICT AND NINE MEMBERS FROM THE STATE AT-LARGE. Ordered for consideration tomorrow. Senator SHEHEEN from the Committee on Judiciary submitted a favorable with amendment report on: S. 990 (Word version) -- Senators Martin, Ford, Ritchie, Knotts and Cleary: A BILL TO AMEND SECTION 2-19-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PUBLIC HEARINGS, SO AS TO REQUIRE THAT WRITTEN STATEMENTS OF PROPOSED TESTIMONY OF ANYONE WISHING TO TESTIFY BEFORE THE JUDICIAL MERIT SELECTION COMMISSION HEARING BE FURNISHED BY THE PERSON WISHING TO TESTIFY NO LESS THAN TWO WEEKS PRIOR TO THE DATE AND TIME SET FOR THE HEARING UNLESS EXIGENT CIRCUMSTANCES ARE SHOWN BY THE SUBMITTING INDIVIDUAL. Ordered for consideration tomorrow. Senator MARTIN from the Committee on Judiciary submitted a favorable report on: H. 3993 (Word version) -- Reps. Duncan, Bedingfield, Davenport, Barfield, Brantley, G. Brown, Ceips, Gambrell, Hiott, Hodges, Jennings, Knight, Leach, Littlejohn, Lowe, Miller, Owens, M.A. Pitts, G.M. Smith, J.R. Smith, Spires and Taylor: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 53-3-125 SO AS TO PROVIDE THAT THE OPENING DAY OF THE ANNUAL MAJOR LEAGUE BASEBALL SEASON EACH YEAR IS DESIGNATED AS "TEXTILE LEAGUE BASEBALL DAY" IN SOUTH CAROLINA. Ordered for consideration tomorrow. Senator VERDIN from the Committee on Agriculture and Natural Resources polled out H. 4447 favorable: H. 4447 (Word version) -- Rep. Cato: A BILL TO AMEND ACT 170 OF 2007, RELATING TO THE CREATION OF A STUDY COMMITTEE TO EXAMINE THE FEASIBILITY OF NATURAL GAS EXPLORATION IN THE ATLANTIC OCEAN OFF THE COAST OF SOUTH CAROLINA, SO AS TO EXTEND FROM FEBRUARY 1, 2008, TO NOVEMBER 1, 2008, THE DATE BY WHICH THE COMMITTEE IS REQUIRED TO MAKE ITS REPORT TO THE GENERAL ASSEMBLY. Poll of the Agriculture and Natural Resources Committee Polled 16; Ayes 16; Nays 0; Not Voting 0 AYES Grooms Leventis Peeler Matthews McGill Hutto Elliott Knotts Cromer Bryant Campsen Cleary Lourie Williams Ritchie Campbell Total--14 NAYS Total--0 Ordered for consideration tomorrow. Message from the House Columbia, S.C., January 29, 2008 Mr. President and Senators: The House respectfully informs your Honorable Body that it insists upon the amendments proposed by the House to: S. 274 (Word version) -- Senators Fair, Verdin, Anderson, Sheheen, Campsen, Thomas, Williams, Bryant, Cromer and Scott: A BILL TO AMEND CHAPTER 21, TITLE 24, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEPARTMENT OF PROBATION, PAROLE AND PARDON SERVICES, BY ADDING ARTICLE 13 SO AS TO ALLOW THE DEPARTMENT TO ESTABLISH DAY REPORTING CENTERS FOR CERTAIN INMATES OR OFFENDERS. asks for a Committee of Conference, and has appointed Reps. M. Smith, Herbkersman and Doug Jennings to the committee on the part of the House. Very respectfully, Speaker of the House S. 274--CONFERENCE COMMITTEE APPOINTED S. 274 (Word version) -- Senators Fair, Verdin, Anderson, Sheheen, Campsen, Thomas, Williams, Bryant, Cromer and Scott: A BILL TO AMEND CHAPTER 21, TITLE 24, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEPARTMENT OF PROBATION, PAROLE AND PARDON SERVICES, BY ADDING ARTICLE 13 SO AS TO ALLOW THE DEPARTMENT TO ESTABLISH DAY REPORTING CENTERS FOR CERTAIN INMATES OR OFFENDERS. Whereupon, Senators FAIR, SHEHEEN and CAMPBELL were appointed to the Committee of Conference on the part of the Senate and a message was sent to the House accordingly. HOUSE CONCURRENCE S. 1029 (Word version) -- Senator Ceips: A CONCURRENT RESOLUTION TO RECOGNIZE BEAUFORT COUNTY AS A VITAL PART OF OUR STATE, AND TO DECLARE JANUARY 30, 2008, "BEAUFORT COUNTY DAY" IN SOUTH CAROLINA. Returned with concurrence. THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR. The following Bills were read the third time and ordered sent to the House of Representatives: S. 858 (Word version) -- Senators McConnell, Rankin, O'Dell, Elliott and McGill: A BILL TO AMEND SECTION 38-73-1095, CODE OF LAWS OF SOUTH CAROLINA, 1976, AS AMENDED, RELATING TO ESSENTIAL PROPERTY INSURANCE AND RATING PLAN FACTORS, SO AS TO PROVIDE CREDITS AND DISCOUNTS OR SURCHARGES AND DEBITS CALCULATED ON CERTAIN RATING FACTORS FOR RETROFITTING PROPERTY IN ALL AREAS OF THE STATE IN ADDITION TO PROVIDING CREDITS AND DISCOUNTS OR SURCHARGES AND DEBITS CALCULATED ON CERTAIN RATING FACTORS FOR RETROFITTING PROPERTY IN THE COASTAL AREA OR SEACOAST AREA. S. 863 (Word version) -- Senator Thomas: A BILL TO AMEND SECTION 34-11-70, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EVIDENCE OF FRAUDULENT INTENT IN DRAWING A DISHONORED CHECK, SO AS TO PROVIDE THAT A CHARGE THAT IS DISMISSED FOR WANT OF PROSECUTION OR BY REASON OF PAYMENT OF RESTITUTION AND COSTS IS NOT A CHARGE THAT EVIDENCES AN ACT OF MORAL TURPITUDE FOR PURPOSES OF AN OFFICIAL BACKGROUND CERTIFICATION; AND TO REPEAL SECTION 34-11-100 RELATING TO THE EFFECT OF PAYMENT AFTER INSTITUTION OF PROSECUTION. The following Bill and Joint Resolution having been read the second time, were ordered placed on the Third Reading Calendar: S. 964 (Word version) -- Senator Thomas: A BILL TO AMEND SECTION 34-3-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO PROHIBITION OF THE USE OF THE WORD "BANK" IN CONNECTION WITH A PURSUIT OTHER THAN BANKING, SO AS TO PROHIBIT THE USE OF A BANKING ENTITY'S LOGO OR NAME IN CONNECTION WITH A FINANCIAL TRANSACTION WITHOUT ITS WRITTEN CONSENT. Senator THOMAS explained the Bill. S. 1034 (Word version) -- Senator Courson: A JOINT RESOLUTION TO EXTEND THE DATE BY WHICH THE HIGHER EDUCATION TASK FORCE MUST SUBMIT RECOMMENDATIONS FOR THE HIGHER EDUCATION STATEWIDE STRATEGIC PLAN TO THE GENERAL ASSEMBLY UNTIL SEPTEMBER 15, 2008. By prior motion of Senator COURSON, with unanimous consent AMENDMENT PROPOSED, OBJECTION S. 535 (Word version) -- Senator Thomas: A BILL TO AMEND SECTION 37-6-502, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO SELECTION OF MEMBERS OF THE COMMISSION ON CONSUMER AFFAIRS, SO AS TO PROVIDE FOR THE ELECTION EVERY FOUR YEARS OF THE COMMISSIONERS ELECTED BY THE GENERAL ASSEMBLY BEGINNING FEBRUARY 1, 2008. The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Senator MASSEY proposed the following amendment (535R001.ASM): Amend the bill, as and if amended, page 2, SECTION 1, by striking line 3 and inserting: / Code of Laws of South Carolina. Beginning February 1, 2011, the successor to any elected or appointed member shall be appointed by the Governor with the advice and consent of the Senate. Terms of members shall be four years and until a successor is appointed and qualifies. With the exception of the ex officio member, a vacancy in the office of a member must be filled by the Governor by appointment for the unexpired term." / Renumber sections to conform. Amend title to conform. Senator MASSEY explained the amendment. Senator JACKSON objected to further consideration of the Bill. CARRIED OVER S. 949 (Word version) -- Senators Lourie, Elliott, Thomas, Malloy, Cleary and Alexander: A BILL TO REDESIGNATE SECTION 38-71-280, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO AUTISM INSURANCE COVERAGE, AS SECTION 38-71-765. On motion of Senator MALLOY, the Bill was carried over H. 3852 (Word version) -- Reps. Harrison and McLeod: A BILL TO AMEND SECTION 44-4-130, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE DEFINITION OF TERMS USED IN THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL'S EMERGENCY HEALTH POWERS, SO AS TO REVISE THE DEFINITION OF "QUALIFYING HEALTH CONDITION" AND "TRIAL COURT"; TO AMEND SECTION 44-4-320, RELATING TO POWERS AND DUTIES REGARDING SAFE DISPOSAL OF HUMAN REMAINS, SO AS TO SPECIFY THAT EXISTING PROVISIONS IN THE STATE EMERGENCY OPERATIONS PLAN GOVERN THE DISPOSAL OF REMAINS AND IF THE PLAN IS NOT SUFFICIENT, MEASURES MAY BE ADOPTED RELATING TO, AMONG OTHER THINGS, DEATH CERTIFICATE AND AUTOPSY PROCEDURES; TO AMEND SECTION 44-4-530, RELATING TO ISOLATION AND QUARANTINE OF INDIVIDUALS OR GROUPS AND PENALTIES FOR NONCOMPLIANCE, SO AS TO CHANGE A MISDEMEANOR OFFENSE TO A FELONY OFFENSE FOR FAILING TO COMPLY WITH THE DEPARTMENT'S ISOLATION AND QUARANTINE RULES AND ORDERS AND TO PROHIBIT AN EMPLOYER FROM FIRING, DEMOTING, OR DISCRIMINATING AGAINST AN EMPLOYEE COMPLYING WITH AN ISOLATION OR QUARANTINE ORDER; TO AMEND SECTION 44-4-540, RELATING TO ISOLATION AND QUARANTINE PROCEDURES, SO AS TO PROVIDE THAT THE ISOLATION AND QUARANTINING OF INDIVIDUALS AND GROUPS UNDER OTHER PROVISIONS OF LAW MUST BE CARRIED OUT PURSUANT TO THIS SECTION; AND TO AMEND SECTION 44-4-570, RELATING TO ADDITIONAL EMERGENCY HEALTH POWERS AND PROCEDURES REGARDING LICENSING OF HEALTH PERSONNEL, SO AS TO FURTHER SPECIFY THE USE OF IN-STATE AND OUT-OF-STATE VOLUNTEER HEALTH CARE PROVIDERS, TO PROVIDE THAT IMMUNITY FROM LIABILITY FOR VOLUNTEER HEALTH CARE PROVIDERS IN A STATE OF PUBLIC HEALTH EMERGENCY APPLIES WHETHER OR NOT THE VOLUNTEER RECEIVES FINANCIAL GAIN FOR THE VOLUNTEER SERVICES, AND TO PROVIDE SUCH IMMUNITY TO EMERGENCY ASSISTANT MEDICAL EXAMINERS OR CORONERS. On motion of Senator LOURIE, the Bill was carried over. AMENDMENT WITHDRAWN, CARRIED OVER H. 3789 (Word version) -- Reps. Kirsh and Cooper: A BILL TO RETITLE ARTICLE 5, CHAPTER 11, TITLE 1, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EMPLOYEES AND RETIREMENT INSURANCE AS "EMPLOYEES AND RETIREES INSURANCE-ACCOUNTING FOR POST-EMPLOYMENT BENEFITS", TO MAKE FINDINGS WITH RESPECT TO THE STATE'S COMPLIANCE WITH NEW REQUIREMENTS OF THE GOVERNMENTAL ACCOUNTING STANDARDS BOARD FOR POST-EMPLOYMENT BENEFITS; BY ADDING SECTIONS 1-11-703, 1-11-705, AND 1-11-707 SO AS TO ESTABLISH THE SOUTH CAROLINA RETIREE HEALTH INSURANCE TRUST FUND (SCRHI TRUST FUND) AND THE SOUTH CAROLINA LONG TERM DISABILITY INSURANCE TRUST FUND AS THE METHOD OF PAYING AND ACCOUNTING FOR RETIREE HEALTH INSURANCE PREMIUMS AND BASIC LONG TERM DISABILITY INCOME BENEFIT PLAN PREMIUMS IN COMPLIANCE WITH NEW ACCOUNTING STANDARDS, TO PROVIDE FOR THE ACTUARIAL FUNDING AND INVESTMENT OF THE ASSETS OF THESE TRUST FUNDS, AND TO PROVIDE DEFINITIONS; TO AMEND SECTION 1-11-710, RELATING TO THE STATE HEALTH AND DENTAL PLANS, SO AS TO PROVIDE FUNDING FOR THE SCRHI TRUST FUND BY MEANS OF INCREASED EMPLOYER CONTRIBUTION RATES; AND TO AMEND SECTION 1-11-730, RELATING TO PERSONS ELIGIBLE FOR POST-EMPLOYMENT PARTICIPATION IN THE STATE HEALTH AND DENTAL PLANS AND ELIGIBILITY FOR EMPLOYER PAID PREMIUMS FOR RETIREES, SO AS TO CONFORM THE PAYMENT OF EMPLOYER PREMIUMS FOR RETIREES TO THE REVISED METHOD PROVIDED IN THIS ACT, PROSPECTIVELY TO REVISE THE ELIGIBILITY REQUIREMENTS FOR EMPLOYER PAID PREMIUMS FOR RETIREES, AND TO DELETE AN OBSOLETE PROVISION. The Senate proceeded to a consideration of the Bill, the question being the adoption of the previously proposed amendment by Senator RYBERG. Senator RYBERG proposed the following amendment (3789R002.WGR), which was withdrawn: Amend the bill, as and if amended, SECTION 5, page 13, by deleting lines 21 through 28. Renumber sections to conform. Amend title to conform. Senator RYBERG asked unanimous consent to withdraw his previously proposed amendment. There was no objection. The amendment was withdrawn. Senator ALEXANDER asked unanimous consent to carry the Bill over. THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD. On motion of Senator MARTIN, the Senate agreed to dispense with the Motion Period. HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE. CONCURRENCE H. 3572 (Word version) -- Reps. Hagood, Rutherford, Bales, Barfield, Branham, G. Brown, Cato, Ceips, Chalk, Coleman, Edge, Gullick, Hardwick, Hayes, Jefferson, Jennings, Limehouse, Littlejohn, Mack, McLeod, Ott, Pinson, Sandifer, Scott, W.D. Smith, Spires, Talley, White, Hart, Whipper and Cotty: A BILL TO AMEND CHAPTER 22, TITLE 17, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PRETRIAL INTERVENTION PROGRAM BY DESIGNATING THE EXISTING SECTIONS AS ARTICLE 1 AND BY ADDING ARTICLE 3 SO AS TO CREATE THE "TRAFFIC DIVERSION PROGRAM ACT", TO PROVIDE THAT EACH SOLICITOR HAS THE AUTHORITY TO ESTABLISH A PROGRAM FOR PERSONS WHO COMMIT TRAFFIC-RELATED OFFENSES PUNISHABLE BY A FINE OR LOSS OF POINTS, TO PROVIDE THAT THE SOLICITOR IS AUTHORIZED TO CONTRACT FOR SERVICES WITH THE APPROPRIATE MUNICIPALITY OR COUNTY, AND TO PROVIDE PROCEDURES FOR THE OPERATION OF A TRAFFIC DIVERSION PROGRAM AND REQUIREMENTS FOR PERSONS DESIRING TO ENTER A PROGRAM. The House returned the Bill with amendments. On motion of Senator SHEHEEN, the Senate concurred in the House amendments and a message was sent to the House accordingly. Ordered that the title be changed to that of an Act and the Act enrolled for Ratification. THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE. S. 856 (Word version) -- Senators McConnell, Grooms, Ritchie, Bryant, Campsen, O'Dell, Alexander, Elliott, McGill, Ceips and Knotts: A CONCURRENT RESOLUTION REQUESTING THE CONGRESS OF THE UNITED STATES TO CALL A CONVENTION FOR THE SOLE AND EXCLUSIVE PURPOSE OF PROPOSING AN AMENDMENT TO THE CONSTITUTION OF THE UNITED STATES TO PROVIDE THAT NO PROVISION OF THE CONSTITUTION SHALL RESTRICT OR LIMIT A STATE FROM ENFORCING FEDERAL LAW WITH REGARD TO IMMIGRATION VIOLATIONS, TO PROVIDE THAT A STATE MAY DECIDE WHAT GOVERNMENT SERVICES FUNDED IN WHOLE OR IN PART BY THE STATE MAY BE PROVIDED TO OR DENIED TO UNDOCUMENTED ALIENS, TO PROVIDE THAT THE STATES SHALL HAVE ANY POWER TO REGULATE IMMIGRATION THAT HAS NOT BEEN SPECIFICALLY PREEMPTED BY CONGRESS, TO PROVIDE THAT EACH STATE HAS THE POWER TO PRESCRIBE STATE CIVIL AND CRIMINAL PENALTIES FOR ILLEGALLY ENTERING THE UNITED STATES, AND TO PROVIDE THAT A STATE HAS THE POWER TO APPREHEND AND EXPEL PERSONS FROM ITS BORDERS WHO ARE IN VIOLATION OF FEDERAL IMMIGRATION LAW, AND THAT THE FEDERAL GOVERNMENT MUST PROVIDE TIMELY ASSISTANCE IN EXPELLING UNDOCUMENTED ALIENS UPON A REQUEST BY A STATE. The Senate proceeded to a consideration of the Concurrent Resolution, the question being the adoption of the Resolution. Senator MARTIN spoke on the Resolution. Senator LEVENTIS spoke on the Resolution. Objection Senator LEVENTIS asked unanimous consent to make a motion to amend the Resolution by striking out certain language and inserting, "The Congress of the United States shall appropriate, prior to any other function of government being funded, an amount adequate to meet any and all functions of Immigration and Naturalization Service and any other functions related to Homeland Security regarding Border Security." Senator McCONNELL objected. Senator LEVENTIS resumed speaking on the Resolution. Senator HUTTO argued contra to the adoption of the Resolution. The Concurrent Resolution was adopted, ordered sent to the House. Recorded Vote Senators PEELER, BRYANT, FORD, JACKSON, MATTHEWS, RYBERG and FAIR desired to be recorded as voting against the adoption of the Resolution. Statement by Senator BRYANT I fully support the tough measures to combat illegal immigration passed in S. 392 and other legislation dealing with illegal immigration. Even though I was a co-sponsor of S. 856, I voted against the resolution after further realizing the complete inability for the General Assembly to maintain any authority over delegates to a constitutional convention once elected. The potential for a constitutional convention to devolve into a process whereby our most fundamental rights and protections might be altered or stricken compels me to oppose the call to a constitutional convention. * * * Statement by Senator RYBERG I fully support the tough measures to combat illegal immigration passed in S. 392 and other legislation dealing with illegal immigration. I voted against S. 856 after further realizing the complete inability for the General Assembly to maintain any authority over delegates to a constitutional convention once elected. The potential for a constitutional convention to devolve into a process whereby our most fundamental rights and protections might be altered or stricken compels me to oppose the call to constitutional convention. * * * THE SENATE PROCEEDED TO THE SPECIAL ORDERS. AMENDMENT PROPOSED, DEBATE INTERRUPTED S. 714 (Word version) -- Senators Leatherman, Reese, Alexander, Patterson, Moore, Thomas, Williams, Ford, Hutto, Malloy, Anderson, Martin, Elliott, Land, O'Dell, Cleary, Rankin, Knotts, Scott, Cromer, Matthews, Pinckney, McGill, Hayes, Drummond, Hawkins, Lourie and Jackson: A BILL TO AMEND SECTION 2-17-10, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS USED REGARDING LOBBYISTS AND LOBBYING, SO AS TO DEFINE A "POLITICAL AWARENESS ORGANIZATION"; BY ADDING SECTION 2-17-27 SO AS TO PROVIDE FOR THE MANNER OF REGISTRATION OF POLITICAL AWARENESS ORGANIZATIONS; BY ADDING SECTION 2-17-37 SO AS TO PROVIDE FOR THE FILING OF A CERTIFIED CONTRIBUTION REPORT BY A POLITICAL AWARENESS ORGANIZATION; AND TO AMEND SECTION 2-17-130, RELATING TO PENALTIES FOR VIOLATIONS BY LOBBYISTS OR LOBBYIST'S PRINCIPALS, SO AS TO PROVIDE A PENALTY FOR A POLITICAL AWARENESS ORGANIZATION WHICH WILFULLY VIOLATES THE PROVISIONS OF CHAPTER 17, TITLE 2, LOBBYISTS AND LOBBYING. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Judiciary. Amendment No. P-1 Senator SHEHEEN proposed the following Amendment No. P-1 (715.VAS): Amend the committee amendment, as and if amended, page 1, by striking lines 30- 40 and inserting the following: / / SECTION 1. The 1976 Code is amended by adding: Section 2-17-16. (a) The Governor, the Lieutenant Governor, any other statewide constitutional officer, a member of the General Assembly, a director or deputy director of a state department appointed by the Governor, or any other elected statewide public official may not organize, serve as a spokesperson for, or solicit funds for (1) a non-profit organization, including, but not limited to, 501(c)(4)'s and 527's, in which the majority of its activities consist of attempting to influence legislation, (2) a leadership political action committee that is directly or indirectly organized by or on behalf of a public official. This does not prohibit any official from supporting any nonprofit organization with his own personal funds. / Renumber sections to conform. Amend title to conform. Senator SHEHEEN explained the amendment. With Senator SHEHEEN retaining the floor, Senator RITCHIE, with unanimous consent, was recognized to explain the committee amendment. PRESIDENT Pro Tempore PRESIDES At 4:18 P.M., Senator McCONNELL assumed the Chair. Senator RITCHIE resumed explaining the committee amendment. Senator SHEHEEN resumed explaining the perfecting amendment. On motion of Senator MARTIN, with unanimous consent, debate was interrupted by adjournment, with Senator SHEHEEN retaining the floor.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3992239534854889, "perplexity": 10482.704821807565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115869264.47/warc/CC-MAIN-20150124161109-00157-ip-10-180-212-252.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/fortran-array-syntax.963716/	# Fortran Fortran: array syntax • Start date #### Telemachus 832 30 Well, I'm trying to move a bit into modern Fortran, and I am more used to Fortran77 syntax. So, for example, when I wanted to make an array whose two of its components equal another array of another dimension, I used to do something like this: Fortran: do k=1,N do j=1,N do i=1,N f(i,j,k)=f(i,j) enddo enddo enddo So that would do the job for what I need. My doubt is if with modern Fortran I could do it this way: Fortran: do k=1,N f(:,:,k)=f(:,:) enddo Related Programming and Computer Science News on Phys.org #### jedishrfu Mentor 10,930 4,439 I think which ever way you do it if it works it will work equally fast. FORTRAN is pretty good at optimizing code. My preference would be the first way as it it’s clear to anyone reading your code. One thing though you need different names for the f array like f and g or f1 and f2. 832 30 Right. Thanks. #### DrClaude Mentor 6,969 3,140 An even better solution in modern Fortran would be Fortran: forall(k=1:N) f2(:,:,k) = f1(:,:) That way, the compiler is not forced to do the assignment following a strict increment of k from 1 to N, allowing for further optimisation. #### Telemachus 832 30 An even better solution in modern Fortran would be Fortran: forall(k=1:N) f2(:,:,k) = f1(:,:) That way, the compiler is not forced to do the assignment following a strict increment of k from 1 to N, allowing for further optimisation. Can a subroutine be called inside the forall statement? #### Mark44 Mentor 32,715 4,458 Can a subroutine be called inside the forall statement? Inside the body of the forall statement? Sure. Later edit: No, subroutine calls are not allowed in a forall statement. Last edited: #### Telemachus 832 30 It gives me an error message, when I use the do loop I have no trouble with it. program.f:817:72: Error: Unexpected CALL statement in FORALL block at (1) I am using the gfortran compiler. BTW, the subroutine is using the index in the forall (k in here) when the call is made. #### Mark44 Mentor 32,715 4,458 It gives me an error message, when I use the do loop I have no trouble with it. program.f:817:72: Error: Unexpected CALL statement in FORALL block at (1) I am using the gfortran compiler. BTW, the subroutine is using the index in the forall (k in here) when the call is made. Please show us the code that generates the error. #### Telemachus 832 30 Fortran: forall(ja=1:N) call calcr(xc(ja),yc(ja),ja,rIp) fxp(:,:,ja)=fx(:,:) fyp(:,:,ja)=fy(:,:) end forall Fortran: do ja=1,2mang call calcr(xc(ja),yc(ja),ja,rIp) fxp(:,:,ja)=fx(:,:) fyp(:,:,ja)=fy(:,:) enddo I have no error messages and everything goes ok. I actually wanted to see if there was any performance improvement with the forall statement. #### Mark44 Mentor 32,715 4,458 I'm going to change my previous answer. As it turns out, forall is actually just an assignment-type statement, and is not a loop. Instead of using forall, you can use a do loop, as you already mentioned. #### Telemachus 832 30 But should it work? or there is a problem with it? Mentor 32,715 4,458 Last edited: #### DrClaude Mentor 6,969 3,140 Fortran: do ja=1,2mang call calcr(xc(ja),yc(ja),ja,rIp) fxp(:,:,ja)=fx(:,:) fyp(:,:,ja)=fy(:,:) enddo This is not efficient. I assume that there isn't a link between the function call and the arrays fx and fy. Therefore, you should have a loop for the call and a forall for the assignments. #### anorlunda Mentor Gold Member 7,499 4,234 But should it work? or there is a problem with it? I had to upgrade my own FORTRAN knowledge in this case (FORTRAN IV and FORTRAN 77 were my experiences.) Your error is thinking that the FORALL is a loop. That's not true. The Wikipedia article that @Mark44 linked says this. When a DO construct is executed, each successive iteration is performed in order and one after the other—an impediment to optimization on a parallel processor. FORALL(i = 1:n) a(i, i) = x(i) where the individual assignments may be carried out in any order, and even simultaneously. The FORALL may be considered to be an array assignment expressed with the help of indices. In other words, the compiler is free to implement the assignment in any way, not necessarily with a loop. It might have been less confusing if the feature was named ARRAY_ASSIGN rather than FORALL. You can have arithmetic operations in the expression, but if you did have a function call within a FORALL (including, it might violate this. Assignment in a FORALL is like an array assignment: as if all the expressions were evaluated in any order, held in temporary storage, then all the assignments performed in any order. That is rather subtle, and it goes against the sequential execution of statements visualized by old fashioned FORTRAN programmers. #### Telemachus 832 30 Great. Thanks. I think I can rearrange things to use forall. There was an slight improvement in the code after changing some do loops for this statement. This was the running time after changing some do loops by forall: 2797.387 seconds. And the time with out those changes: 2964.344 seconds. It is not a great improvement, but I think I can modify the code, using more arrays I should be able to include more forall's, at the expense of using more memory. But I would like to know how much faster could it be running. Also, maybe I can think some way to modify the subroutine call to include a forall in those situations. This is not efficient. I assume that there isn't a link between the function call and the arrays fx and fy. Therefore, you should have a loop for the call and a forall for the assignments. Sadly, there is a link between the call and those arrays. So I think I have to keep the do statement in that case. One last question. The improvement comes from the execution in parallel of the assignments for the arrays? I haven't specified any parallel environment, so I think it shouldn't be that. Thank you all. #### DrClaude Mentor 6,969 3,140 One last question. The improvement comes from the execution in parallel of the assignments for the arrays? I haven't specified any parallel environment, so I think it shouldn't be that. The speed up is not due to parallel execution, but due to memory management. The compiler is free to do the assignment any which way, so it can take advantage of the cache and avoid pagefaults. I guess that in some cases it can also reduce the overhead of the for loop. #### anorlunda Mentor Gold Member 7,499 4,234 One last question. The improvement comes from the execution in parallel of the assignments for the arrays? I haven't specified any parallel environment, so I think it shouldn't be that. Where's your ego? You should expect that your program will be used by millions of people, over and over in all kinds of environments, for eternity. Seriously, if it did everything strictly sequentially, then there would be no speed gain compared to a traditional DO loop. There are behind the curtain things that happen with memory access and cache memory that are completely invisible to you. Edit: I see that @DrClaude beat me to it. #### Telemachus 832 30 Great. Thank you. How do you know all of these things about how the compiler does the optimization? is there any reference, a book or something that explains all this? #### Mark44 Mentor 32,715 4,458 How do you know all of these things about how the compiler does the optimization? By having a deeper level of understanding of the computer's architecture, including instruction pipeline, memory access vs. cache access vs. register access, multi-threading, to name a few. As for optimization, being able to see the code that the compiler actually emits makes it possible to optimize the sections of code that are taking the most time. is there any reference, a book or something that explains all this? Michael Abrash published "Zen of Assembly Language," 1990, and "Zen of Code Optimization," 1994. A more current resource that I use is Agner Fog, a Danish computer scientist (https://agner.org/optimize/). The first manual listed on this page is C++ software optimization. #### harborsparrow Gold Member 524 103 Personally I don't recommend using a difficult-to-read (but shorter) syntax in code. When some future programmer looks at it, or you yourself 2 years later, it will be more helpful to see the longer but quite explicit version. So I like that first code you showed that you are trying to make more concise, and I don't like the more concise versions whatsoever because it is simply trickier to read. #### DrClaude Mentor 6,969 3,140 Personally I don't recommend using a difficult-to-read (but shorter) syntax in code. When some future programmer looks at it, or you yourself 2 years later, it will be more helpful to see the longer but quite explicit version. So I like that first code you showed that you are trying to make more concise, and I don't like the more concise versions whatsoever because it is simply trickier to read. We are not talking about obfuscating code here. We are talking about using the features of a high-level language to get simpler code that can be more easily optimised by a compiler. Come to think of it, it is actually the opposite of obfuscation. The idea is to code what you want the program to do, without having to detail exactly how to do it. "Fortran: array syntax" • Posted Replies 4 Views 1K • Posted Replies 2 Views 4K • Posted Replies 3 Views 3K • Posted Replies 1 Views 7K • Posted Replies 2 Views 561 • Posted Replies 1 Views 3K • Posted Replies 7 Views 7K • Posted Replies 4 Views 11K ### Physics Forums Values We Value Quality • Topics based on mainstream science • Proper English grammar and spelling We Value Civility • Positive and compassionate attitudes • Patience while debating We Value Productivity • Disciplined to remain on-topic • Recognition of own weaknesses • Solo and co-op problem solving	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28020963072776794, "perplexity": 1301.7236013091228}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986653216.3/warc/CC-MAIN-20191014101303-20191014124303-00331.warc.gz"}
https://www.nature.com/articles/s41598-020-72677-1	Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. # Work functioning impairment in the course of pharmacotherapy treatment for depression ## Abstract This study investigated the association between the duration of pharmacotherapy treatment for depression, or discontinuation from treatment, and work functioning impairment. This was a retrospective cohort study examining 30,409 workers. Work functioning impairment was assessed using a questionnaire, and treatment status was assessed using medical claims data. Odds ratios (ORs) of workers with severe work functioning impairment compared with healthy workers (control group) were calculated using logistic regression analysis. Continuous medical treatment was associated with severely impaired work functioning regardless of treatment period [continuous medical treatment; 4 months <: OR = 3.2, 4 months ≥, 10 months <: OR = 2.6, 10 months ≥, 14 months <: OR = 2.3, 14 months ≥, 16 months <: OR = 2.3, which are all statistically significant (p < 0.05)]. Workers who initially received pharmacotherapy treatment but discontinued in < 11 months had a significantly higher OR (treatment discontinuation period; 3 months <: OR = 2.3, 3 months ≥, 8 months <; OR = 2.0, 8 months ≥, 11 months <; OR = 3.0), while those who discontinued at ≥ 11 months did not (OR = 1.4, 95% CI 0.6–3.5). The sensitivity analysis excluding participants with at least one psychiatric comorbidity other than depression did not change the final result. It is important for the occupational health practitioners and attending psychiatrists to follow up in cooperation with each other, paying attention to the decrease in work functioning in addition to the symptoms. ## Introduction Patients with depression are likely to experience many years lived with disability (YLDs). This is a global health issue because major depressive disorder (MDD) is among the five leading causes of YLDs worldwide, contributing 34.1 million of the total YLDs (805 million) as of 20161. Depression reduces quality of life and affects work performance quality2,3. Presenteeism, defined as working while sick, is associated with reduced productivity and is a topic gaining increasing attention. A study found 6.4% of workers met the criteria for 12-month MDD, which is associated with 27.2 lost work days per sick worker per year and, in the United States, an overall loss of 225 million work days and $36.6 billion4. Based on total health-related costs due to absenteeism, presenteeism, and medical and pharmaceutical expenses, mental health disorders, including depression, comprise the largest burden of disease in the United States5 and Japan6. Our past study revealed that the presenteeism costs due to mental and behavioural disorders were$948 per 1000 full-time equivalent per year6. The other study revealed that sickness presence accounted for an average of 45.1 work days lost per employee per year7. Undiagnosed and untreated depression had caused enormous socio-economic losses such as a decrease in labor force and an increase in social security costs due to the severity and chronicity of depression8. It has been shown that mild depression should be an intervention target because it has a high risk of becoming severe9,10. It is important to detect and treat depression during its early stages. Proper treatment throughout the acute phase can relieve related symptoms, and achieve remission and a return to full functioning and quality of life10,11,12,13. It is also strongly recommended to continue pharmacotherapy after remission following successful acute phase treatment for preventing relapse11,14. American Psychiatric Association guidelines recommend treating patients with primary depression with the same dose of antidepressants as used in the acute phase, for 4–9 months or longer after remission, and assuming good and consistent control of depression symptoms11,15. Meanwhile, discontinuation and dose reduction of antidepressant drugs in the early phases can increase the risk of exacerbating symptoms; early discontinuation of antidepressants results in a 77% increase in the risk of relapse and recurrence of depression in two years 16. In order to decide the treatment policy, it is important not only to monitor the patient’s psychiatric status but also to evaluate functional impairment and quality of life11. Many depressed patients present with cognitive dysfunction such as slowed thoughts, poor concentration, distractibility, and reduce capacity to process information11. Understanding the type and extent of cognitive dysfunction is important in assessing the course of treatment. Attending physicians can evaluate functional impairment for their patients, and neuropsychological testing can be performed in the hospital17. However, it is difficult for the attending physician to intervene if the treatment is interrupted. If the patients were workers, the occupational health staff such as occupational physician and occupational health nurse can intervene with them in the workplace. Workers with depression tend to appear disabilities as work functions. Therefore, if the work functioning can be evaluated, it will be possible to find the timing of intervention by the occupational health staff. We previously developed and validated a self-administered questionnaire using the work functioning impairment scale (WFun) for assessment18. We also verified that the results of WFun assessments were correlated with the results of fit-to-work assessments conducted by occupational health nurses19. Clinical treatment aims not only to relieve related symptoms, but to help patients recover their social functioning. Work functioning is an important social function for workers with depression. Information on the degree of work functioning in each phase of the treatment process is useful when deciding the necessity of cooperation between the occupational health staff and the attending physician, and when the attending physician decides the treatment content. However, to the best of our knowledge, there are no reports on changes in work functioning impairment based on treatment duration and discontinuation. The purpose of this study is to describe the degree of work functioning impairment according to the course of pharmacotherapy treatment for depression (Objective 1: the duration of pharmacotherapy treatment, and Objective 2: the duration of discontinuation from pharmacotherapy treatment). ## Methods This was a retrospective cohort study of 45,404 workers, from 13 companies in Japan. All 13 companies were manufacturers (five pharmaceutical, six automobile-related, one nonferrous metals, and one precision equipment). ### Data collection and ethical approval The participants completed the WFun questionnaire between July and October 2015. The objectives of the study were explained to the participants, who were informed that participation was voluntary and that only the researchers, who were unaffiliated with the companies, would have access to the data. Ultimately, of the 45,404 workers, 33,415 (73.6%) participated. We obtained participants’ medical claims data from the companies’ health insurance unions retrospectively, back to 15 months before the WFun questionnaire was given. These claims contained information on the date of any visits to a medical institution (outpatient or inpatient), the name of the institution, the disease(s), treatment/medication(s), and medical expenditures. Because Japan has a universal health insurance system, these claims data contained complete records on services used by the participants and covered under the system. All methods were carried out in accordance with relevant guidelines and regulations. All data were labelled with unique codes assigned to each participant for personal information protection. Informed consent including implied consent was obtained from all subjects. The study was approved by the Ethics Committee of University of Occupational and Environmental Health, Japan (H26-026). ### Measurements for treatment of depression with pharmacotherapy Medical claims data were used for determining whether the participants had visited medical institutions and received pharmacotherapy treatment for depression there each month within the 15 months prior to their completing the WFun questionnaire. Participants were determined to have received pharmacotherapy treatment if they satisfied both of the following two inclusion criteria and one exclusion criteria: We included by two criteria as follow. 1. 1. International Classification of Diseases 10 (ICD 10) codes F30–F39 (mood [affective] disorders) was given as the disease name. 2. 2. Antidepressants and/or psychoneurotic drugs (therapeutic category of drugs in Japan: 117) were prescribed20. We excluded workers who had International Classification of Diseases 10 (ICD 10) codes F30 (Manic episode) or F31 (Bipolar affective disorder) given as the disease name of the claims data. A total of 126 participants had F30 (Manic episode) or F31 (Bipolar affective disorder), and we excluded their data in the final analysis. Based on information obtained from medical claims data and WFun, the participants were divided into five categories in accordance with their duration of pharmacotherapy treatment (Objective 1) and duration of discontinuation from treatment (Objective 2). Detailed definitions are provided below and in Fig. 1. Objective 1: Association between the duration of pharmacotherapy treatment for depression and work functioning impairment. 1. 1. control group (healthy workers with no pharmacotherapy treatment): those who had received no related treatment within 15 months preceding the WFun 2. 2. continuous pharmacotherapy treatment (< 4 months) 3. 3. continuous pharmacotherapy treatment (4 to < 10 months) 4. 4. continuous pharmacotherapy treatment (10 to < 14 months) 5. 5. continuous pharmacotherapy treatment (14 to < 16 months). A total of 315 participants were not classified under any of the above categories because they had received irregular pharmacotherapy treatment. Accordingly, we excluded their data in the final analysis. Objective 2: Association between the duration of discontinuation of pharmacotherapy treatment for depression and work functioning impairment. 1. 1. control group (healthy workers with no pharmacotherapy treatment): those who had received no related treatment within 15 months preceding the WFun 2. 2. treatment discontinuation period (< 3 months) 3. 3. treatment discontinuation period (3 to < 8 months) 4. 4. treatment discontinuation period (8 to < 11 months) 5. 5. treatment discontinuation period (11 to < 14 months). A total of 546 participants were not classified under any of the above categories because they had received irregular pharmacotherapy treatment. Accordingly, we excluded their data in the final analysis. ### Outcome measurements WFun is a self-administered questionnaire developed using the Rasch model18. It assesses the severity of work functioning impairment and has been validated in accordance with the Consensus-based Standards for the Selection of Health Measurement Instruments (COSMIN). Items of WFun and the scoring method was shown in Table 1. A higher total suggests greater work functioning impairment due to health problems. A total of ≥ 21 points suggests severely impaired work functioning: a previous study found approximately 20% of employees had a WFun score of 21 points, and an assessment by occupational health nurses found these people were likely to have severely impaired work functioning and that they demonstrated high detectability with an area under the ROC curve of 0.8319. Cronbach’s alpha coefficient for the seven items of WFun was 0.92 in this study. ### Other measurements We used a self-administered questionnaire to determine the participants’ sex, age, job type and job title. Age in years was categorised into five groups (< 30, 30–39, 40–49, 50–59, and ≥ 60 years), as was job type (clerical and administrative support, sales, research and development, production line, and other), while job title was categorised as manager or rank-and-file employee. ### Statistical analysis In addressing each of the two objectives indicated above, we performed logistic regression analyses using each category as an explanatory variable and a total WFun score of ≥ 21 points as an outcome variable. Using the category of no pharmacotherapy treatment (healthy workers) as a reference, we calculated the OR (and 95% CI) for each category. Stata version 14.2 (StataCorp LLC; TX, USA) was used for analyses, with significance set at < 0.05. ### Sensitivity analysis Many patients can be expected to have at least one psychiatric comorbidity and this can quite significantly alter work functioning. Sensitivity analysis was performed in order to confirm that the results did not change even if these individuals were excluded. We excluded participants below (exclusion criteria) and performed logistic regression analyses in the same way. #### Exclusion criteria 1. 1. International Classification of Diseases 10 (ICD 10) codes F00–F09 (organic, including symptomatic, mental disorders) was given as the disease name. F00-09 includes F00 (Dementia in Alzheimer disease) and F01 (Vascular dementia). 2. 2. International Classification of Diseases 10 (ICD 10) codes F10–F19 (mental and behavioural disorders due to psychoactive substance use) was given as the disease name. F10–F19 includes F10 (mental and behavioural disorders due to use of alcohol) and F11 (mental and behavioural disorders due to use of opioids). 3. 3. International Classification of Diseases 10 (ICD 10) codes F20–F29 (schizophrenia, schizotypal and delusional disorders). ## Results ### Participants’ characteristics Among the 33,415 participants, we were unable to obtain the medical claims data of 2,533 participants and 473 did not answer at least one of the seven WFun questions. After excluding them, we had data from 30,409 participants for analysis. Table 2 shows the participants’ characteristics. Male employees comprised 85% of the participants, and the largest proportion of participants (32%) were 40–49 years old, followed by 30–39 (24%), 50–59 (22%). Participants primarily worked in research and development (20%), clerical and administrative support (18%), and sales (18%). #### Objective 1 Table 3 shows the association between the duration of pharmacotherapy treatment for depression and work functioning impairment. Continuous medical treatment was associated with severely impaired work functioning regardless of treatment period [continuous medical treatment; 4 months <: OR = 3.2, 4 months ≥, 10 months <: OR = 2.6, 10 months ≥, 14 months <: OR = 2.3, 14 months ≥, 16 months <: OR = 2.3, which are all statistically significant (p < 0.05)]. #### Objective 2 Table 4 shows the association between the duration of discontinuation from pharmacotherapy treatment for depression and work functioning impairment. Workers who initially received pharmacotherapy treatment but discontinued in < 11 months had a significantly higher OR (treatment discontinuation period; 3 months <: OR = 2.3, 3 months ≥, 8 months <; OR = 2.0, 8 months ≥, 11 months <; OR = 3.0), while those who discontinued at ≥ 11 months did not show a significantly higher risk of work functioning impairment (OR = 1.4, 95% CI 0.6–3.5). A sensitivity analysis was performed on both objectives 1 and 2. The results excluding participants with at least one psychiatric comorbidity other than depression did not change (Supplementary Table S1, S2). ## Discussion This study investigated the association between the duration of pharmacotherapy treatment and work functioning impairment as well as the association between the duration of discontinuation from pharmacotherapy treatment and work functioning impairment. Continuous medical treatment was associated with severely impaired work functioning regardless of treatment period. Further, workers who initially received pharmacotherapy treatment but discontinued in < 11 months had a significantly higher OR compared to healthy workers (control group), while those who discontinued at ≥ 11 months did not (OR = 1.4, 95% CI 0.6–3.5). The present results have several implications for future interventions. First, in this study, the risk of experiencing severe work functioning impairment was higher even with ≥ 1 year of antidepressant treatment. While most recent systematic reviews have shown antidepressant treatment improves functional outcomes, one reported that 60% of patients had persistent functional impairment even 6 months after symptom remission21. Job performance is also improved over time following symptom amelioration22. These results are consistent with the present findings. Based on these findings, if the symptoms were recovered by the treatment of antidepressants but the work function was deteriorated, it may be necessary to consider a side effects of antidepressants or a cognitive impairment due to causes other than depression such as Alzheimer’s disease. Second, in addition to symptom amelioration, job-related functioning and performance are important for continued employment. Our study suggests the importance of monitoring patients for ≥ 1 year after finishing treatment (Table 4), assuming work performance is only restored after recovery from symptoms. The risk of work functioning impairment is markedly higher, particularly in the acute phase (< 4 months as shown in Table 3), wherein the risk is threefold that of healthy controls. It is therefore important to assess workers’ degree of recovery from impairment after starting treatment, even if their symptoms have remitted. Additionally, given that severe work functioning impairment (WFun ≥ 21 points) can increase the risk of taking sick leave in the future, such assessments are important for preventing depression-related work leave23. Third, in the present study, the risk of severe work functioning impairment remained high for about 1 year after discontinuation of antidepressant treatment (Table 4). This is the first study to assess work functioning following treatment discontinuation. To deter workers impatience with their recovery, attending psychiatrists or occupational physicians should explain the likelihood of being at an increased risk of work functioning impairment for ≥ 1 year after discontinuing antidepressant treatment. This explanation may give motivation to seek medical assistance when experiencing a symptom relapse. Additionally, Japanese companies with > 50 employees are legally obliged to employ corporate healthcare professionals, mainly occupational physicians, in the workplace. In these companies, importance should be placed on collaboration between the attending psychiatrist and healthcare professionals via the patient, and these healthcare professionals should follow-up patients after the patients discontinue antidepressant treatment. The present study has a number of strengths. It is the first study to investigate work functioning impairment in employees across several phases of antidepressant treatment for depression by comparing findings with healthy workers who have never received such treatment. The study also examined work functioning impairment across several phases after discontinuation of pharmacotherapy treatment for depression. Additionally, this study used a large-scale, workplace cohort and was based on mutually exclusive and collectively exhaustive medical claims data obtained via Japan’s universal health insurance system. The study does also have some limitations. First, we did not obtain information on the responsiveness of treatment for depression and the reason for discontinuation of treatment. We could not evaluate the effects of these situations on work functioning. Second, we did not assess depression severity. We therefore did not account for its effect on work functioning impairment. However, a recent systematic review reported, based on several studies, that although antidepressant treatment ameliorates functional outcomes, the severity of depression at the start of treatment does not affect this amelioration2. We were also unable to examine non-pharmaceutical treatments, such as psychotherapy, concurrent with pharmacotherapy; therefore we did not evaluate the effects of such treatments. Additionally, we did not examine other aspects, such as the effects of job styles at certain workplaces, with relation to work performance. Finally, because the study population comprised employees from companies listed on the First Section of the Tokyo Stock Exchange, and thus generally representing those of higher socioeconomic status, care should be taken in generalising the findings. Furthermore, roughly half were pharmaceutical company employees and therefore likely have greater medical knowledge than the general public. People with higher socioeconomic attributes, such as higher education levels, are also more accepting of mental health services24. The proportion of participants who had depression but were not using such services was therefore likely lower than that in the general population. This limitation should be taken into account when interpreting the results. Those taking oral antidepressants accounted for 2.7% of all participants, which is similar to the proportion in a large-scale survey on mood (emotional) disorders among general residents in Japan (in which the 12-month prevalence of depression was 2.1%)25. ## Conclusions The present study showed an association between the duration of pharmacotherapy treatment and work functioning impairment as well as the relationship between the duration of discontinuation from treatment and such impairment. Patients were found to be at an increased risk of severe work functioning impairment for ≥ 1 year after discontinuing antidepressants. It is important for the occupational health practitioners and attending psychiatrists to follow up in cooperation with each other, paying attention to the decrease in work functioning in addition to the symptoms. ## Data availability The analysis presents clinical data of a large-scale workplace-based cohort with ongoing follow-up examinations. This project constitutes a major scientific effort, therefore data are not made available for the scientific community outside. Interested researchers make their requests to the leader of the Collabo-Health Study (Tomohisa Nagata; tomohisa@med.uoeh-u.ac.jp). ## References 1. 1. GBD 2016 Disease and Injury Incidence and Prevalence Collaborators. Disease and Injury Incidence and Prevalence Collaborators, Global, regional, and national incidence, prevalence, and years lived with disability for 328 diseases and injuries for 195 countries, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016. Lancet 390, 1211–1259. https://doi.org/10.1016/S0140-6736(17)32154-2 (2017). 2. 2. Sheehan, D. V., Nakagome, K., Asami, Y., Pappadopulos, E. A. & Boucher, M. Restoring function in major depressive disorder: a systematic review. J. Affect. Disord. 215, 299–313. https://doi.org/10.1016/j.jad.2017.02.029 (2017). 3. 3. World Health Organization. Key facts of depression. World Health Organization https://www.who.int/news-room/fact-sheets/detail/depression (2018). 4. 4. Kessler, R. C. et al. Prevalence and effects of mood disorders on work performance in a nationally representative sample of U.S. workers. Am. J. Psychiatry 163, 1561–1568. https://doi.org/10.1176/appi.ajp.163.9.1561 (2006). 5. 5. Loeppke, R. et al. Health and productivity as a business strategy: a multiemployer study. J. Occup. Environ. Med. 51, 411–428. https://doi.org/10.1097/JOM.0b013e3181a39180 (2009). 6. 6. Nagata, T. et al. Total health-related costs due to absenteeism, presenteeism, and medical and pharmaceutical expenses in Japanese employers. J. Occup. Environ. Med. 60, e273–e280. https://doi.org/10.1097/JOM.0000000000001291 (2018). 7. 7. Chimed-Ochir, O. et al. Potential work time lost due to sickness absence and presence among Japanese workers. J. Occup. Environ. Med. 61, 682–688. https://doi.org/10.1097/JOM.0000000000001646 (2019). 8. 8. McCrone, P., Dhanasiri, S., Patel, A., Knapp, M. & Lawton-Smith, S. Paying the Price: The Cost of Mental Health Care in England to 2026 (The King’s Fund, London, 2008). 9. 9. Cuijpers, P., de Graaf, R. & van Dorsselaer, S. Minor depression: risk profiles, functional disability, health care use and risk of developing major depression. J. Affect. Disord. 79, 71–79. https://doi.org/10.1016/S0165-0327(02)00348-8 (2004). 10. 10. Cuijpers, P. & Smit, F. Subthreshold depression as a risk indicator for major depressive disorder: a systematic review of prospective studies. Acta Psychiatr. Scand. 109, 325–331. https://doi.org/10.1111/j.1600-0447.2004.00301.x (2004). 11. 11. American Psychiatric Association. Practice guideline for the treatment of patients with major depressive disorder, 3rd edn. https://psychiatryonline.org/pb/assets/raw/sitewide/practice_guidelines/guidelines/mdd.pdf (2010). 12. 12. Higuchi, T. Major depressive disorder treatment guidelines in Japan. J. Clin. Psychiatry 71(Suppl E1), e05. https://doi.org/10.4088/JCP.9058se1c.05gry (2010). 13. 13. Kupfer, D. J. Long-term treatment of depression. J. Clin. Psychiatry 52(Suppl), 28–34. https://psycnet.apa.org/record/1991-31033-001 (1991). 14. 14. Preventing recurrent depression: long-term treatment for major depressive disorder. Prim. Care Companion J. Clin. Psychiatry 9, 214–223. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1911177/ (2007) 15. 15. Lam, R. W. et al. Canadian Network for Mood and Anxiety Treatments (CANMAT) clinical guidelines for the management of major depressive disorder in adults. III. Pharmacotherapy. J. Affect. Disord. 117(Suppl 1), S26–S43. https://doi.org/10.1016/j.jad.2009.06.041 (2009). 16. 16. Melfi, C. A. et al. The effects of adherence to antidepressant treatment guidelines on relapse and recurrence of depression. Arch. Gen. Psychiatry 55, 1128–1132. https://doi.org/10.1001/archpsyc.55.12.1128 (1998). 17. 17. Stoudemire, A., Hill, C., Gulley, L. R. & Morris, R. Neuropsychological and biomedical assessment of depression-dementia syndromes. J. Neuropsychiatry Clin. Neurosci. 1, 347–361. https://doi.org/10.1176/jnp.1.4.347 (1989). 18. 18. Fujino, Y. et al. Development and validity of a work functioning impairment scale based on the Rasch model among Japanese workers. J. Occup. Health 57, 521–531. https://doi.org/10.1539/joh.15-0135-OA (2015). 19. 19. Nagata, T. et al. Diagnostic Accuracy of the Work Functioning Impairment Scale (WFun): a method to detect workers who have health problems affecting their work and to evaluate fitness for work. J. Occup. Environ. Med. 59, 557–562. https://doi.org/10.1097/JOM.0000000000001025 (2017). 20. 20. Kyoto Encyclopedia of Genes and Genomes. Therapeutic Category of Drugs in Japan. https://www.genome.jp/kegg-bin/get_htext?&extend=D457D528&highlight=D00754&htext=br08301%2Ekeg (2019). 21. 21. Jaeger, J., Berns, S., Uzelac, S. & Davis-Conway, S. Neurocognitive deficits and disability in major depressive disorder. Psychiatry Res. 145, 39–48. https://doi.org/10.1016/j.psychres.2005.11.011 (2006). 22. 22. Adler, D. A. et al. Job performance deficits due to depression. Am. J. Psychiatry 163, 1569–1576. https://doi.org/10.1176/ajp.2006.163.9.1569 (2006). 23. 23. Fujino, Y. et al. Prospective cohort study of work functioning impairment and subsequent absenteeism among Japanese workers. J. Occup. Environ. Med. 58, e264–e267. https://doi.org/10.1097/JOM.0000000000000788 (2016). 24. 24. Todd, M. & Teitler, J. Darker days? Recent trends in depression disparities among US adults. Am. J. Orthopsychiatry 89, 727–735. https://doi.org/10.1037/ort0000370 (2016). 25. 25. Japan Committee of Prevention and Treatment for Depression. Summary of Treatment for Depression. https://www.jcptd.jp/medical/point_10.pdf (2019). ## Acknowledgements This work was funded by the Collabo-Health Study Group, and partly supported by JSPS KAKENHI Grant Number JP18K10079 and JP19K19471. ## Author information Authors ### Contributions T.N. played a lead role in the study design and the writing of the manuscript, and he contributed to the data interpretation and the data analysis. Y.F. conducted the data analysis, contributed to results interpretation and reviewed drafts of the manuscript. M.O. (Makoto Ohtani) contributed to the study design and data interpretation. K.F. conducted the analysis of receipt data. M.N., S.K., M.O. (Makoto Okawara) and K.M. reviewed drafts of the manuscript. All authors had final approval for submitted and published version of the paper. ### Corresponding author Correspondence to Tomohisa Nagata. ## Ethics declarations ### Competing interests The authors declare no competing interests. ### Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Rights and permissions Reprints and Permissions Nagata, T., Fujino, Y., Ohtani, M. et al. Work functioning impairment in the course of pharmacotherapy treatment for depression. Sci Rep 10, 15712 (2020). https://doi.org/10.1038/s41598-020-72677-1 • Accepted: • Published:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38924381136894226, "perplexity": 7411.6930490373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585737.45/warc/CC-MAIN-20211023162040-20211023192040-00155.warc.gz"}
https://www.rdocumentation.org/packages/TTR/versions/0.23-1/topics/DPO	# DPO 0th Percentile ##### De-Trended Price Oscillator The Detrended Price Oscillator (DPO) removes the trend in prices - or other series - by subtracting a moving average of the price from the price. Keywords ts ##### Usage DPO(x, n = 10, maType, shift = n/2 + 1, percent = FALSE, ...) ##### Arguments x Price, volume, etc. series that is coercible to xts or matrix. n Number of periods for moving average. maType A function or a string naming the function to be called. shift The number of periods to shift the moving average. percent logical; if TRUE, the percentage difference between the slow and fast moving averages is returned, otherwise the difference between the respective averages is returned. Other arguments to be passed to the maType function. ##### Details The Detrended Price shows cycles and overbought / oversold conditions. ##### Value A object of the same class as x or a vector (if try.xts fails) containing the DPO values. ##### Note DPO does not extend to the last date because it is based on a displaced moving average. The calculation shifts the results shift periods, so the last shift periods will be zero. As stated above, the DPO can be used on any univariate series, not just price. ##### References The following site(s) were used to code/document this indicator: http://www.fmlabs.com/reference/DPO.htm http://www.equis.com/Customer/Resources/TAAZ/?c=3&p=48 http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:detrended_price_osci See EMA, SMA, etc. for moving average options; and note Warning section. See MACD for a general oscillator. library(TTR) # NOT RUN { data(ttrc) priceDPO <- DPO(ttrc[,"Close"]) volumeDPO <- DPO(ttrc[,"Volume"]) # }	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2642419934272766, "perplexity": 6879.9184223657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370521574.59/warc/CC-MAIN-20200404073139-20200404103139-00469.warc.gz"}
https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/f01/f01zdf.html	# NAG FL Interfacef01zdf (complex_band_pack) ## ▸▿ Contents Settings help FL Name Style: FL Specification Language: ## 1Purpose f01zdf copies a complex band matrix stored in a packed array into an unpacked array, or vice versa. ## 2Specification Fortran Interface Subroutine f01zdf ( job, m, n, kl, ku, a, lda, b, ldb, Integer, Intent (In) :: m, n, kl, ku, lda, ldb Integer, Intent (Inout) :: ifail Complex (Kind=nag_wp), Intent (Inout) :: a(lda,n), b(ldb,) Character (1), Intent (In) :: job #include <nag.h> void f01zdf_ (const char job, const Integer m, const Integer n, const Integer kl, const Integer ku, Complex a[], const Integer lda, Complex b[], const Integer ldb, Integer ifail, const Charlen length_job) The routine may be called by the names f01zdf or nagf_matop_complex_band_pack. ## 3Description f01zdf unpacks a band matrix that is stored in a packed array, or packs a band matrix that is stored in an unpacked array. The band matrix has $m$ rows, $n$ columns, ${k}_{l}$ nonzero subdiagonals, and ${k}_{u}$ nonzero superdiagonals. This routine is intended for possible use in conjunction with routines from Chapters F06, F07 and F08, where routines that use band matrices store them in the packed form described below. None. ## 5Arguments 1: $\mathbf{job}$Character(1) Input On entry: specifies whether the band matrix is to be packed or unpacked. ${\mathbf{job}}=\text{'P'}$ (Pack) The band matrix is to be packed into array b. ${\mathbf{job}}=\text{'U'}$ (Unpack) The band matrix is to be unpacked into array a. Constraint: ${\mathbf{job}}=\text{'P'}$ or $\text{'U'}$. 2: $\mathbf{m}$Integer Input 3: $\mathbf{n}$Integer Input On entry: $m$ and $n$, the number of rows and columns of the band matrix, respectively. Constraints: • ${\mathbf{m}}>0$; • ${\mathbf{n}}>0$. 4: $\mathbf{kl}$Integer Input On entry: ${k}_{l}$, the number of subdiagonals of the band matrix. Constraint: ${\mathbf{kl}}\ge 0$. 5: $\mathbf{ku}$Integer Input On entry: ${k}_{u}$, the number of superdiagonals of the band matrix. Constraint: ${\mathbf{ku}}\ge 0$. 6: $\mathbf{a}\left({\mathbf{lda}},{\mathbf{n}}\right)$Complex (Kind=nag_wp) array Input/Output On entry: if ${\mathbf{job}}=\text{'P'}$, the leading $m×n$ part of a must contain the band matrix stored in unpacked form. Elements of the array that lie outside the banded part of the matrix are not referenced and need not be assigned. On exit: if ${\mathbf{job}}=\text{'U'}$, the leading $m×n$ part of a contains the band matrix stored in unpacked form. Elements of the leading $m×n$ part of a that are not within the banded part of the matrix are assigned the value zero. 7: $\mathbf{lda}$Integer Input On entry: the first dimension of the array a as declared in the (sub)program from which f01zdf is called. Constraint: ${\mathbf{lda}}\ge {\mathbf{m}}$. 8: $\mathbf{b}\left({\mathbf{ldb}},\right)$Complex (Kind=nag_wp) array Input/Output Note: the second dimension of the array b must be at least $\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{m}}+{\mathbf{ku}},{\mathbf{n}}\right)$. On entry: if ${\mathbf{job}}=\text{'U'}$, b must contain the band matrix in packed form, in the leading $\left({k}_{l}+{k}_{u}+1\right)×\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(m+{k}_{u},n\right)$ part of the array. The matrix is packed column by column, with the leading diagonal of the matrix in row $\left({k}_{u}+1\right)$ of b, the first superdiagonal starting at position $2$ in row ${k}_{u}$, the first subdiagonal starting at position $1$ in row $\left({k}_{u}+2\right)$, and so on. Elements of b that are not needed to store the band matrix, for instance the leading ${k}_{u}×{k}_{u}$ triangle, are not referenced and need not be assigned. On exit: if ${\mathbf{job}}=\text{'P'}$, b contains the band matrix stored in packed form. Elements of b that are not needed to store the band matrix are not referenced. 9: $\mathbf{ldb}$Integer Input On entry: the first dimension of the array b as declared in the (sub)program from which f01zdf is called. Constraint: ${\mathbf{ldb}}\ge \left({\mathbf{kl}}+{\mathbf{ku}}+1\right)$. 10: $\mathbf{ifail}$Integer Input/Output On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected. A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not. If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit. On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6). ## 6Error Indicators and Warnings If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf). Errors or warnings detected by the routine: ${\mathbf{ifail}}=1$ On entry, ${\mathbf{job}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{job}}=\text{'P'}$ or $\text{'U'}$. ${\mathbf{ifail}}=2$ On entry, ${\mathbf{kl}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{kl}}\ge 0$. ${\mathbf{ifail}}=3$ On entry, ${\mathbf{ku}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{ku}}\ge 0$. ${\mathbf{ifail}}=4$ On entry, ${\mathbf{lda}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{lda}}\ge {\mathbf{m}}$. ${\mathbf{ifail}}=5$ On entry, ${\mathbf{ldb}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{kl}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{ku}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{ldb}}\ge {\mathbf{kl}}+{\mathbf{ku}}+1$. ${\mathbf{ifail}}=6$ On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{m}}>0$. On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{n}}>0$. ${\mathbf{ifail}}=-99$ See Section 7 in the Introduction to the NAG Library FL Interface for further information. ${\mathbf{ifail}}=-399$ Your licence key may have expired or may not have been installed correctly. See Section 8 in the Introduction to the NAG Library FL Interface for further information. ${\mathbf{ifail}}=-999$ Dynamic memory allocation failed. See Section 9 in the Introduction to the NAG Library FL Interface for further information. Not applicable. ## 8Parallelism and Performance f01zdf is not threaded in any implementation. None. ## 10Example This example reads a matrix $A$ in unpacked form, and copies it to the packed matrix $B$. ### 10.1Program Text Program Text (f01zdfe.f90) ### 10.2Program Data Program Data (f01zdfe.d) ### 10.3Program Results Program Results (f01zdfe.r)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 87, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7964410781860352, "perplexity": 4316.273140074763}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104432674.76/warc/CC-MAIN-20220704141714-20220704171714-00582.warc.gz"}
https://worldwidescience.org/topicpages/a/ad+multos+transannos.html	#### Sample records for ad multos transannos 1. Theodor Hellbrügge: 85 years of age – Ad multos transannos, sanos, fortunatos et beatos Directory of Open Access Journals (Sweden) Schwartzkopff Othild 2005-03-01 Full Text Available Abstract We honor Theo Hellbrügge's acclaimed endeavors in the rehabilitation, or rather the prehabilitation of handicapped children. So far, he has focused on obvious handicaps, and we trust that he will include concern for everybody's silent handicaps in the future by screening for abnormal variability inside the physiological range. Therein, we introduce cis- and trans-years, components of transdisciplinary spectra that are novel for biology and also in part for physics. These components have periods, respectively, shorter and longer than the calendar year, with a counterpart in magnetoperiodism. Transyears characterize indices of geomagnetic activity and the solar wind's speed and proton density. They are detected, alone or together with circannuals, in physiology as well as in pathology, as illustrated for sudden cardiac death and myocardial infarction, a finding calling for similar studies in sudden infant death syndrome (SIDS. As transyears can beat with circannuals, and depend on local factors, their systematic mapping in space and time by transdisciplinary chronomics may serve a better understanding of their putative influence upon the circadian system. Longitudinal monitoring of blood pressure and heart rate detects chronome alterations underlying cardiovascular disease risk, such as that of myocardial infarction and sudden cardiac death. The challenge is to intervene in a timely fashion, preferably at birth, an opportunity for pediatricians in Theo Hellbrügge's footsteps. International Nuclear Information System (INIS) Anabalón, Andrés; Astefanesei, Dumitru; Choque, David 2016-01-01 We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate. Energy Technology Data Exchange (ETDEWEB) Anabalón, Andrés, E-mail: andres.anabalon@uai.cl [Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Astefanesei, Dumitru, E-mail: dumitru.astefanesei@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Choque, David, E-mail: brst1010123@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso (Chile) 2016-11-10 We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate. CERN Document Server Powers, Shelley 2007-01-01 Ajax can bring many advantages to an existing web application without forcing you to redo the whole thing. This book explains how you can add Ajax to enhance, rather than replace, the way your application works. For instance, if you have a traditional web application based on submitting a form to update a table, you can enhance it by adding the capability to update the table with changes to the form fields, without actually having to submit the form. That's just one example.Adding Ajax is for those of you more interested in extending existing applications than in creating Rich Internet Applica International Nuclear Information System (INIS) Martelli, Dario; Morales, Jose Francisco 2005-01-01 In the light of the recent Lin, Lunin, Maldacena (LLM) results, we investigate 1/2-BPS geometries in minimal (and next to minimal) supergravity in D = 6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a two-torus T 2 specified by two harmonic functions. For a rectangular torus the two functions are related by a non-linear equation with rare solutions: AdS 3 x S 3 , the pp-wave and the multi-center string. 'Bubbling', i.e. superpositions of droplets, is accommodated by allowing the complex structure of the T 2 to vary over the base. The analysis is repeated in the presence of a tensor multiplet and similar conclusions are reached, with generic solutions describing D1D5 (or their dual fundamental string-momentum) systems. In this framework, the profile of the dual fundamental string-momentum system is identified with the boundaries of the droplets in a two-dimensional plane. (author) 6. String Theory on AdS Spaces NARCIS (Netherlands) de Boer, J. 2000-01-01 In these notes we discuss various aspects of string theory in AdS spaces. We briefly review the formulation in terms of Green-Schwarz, NSR, and Berkovits variables, as well as the construction of exact conformal field theories with AdS backgrounds. Based on lectures given at the Kyoto YITP Workshop 7. Duae novae Staphylinidae ex India Orientali (Sumatra) NARCIS (Netherlands) Fauvel, A. 1881-01-01 Ad sectionem fulgidi referendus, prope nasutum Harold (africanum) collocandus. Multo major et robustior. Elougatus, parallelus, nitidissimus, elytris paulo minus, convexus; niger, antennis pedibusque nigro-piceis, palpis tarsisque rufescentibus, elytris rufis, segmentorum 6 et 7 apice rufo-testaceo; International Nuclear Information System (INIS) Anninos, Dionysios; Li Wei; Padi, Megha; Song Wei; Strominger, Andrew 2009-01-01 Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -l -2 and positive Newton constant G admits an AdS 3 vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μl = 1. However we show herein that for every value of μl ≠ 3 there are two other (potentially stable) vacuum solutions given by SL(2,R) x U(1)-invariant warped AdS 3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at μl = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For μl > 3, there are known warped black hole solutions which are asymptotic to warped AdS 3 . We show that these black holes are discrete quotients of warped AdS 3 just as BTZ black holes are discrete quotients of ordinary AdS 3 . Moreover new solutions of this type, relevant to any theory with warped AdS 3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for μl > 3, the warped AdS 3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c R -formula and c L -formula. International Nuclear Information System (INIS) Donos, Aristomenis; Gauntlett, Jerome P.; Kim, Nakwoo 2008-01-01 We present new classes of explicit supersymmetric AdS 3 solutions of type IIB supergravity with non-vanishing five-form flux and AdS 2 solutions of D = 11 supergravity with electric four-form flux. The former are dual to two-dimensional SCFTs with (0,2) supersymmetry and the latter to supersymmetric quantum mechanics with two supercharges. We also investigate more general classes of AdS 3 solutions of type IIB supergravity and AdS 2 solutions of D = 11 supergravity which in addition have non-vanishing three-form flux and magnetic four-form flux, respectively. The construction of these more general solutions makes essential use of the Chern-Simons or 'transgression' terms in the Bianchi identity or the equation of motion of the field strengths in the supergravity theories. We construct infinite new classes of explicit examples and for some of the type IIB solutions determine the central charge of the dual SCFTs. The type IIB solutions with non-vanishing three-form flux that we construct include a two-torus, and after two T-dualities and an S-duality, we obtain new AdS 3 solutions with only the NS fields being non-trivial. 10. Polarised Black Holes in AdS CERN Document Server Costa, Miguel S.; Oliveira, Miguel; Penedones, João; Santos, Jorge E. 2016-05-03 We consider solutions in Einstein-Maxwell theory with a negative cosmological constant that asymptote to global $AdS_{4}$ with conformal boundary $S^{2}\\times\\mathbb{R}_{t}$. At the sphere at infinity we turn on a space-dependent electrostatic potential, which does not destroy the asymptotic $AdS$ behaviour. For simplicity we focus on the case of a dipolar electrostatic potential. We find two new geometries: (i) an $AdS$ soliton that includes the full backreaction of the electric field on the $AdS$ geometry; (ii) a polarised neutral black hole that is deformed by the electric field, accumulating opposite charges in each hemisphere. For both geometries we study boundary data such as the charge density and the stress tensor. For the black hole we also study the horizon charge density and area, and further verify a Smarr formula. Then we consider this system at finite temperature and compute the Gibbs free energy for both $AdS$ soliton and black hole phases. The corresponding phase diagram generalizes the Hawkin... 11. Current status of AdS instability CERN Multimedia CERN. Geneva 2016-01-01 arXiv:1403.6471 and thoroughly developed in arXiv:1407.6273. On the other hand the negative cosmological constant allows for the existence of stable, time-periodic, asymptotically AdS solutions of Einstein equations [arXiv:1303.3186]. OpenAIRE Bel, Ll. 2014-01-01 I propose a generalization of the Klein-Gordon equation in the framework of AdS space-time and exhibit a four parameter family of solutions among which there is a two parameter family of time-dependent bound states. 13. Lorentzian AdS, Wormholes and Holography CERN Document Server Arias, Raul E; Silva, Guillermo A 2011-01-01 We investigate the structure of two point functions for the QFT dual to an asymptotically Lorentzian AdS-wormhole. The bulk geometry is a solution of 5-dimensional second order Einstein Gauss Bonnet gravity and causally connects two asymptotically AdS space times. We revisit the GKPW prescription for computing two-point correlation functions for dual QFT operators O in Lorentzian signature and we propose to express the bulk fields in terms of the independent boundary values phi_0^\\pm at each of the two asymptotic AdS regions, along the way we exhibit how the ambiguity of normalizable modes in the bulk, related to initial and final states, show up in the computations. The independent boundary values are interpreted as sources for dual operators O^\\pm and we argue that, apart from the possibility of entanglement, there exists a coupling between the degrees of freedom leaving at each boundary. The AdS_(1+1) geometry is also discussed in view of its similar boundary structure. Based on the analysis, we propose a ... Energy Technology Data Exchange (ETDEWEB) Elliot-Ripley, Matthew; Winyard, Thomas [Department of Mathematical Sciences, Durham University,South Rd, Durham (United Kingdom) 2015-09-01 We study the baby Skyrme model in a pure AdS background without a mass term. The tail decays and scalings of massless radial solutions are demonstrated to take a similar form to those of the massive flat space model, with the AdS curvature playing a similar role to the flat space pion mass. We also numerically find minimal energy solutions for a range of higher topological charges and find that they form concentric ring-like solutions. Popcorn transitions (named in analogy with studies of toy models of holographic QCD) from an n layer to an n+1-layer configuration are observed at topological charges 9 and 27 and further popcorn transitions for higher charges are predicted. Finally, a point-particle approximation for the model is derived and used to successfully predict the ring structures and popcorn transitions for higher charge solitons. International Nuclear Information System (INIS) Gauntlett, Jerome P.; Waldram, Daniel; Kim, Nakwoo 2007-01-01 We present new supersymmetric AdS 3 solutions of type IIB supergravity and AdS 2 solutions of D = 11 supergravity. The former are dual to conformal field theories in two dimensions with N = (0, 2) supersymmetry while the latter are dual to conformal quantum mechanics with two supercharges. Our construction also includes AdS 2 solutions of D = 11 supergravity that have non-compact internal spaces which are dual to three-dimensional N = 2 superconformal field theories coupled to point-like defects. We also present some new bubble-type solutions, corresponding to BPS states in conformal theories, that preserve four supersymmetries DEFF Research Database (Denmark) Liu, Yawu; Mattila, Jussi; Ruiz, Miguel �ngel Mu�oz 2013-01-01 To compare the accuracies of predicting AD conversion by using a decision support system (PredictAD tool) and current research criteria of prodromal AD as identified by combinations of episodic memory impairment of hippocampal type and visual assessment of medial temporal lobe atrophy (MTA) on MRI... International Nuclear Information System (INIS) Herscovich, Estanislao; Minces, Pablo; Nunez, Carmen 2006-01-01 Correlation functions of one-unit spectral flowed states in string theory on AdS 3 are considered. We present the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by amplitudes containing states in winding sector one and study their solution corresponding to the four point function including one w = 1 field. We compute the three point function involving two one-unit spectral flowed operators and find expressions for amplitudes of three w = 1 states satisfying certain particular relations among the spins of the fields. Several consistency checks are performed Directory of Open Access Journals (Sweden) Palma Peña-Jiménez, Ph.D. 2011-01-01 International Nuclear Information System (INIS) 2016-01-01 We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger http://dx.doi.org/10.1007/JHEP05(2013)152, in agreement with the results of Castro and Song http://arxiv.org/abs/1411.1948. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 ×S 2 or conformally AdS 2 ×S 2 solutions of the STU model in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton solutions coincide 20. Complexity of the AdS soliton Science.gov (United States) Reynolds, Alan P.; Ross, Simon F. 2018-05-01 We consider the holographic complexity conjectures in the context of the AdS soliton, which is the holographic dual of the ground state of a field theory on a torus with antiperiodic boundary conditions for fermions on one cycle. The complexity is a non-trivial function of the size of the circle with antiperiodic boundary conditions, which sets an IR scale in the dual geometry. We find qualitative differences between the calculations of complexity from spatial volume and action (CV and CA). In the CV calculation, the complexity for antiperiodic boundary conditions is smaller than for periodic, and decreases monotonically with increasing IR scale. In the CA calculation, the complexity for antiperiodic boundary conditions is larger than for periodic, and initially increases with increasing IR scale, eventually decreasing to zero as the IR scale becomes of order the UV cutoff. We compare these results to a simple calculation for free fermions on a lattice, where we find the complexity for antiperiodic boundary conditions is larger than for periodic. 1. AdS2 models in an embedding superspace International Nuclear Information System (INIS) McKeon, D.G.C.; Sherry, T.N. 2003-01-01 An embedding superspace, whose bosonic part is the flat (2+1)-dimensional embedding space for AdS 2 , is introduced. Superfields and several supersymmetric models are examined in the embedded AdS 2 superspace CERN Document Server John Wiley & Sons 2004-01-01 "Assimilating the most up-to-date information on research and development activities in this rapidly growing area, Mobile Ad Hoc Networking covers physical, data link, network, and transport layers, as well as application, security, simulation, and power management issues in sensor, local area, personal, and mobile ad hoc networks. Each of the book's sixteen chapters has been written by a top expert and discusses in-depth the most important topics in the field. Mobile Ad Hoc Networking is an excellent reference and guide for professionals seeking an in-depth examination of topics that also provides a comprehensive overview of the current state-of-the-art."--Jacket. International Nuclear Information System (INIS) Bena, Iosif; Heurtier, Lucien; Puhm, Andrea 2016-01-01 It was argued in http://dx.doi.org/10.1007/JHEP03(2013)028 that the five-dimensional near-horizon extremal Kerr (NHEK) geometry can be embedded in String Theory as the infrared region of an infinite family of non-supersymmetric geometries that have D1, D5, momentum and KK monopole charges. We show that there exists a method to embed these geometries into asymptotically-AdS 3 ×S 3 /ℤ N solutions, and hence to obtain infinite families of flows whose infrared is NHEK. This indicates that the CFT dual to the NHEK geometry is the IR fixed point of a Renormalization Group flow from a known local UV CFT and opens the door to its explicit construction. International Nuclear Information System (INIS) Evans, Nick; French, James; Threlfall, Ed; Jensen, Kristan 2010-01-01 We describe hadronization events, using the AdS/CFT Correspondence, which display many of the qualitative features expected in QCD. In particular we study the motion of strings with separating end points in a back-reacted hard wall geometry. The solutions show the development of a linear QCD-like string. The end points oscillate in the absence of string breaking. We introduce string breaking by hand and evolve the new state forward in time to observe the separation of two string segments. A kink associated with this breaking evolves to the end points of the string inducing rho meson production. We explicitly compute the rho meson production at the end point. DEFF Research Database (Denmark) Holmgreen, Lise-Lotte 2014-01-01 jobs by discursively constructing job ads that appeal to both sexes. This argument is part of the broader field of corporate social responsibility, corporate citizenship, and stakeholder management, which involves discussions of the obligations of corporations to acknowledge and mitigate...... the increasingly widespread impact that their activities have on communities and social structures. The article emphasises the need for more active engagement on the part of corporations by analysing the discursive construction of preferred candidates in a small sample of Danish management job ads. By means...... that this agreement reflects a high degree of conservatism in the system where men enjoy a considerable advantage and where procedures that ensure male dominance are perpetuated even in the linguistic and discursive construction of job ads.... International Nuclear Information System (INIS) 2015-01-01 In China the conceptual study of an ADS concept which lasted for about five years ended in 1999. As one project of the National Basic Research Programme of China (973 Programme) in energy domain, which is sponsored by the China Ministry of Science and Technology (MOST), a five year programme of fundamental research of ADS physics and related technology was launched in 2000 and passed national review at the end of 2005. From 2007, another five year 973 Programme Key Technology Research of Accelerator Driven Subcritical System for Nuclear waste Transmutation started. The research activities were focused on HPPA physics and technology, reactor physics of external source driven subcritical assembly, nuclear data base and material study. For HPPA, a high current injector consisting of an ECR ion source, LEBT and an RFQ accelerating structure of 3.5 MeV has been built and were being improved. In reactor physics study, a series of neutron multiplication experimental study has been carrying out. The VENUS I facility has been constructed as the basic experimental platform for neutronics study in ADS blanket. VENUS I a zero power subcritical neutron multiplying assembly driven by external neutron produced by a pulsed neutron generator or 252Cf neutron source. The theoretical, experimental and simulation studies on nuclear data, material properties and nuclear fuel circulation related to ADS are carried out in order to provide the database for ADS system analysis. China Institute of Atomic Energy (CIAE), Institute of High Energy Physics (IHEP) and other Chinese institutes carried out the MOST project together. Besides CIAE, China Academy of Science (CAS) pays more and more attention to Advanced Nuclear Fuel Cycles (ANFC). A large programme of ANFC, including ADS and Th based nuclear fuel cycle, has been launched by CAS CERN Document Server Rashvand, Habib 2013-01-01 Motivated by the exciting new application paradigm of using amalgamated technologies of the Internet and wireless, the next generation communication networks (also called 'ubiquitous', 'complex' and 'unstructured' networking) are changing the way we develop and apply our future systems and services at home and on local, national and global scales. Whatever the interconnection - a WiMAX enabled networked mobile vehicle, MEMS or nanotechnology enabled distributed sensor systems, Vehicular Ad hoc Networking (VANET) or Mobile Ad hoc Networking (MANET) - all can be classified under new networking s DEFF Research Database (Denmark) Engelmark, Jesper; Dahl, Torben; Melgaard, Ebbe 2007-01-01 of them had to be renovated after a shorter period. In stead of just replacing the original roof with a new one, it is now a days rather common to ad an extra storey where that is possible according to local planning. The reason is as a rule based on economical benefits, but very often this extra storey... 9. Globally regular instability of AdS_3 OpenAIRE Bizon, P.; Jałmużna, J. 2013-01-01 We consider three-dimensional AdS gravity minimally coupled to a massless scalar field and study numerically the evolution of small smooth circularly symmetric perturbations of the $AdS_3$ spacetime. As in higher dimensions, for a large class of perturbations, we observe a turbulent cascade of energy to high frequencies which entails instability of $AdS_3$. However, in contrast to higher dimensions, the cascade cannot be terminated by black hole formation because small perturbations have ener... 10. Nonlinear realization of supersymmetric AdS space isometries International Nuclear Information System (INIS) Clark, T. E.; Love, S. T. 2006-01-01 The isometries of AdS 5 space and supersymmetric AdS 5 xS 1 space are nonlinearly realized on four-dimensional Minkowski space. The resultant effective actions in terms of the Nambu-Goldstone modes are constructed. The dilatonic mode governing the motion of the Minkowski space probe brane into the covolume of supersymmetric AdS 5 space is found to be unstable and the bulk of the AdS 5 space is unable to sustain the brane. No such instability appears in the nonsupersymmetric case Directory of Open Access Journals (Sweden) Wulan Roro Retno 2017-01-01 Full Text Available Cosmetics industry created the beauty myth for women through advertising. A cosmetic ad in Indonesia has spread a new concept of white skin: East Asia beauty myth. The white concept of Asia white skin basically derived from colonial legacy. The purpose of the research was analyzing the beauty myth in Indonesia ads using postcolonial perspective. The principal result brought the discourse analysis and postcolonial perspective a new insight in communication research. Particularly on media and cultural studies. Major conclusions showed that the beauty myth since the Dutch colonial period never been change. The main concept is always in colonialism’s idea: “white is better”. The West is better than the East. Directory of Open Access Journals (Sweden) Yu. O. Loboda 2014-06-01 Full Text Available In the paper «Philosophia ad bellum» is being realized an attempt to classify philosophic approaches to the study of phenomenon of war by the analogy with the structure of «Just war theory» – 1. Philosophia ad bellum – «philosophy for war», where are investigated ways of using of philosophic methods of cognition in applied military sciences; 2. Philosophia supra bello – «philosophy above war», which investigates worldview, historicphilosophic, existential, logicepistemological aspects of war; 3. Philosophia contra belli – «philosophy against war», where research of the essence of war gets its logical conclusion in grounding of the absurdity of thinking schemes which justify war as an act of violence. In the article was made historicphilosophic overview of the part «Philosophia ad bellum», where were showed tangent questions, which are considered by philosophic logic and theory of strategic intelligence. It was stated, that specialists if military intelligence admit the important role of researches in logic and theory of cognition in their professional work; were defined basic questions, which have the most essential interest for military professionals. There were analyzed ways of using of philosophic methods in developing military strategies, was made a conclusion that philosophy can be a basis of strategic failures and victories as well. 13. The group approach to AdS space propagators International Nuclear Information System (INIS) Leonhardt, Thorsten; Manvelyan, Ruben; Ruehl, Werner 2003-01-01 We show that AdS two-point functions can be obtained by connecting two points in the interior of AdS space with one point on its boundary by a dual pair of Dobrev's boundary-to-bulk intertwiners and integrating over the boundary point 14. Manifestly T-dual formulation of AdS space International Nuclear Information System (INIS) Hatsuda, Machiko; Kamimura, Kiyoshi; Siegel, Warren 2017-01-01 We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates. 15. Evaporation of large black holes in AdS International Nuclear Information System (INIS) Rocha, Jorge V 2010-01-01 The AdS/CFT correspondence offers a new perspective on the long-standing black hole information paradox. However, to be able to use the available gauge/gravity machinery one is forced to consider so-called 'large' black holes in AdS, and these objects are thermodynamically stable - they do not evaporate. We describe a simple toy model that allows large AdS black holes to decay, by coupling the emitted radiation to an external scalar field propagating in an auxiliary space. This effectively changes the properties of the boundary of AdS, making it partly absorbing. We demonstrate that the evaporation process never ceases by explicitly presenting (a) the transmission coefficient for a wave scattering from the bulk into auxiliary space and (b) the greybody factor for a black 3-brane in an AdS background. Therefore, the model provides an interesting framework to address the information paradox using AdS/CFT techniques. 16. Manifestly T-dual formulation of AdS space Energy Technology Data Exchange (ETDEWEB) Hatsuda, Machiko [Physics Division, Faculty of Medicine, Juntendo University,Chiba 270-1695 (Japan); KEK Theory Center, High Energy Accelerator Research Organization,Tsukuba, Ibaraki 305-0801 (Japan); Kamimura, Kiyoshi [Physics Division, Faculty of Medicine, Juntendo University,Chiba 270-1695 (Japan); Siegel, Warren [C.N. Yang Institute for Theoretical Physics, Stony Brook University,Stony Brook, NY 11794-3840 (United States) 2017-05-12 We present a manifestly T-dual formulation of curved spaces such as an AdS space. For group manifolds related by the orthogonal vielbein fields the three form H=dB in the doubled space is universal at least locally. We construct an affine nondegenerate doubled bosonic AdS algebra to define the AdS space with the Ramond-Ramond flux. The non-zero commutator of the left and right momenta leads to that the left momentum is in an AdS space while the right momentum is in a dS space. Dimensional reduction constraints and the physical AdS algebra are shown to preserve all the doubled coordinates. 17. Open strings on AdS2 branes International Nuclear Information System (INIS) Lee, Peter; Ooguri, Hirosi.; Park, Jongwon; Tannenhauser, Jonathan 2001-01-01 We study the spectrum of open strings on AdS 2 branes in AdS 3 in an NS-NS background, using the SL(2,R) WZW model. When the brane carries no fundamental string charge, the open string spectrum is the holomorphic square root of the spectrum of closed strings in AdS 3 . It contains short and long strings, and is invariant under spectral flow. When the brane carries fundamental string charge, the open string spectrum again contains short and long strings in all winding sectors. However, branes with fundamental string charge break half the spectral flow symmetry. This has different implications for short and long strings. As the fundamental string charge increases, the brane approaches the boundary of AdS 3 . In this limit, the induced electric field on the worldvolume reaches its critical value, producing noncommutative open string theory on AdS 2 Science.gov (United States) Evans, Nick 2016-09-12 Essential facts Leading Change, Adding Value is NHS England's new nursing and midwifery framework. It is designed to build on Compassion in Practice (CiP), which was published 3 years ago and set out the 6Cs: compassion, care, commitment, courage, competence and communication. CiP established the values at the heart of nursing and midwifery, while the new framework sets out how staff can help transform the health and care sectors to meet the aims of the NHS England's Five Year Forward View. 19. Conical singularities in AdS space time International Nuclear Information System (INIS) Ferreira, Cristine Nunes 2011-01-01 Full text: In recent years, the study of conformal gauge theories from 10-D has been motivated by the AdS d+1 /CFT d correspondence, first conjectured by J. Maldacena. The aim of this work is to consider the d = 4 case by analysing the configuration of the N coincident D3 branes. In this context, the work shows that there is a duality between type IIB string theory in AdS 5 x S 5 and N = 4 SU(N) Super Yang-Mills Theory in the IR. The AdS 5 /CFT 4 correspondence brought also new approaches to the strong coupling problem in QCD. Nowadays, there is a whole line of works that focus on the low dimensional correspondence AdS 4 /CFT 3 , like the application to graphene and topological insulators, and the AdS 3 /CFT 2 correspondence, related with the entanglement entropy. In this work, we consider the vortex configuration solution to the AdS 4 and AdS 3 space-time. The most important motivation is to discuss the boundary theory resulting from these solutions. We have examined a straightforward approach to a holographic computation of the graphene and entanglement entropy in the presence of the conical singularity. After this analysis, we consider the scalar field in the bulk in the presence of this metrics and work out the compactification modes. Taking the holographic point of view, we study and discuss the resulting Green function. (author) International Nuclear Information System (INIS) Hubeny, Veronika E; Rangamani, Mukund; Marolf, Donald 2010-01-01 We study Hartle-Hawking-like states of quantum field theories on asymptotically AdS black hole backgrounds, with particular regard to the phase structure of interacting theories. By a suitable analytic continuation we show that the equilibrium dynamics of field theories on large asymptotically AdS black holes can be related to the low-temperature states of the same field theory on the AdS soliton (or pure AdS) background. This allows us to gain insight into Hartle-Hawking-like states on large-radius Schwarzschild- or rotating-AdS black holes. Furthermore, we exploit the AdS/CFT correspondence to explore the physics of strongly coupled large N theories on asymptotically AdS black holes. In particular, we exhibit a plausibly complete set of phases for the M2-brane world-volume superconformal field theory on a BTZ black hole background. Our analysis partially resolves puzzles previously raised in connection with Hawking radiation on large AdS black holes. Directory of Open Access Journals (Sweden) Hong-Chuan Yang 2007-01-01 Full Text Available We study the energy-efficient configuration of multihop paths with automatic repeat request (ARQ mechanism in wireless ad hoc networks. We adopt a cross-layer design approach and take both the quality of each radio hop and the battery capacity of each transmitting node into consideration. Under certain constraints on the maximum tolerable transmission delay and the required packet delivery ratio, we solve optimization problems to jointly schedule the transmitting power of each transmitting node and the retransmission limit over each hop. Numerical results demonstrate that the path configuration methods can either significantly reduce the average energy consumption per packet delivery or considerably extend the average lifetime of the multihop route. 2. AdS Branes from Partial Breaking of Superconformal Symmetries International Nuclear Information System (INIS) Ivanov, E.A. 2005-01-01 It is shown how the static-gauge world-volume superfield actions of diverse superbranes on the AdS d+1 superbackgrounds can be systematically derived from nonlinear realizations of the appropriate AdS supersymmetries. The latter are treated as superconformal symmetries of flat Minkowski superspaces of the bosonic dimension d. Examples include the N = 1 AdS 4 supermembrane, which is associated with the 1/2 partial breaking of the OSp(1\|4) supersymmetry down to the N = 1, d = 3 Poincare supersymmetry, and the T-duality related L3-brane on AdS 5 and scalar 3-brane on AdS 5 x S 1 , which are associated with two different patterns of 1/2 breaking of the SU(2, 2\|1) supersymmetry. Another (closely related) topic is the AdS/CFT equivalence transformation. It maps the world-volume actions of the codimension-one AdS d+1 (super)branes onto the actions of the appropriate Minkowski (super)conformal field theories in the dimension d 3. Supersymmetric warped AdS in extended topologically massive supergravity International Nuclear Information System (INIS) Deger, N.S.; Kaya, A.; Samtleben, H.; Sezgin, E. 2014-01-01 We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS 3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS 3 . This occurs when the coefficient of the Lorentz–Chern–Simons term is related to the AdS radius by μℓ=2. We find that the spacelike-squashed AdS 3 can be modded out by a suitable discrete subgroup of the isometry group, yielding an extremal black hole solution which avoids closed timelike curves NARCIS (Netherlands) Pieters, R.; Wedel, M. 2012-01-01 Most ads in practice receive no more than a single eye fixation. This study investigates the limits of what ads can communicate under such adverse exposure conditions. We find that consumers already know at maximum levels of accuracy and with high degree of certainty whether something is an ad or is 5. Added masses of ship structures CERN Document Server Korotkin, Alexandr I 2008-01-01 This essentially self-contained reference book contains data on added masses of ships and various ship and marine engineering structures. Theoretical and experimental methods for determining added masses of these objects are described. 6. AdS5 black holes with fermionic hair International Nuclear Information System (INIS) Burrington, Benjamin A.; Liu, James T.; Sabra, W. A. 2005-01-01 The study of new Bogomol'nyi-Prasad-Sommerfield (BPS) objects in AdS 5 has led to a deeper understanding of AdS/CFT. To help complete this picture, and to fully explore the consequences of the supersymmetry algebra, it is also important to obtain new solutions with bulk fermions turned on. In this paper we construct superpartners of the 1/2 BPS black hole in AdS 5 using a natural set of fermion zero modes. We demonstrate that these superpartners, carrying fermionic hair, have conserved charges differing from the original bosonic counterpart. To do so, we find the R-charge and dipole moment of the new system, as well as the mass and angular momentum, defined through the boundary stress tensor. The complete set of superpartners fits nicely into a chiral representation of AdS 5 supersymmetry, and the spinning solutions have the expected gyromagnetic ratio, g=1 7. AdS Black Hole with Phantom Scalar Field Directory of Open Access Journals (Sweden) Limei Zhang 2017-01-01 Full Text Available We present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates x and y, which are parameterized by the parameter α. We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively the same as those of AdS Schwarzschild black hole. Namely, there exists a minimal temperature and the large black hole is thermodynamically stable, while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS space-time in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy. 8. Universal regularization prescription for Lovelock AdS gravity International Nuclear Information System (INIS) Kofinas, Georgios; Olea, Rodrigo 2007-01-01 A definite form for the boundary term that produces the finiteness of both the conserved quantities and Euclidean action for any Lovelock gravity with AdS asymptotics is presented. This prescription merely tells even from odd bulk dimensions, regardless the particular theory considered, what is valid even for Einstein-Hilbert and Einstein-Gauss-Bonnet AdS gravity. The boundary term is a given polynomial of the boundary extrinsic and intrinsic curvatures (also referred to as Kounterterms series). Only the coupling constant of the boundary term changes accordingly, such that it always preserves a well-posed variational principle for boundary conditions suitable for asymptotically AdS spaces. The background-independent conserved charges associated to asymptotic symmetries are found. In odd bulk dimensions, this regularization produces a generalized formula for the vacuum energy in Lovelock AdS gravity. The standard entropy for asymptotically AdS black holes is recovered directly from the regularization of the Euclidean action, and not only from the first law of thermodynamics associated to the conserved quantities 9. New Massive Gravity and AdS4 Counterterms International Nuclear Information System (INIS) Jatkar, Dileep P.; Sinha, Aninda 2011-01-01 We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS 4 ). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS 4 Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS 3 gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory. 10. Constrained supermanifolds for AdS M-theory backgrounds International Nuclear Information System (INIS) Fre, Pietro; Grassi, Pietro Antonio 2008-01-01 A long standing problem is the supergauge completion of AdS 4 x ({G/H}) 7 or AdS 5 x ({G/H}) 5 backgrounds which preserve less then maximal supersymmetry. In parallel with the supersolvable realization of the AdS 4 x S 7 background based on κ-symmetry, we develop a technique which amounts to solving the above-mentioned problem in a way useful for pure spinor quantization for supermembranes and superstrings. Instead of gauge fixing some of the superspace coordinates using κ-symmetry, we impose an additional constraint on them reproducing the simplifications of the supersolvable representations. The constraints are quadratic, homogeneous, Sp(4,R)-covariant, and consistent from the quantum point of view in the pure spinor approach. Here we provide the geometrical solution which, in a subsequent work, will be applied to the membrane and the superstring sigma models 11. Asymptotically AdS spacetimes with a timelike Kasner singularity Energy Technology Data Exchange (ETDEWEB) Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel) 2016-07-21 Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction. 12. Holographic description of AdS2 black holes International Nuclear Information System (INIS) Castro, Alejandra; Larsen, Finn; Grumiller, Daniel; McNees, Robert 2008-01-01 We develop the holographic renormalization of AdS 2 gravity systematically. We find that a bulk Maxwell term necessitates a boundary mass term for the gauge field and verify that this unusual term is invariant under gauge transformations that preserve the boundary conditions. We determine the energy-momentum tensor and the central charge, recovering recent results by Hartman and Strominger. We show that our expressions are consistent with dimensional reduction of the AdS 3 energy-momentum tensor and the Brown-Henneaux central charge. As an application of our results we interpret the entropy of AdS 2 black holes as the ground state entropy of a dual CFT. 13. Central charge for AdS2 quantum gravity International Nuclear Information System (INIS) Hartman, Thomas; Strominger, Andrew 2009-01-01 Two-dimensional Maxwell-dilaton quantum gravity on AdS 2 with radius l and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge c = 3kE 2 l 4 /4 where k is the level of the U(1) current. This is an AdS 2 analog of the Brown-Henneaux formula c = 3l/2G for the central charge of quantum gravity on AdS 3 . 14. New supersymmetric AdS4 type II vacua International Nuclear Information System (INIS) Tsimpis, D. 2010-01-01 We review the supersymmetric AdS 4 x w M 6 backgrounds of type IIA/IIB supergravity constructed in[1]. In type IIA the supersymmetry is N=2, and the six-dimensional internal space is locally an S 2 bundle over a four-dimensional Kaehler-Einstein base; in IIB the internal space is the direct product of a circle and a five-dimensional squashed Sasaki-Einstein manifold. These backgrounds do not contain any sources, all fluxes (including the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor are non-constant. The IIA solutions include the massive deformations of the IIA reduction of the eleven-dimensional AdS 4 x Y p,q solutions, and had been predicted to exist on the basis of the AdS 4 /CFT 3 correspondence. (Abstract Copyright [2010], Wiley Periodicals, Inc.) 15. Instantons from geodesics in AdS moduli spaces Science.gov (United States) Ruggeri, Daniele; Trigiante, Mario; Van Riet, Thomas 2018-03-01 We investigate supergravity instantons in Euclidean AdS5 × S5/ℤk. These solutions are expected to be dual to instantons of N = 2 quiver gauge theories. On the supergravity side the (extremal) instanton solutions are neatly described by the (lightlike) geodesics on the AdS moduli space for which we find the explicit expression and compute the on-shell actions in terms of the quantised charges. The lightlike geodesics fall into two categories depending on the degree of nilpotency of the Noether charge matrix carried by the geodesic: for degree 2 the instantons preserve 8 supercharges and for degree 3 they are non-SUSY. We expect that these findings should apply to more general situations in the sense that there is a map between geodesics on moduli-spaces of Euclidean AdS vacua and instantons with holographic counterparts. 16. Loops in AdS from conformal field theory Science.gov (United States) Aharony, Ofer; Alday, Luis F.; Bissi, Agnese; Perlmutter, Eric 2017-07-01 We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1 /N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1 /N 2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ 4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the N = 4 super-Yang-Mills theory. 17. Phases of global AdS black holes International Nuclear Information System (INIS) Basu, Pallab; Krishnan, Chethan; Subramanian, P.N. Bala 2016-01-01 We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime (AdS_4) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit. 18. Minimal surfaces in AdS space and integrable systems Science.gov (United States) Burrington, Benjamin A.; Gao, Peng 2010-04-01 We consider the Pohlmeyer reduction for spacelike minimal area worldsheets in AdS5. The Lax pair for the reduced theory is found, and written entirely in terms of the A3 = D3 root system, generalizing the B2 affine Toda system which appears for the AdS4 string. For the B2 affine Toda system, we show that the area of the worlsheet is obtainable from the moduli space Kähler potential of a related Hitchin system. We also explore the Saveliev-Leznov construction for solutions of the B2 affine Toda system, and recover the rotationally symmetric solution associated to Painleve transcendent. 19. AdS5 magnetized solutions in minimal gauged supergravity Directory of Open Access Journals (Sweden) Jose Luis Blázquez-Salcedo 2017-08-01 Full Text Available We construct a generalization of the AdS charged rotating black holes with two equal magnitude angular momenta in five-dimensional minimal gauged supergravity. In addition to the mass, electric charge and angular momentum, the new solutions possess an extra-parameter associated with a non-zero magnitude of the magnetic potential at infinity. In contrast with the known cases, these new black holes possess a non-trivial zero-horizon size limit which describes a one parameter family of spinning charged solitons. All configurations reported in this work approach asymptotically an AdS5 spacetime in global coordinates and are free of pathologies. 20. Twistor description of spinning particles in AdS Science.gov (United States) Arvanitakis, Alex S.; Barns-Graham, Alec E.; Townsend, Paul K. 2018-01-01 The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D = 4 , 5 , 7, which linearises invariance under the AdS isometry group Sp(4; K ) for K=R,C,H, is generalized to the massless N -extended "spinning particle". The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS5. 1. Holography in Lovelock Chern-Simons AdS gravity Science.gov (United States) Cvetković, Branislav; Miskovic, Olivera; Simić, Dejan 2017-08-01 We analyze holographic field theory dual to Lovelock Chern-Simons anti-de Sitter (AdS) gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute 1-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level. Science.gov (United States) Turco, M.; Milelli, M. 2009-09-01 skill scores of two competitive forecast. It is important to underline that the conclusions refer to the analysis of the Piemonte operational alert system, so they cannot be directly taken as universally true. But we think that some of the main lessons that can be derived from this study could be useful for the meteorological community. In details, the main conclusions are the following: - despite the overall improvement in global scale and the fact that the resolution of the limited area models has increased considerably over recent years, the QPF produced by the meteorological models involved in this study has not improved enough to allow its direct use, that is, the subjective HQPF continues to offer the best performance; - in the forecast process, the step where humans have the largest added value with respect to mathematical models, is the communication. In fact the human characterisation and communication of the forecast uncertainty to end users cannot be replaced by any computer code; - eventually, although there is no novelty in this study, we would like to show that the correct application of appropriated statistical techniques permits a better definition and quantification of the errors and, mostly important, allows a correct (unbiased) communication between forecasters and decision makers. Energy Technology Data Exchange (ETDEWEB) Metsaev, R.R. [Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky prospect 53, Moscow 119991 (Russian Federation) 2015-01-15 Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field evaluated on solution of the Dirichlet problem amounts to the light-cone gauge 2-point vertex of mixed-symmetry anomalous shadow. Also we show that UV divergence of the action for mixed-symmetry massive AdS field with some particular value of mass parameter evaluated on the Dirichlet problem amounts to the action of long mixed-symmetry conformal field, while UV divergence of the action for mixed-symmetry massless AdS field evaluated on the Dirichlet problem amounts to the action of short mixed-symmetry conformal field. We speculate on string theory interpretation of a model which involves short low-spin conformal fields and long higher-spin conformal fields. 4. AdS pure spinor superstring in constant backgrounds International Nuclear Information System (INIS) Chandia, Osvaldo; Bevilaqua, L. Ibiapina; Vallilo, Brenno Carlini 2014-01-01 In this paper we study the pure spinor formulation of the superstring in AdS_5×S"5 around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background OpenAIRE Paul PAŞCU 2014-01-01 Directory of Open Access Journals (Sweden) Paul PAŞCU 2014-05-01 7. Penrose inequality for asymptotically AdS spaces International Nuclear Information System (INIS) Itkin, Igor; Oz, Yaron 2012-01-01 In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces. 8. Penrose inequality for asymptotically AdS spaces Energy Technology Data Exchange (ETDEWEB) Itkin, Igor [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel); Oz, Yaron, E-mail: yaronoz@post.tau.ac.il [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel) 2012-02-28 In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces. 9. Confinement, glueballs and strings from deformed AdS International Nuclear Information System (INIS) Apreda, Riccardo; Crooks, David E.; Evans, Nick; Petrini, Michela 2004-01-01 We study aspects of confinement in two deformed versions of the AdS/CFT correspondence - the GPPZ dual of N = 1* Yang Mills, and the Yang Mills* N 0 dual. Both geometries describe discrete glueball spectra which we calculate numerically. The results agree at the 10% level with previous AdS/CFT computations in the Klebanov Strassler background and AdS Schwarzchild respectively. We also calculate the spectra of bound states of the massive fermions in these geometries and show that they are light, so not decoupled from the dynamics. We then study the behaviour of Wilson loops in the 10d lifts of these geometries. We find a transition from AdS-like strings in the UV to strings that interact with the unknown physics of the central singularity of the space in the IR. (author) 10. Supersymmetric AdS6 solutions of type IIB supergravity International Nuclear Information System (INIS) Kim, Hyojoong; Kim, Nakwoo; Suh, Minwoo 2015-01-01 We study the general requirement for supersymmetric AdS 6 solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the canonical form of the solutions. Our result agrees precisely with the work of Apruzzi et al. (JHEP 1411:099, 2014), which used the pure spinor technique. Hoping to identify the geometry of the problem, we also computed four-dimensional theory through the dimensional reduction of type IIB supergravity on AdS 6 . This effective action is essentially a non-linear sigma model with five scalar fields parametrizing SL(3,ℝ)/SO(2,1), modified by a scalar potential and coupled to Einstein gravity in Euclidean signature. We argue that the scalar potential can be explained by a subgroup CSO(1,1,1) ⊂SL(3,ℝ) in a way analogous to gauged supergravity 11. AdS gravity and the scalar glueball spectrum Energy Technology Data Exchange (ETDEWEB) Vento, Vicente [Departament de Fisica Teorica, Universitat de Valencia y Institut de Fisica Corpuscular, Consejo Superior de Investigaciones Cientificas, Burjassot (Valencia) (Spain) 2017-09-15 The scalar glueball spectrum has attracted much attention since the formulation of Quantum Chromodynamics. Different approaches give very different results for the glueball masses. We revisit the problem from the perspective of the AdS/CFT correspondence. (orig.) 12. Smoothed transitions in higher spin AdS gravity International Nuclear Information System (INIS) Banerjee, Shamik; Shenker, Stephen; Castro, Alejandra; Hellerman, Simeon; Hijano, Eliot; Lepage-Jutier, Arnaud; Maloney, Alexander 2013-01-01 We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS 3 and AdS 4 . Two-dimensional CFTs with W N symmetry are considered in the λ = 0 (k → ∞) limit where they are conjectured to be described by continuous orbifolds. The torus partition function is computed, using reasonable assumptions, and equals that of a free-field theory. We find no phase transition at temperatures of order 1; the usual Hawking–Page phase transition is removed by the highly degenerate light states associated with conical defect states in the bulk. Three-dimensional Chern–Simons matter CFTs with vector-like matter are considered on T 3 , where the dynamics is described by an effective theory for the eigenvalues of the holonomies. Likewise, we find no evidence for a Hawking–Page phase transition at a large level k. (paper) 13. Winding strings and AdS3 black holes International Nuclear Information System (INIS) Troost, Jan 2002-01-01 We start a systematic study of string theory in AdS 3 black hole backgrounds. Firstly, we analyse in detail the geodesic structure of the BTZ black hole, including spacelike geodesics. Secondly, we study the spectrum for massive and massless scalar fields, paying particular attention to the connection between Sl(2,R) subgroups, the theory of special functions and global properties of the BTZ black holes. We construct classical strings that wind the black holes. Finally, we apply the general formalism to the vacuum black hole background, and formulate the boundary spacetime Virasoro algebra in terms of worldsheet operators. We moreover establish the link between a proposal for a ghost free spectrum for Sl(2,R) string propagation and the massless black hole background, thereby claryfing aspects of the AdS 3 /CFT correspondence. (author) 14. AdS strings with torsion: Noncomplex heterotic compactifications International Nuclear Information System (INIS) Frey, Andrew R.; Lippert, Matthew 2005-01-01 Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric AdS 4 compactifications on almost-Hermitian manifolds of SU(3) structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kaehler. We argue that all moduli are fixed, and we show that the Kaehler potential and superpotential proposed in the literature yield the correct AdS 4 radius. In the nearly Kaehler case, we are able to solve the H Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate 15. The Mixed Phase of Charged AdS Black Holes Directory of Open Access Journals (Sweden) Piyabut Burikham 2016-01-01 Full Text Available We study the mixed phase of charged AdS black hole and radiation when the total energy is fixed below the threshold to produce a stable charged black hole branch. The coexistence conditions for the charged AdS black hole and radiation are derived for the generic case when radiation particles carry charge. The phase diagram of the mixed phase is demonstrated for both fixed potential and charge ensemble. In the dual gauge picture, they correspond to the mixed phase of quark-gluon plasma (QGP and hadron gas in the fixed chemical potential and density ensemble, respectively. In the nuclei and heavy-ion collisions at intermediate energies, the mixed phase of exotic QGP and hadron gas could be produced. The mixed phase will condense and evaporate into the hadron gas as the fireball expands. 16. Perturbative entanglement thermodynamics for AdS spacetime: renormalization International Nuclear Information System (INIS) Mishra, Rohit; Singh, Harvendra 2015-01-01 We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that ‘boosted’ AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately ‘renormalized’ at the second order due to the corrections. We work in the perturbative regime where T thermal ≪T E . 17. Generalised structures for N=1 AdS backgrounds Energy Technology Data Exchange (ETDEWEB) Coimbra, André [Institut für Theoretische Physik & Center for Quantum Engineering and Spacetime Research,Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany); Strickland-Constable, Charles [Institut de physique théorique, Université Paris Saclay, CEA, CNRS, Orme des Merisiers, F-91191 Gif-sur-Yvette (France) 2016-11-16 We expand upon a claim made in a recent paper [http://arxiv.org/abs/1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak integrability condition in the language of E{sub d(d)}×ℝ{sup +} generalised geometry. Namely, they are spaces admitting a generalised G-structure set by the Killing spinor and with constant singlet generalised intrinsic torsion. 18. ADS Bumblebee comes of age Science.gov (United States) Accomazzi, Alberto; Kurtz, Michael J.; Henneken, Edwin; Grant, Carolyn S.; Thompson, Donna M.; Chyla, Roman; McDonald, Steven; Shaulis, Taylor J.; Blanco-Cuaresma, Sergi; Shapurian, Golnaz; Hostetler, Timothy W.; Templeton, Matthew R.; Lockhart, Kelly E. 2018-01-01 19. Noncommutative D-branes from covariant AdS superstring International Nuclear Information System (INIS) Sakaguchi, Makoto; Yoshida, Kentaroh 2008-01-01 We study noncommutative (NC) D-branes on AdS 5 xS 5 from κ-invariance of covariant Green-Schwarz action of an open string with a non-trivial world-volume flux. Finding boundary conditions to ensure the κ-invariance, we can see possible configurations of the NC D-branes. With this method 1/4 BPS NC D-branes are discussed. The resulting NC Dp-branes are 1/4 BPS at arbitrary position other than the p=1 case. The exceptional D-string is 1/2 BPS at the origin and 1/4 BPS outside the origin. Those are reduced to possible 1/4 BPS or 1/2 BPS AdS D-branes in the commutative limit. The same analysis is applied to an open superstring in a pp-wave and leads to 1/4 BPS configurations of NC D-branes. These D-branes are consistently obtained from AdS D-branes via the Penrose limit 20. Supersymmetric giant graviton solutions in AdS3 International Nuclear Information System (INIS) Mandal, Gautam; Raju, Suvrat; Smedbaeck, Mikael 2008-01-01 We parametrize all classical probe brane configurations that preserve four supersymmetries in (a) the extremal D1-D5 geometry, (b) the extremal D1-D5-P geometry, (c) the smooth D1-D5 solutions proposed by Lunin and Mathur, and (d) global AdS 3 xS 3 xT 4 /K3. These configurations consist of D1 branes, D5 branes, and bound states of D5 and D1 branes with the property that a particular Killing vector is tangent to the brane world volume at each point. We show that the supersymmetric sector of the D5-brane world volume theory may be analyzed in an effective 1+1 dimensional framework that places it on the same footing as D1 branes. In global AdS and the corresponding Lunin-Mathur solution, the solutions we describe are ''bound'' to the center of AdS for generic parameters and cannot escape to infinity. We show that these probes only exist on the submanifold of moduli space where the background B NS field and theta angle vanish. We quantize these probes in the near-horizon region of the extremal D1-D5 geometry and obtain the theory of long strings discussed by Seiberg and Witten 1. Exploring AdS waves via nonminimal coupling International Nuclear Information System (INIS) Ayon-Beato, Eloy; Hassaiene, Mokhtar 2006-01-01 We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS space restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal-coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal-coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a nonperturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity 2. Enthalpy and the mechanics of AdS black holes International Nuclear Information System (INIS) Kastor, David; Traschen, Jennie; Ray, Sourya 2009-01-01 We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of Λ in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since Λ is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime. 3. Shock wave collisions and thermalization in AdS5 International Nuclear Information System (INIS) Kovchegov, Yuri V. 2011-01-01 We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS 5 . We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS 5 , which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling. (author) 4. Ad skepticisms: Antecedents and consequences Directory of Open Access Journals (Sweden) Rafique Ahmed 2016-11-01 Full Text Available Engaging customer is the burning issue for companies especially the service sector, either online or offline. Minimizing the customer disengagement is the same like reducing dissatisfaction or churn. Customer disengagement may be caused by many factors, ad skepticism is one of them; ad skepticism has two main antecedents personality variable and consumption/influencing varia-bles. This research explores the relationship of ad skepticism with customer disengagement through personality variables which are cynicism, reactance and self-esteem. The unit of analysis is the telecom and banking industry of Pakistan which is foreseeing an era of virtual currency and both are customer oriented industries. Only offline disengagement is researched and data is collected from the Business centers of telecom and banking branches dealing with virtual curren-cy in Pakistan. Hypothetical model is given after digging the relevant literature; model is tested through confirmatory factor analysis and structural equation modeling. Eight hypotheses were purposed from the connections of model, all hypotheses are accepted except the cynicism posi-tive effect on social ad skepticism. This can be due to commonality of social and charity in Paki-stani society, Muslims consider charity as a pious act and they do not think for cynic behavior in charity or social related works. The results manifest that customers in telecom industry are hav-ing ad skepticism and that is becoming the cause of their disengagement. Further, social ad skep-ticism has more impact on the customer disengagement than the general ad skepticism. While the reactance has more effect on general ad skepticism than other antecedents and cynicism has the lowest impact on social ad skepticism than other antecedents. DEFF Research Database (Denmark) Knudsen, Bjarke Gosvig; Jensen, Morten; Birklykke, Alex 2014-01-01 6. Virginia ADS consortium - thorium utilization International Nuclear Information System (INIS) Myneni, Ganapati 2015-01-01 A Virginia ADS consortium, consisting of Virginia Universities (UVa, VCU, VT), Industry (Casting Analysis Corporation, GEMSTAR, MuPlus Inc.), Jefferson Lab and not-for-profit ISOHIM, has been organizing International Accelerator-Driven Sub-Critical Systems (ADS) and Thorium Utilization (ThU) workshops. The third workshop of this series was hosted by VCU in Richmond, Virginia, USA Oct 2014 with CBMM and IAEA sponsorship and was endorsed by International Thorium Energy Committee (IThEC), Geneva and Virginia Nuclear Energy Consortium Authority. In this presentation a brief summary of the successful 3 rd International ADS and ThU workshop proceedings and review the worldwide ADS plans and/or programs is given. Additionally, a report on new start-ups on Molten Salt Reactor (MSR) systems is presented. Further, a discussion on potential simplistic fertile 232 Th to fissile 233 U conversion is made 7. A closer look at two AdS4 branes in an AdS5 bulk International Nuclear Information System (INIS) Thambyahpillai, Shiyamala 2005-01-01 We investigate a scenario with two AdS 4 branes in an AdS 5 bulk. In this scenario there are two gravitons and we investigate the role played by each of them for different positions of the second brane. We show that both gravitons play a significant role only when the turn-around point in the warp factor is approximately equidistant from both branes. We find that the ultralight mode becomes heavy as the second brane approaches the turn-around point, and the physics begins to resemble that of the RS model. Thus we demonstrate the crucial role played by the turn-around in the warp factor in enabling the presence of both gravitons. (author) International Nuclear Information System (INIS) Brodsky, Stanley J.; de Teramond, Guy F. 2007-01-01 9. Wilson lines for AdS5 black strings International Nuclear Information System (INIS) 2015-01-01 We describe a simple method of extending AdS 5 black string solutions of 5d gauged supergravity in a supersymmetric way by addition of Wilson lines along a circular direction in space. When this direction is chosen along the string, and due to the specific form of 5d supergravity that features Chern-Simons terms, the existence of magnetic charges automatically generates conserved electric charges in a 5d analogue of the Witten effect. Therefore we find a rather generic, model-independent way of adding electric charges to already existing solutions with no backreaction from the geometry or breaking of any symmetry. We use this method to explicitly write down more general versions of the Benini-Bobev black strings (http://dx.doi.org/10.1103/PhysRevLett.110.061601, http://dx.doi.org/10.1007/JHEP06(2013)005) and comment on the implications for the dual field theory and the similarities with generalizations of the Cacciatori-Klemm black holes (http://dx.doi.org/10.1007/JHEP01(2010)085) in AdS 4 . 10. An AdS3 dual for minimal model CFTs International Nuclear Information System (INIS) Gaberdiel, Matthias R.; Gopakumar, Rajesh 2011-01-01 We propose a duality between the 2d W N minimal models in the large N't Hooft limit, and a family of higher spin theories on AdS 3 . The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for N=2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS 4 dual for the singlet sector of large N vector models. 11. Heavy ion collisions in AdS5 International Nuclear Information System (INIS) Kovchegov, Yuri V. 2011-01-01 We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. Heavy ion collisions correspond to gravitational shock wave collisions in AdS 5 . We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produced medium. Unfortunately this energy-momentum tensor does not correspond to ideal hydrodynamics, indicating that higher order graviton exchanges are needed to construct the full solution of the problem. We also show that shock waves must completely stop almost immediately after the collision in AdS 5 , which, on the field theory side, corresponds to complete nuclear stopping due to strong coupling effects, likely leading to Landau hydrodynamics. Finally, we perform trapped surface analysis of the shock wave collisions demonstrating that a bulk black hole, corresponding to ideal hydrodynamics on the boundary, has to be created in such collisions, thus constructing a proof of thermalization in heavy ion collisions at strong coupling. Directory of Open Access Journals (Sweden) Matteo Beccaria 2015-03-01 Full Text Available As was shown earlier, the one-loop correction in 10d supergravity on AdS5×S5 corresponds to the contributions to the vacuum energy and 4d boundary conformal anomaly which are minus the values for one N=4 Maxwell supermultiplet, thus reproducing the subleading term in the N2−1 coefficient in the dual SU(N SYM theory. We perform similar one-loop computations in 11d supergravity on AdS7×S4 and 10d supergravity on AdS3×S3×T4. In the AdS7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2,0 tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2,0 theory is 4N3−9/4N−7/4 and thus vanishes for N=1. In the AdS3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4,4 scalar multiplet, i.e. is c=+6. This reproduces the subleading term in the central charge c=6(Q1Q5+1 of the dual 2d CFT describing decoupling limit of D5–D1 system. We also present the expressions for the 6d a-anomaly coefficient and vacuum energy contributions of general-symmetry higher spin field in AdS7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank-2 antisymmetric tensors. 13. Small AdS black holes from SYM International Nuclear Information System (INIS) Asplund, Curtis; Berenstein, David 2009-01-01 We provide a characterization of the set of configurations in N=4 SYM theory that are dual to small AdS black holes. Our construction shows that the black hole dual states are approximately thermal on a SU(M) subset of degrees of freedom of a SU(N) gauge theory. M is determined dynamically and the black hole degrees of freedom are dynamically insulated from the rest. These states are localized on the S 5 and have dynamical processes that correspond to matter absorption that make them behave as black objects 14. On attractor mechanism of AdS4 black holes International Nuclear Information System (INIS) Anabalón, Andrés; Astefanesei, Dumitru 2013-01-01 We construct a general family of exact non-extremal 4-dimensional black holes in AdS gravity with U(1) gauge fields non-minimally coupled to a dilaton and a non-trivial dilaton potential. These black holes can have spherical, toroidal, and hyperbolic horizon topologies. We use the entropy function formalism to obtain the near horizon data in the extremal limit. Due to the non-trivial self-interaction of the scalar field, the zero temperature black holes can have a finite horizon area even if only the electric field is turned on 15. Small black holes in global AdS spacetime Science.gov (United States) Jokela, Niko; Pönni, Arttu; Vuorinen, Aleksi 2016-04-01 We study the properties of two-point functions and quasinormal modes in a strongly coupled field theory holographically dual to a small black hole in global anti-de Sitter spacetime. Our results are seen to smoothly interpolate between known limits corresponding to large black holes and thermal AdS space, demonstrating that the Son-Starinets prescription works even when there is no black hole in the spacetime. Omitting issues related to the internal space, the results can be given a field theory interpretation in terms of the microcanonical ensemble, which provides access to energy densities forbidden in the canonical description. 16. Configurational entropy of charged AdS black holes Directory of Open Access Journals (Sweden) Chong Oh Lee 2017-09-01 Full Text Available When we consider charged AdS black holes in higher dimensional spacetime and a molecule number density along coexistence curves is numerically extended to higher dimensional cases. It is found that a number density difference of a small and large black holes decrease as a total dimension grows up. In particular, we find that a configurational entropy is a concave function of a reduced temperature and reaches a maximum value at a critical (second-order phase transition point. Furthermore, the bigger a total dimension becomes, the more concave function in a configurational entropy while the more convex function in a reduced pressure. 17. Gravitational charges of transverse asymptotically AdS spacetimes International Nuclear Information System (INIS) Cebeci, Hakan; Sarioglu, Oezguer; Tekin, Bayram 2006-01-01 Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to 18. Entanglement entropy and duality in AdS4 Directory of Open Access Journals (Sweden) Ioannis Bakas 2015-07-01 Full Text Available Small variations of the entanglement entropy δS and the expectation value of the modular Hamiltonian δE are computed holographically for circular entangling curves in the boundary of AdS4, using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, δS=δE, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric–magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy–momentum/Cotton tensor duality. 19. The AdS3 central charge in string theory International Nuclear Information System (INIS) Troost, Jan 2011-01-01 We evaluate the vacuum expectation value of the central charge operator in string theory in an AdS 3 vacuum. Our calculation provides a rare non-zero one-point function on a spherical worldsheet. The evaluation involves the regularization both of a worldsheet ultraviolet divergence (associated to the infinite volume of the conformal Killing group), and a space-time infrared divergence (corresponding to the infinite volume of space-time). The two divergences conspire to give a finite result, which is the classical general relativity value for the central charge, corrected in bosonic string theory by an infinite series of tree level higher derivative terms. Science.gov (United States) Accomazzi, Alberto; Kurtz, M. J.; Henneken, E. A.; Grant, C. S.; Thompson, D.; Luker, J.; Chyla, R.; Murray, S. S. 2014-01-01 In the spring of 1993, the Smithsonian/NASA Astrophysics Data System (ADS) first launched its bibliographic search system. It was known then as the ADS Abstract Service, a component of the larger Astrophysics Data System effort which had developed an interoperable data system now seen as a precursor of the Virtual Observatory. As a result of the massive technological and sociological changes in the field of scholarly communication, the ADS is now completing the most ambitious technological upgrade in its twenty-year history. Code-named ADS 2.0, the new system features: an IT platform built on web and digital library standards; a new, extensible, industrial strength search engine; a public API with various access control capabilities; a set of applications supporting search, export, visualization, analysis; a collaborative, open source development model; and enhanced indexing of content which includes the full-text of astronomy and physics publications. The changes in the ADS platform affect all aspects of the system and its operations, including: the process through which data and metadata are harvested, curated and indexed; the interface and paradigm used for searching the database; and the follow-up analysis capabilities available to the users. This poster describes the choices behind the technical overhaul of the system, the technology stack used, and the opportunities which the upgrade is providing us with, namely gains in productivity and enhancements in our system capabilities. 1. Critical gravity on AdS2 spacetimes International Nuclear Information System (INIS) Myung, Yun Soo; Kim, Yong-Wan; Park, Young-Jai 2011-01-01 We study the critical gravity in two-dimensional anti-de Sitter (AdS 2 ) spacetimes, which was obtained from the cosmological topologically massive gravity (TMG Λ ) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS 2 , which may correspond to the near-horizon geometry of the extremal Banados, Teitelboim, and Zanelli (BTZ) black hole obtained from the TMG Λ with identification upon uplifting three dimensions. A massive propagating scalar mode δF satisfies the second-order differential equation away from the critical point of K=l, whose solution is given by the Bessel functions. On the other hand, δF satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar δF ml and its logarithmic partner δF log 4th . 2. AdS pure spinor superstring in constant backgrounds Energy Technology Data Exchange (ETDEWEB) Chandia, Osvaldo [Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez,Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez,Diagonal Las Torres 2640, Peñalolén, Santiago (Chile); Bevilaqua, L. Ibiapina [Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte,Caixa Postal 1524, 59072-970, Natal, RN (Brazil); Vallilo, Brenno Carlini [Facultad de Ciencias Exactas, Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile) 2014-06-05 In this paper we study the pure spinor formulation of the superstring in AdS{sub 5}×S{sup 5} around point particle solutions of the classical equations of motion. As a particular example we quantize the pure spinor string in the BMN background. 3. Crystal manyfold universes in /AdS space Science.gov (United States) Kaloper, N. 2000-02-01 We derive crystal braneworld solutions, comprising of intersecting families of parallel /n+2-branes in a /4+n-dimensional /AdS space. Each family consists of alternating positive and negative tension branes. In the simplest case of exactly orthogonal families, there arise different crystals with unbroken /4D Poincaré invariance on the intersections, where our world can reside. A crystal can be finite along some direction, either because that direction is compact, or because it ends on a segment of /AdS bulk, or infinite, where the branes continue forever. If the crystal is interlaced by connected /3-branes directed both along the intersections and orthogonal to them, it can be viewed as an example of a Manyfold universe proposed recently by Arkani-Hamed, Dimopoulos, Dvali and the author. There are new ways for generating hierarchies, since the bulk volume of the crystal and the lattice spacing affect the /4D Planck mass. The low energy physics is sensitive to the boundary conditions in the bulk, and has to satisfy the same constraints discussed in the Manyfold universe. Phenomenological considerations favor either finite crystals, or crystals which are infinite but have broken translational invariance in the bulk. The most distinctive signature of the bulk structure is that the bulk gravitons are Bloch waves, with a band spectrum, which we explicitly construct in the case of a /5-dimensional theory. DEFF Research Database (Denmark) Antila, Kari; Lötjönen, Jyrki; Thurfjell, Lennart 2013-01-01 Alzheimer's disease (AD) is the most common cause of dementia affecting 36 million people worldwide. As the demographic transition in the developed countries progresses towards older population, the worsening ratio of workers per retirees and the growing number of patients with age-related illnes...... candidates and implement the framework in software. The results are currently used in several research projects, licensed to commercial use and being tested for clinical use in several trials....... objective of the PredictAD project was to find and integrate efficient biomarkers from heterogeneous patient data to make early diagnosis and to monitor the progress of AD in a more efficient, reliable and objective manner. The project focused on discovering biomarkers from biomolecular data... 5. Facilities Management and Added Value DEFF Research Database (Denmark) Jensen, Per Anker 2010-01-01 Aim: This paper aims to present different models of the concept of the added value of Facilities Management (FM), including the FM Value Map, which forms the basis of research group in EuroFM, and to present some of the results of this research collaboration. Approach and methodology: The paper...... is based on literature reviews of the most influential journals within the academic fields of FM, Corporate Real Estate Management and Business to Business Marketing and discussions between participants of the research group working on a further exploration and testing of the FM Value Map. Conclusions......: The research shows a number of different definitions and focus points of Added Value of FM, dependent on the academic field and the area of application. The different research perspectives explored a holistic view on the added value of FM by the integration of an external market based view (with a focus... 6. Smooth causal patches for AdS black holes Science.gov (United States) Raju, Suvrat 2017-06-01 We review the paradox of low energy excitations of a black hole in anti-de Sitter space (AdS). An appropriately chosen unitary operator in the boundary theory can create a locally strong excitation near the black hole horizon, whose global energy is small as a result of the gravitational redshift. The paradox is that this seems to violate a general rule of statistical mechanics, which states that an operator with energy parametrically smaller than k T cannot create a significant excitation in a thermal system. When we carefully examine the position dependence of the boundary unitary operator that produces the excitation and the bulk observable necessary to detect the anomalously large effect, we find that they do not both fit in a single causal patch. This follows from a remarkable property of position-space AdS correlators that we establish explicitly and resolves the paradox in a generic state of the system, since no combination of observers can both create the excitation and observe its effect. As a special case of our analysis, we show how this resolves the "Born rule" paradox of Marolf and Polchinski [J. High Energy Phys. 01 (2016) 008, 10.1007/JHEP01(2016)008] and we verify our solution using an independent calculation. We then consider boundary states that are finely tuned to display a spontaneous excitation outside the causal patch of the infalling observer, and we propose a version of causal patch complementarity in AdS/CFT that resolves the paradox for such states as well. 7. Smart AD and DA Converters NARCIS (Netherlands) Roermund, van A.H.M.; Hegt, J.A.; Harpe, P.J.A.; Radulov, G.I.; Zanikopoulos, A.; Doris, K.; Quinn, P.J. 2005-01-01 In this paper, a concept is proposed to solve the problems related to the embedding of AD and DA converters in system-on-chips, FPGAs or other VLSI solutions. Problems like embedded testing, yield, reliability and reduced design space become crucial bottlenecks in the integration of high-performance Directory of Open Access Journals (Sweden) REA Editor 2012-02-01 Full Text Available Agradecemos aos professores Nildo Viana (UFG e Flavio Sofiati (UFG, organizadores do DOSSIÊ JUVENTUDE & SOCIEDADE, e aos Consultores Ad hoc pela leitura e apreciação crítica dos artigos submetidos e publicados nesta edição. 9. An investigation of AdS2 backreaction and holography International Nuclear Information System (INIS) Engelsöy, Julius; Mertens, Thomas G.; Verlinde, Herman 2016-01-01 We investigate a dilaton gravity model in AdS 2 proposed by Almheiri and Polchinski http://dx.doi.org/10.1007/JHEP11(2015)014 and develop a 1d effective description in terms of a dynamical boundary time with a Schwarzian derivative action. We show that the effective model is equivalent to a 1d version of Liouville theory, and investigate its dynamics and symmetries via a standard canonical framework. We include the coupling to arbitrary conformal matter and analyze the effective action in the presence of possible sources. We compute commutators of local operators at large time separation, and match the result with the time shift due to a gravitational shockwave interaction. We study a black hole evaporation process and comment on the role of entropy in this model. 10. Chiral gauge theory on AdS domain wall International Nuclear Information System (INIS) Shirman, Yuri 2005-01-01 We describe a realization of chiral gauge theories based on the domaim wall fermion construction implemented on an interval in five dimensional AdS spacetime. At semi-classical level deconstructed description of the theory is given in terms of 4-dimensional Minkowski slices supporting chiral zero modes at the ends. Energy scales warp down along the fifth dimension. When the theory is augmented by 4-dimensional neutral Majorana spinors together with the Higgs mechanism at the low energy end, we can arrange for a theory where the lightest gauge boson mode as well as chiral zero mode at the high energy end are parametrically lighter than other states. Triangle anomalies and instanton effects are expected to make gauge bosons heavy if the resulting effective theory is anomalous. Due to the strong coupling effects at the quantum level, full non-perturbative calculation will be necessary to validate this construction 11. From free fields to AdS space: Thermal case International Nuclear Information System (INIS) Furuuchi, Kazuyuki 2005-01-01 We analyze the reorganization of free field theory correlators to closed string amplitudes investigated in previous papers in the case of Euclidean thermal field theory and study how the dual bulk geometry is encoded on them. The expectation value of Polyakov loop, which is an order parameter for confinement-deconfinement transition, is directly reflected on the dual bulk geometry. The dual geometry of the confined phase is found to be AdS space periodically identified in Euclidean time direction. The gluing of Schwinger parameters, which is a key step for the reorganization of field theory correlators, works in the same way as in the nonthermal case. In the deconfined phase the gluing is made possible only by taking the dual geometry correctly. The dual geometry for the deconfined phase does not have a noncontractable circle in the Euclidean time direction 12. Fine Grained Chaos in AdS_{2} Gravity. Science.gov (United States) Haehl, Felix M; Rozali, Moshe 2018-03-23 Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{}^{(k)}∼(k-1)u[over ^]_{}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values. 13. Aspects of warped AdS3/CFT2 correspondence Science.gov (United States) Chen, Bin; Zhang, Jia-Ju; Zhang, Jian-Dong; Zhong, De-Liang 2013-04-01 In this paper we apply the thermodynamics method to investigate the holographic pictures for the BTZ black hole, the spacelike and the null warped black holes in three-dimensional topologically massive gravity (TMG) and new massive gravity (NMG). Even though there are higher derivative terms in these theories, the thermodynamics method is still effective. It gives consistent results with the ones obtained by using asymptotical symmetry group (ASG) analysis. In doing the ASG analysis we develop a brute-force realization of the Barnich-Brandt-Compere formalism with Mathematica code, which also allows us to calculate the masses and the angular momenta of the black holes. In particular, we propose the warped AdS3/CFT2 correspondence in the new massive gravity, which states that quantum gravity in the warped spacetime could holographically dual to a two-dimensional CFT with {c_R}={c_L}=24 /{Gm{β^2√{{2( {21-4{β^2}} )}}}}. 14. Thermodynamics of charged Lovelock: AdS black holes International Nuclear Information System (INIS) Prasobh, C.B.; Suresh, Jishnu; Kuriakose, V.C. 2016-01-01 We investigate the thermodynamic behavior of maximally symmetric charged, asymptotically AdS black hole solutions of Lovelock gravity. We explore the thermodynamic stability of such solutions by the ordinary method of calculating the specific heat of the black holes and investigating its divergences which signal second-order phase transitions between black hole states. We then utilize the methods of thermodynamic geometry of black hole spacetimes in order to explain the origin of these points of divergence. We calculate the curvature scalar corresponding to a Legendre-invariant thermodynamic metric of these spacetimes and find that the divergences in the black hole specific heat correspond to singularities in the thermodynamic phase space. We also calculate the area spectrum for large black holes in the model by applying the Bohr-Sommerfeld quantization to the adiabatic invariant calculated for the spacetime. (orig.) 15. Higher-derivative superparticle in AdS3 space Science.gov (United States) Kozyrev, Nikolay; Krivonos, Sergey; Lechtenfeld, Olaf 2016-03-01 Employing the coset approach we construct component actions for a superparticle moving in AdS3 with N =(2 ,0 ), D =3 supersymmetry partially broken to N =2 , d =1 . These actions may contain higher time-derivative terms, which are chosen to possess the same (super)symmetries as the free superparticle. In terms of the nonlinear-realization superfields, the component actions always take a simpler form when written in terms of covariant Cartan forms. We also consider in detail the reduction to the nonrelativistic case and construct the corresponding action of a Newton-Hooke superparticle and its higher-derivative generalizations. The structure of these higher time-derivative generalizations is completely fixed by invariance under the supersymmetric Newton-Hooke algebra extended by two central charges. 16. Fine Grained Chaos in AdS2 Gravity Science.gov (United States) Haehl, Felix M.; Rozali, Moshe 2018-03-01 Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^(k)˜(k -1 )u^. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values. Energy Technology Data Exchange (ETDEWEB) Carracedo, Pablo [Meteo-Galicia,Santiago de Compostela E-15782 (Spain); Mas, Javier; Musso, Daniele; Serantes, Alexandre [Departamento de Física de Partículas, Universidade de Santiago de Compostela,Santiago de Compostela E-15782 (Spain); Instituto Galego de Física de Altas Enerxías (IGFAE),Santiago de Compostela E-15782 (Spain) 2017-05-26 We construct a family of very simple stationary solutions to gravity coupled to a massless scalar field in global AdS. They involve a constantly rising source for the scalar field at the boundary and thereby we name them pumping solutions. We construct them numerically in D=4. They are regular and, generically, have negative mass. We perform a study of linear and nonlinear stability and find both stable and unstable branches. In the latter case, solutions belonging to different sub-branches can either decay to black holes or to limiting cycles. This observation motivates the search for non-stationary exactly time-periodic solutions which we actually construct. We clarify the role of pumping solutions in the context of quasistatic adiabatic quenches. In D=3 the pumping solutions can be related to other previously known solutions, like magnetic or translationally-breaking backgrounds. From this we derive an analytic expression. 18. Thermodynamics of charged Lovelock: AdS black holes Science.gov (United States) Prasobh, C. B.; Suresh, Jishnu; Kuriakose, V. C. 2016-04-01 We investigate the thermodynamic behavior of maximally symmetric charged, asymptotically AdS black hole solutions of Lovelock gravity. We explore the thermodynamic stability of such solutions by the ordinary method of calculating the specific heat of the black holes and investigating its divergences which signal second-order phase transitions between black hole states. We then utilize the methods of thermodynamic geometry of black hole spacetimes in order to explain the origin of these points of divergence. We calculate the curvature scalar corresponding to a Legendre-invariant thermodynamic metric of these spacetimes and find that the divergences in the black hole specific heat correspond to singularities in the thermodynamic phase space. We also calculate the area spectrum for large black holes in the model by applying the Bohr-Sommerfeld quantization to the adiabatic invariant calculated for the spacetime. 19. Worldsheet dilatation operator for the AdS superstring Energy Technology Data Exchange (ETDEWEB) Ramírez, Israel [Departamento de Física, Universidad Técnica Federico Santa María,Casilla 110-V, Valparaíso (Chile); Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Haus, Zum Großen Windkanal 6, 12489 Berlin (Germany); Vallilo, Brenno Carlini [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile) 2016-05-23 In this work we propose a systematic way to compute the logarithmic divergences of composite operators in the pure spinor description of the AdS{sub 5}×S{sup 5} superstring. The computations of these divergences can be summarized in terms of a dilatation operator acting on the local operators. We check our results with some important composite operators of the formalism. 20. Holography beyond conformal invariance and AdS isometry? CERN Document Server Barvinsky, A.O. 2015-01-01 We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem from the bulk spacetime. This relation holds for operators of general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous $O(N^0)$ tests of AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies and conformal anomalies. The generalized holographic duality is discussed within the concept of the "double-trace" deformation of the boundary theory, which is responsible in the case of large $N$ CFT coupled to the tower of higher spin gauge fields for t... 1. Neutronic design of an ADS International Nuclear Information System (INIS) Cintas, A; Lopasso, E.M; Marquez Damian, J.I 2009-01-01 We present a LEU-ADS design based on an existing Argentine experimental facility, the RA-8 pool type zero power reactor. The versatility of this reactor allows measurement of different core configurations using different fuel enrichment, burnable poison rods, water perturbations and different control rods types in critical or subcritical configurations with an external source. To assess the feasibility of the LEU-ADS, multiplication factors, kinetic parameters, spectra, and time flux evolution were computed. Two external sources were considered: an isotopic 252 C f source, and a D-D pulsed neutron source. Parameters for different core configurations were calculated, and the feasibility of using continuous and pulsed neutron sources was verified. [es Science.gov (United States) Bunday, Benjamin; Lipscomb, Pete; Allgair, John; Patel, Dilip; Caldwell, Mark; Solecky, Eric; Archie, Chas; Morningstar, Jennifer; Rice, Bryan J.; Singh, Bhanwar; Cain, Jason; Emami, Iraj; Banke, Bill, Jr.; Herrera, Alfredo; Ukraintsev, Vladamir; Schlessinger, Jerry; Ritchison, Jeff 2007-03-01 The conventional premise that metrology is a "non-value-added necessary evil" is a misleading and dangerous assertion, which must be viewed as obsolete thinking. Many metrology applications are key enablers to traditionally labeled "value-added" processing steps in lithography and etch, such that they can be considered integral parts of the processes. Various key trends in modern, state-of-the-art processing such as optical proximity correction (OPC), design for manufacturability (DFM), and advanced process control (APC) are based, at their hearts, on the assumption of fine-tuned metrology, in terms of uncertainty and accuracy. These trends are vehicles where metrology thus has large opportunities to create value through the engineering of tight and targetable process distributions. Such distributions make possible predictability in speed-sorts and in other parameters, which results in high-end product. Additionally, significant reliance has also been placed on defect metrology to predict, improve, and reduce yield variability. The necessary quality metrology is strongly influenced by not only the choice of equipment, but also the quality application of these tools in a production environment. The ultimate value added by metrology is a result of quality tools run by a quality metrology team using quality practices. This paper will explore the relationships among present and future trends and challenges in metrology, including equipment, key applications, and metrology deployment in the manufacturing flow. Of key importance are metrology personnel, with their expertise, practices, and metrics in achieving and maintaining the required level of metrology performance, including where precision, matching, and accuracy fit into these considerations. The value of metrology will be demonstrated to have shifted to "key enabler of large revenues," debunking the out-of-date premise that metrology is "non-value-added." Examples used will be from critical dimension (CD 3. From free fields to AdS space. II International Nuclear Information System (INIS) Gopakumar, Rajesh 2004-01-01 We continue with the program of paper I [Phys. Rev. D 70, 025009 (2004)] to implement open-closed string duality on free gauge field theory (in the large-N limit). In this paper we consider correlators such as i=1 n TrΦ J i (x i )>. The Schwinger parametrization of this n-point function exhibits a partial gluing up into a set of basic skeleton graphs. We argue that the moduli space of the planar skeleton graphs is exactly the same as the moduli space of genus zero Riemann surfaces with n holes. In other words, we can explicitly rewrite the n-point (planar) free-field correlator as an integral over the moduli space of a sphere with n holes. A preliminary study of the integrand also indicates compatibility with a string theory on AdS space. The details of our argument are quite insensitive to the specific form of the operators and generalize to diagrams of a higher genus as well. We take this as evidence of the field theory's ability to reorganize itself into a string theory 4. On modular properties of the AdS3 CFT International Nuclear Information System (INIS) Baron, Walter H.; Nunez, Carmen A. 2011-01-01 We study modular properties of the AdS 3 Wess-Zumino-Novikov-Witten model. Although the Euclidean partition function is modular invariant, the characters on the Euclidean torus diverge and the regularization proposed in the literature removes information on the spectrum and the usual one to one map between characters and representations of rational models is lost. Reconsidering the characters defined on the Lorentzian torus and focusing on their structure as distributions, we obtain expressions that recover those properties. We study their modular transformations and find a generalized S matrix, depending on the sign of the real modular parameters, which has two diagonal blocks and one off-diagonal block, mixing discrete and continuous representations, that we fully determine. We then explore the relations among the modular transformations, the fusion algebra and the boundary states. We explicitly construct Ishibashi states for the maximally symmetric D-branes and show that the generalized S matrix defines the one-point functions associated to pointlike and H 2 -branes as well as the fusion rules of the degenerate representations of sl(2,R) appearing in the open string spectrum of the pointlike D-branes, through a generalized Verlinde theorem. 5. Quantum Black Holes as Holograms in AdS Braneworlds CERN Document Server Emparan, R; Kaloper, Nemanja; Emparan, Roberto; Fabbri, Alessandro; Kaloper, Nemanja 2002-01-01 We propose a new approach for using the AdS/CFT correspondence to study quantum black hole physics. The black holes on a brane in an AdS$_{D+1}$ braneworld that solve the classical bulk equations are interpreted as duals of {\\it quantum-corrected} $D$-dimensional black holes, rather than classical ones, of a conformal field theory coupled to gravity. We check this explicitly in D=3 and D=4. In D=3 we reinterpret the existing exact solutions on a flat membrane as states of the dual 2+1 CFT. We show that states with a sufficiently large mass really are 2+1 black holes where the quantum corrections dress the classical conical singularity with a horizon and censor it from the outside. On a negatively curved membrane, we reinterpret the classical bulk solutions as quantum-corrected BTZ black holes. In D=4 we argue that the bulk solution for the brane black hole should include a radiation component in order to describe a quantum-corrected black hole in the 3+1 dual. Hawking radiation of the conformal field is then ... 6. Ad valorem versus unit taxes DEFF Research Database (Denmark) Schröder, Philipp J.H.; Sørensen, Allan 2010-01-01 a general equilibrium monopolistic competition model with heterogeneous firms and intra-industry reallocations. We show that the welfare superiority of ad valorem over unit taxes under imperfect competition is not only preserved but amplified. The additional difference between the tools arises because unit...... taxes distort relative prices, which in turn reduces average industry productivity through reallocations (the survival and increased market share of lower productivity firms). Importantly, numerical solutions of the model reveal that the relative welfare loss from using the unit tax increases... 7. Entanglement Entropy of AdS Black Holes Directory of Open Access Journals (Sweden) Maurizio Melis 2010-11-01 Full Text Available We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. 8. Antismoking Ads at the Point of Sale: The Influence of Ad Type and Context on Ad Reactions. Science.gov (United States) Kim, Annice; Nonnemaker, James; Guillory, Jamie; Shafer, Paul; Parvanta, Sarah; Holloway, John; Farrelly, Matthew 2017-06-01 9. MUSICAL ARRANGEMENT OF MEDIA ADS Directory of Open Access Journals (Sweden) Chernyshov Alexander V. 2015-01-01 Full Text Available The music-compositional principles of commercial and political advertising and also the self-promotion of electronic media (radio, television, Internet are considered in this mediatext: from the elementary beeps, symbolic functions, emblems/logos and musical brands to the sound engineering technology to underscore the product's name and the complex synthesis between music and intra movements and color-light design of frames. Simultaneously examines, how the musical arrangement of ethereal advertising is involved in creation the emotional drama or bravado which reach the level of explicit or associative counterpoint 'music with the advertised object or subject' and which extend to expression of cultural image of all the broadcast channel. The article explores the works of the next genres like infomercial, teleshopping, film-ad, and autonomous commercials that have been produced in European countries or USA. 10. Adding timing to the VELO CERN Document Server Mitreska, Biljana 2017-01-01 The LHCb experiment is designed to perform high precision measurements of matter-antimatter asymmetries and searches for rare and forbidden decays, with the aim of discovering new and unexpected particles and forces. In 2030 the LHC beam intensity will increase by a factor of 50 compared to current operations. This means increased samples of the particles we need to study, but it also presents experimental challenges. In particular, with current technology it becomes impossible to differentiate the many (>50) separate proton-proton collisions which occur for each bunch crossing.\\\\ In this project a Monte Carlo simulation was developed to model the operation of a silicon pixel vertex detector surrounding the collision region at LHCb, under the conditions expected after 2030, after the second upgrade of the Vertex Locator(VELO).The main goal was studying the effect of adding '4D' detectors which save high-precision timing information, in addition to the usual three spatial coordinates, as charged particles pas... 11. Thermodynamic and classical instability of AdS black holes in fourth-order gravity International Nuclear Information System (INIS) Myung, Yun Soo; Moon, Taeyoon 2014-01-01 We study thermodynamic and classical instability of AdS black holes in fourth-order gravity. These include the BTZ black hole in new massive gravity, Schwarzschild-AdS black hole, and higher-dimensional AdS black holes in fourth-order gravity. All thermodynamic quantities which are computed using the Abbot-Deser-Tekin method are used to study thermodynamic instability of AdS black holes. On the other hand, we investigate the s-mode Gregory-Laflamme instability of the massive graviton propagating around the AdS black holes. We establish the connection between the thermodynamic instability and the GL instability of AdS black holes in fourth-order gravity. This shows that the Gubser-Mitra conjecture holds for AdS black holes found from fourth-order gravity 12. III Adli Bilimler Kongresi - Posterler Directory of Open Access Journals (Sweden) 2000-08-01 Full Text Available POSTER ÖZETLERİ OTOPSİ UYGULAMASINA TOPLUMSAL YAKLAŞIM C. Haluk İNCE, Nurhan İNCE , Şebnem Korur FİNCANCI, Yıldız TÜMERDEM*. ÖZET Otopsi sayısı, bir ülkenin sağlık ve yargı yönünden gelişmişliğinin kriterlerinden biridir. Çalışma bireylerin konu ile ilgili bilgi ve davranışları öğrenildiği takdirde otopsi ile ilgili olumsuz davranışlarının da en aza indirgenecek bir yöntemle eğitilmelerinin sağlanabileceği savı ile gerçekleştirilmiştir. Verileri İstanbul kentinde farklı sosyoekonomik kültürel (SEK düzeyli toplum yapısının gözlendiği ilçelerden rastlantısal örnekleme ile seçilen 342 katılıcıdan çok sorulu anketi (ön seçimli yüzyüze uygulama yöntemi ile toplanmıştır. 342 katılımcının %6l.4 (n=210'ü kadın, %38.6 (n=132'si erkektir. % 9.1 kişinin ailesinde bir otopsi deneyimi yaşamıştır. %76.9 (n:263 kişi otopsinin gerekli olduğunu ifade etmiştir. Bireylerin eğitim durumlarına göre otopsiye izin verme konusundaki görüşlerinin arasında öğrenim düzeyi yüksek olanların lehine istatistiksi açıdan anlamlı sonuç çıkmıştır. Her iki cinste de ailelerinde hangi birey olursa olsun otopsiye rıza konusundaki görüşlerinde farklılığın olmaması dikkat çekici bulunmuştur. % 16.1 (n:5' i ise dini inançlarına aykırı olduğu için otopsiye asla izin veremeyeceklerini ifade etmiştir. Toplumun SEK yapısından kaynaklanan yetersiz bilgi ülkemizdeki otopsi sayısının gelişmiş ülkelere oranla olumsuz etkilemektedir. Ancak hekim ve hekim dışı sağlık çalışanlarının da otopsi konusunda bilgi ve donanımlarını geliştirmeleri gerekmektedir. Bu çalışma otopsi sayısındaki düşüklüğün rolünü araştırmak üzere düzenlenmiştir. Anahtar Kelimeler: Otopsi, toplumsal yargı, bilgilendirme. TRAKTÖR KAZALARINDA ÖLEN OLGULARIN DEĞERLENDİRİLMESİ M.Selim ÖZKÖK, Ufuk KATKICI. ÖZET Trafik kazaları adli tıp pratiğinde Energy Technology Data Exchange (ETDEWEB) Metsaev, R.R. [Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prospect 53, Moscow 119991 (Russian Federation) 2015-10-16 14. Recurring Anomaly Detection System (ReADS) Data.gov (United States) National Aeronautics and Space Administration — Overview: ReADS can analyze text reports, such as aviation reports and problem or maintenance records. ReADS uses text clustering algorithms to group loosely related... CERN Document Server Penedones, Joao 2017-01-01 We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of the main properties of Mellin amplitudes for CFT correlation functions and their uses in the context of AdS/CFT. Science.gov (United States) TNTP, 2011 2011-01-01 This paper presents myths as well as facts about value-added analysis. These myths include: (1) "Value-added isn't fair to teachers who work in high-need schools, where students tend to lag far behind academically"; (2) "Value-added scores are too volatile from year-to-year to be trusted"; (3) "There's no research behind value-added"; (4) "Using… OpenAIRE Fan, JiJi 2011-01-01 For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double- trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a dou... 18. 16 CFR 460.18 - Insulation ads. Science.gov (United States) 2010-01-01 ... Commercial Practices FEDERAL TRADE COMMISSION TRADE REGULATION RULES LABELING AND ADVERTISING OF HOME INSULATION § 460.18 Insulation ads. (a) If your ad gives an R-value, you must give the type of insulation and... your ad gives a price, you must give the type of insulation, the R-value at a specific thickness, the... NARCIS (Netherlands) L.E. Couwenberg (Linda) 2017-01-01 markdownabstractMarketing experts commonly refer to ads as either “emotional” or “rational” in their appeal to consumers. This dichotomy of “thinking versus feeling” is most evident when it comes to discussions around what makes an ad effective. Some studies suggest that an ad that pulls on the 20. Automated Experiments on Ad Privacy Settings Directory of Open Access Journals (Sweden) Datta Amit 2015-04-01 OpenAIRE 2008-01-01 The thesis introduces contextual advertising on internet using Google AdWords. The paper describes individual steps of an ad campaign (product choosing, ad types, keywords), its management and success evaluation (calculation of ROI and modified ROI). 2. Historical Literature in the ADS Science.gov (United States) Eichhorn, G.; Kurtz, M. J.; Accomazzi, A.; Grant, C. S. 1997-12-01 The Astrophysics Data System at http://adswww.harvard.edu is in the process of scanning the historical astronomical literature and making it available through the World Wide Web. We have scanned several volumes from the early 1800's of the "Astronomische Nachrichten", and the "Monthly Notices of the Royal Astronomical Society", the two oldest astronomical journals. We also have several of the early volumes of the "Astrophysical Journal" and the "Astronomical Journal" available. For all the journals that we cover, we have scanned volume 1. These early volumes can be accessed on a page-by-page basis. We plan to continue to scan this historical literature and complete these journals within the next year. We are also collaborating with a preservation project at Harvard University. This project will microfilm selected parts of astronomical Observatory reports. We plan to scan these microfilms to produce electronic images of these reports and put them on-line in the ADS. We hope to eventually cover most of the astronomical literature. In order to organize the scanned pages into articles, we need tables of contents (ToC). The early issues of the journals did not have printed ToC pages, so this needs to be done by hand. We do not have the financial resources to build these ToCs. We are looking for collaborators who would be willing to work with us in building these ToCs for the older journals and observatory reports. If you are interested in such a project, please contact the first author at gei@cfa.harvard.edu. 3. Ad-hoc networking towards seamless communications CERN Document Server Gavrilovska, Liljana 2006-01-01 Ad-Hoc Networking Towards Seamless Communications is dedicated to an area that attracts growing interest in academia and industry and concentrates on wireless ad hoc networking paradigm. The persistent efforts to acquire the ability to establish dynamic wireless connections from anywhere to anyone with any device without prerequisite imbedded infrastructure move the communications boundaries towards ad-hoc networks. Recently, ad hoc networking has attracted growing interest due to advances in wireless communications, and developed framework for running IP based protocols. The expected degree of penetration of these networks will depend on the successful resolution of the key features. Ad-hoc networks pose many complex and open problems for researchers. Ad-Hoc Networking Towards Seamless Communications reveals the state-of-the-art in wireless ad-hoc networking and discusses some of the key research topics that are expected to promote and accelerate the commercial applications of these networks (e.g., MAC, rout... 4. Protein domain organisation: adding order Directory of Open Access Journals (Sweden) Kummerfeld Sarah K 2009-01-01 Full Text Available Abstract Background Domains are the building blocks of proteins. During evolution, they have been duplicated, fused and recombined, to produce proteins with novel structures and functions. Structural and genome-scale studies have shown that pairs or groups of domains observed together in a protein are almost always found in only one N to C terminal order and are the result of a single recombination event that has been propagated by duplication of the multi-domain unit. Previous studies of domain organisation have used graph theory to represent the co-occurrence of domains within proteins. We build on this approach by adding directionality to the graphs and connecting nodes based on their relative order in the protein. Most of the time, the linear order of domains is conserved. However, using the directed graph representation we have identified non-linear features of domain organization that are over-represented in genomes. Recognising these patterns and unravelling how they have arisen may allow us to understand the functional relationships between domains and understand how the protein repertoire has evolved. Results We identify groups of domains that are not linearly conserved, but instead have been shuffled during evolution so that they occur in multiple different orders. We consider 192 genomes across all three kingdoms of life and use domain and protein annotation to understand their functional significance. To identify these features and assess their statistical significance, we represent the linear order of domains in proteins as a directed graph and apply graph theoretical methods. We describe two higher-order patterns of domain organisation: clusters and bi-directionally associated domain pairs and explore their functional importance and phylogenetic conservation. Conclusion Taking into account the order of domains, we have derived a novel picture of global protein organization. We found that all genomes have a higher than expected 5. Protein domain organisation: adding order. Science.gov (United States) Kummerfeld, Sarah K; Teichmann, Sarah A 2009-01-29 Domains are the building blocks of proteins. During evolution, they have been duplicated, fused and recombined, to produce proteins with novel structures and functions. Structural and genome-scale studies have shown that pairs or groups of domains observed together in a protein are almost always found in only one N to C terminal order and are the result of a single recombination event that has been propagated by duplication of the multi-domain unit. Previous studies of domain organisation have used graph theory to represent the co-occurrence of domains within proteins. We build on this approach by adding directionality to the graphs and connecting nodes based on their relative order in the protein. Most of the time, the linear order of domains is conserved. However, using the directed graph representation we have identified non-linear features of domain organization that are over-represented in genomes. Recognising these patterns and unravelling how they have arisen may allow us to understand the functional relationships between domains and understand how the protein repertoire has evolved. We identify groups of domains that are not linearly conserved, but instead have been shuffled during evolution so that they occur in multiple different orders. We consider 192 genomes across all three kingdoms of life and use domain and protein annotation to understand their functional significance. To identify these features and assess their statistical significance, we represent the linear order of domains in proteins as a directed graph and apply graph theoretical methods. We describe two higher-order patterns of domain organisation: clusters and bi-directionally associated domain pairs and explore their functional importance and phylogenetic conservation. Taking into account the order of domains, we have derived a novel picture of global protein organization. We found that all genomes have a higher than expected degree of clustering and more domain pairs in forward and 6. Non-relativistic AdS branes and Newton-Hooke superalgebra International Nuclear Information System (INIS) Sakaguchi, Makoto; Yoshida, Kentaroh 2006-01-01 7. Light-cone gauge formulation for AdS4 x CP3 International Nuclear Information System (INIS) Uvarov, D.V. 2011-01-01 We review the Type IIA superstring on the AdS 4 x CP 3 background in the k-symmetry light-cone gauge characterized by the choice of the lightlike directions from the D = 3 Minkowski boundary of AdS 4 both in the Lagrangian and Hamiltonian formulations 8. Joule-Thomson expansion of the charged AdS black holes International Nuclear Information System (INIS) Oekcue, Oezguer; Aydiner, Ekrem 2017-01-01 In this paper, we study Joule-Thomson effects for charged AdS black holes. We obtain inversion temperatures and curves. We investigate similarities and differences between van der Waals fluids and charged AdS black holes for the expansion. We obtain isenthalpic curves for both systems in the T-P plane and determine the cooling-heating regions. (orig.) 9. Joule-Thomson expansion of the charged AdS black holes Energy Technology Data Exchange (ETDEWEB) Oekcue, Oezguer; Aydiner, Ekrem [Istanbul University, Department of Physics, Faculty of Science, Vezneciler, Istanbul (Turkey) 2017-01-15 In this paper, we study Joule-Thomson effects for charged AdS black holes. We obtain inversion temperatures and curves. We investigate similarities and differences between van der Waals fluids and charged AdS black holes for the expansion. We obtain isenthalpic curves for both systems in the T-P plane and determine the cooling-heating regions. (orig.) 10. LWR [Light Water Reactor] power plant simulations using the AD10 and AD100 systems International Nuclear Information System (INIS) Wulff, W.; Cheng, H.S.; Chien, C.J.; Jang, J.Y.; Lin, H.C.; Mallen, A.N.; Wang, S.J. 1989-01-01 Boiling (BWR) and Pressurized (PWR) Water Reactor Power Plants are being simulated at BNL with the AD10 and AD100 Peripheral Processor Systems. The AD10 system has been used for BWR simulations since 1984 for safety analyses, emergency training and optimization studies. BWR simulation capabilities have been implemented recently on the AD100 system and PWR simulation capabilities are currently being developed under the auspices of international cooperation. Modeling and simulation methods are presented with emphasis on the simulation of the Nuclear Steam Supply System. Results are presented for BWR simulation and performance characteristics are compared of the AD10 and AD100 systems. It will be shown that the AD100 simulates two times faster than two AD10 processors operating in parallel and that the computing capacity of one AD100 (with FMU processor) is twice as large as that of two AD10 processors. 9 refs., 5 figs., 1 tab DEFF Research Database (Denmark) Frattasi, Simone; Monti, Marco 2008-01-01 In this paper, we propose an innovative solution for positioning determination in 4G wireless networks by introducing the Ad-Coop Positioning System (ACPS). The ACPS is supported by a hybrid cellular ad-hoc architecture, where the cellular network has a centralized control over the ad-hoc connect......In this paper, we propose an innovative solution for positioning determination in 4G wireless networks by introducing the Ad-Coop Positioning System (ACPS). The ACPS is supported by a hybrid cellular ad-hoc architecture, where the cellular network has a centralized control over the ad...... method for the ACPS, which appropriately combines and weights the long- and short-range location information in a non-linear least square (NLLS) minimization procedure. The numerical results shown in the paper demonstrate that the ACPS enhances the location estimation accuracy with respect... International Nuclear Information System (INIS) Artsukevich, A. Yu.; Vasiliev, M. A. 2009-01-01 We analyze the pattern of fields in (d+1)-dimensional anti-de Sitter space in terms of those in d-dimensional anti-de Sitter space. The procedure, which is neither dimensional reduction nor dimensional compactification, is called dimensional degression. The analysis is performed group theoretically for all totally symmetric bosonic and fermionic representations of the anti-de Sitter algebra. The field-theoretical analysis is done for a massive scalar field in AdS d+d ' and massless spin-one-half, spin-one, and spin-two fields in AdS d+1 . The mass spectra of the resulting towers of fields in AdS d are found. For the scalar field case, the obtained results extend to the shadow sector those obtained by Metsaev [Nucl. Phys. B, Proc. Suppl. 102, 100 (2001)] by a different method. International Nuclear Information System (INIS) Takayama, Koichi; Reynolds, Paul N.; Short, Joshua J.; Kawakami, Yosuke; Adachi, Yasuo; Glasgow, Joel N.; Rots, Marianne G.; Krasnykh, Victor; Douglas, Joanne T.; Curiel, David T. 2003-01-01 OpenAIRE Couwenberg, Linda 2017-01-01 markdownabstractMarketing experts commonly refer to ads as either “emotional” or “rational” in their appeal to consumers. This dichotomy of “thinking versus feeling” is most evident when it comes to discussions around what makes an ad effective. Some studies suggest that an ad that pulls on the heart strings will pack the most punch; others suggest a blend of logic and emotion. However, new research reveals which areas of the brain are stimulated by different ad appeals – and the brain activi... 15. Queueing Models for Mobile Ad Hoc Networks NARCIS (Netherlands) de Haan, Roland 2009-01-01 This thesis presents models for the performance analysis of a recent communication paradigm: \\emph{mobile ad hoc networking}. The objective of mobile ad hoc networking is to provide wireless connectivity between stations in a highly dynamic environment. These dynamics are driven by the mobility of 16. Context discovery in ad-hoc networks NARCIS (Netherlands) Liu, F. 2011-01-01 With the rapid development of wireless technology and portable devices, mobile ad-hoc networks (MANETs) are more and more present in our daily life. Ad-hoc networks are often composed of mobile and battery-supplied devices, like laptops, mobile phones, and PDAs. With no requirement for Science.gov (United States) Agee, Warren K. 1979-01-01 Findings from a national study of 113 schools show that more copywriting and internship courses have been added to advertising school programs than courses in any other subject areas. Among supporting courses, marketing has been most frequently added as a requirement. (RL) Czech Academy of Sciences Publication Activity Database 2016-01-01 Roč. 104, č. 3 (2016), s. 389-415 ISSN 0039-3215 R&D Projects: GA ČR GAP202/10/1826 Institutional support: RVO:67985807 Keywords : de Morgan algebras * contradiction * reductio ad contradictionem * reductio ad absurdum * four-valued logic * paraconsistent logic * inconsistency * completeness Subject RIV: BA - General Mathematics Impact factor: 0.589, year: 2016 19. Holographic complexity and fidelity susceptibility as holographic information dual to different volumes in AdS Directory of Open Access Journals (Sweden) N.S. Mazhari 2017-03-01 Full Text Available The holographic complexity and fidelity susceptibility have been defined as new quantities dual to different volumes in AdS. In this paper, we will use these new proposals to calculate both of these quantities for a variety of interesting deformations of AdS. We obtain the holographic complexity and fidelity susceptibility for an AdS black hole, Janus solution, a solution with cylindrical symmetry, an inhomogeneous background and a hyperscaling violating background. It is observed that the holographic complexity depends on the size of the subsystem for all these solutions and the fidelity susceptibility does not have any such dependence. 20. Thermodynamic geometry and phase transitions of AdS braneworld black holes Energy Technology Data Exchange (ETDEWEB) Chaturvedi, Pankaj, E-mail: cpankaj@iitk.ac.in; Sengupta, Gautam, E-mail: sengupta@iitk.ac.in 2017-02-10 The thermodynamics and phase transitions of charged RN–AdS and rotating Kerr–AdS black holes in a generalized Randall–Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structures on the braneworld parameter for these black holes. CERN Document Server Davis, Harold 2010-01-01 2. Holographic complexity and fidelity susceptibility as holographic information dual to different volumes in AdS Energy Technology Data Exchange (ETDEWEB) Mazhari, N.S., E-mail: najmemazhari86@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Momeni, Davood, E-mail: davoodmomeni78@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Bahamonde, Sebastian, E-mail: sebastian.beltran.14@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Faizal, Mir, E-mail: mirfaizalmir@googlemail.com [Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, 3333 University Way, Kelowna, British Columbia, V1V 1V7 (Canada); Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada); Myrzakulov, Ratbay, E-mail: rmyrzakulov@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan) 2017-03-10 The holographic complexity and fidelity susceptibility have been defined as new quantities dual to different volumes in AdS. In this paper, we will use these new proposals to calculate both of these quantities for a variety of interesting deformations of AdS. We obtain the holographic complexity and fidelity susceptibility for an AdS black hole, Janus solution, a solution with cylindrical symmetry, an inhomogeneous background and a hyperscaling violating background. It is observed that the holographic complexity depends on the size of the subsystem for all these solutions and the fidelity susceptibility does not have any such dependence. 3. Factorized tree-level scattering in AdS4 x CP3 International Nuclear Information System (INIS) Kalousios, Chrysostomos; Vergu, C.; Volovich, Anastasia 2009-01-01 AdS 4 /CFT 3 duality relating IIA string theory on AdS 4 x CP 3 to N = 6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS 4 x CP 3 . We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production. Energy Technology Data Exchange (ETDEWEB) Freivogel, Ben; /Stanford U., Phys. Dept. /LBL, Berkeley; Hubeny, Veronika E.; /LBL, Berkeley /Durham U., Dept. of Math.; Maloney, Alexander; /Stanford U., Phys. Dept.; Myers, Rob; /Perimeter Inst. Theor. Phys. /Waterloo U.; Rangamani, Mukund; /LBL, Berkeley /Durham U., Dept. of Math.; Shenker, Stephen; /Stanford U., Phys. Dept. 2005-10-07 We study the realization of inflation within the AdS/CFT correspondence. We assume the existence of a string landscape containing at least one stable AdS vacuum and a (nearby) metastable de Sitter state. Standard arguments imply that the bulk physics in the vicinity of the AdS minimum is described by a boundary CFT. We argue that large enough bubbles of the dS phase, including those able to inflate, are described by mixed states in the CFT. Inflating degrees of freedom are traced over and do not appear explicitly in the boundary description. They nevertheless leave a distinct imprint on the mixed state. Analytic continuation allows us, in principle, to recover a large amount of nonperturbatively defined information about the inflating regime. Our work also shows that no scattering process can create an inflating region, even by quantum tunneling, since a pure state can never evolve into a mixed state under unitary evolution.We study the realization of inflation within the AdS/CFT correspondence. We assume the existence of a string landscape containing at least one stable AdS vacuum and a (nearby) metastable de Sitter state. Standard arguments imply that the bulk physics in the vicinity of the AdS minimum is described by a boundary CFT. We argue that large enough bubbles of the dS phase, including those able to inflate, are described by mixed states in the CFT. Inflating degrees of freedom are traced over and do not appear explicitly in the boundary description. They nevertheless leave a distinct imprint on the mixed state. Analytic continuation allows us, in principle, to recover a large amount of nonperturbatively defined information about the inflating regime. Our work also shows that no scattering process can create an inflating region, even by quantum tunneling, since a pure state can never evolve into a mixed state under unitary evolution. 5. The eleven observations of comets between 687 AD and 1114 AD recorded in the Anglo Saxon Chronicle Science.gov (United States) Mardon, E. G.; Mardon, A. A.; Williams, J. 1992-12-01 6. A Grassmann path from AdS3 to flat space International Nuclear Information System (INIS) Krishnan, Chethan; Raju, Avinash; Roy, Shubho 2014-01-01 We show that interpreting the inverse AdS 3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS 3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS 3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS 3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application 7. Simplifying superstring and D-brane actions in AdS4 x CP3 superbackground International Nuclear Information System (INIS) Grassi, Pietro Antonio; Sorokin, Dmitri; Wulff, Linus 2009-01-01 By making an appropriate choice for gauge fixing kappa-symmetry we obtain a relatively simple form of the actions for a D = 11 superparticle in AdS 4 x S 7 /Z k , and for a D0-brane, fundamental string and D2-branes in the AdS 4 x CP 3 superbackground. They can be used to study various problems of string theory and the AdS 4 /CFT 3 correspondence, especially in regions of the theory which are not reachable by the OSp(6\|4)/U(3) x SO(1,3) supercoset sigma-model. In particular, we present a simple form of the gauge-fixed superstring action in AdS 4 x CP 3 and briefly discuss issues of its T-dualization. 8. Folded three-spin string solutions in AdS5 x S5 International Nuclear Information System (INIS) Ryang Shijong 2004-01-01 We construct a spinning closed string solution in AdS 5 x S 5 which is folded in the radial direction and has two equal spins in AdS 5 and a spin in S 5 . The energy expression of the three-spin solution specified by the folding and winding numbers for the small S 5 spin shows a logarithmic behavior and a one-third power behavior of the large total AdS 5 spin, in the long string and in the short string located near the boundary of AdS 5 respectively. It exhibits the non-regular expansion in the 't Hooft coupling constant, while it takes the regular one when the S 5 spin becomes large. (author) 9. On thermodynamics of AdS black holes in M-theory International Nuclear Information System (INIS) Belhaj, A.; Chabab, M.; Masmar, K.; El Moumni, H.; Sedra, M.B. 2016-01-01 Motivated by recent work on asymptotically AdS 4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2- and M5-branes. Concretely, we consider AdS black holes in AdS p+2 x S 11-p-2 , where p = 2,5 by interpreting the number of M2- (and M5-branes) as a thermodynamical variable. More precisely, we study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then we compute the thermodynamical curvatures from the Quevedo metric for M2- and M5-branes geometries to reconsider the stability of such black holes. The Quevedo metric singularities recover similar stability results provided by the phase-transition program. It has been shown that similar behaviors are also present in the limit of large N. (orig.) Directory of Open Access Journals (Sweden) Narahyana Bom de Araujo 2014-09-01 Full Text Available Objective To assess cognition in major depressed (MD, Alzheimer's disease (AD, and depression in AD elderly. Method Subjects were evaluated by Mini Mental, Rey Auditory Verbal Learning Test, Rey Complex Figure, Digit Span, Similarities, Trail Making A/B, Verbal Fluency and Stroop. One-way ANOVA and multivariate models were used to compare the performance of each group on neuropsychological tests. Results We evaluated 212 subjects. Compared to MD, attention, working memory, processing speed and recall showed significantly better in controls. Controls showed significantly higher performance in all cognitive measures, except in attention compared to AD. Verbal fluency, memory, processing speed and abstract reasoning in MD was significantly higher compared to AD. AD was significantly better in general cognitive state than depression in AD. All other cognitive domains were similar. Conclusion A decreasing gradient in cognition appeared from the control to depression in AD, with MD and AD in an intermediate position. 11. Quantum spectral curve for the η-deformed AdS5 × S5 superstring Science.gov (United States) Klabbers, Rob; van Tongeren, Stijn J. 2017-12-01 The spectral problem for the AdS5 ×S5 superstring and its dual planar maximally supersymmetric Yang-Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We discuss how the same concepts apply to the η-deformed AdS5 ×S5 superstring, an integrable deformation of the AdS5 ×S5 superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS5 ×S5 superstring, like the relation between the XXZ and XXX spin chains, or the sausage and the S2 sigma models for instance. We derive the quantum spectral curve for the η-deformed string by reformulating the corresponding ground-state thermodynamic Bethe ansatz equations as an analytic Y system, and map this to an analytic T system which upon suitable gauge fixing leads to a Pμ system - the quantum spectral curve. We then discuss constraints on the asymptotics of this system to single out particular excited states. At the spectral level the η-deformed string and its quantum spectral curve interpolate between the AdS5 ×S5 superstring and a superstring on "mirror" AdS5 ×S5, reflecting a more general relationship between the spectral and thermodynamic data of the η-deformed string. In particular, the spectral problem of the mirror AdS5 ×S5 string, and the thermodynamics of the undeformed AdS5 ×S5 string, are described by a second rational limit of our trigonometric quantum spectral curve, distinct from the regular undeformed limit. 12. Integrable systems from membranes on AdS4 x S7 International Nuclear Information System (INIS) Bozhilov, P. 2008-01-01 We describe how Neumann and Neumann-Rosochatius type integrable systems, as well as the continuous limit of the SU(2) integrable spin chain, can be obtained from membranes on AdS 4 x S 7 background, in the framework of AdS/CFT correspondence. (Abstract Copyright [2008], Wiley Periodicals, Inc.) 13. Financial and health literacy predict incident AD dementia and AD pathology Science.gov (United States) Yu, Lei; Wilson, Robert S.; Schneider, Julie A.; Bennett, David A.; Boyle, Patricia A. 2017-01-01 14. Microbial production of value-added nutraceuticals. Science.gov (United States) Wang, Jian; Guleria, Sanjay; Koffas, Mattheos Ag; Yan, Yajun 2016-02-01 Nutraceuticals are important natural bioactive compounds that confer health-promoting and medical benefits to humans. Globally growing demands for value-added nutraceuticals for prevention and treatment of human diseases have rendered nutraceuticals a multi-billion dollar market. However, supply limitations and extraction difficulties from natural sources such as plants, animals or fungi, restrict the large-scale use of nutraceuticals. Metabolic engineering via microbial production platforms has been advanced as an eco-friendly alternative approach for production of value-added nutraceuticals from simple carbon sources. Microbial platforms like the most widely used Escherichia coli and Saccharomyces cerevisiae have been engineered as versatile cell factories for production of diverse and complex value-added chemicals such as phytochemicals, prebiotics, polysaccaharides and poly amino acids. This review highlights the recent progresses in biological production of value-added nutraceuticals via metabolic engineering approaches. Copyright © 2015 Elsevier Ltd. All rights reserved. 15. Research of Ad Hoc Networks Access Algorithm Science.gov (United States) Xiang, Ma With the continuous development of mobile communication technology, Ad Hoc access network has become a hot research, Ad Hoc access network nodes can be used to expand capacity of multi-hop communication range of mobile communication system, even business adjacent to the community, improve edge data rates. When the ad hoc network is the access network of the internet, the gateway discovery protocol is very important to choose the most appropriate gateway to guarantee the connectivity between ad hoc network and IP based fixed networks. The paper proposes a QoS gateway discovery protocol which uses the time delay and stable route to the gateway selection conditions. And according to the gateway discovery protocol, it also proposes a fast handover scheme which can decrease the handover time and improve the handover efficiency. 16. 27 CFR 19.456 - Adding denaturants. Science.gov (United States) 2010-04-01 ... proprietor shall submit a flow diagram of the intended process or method of adding denaturants. (Sec. 201... OF THE TREASURY LIQUORS DISTILLED SPIRITS PLANTS Denaturing Operations and Manufacture of Articles... 17. Model checking mobile ad hoc networks NARCIS (Netherlands) Ghassemi, Fatemeh; Fokkink, Wan 2016-01-01 Modeling arbitrary connectivity changes within mobile ad hoc networks (MANETs) makes application of automated formal verification challenging. We use constrained labeled transition systems as a semantic model to represent mobility. To model check MANET protocols with respect to the underlying 18. The contribution of technology to added value CERN Document Server Fernandes, António S C 2013-01-01 There is a wide consensus that introduction of technology to the production process contributes to an overall economic value, however, confusion between technology, knowledge and capital often makes value calculations ambiguous and non-objective. The Contribution of Technology to Added Value addresses not only this issue of definition but also provides a production model to assess the value contribution of technology within the production process. A clarification of fundamental semantics provides a significant taxonomy for technology dependence, and allows understanding and modeling of how knowledge, technology and capital individually contribute to production and to value adding. A new technology dependence taxonomy is proposed and assessed following chapters explaining growth models, the KTC model and technology index values. Balancing theoretical knowledge with real-world data and applications The Contribution of Technology to Added Value clarifies the issue of value adding for a range of different vie... 19. ADS with HEU in the Vinca Institute International Nuclear Information System (INIS) Pesic, M.; Sobolevsky, N. 2000-01-01 The 'Conceptual design of ADS' is a new project proposed in the Vin.a Institute for the next three years. In this paper, an option in the project - an idea of high-enriched uranium (HEU) - H 2 O low-flux ADS is shown. Preliminary results of design study and calculations of the beam-target interaction and neutronics of proposed sub-critical system are given. (author) 20. Automated music selection of video ads Directory of Open Access Journals (Sweden) Wiesener Oliver 2017-07-01 1. Wess-Zumino terms for AdS D-branes International Nuclear Information System (INIS) Hatsuda, Machiko; Kamimura, Kiyoshi 2004-01-01 We show that Wess-Zumino terms for Dp branes with p>0 in the anti-de Sitter (AdS) space are given in terms of 'left-invariant' currents on the super-AdS group or the 'expanded' super-AdS group. As a result there is no topological extension of the super-AdS algebra. In the flat limit the global Lorentz rotational charges of the AdS space turn out to be brane charges of the supertranslation algebra representing the BPS mass. We also show that a D-instanton is described by the GL(1) degree of freedom in the Roiban-Siegel formalism based on the GL(4 vertical bar 4)/[Sp(4)xGL(1)]2 coset 2. Supersymmetric black holes in AdS4 from very special geometry International Nuclear Information System (INIS) Gnecchi, Alessandra; Halmagyi, Nick 2014-01-01 Supersymmetric black holes in AdS spacetime are inherently interesting for the AdS/CFT correspondence. Within a four dimensional gauged supergravity theory coupled to vector multiplets, the only analytic solutions for regular, supersymmetric, static black holes in AdS 4 are those in the STU-model due to Cacciatori and Klemm. We study a class of U(1)-gauged supergravity theories coupled to vector multiplets which have a cubic prepotential, the scalar manifold is then a very special Kähler manifold. When the resulting very special Kähler manifold is a homogeneous space, we find analytic solutions for static, supersymmetric AdS 4 black holes with vanishing axions. The horizon geometries of our solutions are constant curvature Riemann surfaces of arbitrary genus 3. Closed string tachyons on AdS orbifolds and dual Yang-Mills instantons Energy Technology Data Exchange (ETDEWEB) Hikida, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Iizuka, N. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics 2007-06-15 We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS{sub 5}/Z{sub k} to AdS{sub 3}/Z{sub k} case, and we proposed that the AdS{sub 3}/Z{sub k} decays into AdS{sub 3}/Z{sub k'} with k{sup '} < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in different parameter regimes of 't Hooft coupling. We also consider AdS{sub 5} orbifold. The decay of AdS{sub 5}/Z{sub k} is dual to the transition between the vacua of dual gauge theory on R{sub t} x S{sup 3}/Z{sub k}. We constructed the instanton solutions describing the transitions by making use of instanton solutions on R{sub t} x S{sup 2}. (orig.) 4. Invariant differential operators and characters of the AdS4 algebra International Nuclear Information System (INIS) Dobrev, V K 2006-01-01 The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalized to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors of the reducible AdS 4 Verma modules. These are used to obtain the AdS 4 invariant differential operators. Using this we display a new structure-a diagram involving four partially equivalent reducible representations one of which contains all finite-dimensional irreps of the AdS 4 algebra. We study in more detail the cases involving UIRs, in particular, the Di and the Rac singletons, and the massless UIRs. In the massless case, we discover the structure of sets of 2s 0 - 1 conserved currents for each spin s 0 UIR, s 0 = 1, 3/2,.... All massless cases are contained in a one-parameter subfamily of the quartet diagrams mentioned above, the parameter being the spin s 0 . Further we give the classification of the so(5,C) irreps presented in a diagrammatic way which makes easy the derivation of all character formulae. The paper concludes with a speculation on the possible applications of the character formulae to integrable models 5. Ad Hoc Access Gateway Selection Algorithm Science.gov (United States) Jie, Liu With the continuous development of mobile communication technology, Ad Hoc access network has become a hot research, Ad Hoc access network nodes can be used to expand capacity of multi-hop communication range of mobile communication system, even business adjacent to the community, improve edge data rates. For mobile nodes in Ad Hoc network to internet, internet communications in the peer nodes must be achieved through the gateway. Therefore, the key Ad Hoc Access Networks will focus on the discovery gateway, as well as gateway selection in the case of multi-gateway and handover problems between different gateways. This paper considers the mobile node and the gateway, based on the average number of hops from an average access time and the stability of routes, improved gateway selection algorithm were proposed. An improved gateway selection algorithm, which mainly considers the algorithm can improve the access time of Ad Hoc nodes and the continuity of communication between the gateways, were proposed. This can improve the quality of communication across the network. CERN Document Server Natsuume, Makoto 2015-01-01 This book describes applications of the AdS/CFT duality to the "real world." The AdS/CFT duality is an idea that originated from string theory and is a powerful tool for analyzing strongly-coupled gauge theories using classical gravitational theories. In recent years, it has been shown that one prediction of AdS/CFT is indeed close to the experimental result of the real quark–gluon plasma. Since then, the AdS/CFT duality has been applied to various fields of physics; examples are QCD, nuclear physics, condensed-matter physics, and nonequilibrium physics. The aim of this book is to provide background materials such as string theory, black holes, nuclear physics, condensed-matter physics, and nonequilibrium physics as well as key applications of the AdS/CFT duality in a single volume. The emphasis throughout the book is on a pedagogical and intuitive approach focusing on the underlying physical concepts. It also includes step-by-step computations for important results, which are useful for beginners. Th... 7. Spinning strings in AdS3×S3 with NS–NS flux Directory of Open Access Journals (Sweden) Rafael Hernández 2014-11-01 Full Text Available The sigma model describing closed strings rotating in AdS3×S3 is known to reduce to the one-dimensional Neumann–Rosochatius integrable system. In this article we show that closed spinning strings in AdS3×S3×T4 in the presence of NS–NS three-form flux can be described by an extension of the Neumann–Rosochatius system. We consider closed strings rotating with one spin in AdS3 and two different angular momenta in S3. For a class of solutions with constant radii we find the dependence of the classical energy on the spin and the angular momenta as an expansion in the square of the 't Hooft coupling of the theory. 8. On thermodynamics of AdS black holes in M-theory Energy Technology Data Exchange (ETDEWEB) Belhaj, A. [Universite Sultan Moulay Slimane, Departement de Physique, LIRST, Faculte Polydisciplinaire, Beni Mellal (Morocco); Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, FSSM, Marrakesh (Morocco); Chabab, M.; Masmar, K. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, FSSM, Marrakesh (Morocco); El Moumni, H. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, FSSM, Marrakesh (Morocco); Universite Ibn Zohr, Departement de Physique, Faculte des Sciences, Agadir (Morocco); Sedra, M.B. [Universite Ibn Tofail, Departement de Physique, LASIMO, Faculte des Sciences, Kenitra (Morocco) 2016-02-15 Motivated by recent work on asymptotically AdS{sub 4} black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2- and M5-branes. Concretely, we consider AdS black holes in AdS{sub p+2} x S{sup 11-p-2}, where p = 2,5 by interpreting the number of M2- (and M5-branes) as a thermodynamical variable. More precisely, we study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then we compute the thermodynamical curvatures from the Quevedo metric for M2- and M5-branes geometries to reconsider the stability of such black holes. The Quevedo metric singularities recover similar stability results provided by the phase-transition program. It has been shown that similar behaviors are also present in the limit of large N. (orig.) 9. Stability of warped AdS3 vacua of topologically massive gravity International Nuclear Information System (INIS) Anninos, Dionysios; Esole, Mboyo; Guica, Monica 2009-01-01 AdS 3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μl = 1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS 3 vacua with Compere-Detournay boundary conditions are indeed stable in the range μl>3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS 3 vacuum. The situation somewhat resembles chiral gravity: although negative energy modes do exist, they are all excluded by the boundary conditions, and the perturbative spectrum solely consists of boundary (pure large gauge) gravitons. 10. Electric/magnetic deformations of S3 and AdS3, and geometric cosets International Nuclear Information System (INIS) Israel, D.; Kounnas, C.; Marios Petropoulos, P.; Orlando, D. 2005-01-01 We analyze asymmetric marginal deformations of SU(2) k and SL(2,R) k WZW models. These appear in heterotic string backgrounds with non-vanishing Neveu-Schwarz three-forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S 3 or AdS 3 , include in particular geometric cosets such as S 2 , AdS 2 or H 2 . Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS 2 x S 2 background. We also comment on potential holographic applications. (Abstract Copyright [2005], Wiley Periodicals, Inc.) 11. Analytical study on holographic superfluid in AdS soliton background International Nuclear Information System (INIS) Lai, Chuyu; Pan, Qiyuan; Jing, Jiliang; Wang, Yongjiu 2016-01-01 We analytically study the holographic superfluid phase transition in the AdS soliton background by using the variational method for the Sturm–Liouville eigenvalue problem. By investigating the holographic s-wave and p-wave superfluid models in the probe limit, we observe that the spatial component of the gauge field will hinder the phase transition. Moreover, we note that, different from the AdS black hole spacetime, in the AdS soliton background the holographic superfluid phase transition always belongs to the second order and the critical exponent of the system takes the mean-field value in both s-wave and p-wave models. Our analytical results are found to be in good agreement with the numerical findings. 12. Vacuum degeneracy and Conformal Mass in Lovelock AdS gravity Science.gov (United States) Arenas-Henriquez, Gabriel; Miskovic, Olivera; Olea, Rodrigo 2017-11-01 It is shown that the notion of Conformal Mass can be defined within a given anti-de Sitter (AdS) branch of a Lovelock gravity theory as long as the corresponding vacuum is not degenerate. Indeed, conserved charges obtained by the addition of Kounterterms to the bulk action turn out to be proportional to the electric part of the Weyl tensor, when the fall-off of a generic solution in that AdS branch is considered. The factor of proportionality is the degeneracy condition for the vacua in the particular Lovelock AdS theory under study. This last feature explains the obstruction to define Conformal Mass in the degenerate case. OpenAIRE Oral, Mustafa 2013-01-01 Tarihsel gerçeklerin araştırılıp ortaya koyulması yollarından biri de toponomik yadigârların etnonomik,etimolojik ve filolojik açılardan incelenmesidir. Eski kavimlerin birer kültürel varlık olarakgeride bıraktıkları bu adlar, etimolojik ve filolojik olduğu kadar tarihsel kanıtlar ve tanımlar olarak dakullanılabilir. Bu konuda önümüzde bir sorunsal gibi duran Serik adı bunlardan biridir. Türkiye’de tekve özgün meskûn yer adı olması da konuya özel bir önem kazandırmaktadır. Şimdiki Serik adını... CERN Document Server Nastase, Horatiu 2015-01-01 Providing a pedagogical introduction to the rapidly developing field of AdS/CFT correspondence, this is one of the first texts to provide an accessible introduction to all the necessary concepts needed to engage with the methods, tools and applications of AdS/CFT. Without assuming anything beyond an introductory course in quantum field theory, it begins by guiding the reader through the basic concepts of field theory and gauge theory, general relativity, supersymmetry, supergravity, string theory and conformal field theory, before moving on to give a clear and rigorous account of AdS/CFT correspondence. The final section discusses the more specialised applications, including QCD, quark-gluon plasma and condensed matter. This book is self-contained and learner-focused, featuring numerous exercises and examples. It is essential reading for both students and researchers across the fields of particle, nuclear and condensed matter physics. 15. Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes International Nuclear Information System (INIS) Kachru, Shamit; Kundu, Nilay; Saha, Arpan; Samanta, Rickmoy; Trivedi, Sandip P. 2014-01-01 We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS 2 ×S 3 geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or AdS 2 ×S 3 geometries can in turn be connected to AdS 5 spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to AdS 5 spacetime. The asymptotic AdS 5 spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points 16. New Features in the ADS Abstract Service Science.gov (United States) Eichhorn, G.; Accomazzi, A.; Grant, C. S.; Kurtz, M. J.; ReyBacaicoa, V.; Murray, S. S. 2001-11-01 17. What's the point? Hole-ography in Poincare AdS International Nuclear Information System (INIS) Espindola, Ricardo; Gueijosa, Alberto; Landetta, Alberto; Pedraza, Juan F. 2018-01-01 In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS 3 via hole-ography, i.e., in terms of differential entropy of the dual CFT 2 . Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.) 18. The BRST quantization and the no-ghost theorem for AdS3 International Nuclear Information System (INIS) Asano, Masako; Natsuume, Makoto 2003-01-01 In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author) 19. Quantum corrections to short folded superstring in AdS × S × M DEFF Research Database (Denmark) Beccaria, M.; Macorini, G. 2013-01-01 We consider integrable superstring theory on AdS × S × M where M = T or M = S × S with generic ratio of the radii of the two 3-spheres. We compute the one-loop energy of a short folded string spinning in AdS and rotating in S. The computation is performed by world-sheet small spin perturbation...... theory as well as by quantizing the classical algebraic curve characterizing the finite-gap equations. The two methods give equal results up to regularization contributions that are under control. One important byproduct of the calculation is the part of the energy which is due to the dressing phase... 20. Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics Science.gov (United States) Guilleminot, Pablo; Olea, Rodrigo; Petrov, Alexander N. 2018-03-01 We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a D -dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a (D -2 )-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations. 1. Foundations of the AdS5 x S5 superstring: I International Nuclear Information System (INIS) Arutyunov, Gleb; Frolov, Sergey 2009-01-01 We review the recent advances towards finding the spectrum of the AdS 5 x S 5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present part I deals with foundations of classical string theory in AdS 5 x S 5 , light-cone perturbative quantization and the derivation of the exact light-cone world-sheet scattering matrix 2. Spiky strings on AdS3 x S3 with NS-NS flux CERN Document Server 2014-01-01 We study rigidly rotating strings in the background of AdS3 x S3 with Neveu-Schwarz (NS) fluxes. We find two interesting limiting cases corresponding to the known giant magnon and the new single spike solution of strings in the above background and write down the dispersion relations among various conserved charges. We use proper regularization to find the correct relations among them. We further study the circular and infinite spiky strings on AdS and study their properties. International Nuclear Information System (INIS) Geng Huiping; Tang Jingyu; Li Zhihui; Yan Fang; Ouyang Huafu 2012-01-01 In proton accelerators, the Medium Energy Beam Transport (MEBT) line is an essential part for transporting and matching the beam from the RFQ to the next type of accelerating structure. The MEBT is also very important in machine commissioning and tuning. The design of the China Accelerator Driven System is making great progress. The C-ADS project is composed of two independent injectors; therefore, two MEBT lines will be designed independently. In this paper, we will give a detailed description of the MEBT design (including parameter selection and beam dynamics calculation) for the injector I of the C-ADS project. (authors) 4. Ad hoc networks telecommunications and game theory CERN Document Server 2015-01-01 Random SALOHA and CSMA protocols that are used to access MAC in ad hoc networks are very small compared to the multiple and spontaneous use of the transmission channel. So they have low immunity to the problems of packet collisions. Indeed, the transmission time is the critical factor in the operation of such networks. The simulations demonstrate the positive impact of erasure codes on the throughput of the transmission in ad hoc networks. However, the network still suffers from the intermittency and volatility of its efficiency throughout its operation, and it switches quickly to the satura International Nuclear Information System (INIS) Kawano, Teruhiko; Okuyama, Kazumi 2000-01-01 We explicitly calculate a Witten diagram with general spinor field exchange on (d+1)-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the AdS/CFT correspondence, especially in supersymmetric cases. We also show that the amplitude can be reduced to a scalar exchange amplitude. We discuss the operator product expansion of the dual conformal field theory by interpreting the short distance expansion of the amplitude according to the AdS/CFT correspondence CERN Document Server Collier, Ben 2012-01-01 This beginner's guide focuses on getting you through all the major learning points in a smooth, logical order. You'll also see how to avoid some common pitfalls. This book is for brands, advertisers and developers who want to create compelling, emotive, iAd advertisements that generate revenue and increase brand awareness. You don't need previous experience of creating adverts or apps for iPhone and iPad, as you'll be taken through the entire process to make motion-rich, beautiful ads. DEFF Research Database (Denmark) Bechi, Jacopo 2009-01-01 This paper focuses on some issues about condensates and renormalization in AdS/QCD models. In particular we consider the consistency of the AdS/QCD approach for scale dependent quantities as the chiral condensate questioned in some recent papers and the 4D meaning of the 5D cosmological constant...... in a model in which the QCD is dual to a 5D gravity theory. We will be able to give some arguments that the cosmological constant is related to the QCD gluon condensate.... 8. Secondary decay of espalation in ADS reactors International Nuclear Information System (INIS) Rodrigues, Marcos Guedes; Santiago, A.J.; Silva, C.E. da 2013-01-01 We study the problem of evaporation in the context of nuclear spallation reactions in nuclear reactors ADS. The calculation was developed based on the theory of Weisskopf evaporation and in the model of thermal liquid drop. Evaporation affects the 'economy' of neutrons and the design of a ADS reactor in various aspects. It offers abundant amount of neutrons in the nuclear medium, with a wide energy range. For an excitation energy of 3 MeV/n a typical core evaporates about 10% of its mass in the form of light particles (mostly neutrons) 9. Vehicular ad hoc network security and privacy CERN Document Server Lin, X 2015-01-01 Unlike any other book in this area, this book provides innovative solutions to security issues, making this book a must read for anyone working with or studying security measures. Vehicular Ad Hoc Network Security and Privacy mainly focuses on security and privacy issues related to vehicular communication systems. It begins with a comprehensive introduction to vehicular ad hoc network and its unique security threats and privacy concerns and then illustrates how to address those challenges in highly dynamic and large size wireless network environments from multiple perspectives. This book is richly illustrated with detailed designs and results for approaching security and privacy threats. 10. Added Value of Employee Financial Participation NARCIS (Netherlands) Poutsma, F.; Kaarsemaker, E.C.A.; Andresen, M.; Nowak, C. 2015-01-01 This chapter broadens our understanding of the added value of employee financial participation. Financial participation is a generic term for the participation of employees in profit and enterprise results including equity of their employing firm. In general, there are two forms of employee 11. CERN Enters the Second Year AD CERN Document Server 2001-01-01 2001 is the year that physics at CERN's new Antiproton Decelerator (AD) really gets up to speed. Changes to the AD since 2000 mean that this year the three experiments, ASACUSA, ATHENA, and ATRAP have had more intense antiproton beams to work with since physics started on 7 May. CERN's Antiproton Decelerator - major improvements for 2001. The AD is a unique machine. Its job is to decelerate not accelerate particle beams, and it has to handle beam energies that vary by an unprecedented factor of 35 from injection to ejection. Since the machine was designed to operate at fixed energy in its first incarnation as a collector of antiprotons for CERN's 1980s proton antiproton collider, this factor of 35 presented a big challenge to the AD team. The team's design goal was to hang onto a quarter of the injected antiprotons through their vertiginous fall in energy, and to repeat the deceleration cycle once per minute. Improvements to the machine over the winter shutdown and through the first four weeks of 2001 run... Science.gov (United States) Amiri-Sharifi, S.; Ali-Akbari, M.; Kishani-Farahani, A.; Shafie, N. 2016-08-01 We exploit the AdS/CFT correspondence to investigate thermalization in an N = 2 strongly coupled gauge theory including massless fundamental matter (quark). More precisely, we consider the response of a zero temperature state of the gauge theory under influence of an external electric field which leads to a time-dependent current. The holographic dual of the above set-up is given by introducing a time-dependent electric field on the probe D7-brane embedded in an AdS5 ×S5 background. In the dual gravity theory an apparent horizon forms on the brane which, according to AdS/CFT dictionary, is the counterpart of the thermalization process in the gauge theory side. We classify different functions for time-dependent electric field and study their effect on the apparent horizon formation. In the case of pulse functions, where the electric field varies from zero to zero, apart from non-equilibrium phase, we observe the formation of two separate apparent horizons on the brane. This means that the state of the gauge theory experiences two different temperature regimes during its time evolution. NARCIS (Netherlands) Vliet, Harry van An overview of innovations in a particular area, for example retail developments in the fashion sector (Van Vliet, 2014), and a subsequent discussion about the probability as to whether these innovations will realise a ‘breakthrough’, has to be supplemented with the question of what the added value 14. Added Mass of a Spherical Cap Body Czech Academy of Sciences Publication Activity Database Šimčík, Miroslav; Punčochář, Miroslav; Růžička, Marek 2014-01-01 Roč. 118, OCT 18 (2014), s. 1-8 ISSN 0009-2509 R&D Projects: GA MŠk(CZ) LD13018 Institutional support: RVO:67985858 Keywords : spherical cap * added mass * single particle Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 2.337, year: 2014 15. ENEA presenta sistema ADS per trattamento scorie CERN Multimedia 2002-01-01 "Arriva il sistema Ads (Accelerator driven system) per il trattamento dei rifiuti radioattivi. Lo studio di fattibilita' per l' innovativa tecnologia, realizzato da un gruppo di lavoro congiunto Enea, Cea, Cern e Ansaldo, e' stato presentato oggi nel corso di un workshop presieduto dal premio Nobel per la fisica, Carlo Rubbia" (1/2 page). 16. Added value: The differences that count Directory of Open Access Journals (Sweden) Dominique Bouchet 2012-08-01 Full Text Available Clinging to a simplistic conceptualization of the concept of added value might impair our capability to develop insights to what really matters today when companies seek to make differences within the global market. Today it is more necessary than ever to take into account the importance of language and culture as competitive factors. International Nuclear Information System (INIS) Dobrev, V.K. 2002-05-01 We use the group-theoretic interpretation of the AdS/CFT correspondence which we proposed earlier in order to lift intertwining operators acting between boundary conformal representations to intertwining operators acting between bulk conformal representations. Further, we present the classification of the positive energy (lowest weight) unitary irreducible representations of the D=6 superconformal algebras osp(8/2N). (author) 18. First TV ad for dementia care. Science.gov (United States) 2008-12-10 Last month, viewers saw the first-ever TV advertisement about providing care for people with dementia. Screened as part of Bupa's initiative, bringing the issue of dementia care 'out of the shadows,' the ad features Ernie visiting his sister June, who has dementia, in a Bupa care home and shows the personalised care being delivered by specially trained staff. 19. The Concept of added value of FM NARCIS (Netherlands) Jensen, PA; van der Voordt, Theo; Coenen, C; von Felten, D; Balslev-Nielsen, S; Sarasoja, AL; Riratanaphong, C.; Pfenninger, M; Jensen, PA; van der Voordt, DJM; Coenen, C 2012-01-01 Purpose: This chapter presents research perspectives and theoretical reflections on the concept of added value of FM from a variety of academic fields. Methodology: A literature review of the most influential journals within the academic fields of Facilities Management (FM), Corporate Real 20. Hypoglycaemia when adding sulphonylurea to metformin DEFF Research Database (Denmark) Andersen, Stig Ejdrup; Christensen, Mikkel 2016-01-01 AIMS: The risk of hypoglycaemia may differ among sulphonylureas (SUs), but evidence from head-to-head comparisons is sparse. Performing a network meta-analysis to use indirect evidence from randomized controlled trials (RCTs), we compared the relative risk of hypoglycaemia with newer generation SUs...... when added to metformin. METHODS: A systematic review identified RCTs lasting 12-52 weeks and evaluating SUs added to inadequate metformin monotherapy (≥1000 mg/day) in type 2 diabetes. Adding RCTs investigating the active comparators from the identified SU trials, we established a coherent network...... of hypoglycaemia was lowest with gliclazide compared to glipizide (OR 0.22, CrI: 0.05 to 0.96), glimepiride (OR 0.40, CrI: 0.13 to 1.27), and glibenclamide (OR 0.21, CrI: 0.03 to 1.48). A major limitation is varying definitions of hypoglycaemia across studies. CONCLUSIONS: When added to metformin, gliclazide... 1. Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS_5×S"5 spacetime International Nuclear Information System (INIS) Zhang, Jia-Lin; Cai, Rong-Gen; Yu, Hongwei 2015-01-01 We study the thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in AdS_5×S"5 spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we find that the scalar curvature in the Weinhold metric is always vanishing, while in the Ruppeiner metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed chemical potential, and in the Quevedo metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed number of colors and to the vanishing of the heat capacity with fixed chemical potential. 2. Adding Users to the Website Design Process Science.gov (United States) Tomeo, Megan L. 2012-01-01 Alden Library began redesigning its website over a year ago. Throughout the redesign process the students, faculty, and staff that make up the user base were added to the conversation by utilizing several usability test methods. This article focuses on the usability testing conducted at Alden Library and delves into future usability testing, which… 3. Distinguishing between AD and BS Education Science.gov (United States) Michelmore, Ellen 1977-01-01 Topics in this discussion of the differences between associate degree (AD) and baccalaureate (BS) curricula in theoretical content and clinical experience include the following: Distinction by knowledge, the underlying curriculum concepts of national health problems, nursing process, and transfer; simple vs. complex contents; and different… 4. Safety analysis for reactivity insertion on ADS Energy Technology Data Exchange (ETDEWEB) Santos, Marcia S.; Velasquez, Carlos E.; Pereira, Claubia; Veloso, Maria Auxiliadora F.; Costa, Antonella L. [Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG (Brazil). Departamento de Engenharia Nuclear; Barros, Graiciany de P. [Comissão Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil) 2017-07-01 In this work, an accelerator driven system (ADS) has been studied to fuel regeneration, partitioning and transmutation using fuel removed from LWR-spent fuel. This spent fuel was reprocessed by GANEX and then spiked with thorium. Monteburns 2.0 (MCNP5/ORIGEN 2.1) code was used to simulate burnup and neutronic parameters of the systems. However, these systems might be interrupted for some technical problems during few days or long periods to perform maintenance of accelerator systems without shutdown the fission system. Therefore, in this work, the aim was to investigate the nuclear fuel evolution in three different cases with reactivity insertions and variations in the functionality of the ADS. The evaluation has been performed for a burnup of 3 years, which are the most dangerous years in case of reactivity insertions. Therefore, in the first case the ADS during its burnup the external source (spallation source) is cutting off from the system several times during the first year of burnup. In the second case, it is simulated the reactor at different power from 0 (shutdown) to 1.5 times the 515MWt. The results shows the safety limits of the ADS for different situation. (author) 5. Finite temperature effective action, AdS5 black holes, and 1/N expansion International Nuclear Information System (INIS) Alvarez-Gaume, Luis; Gomez, Cesar; Liu Hong; Wadia, Spenta R. 2005-01-01 We propose a phenomenological matrix model to study string theory in AdS 5 xS 5 in the canonical ensemble. The model reproduces all the known qualitative features of the theory. In particular, it gives a simple effective potential description of Euclidean black hole nucleation and the tunneling between thermal anti-de Sitter (AdS) and the big black hole. It also has some interesting predictions. We find that there exists a critical temperature at which the Euclidean small black hole undergoes a Gross-Witten phase transition. We identify the phase transition with the Horowitz-Polchinski point where the black hole horizon size becomes comparable to the string scale. The appearance of the Hagedorn divergence of thermal AdS is due to the merger of saddle points corresponding to the Euclidean small black hole and thermal AdS. The merger can be described in terms of a cusp (A 3 ) catastrophe and divergences at the perturbative string level are smoothed out at finite string coupling using standard techniques of catastrophe theory 6. Jordanian deformations of the AdS5×S5 superstring NARCIS (Netherlands) Kawaguchi, I.; Matsumoto, T.; Yoshida, K 2014-01-01 We consider Jordanian deformations of the AdS_5xS^5 superstring action. The deformations correspond to non-standard q-deformation. In particular, it is possible to perform partial deformations, for example, only for the S^5 part. Then the classical action and the Lax pair are constructed with a 7. What's the point? Hole-ography in Poincare AdS Energy Technology Data Exchange (ETDEWEB) Espindola, Ricardo [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); University of Southampton, Mathematical Sciences and STAG Research Centre, Southampton (United Kingdom); Gueijosa, Alberto; Landetta, Alberto [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); Pedraza, Juan F. [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands) 2018-01-15 In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS{sub 3} via hole-ography, i.e., in terms of differential entropy of the dual CFT{sub 2}. Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.) NARCIS (Netherlands) Smit, E.G.; Neijens, P.C.; Heath, R. 2013-01-01 Building on previous research on the processing of newspaper ads, this comprehensive field study, with 26,556 newspaper readers and 290 unique advertisements, investigated the combined effects of position in the newspaper, ad characteristics and reader characteristics. The results show a 9. Simplified TBA equations of the AdS5 × S5 mirror model NARCIS (Netherlands) Arutyunov, G.E.; Frolov, S. 2009-01-01 We use the recently found integral representation for the dressing phase in the kinematic region of the mirror theory to simplify the TBA equations for the AdS5 × S5 mirror model. The resulting set of equations provides an efficient starting point for both analytic and numerical studies. 10. AdS3/CFT2, finite-gap equations and massless modes International Nuclear Information System (INIS) Lloyd, Thomas; Stefański, Bogdan Jr. 2014-01-01 It is known that string theory on AdS 3 ×M 7 backgrounds, where M 7 =S 3 ×S 3 ×S 1 or S 3 ×T 4 , is classically integrable. This integrability has been previously used to write down a set of integral equations, known as the finite-gap equations. These equations can be solved for the closed string spectrum of the theory. However, it has been known for some time that the finite-gap equations on these AdS 3 ×M 7 backgrounds do not capture the dynamics of the massless modes of the closed string theory. In this paper we re-examine the derivation of the AdS 3 ×M 7 finite-gap system. We find that the conditions that had previously been imposed on these integral equations in order to implement the Virasoro constraints are too strict, and are in fact not required. We identify the correct implementation of the Virasoro constraints on finite-gap equations and show that this new, less restrictive condition captures the complete closed string spectrum on AdS 3 ×M 7 11. Superstrings on AdS4xCP3 from supergravity International Nuclear Information System (INIS) D'Auria, Riccardo; Trigiante, Mario; Fre, Pietro; Grassi, Pietro Antonio 2009-01-01 We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the AdS 4 xCP 3 background. We provide a complete geometrical characterization of the structure of the superfields involved in the action. 12. Entropy of near-extremal black holes in AdS_5 NARCIS (Netherlands) Balasubramanian, V.; de Boer, J.; Jejjala, V.; Simón, J. 2008-01-01 We construct the microstates of near-extremal black holes in AdS_5 x S^5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S^5, and we show that they dominate the entropy by directly 13. Position space analysis of the AdS (in)stability problem NARCIS (Netherlands) Dimitrakopoulos, F.V.; Freivogel, B.; Lippert, M.; Yang, I.S. 2015-01-01 We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the 14. Unitary Supermultiplets of $OSp(8^{}\|4)$ and the $AdS_{7}/CFT_{6}$ Duality CERN Document Server Günaydin, M; Gunaydin, Murat; Takemae, Seiji 2000-01-01 We study the unitary supermultiplets of the N=4 d=7 anti-de Sitter (AdS_7) superalgebra OSp(8^\|4), with the even subalgebra SO(6,2) X USp(4), which is the symmetry superalgebra of M-theory on AdS_7 X S^4. We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8^\|4) . The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS_7 and correspond to superconformal field theories on the boundary of AdS_7 which can be identified with d=6 Minkowski space. We show that the six dimensional Poincare mass operator vanishes identically for the doubleton representations. By going from the compact U(4) basis of SO^(8)=SO(6,2) to the noncompact basis SU^(4)XD (d=6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO^(8) with conformal fields transforming covariantly under the Lorentz group in d=6. The oscillator method used for the construction of the unitary supermultiplets of OSp(8^\|4) can be given ... 15. Foundations of the AdS5 × S5 Superstring Part I NARCIS (Netherlands) Arutyunov, G.E.; Frolov, S. 2009-01-01 We review the recent advances towards finding the spectrum of the AdS_5 x S^5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing 16. Magnetic charges in the AdS(4) superalgebra osp(4 vertical bar 2) NARCIS (Netherlands) Dibitetto, Giuseppe; Klemm, Dietmar 2010-01-01 We discuss the issue of how to include magnetic charges in the AdS(4) superalgebra osp(4 vertical bar 2). It is shown that the usual way of introducing a pseudoscalar central charge on the right hand side of the basic anticommutator does not work, because this breaks SO(2, 3) covariance. We propose 17. Black hole formation in AdS Einstein-Gauss-Bonnet gravity Energy Technology Data Exchange (ETDEWEB) Deppe, Nils [Cornell Center for Astrophysics and Planetary Science andDepartment of Physics, Cornell University,122 Sciences Drive, Ithaca, New York 14853 (United States); Kolly, Allison [Department of Atmospheric and Oceanic Sciences, McGill University,805 Sherbrooke Street West, Montréal, Québec H3A 0B9 (Canada); Frey, Andrew R.; Kunstatter, Gabor [Department of Physics and Winnipeg Institute for Theoretical Physics, University of Winnipeg,515 Portage Avenue, Winnipeg, Manitoba R3B 2E9 (Canada) 2016-10-17 AdS spacetime has been shown numerically to be unstable against a large class of arbitrarily small perturbations. In http://dx.doi.org/10.1103/PhysRevLett.114.071102, the authors presented a preliminary study of the effects on stability of changing the local dynamics by adding a Gauss-Bonnet term to the Einstein action. Here we provide further details as well as new results with improved numerical methods. In particular, we elucidate new structure in Choptuik scaling plots. We also provide evidence of chaotic behavior at the transition between immediate horizon formation and horizon formation after the matter pulse reflects from the AdS conformal boundary. Finally, we present data suggesting the formation of naked singularities in spacetimes with ADM mass below the algebraic bound for black hole formation. 18. Synthesis of studies for ADS development International Nuclear Information System (INIS) Alamo, A.; Balbaud, F.; Beauvais, P.Y.; Courouau, J.L.; Debu, P.; Granget, G.; Latge, Ch.; Leray, S.; Mellier, F.; Pillon, S.; Richard, P.; Rimbault, G.; Salvatores, M.; Terlain, A.; Varaine, F.; Warin, D.; Brissot, R.; Doubre, H.; Flocard, H.; Kirchner, Th.; Mueller, A.; Steckmeyer, J.C.; Carluec, B.; Giraud, B. 2005-01-01 19. Towards an improved duality between tensor network states and AdS spacetime Energy Technology Data Exchange (ETDEWEB) Papadopoulos, Charalampos; Orus, Roman [Institute of Physics, Johannes Gutenberg University, 55099 Mainz (Germany) 2016-07-01 The conjectured AdS/CFT Correspondence, which states that a Conformal Field Theory (CFT) in Minkowski spacetime has a gravity dual in an asymptotically Anti-de Sitter space (AdS), is one of the best understood examples of the holographic principle, and has important applications in condensed matter physics. Tensor Networks (TNs) are a efficient way to calculate low-energy properties for strongly-correlated quantum many-body systems. The Multi-scale Entanglement Renormalization Ansatz (MERA) is a specific TN for a efficient description of critical quantum systems (CFTs). It was recently suggested that the MERA provides naturally a discretization of AdS spacetime on a lattice. It is however known that a conventional MERA can not reproduce the so-called ''Bousso Bound'', also called holographic entropy bound, which is a bound on the bulk entropy in spacetime. In this context, our aim is to generalize the proposed AdS/MERA correspondence to a more general AdS/TN duality, where the Bousso bound is satisfied. Progress in this direction as well as connections to strongly correlated systems will be discussed. 20. Holographic Rényi entropy in AdS3/LCFT2 correspondence International Nuclear Information System (INIS) Chen, Bin; Song, Feng-yan; Zhang, Jia-ju 2014-01-01 The recent study in AdS 3 /CFT 2 correspondence shows that the tree level contribution and 1-loop correction of holographic Rényi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the Rényi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of Rényi entanglement entropy in pure AdS 3 gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the Rényi entanglement entropy of two disjoint intervals with small cross ratio x, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order x 6 . To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS 3 gravity International Nuclear Information System (INIS) Hubeny, Veronika E 2015-01-01 We give a brief review of the AdS/CFT correspondence, which posits the equivalence between a certain gravitational theory and a lower-dimensional non-gravitational one. This remarkable duality, formulated in 1997, has sparked a vigorous research program that has gained in breadth over the years, with applications to many aspects of theoretical (and even experimental) physics, not least to general relativity and quantum gravity. To put the AdS/CFT correspondence into historical context, we start by reviewing the relevant aspects of string theory (of which no prior knowledge is assumed). We then develop the statement of the correspondence, and explain how the two sides of the duality map into each other. Finally, we discuss the implications and applications of the correspondence, and indicate some of the current trends in this subject. The presentation attempts to convey the main concepts in a simple and self-contained manner, relegating supplementary remarks to footnotes. (paper) 2. Profiling value added position in FM DEFF Research Database (Denmark) Katchamart, Akarapong . It is argued that being strategic is not the pre-requisite condition to add value to the core business and stakeholders but rather matching what does FM organization offer - so called FM product - with how does it being offered - so called FM process? By matching FM products with the right FM process, FM...... organizations can best add value. Based on comprehensive literature studies and 7 case studies of private and public organisations from Denmark, Holland, Hong Kong and Thailand, the dissertation analyses, how FM organizations can best create added value. From the analyses the following four value added...... positions have emerged: 1. Support - FM organizations create benefit to its host organization from economies of scope and scale 2. Enable - FM organizations increase the one-off organizational capacity and capability 3. Ensure - FM organizations contribute the business continuity and reliability 4. Enhance... 3. Supporting Dynamic Ad hoc Collaboration Capabilities CERN Document Server Agarwal, D 2003-01-01 Modern HENP experiments such as CMS and Atlas involve as many as 2000 collaborators around the world. Collaborations this large will be unable to meet often enough to support working closely together. Many of the tools currently available for collaboration focus on heavy-weight applications such as videoconferencing tools. While these are important, there is a more basic need for tools that support connecting physicists to work together on an ad hoc or continuous basis. Tools that support the day-to-day connectivity and underlying needs of a group of collaborators are important for providing light-weight, non-intrusive, and flexible ways to work collaboratively. Some example tools include messaging, file-sharing, and shared plot viewers. An important component of the environment is a scalable underlying communication framework. In this paper we will describe our current progress on building a dynamic and ad hoc collaboration environment and our vision for its evolution into a HENP collaboration environment. 4. Evolutionary algorithms for mobile ad hoc networks CERN Document Server Dorronsoro, Bernabé; Danoy, Grégoire; Pigné, Yoann; Bouvry, Pascal 2014-01-01 Describes how evolutionary algorithms (EAs) can be used to identify, model, and minimize day-to-day problems that arise for researchers in optimization and mobile networking. Mobile ad hoc networks (MANETs), vehicular networks (VANETs), sensor networks (SNs), and hybrid networks—each of these require a designer’s keen sense and knowledge of evolutionary algorithms in order to help with the common issues that plague professionals involved in optimization and mobile networking. This book introduces readers to both mobile ad hoc networks and evolutionary algorithms, presenting basic concepts as well as detailed descriptions of each. It demonstrates how metaheuristics and evolutionary algorithms (EAs) can be used to help provide low-cost operations in the optimization process—allowing designers to put some “intelligence” or sophistication into the design. It also offers efficient and accurate information on dissemination algorithms topology management, and mobility models to address challenges in the ... 5. AD/HD: POSSIBLE DIAGNOSIS AND TREATMENT Directory of Open Access Journals (Sweden) Karl REICHELT 2008-12-01 Full Text Available The purpose of this paper is to show that a more exact diagnosis and dietary intervention in AD/HD (Attention Deficit/Hyperactivity Disorder is possible and probable. The clinical symptom based diagnosis we suggest may be supplemented with physiological tests. A genetic and environmental inter-action is clearly involved and explainable using phenylketonuria as a model.Method: Examining peer reviewed published papers on gut to blood, blood to brain interaction and effect of interventions in AD/HD and our own studies in the field. The various treatment options are discussed.Results: It can be shown that a gut to brain activity is possible and probable, and dietary intervention is useful and probably safer than drugs. Preliminary data on a small five year follow up of dietary intervention is shown. 6. AD codes of practice 'pressure vessels' International Nuclear Information System (INIS) Schefe, G. 1978-01-01 Within the AD-Regelwerk, a manual of regulations, the AD codes of practice HP1 and HP20 have been published for the first time. In contrast to the already existing codes of practice of the series HP, these leaflets do not mainly contain changes in the test details and the course of the procedure, but, in a summarized form, that which has been practiced for years. Comments on the new codes concentrate mainly on those things, which are really new, or which might appear to be new. Furthermore, control lists and proposals for printed forms, addressed to designers and supervisors on the side of the manufacturers, are to contribute to the tests being carried out economically. (orig./RW) [de Science.gov (United States) Hasanpour, M.; Shariat, S.; Barnaghi, P.; Hoseinitabatabaei, S. A.; Vahid, S.; Tafazolli, R. 2017-06-01 This paper presents a novel approach in targeting load balancing in ad hoc networks utilizing the properties of quantum game theory. This approach benefits from the instantaneous and information-less capability of entangled particles to synchronize the load balancing strategies in ad hoc networks. The quantum load balancing (QLB) algorithm proposed by this work is implemented on top of OLSR as the baseline routing protocol; its performance is analyzed against the baseline OLSR, and considerable gain is reported regarding some of the main QoS metrics such as delay and jitter. Furthermore, it is shown that QLB algorithm supports a solid stability gain in terms of throughput which stands a proof of concept for the load balancing properties of the proposed theory. 8. Supporting Dynamic Ad hoc Collaboration Capabilities International Nuclear Information System (INIS) Agarwal, Deborah A.; Berket, Karlo 2003-01-01 Modern HENP experiments such as CMS and Atlas involve as many as 2000 collaborators around the world. Collaborations this large will be unable to meet often enough to support working closely together. Many of the tools currently available for collaboration focus on heavy-weight applications such as videoconferencing tools. While these are important, there is a more basic need for tools that support connecting physicists to work together on an ad hoc or continuous basis. Tools that support the day-to-day connectivity and underlying needs of a group of collaborators are important for providing light-weight, non-intrusive, and flexible ways to work collaboratively. Some example tools include messaging, file-sharing, and shared plot viewers. An important component of the environment is a scalable underlying communication framework. In this paper we will describe our current progress on building a dynamic and ad hoc collaboration environment and our vision for its evolution into a HENP collaboration environment 9. LINAC for ADS application - accelerator technologies International Nuclear Information System (INIS) Garnett, Robert W.; Sheffreld, Richard L. 2009-01-01 Sifnificant high-current, high-intensity accelerator research and development have been done in the recent past in the US, centered primarily at Los Alamos National Laboratory. These efforts have included designs for the Accelerator Production of Tritium Project, Accelerator Transmutation of Waste, and Accelerator Driven Systems, as well as many others. This past work and some specific design principles that were developed to optimie linac designs for ADS and other high-intensity applications will be discussed briefly. CERN Document Server Auzzi, Roberto; Gudnason, Sven Bjarke; Rabinovici, Eliezer 2013-01-01 We use the AdS/CFT correspondence to study a thermally isolated conformal field theory in four dimensions which undergoes a repeated deformation by an external periodic time-dependent source coupled to an operator of dimension Delta. The initial state of the theory is taken to be at a finite temperature. We compute the energy dissipated in the system as a function of the frequency and of the dimension Delta of the perturbing operator. This is done in the linear response regime. In order to study the details of thermalization in the dual field theory, the leading-order backreaction on the AdS black brane metric is computed. The evolution of the event and the apparent horizons is monitored; the increase of area in each cycle coincides with the increase in the equilibrium entropy corresponding to the amount of energy dissipated. The time evolution of the entanglement entropy of a spherical region and that of the two-points function of a probe operator with a large dimension are also inspected; we find a delay in... OpenAIRE Ochando, Manuel Blázquez 2015-01-01 12. AD HOC Networks for the Autonomous Car Science.gov (United States) Ron, Davidescu; Negrus, Eugen 2017-10-01 13. Recent developments in nuclear data for ADS International Nuclear Information System (INIS) Talou, P.; Chadwick, M.B.; Young, P.G. 2003-01-01 Modern particle accelerators offer new opportunities to dramatically reshape the way we think about nuclear energy, and challenge some of the thorniest problems linked to its industrial use, e.g. nuclear waste. A powerful proton accelerator driving a sub-critical fission reactor could be used for producing energy more safely and burning up the extra spent fuel which so far has been stored in geological repositories. Although large R and D efforts are required to successfully implement such Accelerator Driven Systems (ADS), an important theoretical effort is also required to extend the nuclear data libraries, originally developed for existing nuclear reactors needs. The energies and isotopes involved in ADS do not necessarily overlap the range covered by the current nuclear reactors, and therefore there is a strong and urgent need to review and complement the nuclear cross sections databases to efficiently and safely build these ADS. In this workshop, we will review some of the strength and deficiencies in the existing nuclear data libraries, for applications to ADS projects. A major step forward to extend these libraries has been achieved recently by the release of the LA150 cross section library [M.B. Chadwick et al., NSE 131, 293 (1999)], evaluating reactions cross sections for different materials important for ADS, up to 150 MeV incident energies. We will devote a rather large fraction of theses lectures to present the latest developments in LA150. We will also present various numerical simulations performed in order to test and benchmark this new data library. Such evaluations rely on nuclear reaction calculations performed with the GNASH code, and on available experimental data. We will therefore briefly review the physical models used in these calculations and present their importance in the GNASH code. Another part in developing accurate nuclear data library consists in the evaluation of available experimental data, as an attempt to significantly reduce the 14. Recent developments in nuclear data for ADS Energy Technology Data Exchange (ETDEWEB) Talou, P [T-16, Nuclear Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos (United States); Chadwick, M B [T-16, Nuclear Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos (United States); Young, P G [T-16, Nuclear Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos (United States) 2003-06-15 Modern particle accelerators offer new opportunities to dramatically reshape the way we think about nuclear energy, and challenge some of the thorniest problems linked to its industrial use, e.g. nuclear waste. A powerful proton accelerator driving a sub-critical fission reactor could be used for producing energy more safely and burning up the extra spent fuel which so far has been stored in geological repositories. Although large R and D efforts are required to successfully implement such Accelerator Driven Systems (ADS), an important theoretical effort is also required to extend the nuclear data libraries, originally developed for existing nuclear reactors needs. The energies and isotopes involved in ADS do not necessarily overlap the range covered by the current nuclear reactors, and therefore there is a strong and urgent need to review and complement the nuclear cross sections databases to efficiently and safely build these ADS. In this workshop, we will review some of the strength and deficiencies in the existing nuclear data libraries, for applications to ADS projects. A major step forward to extend these libraries has been achieved recently by the release of the LA150 cross section library [M.B. Chadwick et al., NSE 131, 293 (1999)], evaluating reactions cross sections for different materials important for ADS, up to 150 MeV incident energies. We will devote a rather large fraction of theses lectures to present the latest developments in LA150. We will also present various numerical simulations performed in order to test and benchmark this new data library. Such evaluations rely on nuclear reaction calculations performed with the GNASH code, and on available experimental data. We will therefore briefly review the physical models used in these calculations and present their importance in the GNASH code. Another part in developing accurate nuclear data library consists in the evaluation of available experimental data, as an attempt to significantly reduce the 15. Partition functions with spin in AdS2 via quasinormal mode methods International Nuclear Information System (INIS) Keeler, Cynthia; Lisbão, Pedro; Ng, Gim Seng 2016-01-01 We extend the results of http://dx.doi.org/10.1007/JHEP06(2014)099, computing one loop partition functions for massive fields with spin half in AdS 2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev http://dx.doi.org/10.1088/0264-9381/27/12/125001. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state \|h〉 and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS 2n and higher spins. 16. Phases of planar AdS black holes with axionic charge International Nuclear Information System (INIS) Caldarelli, Marco M.; Christodoulou, Ariana; Papadimitriou, Ioannis; Skenderis, Kostas 2017-01-01 Planar AdS black holes with axionic charge have finite DC conductivity due to momentum relaxation. We obtain a new family of exact asymptotically AdS 4 black branes with scalar hair, carrying magnetic and axion charge, and we study the thermodynamics and dynamic stability of these, as well as of a number of previously known electric and dyonic solutions with axion charge and scalar hair. The scalar hair for all solutions satisfy mixed boundary conditions, which lead to modified holographic Ward identities, conserved charges and free energy, relative to those following from the more standard Dirichlet boundary conditions. We show that properly accounting for the scalar boundary conditions leads to well defined first law and other thermodynamic relations. Finally, we compute the holographic quantum effective potential for the dual scalar operator and show that dynamical stability of the hairy black branes is equivalent to positivity of the energy density. 17. Vector condensate and AdS soliton instability induced by a magnetic field International Nuclear Information System (INIS) Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wu, You 2014-01-01 We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio 18. Massive quiver matrix models for massive charged particles in AdS Energy Technology Data Exchange (ETDEWEB) Asplund, Curtis T.; Denef, Frederik [Department of Physics, Columbia University,538 West 120th Street, New York, New York 10027 (United States); Dzienkowski, Eric [Department of Physics, Broida Hall, University of California Santa Barbara,Santa Barbara, California 93106 (United States) 2016-01-11 We present a new class of N=4 supersymmetric quiver matrix models and argue that it describes the stringy low-energy dynamics of internally wrapped D-branes in four-dimensional anti-de Sitter (AdS) flux compactifications. The Lagrangians of these models differ from previously studied quiver matrix models by the presence of mass terms, associated with the AdS gravitational potential, as well as additional terms dictated by supersymmetry. These give rise to dynamical phenomena typically associated with the presence of fluxes, such as fuzzy membranes, internal cyclotron motion and the appearance of confining strings. We also show how these models can be obtained by dimensional reduction of four-dimensional supersymmetric quiver gauge theories on a three-sphere. 19. The AdS5xS5 superstring worldsheet S matrix and crossing symmetry International Nuclear Information System (INIS) Janik, Romuald A. 2006-01-01 An S matrix satisfying the Yang-Baxter equation with symmetries relevant to the AdS 5 xS 5 superstring recently has been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations; however, due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS 5 xS 5 superstring worldsheet S matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling-constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S matrix in the generalized rapidity plane 20. On supersymmetric AdS6 solutions in 10 and 11 dimensions Science.gov (United States) 2017-12-01 We prove a non-existence theorem for smooth, supersymmetric, warped AdS 6 solutions with connected, compact without boundary internal space in D = 11 and (massive) IIA supergravities. In IIB supergravity we show that if such AdS 6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bilinears must be appropriately restricted. Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two. We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F × S 2, where F is an oriented surface. 1. A universal counting of black hole microstates in AdS4 Science.gov (United States) Azzurli, Francesco; Bobev, Nikolay; Crichigno, P. Marcos; Min, Vincent S.; Zaffaroni, Alberto 2018-02-01 Many three-dimensional N=2 SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS4 magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS2 solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces. Directory of Open Access Journals (Sweden) Dao-Quan Sun 2017-01-01 Full Text Available It is well-known that the nonstrictly thermal character of the Hawking radiation spectrum generates a natural correspondence between Hawking radiation and black hole quasinormal modes. This main issue has been analyzed in the framework of Schwarzschild black holes, Kerr black holes, and nonextremal Reissner-Nordstrom black holes. In this paper, by introducing the effective temperature, we reanalyze the nonstrictly thermal character of large AdS black holes. The results show that the effective mass corresponding to the effective temperature is approximatively the average one in any dimension. And the other effective quantities can also be obtained. Based on the known forms of frequency in quasinormal modes, we reanalyze the asymptotic frequencies of the large AdS black hole in three and five dimensions. Then we get the formulas of the Bekenstein-Hawking entropy and the horizon’s area quantization with functions of the quantum “overtone” number n. 3. Radiatively induced symmetry breaking and the conformally coupled magnetic monopole in AdS space Science.gov (United States) Edery, Ariel; Graham, Noah 2013-11-01 We implement quantum corrections for a magnetic monopole in a classically conformally invariant theory containing gravity. This yields the trace (conformal) anomaly and introduces a length scale in a natural fashion via the process of renormalization. We evaluate the one-loop effective potential and extract the vacuum expectation value (VEV) from it; spontaneous symmetry breaking is radiatively induced. The VEV is set at the renormalization scale M and we exchange the dimensionless scalar coupling constant for the dimensionful VEV via dimensional transmutation. The asymptotic (background) spacetime is anti-de Sitter (AdS) and its Ricci scalar is determined entirely by the VEV. We obtain analytical asymptotic solutions to the coupled set of equations governing gravitational, gauge and scalar fields that yield the magnetic monopole in an AdS spacetime. 4. Dualities in D=5, N=2 supergravity, black hole entropy, and AdS central charges International Nuclear Information System (INIS) Klemm, D. 2001-01-01 The issue of microstate counting for general black holes in D=5, N=2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS 2 . Furthermore, we show that the considered supergravity theory enjoys a duality invariance which connects electrically charged black holes and magnetically charged black strings. The near-horizon geometry of the latter turns out to be AdS 3 x S 2 , which allows a microscopic calculation of their entropy using the Brown-Hennaux central charges in Cardy's formula. In both approaches we find perfect agreement between statistical and thermodynamical entropy. (orig.) 5. Renormalization, averaging, conservation laws and AdS (in)stability International Nuclear Information System (INIS) Craps, Ben; Evnin, Oleg; Vanhoof, Joris 2015-01-01 We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory. 6. Infrared realization of dS2 in AdS2 Science.gov (United States) Anninos, Dionysios; Hofman, Diego M. 2018-04-01 We describe a two-dimensional geometry that smoothly interpolates between an asymptotically AdS2 geometry and the static patch of dS2. We find this ‘centaur’ geometry to be a solution of dilaton gravity with a specific class of potentials for the dilaton. We interpret the centaur geometry as a thermal state in the putative quantum mechanics dual to the AdS2 evolved with the global Hamiltonian. We compute the thermodynamic properties and observe that the centaur state has finite entropy and positive specific heat. The static patch is the infrared part of the centaur geometry. We discuss boundary observables sensitive to the static patch region. 7. Position space analysis of the AdS (in)stability problem Science.gov (United States) Dimitrakopoulos, Fotios V.; Freivogel, Ben; Lippert, Matthew; Yang, I.-Sheng 2015-08-01 We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the space of initial conditions does not collapse on this time scale. We perform an analysis in position space to study this puzzle, and our formalism allows us to directly study the vanishing-amplitude limit. We show that gravitational self-interaction leads to tidal deformations which are equally likely to focus or defocus energy, and we sketch the phase diagram accordingly. We also clarify the connection between gravitational evolution in global AdS and holographic thermalization. 8. Position space analysis of the AdS (in)stability problem Energy Technology Data Exchange (ETDEWEB) Dimitrakopoulos, Fotios V.; Freivogel, Ben; Lippert, Matthew; Yang, I-Sheng [ITFA and GRAPPA, Universiteit van Amsterdam,Science Park 904, 1090 GL Amsterdam (Netherlands) 2015-08-17 We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the space of initial conditions does not collapse on this time scale. We perform an analysis in position space to study this puzzle, and our formalism allows us to directly study the vanishing-amplitude limit. We show that gravitational self-interaction leads to tidal deformations which are equally likely to focus or defocus energy, and we sketch the phase diagram accordingly. We also clarify the connection between gravitational evolution in global AdS and holographic thermalization. 9. Bulk Fields and Supersymmetry in a Slice of AdS CERN Document Server Gherghetta, Tony; Gherghetta, Tony; Pomarol, Alex 2000-01-01 Five-dimensional models where the bulk is a slice of AdS have the virtue of solving the hierarchy problem. The electroweak scale is generated by a warp'' factor of the induced metric on the brane where the standard model fields live. However, it is not necessary to confine the standard model fields on the brane and we analyze the possibility of having the fields actually living in the slice of AdS. Specifically, we study the behaviour of fermions, gauge bosons and scalars in this geometry and their implications on electroweak physics. These scenarios can provide an explanation of the fermion mass hierarchy by warp factors. We also consider the case of supersymmetry in the bulk, and analyze the conditions on the mass spectrum. Finally, a model is proposed where the warp factor generates a small (TeV) supersymmetry-breaking scale, with the gauge interactions mediating the breaking to the scalar sector. 10. Extremal static AdS black hole/CFT correspondence in gauged supergravities International Nuclear Information System (INIS) Lue, H.; Mei Jianwei; Pope, C.N.; Vazquez-Poritz, Justin F. 2009-01-01 A recently proposed holographic duality allows the Bekenstein-Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza-Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions 11. Partition functions in even dimensional AdS via quasinormal mode methods International Nuclear Information System (INIS) Keeler, Cynthia; Ng, Gim Seng 2014-01-01 In this note, we calculate the one-loop determinant for a massive scalar (with conformal dimension Δ) in even-dimensional AdS d+1 space, using the quasinormal mode method developed in http://dx.doi.org/10.1088/0264-9381/27/12/125001 by Denef, Hartnoll, and Sachdev. Working first in two dimensions on the related Euclidean hyperbolic plane H 2 , we find a series of zero modes for negative real values of Δ whose presence indicates a series of poles in the one-loop partition function Z(Δ) in the Δ complex plane; these poles contribute temperature-independent terms to the thermal AdS partition function computed in http://dx.doi.org/10.1088/0264-9381/27/12/125001. Our results match those in a series of papers by Camporesi and Higuchi, as well as Gopakumar et al. http://dx.doi.org/10.1007/JHEP11(2011)010 and Banerjee et al. http://dx.doi.org/10.1007/JHEP03(2011)147. We additionally examine the meaning of these zero modes, finding that they Wick-rotate to quasinormal modes of the AdS 2 black hole. They are also interpretable as matrix elements of the discrete series representations of SO(2,1) in the space of smooth functions on S 1 . We generalize our results to general even dimensional AdS 2n , again finding a series of zero modes which are related to discrete series representations of SO(2n,1), the motion group of H 2n . International Nuclear Information System (INIS) Kim, Nakwoo; Park, Jong-Dae 2006-01-01 We study the supersymmetric solutions of 11-dimensional supergravity with a factor of AdS 2 made of M2-branes. Such solutions can provide gravity duals of superconformal quantum mechanics, or through double Wick rotation, the generic bubbling geometry of M-theory which are 1/16-BPS. We show that, when the internal manifold is compact, it should take the form of a warped U(1)-fibration over an 8-dimensional Kaehler space 13. New holographic limit of AdS5(multiply-in-circle sign)S5 International Nuclear Information System (INIS) Hatsuda, Machiko; Siegel, Warren 2003-01-01 We reexamine the projective light cone limit of the gauge-invariant Green-Schwarz action on five-dimensional anti-de Sitter (multiply-in-circle sign) the five-sphere. It implies the usual holography for AdS 5 , but also (a complex) one for S 5 . The result is N=4 projective superspace, which unlike N=4 harmonic superspace can describe N=4 super Yang-Mills theory off shell 14. Time-dependent AdS backgrounds from S-branes Energy Technology Data Exchange (ETDEWEB) Deger, Nihat Sadik, E-mail: sadik.deger@boun.edu.tr [Department of Mathematics, Bogazici University, Bebek, 34342, Istanbul (Turkey); Feza Gursey Center for Physics and Mathematics, Bogazici University, Kandilli, 34684, Istanbul (Turkey) 2016-11-10 We construct time and radial dependent solutions that describe p-branes in chargeless S-brane backgrounds. In particular, there are some new M5- and D3-branes among our solutions which have AdS limits and contain a cosmological singularity as well. We also find a time-dependent version of the dyonic membrane configuration in 11-dimensions by applying a Lunin–Maldacena deformation to our new M5-brane solution. 15. Exact microstate counting for dyonic black holes in AdS4 Science.gov (United States) Benini, Francesco; Hristov, Kiril; Zaffaroni, Alberto 2017-08-01 We present a counting of microstates of a class of dyonic BPS black holes in AdS4 which precisely reproduces their Bekenstein-Hawking entropy. The counting is performed in the dual boundary description, that provides a non-perturbative definition of quantum gravity, in terms of a twisted and mass-deformed ABJM theory. We evaluate its twisted index and propose an extremization principle to extract the entropy, which reproduces the attractor mechanism in gauged supergravity. 16. Exact microstate counting for dyonic black holes in AdS4 Directory of Open Access Journals (Sweden) Francesco Benini 2017-08-01 Full Text Available We present a counting of microstates of a class of dyonic BPS black holes in AdS4 which precisely reproduces their Bekenstein–Hawking entropy. The counting is performed in the dual boundary description, that provides a non-perturbative definition of quantum gravity, in terms of a twisted and mass-deformed ABJM theory. We evaluate its twisted index and propose an extremization principle to extract the entropy, which reproduces the attractor mechanism in gauged supergravity. 17. Perturbative calculation of quasinormal modes of AdS Schwarzschild black holes International Nuclear Information System (INIS) Musiri, Suphot; Ness, Scott; Siopsis, George 2006-01-01 We calculate analytically quasinormal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasinormal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic 18. On the Rotating and Oscillating strings in $(AdS_3\\times S^3)_{\\varkappa}$ CERN Document Server Banerjee, Aritra 2014-01-01 We study rigidly rotating strings in the $\\varkappa$-deformed $AdS_3 \\times S^3$ background. We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating is two $S^2_{\\varkappa}$ subspace of rotations reduced along two different isometries. We verify that the dispersion relations reduce to the well known relation in the $\\varkappa\\rightarrow 0$ limit. We further study some oscillating string solutions in the $S^3_{\\varkappa}$ subspace. 19. Perbedaan Perusahan Pencipta Economic Value Added Positif Dengan Economic Value Added Negatif OpenAIRE Suripto, Suripto 2008-01-01 This research was to explain and analyze the different variable of Inflation Rate,Exchange Rate, Interest Rate, Ratio Plant Asset, Size Measure Company, Profitability, Growth ,LD / E, TD / TA, Stock of Return, Book To Market between company having Economic ValueAdded ( Positive ) and company having Economic Value Added ( Negative ). Analysis which wasused in this research was multivariate analysis of variant (MANOVA). There was different variableof Inflation Rate, Exchange Rate, Interest Rate... 20. Sound modes in holographic hydrodynamics for charged AdS black hole International Nuclear Information System (INIS) Matsuo, Yoshinori; Sin, Sang-Jin; Takeuchi, Shingo; Tsukioka, Takuya; Yoo, Chul-Moon 2009-01-01 In the previous paper we studied the transport coefficients of quark-gluon plasma in finite temperature and finite density in vector and tensor modes. In this paper, we extend it to the scalar modes. We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity. We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly. 1. One loop partition function of six dimensional conformal gravity using heat kernel on AdS Energy Technology Data Exchange (ETDEWEB) Lovreković, Iva [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria) 2016-10-13 We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach introduced in http://dx.doi.org/10.1007/JHEP11(2011)010 and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost and two modes that contain mass. 2. Closed-String Tachyons and the Hagedorn Transition in AdS Space CERN Document Server Barbón, José L F 2002-01-01 We discuss some aspects of the behaviour of a string gas at the Hagedorn temperature from a Euclidean point of view. Using AdS space as an infrared regulator, the Hagedorn tachyon can be effectively quasi-localized and its dynamics controled by a finite energetic balance. We propose that the off-shell RG flow matches to an Euclidean AdS black hole geometry in a generalization of the string/black-hole correspondence principle. The final stage of the RG flow can be interpreted semiclassically as the growth of a cool black hole in a hotter radiation bath. The end-point of the condensation is the large Euclidan AdS black hole, and the part of spacetime behind the horizon has been removed. In the flat-space limit, holography is manifest by the system creating its own transverse screen at infinity. This leads to an argument, based on the energetics of the system, explaining why the non-supersymmetric type 0A string theory decays into the supersymmetric type IIB vacuum. We also suggest a notion of `boundary entropy'... 3. Holographic dual of de Sitter universe with AdS bubbles International Nuclear Information System (INIS) Kanno, Sugumi; Sasaki, Misao; Soda, Jiro 2012-01-01 We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general d+1 spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or odd. We find that the absorption process of gravitons from the dS universe by CFT matter is controlled by localized gravitons (massive bound state modes in the Kaluza-Klein decomposition) in the dS universe. The absorption probability is determined by the effective degrees of freedom of the CFT matter and the effective gravitational coupling constant which encodes information of localized gravitons. We speculate that the dual of (d+1)-dimensional dS universe with an AdS bubble is also dual to a d-dimensional dS universe with CFT matter. 4. State Operator Correspondence and Entanglement in AdS2/CFT1 Directory of Open Access Journals (Sweden) Ashoke Sen 2011-07-01 Full Text Available Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS2 × K are described by the twisted version of the Hartle–Hawking states, the twists being generated by a large unitary group of symmetries that this string theory must possess. This formalism makes natural the dual interpretation of the black hole entropy—as the logarithm of the degeneracy of ground states of the quantum mechanics describing the low energy dynamics of the black hole, and also as an entanglement entropy between the two copies of the same quantum theory living on the two boundaries of global AdS2 separated by the event horizon. Directory of Open Access Journals (Sweden) Rosa Maria Martelo 2004-10-01 6. Vacuum currents in braneworlds on AdS bulk with compact dimensions Science.gov (United States) Bellucci, S.; Saharian, A. A.; Vardanyan, V. 2015-11-01 The two-point function and the vacuum expectation value (VEV) of the current density are investigated for a massive charged scalar field with arbitrary curvature coupling in the geometry of a brane on the background of AdS spacetime with partial toroidal compactification. The presence of a gauge field flux, enclosed by compact dimensions, is assumed. On the brane the field obeys Robin boundary condition and along compact dimensions periodicity conditions with general phases are imposed. There is a range in the space of the values for the coefficient in the boundary condition where the Poincaré vacuum is unstable. This range depends on the location of the brane and is different for the regions between the brane and AdS boundary and between the brane and the horizon. In models with compact dimensions the stability condition is less restrictive than that for the AdS bulk with trivial topology. The vacuum charge density and the components of the current along non-compact dimensions vanish. The VEV of the current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It is decomposed into the boundary-free and brane-induced contributions. The asymptotic behavior of the latter is investigated near the brane, near the AdS boundary and near the horizon. It is shown that, in contrast to the VEVs of the field squared an denergy-momentum tensor, the current density is finite on the brane and vanishes for the special case of Dirichlet boundary condition. Both the boundary-free and brane-induced contributions vanish on the AdS boundary. The brane-induced contribution vanishes on the horizon and for points near the horizon the current is dominated by the boundary-free part. In the near-horizon limit, the latter is connected to the corresponding quantity for a massless field in the Minkowski bulk by a simple conformal relation. Depending on the value of the Robin coefficient, the presence of the brane can either 7. F-theory and AdS3/CFT2 (2, 0) Science.gov (United States) Couzens, Christopher; Martelli, Dario; Schäfer-Nameki, Sakura 2018-06-01 We continue to develop the program initiated in [1] of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d N=(0,2) supersymmetry,wederivethegeneralconditionsonthegeometryforTypeIIB AdS3 solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold Y_8^{τ } , which is elliptically fibered over a base \\tilde{M}_6 . We construct two classes of solutions given in terms of a product ansatz \\tilde{M}_6}=Σ × {M}_4 , where Σ is a complex curve and \\tilde{M}_4 is locally a Kähler surface. In the first class \\tilde{M}_4 is globally a Kähler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS3 × K3 × ℳ 5 τ , dual to 2d (0, 2) SCFTs, and AdS3 × S 3/Γ × CY 3, dual to 2d (0, 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d N=(2,2) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs. Science.gov (United States) Avery, Steven G.; Chowdhury, Borun D. 2014-10-01 Several recent papers argue against firewalls by relaxing the requirement for locality outside the stretched horizon. In the firewall argument, locality essentially serves the purpose of ensuring that the degrees of freedom required for infall are those in the proximity of the black hole and not the ones in the early radiation. We make the firewall argument sharper by utilizing the AdS/CFT framework and claim that the firewall argument essentially states that the dual to a thermal state in the CFT is a firewall. 9. The concept of added value of FM DEFF Research Database (Denmark) Jensen, Per Anker; van der Voordt, Theo; Coenen, Christian 2012-01-01 Management (CREM) and Business to Business Marketing (B2B Marketing). Findings: The research shows different definitions and focus points, dependent on the academic field and the area of application. The different research perspectives explored a holistic view on the added value of FM by the integration...... of an external market based view (with a focus on the aimed output) and the internal resource based view (with a focus on the input from FM and real estate). Good relationship management and building on trust shows to be equally important as delivering the agreed services. Practical implications: A clear... Directory of Open Access Journals (Sweden) Borivoj Galović 2002-01-01 Full Text Available The CU/Tent system of air traffic is facing many drawbacksand problems that restrict its further development and makes itdifficult to follow the trends of increase in the traffic volume.By means of their technology, the systems such as ADS-8create rhe basis for further building, upgrading, improving anddeveloping of a completely new concept of the air traffic system.Through their functions they fully fit into and support the basicfunctions of communication, navigation and swveillancewhich form the basis of the new concept that needs to be implementedas soon as possible. 11. Status of Cea spallation modules for ads International Nuclear Information System (INIS) Enderle, R.; Poitevin, Y.; Deffain, J.P.; Bergeron, J. 2001-01-01 In the framework of CEA studies on ADS dedicated to waste transmutation, a liquid metal reference concept and an alternative solid target have been evaluated to produce neutrons inside the spallation module. This work examines the design (neutronic, thermohydraulic and mechanical aspects) and the performances of both options. It is shown that a liquid Pb-Bi target offers more possibilities regarding to high protons current densities (possible industrial extrapolation) but that a solid target made with tungsten particles offers also interesting ability to create a neutrons flux appropriated (strong spectrum and flat axial distribution) to an sub-critical core dedicated to incineration. (author) 12. Adding value through social media : case Autokiila OpenAIRE Terinkoski, Topias 2012-01-01 Social media has reached wide popularity among people during its short history. It has even displaced forms of traditional media like TV in people’s daily time consumption. Social media has given voice to consumers who are very eager to share their experiences with others. This has created a whole new problem for companies. Companies don’t master customers with ad-vertisements any more but experiences of other consumers have become important aspect on purchase decision-making. Free-flowin... 13. Adding control to arbitrary unknown quantum operations Science.gov (United States) Zhou, Xiao-Qi; Ralph, Timothy C.; Kalasuwan, Pruet; Zhang, Mian; Peruzzo, Alberto; Lanyon, Benjamin P.; O'Brien, Jeremy L. 2011-01-01 Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity. PMID:21811242 14. AORTA: Adding Organizational Reasoning to Agents DEFF Research Database (Denmark) Jensen, Andreas Schmidt; Dignum, Virginia 2014-01-01 the expected behavior of the agents. Agents need to be able to reason about the regulations, so that they can act within the expected boundaries and work towards the objectives of the organization. This extended abstract introduces AORTA, a component that can be integrated into agents’ reasoning mechanism......, allowing them to reason about (and act upon) regulations specified by an organizational model using simple reasoning rules. The added value is that the organizational model is independent of that of the agents, and that the approach is not tied to a specific organizational model.... 15. Visual attention: the interplay between ad characteristics and context factors NARCIS (Netherlands) Boerman, S.; Smit, E.; van Meurs, A. 2011-01-01 Using eye-tracking data, we tested what elements of the ad are able to catch the eye and whether the context of the ad can draw visual attention away. Characteristics of 183 magazine ads and their direct context were systematically coded and linked to eye-tracking data. Results showed that indeed ad 16. The AD: The unique anti-accelerator CERN Multimedia Slide show by Maximilien Brice. Voice (French only): Jacques Fichet. Content: Paola Catapano, Django Manglunki, CERN Bulletin 2011-01-01 Unlike other machines whose performance is measured in terms of energy records, AD's uniqueness resides in the fact that it can very effectively decelerate beams. At the hearth of antimatter production at CERN, the AD is making headlines in the world's press. This provides an excellent opportunity for us to retrace its history in images. var flash_video_player=get_video_player_path(); insert_player_for_external('Video/Public/Movies/2011/CERN-MOVIE-2011-083/CERN-MOVIE-2011-083-0753-kbps-480x360-25-fps-audio-64-kbps-44-kHz-stereo', 'mms://mediastream.cern.ch/MediaArchive/Video/Public/Movies/2011/CERN-MOVIE-2011-083/CERN-MOVIE-2011-083-0480-kbps-384x288-25-fps-audio-128-kbps-48-kHz-stereo.wmv', 'false', 480, 360, 'http://mediaarchive.cern.ch/MediaArchive/Video/Public/Movies/2011/CERN-MOVIE-2011-083/CERN-MOVIE-2011-083-posterframe-480x360-at-5-percent.jpg', '1357551', true, ''); 17. Added values of photovoltaic power systems International Nuclear Information System (INIS) 2001-03-01 The structure, ownership and operation of electricity systems around the world are changing in response to industry restructuring, the availability of new technologies and increasing environmental awareness. At the same time, many countries have yet to provide basic energy services for their populations, particularly in areas not served by the electricity grid. Large-scale, central power generation and distribution which characterized the electricity industry for much of the 20 th century is being challenged by new technologies, which are cleaner, faster to deploy and better matched to local requirements. Higher values are being placed on ancillary services, such as power system reliability and voltage stability, so that a simple comparison of energy cost is no longer appropriate as a measure of competitiveness. Solar photovoltaic electricity is unique amongst the new energy sources for the wide range of energy and non-energy benefits which can be provided, while the use of photovoltaic power systems as an integral part of a building provides the greatest opportunity for exploiting non-energy benefits and for adding value to the photovoltaic power system. This report documents the potential added values or non-energy benefits photovoltaic power systems can provide, the current state of market development and the key barriers faced by renewable energy technologies generally and photovoltaic power systems in particular. Means by which non-energy benefits may be used to overcome barriers to the use of photovoltaic power systems are then discussed, with specific attention to the use of building integrated photovoltaics. (author) 18. Added values of photovoltaic power systems Energy Technology Data Exchange (ETDEWEB) NONE 2001-03-15 The structure, ownership and operation of electricity systems around the world are changing in response to industry restructuring, the availability of new technologies and increasing environmental awareness. At the same time, many countries have yet to provide basic energy services for their populations, particularly in areas not served by the electricity grid. Large-scale, central power generation and distribution which characterized the electricity industry for much of the 20{sup th} century is being challenged by new technologies, which are cleaner, faster to deploy and better matched to local requirements. Higher values are being placed on ancillary services, such as power system reliability and voltage stability, so that a simple comparison of energy cost is no longer appropriate as a measure of competitiveness. Solar photovoltaic electricity is unique amongst the new energy sources for the wide range of energy and non-energy benefits which can be provided, while the use of photovoltaic power systems as an integral part of a building provides the greatest opportunity for exploiting non-energy benefits and for adding value to the photovoltaic power system. This report documents the potential added values or non-energy benefits photovoltaic power systems can provide, the current state of market development and the key barriers faced by renewable energy technologies generally and photovoltaic power systems in particular. Means by which non-energy benefits may be used to overcome barriers to the use of photovoltaic power systems are then discussed, with specific attention to the use of building integrated photovoltaics. (author) 19. AD performance and its extension towards ELENA Energy Technology Data Exchange (ETDEWEB) Oelert, Walter, E-mail: w.oelert@fz-juelich.de [Forschungszentrum Juelich (Germany); Eriksson, Tommy, E-mail: Tommy.Eriksson@cern.ch; Belochitskii, Pavel, E-mail: Pavel.Beloshitsky@cern.ch; Tranquille, Gerard, E-mail: Gerard.Tranquille@cern.ch [CERN (Switzerland) 2012-12-15 The CERN's Antiproton Decelerator (AD) is devoted to special experiments with low energy antiprotons. A main topic is the antihydrogen production with the present aim to produce these antimatter atoms with such low energy that they can be trapped in a magnetic gradient field. First very convincing results have been published recently by ALPHA. Still, it appears to be cumbersome, time consuming and ineffective when collecting the needed large numbers and high densities of antiproton clouds with the present AD. Both the effectiveness and the availability for additional experiments at this unique facility would drastically increase, if the antiproton beam of presently 5 MeV kinetic energy would be reduced by an additional decelerator to something like 100 keV. Such a facility 'ELENA', as an abbreviation for Extra Low ENergy Antiproton Ring and first discussed in 1982 for LEAR, was freshly proposed with a substantial new design and revised layout and is presently under consideration. ELENA will increase the number of useful antiprotons by up to two orders of magnitude and will allow to serve up to four experiments in parallel. 20. AD performance and its extension towards ELENA International Nuclear Information System (INIS) Oelert, Walter; Eriksson, Tommy; Belochitskii, Pavel; Tranquille, Gerard 2012-01-01 The CERN’s Antiproton Decelerator (AD) is devoted to special experiments with low energy antiprotons. A main topic is the antihydrogen production with the present aim to produce these antimatter atoms with such low energy that they can be trapped in a magnetic gradient field. First very convincing results have been published recently by ALPHA. Still, it appears to be cumbersome, time consuming and ineffective when collecting the needed large numbers and high densities of antiproton clouds with the present AD. Both the effectiveness and the availability for additional experiments at this unique facility would drastically increase, if the antiproton beam of presently 5 MeV kinetic energy would be reduced by an additional decelerator to something like 100 keV. Such a facility ”ELENA”, as an abbreviation for Extra Low ENergy Antiproton Ring and first discussed in 1982 for LEAR, was freshly proposed with a substantial new design and revised layout and is presently under consideration. ELENA will increase the number of useful antiprotons by up to two orders of magnitude and will allow to serve up to four experiments in parallel. 1. Neutronics and shielding issues of ADS International Nuclear Information System (INIS) Abderrahim, H. A.; Aoust, T.; Haeck, W.; Malambu, E.; Van den Eynde, G.; Gonzalez, E.; Vicente, C.; Martinez-Val, J. M.; Romanets, Y.; Vaz, P. 2007-01-01 Accelerator Driven Systems (ADS) are hybrid systems consisting of a high-intensity proton accelerator with beam energy in the hundreds of MeV range impinging in a target of a heavy element and coupled to a sub-critical core. The intense (of the order of 10 1 5 n/cm 2 /s) and fast neutron fluxes produced by the spallation reactions triggered by the impinging protons in the target can be used to induce fission reactions in the actinides and capture reactions in the longlived fission products in the fuel assemblies in the core of the system. ADS have been considered during the last fifteen years as one of the promising technological solutions for the transmutation of nuclear waste, reducing the radiotoxicity of the high-level nuclear waste and reducing the burden to the geological repositories. The European Commission's Green Paper entitled 'Towards a European Strategy for the Security of Energy Supply' clearly pointed out the importance of nuclear energy in Europe. With 145 operating reactors producing a total power of 125 GWe, the resulting energy generation of 850 TWh per year provides 35% of the electricity consumption of the European Union. The Green Paper also points out that the nuclear industry has mastered the entire nuclear fuel cycle with the exception of waste management and for this reason, 'focusing on waste management has to be continued'. Amongst the several solutions being studied in recent years, MYRRHA (concept developed at SCK-CEN, Belgium), XADS (design studies co-funded by the European Union in the framework of the 5th Framework Programme) and XT-ADS and EFIT (acronyms standing for an experimental machine and for the long term transmuter to be deployed on an industrial scale, both in the EUROTRANS project of the 6th Framework Programme) have deserved the attention of different communities of specialists in the field of Nuclear Technology and Radioactive Waste Management. Although these machines have been designed with different parameters, their 2. An alternative path to the boundary: The CFT as the Fourier space of AdS Science.gov (United States) Tolfree, Ian M. 2009-12-01 In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the 3. Zooming in on AdS3/CFT2 near a BPS bound Science.gov (United States) Hartong, Jelle; Lei, Yang; Obers, Niels; Oling, Gerben 2018-05-01 Any ( d + 1)-dimensional CFT with a U(1) flavor symmetry, a BPS bound and an exactly marginal coupling admits a decoupling limit in which one zooms in on the spectrum close to the bound. This limit is an Inönü-Wigner contraction of so(2 , d+1)⊕ u(1) that leads to a relativistic algebra with a scaling generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian and by adding a second u(1) we find a contraction of two copies of sl(2, ℝ) ⊕ u(1) to two copies of P 2 c , the 2-dimensional centrally extended Poincaré algebra. We show that the bulk is described by a novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan geometry. Both the Chern-Simons action on sl(2, ℝ) ⊕ u(1) and the entire phase space of asymptotically AdS3 spacetimes are well-behaved in the corresponding limit if we fix the radial component for the u(1) connection. With this choice, the resulting Newton-Cartan foliation structure is now associated not with time, but with the emerging holographic direction. Since the leaves of this foliation do not mix, the emergence of the holographic direction is much simpler than in AdS3 holography. Furthermore, we show that the asymptotic symmetry algebra of the limit theory consists of a left- and a right-moving warped Virasoro algebra. 4. The effects of openness on attitude toward the ad, attitude toward the brand, and brand beliefs in Dutch magazine ads NARCIS (Netherlands) Ketelaar, P.E.; Gisbergen, M.S. van; Bosman, J.A.M.; Beentjes, J.W.J. 2010-01-01 In recent decades, magazine advertisers have used an increasing number of open ads. Open ads do not guide consumers towards a specific interpretation as traditional ads do, and they require more effort to decipher. An experiment was carried out to determine the effects of ad openness on the attitude 5. Wess-Zumino term for the AdS superstring and generalized Inoenue-Wigner contraction International Nuclear Information System (INIS) Hatsuda, Machiko; Sakaguchi, Makoto 2003-01-01 We examine a Wess-Zumino term, written in a form of bilinear in superinvariant currents, for a superstring in anti-de Sitter (AdS) space, and derive a procedure for obtaining the correct flat limit. The standard Inoenue-Wigner contraction does not give the correct flat limit but, rather, gives zero. This erroneous result originates from the fact that the fermionic metric of the super-Poincare group is degenerate. We propose a generalization of the Inoenue-Wigner contraction from which a 'nondegenerate' super-Poincare group is derived from the super-AdS group. For this reason, this contraction gives the correct flat limit of this Wess-Zumino term. We also discuss the M-algebra obtained using this generalized Inoenue-Wigner contraction from osp(1\|32). (author) 6. Higher conserved charges and integrability for spinning strings in AdS5 x S5 International Nuclear Information System (INIS) Engquist, Johan 2004-01-01 We demonstrate the existence of an infinite number of local commuting charges for classical solutions of the string sigma model on AdS 5 x S 5 associated with a certain circular three-spin solution spinning with large angular momenta in three orthogonal directions on the five-sphere. Using the AdS/CFT correspondence we find agreement to one-loop with the tower of conserved higher charges in planar N = 4 super Yang-Mills theory associated with the dual composite single-trace operator in the highest weight representation (J 1 ,J 2 ,J 2 ) of SO(6). The agreement can be explained by the presence of integrability on both sides of the duality. (author) International Nuclear Information System (INIS) Morita, Takeshi 2009-01-01 In order to understand a boundary description of Hawking radiation in the AdS/CFT correspondence, we investigate the trace anomaly method in AdS 2 space. In this method, Hawking radiation is derived from the trace anomaly of the energy-momentum tensor in the bulk. We find a correspondence between the energy-momentum tensor and a composite operator in CFT 1 and understand the anomalous properties of the energy-momentum tensor in terms of this composite operator. By using this correspondence, we reproduce Hawking radiation from the boundary description. In addition, we find a correspondence between higher-spin currents in the bulk and composite operators in the boundary. 8. Phases of planar AdS black holes with axionic charge Energy Technology Data Exchange (ETDEWEB) Caldarelli, Marco M.; Christodoulou, Ariana [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton SO17 1BJ (United Kingdom); Papadimitriou, Ioannis [SISSA and INFN - Sezione di Trieste,Via Bonomea 265, I 34136 Trieste (Italy); Skenderis, Kostas [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton SO17 1BJ (United Kingdom) 2017-04-03 Planar AdS black holes with axionic charge have finite DC conductivity due to momentum relaxation. We obtain a new family of exact asymptotically AdS{sub 4} black branes with scalar hair, carrying magnetic and axion charge, and we study the thermodynamics and dynamic stability of these, as well as of a number of previously known electric and dyonic solutions with axion charge and scalar hair. The scalar hair for all solutions satisfy mixed boundary conditions, which lead to modified holographic Ward identities, conserved charges and free energy, relative to those following from the more standard Dirichlet boundary conditions. We show that properly accounting for the scalar boundary conditions leads to well defined first law and other thermodynamic relations. Finally, we compute the holographic quantum effective potential for the dual scalar operator and show that dynamical stability of the hairy black branes is equivalent to positivity of the energy density. 9. Implementation of Economic Value Added and Market Value Added Analysis as Valuation Tools of Invest Feasibility Directory of Open Access Journals (Sweden) 2017-09-01 Full Text Available For the investors, financial statement is a benchmark of investors in assessing the company's performance. In fact, investors are not always receiving the accurate company's financial statements information and its levels of fairness are in doubt. The financial statement analysis with using financial ratios is not enough. The investors may need to use alternatives financial statement analyses techniques that reflect the actual company's performance. Therefore, both of the investors and the prospective can use Economic Value Added (EVA and Market Value Added (MVA analysis. With these technical analyses, the investors may know the company's performance where they are invested or to be used as a place to invest whether it has value added or not. With the results of these analyses, it is the expected for the investors to be more confident in making decision whether to buy, sell or hold the ownership in the company. 10. Critical Phenomena in Higher Curvature Charged AdS Black Holes Directory of Open Access Journals (Sweden) Arindam Lala 2013-01-01 Full Text Available In this paper, we have studied the critical phenomena in higher curvature charged AdS black holes. We have considered Lovelock-Born-Infeld-AdS black hole as an example. The thermodynamics of the black hole have been studied which reveals the onset of a higher-order phase transition in the black hole in the canonical ensemble (fixed charge ensemble framework. We have analytically derived the critical exponents associated with these thermodynamic quantities. We find that our results fit well with the thermodynamic scaling laws and consistent with the mean field theory approximation. The suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface have been derived. 11. Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave OpenAIRE Callan, Jr., Curtis G.; Lee, Hok Kong; McLoughlin, Tristan; Schwarz, John H.; Swanson, Ian; Wu, Xinkai 2003-01-01 In a certain kinematic limit, where the effects of spacetime curvature (and other background fields) greatly simplify, the light-cone gauge world-sheet action for a type IIB superstring on AdS_5 x S^5 reduces to that of a free field theory. It has been conjectured by Berenstein, Maldacena, and Nastase that the energy spectrum of this string theory matches the dimensions of operators in the appropriately defined large R-charge large-N_c sector of N=4 supersymmetric Yang--Mills theory in four d... 12. Critical phenomena of static charged AdS black holes in conformal gravity Directory of Open Access Journals (Sweden) Wei Xu 2014-09-01 Full Text Available The extended thermodynamics of static charged AdS black holes in conformal gravity is analyzed. The P–V criticality of these black holes has some unusual features. There exists a single critical point with critical temperature Tc and critical pressure Pc. At fixed T>Tc (or at fixed P>Pc, there are two zeroth order phase transition points but no first order phase transition points. The systems favors large pressure states at constant T, or high temperature states at constant P. 13. THE EFFECT OF LEVERAGE AND ECONOMIC VALUE ADDED ON MARKET VALUE ADDED OpenAIRE Kristína Jančovičová BOGNÁROVÁ 2018-01-01 Economic value added (EVA) is a performance measure developed by Stern Stewart & Co.) that attempts to measure the true economic profit produced by a company. Such a metric is useful for investors who wish to determine how well a company has produced value for its investors, and it can be compared against the company's peers for a quick analysis of how well the company is operating in its industry. Market value added (MVA), on the other hand, is simply the difference between the c... 14. Transition from AdS universe to DS universe in the BPP model International Nuclear Information System (INIS) Kim, Wontae; Yoon, Myungseok 2007-01-01 It can be shown that in the BPP model the smooth phase transition from the asymptotically decelerated AdS universe to the asymptotically accelerated DS universe is possible by solving the modified semiclassical equations of motion. This transition comes from noncommutative Poisson algebra, which gives the constant curvature scalars asymptotically. The decelerated expansion of the early universe is due to the negative energy density with the negative pressure induced by quantum back reaction, and the accelerated late-time universe comes from the positive energy and the negative pressure which behave like dark energy source in recent cosmological models 15. THE INFLUENCE OF ECONOMIC VALUE ADDED AND MARKET VALUE ADDED ON CORPORATE VALUE Directory of Open Access Journals (Sweden) Taslim F.A. 2018-02-01 Full Text Available This research aims to determine the influence of economic value added and market value added on corporate value of manufacturing companies on sector consumer goods industry listed in Indonesia Stock Exchanges of 2011-2014. The sample of this research was 10 manufacturing companies on sector consumer goods industry listed in Indonesia Stock Exchanges. The method used was purposive sampling technique. This research used confirmatory factor analysis to form a combined proxy of corporate value comprised price earning ratio, price to book value and Tobin's Q. 16. On boundary conditions in three-dimensional AdS gravity Energy Technology Data Exchange (ETDEWEB) Miskovic, Olivera [Instituto de Fisica, P. Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile) and Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)]. E-mail: olivera.miskovic@ucv.cl; Olea, Rodrigo [Departamento de Fisica, P. Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile) and Centro Multidisciplinar de Astrofisica, CENTRA, Departamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: rolea@fisica.ist.utl.pt 2006-09-07 A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary term that is one half the Gibbons-Hawking term, that makes the Euclidean action and the Noether charges finite without additional Dirichlet counterterms. The consistency of this boundary condition with the Dirichlet problem in AdS gravity and the Chern-Simons formulation in three dimensions, and its suitability for the higher odd-dimensional case, are also discussed. 17. Adding gauge fields to Kaplan's fermions International Nuclear Information System (INIS) Blum, T.; Kaerkkaeinen, L. 1994-01-01 We experiment with adding dynamical gauge field to Kaplan (defect) fermions. In the case of U(1) gauge theory we use an inhomogeneous Higgs mechanism to restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d theory produce the correct 2d gauge dynamics. We measure fermion propagators with dynamical gauge fields. They posses the correct chiral structure. The fermions at the boundary of the support of the gauge field (waveguide) are non-chiral, and have a mass two times heavier than the chiral modes. Moreover, these modes cannot be excited by a source at the defect; implying that they are dynamically decoupled. We have also checked that the anomaly relation is fullfilled for the case of a smooth external gauge field. (orig.) 18. Worm epidemics in wireless ad hoc networks Energy Technology Data Exchange (ETDEWEB) Nekovee, Maziar [BT Research, Polaris 134, Adastral Park, Martlesham, Suffolk IP5 3RE (United Kingdom); Centre for Computational Science, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom) 2007-06-15 A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet. 19. MR enterography: how to deliver added value International Nuclear Information System (INIS) Dillman, Jonathan R.; Trout, Andrew T.; Smith, Ethan A. 2016-01-01 MR enterography (MRE) is increasingly vital to the diagnosis and follow-up of children with Crohn disease. This diagnostic test, which can provide valuable information regarding the presence of intestinal inflammation, intestinal and intra-abdominal complications, and extra-intestinal disease-related manifestations, has the potential to directly impact both medical and surgical decision-making. Consequently, it is imperative that the interpretation and reporting of these examinations provide as much clinical information as possible. This article reviews specific ways radiologists can provide added value when interpreting MRE examinations in the setting of pediatric Crohn disease by (1) establishing the true extent of disease involvement, (2) subjectively and objectively assessing response to medical treatment and (3) accurately characterizing disease-related complications. (orig.) 20. Value Adding Space Management in Higher Education DEFF Research Database (Denmark) Tinsfeldt, Mette; Jensen, Per Anker 2014-01-01 Purpose : Develop a methodology for space optimisation in educational facilities, that can add value to organisations with particular focus on gymnasiums in Denmark. Background : Gymnasiums are pre-university higher educational institutions, which in 2007 went from being state-owned to being self...... evaluation of the combined use of POE and USEtool and represents an original contribution to the development of knowledge and methodology of value adding space management.......Purpose : Develop a methodology for space optimisation in educational facilities, that can add value to organisations with particular focus on gymnasiums in Denmark. Background : Gymnasiums are pre-university higher educational institutions, which in 2007 went from being state-owned to being self......-governing. Many older gymnasiums face the challenge that the institutions’ buildings and spaces are unsuitable to support modern teaching methods. A space optimisation process can help overcome some of these challenges as long as it makes use of a holistic analysis, is related to the strategic objectives... 1. Worm epidemics in wireless ad hoc networks Science.gov (United States) Nekovee, Maziar 2007-06-01 A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet. 2. Worm epidemics in wireless ad hoc networks International Nuclear Information System (INIS) Nekovee, Maziar 2007-01-01 A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet 3. ADS project in the Vinca Institute International Nuclear Information System (INIS) Pesic, M.; Neskovic, N.; Plecas, I. 1999-01-01 Among the six scientific programmes proposed for future research in the Vinca Institute, the nuclear one is connected to the nuclear reactors and waste management activities. One of the projects within the nuclear programme is associated to a proposal for designing a small modern subcritical research reactor driven by an accelerator beam. The idea of this Project is based on the facts that the construction of the Tesla accelerator installation is in the final phase and that a rich experience is gained in design, construction, operation and maintenance of both research reactors in the Institute in the last 40 years. Preliminary scope of the ADS project in the Vinca Institute, including some details and options, are given (author) 4. An experimental study on the effect of ad placement, product involvement and motives on Facebook ad avoidance OpenAIRE Broeck, Van den, Evert; Poels, Karolien; Walrave, Michel 2018-01-01 Abstract: Facebook users do not visit the social networking site to see advertising. They are either just surfing the platform or searching for information. Therefore, advertising content is vulnerable to ad avoidance. In this study, the effect of two Facebook ad placements, sidebar ads and message stream ads, on ad avoidance intention was investigated through an online experiment. Sidebar placements are put next to the content stream, while message stream advertising is interwoven with the o... 5. Detecting Anti Ad-blockers in the Wild Directory of Open Access Journals (Sweden) 2017-07-01 6. Super-Galilean conformal algebra in AdS/CFT International Nuclear Information System (INIS) Sakaguchi, Makoto 2010-01-01 Galilean conformal algebra (GCA) is an Inoenue-Wigner (IW) contraction of a conformal algebra, while Newton-Hooke string algebra is an IW contraction of an Anti-de Sitter (AdS) algebra, which is the isometry of an AdS space. It is shown that the GCA is a boundary realization of the Newton-Hooke string algebra in the bulk AdS. The string lies along the direction transverse to the boundary, and the worldsheet is AdS 2 . The one-dimensional conformal symmetry so(2,1) and rotational symmetry so(d) contained in the GCA are realized as the symmetry on the AdS 2 string worldsheet and rotational symmetry in the space transverse to the AdS 2 in AdS d+2 , respectively. It follows from this correspondence that 32 supersymmetric GCAs can be derived as IW contractions of superconformal algebras, psu(2,2\|4), osp(8\|4), and osp(8\|4). We also derive less supersymmetric GCAs from su(2,2\|2), osp(4\|4), osp(2\|4), and osp(8\|2). 7. On stringy AdS5 x S5 and higher spin holography International Nuclear Information System (INIS) Bianchi, Massimo; Morales, Jose F.; Samtleben, Henning 2003-01-01 We derive the spectrum of Kaluza-Klein descendants of string excitations on AdS 5 x S 5 . String states are organized in long multiplets of the AdS supergroup SU(2,2\|4,R) with a rich pattern of shortenings at the higher spin enhancement point λ=0. The string states holographically dual to the higher spin currents of SYM theory in the strict zero coupling limit are identified together with the corresponding Goldstone particles responsible for the Higgsing of the higher spin symmetry at λ≠ 0. Exploiting higher spin symmetry we propose a very simple yet effective mass formula and establish a one-to-one correspondence between the complete spectrum of Δ 0 ≤ 4 string states and relevant/marginal single-trace deformations in N = 4 SYM theory at large N. To this end, we describe how to efficiently enumerate scaling operators in 'free' YM theory, with the inclusion of fermionic 'letters', by resorting to Polya theory. Comparison between the spectra of 1/4-BPS states is also presented. Finally, we discuss how to organize the spectrum of N = 4 SYM theory in SU(2,2\|4,R) supermultiplets by means of some kind of 'Eratostenes's sieve'. (author) 8. Gribov ambiguity in asymptotically AdS three-dimensional gravity International Nuclear Information System (INIS) Anabalon, Andres; Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio 2011-01-01 In this paper the zero modes of the de Donder gauge Faddeev-Popov operator for three-dimensional gravity with negative cosmological constant are analyzed. It is found that the AdS 3 vacuum produces (infinitely many) normalizable smooth zero modes of the Faddeev-Popov operator. On the other hand, it is found that the Banados-Teitelboim-Zanelli black hole (including the zero mass black hole) does not generate zero modes. This differs from the usual Gribov problem in QCD where, close to the maximally symmetric vacuum, the Faddeev-Popov determinant is positive definite while 'far enough' from the vacuum it can vanish. This suggests that the zero mass Banados-Teitelboim-Zanelli black hole could be a suitable ground state of three-dimensional gravity with negative cosmological constant. Because of the kinematic origin of this result, it also applies for other covariant gravity theories in three dimensions with AdS 3 as maximally symmetric solution, such as new massive gravity and topologically massive gravity. The relevance of these results for supersymmetry breaking is pointed out. 9. Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models International Nuclear Information System (INIS) Hatsuda, Yasuyuki; Ito, Katsushi; Satoh, Yuji 2012-11-01 We study the null-polygonal minimal surfaces in AdS 4 , which correspond to the gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with n cusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n-4) 4 /U(1) n-5 generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbed W minimal models, we solve the TBA equations by using the conformal perturbation theory, and obtain the analytic expansion of the remainder function around the UV/regular-polygonal limit for n = 6 and 7. We compare the rescaled remainder function for n=6 with the two-loop one, to observe that they are close to each other similarly to the AdS 3 case. 10. AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence NARCIS (Netherlands) Skenderis, K.; Taylor, M.; van Rees, B.C. 2009-01-01 The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the 11. Exploring the bulk in AdS /CFT : A covariant approach Science.gov (United States) Engelhardt, Netta 2017-03-01 I propose a general, covariant way of defining when one region is "deeper in the bulk" than another. This definition is formulated outside of an event horizon (or in the absence thereof) in generic geometries; it may be applied to both points and surfaces, and it may be used to compare the depth of bulk points or surfaces relative to a particular boundary subregion or relative to the entire boundary. Using the recently proposed "light-cone cut" formalism, the comparative depth between two bulk points can be determined from the singularity structure of Lorentzian correlators in the dual field theory. I prove that, by this definition, causal wedges of progressively larger regions probe monotonically deeper in the bulk. The definition furthermore matches expectations in pure AdS and in static AdS black holes with isotropic spatial slices, where a well-defined holographic coordinate exists. In terms of holographic renormalization group flow, this new definition of bulk depth makes contact with coarse graining over both large distances and long time scales. 12. On the Pulsating Strings in AdS4×ℂℙ3 Directory of Open Access Journals (Sweden) H. Dimov 2009-01-01 we quasiclassically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual 𝒩=6 Chern-Simons theory. 13. Particle collisions near a three-dimensional warped AdS black hole Science.gov (United States) Bécar, Ramón; González, P. A.; Vásquez, Yerko 2018-04-01 In this paper we consider the warped AdS3 black hole solution of topologically massive gravity with a negative cosmological constant, and we study the possibility that it acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon, which is known as the Bañnados, Silk and West (BSW) process. Mainly, we show that the critical angular momentum (L_c) of the particle decreases when the warping parameter(ν ) increases. Also, we show that despite the particle with L_c being able to exist for certain values of the conserved energy outside the horizon, it will never reach the event horizon; therefore, the black hole cannot act as a particle accelerator with arbitrarily high CM energy on the event horizon. However, such a particle could also exist inside the outer horizon, with the BSW process being possible on the inner horizon. On the other hand, for the extremal warped AdS3 black hole, the particle with L_c and energy E could exist outside the event horizon and, the CM energy blows up on the event horizon if its conserved energy fulfills the condition E2>(ν 2+3)l2/3(ν ^{2-1)}, with the BSW process being possible. 14. Thermodynamics of AdS black holes in Einstein-Scalar gravity Energy Technology Data Exchange (ETDEWEB) Lü, H. [Department of Physics, Beijing Normal University,Beijing 100875 (China); Pope, C.N. [George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843 (United States); DAMTP, Centre for Mathematical Sciences, Cambridge University,Wilberforce Road, Cambridge CB3 OWA (United Kingdom); Wen, Qiang [Department of Physics, Renmin University of China,Beijing 100872 (China) 2015-03-31 We study the thermodynamics of n-dimensional static asymptotically AdS black holes in Einstein gravity coupled to a scalar field with a potential admitting a stationary point with an AdS vacuum. Such black holes with non-trivial scalar hair can exist provided that the mass-squared of the scalar field is negative, and above the Breitenlohner-Freedman bound. We use the Wald procedure to derive the first law of thermodynamics for these black holes, showing how the scalar hair (or “charge”) contributes non-trivially in the expression. We show in general that a black hole mass can be deduced by isolating an integrable contribution to the (non-integrable) variation of the Hamiltonian arising in the Wald construction, and that this is consistent with the mass calculated using the renormalised holographic stress tensor and also, in those cases where it is defined, with the mass calculated using the conformal method of Ashtekar, Magnon and Das. Similar arguments can also be given for the smooth solitonic solutions in these theories. Neither the black hole nor the soliton solutions can be constructed explicitly, and we carry out a numerical analysis to demonstrate their existence and to provide approximate checks on some of our thermodynamic results. the 4D KK-AdS black hole solution was generalized to the one in arbitrary dimensions. [28]. After obtaining a black hole solution, it is very important to compute its thermodynam- ical quantities, such as the mass, the charge, the angular momentum, the entropy and the temperature. All these quantities are presented in ref. 16. Three-spin Strings on AdS_5 x S^5 from N=4 SYM DEFF Research Database (Denmark) Kristjansen, C. 2004-01-01 Using the integrable spin chain picture we study the one-loop anomalous dimension of certain single trace scalar operators of N=4 SYM expected to correspond to semi-classical string states on AdS_5 x S^5 with three large angular momenta (J_1,J_2,J_3) on S^5. In particular, we investigate the anal......Using the integrable spin chain picture we study the one-loop anomalous dimension of certain single trace scalar operators of N=4 SYM expected to correspond to semi-classical string states on AdS_5 x S^5 with three large angular momenta (J_1,J_2,J_3) on S^5. In particular, we investigate...... the analyticity structure encoded in the Bethe equations for various distributions of Bethe roots. In a certain region of the parameter space our operators reduce to the gauge theory duals of the folded string with two large angular momenta and in another region to the duals of the circular string with angular...... momentum assignment (J,J',J'), J>J'. In between we locate a critical line. We propose that the operators above the critical line are the gauge theory duals of the circular elliptic string with three different spins and support this by a perturbative calculation.... 17. RG flow and thermodynamics of causal horizons in higher-derivative AdS gravity International Nuclear Information System (INIS) Banerjee, Shamik; Bhattacharyya, Arpan 2016-01-01 In http://arxiv.org/abs/1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary c-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in http://arxiv.org/abs/1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory. Energy Technology Data Exchange (ETDEWEB) Cvetič, Mirjam [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104-6396 (United States); Center for Applied Mathematics and Theoretical Physics,University of Maribor, SI2000 Maribor (Slovenia); Papadimitriou, Ioannis [SISSA and INFN - Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy) 2016-12-02 We construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetries and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger http://dx.doi.org/10.1007/JHEP05(2013)152, in agreement with the results of Castro and Song http://arxiv.org/abs/1411.1948. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS{sub 2}×S{sup 2} or conformally AdS{sub 2}×S{sup 2} solutions of the STU model in four dimensions, including non extremal black holes. The four dimensional solutions obtained by uplifting the running dilaton 19. Superstring Theory on $AdS_{3} x G/H$ and Boundary N=3 Superconformal Symmetry CERN Document Server Argurio, R; Shomer, A; Argurio, Riccardo; Giveon, Amit; Shomer, Assaf 2000-01-01 Superstrings propagating on backgrounds of the form AdS_3 x G/H are studiedusing the coset CFT approach. We focus on seven dimensional cosets which have asemiclassical limit, and which give rise to N=3 superconformal symmetry in thedual CFT. This is realized for the two cases AdS_3 x SU(3)/U(1) and AdS_3 xSO(5)/SO(3), for which we present an explicit construction. We also providesufficient conditions on a CFT background to enable a similar construction, andcomment on the geometrical interpretation of our results. 20. Solubility of heavy metals added to MSW International Nuclear Information System (INIS) Lo, H.M.; Lin, K.C.; Liu, M.H.; Pai, T.Z.; Lin, C.Y.; Liu, W.F.; Fang, G.C.; Lu, C.; Chiang, C.F.; Wang, S.C.; Chen, P.H.; Chen, J.K.; Chiu, H.Y.; Wu, K.C. 2009-01-01 This paper aims to investigate the six heavy metal levels (Cd, Cr, Cu, Pb, Ni and Zn) in municipal solid waste (MSW) at different pHs. It intends to provide the baseline information of metals solubility in MSW co-disposed or co-digested with MSW incinerator ashes in landfill or anaerobic bioreactors or heavy metals contaminated in anaerobic digesters. One milliliter (equal to 1 mg) of each metal was added to the 100 ml MSW and the batch reactor test was carried out. The results showed that higher HNO 3 and NaOH were consumed at extreme pH of 1 and 13 compared to those from pH 2 to 11 due to the comparably higher buffer capacity. Pb was found to have the least soluble level, highest metal adsorption (%) and highest partitioning K d (l g -1 ) between pH 3 and 12. In contrast, Ni showed the highest soluble level, lowest metal adsorption (%) and lowest K d (l g -1 ) between pH 4 and 12. Except Ni and Cr, other four metals seemed to show the amphibious properties as comparative higher solubility was found in the acidic and basic conditions 1. Solubility of heavy metals added to MSW Energy Technology Data Exchange (ETDEWEB) Lo, H.M. [Department of Environmental Engineering and Management, Chaoyang University of Technology, 168 Gifong E. Road, Wufong, Taichung County 41349, Taiwan (China)], E-mail: hmlo@cyut.edu.tw; Lin, K.C. [Department of Occupational Safety and Health, Chung Shan Medical University, 110, Sec. 1, Jiangguo N. Rd., Taichung 402, Taiwan (China); Liu, M.H.; Pai, T.Z. [Department of Environmental Engineering and Management, Chaoyang University of Technology, 168 Gifong E. Road, Wufong, Taichung County 41349, Taiwan (China); Lin, C.Y. [Department of Soil and Water Conservation, Chung Hsing University, 250 Kuokuang Road, Taichung 402, Taiwan (China); Liu, W.F. [Department of Electronical Engineering, Feng Chia University, 100 Wenhwa Road, Taichung 407, Taiwan (China); Fang, G.C. [Department of Environmental Engineering, Hungkuang University, 34 Chung-Chie Road, Sha Lu, Taichung 433, Taiwan (China); Lu, C. [Department of Environmental Engineering, Chung Hsing University, 250 Kuokuang Road, Taichung 402, Taiwan (China); Chiang, C.F. [Department of Health Risk Management, China Medical University, No. 91 Hsueh-Shih Road, Taichung 40402, Taiwan (China); Wang, S.C.; Chen, P.H.; Chen, J.K.; Chiu, H.Y.; Wu, K.C. [Department of Environmental Engineering and Management, Chaoyang University of Technology, 168 Gifong E. Road, Wufong, Taichung County 41349, Taiwan (China) 2009-01-15 This paper aims to investigate the six heavy metal levels (Cd, Cr, Cu, Pb, Ni and Zn) in municipal solid waste (MSW) at different pHs. It intends to provide the baseline information of metals solubility in MSW co-disposed or co-digested with MSW incinerator ashes in landfill or anaerobic bioreactors or heavy metals contaminated in anaerobic digesters. One milliliter (equal to 1 mg) of each metal was added to the 100 ml MSW and the batch reactor test was carried out. The results showed that higher HNO{sub 3} and NaOH were consumed at extreme pH of 1 and 13 compared to those from pH 2 to 11 due to the comparably higher buffer capacity. Pb was found to have the least soluble level, highest metal adsorption (%) and highest partitioning K{sub d} (l g{sup -1}) between pH 3 and 12. In contrast, Ni showed the highest soluble level, lowest metal adsorption (%) and lowest K{sub d} (l g{sup -1}) between pH 4 and 12. Except Ni and Cr, other four metals seemed to show the amphibious properties as comparative higher solubility was found in the acidic and basic conditions. 2. Ad hoc committee on reactor physics benchmarks International Nuclear Information System (INIS) Diamond, D.J.; Mosteller, R.D.; Gehin, J.C. 1996-01-01 In the spring of 1994, an ad hoc committee on reactor physics benchmarks was formed under the leadership of two American Nuclear Society (ANS) organizations. The ANS-19 Standards Subcommittee of the Reactor Physics Division and the Computational Benchmark Problem Committee of the Mathematics and Computation Division had both seen a need for additional benchmarks to help validate computer codes used for light water reactor (LWR) neutronics calculations. Although individual organizations had employed various means to validate the reactor physics methods that they used for fuel management, operations, and safety, additional work in code development and refinement is under way, and to increase accuracy, there is a need for a corresponding increase in validation. Both organizations thought that there was a need to promulgate benchmarks based on measured data to supplement the LWR computational benchmarks that have been published in the past. By having an organized benchmark activity, the participants also gain by being able to discuss their problems and achievements with others traveling the same route 3. Spontaneous ad hoc mobile cloud computing network. Science.gov (United States) Lacuesta, Raquel; Lloret, Jaime; Sendra, Sandra; Peñalver, Lourdes 2014-01-01 Cloud computing helps users and companies to share computing resources instead of having local servers or personal devices to handle the applications. Smart devices are becoming one of the main information processing devices. Their computing features are reaching levels that let them create a mobile cloud computing network. But sometimes they are not able to create it and collaborate actively in the cloud because it is difficult for them to build easily a spontaneous network and configure its parameters. For this reason, in this paper, we are going to present the design and deployment of a spontaneous ad hoc mobile cloud computing network. In order to perform it, we have developed a trusted algorithm that is able to manage the activity of the nodes when they join and leave the network. The paper shows the network procedures and classes that have been designed. Our simulation results using Castalia show that our proposal presents a good efficiency and network performance even by using high number of nodes. 4. A code system for ADS transmutation studies International Nuclear Information System (INIS) Brolly, A.; Vertes, P. 2001-01-01 An accelerator driven reactor physical system can be divided into two different subsystems. One is the neutron source the other is the subcritical reactor. Similarly, the modelling of such system is also split into two parts. The first step is the determination of the spatial distribution and angle-energy spectrum of neutron source in the target region; the second one is the calculation of neutron flux which is responsible for the transmutation process in the subcritical system. Accelerators can make neutrons from high energy protons by spallation or photoneutrons from accelerated electrons by Bremsstrahlung (e-n converter). The Monte Carlo approach is the only way of modelling such processes and it might be extended to the whole subcritical system as well. However, a subcritical reactor may be large, it may contain thermal regions and the lifetime of neutrons may be long. Therefore a comprehensive Monte Carlo modelling of such system is a very time consuming computational process. It is unprofitable as well when applied to system optimization that requires a comparative study of large number of system variants. An appropriate method of deterministic transport calculation may adequately satisfy these requirements. Thus, we have built up a coupled calculational model for ADS to be used for transmutation of nuclear waste which we refer further as M-c-T system. Flow chart is shown in Figure. (author) 5. SILAGE CANE SUGAR ADDED WITH DRIED BREWER Directory of Open Access Journals (Sweden) W. J. R. Castro 2015-02-01 Full Text Available The objective of this experiment was to evaluate the fermentative parameters and chemical composition of silage cane sugar added with residue dried brewery. The experimental design was completely randomized with four treatments and four replications: 100% cane sugar; 90% of cane sugar + 10% residue dried brewer; 80% of cane sugar + 20% residue dried brewer and 70% cane sugar + 30% dried brewer based on natural matter, composed silages. The sugar cane was chopped in a stationary machine with forage particle size of approximately 2 cm, and homogenized manually with the additives. For storage chopped fresh weight were used in experimental silos capacity of about 4 liters. The results showed that the contents of dry matter and crude protein showed positive linear (P0.05 with mean value of 3.81, while for ether extract and ash results were positive linear (P0.05 for N ammonia presented average value of 4.18. It is concluded that the addition of brewer dehydrated improves the fermentation process of silage cane sugar, in addition to improving their nutritional characteristics. Energy Technology Data Exchange (ETDEWEB) Dingeon, B; Collombel, C 1973-01-01 7. Ad Oculos. Images, Imagination and Abstract Thinking Directory of Open Access Journals (Sweden) Alessandra Cirafici 2018-03-01 Full Text Available The unusual edition of Elements of Euclid released for publishing in 1847 by Oliver Byrne offers the occasion to suggest a few elements for discussion on the uniqueness of the ‘representation’ of geometric-mathematical thinking—and more in general of the abstract thinking—enshrined in its ‘nature of a pure imaginative vision able to connect the intelligible with the tangible’. The purpose is, thus, a reasoning on images and communicative artefacts, that, when articulated, provide different variations of the idea of ‘transcription’ of complex theoretical structures from one language (that of abstract logic to another (that of sensory experience, with a view to facilitate, ease and make more accurate the noetic process. Images able over time to facilitate the understanding of complex and abstract theoretical principles—since able to show them in an extremely concrete way, ad oculos,—and which at some points could reveal the horizons of art interpretation to inscrutable and figurative meaningless formulas. 8. Adding a scripting interface to Gaudi International Nuclear Information System (INIS) Day, C.T.; Quarrie, D.; Tull, C. 2001-01-01 Athena, the Software Framework for ATLAS' offline software, is based on the Gaudi Framework from LHCb. The Processing Model of Gaudi is essentially that of a batch-oriented system - a User prepares a file detailing the configuration of which Algorithms are to be applied to the input data of a job and the parameter values that control the behavior of each Algorithm instance. The Framework then reads that file once at the beginning of a job and runs to completion with no further interaction with the User. The authors have enhanced the Processing Model to include an interactive mode where a User can control the event loop of a running job and modify the algorithms and parameters on the fly. The authors changed only a very small number of Gaudi Classes to provide access to parameters from an embedded Python interpreter. No change was made to the Gaudi Programming Model, i.e, developers need not change anything to make use of this added interface. The authors present details of the design and implementation of the interactive Python interface for Athena 9. Value adding management: A concept and a case DEFF Research Database (Denmark) Jensen, Per Anker; Katchamart, Akarapong 2012-01-01 be used more directly and proactively by facilities managers to implement adding value strategies and practices. Methodology: The development of the concept of Value Adding Management is based on the management model for FM included in the European FM standards, recent theories on added value of FM...... practice value adding management. It underlines the importance of stakeholder and relationship management as part of adding value. The case study confirms the relevance of the basic concept of Value Adding Management. Practical implications: The concept of Value Adding Management is expected to increase......Purpose: To develop a management concept that can assist facilities managers in implementing value adding strategies and practices. The FM Value Map has been developed to analyse and demonstrate the different ways FM can add value. However, there is a need to develop management tools that can... 10. Aspects of AdS, CFT. Black solutions in gauged supergravity and holographic conductivities International Nuclear Information System (INIS) Barisch-Dick, Susanne 2013-01-01 We have met some interesting results within the wide subject of the AdS/CFT correspondence. We have seen how to apply AdS/CFT techniques to calculate the frequency dependent conductivity tensor for field theories dual to a black hole in Einstein-Yang-Mills theory with SU(2) gauge group. Further, we have constructed several new black solutions in N=2 U(1) gauged supergravity in four and five dimensions. The larger part of these solutions behave asymptotically like AdS which makes them interesting within the AdS/CFT context. In addition we found extremal black branes with zero entropy density - the Nernst branes. Nonetheless we are left with some yet unsolved problems. It is very interesting to see what causes the negative entropy production rate we found in chapter 4 for the normal state of the field theory. The next task is to see whether we can find an instability on the gravity side looking at the full Einstein-Yang-Mills equations. Also our work on supergravity solutions in four and five dimension exhibits some ''loose ends''. Since all our four-dimensional Nernst solutions were axion-free it would be nice to find one with axions excited. Moreover, it would be interesting to see whether the singular solutions with flowing γ could be cured by taking into account higher derivative corrections or whether there exist non-singular solutions with non-constant γ. In five dimensions we met problems when adding electric charge. At present we could not find a dyonic solution and we had the impression that having electric charges and having magnetic fields seemed to be somehow complementary to each other. We saw these difficulties even at the beginning when we performed the first-order rewriting since the first-order rewriting in chapter 6 leads to flow equations for the scalars X A which only contain magnetic fields and fluxes but no electric charges. The latter only influence the equations of motion for the X A in an indirect way. However it is possible to find 11. Added sugars in kids' meals from chain restaurants OpenAIRE Scourboutakos, Mary J.; Semnani-Azad, Zhila; L'Abbé, Mary R. 2016-01-01 Objective To analyze the added sugars in kids' meals from Canadian chain restaurants in relation to the World Health Organization's proposed sugar recommendation (less than 5% of total daily calories should come from added sugars) and current recommendation (less than 10% of total daily calories should come from added sugars). Methods Total sugar levels were retrieved from the websites of 10 fast-food and 7 sit-down restaurants in 2010. The added sugar levels in 3178 kids' meals from Canadian... OpenAIRE Gita Aprinta 2016-01-01 13. Instantons and quark zero modes in AdS/QCD DEFF Research Database (Denmark) Bechi, Jacopo 2009-01-01 In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk.......In this paper the quark zero modes creation effect is studied in the context of the AdS/QCD approach. This effect is generated, in presence of instantons, by a new that can be added in the bulk.... 14. Introduction to the concept of added mass in fluid mechanics International Nuclear Information System (INIS) Pham Dan Tam. 1977-07-01 The physical phenomenum which leads to the concept of added mass for an inviscid fluid is recalled. The added-mass tensor for a solid body moving through an unbounded fluid is defined and some of its properties are presented. The Taylor theorem is exposed, which enables some of the tensor components to be analytically derived in particular cases. Added-mass values are provided for bodies of particular shape. Applications of the added-mass concept to different problems are given [fr Directory of Open Access Journals (Sweden) Nguyen TV 2018-05-01 16. Boundary stress tensor and asymptotically AdS3 non-Einstein spaces at the chiral point International Nuclear Information System (INIS) Giribet, Gaston; Goya, Andres; Leston, Mauricio 2011-01-01 17. Evaluating Teachers: The Important Role of Value-Added Science.gov (United States) Glazerman, Steven; Loeb, Susanna; Goldhaber, Dan; Staiger, Douglas; Raudenbush, Stephen; Whitehurst, Grover 2010-01-01 The evaluation of teachers based on the contribution they make to the learning of their students, "value-added", is an increasingly popular but controversial education reform policy. In this report, the authors highlight and try to clarify four areas of confusion about value-added. The first is between value-added information and the… 18. Holographic fermionic spectrum from Born–Infeld AdS black hole Directory of Open Access Journals (Sweden) Jian-Pin Wu 2016-07-01 Full Text Available In this letter, we systematically explore the holographic (non-relativistic fermionic spectrum without/with dipole coupling dual to Born–Infeld anti-de Sitter (BI-AdS black hole. For the relativistic fermionic fixed point, this holographic fermionic system exhibits non-Fermi liquid behavior. Also, with the increase of BI parameter γ, the non-Fermi liquid becomes even “more non-Fermi”. When the dipole coupling term is included, we find that the BI term makes it a lot tougher to form the gap. While for the non-relativistic fermionic system with large dipole coupling in BI-AdS background, with the increase of BI parameter, the gap comes into being again. 19. Linking Baecklund and monodromy charges for strings on AdS5 x S5 International Nuclear Information System (INIS) Arutyunov, Gleb; Zamaklar, Marija 2005-01-01 We find an explicit relation between the two known ways of generating an infinite set of local conserved charges for the string sigma model on AdS 5 x S 5 : the Baecklund and monodromy approaches. We start by constructing the two-parameter family of Baecklund transformations for the string with an arbitrary world-sheet metric. We then show that only for a special value of one of the parameters the solutions generated by this transformation are compatible with the Virasoro constraints. By solving the Baecklund equations in a non-perturbative fashion, we finally show that the generating functional of the Baecklund conservation laws is equal to a certain sum of the quasi-momenta. The positions of the quasi-momenta in the complex spectral plane are uniquely determined by the real parameter of the Baecklund transform Science.gov (United States) Dias, Óscar J C; Santos, Jorge E; Way, Benson 2016-10-07 According to heuristic arguments, global AdS_{5}×S^{5} black holes are expected to undergo a phase transition in the microcanonical ensemble. At high energies, one expects black holes that respect the symmetries of the S^{5}; at low energies, one expects "localized" black holes that appear pointlike on the S^{5}. According to anti-de Sitter/conformal field theory correspondence, N=4 supersymmetric Yang-Mills (SYM) theory on a 3-sphere should therefore exhibit spontaneous R-symmetry breaking at strong coupling. In this Letter, we numerically construct these localized black holes. We extrapolate the location of this phase transition, and compute the expectation value of the broken scalar operator with lowest conformal dimension. Via the correspondence, these results offer quantitative predictions for N=4 SYM theory. 1. Thermodynamic geometry and phase transitions of dyonic charged AdS black holes Energy Technology Data Exchange (ETDEWEB) Chaturvedi, Pankaj; Sengupta, Gautam [Indian Institute of Technology Kanpur, Department of Physics, Kanpur (India); Das, Anirban [Tata Institute of Fundamental Research, Department of Theoretical Physics, Mumbai (India) 2017-02-15 We investigate phase transitions and critical phenomena of four dimensional dyonic charged AdS black holes in the framework of thermodynamic geometry. In a mixed canonical-grand canonical ensemble with a fixed electric charge and varying magnetic charge these black holes exhibit a liquid-gas like first order phase transition culminating in a second order critical point similar to the van der Waals gas. We show that the thermodynamic scalar curvature R for these black holes follow our proposed geometrical characterization of the R-crossing Method for the first order liquid-gas like phase transition and exhibits a divergence at the second order critical point. The pattern of R crossing and divergence exactly corresponds to those of a van der Waals gas described by us in an earlier work. (orig.) 2. Two-Phase Equilibrium Properties in Charged Topological Dilaton AdS Black Holes Directory of Open Access Journals (Sweden) Hui-Hua Zhao 2016-01-01 Full Text Available We discuss phase transition of the charged topological dilaton AdS black holes by Maxwell equal area law. The two phases involved in the phase transition could coexist and we depict the coexistence region in P-v diagrams. The two-phase equilibrium curves in P-T diagrams are plotted, the Clapeyron equation for the black hole is derived, and the latent heat of isothermal phase transition is investigated. We also analyze the parameters of the black hole that could have an effect on the two-phase coexistence. The results show that the black holes may go through a small-large phase transition similar to that of a usual nongravity thermodynamic system. 3. Resurgence of the dressing phase for AdS5 × S5 Science.gov (United States) Arutyunov, Gleb; Dorigoni, Daniele; Savin, Sergei 2017-01-01 We discuss the resummation of the strong coupling asymptotic expansion of the dressing phase of the AdS5 × S5 superstring. The dressing phase proposed by Beisert, Eden and Staudacher can be recovered from a modified Borel-Ecalle resummation of this asymptotic expansion only by completing it with new, non-perturbative and exponentially suppressed terms that can be organized into different sectors labelled by an instanton-like number. We compute the contribution to the dressing phase coming from the sum over all the instanton sectors and show that it satisfies the homogeneous crossing symmetry equation. We comment on the semiclassical origin of the non-perturbative terms from the world-sheet theory point of view even though their precise explanation remains still quite mysterious. 4. Noncentral extension of the $AdS_5 x S^5$ superalgebra supermultiplet of brane charges CERN Document Server Lee, S; Lee, Sangmin; Park, Jeong-Hyuck 2004-01-01 We propose an extension of the su(2,2\|4) superalgebra to incorporate the F1/D1 string charges in type IIB string theory on the AdS_5 X S^5 background, or the electro-magnetic charges in the dual super Yang-Mills theory. With the charges introduced, the superalgebra inevitably undergoes a noncentral extension, as noted recently in [1]. After developing a group theoretical method of obtaining the noncentral extension, we show that the charges form a certain nonunitary representation of the original unextended superalgebra, subject to some constraints. We solve the constraints completely and show that, apart from the su(2,2\|4) generators, there exist 899 complex brane charges in the extended algebra. Explicitly we present all the super-commutators among them. 5. Charge loss (or the lack thereof) for AdS black holes International Nuclear Information System (INIS) Ong, Yen Chin; Chen, Pisin 2014-01-01 The evolution of evaporating charged black holes is complicated to model in general, but is nevertheless important since the hints to the Information Loss Paradox and its recent firewall incarnation may lie in understanding more generic geometries than that of Schwarzschild spacetime. Fortunately, for sufficiently large asymptotically flat Reissner-Nordström black holes, the evaporation process can be modeled via a system of coupled linear ordinary differential equations, with charge loss rate governed by Schwinger pair-production process. The same model can be generalized to study the evaporation of AdS Reissner-Nordström black holes with flat horizon. It was recently found that such black holes always evolve towards extremality since charge loss is inefficient. This property is completely opposite to the asymptotically flat case in which the black hole eventually loses its charges and tends towards Schwarzschild limit. We clarify the underlying reason for this different behavior. 6. Comparison between various notions of conserved charges in asymptotically AdS spacetimes International Nuclear Information System (INIS) Hollands, Stefan; Ishibashi, Akihiro; Marolf, Donald 2005-01-01 We derive Hamiltonian generators of asymptotic symmetries for general relativity with asymptotic AdS boundary conditions using the 'covariant phase space' method of Wald et al. We then compare our results with other definitions that have been proposed in the literature. We find that our definition agrees with that proposed by Ashtekar et al, with the spinor definition, and with the background-dependent definition of Henneaux and Teitelboim. Our definition disagrees with that obtained from the 'counterterm subtraction method', but the difference is found to consist only of a 'constant offset' that is determined entirely in terms of the boundary metric. We finally discuss and justify our boundary conditions by a linear perturbation analysis, and we comment on generalizations of our boundary conditions, as well as inclusion of matter fields 7. Chern-Simons supergravity plus matter near the boundary of AdS3 International Nuclear Information System (INIS) Deger, N.S.; Kaya, A.; Sezgin, E.; Sundell, P.; Tanii, Y. 2001-01-01 We examine the boundary behaviour of the gauged N=(2,0) supergravity in D=3 coupled to an arbitrary number of scalar supermultiplets which parametrize a Kaehler manifold. In addition to the gravitational coupling constant, the model depends on two parameters, namely the cosmological constant and the size of the Kaehler manifold. It is shown that regular and irregular boundary conditions can be imposed on the matter fields depending on the size of the sigma model manifold. It is also shown that the super AdS transformations in the bulk produce the transformations of the N=(2,0) conformal supergravity and scalar multiplets on the boundary, containing fields with nonvanishing Weyl weights determined by the ratio of the sigma model and the gravitational coupling constants. Various types of (2,0) superconformal multiplets are found on the boundary and in one case the superconformal symmetry is shown to be realized in an unconventional way 8. Effect of adding a swirl on flow pattern and recirculation zone in ADS windowless spallation target Energy Technology Data Exchange (ETDEWEB) Liu, Jie, E-mail: nauty@ucas.ac.cn [School of Physics, University of Chinese Academy of Sciences, Beijing (China); Gao, Lei [School of Physics, University of Chinese Academy of Sciences, Beijing (China); Yang, Lei [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou (China); Lu, Wen-qiang [School of Physics, University of Chinese Academy of Sciences, Beijing (China) 2014-09-15 9. Effect of adding a swirl on flow pattern and recirculation zone in ADS windowless spallation target International Nuclear Information System (INIS) Liu, Jie; Gao, Lei; Yang, Lei; Lu, Wen-qiang 2014-01-01 10. Logarithmic corrections to entropy of magnetically charged AdS4 black holes Directory of Open Access Journals (Sweden) Imtak Jeon 2017-11-01 Full Text Available Logarithmic terms are quantum corrections to black hole entropy determined completely from classical data, thus providing a strong check for candidate theories of quantum gravity purely from physics in the infrared. We compute these terms in the entropy associated to the horizon of a magnetically charged extremal black hole in AdS×4S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions. 11. Regge limit of R-current correlators in AdS supergravity International Nuclear Information System (INIS) Bartels, J.; Kotanski, J.; Mischler, A.M.; Schomerus, V. 2009-08-01 Four-point functions of R-currents are discussed within Anti-de Sitter supergravity. In particular, we compute Witten diagrams with graviton and gauge boson exchange in the high energy Regge limit. Assuming validity of the AdS/CFT correspondence, our results apply to R-current four-point functions of N=4 super Yang-Mills theory at strong coupling. (orig.) 12. Snacks, sweetened beverages, added sugars, and schools. Science.gov (United States) 2015-03-01 13. Value Added Products from Renewable Biofuels Energy Technology Data Exchange (ETDEWEB) Blum, Paul [Univ. of Nebraska, Lincoln, NE (United States) 2014-07-31 Cellulosic ethanol is an emerging biofuel that will make strong contributions to American domestic energy needs. In the US midwest the standard method for pretreatment of biomass uses hot acid to deconstruct lignocellulose. While other methods work, they are not in common use. Therefore it is necessary to work within this context to achieve process improvements and reductions in biofuel cost. Technology underlying this process could supplement and even replace commodity enzymes with engineered microbes to convert biomass-derived lignocellulose feedstocks into biofuels and valueadded chemicals. The approach that was used here was based on consolidated bioprocessing. Thermoacidophilic microbes belonging to the Domain Archaea were evaluated and modfied to promote deconvolution and saccharification of lignocellulose. Biomass pretreatment (hot acid) was combined with fermentation using an extremely thermoacidophilic microbial platform. The identity and fate of released sugars was controlled using metabolic blocks combined with added biochemical traits where needed. LC/MS analysis supported through the newly established Nebraska Bioenergy Facility provided general support for bioenergy researchers at the University of Nebraska. The primary project strategy was to use microbes that naturally flourish in hot acid (thermoacidophiles) with conventional biomass pretreatment that uses hot acid. The specific objectives were: to screen thermoacidophilic taxa for the ability to deconvolute lignocellulose and depolymerize associated carbohydrates; evaluate and respond to formation of “inhibitors” that arose during incubation of lignocellulose under heated acidic conditions; identify and engineer “sugar flux channeling and catabolic blocks” that redirect metabolic pathways to maximize sugar concentrations; expand the hydrolytic capacity of extremely thermoacidophilic microbes through the addition of deconvolution traits; and establish the Nebraska Bioenergy Facility (NBF 14. Pair of accelerated black holes in an anti-de Sitter background: The AdS C metric International Nuclear Information System (INIS) Dias, Oscar J.C.; Lemos, Jose P.S. 2003-01-01 The anti-de Sitter C metric (AdS C metric) is characterized by a quite interesting new feature when compared with the C metric in flat or de Sitter backgrounds. Indeed, contrary to what happens in these two last exact solutions, the AdS C metric only describes a pair of accelerated black holes if the acceleration parameter satisfies A>1/l, where l is the cosmological length. The two black holes cannot interact gravitationally and their acceleration is totally provided by the pressure exerted by a strut that pushes the black holes apart. Our analysis is based on the study of the causal structure, on the description of the solution in the AdS 4-hyperboloid in a 5D Minkowski spacetime, and on the physics of the strut. We also analyze the cases A=1/l and A<1/l that represent a single accelerated black hole in the AdS background 15. Weak field black hole formation in asymptotically AdS spacetimes International Nuclear Information System (INIS) Bhattacharyya, Sayantani; Minwalla, Shiraz 2009-01-01 We use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator. The source is taken to be of small amplitude and finite duration, but is otherwise an arbitrary function of time. When the field theory lives on R d-1,1 , the source sets up a translationally invariant wave in the dual gravitational description. This wave propagates radially inwards in AdS d+1 space and collapses to form a black brane. Outside its horizon the bulk spacetime for this collapse process may systematically be constructed in an expansion in the amplitude of the source function, and takes the Vaidya form at leading order in the source amplitude. This solution is dual to a remarkably rapid and intriguingly scale dependent thermalization process in the field theory. When the field theory lives on a sphere the resultant wave either slowly scatters into a thermal gas (dual to a glueball type phase in the boundary theory) or rapidly collapses into a black hole (dual to a plasma type phase in the field theory) depending on the time scale and amplitude of the source function. The transition between these two behaviors is sharp and can be tuned to the Choptuik scaling solution in R d,1 . 16. Three dimensional nonlinear magnetic AdS solutions through topological defects International Nuclear Information System (INIS) Hendi, S.H.; Panah, B.E.; Momennia, M.; Panahiyan, S. 2015-01-01 Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known Born-Infeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too. (orig.) 17. The exceptional generalised geometry of supersymmetric AdS flux backgrounds Energy Technology Data Exchange (ETDEWEB) Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford, Andrew Wiles Building,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Petrini, Michela [Sorbonne Université, UPMC Paris 06, UMR 7589,LPTHE, 75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom) 2016-12-29 We analyse generic AdS flux backgrounds preserving eight supercharges in D=4 and D=5 dimensions using exceptional generalised geometry. We show that they are described by a pair of globally defined, generalised structures, identical to those that appear for flat flux backgrounds but with different integrability conditions. We give a number of explicit examples of such “exceptional Sasaki-Einstein” backgrounds in type IIB supergravity and M-theory. In particular, we give the complete analysis of the generic AdS{sub 5} M-theory backgrounds. We also briefly discuss the structure of the moduli space of solutions. In all cases, one structure defines a “generalised Reeb vector” that generates a Killing symmetry of the background corresponding to the R-symmetry of the dual field theory, and in addition encodes the generic contact structures that appear in the D=4 M-theory and D=5 type IIB cases. Finally, we investigate the relation between generalised structures and quantities in the dual field theory, showing that the central charge and R-charge of BPS wrapped-brane states are both encoded by the generalised Reeb vector, as well as discussing how volume minimisation (the dual of a- and F-maximisation) is encoded. 18. ECONOMIC VALUE ADDED AND MARKET VALUE ADDED - MODERN INDICATORS FOR ASSESSMENT THE FIRM’S VALUE Directory of Open Access Journals (Sweden) NICOLAE SICHIGEA 2015-12-01 Full Text Available The financial theory developed different categories of indicators - traditional and modern - in order to evaluate the firm’s value creation. The shareholders are directly interested by the value added in the company. The value creation is a complex process that implies correct decisions, common responsibility (managers and shareholders and actions towards an efficient and profitable activity. The traditional indicators of performance are not teoritically correlated with the the value creation and in these circumstances, should be used appropriate financial indicators in order to reflect the value of the company. Therefore, the modern indicators used in the value based management framework offer a greater flexibility and efficiency and represent a good alternative for companies. Such performance indicators used to measure the financial results correlated with shareholder wealth are the Economic Value Added (EVA, as a measure of internal performance and the Market Value Added (MVA as a measure of external performance of the company. Starting from the main deficiencies of the accounting indicators, the objective of this this study is to present the relationship between EVA and MVA and their implications on firms’valuation. Thus, the presentation and analysis of these indicators – EVA and MVA - will underline the main features, their correlations, and influence factors but also the main advantage and disadvantage of each indicator, which will enable the managers to make the correct choice and subsequently the best decision regarding the performance measures. Science.gov (United States) 2016-01-01 Decreasing the route rediscovery time process in reactive routing protocols is challenging in mobile ad hoc networks. Links between nodes are continuously established and broken because of the characteristics of the network. Finding multiple routes to increase the reliability is also important but requires a fast update, especially in high traffic load and high mobility where paths can be broken as well. The sender node keeps re-establishing path discovery to find new paths, which makes for long time delay. In this paper we propose an improved multipath routing protocol, called Receiver-based ad hoc on demand multipath routing protocol (RB-AOMDV), which takes advantage of the reliability of the state of the art ad hoc on demand multipath distance vector (AOMDV) protocol with less re-established discovery time. The receiver node assumes the role of discovering paths when finding data packets that have not been received after a period of time. Simulation results show the delay and delivery ratio performances are improved compared with AOMDV. 20. On N=8 supergravity in AdS5 and N=4 superconformal Yang-Mills theory International Nuclear Information System (INIS) Ferrara, S.; Zaffaroni, A.; Froensdal, C. 1998-01-01 We discuss the spectrum of states of IIB supergravity on AdS 5 x S 5 in a manifest SU(2,2/4) invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in AdS 5 and superconformal invariant singleton theory at the boundary is formulated in a N=4 superfield covariant language. (orig.) 1. Fermions in nonrelativistic AdS/CFT correspondence International Nuclear Information System (INIS) Akhavan, Amin; Alishahiha, Mohsen; Davody, Ali; Vahedi, Ali 2009-01-01 We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schroedinger group isometry. Although the boundary of the geometries with Schroedinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in nonrelativistic CFTs, though a nontrivial regularization may be needed. 2. Accelerated detectors and worldsheet horizons in AdS/CFT OpenAIRE Chernicoff, Mariano; Paredes, Angel 2010-01-01 We use the AdS/CFT correspondence to discuss the response of an accelerated observer to the quantum vacuum fluctuations. In particular, we study heavy quarks probing a strongly coupled CFT by analysing strings moving in AdS. We propose that, in this context, a non-trivial detection rate is associated to the existence of a worldsheet horizon and we find an Unruh-like expression for the worldsheet temperature. Finally, by examining a rotating string in global AdS we find that there is a transit... 3. New Penrose limits and AdS/CFT DEFF Research Database (Denmark) Grignani, Gianluca; Harmark, Troels; Marini, Andrea 2010-01-01 We find a new Penrose limit of AdS 5 × S 5 giving the maximally supersymmetric pp-wave background with two explicit space-like isometries. This is an important missing piece in studying the AdS/CFT correspondence in certain subsectors. In particular whereas the Penrose limit giving one space......-like isometry is useful for the SU(2) sector of N = 4 SYM, this new Penrose limit is instead useful for studying the SU(2\|3) and SU(1, 2\|3) sectors. In addition to the new Penrose limit of AdS 5 × S 5 we also find a new Penrose limit of AdS4 × ℂP 3.... 4. Aspects of AdS, CFT. Black solutions in gauged supergravity and holographic conductivities Energy Technology Data Exchange (ETDEWEB) Barisch-Dick, Susanne 2013-04-26 We have met some interesting results within the wide subject of the AdS/CFT correspondence. We have seen how to apply AdS/CFT techniques to calculate the frequency dependent conductivity tensor for field theories dual to a black hole in Einstein-Yang-Mills theory with SU(2) gauge group. Further, we have constructed several new black solutions in N=2 U(1) gauged supergravity in four and five dimensions. The larger part of these solutions behave asymptotically like AdS which makes them interesting within the AdS/CFT context. In addition we found extremal black branes with zero entropy density - the Nernst branes. Nonetheless we are left with some yet unsolved problems. It is very interesting to see what causes the negative entropy production rate we found in chapter 4 for the normal state of the field theory. The next task is to see whether we can find an instability on the gravity side looking at the full Einstein-Yang-Mills equations. Also our work on supergravity solutions in four and five dimension exhibits some ''loose ends''. Since all our four-dimensional Nernst solutions were axion-free it would be nice to find one with axions excited. Moreover, it would be interesting to see whether the singular solutions with flowing γ could be cured by taking into account higher derivative corrections or whether there exist non-singular solutions with non-constant γ. In five dimensions we met problems when adding electric charge. At present we could not find a dyonic solution and we had the impression that having electric charges and having magnetic fields seemed to be somehow complementary to each other. We saw these difficulties even at the beginning when we performed the first-order rewriting since the first-order rewriting in chapter 6 leads to flow equations for the scalars X{sup A} which only contain magnetic fields and fluxes but no electric charges. The latter only influence the equations of motion for the X{sup A} in an indirect way. However 5. What makes an ad a cigarette ad? Commercial tobacco imagery in the lesbian, gay, and bisexual press Science.gov (United States) Smith, E.; Offen, N.; Malone, R. 2005-01-01 6. AdS5/CFT4 four-point functions of chiral primary operators: Cubic vertices International Nuclear Information System (INIS) Lee, Sangmin 1999-01-01 We study the exchange diagrams in the computation of four-point functions of all chiral primary operators in D=4, N=4 super Yang-Mills using AdS/CFT correspondence. We identify all supergravity fields that can be exchanged and compute the cubic couplings. As a byproduct, we also rederive the normalization of the quadratic action of the exchanged fields. The cubic couplings computed in this paper and the propagators studied extensively in the literature can be used to compute almost all the exchange diagrams explicitly. Some issues in computing the complete four-point function in the 'massless sector' are discussed 7. Introduction to the AdS/CFT Correspondence Science.gov (United States) Nąstase, Horaǧiu 2015-09-01 Preface; Introduction; Part I. Background: 1. Elements of quantum field theory and gauge theory; 2. Basics of general relativity. Anti-de Sitter space; 3. Basics of supersymmetry; 4. Basics of supergravity; 5. Kaluza-Klein dimensional reduction; 6. Black holes and p-branes; 7. String theory actions and spectra; 8. Elements of conformal field theory; 9. D-branes; Part II. Basics of AdS/CFT for N = 4 SYM vs AdS5 × S5: 10. The AdS/CFT correspondence: motivation, definition and spectra; 11. Witten prescription and 3-point correlator calculations; 12. Holography in Lorentzian signature: Poincaré and global; 13. Solitonic objects in AdS/CFT; 14. Quarks and the Wilson loop; 15. Finite temperature and N = 4 SYM plasmas; 16. Scattering processes and gravitational shockwave limit; 17. The pp-wave correspondence; 18. Spin chains; Part III. AdS/CFT Developments and Gauge-Gravity Dualities: 19. Other conformal cases; 20. The 3 dimensional ABJM model vs. AdS4 × CP3; 21. Gravity duals; 22. Holographic renormalization; 23. RG flow between fixed points; 24. Phenomenological gauge-gravity duality I: AdS/QCD; 25. Phenomenological gauge-gravity duality II: AdS/CMT; 26. Gluon scattering: the Alday-Maldacena prescription; 27. Holographic entanglement entropy: the Ryu-Takayanagi prescription. 8. Value added services to CANDU plants International Nuclear Information System (INIS) Kakaria, B.K. 2003-01-01 if applicable, new entities which will enhance its ability to deliver that value. Secondly, AECL is beginning to look at its customers in a different light. That is, as partners, rather than just clients. The key to success of any partnership is the goal that partners share in working together to add value to each other's business, sharing risks and rewards. This is a departure from AECL's traditional customer/supplier model. Forging partnerships requires establishing long-term relationships and setting long term performance goals. This means adjusting over time AECL's business processes, information technology, quality programs, and staffing resources to meet the changing needs of its clients. In light of this changing environment, AECL recently implemented a new operational structure, effective April 1, 2003. In this restructuring, five business units have been created, each focussing on key business offerings to its client base. The Services Business (SBU) is one of the units and will focus on providing value added services to AECL's partners. This paper will describe key elements of the new SBU and the themes that have influenced the design and organization and also provide an update on AECL's achievements in the Service Area. (author) 9. The forecaster's added value in QPF Science.gov (United States) Turco, M.; Milelli, M. 2010-03-01 : - despite the overall improvement in global scale and the fact that the resolution of the limited area models has increased considerably over recent years, the QPF produced by the meteorological models involved in this study has not improved enough to allow its direct use: the subjective HQPF continues to offer the best performance for the period +24 h/+48 h (i.e. the warning period in the Piemonte system); - in the forecast process, the step where humans have the largest added value with respect to mathematical models, is the communication. In fact the human characterization and communication of the forecast uncertainty to end users cannot be replaced by any computer code; - eventually, although there is no novelty in this study, we would like to show that the correct application of appropriated statistical techniques permits a better definition and quantification of the errors and, mostly important, allows a correct (unbiased) communication between forecasters and decision makers. Science.gov (United States) Borsato, Riccardo; Torrielli, Alessandro 2018-03-01 We consider the exact S-matrix governing the planar spectral problem for strings on AdS5 ×S5 and N = 4 super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu (2 \| 2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra Uq (sl2 ˆ) in Drinfeld's second realisation. 11. Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes Directory of Open Access Journals (Sweden) Eloy Ayón-Beato 2016-01-01 Full Text Available We present a self-gravitating, analytic and globally regular Skyrmion solution of the Einstein–Skyrme system with winding number w=±1, in presence of a cosmological constant. The static spacetime metric is the direct product R×S3 and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback with unit topological charge. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX with time-dependent scale and squashing coefficients. Remarkably, the Skyrme equations are still identically satisfied for all values of these parameters. Thus, the complete set of field equations for the Einstein–Skyrme–Λ system in the topological sector reduces to a pair of coupled, autonomous, nonlinear differential equations for the scale factor and a squashing coefficient. These equations admit analytic bouncing cosmological solutions in which the universe contracts to a minimum non-vanishing size, and then expands. A non-trivial byproduct of this solution is that a minor modification of the construction gives rise to a family of stationary, regular configurations in General Relativity with negative cosmological constant supported by an SU(2 nonlinear sigma model. These solutions represent traversable AdS wormholes with NUT parameter in which the only “exotic matter” required for their construction is a negative cosmological constant. 12. Lumpy AdS5× S5 black holes and black belts International Nuclear Information System (INIS) Dias, Óscar J.C.; Santos, Jorge E.; Way, Benson 2015-01-01 Sufficiently small Schwarzschild black holes in global AdS 5 ×S 5 are Gregory-Laflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S 5 down to SO(5). These new “lumpy" solutions are labelled by the harmonics ℓ. We find evidence that the ℓ=1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S 8 topology. We argue that these S 8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with ℓ=2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S 4 ×S 4 which we call a “black belt”. Directory of Open Access Journals (Sweden) Riccardo Borsato 2018-03-01 Full Text Available We consider the exact S-matrix governing the planar spectral problem for strings on AdS5×S5 and N=4 super Yang–Mills, and we show that it is invariant under a novel “boost” symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu(2\|2 symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory and weak-coupling (spin-chain description of the gauge theory limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra Uq(sl2ˆ in Drinfeld's second realisation. 14. Exploring the spectrum of planar AdS4 /CFT3 at finite coupling Science.gov (United States) Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto 2018-04-01 The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big\|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided. International Nuclear Information System (INIS) Arutyunov, Gleb; Borsato, Riccardo; Frolov, Sergey 2015-01-01 We derive the part of the Lagrangian for the sigma model on the η-deformed AdS_5×S"5 space which is quadratic in fermions and has the full dependence on bosons. We then show that there exists a field redefinition which brings the corresponding Lagrangian to the standard form of type IIB Green-Schwarz superstring. Reading off the corresponding RR couplings, we observe that they fail to satisfy the supergravity equations of motion, despite the presence of κ-symmetry. However, in a special scaling limit our solution reproduces the supergravity background found by Maldacena and Russo. Further, using the fermionic Lagrangian, we compute a number of new matrix elements of the tree level world-sheet scattering matrix. We then show that after a unitary transformation on the basis of two-particle states which is not one-particle factorisable, the corresponding T-matrix factorises into two equivalent parts. Each part satisfies the classical Yang-Baxter equation and coincides with the large tension limit of the q-deformed S-matrix. 16. Aerodigitalni senzori - LH Systems ADS 40 / Airborne digital sensors: LH Systems ADS 40 Directory of Open Access Journals (Sweden) Marko Pejić 2004-01-01 Full Text Available U radu su prezentovane osnove prikupljanja prostornih podataka metodom daljinske detekcije i klasičnim fotogrametrijskim metodom. Ukazano je na kompromis između dva metoda koji nudi digitalna aerokamera. Kompanija LH Systems proizvela je digitalnu aerokameru ADS 40 koja nudi sasvim nov koncept prikupljanja prostornih podataka. Sistem kamere obezbeđuje panhromatske i trodimenzionalne informacije koristeći tri CCD linije i opciono još pet linija iz multispektralnog opsega. Kamera skenira teren sa prostornom rezolucijom od 25 cm, površine od 300 kvadratnih kilometara, uz vreme trajanja leta koje je nešto kraće od jednog sata. / This paper presents basics of collecting spatial data with remote sensing and the classical photogrammetric method. A compromise between two methods, offered by a digital aero camera, is also suggested. The LH Systems has produced a new camera concept called Airborne Digital Sensor (ADS 40 which uses a new way of collecting spatial data. The camera system provides panchromatic and stereo information using three CCD lines and up to five more lines for multispectral imagery. The performance of the camera allows a three dimensional and multispectral image with a ground sample distance of 25 cm for an area of 300 square miles within a flight time shorter than one hour. 17. Superconformal Chern-Simons theories and AdS4/CFT3 correspondence International Nuclear Information System (INIS) Benna, Marcus; Klebanov, Igor; Klose, Thomas; Smedbaeck, Mikael 2008-01-01 We discuss the N = 2 superspace formulation of the N = 8 superconformal Bagger-Lambert-Gustavsson theory, and of the N = 6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N) x U(N) Chern-Simons theory. In particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then consider orbifold projections of this theory that give non-chiral and chiral (U(N) x U(N)) n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS 4 x S 7 /(Z n x Z k -tilde) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the N = 8 theory flow to a N = 2 superconformal gauge theory with a sextic superpotential. We conjecture that this gauge theory is dual to the U(1) R x SU(3) invariant extremum of the N = 8 gauged supergravity, which was discovered by N. Warner 25 years ago and whose uplifting to 11 dimensions was found more recently. 18. Applications of electron linacs to ADS: one potential path forward International Nuclear Information System (INIS) Wells, D.P.; Harmon, J.F. 2011-01-01 19. Interacting fields in real-time AdS/CFT Energy Technology Data Exchange (ETDEWEB) Botta-Cantcheff, Marcelo; Martínez, Pedro J. [Instituto de Física de La Plata, CCT La Plata, CONICET & Departamento de Física,Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Silva, Guillermo A. [Instituto de Física de La Plata, CCT La Plata, CONICET & Departamento de Física,Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Abdus Salam International Centre for Theoretical Physics, Associate Scheme,Strada Costiera 11, 34151 Trieste (Italy) 2017-03-28 We compute time-ordered 2- and 3-pt correlation functions of CFT scalar operators between generic in/out states. The calculation is holographically carried out by considering a non backreacting AdS scalar field with a λϕ{sup 3} self-interaction term on a combination of Euclidean and Lorentzian AdS sections following the Skenderis-van Rees prescription. We show that, although working in an essentially different set up, the final result for the 3-pt correlators agree with those of Rastelli et al. for Euclidean AdS. By analyzing the inner product between the in/out excited states in the large N approximation, we argue that a cubic bulk interaction deforms the excited states from coherent into squeezed. Finally, a diagrammatic interpretation of the results suggests some general properties for the n-point correlation functions between excited states. 20. Low Power High Dynamic Range A/D Conversion Channel DEFF Research Database (Denmark) Marker-Villumsen, Niels; Rombach, Pirmin in the conversion channel in order to avoid distortion for large input signals. In combination with a low resolution A/D converter (ADC) and a digital gain block, the adaptive A/D conversion channel achieves an extended dynamic range beyond that of the ADC. This in turn reduces the current consumption......This work concerns the analysis of an adaptive analog-to-digital (A/D) conversion channel for use with a micro electromechanical system (MEMS) microphone for audio applications. The adaptive A/D conversion channel uses an automatic gain control (AGC) for adjusting the analog preamplifier gain...... of the conversion channel in comparison to a static A/D conversion channel; this at the cost of a reduced peak signal-to-noise ratio (SNR). The adaptive A/D conversion channel compensates for the change in analog gain by a digital gain, thus achieving a constant channel gain in the full dynamic range. However... 1. Dilatation operator and the Super Yang-Mills duals of open strings on AdS giant gravitons International Nuclear Information System (INIS) Correa, Diego H.; Silva, Guillermo A. 2006-01-01 We study the one-loop anomalous dimensions of the Super Yang-Mills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of scalar fields, carrying the appropriate R-charge, with a totally symmetric tensor. We represent the open string motion along AdS directions by appending to the giant graviton operator a product of fields including covariant derivatives. We derive a bosonic lattice Hamiltonian that describes the mixing of these excited AdS giants operators under the action of the one-loop dilatation operator of N = 4 SYM. This Hamiltonian captures several intuitive differences with respect to the case of sphere giant gravitons. A semiclassical analysis of the Hamiltonian allows us to give a geometrical interpretation for the labeling used to describe the fields products appended to the AdS giant operators. It also allows us to show evidence for the existence of continuous bands in the Hamiltonian spectrum 2. Near-horizon limit of the charged BTZ black hole and AdS2 quantum gravity International Nuclear Information System (INIS) 2008-01-01 We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, near-horizon AdS 2 geometry with constant dilaton and U(1) field and an asymptotic AdS 2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS 2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge c as of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, c as = 3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, c nh ∝lQ/√G. OpenAIRE Mumtaz, Shahid; Gameiro, Atilio 2010-01-01 Emerging research in game theory based power control applied to ad hoc opportunist networks shows much promise to help understand the complex interactions between OR nodes in this highly dynamic and distributed environment. Also, the employment of game theory in modeling dynamic situations for opportunist ad hoc networks where OR nodes have incomplete information has led to the application of largely unexplored games such as games of imperfect monitoring. Ad hoc security using game theory is ... 4. Ad hoc mobile wireless networks principles, protocols and applications CERN Document Server 2007-01-01 Ad hoc mobile wireless networks have seen increased adaptation in a variety of disciplines because they can be deployed with simple infrastructures and virtually no central administration. In particular, the development of ad hoc wireless and sensor networks provides tremendous opportunities in areas including disaster recovery, defense, health care, and industrial environments. Ad Hoc Mobile Wireless Networks: Principles, Protocols and Applications explains the concepts, mechanisms, design, and performance of these systems. It presents in-depth explanations of the latest wireless technologies 5. Ad hoc mobile wireless networks principles, protocols, and applications CERN Document Server Sarkar, Subir Kumar 2013-01-01 The military, the research community, emergency services, and industrial environments all rely on ad hoc mobile wireless networks because of their simple infrastructure and minimal central administration. Now in its second edition, Ad Hoc Mobile Wireless Networks: Principles, Protocols, and Applications explains the concepts, mechanism, design, and performance of these highly valued systems. Following an overview of wireless network fundamentals, the book explores MAC layer, routing, multicast, and transport layer protocols for ad hoc mobile wireless networks. Next, it examines quality of serv 6. Active and separate secretion of fiber and penton base during the early phase of Ad2 or Ad5 infection Energy Technology Data Exchange (ETDEWEB) Yan, Yuhua; Zhang, Bo; Hou, Weihong; Lin, Hongyu [Beijing Key Laboratory of Gene Resource and Molecular Development, Beijing Normal University, Beijing (China); Rebetz, Johan [The Rausing Laboratory, Department of Neurosurgery, Lund University, Lund (Sweden); Hong, Saw-See [Viral Infections & Comparative Pathology, UMR-754 UCBL-INRA-EPHE, Université Lyon 1, Lyon Cedex 07 (France); Wang, Youjun; Ran, Liang [Beijing Key Laboratory of Gene Resource and Molecular Development, Beijing Normal University, Beijing (China); Fan, Xiaolong, E-mail: XFan@bnu.edu.cn [Beijing Key Laboratory of Gene Resource and Molecular Development, Beijing Normal University, Beijing (China) 2017-05-15 7. Flexibility of ADS for minor actinides transmutation in different two-stage PWR-ADS fuel cycle scenarios International Nuclear Information System (INIS) Zhou, Shengcheng; Wu, Hongchun; Zheng, Youqi 2018-01-01 8. Active and separate secretion of fiber and penton base during the early phase of Ad2 or Ad5 infection International Nuclear Information System (INIS) Yan, Yuhua; Zhang, Bo; Hou, Weihong; Lin, Hongyu; Rebetz, Johan; Hong, Saw-See; Wang, Youjun; Ran, Liang; Fan, Xiaolong 2017-01-01 9. Are restrictive guidelines for added sugars science based? Science.gov (United States) Erickson, Jennifer; Slavin, Joanne 2015-12-12 10. Light-Front Holography and AdS/QCD Correspondence Energy Technology Data Exchange (ETDEWEB) Brodsky, Stanley J.; de Teramond, Guy F. 2008-04-23 Light-Front Holography is a remarkable consequence of the correspondence between string theory in AdS space and conformal field theories in physical-space time. It allows string modes {Phi}(z) in the AdS fifth dimension to be precisely mapped to the light-front wavefunctions of hadrons in terms of a specific light-front impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron. This mapping was originally obtained by matching the exact expression for electromagnetic current matrix elements in AdS space with the corresponding exact expression for the current matrix element using light-front theory in physical space-time. More recently we have shown that one obtains the identical holographic mapping using matrix elements of the energy-momentum tensor, thus providing an important consistency test and verification of holographic mapping from AdS to physical observables defined on the light-front. The resulting light-front Schrodinger equations predicted from AdS/QCD give a good representation of the observed meson and baryon spectra and give excellent phenomenological predictions for amplitudes such as electromagnetic form factors and decay constants. Directory of Open Access Journals (Sweden) Gita Aprinta 2016-04-01 OpenAIRE Klaučo, Jakub 2012-01-01 The goal of this Bachelor thesis is to describe possibilities of the internet advertising programs. Thesis is focused on monetizing web content for the owners of smaller web sites. It shows the solutions to the problems connected with the use of Google AdSense, and describes the ad formats and optimization. Thesis is divided into three main parts. Part one contains the current forms of internet advertisement and ad formats used in AdSense program. Second part deals with the possibilities of e... 13. Intrusion detection in wireless ad-hoc networks CERN Document Server Chaki, Nabendu 2014-01-01 Presenting cutting-edge research, Intrusion Detection in Wireless Ad-Hoc Networks explores the security aspects of the basic categories of wireless ad-hoc networks and related application areas. Focusing on intrusion detection systems (IDSs), it explains how to establish security solutions for the range of wireless networks, including mobile ad-hoc networks, hybrid wireless networks, and sensor networks.This edited volume reviews and analyzes state-of-the-art IDSs for various wireless ad-hoc networks. It includes case studies on honesty-based intrusion detection systems, cluster oriented-based 14. Generalized Gribov-Lipatov Reciprocity and AdS/CFT International Nuclear Information System (INIS) Beccaria, M.; Macorini, G.; Forini, V. 2010-01-01 Planar □=4 SYM theory and QCD share the gluon sector, suggesting the investigation of Gribov-Lipatov reciprocity in the supersymmetric theory. Since the AdS/CFT correspondence links □=4 SYM and superstring dynamics on AdS 5 x S5, reciprocity is also expected to show up in the quantum corrected energies of certain classical string configurations dual to gauge theory twist-operators. We review recent results confirming this picture and revisiting the old idea of Gribov-Lipatov reciprocity as a modern theoretical tool useful for the study of open problems in AdS/CFT. 15. Annuitants Added to the Annuity Roll Processing System (ARPS) Data.gov (United States) Office of Personnel Management — Small table showing the total Civil Service Retirement System (CSRS) and Federal Employees Retirement System (FERS) Annuitants added to the Annuity Roll Processing... 16. SL(2, Z) invariant rotating (m, n) strings in AdS_3 x S"3 with mixed flux International Nuclear Information System (INIS) Barik, M.S.P.; Panigrahi, Kamal L.; Khouchen, Malak; Kluson, Josef 2017-01-01 We study rigidly rotating and pulsating (m, n) strings in AdS_3 x S"3 with mixed three form flux. The AdS_3 x S"3 background with mixed three form flux is obtained in the near horizon limit of SL(2, Z)-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe (m, n)-string in this background by solving the manifest SL(2, Z)-covariant form of the action. We find the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find various relationships among the conserved charges. We further study a class of pulsating (m, n) string in AdS_3 with mixed three form flux. (orig.) 17. A requiem for AdS4×C P3 fermionic self-T duality Science.gov (United States) O'Colgáin, E.; Pittelli, A. 2016-11-01 Strong evidence for dual superconformal symmetry in N =6 superconformal Chern-Simons theory has fueled expectations that the AdS /CFT dual geometry AdS4×C P3 is self-dual under T duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T duality, a symmetry originally proposed by Berkovits and Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T duality and comment on T duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T duality for AdS4×C P3 or its TsT deformations but leave the door open for new possibilities. 18. Global dynamics of asymptotically locally AdS spacetimes with negative mass Science.gov (United States) Dold, Dominic 2018-05-01 The Einstein vacuum equations in 5D with negative cosmological constant are studied in biaxial Bianchi IX symmetry. We show that if initial data of Eguchi–Hanson type, modelled after the 4D Riemannian Eguchi–Hanson space, have negative mass, the future maximal development does not contain horizons, i. e. the complement of the causal past of null infinity is empty. In particular, perturbations of Eguchi–Hanson–AdS spacetimes within the biaxial Bianchi IX symmetry class cannot form horizons, suggesting that such spacetimes are potential candidates for a naked singularity to form. The proof relies on an extension principle proven for this system and a priori estimates following from the monotonicity of the Hawking mass. 19. Stellar survivor from explosion in 1572 AD Science.gov (United States) 2004-10-01 burned-out 'white dwarf' star. The normal star spills material onto the dwarf, eventually triggering an explosion. The results of this research, led by Pilar Ruiz-Lapuente of the University of Barcelona, Spain, are published in the 28 October issue of the British science journal Nature. "There was no previous evidence pointing to any specific kind of companion star out of the many that had been proposed. Here we have identified a clear path: the feeding star is similar to our sun, but slightly older," said Ruiz-Lapuente. "The high speed of the star called our attention to it," she added. Type Ia supernovae are used to measure the history of the expansion rate of the Universe and so are fundamental in helping astronomers understand the behaviour of 'dark energy', an unknown force that is accelerating the expansion of the Universe. Finding evidence to confirm the theory as to how Type Ia supernovae explode is critical to assuring astronomers that the objects can be better understood as reliable calibrators of the expansion of space. Although today's astronomers are looking at this event 432 years too late, they were still able to see a star rushing away from the location of the explosion (which is now enveloped in a vast bubble of hot gas called 'Tycho's Supernova Remnant'). The runaway star and its surroundings have been studied with a variety of telescopes for the past seven years. The NASA/ESA Hubble Space Telescope played a key role in the process by measuring the star's motion against the sky background precisely. The star is breaking the speed limit for that particular region of the Milky Way Galaxy by moving three times faster than the surrounding stars. When the system was disrupted by the white dwarf's explosion, the companion star went hurtling off into space, like a stone thrown by a sling, retaining the velocity of its orbital motion. However there are alternative explanations for this motion. It could be falling into the region from the galactic halo that 20. Critical phenomena and chemical potential of a charged AdS black hole Science.gov (United States) Wei, Shao-Wen; Liang, Bin; Liu, Yu-Xiao 2017-12-01 Inspired by the interpretation of the cosmological constant from the boundary gauge theory, we here treat it as the number of colors N and its conjugate quantity as the associated chemical potential μ in the black hole side. Then the thermodynamics and the chemical potential for a five-dimensional charged AdS black hole are studied. It is found that there exists a small-large black hole phase transition of van der Waals type. The critical phenomena are investigated in the N2-μ chart. The result implies that the phase transition can occur for large number of colors N , while is forbidden for small number. This to some extent implies that the interaction of the system increases with the number. In particular, in the reduced parameter space, all the thermodynamic quantities can be rescaled with the black hole charge such that these reduced quantities are charge-independent. Then we obtain the coexistence curve and the phase diagram. The latent heat is also numerically calculated. Moreover, the heat capacity and the thermodynamic scalar are studied. The result indicates that the information of the first-order black hole phase transition is encoded in the heat capacity and scalar. However, the phase transition point cannot be directly calculated with them. Nevertheless, the critical point linked to a second-order phase transition can be determined by either the heat capacity or the scalar. In addition, we calculate the critical exponents of the heat capacity and the scalar for the saturated small and large black holes near the critical point. 1. THE EFFECT OF LEVERAGE AND ECONOMIC VALUE ADDED ON MARKET VALUE ADDED Directory of Open Access Journals (Sweden) Kristína Jančovičová BOGNÁROVÁ 2018-05-01 Full Text Available Economic value added (EVA is a performance measure developed by Stern Stewart & Co. that attempts to measure the true economic profit produced by a company. Such a metric is useful for investors who wish to determine how well a company has produced value for its investors, and it can be compared against the company's peers for a quick analysis of how well the company is operating in its industry. Market value added (MVA, on the other hand, is simply the difference between the current total market value of a company and the capital contributed by investors (including both shareholders and bondholders. It is typically used for companies that are larger and publicly-traded. MVA is not a performance metric like EVA, but instead is a wealth metric, measuring the level of value a company has accumulated over time. In order to maximise the value for shareholders, companies should strive towards maximising MVA and not necessarily their total market value. It is believed, that the best way to do so is to maximize EVA, which reflects a company’s ability to earn returns above the cost of capital. The leverage available to companies that incur fixed costs and use borrowed capital with a fixed interest charge has been known and quantified by financial managers for some time. In this research the effect of leverage and EVA on MVA as the measure of shareholder wealth creation was analysed. Leverage and EVA have been used as the independent variables whereas MVA has been used as the measure of shareholder wealth creation. Correlation and regression methods have been employed to find out in what way financial managers can practice the effects of leverage and EVA to maximize MVA. The results showed that EVA and leverage have no profound impact on MVA of the selected Slovak companies International Nuclear Information System (INIS) Kilbourn, M.R.; Welch, M.J.; Dence, C.S.; Tewson, T.J.; Saji, H.; Maeda, M. 1984-01-01 Syntheses of [ 18 F]haloperidol and [ 18 F]spiroperidol in both no-carrier-added and carrier-added forms have been accomplished. The no-carrier-added [ 18 F]butyrophenone neuroleptics were prepared in low ( 18 F-neuroleptics were prepared in better (5-17%) yields by 18 F-for- 19 F nucleophilic aromatic substitution. The preparation of all synthetic precursors, and procedures for radiolabeling are fully described. (author) 3. Neumann and Neumann-Rosochatius integrable systems from membranes on AdS4 x S7 International Nuclear Information System (INIS) Bozhilov, Plamen 2007-01-01 It is known that large class of classical string solutions in the type IIB AdS 5 x S 5 background is related to the Neumann and Neumann-Rosochatius integrable systems, including spiky strings and giant magnons. It is also interesting if these integrable systems can be associated with some membrane configurations in M-theory. We show here that this is indeed the case by presenting explicitly several types of membrane embedding in AdS 4 x S 7 with the searched properties 4. Unitary representations of some infinite-dimensional Lie algebras motivated by string theory on AdS3 International Nuclear Information System (INIS) Andreev, Oleg 1999-01-01 We consider some unitary representations of infinite-dimensional Lie algebras motivated by string theory on AdS 3 . These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS 3 exists 5. On the Thermodynamics of a Gas of AdS Black Holes and the Quark-Hadron Phase Transition CERN Document Server Ellis, Jonathan Richard; Mavromatos, Nikolaos E; Ellis, John 1999-01-01 We discuss the thermodynamics of a gas of black holes in five-dimensional anti-de-Sitter (AdS) space, showing that they are described by a van der Waals equation of state. Motivated by the Maldacena conjecture, we relate the energy density and pressure of this non-ideal AdS black-hole gas to those of four-dimensional gauge theory in the unconfined phase. We find that the energy density rises rapidly above the deconfinement transition temperature, whilst the pressure rises more slowly towards its asymptotic high-temperature value, in qualitative agreement with lattice simulations. 6. Logarithmic corrections to entropy and AdS/CFT Abstract. We calculate the correction to the Bekenstein-Hawking entropy formula for five-dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence. 7. Ad populum. Parlare alla pancia: retoriche del populismo in Europa Directory of Open Access Journals (Sweden) Yulia Ivanova 2016-12-01 Full Text Available Recensiamo il libro Ad populum. Parlare alla pancia: retorica del populismo in Europa. Eds. Bruno Capaci e Giuditta Spassini. Bologna: I libri di Emil di Odoya srl., 2016. Stampa. Review of Ad populum. Parlare alla pancia: retorica del populismo in Europa. Eds. Bruno Capaci and Giuditta Spassini. Bologna: I libri di Emil di Odoya srl., 2016. Print 8. Asymptotics of Multivariate Regression with Consecutively Added Dependent Varibles NARCIS (Netherlands) Raats, V.M.; van der Genugten, B.B.; Moors, J.J.A. 2004-01-01 We consider multivariate regression where new dependent variables are consecutively added during the experiment (or in time).So, viewed at the end of the experiment, the number of observations decreases with each added variable. The explanatory variables are observed throughout.In a previous paper 9. Analysis of Added Value of Subscores with Respect to Classification Science.gov (United States) Sinharay, Sandip 2014-01-01 Brennan noted that users of test scores often want (indeed, demand) that subscores be reported, along with total test scores, for diagnostic purposes. Haberman suggested a method based on classical test theory (CTT) to determine if subscores have added value over the total score. One way to interpret the method is that a subscore has added value… 10. Improved Functionality and Curation Support in the ADS Science.gov (United States) Accomazzi, Alberto; Kurtz, Michael J.; Henneken, Edwin A.; Grant, Carolyn S.; Thompson, Donna; Chyla, Roman; Holachek, Alexandra; Sudilovsky, Vladimir; Murray, Stephen S. 2015-01-01 11. Western hardwoods : value-added research and demonstration program Science.gov (United States) D. W. Green; W. W. Von Segen; S. A. Willits 1995-01-01 Research results from the value-added research and demonstration program for western hardwoods are summarized in this report. The intent of the program was to enhance the economy of the Pacific Northwest by helping local communities and forest industries produce wood products more efficiently. Emphasis was given to value-added products and barriers to increased... 12. The added value of Facility management in the educational environment NARCIS (Netherlands) Kok, H.B.; Mobach, M.; Omta, S.W.F. 2011-01-01 Purpose – The purpose of this paper is to define the added value of facility management (FM) in general and to develop a typology of facility services based on their added value in the educational environment. Design/methodology/approach – This paper is based on a literature review and first 13. Tomography of photon-added and photon-subtracted states NARCIS (Netherlands) Bazrafkan, MR; Man'ko, [No Value The purpose of this paper is to introduce symplectic and optical tomograms of photon-added and photon-subtracted quantum states. Explicit relations for the tomograms of photon-added and photon-subtracted squeezed coherent states and squeezed number states are obtained. Generating functions for the 14. Exogenous Variables and Value-Added Assessments: A Fatal Flaw Science.gov (United States) Berliner, David C. 2014-01-01 Background: There has been rapid growth in value-added assessment of teachers to meet the widely supported policy goal of identifying the most effective and the most ineffective teachers in a school system. The former group is to be rewarded while the latter group is to be helped or fired for their poor performance. But, value-added approaches to… 15. Value Added Methods: Moving from Univariate to Multivariate Criteria Science.gov (United States) Newman, David; Newman, Isadore; Ridenour, Carolyn; Morales, Jennifer 2014-01-01 The authors describe five value-added methods (VAM) used in school assessment as the backdrop to their main thesis. Then they review the assumptions underlying measurement and evaluation, the foundation of all assessment systems, including value-added. They discuss the traditional criterion variable used in VAM: a standardized test score. Next,… Science.gov (United States) Recommendations for intakes of added sugars have varied considerably and the scientific basis supporting these recommendations has been inconsistent. The goal of this study was to examine the association of usual intake (UI) of added sugars and nutrient adequacy in those participating in NHANES 2009... 17. Decentralized position verification in geographic ad hoc routing NARCIS (Netherlands) Leinmüller, Tim; Schoch, Elmar; Kargl, Frank; Maihöfer, Christian Inter-vehicle communication is regarded as one of the major applications of mobile ad hoc networks (MANETs). Compared to MANETs or wireless sensor networks (WSNs), these so-called vehicular ad hoc networks (VANETs) have unique requirements on network protocols. The requirements result mainly from 18. Secure ADS-B authentication system and method Science.gov (United States) Viggiano, Marc J (Inventor); Valovage, Edward M (Inventor); Samuelson, Kenneth B (Inventor); Hall, Dana L (Inventor) 2010-01-01 19. Exploring Value-Added Options - Opportunities in Mouldings and Millwork Science.gov (United States) Bob Smith; Philip A. Araman 1997-01-01 The millwork industry, which includes manufacture of doors, windows, stair parts, blinds, mouldings, picture frame material, and assorted trim, can be a lucrative value-added opportunity for sawmills. Those entering the value-added millwork market often find that it is a great opportunity to generate greater profits from upper grades and utility species, such as yellow... 20. Adding Value by FM and CREM in Dutch hospitals NARCIS (Netherlands) van der Voordt, D.J.M.; Prevosth, J.; van der Zwart, J. 2012-01-01 Purpose: To explore if and how Dutch hospital managers steer on adding value by well-considered Facility Management (FM) and Corporate Real Estate Management (CREM), which values are leading, and how adding value is being translated into concrete interventions. Methodology: In addition to a review 1. Creating value added to customers: Marketing and sales role Directory of Open Access Journals (Sweden) Damnjanović Vesna 2006-01-01 Full Text Available This paper presents the new trends in sales and marketing areas which reshaping markets and changing the way business is done. Marketing and sales management need a well-defined strategy for added value exploration, creation and delivery. The holistic marketing process involves all stakeholders and required them to participate in the value added creation process. Science.gov (United States) Clarke, Theresa B.; Murphy, Jamie; Wetsch, Lyle R.; Boeck, Harold 2018-01-01 Instructors may find it difficult to stay abreast of the rapidly changing nature of search engine marketing (SEM) and to incorporate hands-on, practical classroom experiences. One solution is Google Ad Grants, a nonprofit edition of Google AdWords that provides up to \$10,000 monthly in free advertising. A quasi-experiment revealed no differences… 3. Introduction to the AdS/CFT correspondence NARCIS (Netherlands) de Boer, J.; Baulieu, L.; Benakli, K.; Douglas, M.R.; Mansoulié, B.; Rabinovici, E.; Cugliandolo, L.F. 2015-01-01 This chapter provides a summary of some of the most important aspects of the AdS/CFT correspondence, together with pointers to some of the vast number of papers that have been published on this subject. The AdS/CFT correspondence is one of the most exciting discoveries in theoretical physics of the 4. Creating value added to customers: Marketing and sales role OpenAIRE Damnjanović Vesna; Filipović Vinka 2006-01-01 This paper presents the new trends in sales and marketing areas which reshaping markets and changing the way business is done. Marketing and sales management need a well-defined strategy for added value exploration, creation and delivery. The holistic marketing process involves all stakeholders and required them to participate in the value added creation process. 5. 25 CFR 11.904 - Guardian ad litem. Science.gov (United States) 2010-04-01 ... 25 Indians 1 2010-04-01 2010-04-01 false Guardian ad litem. 11.904 Section 11.904 Indians BUREAU OF INDIAN AFFAIRS, DEPARTMENT OF THE INTERIOR LAW AND ORDER COURTS OF INDIAN OFFENSES AND LAW AND ORDER CODE Children's Court § 11.904 Guardian ad litem. The children's court, under any proceeding... 6. Assured Resource Sharing in Ad-Hoc Collaboration Energy Technology Data Exchange (ETDEWEB) Ahn, Gail-Joon [Arizona State Univ., Tempe, AZ (United States) 2015-12-19 The project seeks an innovative framework to enable users to access and selectively share resources in distributed environments, enhancing the scalability of information sharing. We have investigated secure sharing & assurance approaches for ad-hoc collaboration, focused on Grids, Clouds, and ad-hoc network environments. 7. Measuring the added value of IT in construction firms NARCIS (Netherlands) Laan, Albertus; Voordijk, Johannes T.; Kolkman, S.; Greenwood, D.J. 2003-01-01 The added value of information technology (IT) varies widely along firms. The objective of this paper is to analyse the underlying factors that enlarge or reduce the added value of information systems and IT-applications in construction firms. By applying the process-oriented approach of Tallon et 8. Reflecting on future research concerning the added value of FM NARCIS (Netherlands) Jensen, PA; van der Voordt, Theo; Coenen, C; Sarasoja, AL 2014-01-01 Purpose: To summarize recent research findings and reflections on The Added Value of Facilities Management and to outline perspectives for future research and development of the added value of FM. Methodology - The article is based on reflections on contributions to the recently published book 9. Degenerate stars and gravitational collapse in AdS/CFT NARCIS (Netherlands) Arsiwala, X.; de Boer, J.; Papadodimas, K.; Verlinde, E. 2010-01-01 We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi 10. Degenerate stars and gravitational collapse in AdS/CFT NARCIS (Netherlands) Arsiwalla, X.; de Boer, J.; Papadodimas, K.; Verlinde, E. 2011-01-01 We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi 11. Degenerate stars and gravitational collapse in AdS/CFT NARCIS (Netherlands) Arsiwalla, Xerxes; de Boer, Jan; Papadodimas, Kyriakos; Verlinde, Erik We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi Science.gov (United States) Gombeski, William R; Taylor, Jan; Krauss, Katie; Medeiros, Clayton 2003-01-01 13. Loop effects in AdS/CFT and beyond International Nuclear Information System (INIS) Gubser, Steven S. 2003-01-01 Double-trace operators which are relevant deformations of large N conformal field theories give rise to renormalization group flows that can be studied on both sides of the AdS/CFT duality. One-loop calculations in AdS can be compared successfully to results derived in field theory using the Hubbard-Stratonovich transformation. The calculations do not rely on supersymmetry, and they apply in any dimension, provided the original conformal field theory and its AdS dual are well-defined. A speculative idea is proposed for solving the cosmological constant problem based on non-gravitational strings that become light as the universe expands. This is a summary of my talk presented at the Nishinomiya-Yukawa Symposium in Nishinomiya, Japan. (author) 14. The progress of basic research for ADS in China International Nuclear Information System (INIS) Xia Haihong; Zhao Zhixiang; Ding Dazhao 2002-01-01 The conceptual study of Accelerator Driven System (ADS), which is an entirely new approach for the exploitation of next generation nuclear energy, had lasted for about five years and ended in 1999 in China. From then a five years program of basic research for ADS has been launched. According to present technical and budget status in China, a moderate style multi-purpose verification system is under consideration, which consists of a low energy accelerator (150MeV/3mA proton linac) and a swimming pool light water sub-critical reactor. CIAE (China Institute of Atomic Energy), IHEP (Institute of High Energy Physics), PKU-IHIP (Institute of Heavy Ion Physics in Peking University) and other institutions are jointly carrying on the basic research of ADS. The main results on ADS system optimization, ADS related reactor physics study, nuclear physics study, accelerator physics and technology study, material compatibility study, material radiation effects study has been reported. (author) 15. Gauge boson exchange in AdSd+1 International Nuclear Information System (INIS) D'Hoker, Eric; Freedman, Daniel Z. 1999-01-01 We study the amplitude for exchange of massless gauge bosons between pairs of massive scalar fields in anti-de Sitter space. In the AdS/CFT correspondence this amplitude describes the contribution of conserved flavor symmetry currents to 4-point functions of scalar operators in the boundary conformal theory. A concise, covariant, Y2K compatible derivation of the gauge boson propagator in AdS d+ 1 is given. Techniques are developed to calculate the two bulk integrals over AdS space leading to explicit expressions or convenient, simple integral representations for the amplitude. The amplitude contains leading power and sub-leading logarithmic singularities in the gauge boson channel and leading logarithms in the crossed channel. The new methods of this paper are expected to have other applications in the study of the Maldacena conjecture 16. AD HOC TEAMWORK BEHAVIORS FOR INFLUENCING A FLOCK Directory of Open Access Journals (Sweden) Katie Genter 2016-02-01 Full Text Available Ad hoc teamwork refers to the challenge of designing agents that can influence the behavior of a team, without prior coordination with its teammates. This paper considers influencing a flock of simple robotic agents to adopt a desired behavior within the context of ad hoc teamwork. Specifically, we examine how the ad hoc agents should behave in order to orient a flock towards a target heading as quickly as possible when given knowledge of, but no direct control over, the behavior of the flock. We introduce three algorithms which the ad hoc agents can use to influence the flock, and we examine the relative importance of coordinating the ad hoc agents versus planning farther ahead when given fixed computational resources. We present detailed experimental results for each of these algorithms, concluding that in this setting, inter-agent coordination and deeper lookahead planning are no more beneficial than short-term lookahead planning. 17. Accelerated detectors and worldsheet horizons in AdS/CFT Science.gov (United States) Chernicoff, Mariano; Paredes, Angel 2011-03-01 We use the AdS/CFT correspondence to discuss the response of an accelerated observer to the quantum vacuum fluctuations. In particular, we study heavy quarks probing a strongly coupled CFT by analysing strings moving in AdS. We propose that, in this context, a non-trivial detection rate is associated to the existence of a worldsheet horizon and we find an Unruh-like expression for the worldsheet temperature. Finally, by examining a rotating string in global AdS we find that there is a transition between string embeddings with and without worldsheet horizon. The dual picture corresponds to having non-trivial or trivial interaction with the quantum vacuum respectively. This is in qualitative agreement with results of Davies et al. 18. Value Adding Management: A New Facilities Management Concept DEFF Research Database (Denmark) Jensen, Per Anker; Katchamart, Akarapong 2011-01-01 Purpose: To investigate how Facilities Management (FM) can add value and develop a management concept that can assist facilities managers in implementing value adding strategies and practices. Theory: The study is based on the management model for FM included in the European FM standards, recent...... is investigated, tested and discussed based on a case study of an international corporation. Findings: The study shows that the management model for FM creates a relevant starting point but also that stakeholder and relationship management is an essential aspect of Value Adding Management. The case study confirms...... the relevance of the basic concept and provides an important example of how Value Adding Management can be implemented and added value measured. Originality/value: The study develops a concept of Value Adding Management, which is new in FM literature. It is expected to increase the awareness of the impacts... 19. Facilities Management and Value Adding - The LEGO case DEFF Research Database (Denmark) Jensen, Per Anker; Katchamart, Akarapong on the management model for FM included in the European FM standards, recent theories on added value of FM and real estate and the related concept of Value Management from building projects. The paper outlines a preliminary theoretical based management concept, which is investigated, tested and discussed based...... on a case study of LEGO. Results: The study shows that the management model for FM creates a relevant starting point but also that stakeholder and relationship management is an essential aspect of Value Adding Management. The case study confirms the relevance of the basic concept and provides an important...... example of how Value Adding Management can be implemented and added value measured. Practical Implications: The concept of Value Adding Management is expected to increase the awareness of the impacts and strategic importance of FM for organisations and can be a practical tool for facilities managers... 20. "Transmarina vel orientalis especies magno labore quaesita, multo predo empta". Especias y Sociedad en el Mediterráneo Noroccidental en el siglo XII Directory of Open Access Journals (Sweden) Riera i Melis, Antonio 2000-12-01 Full Text Available During the 12th century, spices were known and appreciated in Catalonia and Languedoc by a great part of society. The success of spices was a result of their organoleptic qualities, their dietetic virtues and their exoticism due to their remote origin. To have pepper, ginger or cloves became a sign of distinction and good taste. In the central centuries of the Middle Ages, oriental seasonings had a social and cultural role much more important than it has been thought.[fr] Au XIIᵉ siècle, les épices furent connues et appréciées en Catalogne et en Languedoc par un grand secteur de la société. Son succès était une conséquence de ses qualités organoleptiques, de ses vertues diététiques et du caractère exotique que leur proportionnait son lointain origine. Assaisonner avec du poivre, du gingembre or du clou devint un signe de clase et de bon goût. Aux siècles centrales du Moyen Âge, les condiments provenant de l'Orient jouaient un rôle sociale et culturelle plus important qu'on n'avait pas été considéré jusqu'aujourd'hui. 1. On the Fock space realizations of nonlinear algebras describing the high spin fields in AdS spaces International Nuclear Information System (INIS) Burdik, C.; Navratil, O.; Pashnev, A. 2002-01-01 The method of construction of Fock space realizations of Lie algebras is generalized for nonlinear algebras. We consider as an example the nonlinear algebra of constraints which describe the totally symmetric fields with higher spins in the AdS space-time 2. Authoritative parenting and issue involvement as indicators of ad recall: an empirical investigation of anti-drug ads for parents. Science.gov (United States) Quick, Brian L; Stephenson, Michael T 2007-01-01 This investigation explores the role of authoritative parenting and issue involvement in regard to the recall of parental anti-drug ads encouraging child monitoring. In addition, the study tested whether issue involvement mediates the association between authoritative parenting and recall of parental anti-drug television ads among parents (N = 185) with adolescents in Grades 6, 7, and 8. The results indicate that (a) authoritative parenting is positively associated with favorable attitudes toward monitoring children and issue involvement regarding adolescent drug use, (b) issue involvement is associated with ad recall, (c) issue involvement mediates the relationship between authoritative parenting and ad recall, (d) ad recall is not associated with favorable attitudes toward parental monitoring, and (e) favorable attitudes regarding parental monitoring are positively associated with intentions to engage in monitoring within the next 6 months. 3. Thermodynamics of (d+1)-dimensional NUT-charged AdS spacetimes International Nuclear Information System (INIS) Clarkson, R.; Fatibene, L.; Mann, R.B. 2003-01-01 We consider the thermodynamic properties of (d+1)-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti-de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either (d-1)-dimensional (called 'bolts') or of lower dimensionality (pure 'NUTs'). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge methods and the AdS/CFT-inspired counterterm approach. We then generalize these results to arbitrary dimensionality. We find in 4k+2 dimensions that there are no regions in parameter space in the pure NUT case for which the entropy and specific heat are both positive, and so all such spacetimes are thermodynamically unstable. For the pure NUT case in 4k dimensions a region of stability exists in parameter space that decreases in size with increasing dimensionality. All bolt cases have some region of parameter space for which thermodynamic stability can be realized 4. Superconformal symmetry in the Kaluza-Klein spectrum of warped AdS(3) Energy Technology Data Exchange (ETDEWEB) Schmude, Johannes; Vasilakis, Orestis [Department of Physics, Universidad de Oviedo, Avda. Calvo Sotelo 18, 33007, Oviedo (Spain) 2016-10-18 We study the Kaluza-Klein spectrum of warped AdS{sub 3} compactifications of type IIB with five-form flux which are dual to N=(0,2) SCFTs in two dimensions. We prove that the spectra of fluctuations of both the spin 2 sector of the graviton and the axio-dilaton are bounded. At the bound the modes have the correct quantum numbers to be chiral primaries and descendants thereof respectively. Moreover, we prove that the same modes give rise to superpartners in the dilatino spectrum. Our results show that a subset of the mesonic chiral ring of the dual SCFT is isomorphic to the first Kohn-Rossi cohomology groups. As an example, we consider the compactification of four-dimensional Y{sup p,q} theories on Riemann surfaces for the case of the universal twist. We conclude by studying fluctuations of the three-form, where we are able to identify Betti multiplets after imposing some mild assumptions. 5. Estimating Free and Added Sugar Intakes in New Zealand. Science.gov (United States) Kibblewhite, Rachael; Nettleton, Alice; McLean, Rachael; Haszard, Jillian; Fleming, Elizabeth; Kruimer, Devonia; Te Morenga, Lisa 2017-11-27 6. Added Sugars and Cardiovascular Disease Risk in Children Science.gov (United States) Vos, Miriam B.; Kaar, Jill L.; Welsh, Jean A.; Van Horn, Linda V.; Feig, Daniel I.; Anderson, Cheryl A.M.; Patel, Mahesh J.; Munos, Jessica Cruz; Krebs, Nancy F.; Xanthakos, Stavra A.; Johnson, Rachel K. 2017-01-01 7. Estimating Free and Added Sugar Intakes in New Zealand Directory of Open Access Journals (Sweden) Rachael Kibblewhite 2017-11-01 8. School system evaluation by value added analysis under endogeneity. Science.gov (United States) Manzi, Jorge; San Martín, Ernesto; Van Bellegem, Sébastien 2014-01-01 Value added is a common tool in educational research on effectiveness. It is often modeled as a (prediction of a) random effect in a specific hierarchical linear model. This paper shows that this modeling strategy is not valid when endogeneity is present. Endogeneity stems, for instance, from a correlation between the random effect in the hierarchical model and some of its covariates. This paper shows that this phenomenon is far from exceptional and can even be a generic problem when the covariates contain the prior score attainments, a typical situation in value added modeling. Starting from a general, model-free definition of value added, the paper derives an explicit expression of the value added in an endogeneous hierarchical linear Gaussian model. Inference on value added is proposed using an instrumental variable approach. The impact of endogeneity on the value added and the estimated value added is calculated accurately. This is also illustrated on a large data set of individual scores of about 200,000 students in Chile. 9. ADS 2.0: New Architecture, API and Services Science.gov (United States) Chyla, R.; Accomazzi, A.; Holachek, A.; Grant, C. S.; Elliott, J.; Henneken, E. A.; Thompson, D. M.; Kurtz, M. J.; Murray, S. S.; Sudilovsky, V. 2015-09-01 10. Estimating Free and Added Sugar Intakes in New Zealand Science.gov (United States) Kibblewhite, Rachael; Nettleton, Alice; McLean, Rachael; Haszard, Jillian; Fleming, Elizabeth; Kruimer, Devonia 2017-01-01 11. Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3 International Nuclear Information System (INIS) Kovacs, Stefano; Sato, Yuki; Shimada, Hidehiko 2014-01-01 We study the duality between M-theory in AdS 4 ×S 7 /ℤ k and the ABJM N=6 Chern–Simons-matter theory with gauge group U(N)×U(N) and level k, taking N large and k of order 1. In this M-theoretic regime the lack of an explicit formulation of M-theory in AdS 4 ×S 7 /ℤ k makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. We focus on states on the gravity side with large angular momentum J≫1 associated with a single plane of rotation in S 7 and identify their dual operators in the CFT. We show that natural approximation schemes arise on both sides thanks to the presence of the small parameter 1/J. On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size J/k. A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS 4 ×S 7 /ℤ k when N 1/3 ≪J≪N 1/2 . On the CFT side, we study the theory on S 2 ×ℝ with magnetic flux J/k. A Born–Oppenheimer-type expansion arises naturally for large J in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS 4 /CFT 3 correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime 12. Intake of added sugar in Malaysia: a review. Science.gov (United States) Amarra, Maria Sofia V; Khor, Geok Lin; Chan, Pauline 2016-01-01 Science.gov (United States) Laclaustra, Martin; Rodriguez-Artalejo, Fernando; Guallar-Castillon, Pilar; Banegas, Jose R; Graciani, Auxiliadora; Garcia-Esquinas, Esther; Ordovas, Jose; Lopez-Garcia, Esther 2018-04-09 CERN Document Server Song, Yi 2014-01-01 15. Autism Disorder (AD): An Updated Review for Paediatric Dentists. Science.gov (United States) J, Udhya; M M, Varadharaja; J, Parthiban; Srinivasan, Ila 2014-02-01 Over the past two decades, there has been an explosion of interest in Autism Disorder (AD). Knowledge and awareness on the condition has grown exponentially at all levels among the general public, parents, health professionals, the research community and more recently, at parliamentary level. The world has begun to recognize the scope of this problem and act internationally and locally to improve the lives of the growing number of individuals and families affected by this devastating disorder. This article reviews the dental literature since 1969 and it summarizes characteristics of patients with AD, oral health status and dental management of patients with AD. 16. Ad hoc laser networks component technology for modular spacecraft Science.gov (United States) Huang, Xiujun; Shi, Dele; Shen, Jingshi 2017-10-01 Distributed reconfigurable satellite is a new kind of spacecraft system, which is based on a flexible platform of modularization and standardization. Based on the module data flow analysis of the spacecraft, this paper proposes a network component of ad hoc Laser networks architecture. Low speed control network with high speed load network of Microwave-Laser communication mode, no mesh network mode, to improve the flexibility of the network. Ad hoc Laser networks component technology was developed, and carried out the related performance testing and experiment. The results showed that ad hoc Laser networks components can meet the demand of future networking between the module of spacecraft. 17. Regulating debit cards: the case of ad valorem fees OpenAIRE Zhu Wang 2010-01-01 Debit cards have become an indispensable part of the U.S. payments system, accounting for more than a third of consumer payments at point of sale. With this development has come controversy: Card networks charge merchants fees that merchants believe are too high. And most of the fees are ad valorem that is, based on transaction value rather than fixed fees per transaction. ; Given that debit cards incur a fixed cost per transaction, why do networks charge ad valorem fees? How do ad valorem fe... 18. Optimize-and-Dispatch Architecture for Expressive Ad Auctions OpenAIRE Parkes, David C.; Sandholm, Tuomas 2005-01-01 Ad auctions are generating massive amounts of revenue for online search engines such as Google. Yet, the level of expressiveness provided to participants in ad auctions could be significantly enhanced. An advantage of this could be improved competition and thus improved revenue to a seller of the right to advertise to a stream of search queries. In this paper, we outline the kinds of expressiveness that one might expect to be useful for ad auctions and introduce a high-level “optimize-and-... 19. Preliminary AD-Horn Thermomechanical and Electrodynamic Simulations CERN Document Server AUTHOR\|(CDS)2095747; Horvath, David; Calviani, Marco 2016-01-01 As part of the Antiproton Decelerator (AD) target area consolidation activities planned for LS2, it has been necessary to perform a comprehensive study of the thermo-structural behaviour of the AD magnetic horn during operation, in order to detail specific requirements for the upgrade projects and testing procedures. The present work illustrates the preliminary results of the finite element analysis carried out to evaluate the thermal and structural behaviour of the device, as well as the methodology used to model and solve the thermomechanical and electrodynamic simulations performed in the AD magnetic horn. 20. On 'Money' in ISLM and AD/AS Models OpenAIRE Thomas K. Rymes; Colin Rogers 2000-01-01 Hicks's ISLM model interpretation of Keynes's theory is subject to much controversy. In this paper, we focus upon the 'real balance' effect and its role in ISLM and AD/AS analyses. We shall argue that ISLM and AD/AS require 'nominal anchors'. We live in a world where, increasingly, the 'money' in the ISLM and AD/AS model no longer exists (as Keynes imperfectly understood in his TREATISE ON MONEy). There are no longer any nominal anchors, rather they have been replaced by discretionary policy.... 1. Hypothetical atopic dermatitis-myeloproliferative neoplasm (AD-MPN syndrome Directory of Open Access Journals (Sweden) Toshiaki eKawakami 2015-08-01 Full Text Available Atopic dermatitis (AD is a chronic inflammatory skin disease. Myeloproliferative neoplasms (MPNs are hematopoietic malignancies caused by uncontrolled proliferation of hematopoietic stem/progenitor cells. Recent studies have described several mutant mice exhibiting both AD-like skin inflammation and MPN. Common pathways for skin inflammation encompass overexpression of thymic stromal lymphopoietin and reduced signaling of epidermal growth factor receptor in the epidermis, while overproduction of granulocyte-colony stimulating factor by keratinocytes and constitutive activation of Stat5 in hematopoietic stem cells are important for the development of MPN. The murine studies suggest the existence of a similar human disease tentatively termed the AD-MPN syndrome. 2. Schwinger-Keldysh propagators from AdS/CFT correspondence International Nuclear Information System (INIS) Herzog, C.P.; Son, D.T. 2003-01-01 We demonstrate how to compute real-time Green's functions for a class of finite temperature field theories from their AdS gravity duals. In particular, we reproduce the two-by-two Schwinger-Keldysh matrix propagator from a gravity calculation. Our methods should work also for computing higher point lorentzian signature correlators. We elucidate the boundary condition subtleties which hampered previous efforts to build a lorentzian-signature AdS/CFT correspondence. For two-point correlators, our construction is automatically equivalent to the previously formulated prescription for the retarded propagator. (author) 3. Three spin string configuration in γ-Deformed AdS5xS5 background International Nuclear Information System (INIS) Bobev, N.; Rashkov, R.; Dimov, H. 2006-01-01 The aim of this paper is to investigate semiclassical rotating string configurations in the recently found Lunin-Maldacena background. This background is conjectured to be dual to the Leigh-Strassler β-deformation of N = 4 SYM and therefore a good laboratory for tests of the AdS/CFT correspondence beyond the well explored AdS 5 xS 5 case. We consider different multispin configurations of rotating strings by allowing the strings to move in both the AdS 5 and the deformed S 5 part of the Lunin-Maldacena background. For all of these configurations we compute the string energy in terms of the angular momenta and the string winding numbers and thus provide the possibility of reproducing our results from a computation of the anomalous dimension of the corresponding dilatation operator. This can be achieved by means of the Bethe ansatz techniques for the relevant sectors of the corresponding Yang-Mills theory. We also compare our results to those for multispin rotating strings on AdS 5 xS 5 . (authors) 4. On thermodynamics of charged AdS black holes in extended phases space via M2-branes background International Nuclear Information System (INIS) Chabab, M.; Masmar, K.; El Moumni, H. 2016-01-01 Motivated by a recent work on asymptotically AdS 4 black holes in M-theory, we investigate both thermodynamics and the thermodynamical geometry of Reissner-Nordstrom-AdS black holes from M2-branes. More precisely, we study AdS black holes in AdS 4 x S 7 , with the number of M2-branes interpreted as a thermodynamical variable. In this context, we calculate various thermodynamical quantities including the chemical potential, and examine their phase transitions along with the corresponding stability behaviors. In addition, we also evaluate the thermodynamical curvatures of the Weinhold, Ruppeiner, and Quevedo metrics for M2-branes geometry to study the stability of such a black object. We show that the singularities of these scalar curvature's metrics reproduce similar stability results to those obtained by the phase transition diagram via the heat capacities in different ensembles either when the number of the M2 branes or the charge is held fixed. Also, we note that all results derived in Belhaj et al. (Eur Phys J C 76(2):73, 2016) are recovered in the limit of the vanishing charge. (orig.) 5. Interference in wireless ad hoc networks with smart antennas KAUST Repository Alabdulmohsin, Ibrahim 2014-01-01 In this paper, we show that the use of directional antennas in wireless ad hoc networks can actually increase interference due to limitations of virtual carrier sensing. We derive a simple mathematical expression for interference in both physical 6. Development of ADS virtual accelerator based on XAL International Nuclear Information System (INIS) Wang Pengfei; Cao Jianshe; Ye Qiang 2014-01-01 XAL is a high level accelerator application framework that was originally developed by the Spallation Neutron Source (SNS), Oak Ridge National Laboratory. It has an advanced design concept and has been adopted by many international accelerator laboratories. Adopting XAL for ADS is a key subject in the long term. This paper will present the modifications to the original XAL applications for ADS. The work includes a proper relational database schema modification in order to better suit the requirements of ADS configuration data, redesigning and re-implementing db2xal application, and modifying the virtual accelerator application. In addition, the new device types and new device attributes for ADS online modeling purpose are also described here. (authors) Data.gov (United States) National Aeronautics and Space Administration — This dataset is derived under the Cross-Calibrated Multi-Platform (CCMP) project and contains a value-added 5-day mean ocean surface wind and pseudostress to... 8. Semiclassical equivalence of Green–Schwarz and pure–spinor/hybrid formulations of superstrings in AdS5 × S5 and AdS2 × S2 × T6 International Nuclear Information System (INIS) Cagnazzo, Alessandra; Sorokin, Dmitri; Tseytlin, Arkady A; Wulff, Linus 2013-01-01 We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green–Schwarz and in the pure–spinor formulations of superstrings in AdS 5 × S 5 . While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first versus second-derivative kinetic terms, presence versus absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of 16 fermionic modes of the pure–spinor formulation is the same as in the Green–Schwarz superstring and the contribution of the extra ‘massless’ fermionic modes cancels against that of the pure–spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green–Schwarz and the hybrid formulations of superstrings in AdS 2 × S 2 × T 6 by studying several particular examples of string solutions. (paper) 9. Source Authentication for Multicast in Mobile Ad Hoc Networks National Research Council Canada - National Science Library Ramachandran, Prabha 2003-01-01 Recent emergence and popularity of mobile ad hoc networks in a host of current-day applications has instigated a suite of research challenges, primarily in routing and security issues for such networks... DEFF Research Database (Denmark) Nell, Phillip C.; Beugelsdijk, Sjoerd; Ambos, Björn 2014-01-01 National Research Council Canada - National Science Library Shults, Gary 1998-01-01 .... Textured soy protein (TSP) was also added at a 20% level. A trained eight-member panel evaluated the products for flavor, odor, color, texture and appearance using an eight points intensity scale... 12. Reliability and fault tolerance in the European ADS project International Nuclear Information System (INIS) Biarrotte, Jean-Luc 2013-01-01 After an introduction to the theory of reliability, this paper focuses on a description of the linear proton accelerator proposed for the European ADS demonstration project. Design issues are discussed and examples of cases of fault tolerance are given. (author) 13. Application of consistent fluid added mass matrix to core seismic International Nuclear Information System (INIS) Koo, K. H.; Lee, J. H. 2003-01-01 In this paper, the application algorithm of a consistent fluid added mass matrix including the coupling terms to the core seismic analysis is developed and installed at SAC-CORE3.0 code. As an example, we assumed the 7-hexagon system of the LMR core and carried out the vibration modal analysis and the nonlinear time history seismic response analysis using SAC-CORE3.0. Used consistent fluid added mass matrix is obtained by using the finite element program of the FAMD(Fluid Added Mass and Damping) code. From the results of the vibration modal analysis, the core duct assemblies reveal strongly coupled vibration modes, which are so different from the case of in-air condition. From the results of the time history seismic analysis, it was verified that the effects of the coupled terms of the consistent fluid added mass matrix are significant in impact responses and the dynamic responses 14. Effect of exogenously added rhamnolipids on citric acid production ... African Journals Online (AJOL) Effect of exogenously added rhamnolipids on citric acid production yield. Wojciech Białas, Roman Marecik, Alicja Szulc, Łukasz Ławniczak, Łukasz Chrzanowski, Filip Ciesielczyk, Teofil Jesionowski, Andreas Aurich ... 15. Seismicity Catalog Collection, 2150 BC to 1996 AD Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — The Seismicity Catalog Collection is a compilation data on over four million earthquakes dating from 2150 BC to 1996 AD from NOAA's National Geophysical Data Center... 16. Regulatory Approaches for Adding Capacity to Existing Hydropower Facilities Energy Technology Data Exchange (ETDEWEB) Levine, Aaron L. [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Curtis, Taylor L. [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Kazerooni, Borna [National Renewable Energy Laboratory (NREL), Golden, CO (United States) 2017-10-24 In 2015, hydroelectric generation accounted for more than 6 percent of total net electricity generation in the United States and 46 percent of electricity generation from all renewables. The United States has considerable hydroelectric potential beyond what is already being developed. Nearly 7 GW of this potential is found by adding capacity to existing hydropower facilities. To optimize the value of hydroelectric generation, the U.S. Department of Energy's Hydropower Vision Study highlights the importance of adding capacity to existing facilities. This report provides strategic approaches and considerations for Federal Energy Regulatory Commission licensed and exempt hydropower facilities seeking to increase generation capacity, which may include increases from efficiency upgrades. The regulatory approaches reviewed for this report include capacity and non-capacity amendments, adding capacity during relicensing, and adding capacity when converting a license to a 10-MW exemption. 17. Internet-Based Mobile Ad Hoc Networking (Preprint) National Research Council Canada - National Science Library Corson, M. S; Macker, Joseph P; Cirincione, Gregory H 1999-01-01 Internet-based Mobile Ad Hoc Networking is an emerging technology that supports self-organizing, mobile networking infrastructures, and is one which appears well-suited for use in future commercial... 18. Auto correct method of AD converters precision based on ethernet Directory of Open Access Journals (Sweden) NI Jifeng 2013-10-01 Full Text Available Ideal AD conversion should be a straight zero-crossing line in the Cartesian coordinate axis system. While in practical engineering, the signal processing circuit, chip performance and other factors have an impact on the accuracy of conversion. Therefore a linear fitting method is adopted to improve the conversion accuracy. An automatic modification of AD conversion based on Ethernet is presented by using software and hardware. Just by tapping the mouse, all the AD converter channel linearity correction can be automatically completed, and the error, SNR and ENOB (effective number of bits are calculated. Then the coefficients of linear modification are loaded into the onboard AD converter card's EEPROM. Compared with traditional methods, this method is more convenient, accurate and efficient，and has a broad application prospects. 19. Bioconversion of sago residue into value added products \| Awg ... African Journals Online (AJOL) ... value added products. DS Awg-Adeni, S Abd-Aziz, K Bujang, MA Hassan ... sago processing mills. This review focuses on the developments in processes and products for the value addition of sago residues through biotechnological means. 20. Effects of adding cellulose on rheological characteristics of wheat ... African Journals Online (AJOL) Nafiisah plants and are finding applications as food ingredient in many products (Bahr,. 1996). Cereals, like .... might continue to absorb more water as higher levels of cellulose would be added. ... the dough and retention of carbon dioxide. Some other ...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7595789432525635, "perplexity": 2238.3469292551026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591578.1/warc/CC-MAIN-20180720100114-20180720120114-00623.warc.gz"}
http://www.jiskha.com/search/index.cgi?query=tire&page=2	Thursday October 8, 2015 # Search: tire Number of results: 580 physics A rope attaches a tire to an overhanging tree limb. A girl swinging on the tire has a centripetal acceleration of 3.0 m/s^2. If the length of the rope is 2.1 m, what is the girl's tangential speed? November 16, 2010 by helmuth Chem The total pressure in an 11.1L automobile tire is 40psi at 13 degree celcius. By how much does the pressure in the tire rise if it warms to a temperature of 56 degrees celcius and the volume remains at 11.1L ? April 10, 2011 by Maria Math If a wheel has a nail stuck in the tire, the tire is 60m in diameter and the wheel drove R -234(1,0) how far did the nail travel? January 27, 2013 by Ronald physics The gauge pressure in both tires of a bicycle is 720 kPa. If the bicycle and the rider have a combined mass of 87.0 kg, what is the area of contact of each tire with the ground? (Assume that each tire supports half the total weight of the bicycle.) January 23, 2013 by Anonymous Physical Science A 12 kilogram tire is to be pulled by three ropes. One force, F1, has a magnitude of 50N. Orient the other two forces so that the magnitude of the resulting acceleration of the tire is least. And find that magnitude if: F2=30N, F3= 20N. September 18, 2014 by Akila math A tire company determines that to manufacture a certain type of tire, it costs $9000 to set up the production process. Each tire that is produced costs$21 in material and labor. The company sells this tire to wholesale distributors for 49 each. (a) Find a linear function C ... August 4, 2014 by Marie P. Physics A person who weighs 506 N is riding a 94-N mountain bike. Suppose the entire weight of the rider plus bike is supported equally by the two tires. If the gauge pressure in each tire is 6.70 x 105 Pa, what is the area of contact between each tire and the ground? February 8, 2013 by Ashley physics A person who weighs 691 N is riding a 89-N mountain bike. Suppose the entire weight of the rider plus bike is supported equally by the two tires. If the gauge pressure in each tire is 8.40 x 105 Pa, what is the area of contact between each tire and the ground? November 18, 2013 by Anonymous physics 1 A person who weighs 869 N is riding a 98-N mountain bike. Suppose the entire weight of the rider plus bike is supported equally by the two tires. If the gauge pressure in each tire is 7.80 x 105 Pa, what is the area of contact between each tire and the ground? April 22, 2014 by Anonymous physics A person who weighs 717 N is riding a 80-N mountain bike. Suppose the entire weight of the rider plus bike is supported equally by the two tires. If the gauge pressure in each tire is 8.10 x 105 Pa, what is the area of contact between each tire and the ground? August 16, 2015 by victor math A company has two factories that manufacture tires. Suppose 65% of the tires are manufactured in factory 1 and 35% are manufactured in factory 2. In factory 1, 5% of the tires are defective. In factory 2, 2% of the tires are defective. a) Determine the probability that a ... May 23, 2011 by corey Math The air pressure in a tire is 800.000kPa.The internal surface area of the tire is 550.000cm^2. Determine the total force applied by the air to the tire. (Round to 3 decimal places). ANS = 44.000kN Force = Pressure x Area = 800.000kPa x 550.000 = 440000.000N = 440.000kN I keep ... December 26, 2013 by Danny math It takes about735 turns of an average of average 5 th grade byicycle tire to go 1 mile .to the nearest thousand how many times would your tire turn around if you biked besides the runners in a 26-mile marathon? March 7, 2011 by cindy physics A stone has a mass of 6.01 g and is wedged into the tread of an automobile tire, as the drawing shows. The coefficient of static friction between the stone and each side of the tread channel is 0.948. When the tire surface is rotating at 14.7 m/s, the stone flies out of the ... February 23, 2011 by heather physics A stone has a mass of 3.40 g and is wedged into the tread of an automobile tire, as the drawing shows. The coefficient of static friction between the stone and each side of the tread channel is 0.916. When the tire surface is rotating at 18.8 m/s, the stone flies out of the ... April 30, 2012 by Anonymous Physics A stone has a mass of 6.00 10-3 kg and is wedged into the tread of an automobile tire, as the drawing shows. The coefficient of static friction between the stone and each side of the tread channel is 0.73. When the tire surface is rotating at a maximum speed of 17 m/s, the ... November 7, 2012 by Don Trig if a tire is out of round so that the radius in a certain direction is 1 inch more than in the opposite direction, what is the difference in linear speed between these two points on the tire? Angular speed is 40 radians per second September 12, 2007 by Kay Trig/Physics A car's wheel (with tire) is 26 inches in diameter and its center is 12 inches above the road. If the car is traveling at 60 feet per second, how fast is the highest point of the tire moving relative to the ground? September 23, 2007 by Vash Physics A tire cruises up an embankment at 30° for 1 meter before launching across Piranha Lake. What is the velocity of the tire at the top of the embankment in m/s? HELP: Inital KE of the tire is 1/2MV2 + 1/2I(V/R)2; both rotational and translational Final KE = Initial KE - Mg... October 26, 2009 by Sara Math The diameter of a car's tire is 60cm . While the car is being driven , the tire picks up a nail .How high above the ground is the nail after the car has travelled 1km December 8, 2011 by Melissa Math A street is 282 m long is covered with snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn 47 times in traveling the length of the street. What is the diameter of the tire? December 21, 2012 by Josh physics a 40 kg student is riding a bicycle to school. the bicycle has a mass of 12 kg. the area that each tire makes contact with the road can be approximated by a rectangle of dimensions 6 cm x 4 cm. what is the pressure that each tire exerts on the road? give your answer in kPa to ... April 10, 2013 by Anjali physics a 40 kg student is riding a bicycle to school. the bicycle has a mass of 12 kg. the area that each tire makes contact with the road can be approximated by a rectangle of dimensions 6 cm x 4 cm. what is the pressure that each tire exerts on the road? give your answer in kPa to ... April 10, 2013 by Anjali physics a 40 kg student is riding a bicycle to school. the bicycle has a mass of 12 kg. the area that each tire makes contact with the road can be approximated by a rectangle of dimensions 6 cm x 4 cm. what is the pressure that each tire exerts on the road? give your answer in kPa to ... April 10, 2013 by Anjali Behavioral Statistics I need someone to explain HOW to do this..I don't want just the answer I have got to figure out how to do this before my mid-term, and I'm completely clueless! 3. One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,... February 10, 2014 by Jen 5th grade Math I need help with the question below. A bicyle tire has a diameter of 24 inches. If a tire rotates for 20 revolutions about how far has the bike rider ridden? Use 3.14 for pi. I know to find the circumference you would do 24 x 3.14 which equal 75.36. I'm not sure what to do ... March 19, 2012 by Brandi Physics please check A person who weighs 655 N is riding a 98 N mountain bike. Suppose the entire weight of the rider and bike is supported equally by the two tires. If the gauge pressure in each tire is 8.70 X 10^5 Pa, what is the area of contact between each tire and the ground? P=F/A A=F/P A=... April 8, 2007 by Mary Grade 11 math - HELP! The diameter of a car's tire is 52 cm. While the car is being driven, the tire picks up a nail. How high above the ground will the nail be after the car has travelled 0.1 km? can someone please explain how to solve this question? December 12, 2010 by Allison physical Part A Each blade on a wind turbine is engineered to produce an effective force through its center of mass that is perpendicular to its long axis. (Part A figure) The magnitude of the force produced by each blade in a wind of speed v is F=(40.0~{\rm kg/s})v. If the center of ... April 6, 2011 by gary Math The air pressure in a tire is 150.000 kPa. The internal surface area of the tire is 1150.000 cm^2. Determine the total force applied by the air to the tire. (Round to 3 decimal places) Answer = kN 150.000 kPa x 1000 = 150000 Nm 1150.000 cm / 100 cm = 11.5 m Force = Pressure x ... December 26, 2013 by Danny chem The air in a bicycle tire is bubbled through water and collected at 25 C. If the total volume of gas collected is 5.65 L at a temperature of 25 C and a pressure of 735 torr, how many moles of gas was in the bicycle tire? October 13, 2008 by nikki Geometry Write the ratio of the first measurement to the second measurement. Diameter of care tire:40cm Diameter of care tire:18mm I'm not sure hoow to do this. May someone explain how to do this problem. February 12, 2014 by Candy Chemistry 105 The air in a bicycle tire is bubbled through water and collected at 25 C. If the total volume of gas collected is 5.65 L at a temperature of 25 C and a pressure of 729 torr, how many moles of gas was in the bicycle tire? October 23, 2011 by JULIE algebra 1. Are the rotations of figures always congruent? Why are or why not? 2. A car tire rotates when you drive. How is this type of rotation different from a rotation in Geometry? What other type of transformation is happening to the car tire? Explain. September 6, 2013 by Unknown math HELP PLEASE! I don't understand how to do the problem! Please help thanks(: The problem is: your bike tire has a radius of 14 inches. If your tire makes 100 revolutions, how many feet does your bike travel? THANKS! :D April 25, 2012 by hannah Math When a tire is labeled "185/70/14" that means it is 185 mm wide, the sidewall height (from the rim to the road) is 70% of its width, and the wheel has a diameter of 14 in. What is the tire's sidewall height? January 15, 2015 by Anonymous English Are these two sentences right? gerund object - I stopped to fix the flat tire. infinitival object - I stopped fixing the flat tire. November 23, 2008 by Bethany PhYsIcS - RoTaTiOnAl MoTiOn A tire (0.8 m diameter) starts at rest and has an angular acceleration of 5 rad/s^2. If it moves for 10 seconds and then stops abruptly causing a blob of mud at the top of the tire to fly off, how far along the ground will the blob travel until it hits the ground? December 7, 2008 by Robert Math Betty and Tracy planned a 5000km trip in an automobile with five tires, of which four are in use at any time. They plan to interchange them so that each tire is used the same number of kilometers. What is the number of kilometers each tire will be used? I dont get this ... April 26, 2012 by Rezu physics.......please help!!! In which of the situations listed below is energy being transferred as heat to the system in order for the system to do work? In which situation is work being done on the system in order for energy to be transferred from the system as heat? a. Two sticks are rubbed together to... February 9, 2007 by anonymous physics A 1.1 pebble is stuck in a tread of a 0.85 diameter automobile tire, held in place by static friction that can be at most 3.9 . The car starts from rest and gradually accelerates on a straight road.How fast is the car moving when the pebble flies out of the tire tread? March 11, 2012 by Anonymous Physics In which of the situations listed below is energy being transferred as heat to the system in order for the system to do work? In which situation is work being done on the system in order for energy to be transferred from the system as heat? a. Two sticks are rubbed together to... March 29, 2010 by Edward Chemistry Each of 2 front tires in the car is filled with a different gas. One tire contains 116 g of helium, another tire has 160 g of unknown gas. How many times heavier is a molecule of the unknown gas than an atom of helium? November 10, 2012 by Christina chem 3. Each of 2 front tires in the car is filled with a different gas. One tire contains 116 g of helium, another tire has 160 g of unknown gas. How many times heavier is a molecule of the unknown gas than an atom of helium? April 13, 2013 by Anonymous Chem A bicycle tire is filled with air to a pressure of 100 psi at a temperature of 19C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58C. The volume increases by 4%. What is the new pressure of the tire? Convert the temps to Kelvins, then use ... September 30, 2006 by Mew math The tread life of a particular tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2000 miles. What is the probability that a randomly selected tire of this brand will last longer than 58,000 miles? A.0.7266... September 18, 2010 by Madison physics Tires on a car have a diameter of 2 ft and are warranted for 60 000 miles. a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. b) How m,any revolutions of the tire are equivalent to your answer in, part a)? i have drawn ... February 24, 2015 by 7876 English Are these two sentences right using "I stopped?" gerund object - I stopped to fix the flat tire. infinitival object - I stopped fixing the flat tire. November 23, 2008 by Bethany POM Acme Tire Service completed 100 tire changes, 6 brake jobs, and 16 alignments in an eight hour day with his standard crew of 6 mechanics. A brake specialist cost16 per hour, a tire changer costs $8 per hour and an alighnment mechanic cost$14 per hour. The materials cost for... January 12, 2011 by Lanks chemistry A bicycle tire fitted was fitted with the air pressure of 75 psi at temperature 19 degree C riding the bike on a asphalt on a hot day increases temperature of the tire to 58 degree C. The volume increase by 4% . What is the new pressure October 26, 2014 by mathew trig A computerized spin balance machine rotates a 35-inch-diameter tire at 400 revolutions per minute. (a) Find the road speed (in miles per hour) at which the tire is being balanced. (Round your answer to two decimal places.) (b) At what rate should the spin balance machine be ... January 23, 2014 by Jesse phsical science a tire contains air ata pressure of 2.8 bar at 10 degree celsius.if the tires volume is unchanged what will the air pressure in it be when the tire warms up to 35 degree celsius if the car is driven. June 20, 2012 by natalie Physics A bicycle tire whose volume is 4.1 x 10-4 m3 has a temperature of 296 K and an absolute pressure of 4.69 x 105 Pa. A cyclist brings the pressure up to 6.75 x 105 Pa without changing the temperature or volume. How many moles of air must be pumped into the tire? December 1, 2006 by maysam Physical Science A tire contains air at a pressure of 2.8 bar at 10 degrees Celsius. If the tires volume is unchanged, what will the air pressure in it be when the tire warms up to 35 degrees Celsius as the car is driven? Physics A tire contains air at a pressure of 2 bar at 15 degrees Celsius. If the tires volume is unchanged, what will the air pressure in it be when the tire warms up to 40 degrees Celsius as the car is driven? November 2, 2011 by Diana math Dana rode her bicycle 600 miles one summer before she had to replace the tire on her front wheel. The diameter of the front wheel is 24 inches. What is the best estimate of the number of revolutions made by the tire before it had to be replaced? March 31, 2014 by Tanya physics An automobile tire has a pressure of 325 kPa when the temperature is 10 degrees Celsius. If the temperature of the tire rises to 50 degrees Celsius and its volume is constant,what is the new pressure? February 16, 2014 by victoria Chemistry How many moles of gas must be forced into a 4.8L tire to give it a gauge pressure of 30.8psi at 30 degrees celsius? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.5L so that the total pressure in the tire is 45.3psi. What formula... February 20, 2013 by Claire algebra An advertisement for a steel-belted radial tire states that this tire delivers 14% better gas mileage. If the present gas mileage is 25.5 mpg, what mileage would you expect if you purchased these tires? Round your answer to the nearest tenth of a mile per gallon. I know the ... May 7, 2015 by Mary Physics Hey can someone help, im having trouble converting alot. IP The weight of your 1440 kg car is supported equally by its four tires, each inflated to a gauge pressure of 30.0 lb/in^2. What is the area of contact each tire makes with the road? What gauge pressure is required to ... December 3, 2009 by Elizabeth chemistry Before a trip from New York to Boston, the pressure in an automobile tire is 2.5 atm at 272 K. At the end of the trip, the pressure gauge reads 1.94 atm. What is the new Celsius temperature of the air inside the tire? (Assume tires with constant volume.) Answer in units of ... mathematics The members of a high school basketball team are driving from calgary to vancouver,which is a distance of 675km.Each tire of their van has a radius of 32cm.If the team members drive at constant speed and cover the distance in 6h 45 min,what is the angular velocity,in radians/... November 12, 2013 by rahul physics The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its geometric... November 3, 2014 by Anonymous physics The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its ... November 4, 2014 by help please physics In which of the situations listed below is energy being transferred as heat to the system in order for the system to do work? In which situation is work being done on the system in order for energy to be transferred from the system as heat? a. Two sticks are rubbed together to... February 8, 2007 by anonymous rolling motion The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its geometric... November 3, 2014 by Anonymous Geometry A car tire rotates when you drive. How is this type of rotation different from a rotation in Geometry? What other type of transformation is happening to the car tire? Thanks! March 11, 2014 by Ismary Gas laws and pressure An automobile tire has a pressure of 325 kPa when the temperature is 10 degrees Celsius. If the temperature of the tire rises to 50 degrees Celsius and its volume is constant, what is the new pressure? October 3, 2012 by Britani physics The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its geometric... November 3, 2014 by help Trig a child puts beads on one spoke of a bicycle wheel. the tire has a diameter of 2ft. if the child rides so that the tire makes one full rotation every 15 sec, and the beads begin in the horizontal outward position, find an equation that models the position of the beads at time t. October 7, 2013 by Bailey physics You are riding your bike and the tire has a radius of 0.33 m and mass 1.5 kg rotating at 98.7 rad/s. You just notice you are just seconds to riding off a cliff what torque will you need to stop the tire in 2.0 s before you find yourself at the bottom of a 1000 m cliff. New ... April 5, 2015 by Anonymous accounting What does it mean to evaluate the financial health of Goodyear Tire and Rubber Company? I have to do an outline of the financial health of Goodyear Tire and Rubber Company; and I do not understand what any of this means. Can somebody please explain this to me? August 25, 2009 by Angel of 8 Language Arts Need help figuring out which is the correct way to write the sentence. 1. In the summer we were going to the beach, and had a flat tire. 2. In the summer, when we were going to the beach, we had a flat tire. Thanks.... March 19, 2013 by Brandi algebra Company makes tire rims. Estimates the the profit, P, of selling x tire rims is given by: P= -0.01x^2 + 8x + 1500 Plugging in 1000 for P and solving, I get 400. Is that correct? b) find the number of rims that must be sold to maximize profit. plugging in 400 for x, I get $3100... October 11, 2011 by Nabil Physics Hi I tried asking this question yesterday but still had some confusion.Since the area must be in cm^2. IP The weight of your 1440 kg car is supported equally by its four tires, each inflated to a gauge pressure of 30.0 lb/in^2 . What is the area of contact each tire makes with... December 4, 2009 by Elizabeth physics You inflate your car tires to a gauge pressure of 2.43 atmospheres at a temperature of 24 degrees C. After driving a couple of miles the temperature of the tire increases by 46 degrees C. What is the new gauge pressure to the nearest hundredth of an atmosphere? What fraction ... October 21, 2010 by sandhu Physics A stone has a mass of 3.0 10-3 kg and is wedged into the tread of an automobile tire, as the drawing shows. The coefficient of static friction between the stone and each side of the tread channel is 0.86. When the tire surface is rotating at 10 m/s, the stone flies out of the ... October 7, 2007 by Student physics a) calculate the acceleration of a 0.55-m-diameter car tire while the car is traveling at a constant speed of 25m/sec. b) compare this with acceleration experienced by a jet car tire of diameter 1.0m when setting a land speed record of 310m/sec September 26, 2011 by lucy Math There 18 swings 3/9 are tire swings. How many are tire? December 18, 2012 by Anonymous Math Would someone like to help me with these questions? Steps appreciated~ 1. If the diameter of a monster truck tire is 3.5 m and it makes one rotation every 5 seconds, how far does the tire roll in 1 minute? -------------------------------------- 2. At t=0 a car is due 2 km ... January 19, 2012 by Melinda math The tread depth of the tires on your family's new car is 3/8 inch. you predict that, as a result of driving the car, the change in tire tread depth will be about -3/64 inch per year. A. write a variable expression for the tire tread depth after y years of driving. Use your ... January 7, 2009 by matt physics help! A tire is filled with air at 17 degreees C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 39 degrees C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained? Please help step by step! May 2, 2010 by Anonymous statistics According to internal testing done by the Get-A-Grip tire company, the mean lifetime of tires sold on new cars is 23,000 miles, with a standard deviation of 2500 miles. a) If the claim by Get-A-Grip is true, what is the mean of the sampling distribution of for samples of size... March 26, 2012 by tea Physics I have to compare and contrast three types of tires, and relate them to physics. I've chosen: <li> Racing tires <li> Winter tires <li> All season tires I've chosen to compare them on: <li> Tire tread pattern <li> Rubber compound <li> ??? As ... March 1, 2008 by Lucy calculus the demand for a certain type of auto tire is given by x=f(p) 50(1+e^-p/60). a)if the weekly quantity demanded is 60000 tires find the price? b)if the current price is$120 per tire and is increasing at a rate of $2 per week, what is the rate of change of the demand per week? ... April 20, 2013 by anonymous Chemistry How many moles of gas must be forced into a 5.2 L tire to give it a gauge pressure of 30.6 psi at 26 ∘C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.9 psi so that the total pressure in the tire is 45.5 psi . July 14, 2015 by Cici Physics Quick! A tire 0.650 m in radius rotates at a constant rate of 240 rev/min. Find the speed of a small stone lodged in the tread of the tire (on its outer edge). (Hint: In one revolution, the stone travels a distance equal to the circumference of its path, 2¥ðr.) What is the ... August 19, 2012 by kk2 Statistics Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Life tests revealed that the mean mileage is 47,900 miles and the standard deviation is 2,050. The manufacturer wants to set the guaranteed mileage so that no more than five percent of the ... November 24, 2011 by Brea Algebra 1 Your uncle buys a new car that comes with seven new tires, one for each wheel, and three spares. He decides to be economical by using the three spares as much as the other four. If he drives 22, 750 miles and each tire has been used equally, what will be the wear in miles on ... May 7, 2008 by Libby math An advertisement for a steel-belted radial tire states that this tire delivers 16% better gas mileage. If the present gas mileage is 24.5 mpg, what mileage would you expect if you purchased these tires? Round your answer to the nearest tenth of a mile per gallon. 26.5/X = 12/... September 27, 2015 by Valerie math The distance from Philadelphia to Sea Isle is 100 mi. A car was driven this distance using tires with a radius of 14 in. How many revolutions of each tire occurred on the trip? (Hint: one revolution is equivalent to one circumference distance traveled. Thus, need to find how ... July 22, 2009 by sharon physics I need help with solving these word problems. Marion rides her racing bicycle @ speed of 8 m/s. Bicycle wheels have a radius of 34 cm. What is the angular speed of wheels? How many times does each wheel go around during a 10-min race? A car tire has radius of 33cm. Tire turns ... December 1, 2008 by physics Physics I need help with solving these word problems. Marion rides her racing bicycle @ speed of 8 m/s. Bicycle wheels have a radius of 34 cm. What is the angular speed of wheels? How many times does each wheel go around during a 10-min race? A car tire has radius of 33cm. Tire turns... December 1, 2008 by physics Geometry check my answer? The diameter of a car tire is approximately 0.6meters. The warranty is good for 70,000 km. About how many revolutions will the tire make before the warranty is up? More than a million? a billion? ----------------------- my work c=pid c=3.140.6 c=1.884 meters 1km=1000 meters ... January 23, 2011 by Skye Physics As you approach the I-90 exit in your uncle's little red sports car convertible, you happen to notice a cat crossing the road. Not that you have any particular love of cats (especially this one, whose snooty disposition seems to beckon for a game of chicken), but you swerve ... November 1, 2010 by Anne Chemistry We're doing gas problems in chemsitry. I have no idea where to even begin on this problem: Air is 20% oxygen and 80% nitrogen. What is the mass of air in an automobile tire of 19.7 L and internal pressure of 46.7 PSI at 24 degrees celsius? (That pressure is the same as the 32 ... March 29, 2010 by Avalon math A park has 18 swings. 3/9 of them are tire swings. how many of the swings are tire swings? January 30, 2012 by Layla math a tire manufacturer believes that the tread life of its tires are normally distributed and will lst an average of 60,000 miles with a standard deviation of 3,000 miles. sixty-four randomly selected tires were tested and the average miles where the tire failed were recorded. ... May 31, 2011 by monk University Physics In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of Fig. 5-33. The tire remains stationary in spite of the three pulls. Alex pulls withe force Fa of magnitude 220N and Charles pulls with ... March 14, 2013 by Brandon Ochoa micro economics Marginal cost is a constant$10 per tire.quantities are measured in thousands per month ans price refers to the wholesale price. marginal cost is a constant $10 per tire. american currently sells brand name tires at a wholesale price of$28.50 and private label tires for a ... February 28, 2008 by Anonymous 1. Pages: 2. <<Prev 3. 1 4. 2 5. 3 6. 4 7. 5 8. 6 9. Next>> Members	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5062906742095947, "perplexity": 827.5737072026585}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737904854.54/warc/CC-MAIN-20151001221824-00092-ip-10-137-6-227.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/244954/antiderivative-of-a-function-f	# Antiderivative of a function $f$ Can you help me to find which functions $F_1,\ldots,F_6$ are antiderivatives of $f$? - When is $f$ positive? When is $f$ negative? When does $f$ cross the $x$-axis? Yep, and what have you tried? – FrenzY DT. Nov 26 '12 at 13:33 You should tag this as homework, as well as show some effort on your part. I imagine the lack of these is the source of the downvotes. – Zach L. Nov 26 '12 at 13:35 This is not homework. – Reader Nov 26 '12 at 13:36 Honest? This is NOT homework? Really? Because people will still help you, but if you tag the question as "homework" then all will know you must work by yourself problems and will give some good hints... – DonAntonio Nov 26 '12 at 13:42 Is it correct that answer is $F_1, F_2$ and $F_6$ – Reader Nov 26 '12 at 13:42 HINT: What does $f(x)\begin{cases}<0\\=0\\>0 \end{cases}$ mean for the antiderivative at the point $x$? And be careful, there might be more than one solution...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6027824282646179, "perplexity": 822.7281181976066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500830746.39/warc/CC-MAIN-20140820021350-00472-ip-10-180-136-8.ec2.internal.warc.gz"}
https://mathemerize.com/tag/equation-of-tangent-to-ellipse/	## Equation of Tangent to Ellipse in all Forms Equation of Tangent to Ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1 : (a) Point form : The equation of tangent to the given ellipse at its point ($$x_1, y_1$$) is $$x{x_1}\over a^2$$ + $$y{y_1}\over b^2$$ = 1. Note – For general ellipse replace $$x^2$$ by $$xx_1$$, $$y^2$$ by $$yy_1$$, 2x by $$x + x_1$$, …	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9513505697250366, "perplexity": 340.67778447971193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710218.49/warc/CC-MAIN-20221127073607-20221127103607-00364.warc.gz"}
https://bhxb.buaa.edu.cn/CN/10.13700/j.bh.1001-5965.2018.0615	• 论文 • ### 垂直旋转圆盘边缘液体形态 1. 北京航空航天大学能源与动力工程学院, 北京 100083 • 收稿日期:2018-10-26 出版日期:2019-06-20 发布日期:2019-06-18 • 通讯作者: 张荣春 E-mail:zhangrongchun@buaa.edu.cn • 作者简介:覃文隆男,博士研究生。主要研究方向:机械旋转雾化;张荣春男,博士,讲师。主要研究方向:航空发动机燃烧室燃烧。 • 基金资助: 国家自然科学基金（51506003） ### Liquid morphology at edge of vertical rotating disc TAN Wenlong, FAN Weijun, SHI Qiang, XU Hanqing, ZHANG Rongchun 1. School of Energy and Power Engineering, Beihang University, Beijing 100083, China • Received:2018-10-26 Online:2019-06-20 Published:2019-06-18 Abstract: For finding how the gravity affects the liquid on the rotating disc, the liquid morphology at the edge of the vertical rotating disc was experimentally studied by high-speed photography. The results show that there are three liquid morphologies at the edge of the vertical rotating disc:column, film and column film entanglement, which is different with the three morphologies at the horizontal rotating disc edge:direct drop, column and film. The liquid morphology at the bottom of the vertical disc does not match the top one, and the film morphology does not occur at the bottom. When the mass flow rate is less than 24 g/s, the liquid shows column morphology at the bottom, and when the mass flow rate is greater than or equal to 30 g/s, the liquid shows column film entanglement morphology. When the mass flow rate is between 12 g/s and 21 g/s and the rotating speed is between 1 000 r/min and 2 100 r/min, the liquid film morphology appears at the top of the disc. The liquid morphology is column when the mass flow rate is less than 12 g/s; if the mass flow rate is greater than 12 g/s, it will be replaced by column film entanglement. Due to the influence of gravity, the liquid morphology at the vertical disc edge changes much more than the horizontal disc; when the mass flow rate is large enough, the rotating speed required to form the liquid column at the bottom of the disc is greatly increased.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35390377044677734, "perplexity": 1754.8117721526662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370492125.18/warc/CC-MAIN-20200328164156-20200328194156-00389.warc.gz"}
https://stats.stackexchange.com/questions/252619/percent-deviation-for-linear-regression	# percent deviation for linear regression I have 2 sets of experimental data to which I applied a linear fit using Matlab. I can use the slope value to compare between both of them. My question is: can I use the following percent deviation equation for the linear fit to compare between these 2 sets? $$\%\text{ deviation} = \frac{\text{last point - first point}}{\text{last point}}\times 100$$ The first point of the linear fitting when (x=0), the last point where my data end (x=311 in this example) In this example the slope is -0.01569 and the %deviation is -4.063% The results are different from the slope results. Example: Let's say your sets both consist of 2 points. Set a: y1=0 y2=1 Set b:y1=4 y2=5 Slopes are both equal to 1. But a%=100% b%=20% Edit: Another problem arises if the two sets are not of equal length. • Thanks for your answer, The linear regression slope also have the same problem if the lengths are not equal. in my opinion (I don't know if it's correct or not) the %deviation shows how much the %change between the start condition and the last condition. if your presented data are representing 2 cars speed then the first one has changed 100% from 0 speed to 1, while the second car changed speed by only 20% from 4 to 5, the slope shows the increasing or decreasing while the %change shows the change from the start condition. (forgive my bad English). – Mustafa Mahmood Dec 21 '16 at 13:54 • @MustafaMahmood The slope shows the absolute increase per unit of the x-axis. The %deviation shows the percentual increase per unit of the x-axis. – Mr Pi Jan 3 '17 at 14:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7832805514335632, "perplexity": 813.3663121225526}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505730.14/warc/CC-MAIN-20200401100029-20200401130029-00339.warc.gz"}
https://gitlab.xiph.org/xiph/aom-rav1e/-/blame/0e6459caface5793f47f05af93cf63174a07e58b/usage.dox	usage.dox 6.57 KB John Koleszar committed May 18, 2010 1 2 /!\page usage Usage James Zern committed Mar 15, 2012 3 The vpx multi-format codec SDK provides a unified interface amongst its John Koleszar committed May 18, 2010 4 5 6 7 8 9 10 11 12 13 14 15 16 supported codecs. This abstraction allows applications using this SDK to easily support multiple video formats with minimal code duplication or "special casing." This section describes the interface common to all codecs. For codec-specific details, see the \ref codecs page. The following sections are common to all codecs: - \ref usage_types - \ref usage_features - \ref usage_init - \ref usage_errors Fore more information on decoder and encoder specific usage, see the following pages: James Zern committed Mar 15, 2012 17 18 19 20 21 22 \if decoder - \subpage usage_decode \endif \if decoder - \subpage usage_encode \endif John Koleszar committed May 18, 2010 23 24 25 26 27 28 29 30 31 \section usage_types Important Data Types There are two important data structures to consider in this interface. \subsection usage_ctxs Contexts A context is a storage area allocated by the calling application that the codec may write into to store details about a single instance of that codec. Most of the context is implementation specific, and thus opaque to the application. The context structure as seen by the application is of fixed James Zern committed Feb 16, 2011 32 size, and thus can be allocated with automatic storage or dynamically John Koleszar committed May 18, 2010 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 on the heap. Most operations require an initialized codec context. Codec context instances are codec specific. That is, the codec to be used for the encoded video must be known at initialization time. See #vpx_codec_ctx_t for further information. \subsection usage_ifaces Interfaces A codec interface is an opaque structure that controls how function calls into the generic interface are dispatched to their codec-specific implementations. Applications \ref MUSTNOT attempt to examine or override this storage, as it contains internal implementation details likely to change from release to release. Each supported codec will expose an interface structure to the application as an extern reference to a structure of the incomplete type #vpx_codec_iface_t. \section usage_features Features Several "features" are defined that are optionally implemented by codec algorithms. Indeed, the same algorithm may support different features on different platforms. The purpose of defining these features is that when they are implemented, they conform to a common interface. The features, or capabilities, of an algorithm can be queried from it's interface by using the vpx_codec_get_caps() method. Attempts to invoke features not supported by an algorithm will generally result in #VPX_CODEC_INCAPABLE. \if decoder Currently defined decoder features include: - \ref usage_cb - \ref usage_postproc \endif \section usage_init Initialization To initialize a codec instance, the address of the codec context and interface structures are passed to an initialization function. Depending on the \ref usage_features that the codec supports, the codec could be James Zern committed Aug 11, 2014 70 initialized in different modes. John Koleszar committed May 18, 2010 71 72 73 74 75 To prevent cases of confusion where the ABI of the library changes, the ABI is versioned. The ABI version number must be passed at initialization time to ensure the application is using a header file that matches the library. The current ABI version number is stored in the James Zern committed Feb 16, 2011 76 preprocessor macros #VPX_CODEC_ABI_VERSION, #VPX_ENCODER_ABI_VERSION, and John Koleszar committed May 18, 2010 77 78 79 80 81 82 #VPX_DECODER_ABI_VERSION. For convenience, each initialization function has a wrapper macro that inserts the correct version number. These macros are named like the initialization methods, but without the _ver suffix. The available initialization methods are: Yaowu Xu committed Jan 15, 2015 83 84 85 86 87 \if encoder - #vpx_codec_enc_init (calls vpx_codec_enc_init_ver()) - #vpx_codec_enc_init_multi (calls vpx_codec_enc_init_multi_ver()) . \endif John Koleszar committed May 18, 2010 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 \if decoder - #vpx_codec_dec_init (calls vpx_codec_dec_init_ver()) \endif \section usage_errors Error Handling Almost all codec functions return an error status of type #vpx_codec_err_t. The semantics of how each error condition should be processed is clearly defined in the definitions of each enumerated value. Error values can be converted into ASCII strings with the vpx_codec_error() and vpx_codec_err_to_string() methods. The difference between these two methods is that vpx_codec_error() returns the error state from an initialized context, whereas vpx_codec_err_to_string() can be used in cases where an error occurs outside any context. The enumerated value returned from the last call can be retrieved from the err member of the decoder context as well. Finally, more detailed error information may be able to be obtained by using the vpx_codec_error_detail() method. Not all errors produce detailed error information. In addition to error information, the codec library's build configuration is available at runtime on some platforms. This information can be returned by calling vpx_codec_build_config(), and is formatted as a base64 coded string (comprised of characters in the set [a-z_a-Z0-9+/]). This information is not useful to an application at runtime, but may be of use to vpx for support. \section usage_deadline Deadline Both the encoding and decoding functions have a deadline parameter. This parameter indicates the amount of time, in microseconds (us), that the application wants the codec to spend processing before returning. This is a soft deadline -- that is, the semantics of the requested operation take precedence over meeting the deadline. If, for example, an application sets a deadline of 1000us, and the frame takes 2000us to decode, the call to vpx_codec_decode() will return after 2000us. In this case the deadline is not met, but the semantics of the function are preserved. If, for the same frame, an application instead sets a deadline of 5000us, the decoder will see that it has 3000us remaining in its time slice when decoding completes. It could then choose to run a set of \ref usage_postproc filters, and perhaps would return after 4000us (instead of the allocated 5000us). In this case the deadline is met, and the semantics of the call are preserved, as before. The special value 0 is reserved to represent an infinite deadline. In this case, the codec will perform as much processing as James Zern committed Feb 16, 2011 131 possible to yield the highest quality frame. John Koleszar committed May 18, 2010 132 133 134 135 136 By convention, the value 1 is used to mean "return as fast as possible." /	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6960699558258057, "perplexity": 1615.9056338584094}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657140337.79/warc/CC-MAIN-20200712211314-20200713001314-00073.warc.gz"}
https://indico.cern.ch/event/181055/contributions/308923/	# Quark Matter 2012 12-18 August 2012 US/Eastern timezone ## Study of correlations between neutral bosons and jets in lead-lead collisions at 2.76 TeV with the ATLAS detector 14 Aug 2012, 14:35 20m Oral Presentation ### Speaker Zvi Citron (Weizmann Institute of Science (IL)) ### Description The correlations of jets with neutral bosons is a particularly powerful tool to probe the underlying physics of jet quenching. To gain insight into the physics of this process we can study Z-jet and gamma-jet correlations. Because the Z and photons do not directly couple to the strong force, in a jet+boson event the unmodified bosons allow us to access the modification of the opposite side jet; unlike dijet events, where both jets potentially lose energy, these bosons provide an excellent calibration of the energy of the recoil jet. The jets are measured in the same calorimeter, over a range of jet radii, and benefit from the detailed information about the shower profile. The ATLAS experiment has measured jet correlations with both direct photons as well as with Z bosons via dilepton channels in Pb+Pb collisions with sqrt(s_NN)=2.76 TeV in a data sample of nearly 150 ub^-1 of integrated luminosity. The measurement of these correlations will be presented. ### Primary author Zdenek ATLAS Collaboration (Charles University Prague) ### Presentation Materials QM_2012_v2_inanimate.pdf QM_2012_v2.pptx Paper files:	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.938934326171875, "perplexity": 3721.8131023605506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107891203.69/warc/CC-MAIN-20201026090458-20201026120458-00066.warc.gz"}
https://notebook.community/AllenDowney/ModSimPy/soln/spiderman_soln	Modeling and Simulation in Python Case study: Spider-Man In [1]: # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * I'll start by getting the units we'll need from Pint. In [2]: m = UNITS.meter s = UNITS.second kg = UNITS.kilogram N = UNITS.newton degree = UNITS.degree Out[2]: Spider-Man In this case study we'll develop a model of Spider-Man swinging from a springy cable of webbing attached to the top of the Empire State Building. Initially, Spider-Man is at the top of a nearby building, as shown in this diagram. The origin, O⃗, is at the base of the Empire State Building. The vector H⃗ represents the position where the webbing is attached to the building, relative to O⃗. The vector P⃗ is the position of Spider-Man relative to O⃗. And L⃗ is the vector from the attachment point to Spider-Man. By following the arrows from O⃗, along H⃗, and along L⃗, we can see that H⃗ + L⃗ = P⃗ So we can compute L⃗ like this: L⃗ = P⃗ - H⃗ The goals of this case study are: 1. Implement a model of this scenario to predict Spider-Man's trajectory. 2. Choose the right time for Spider-Man to let go of the webbing in order to maximize the distance he travels before landing. 3. Choose the best angle for Spider-Man to jump off the building, and let go of the webbing, to maximize range. I'll create a Params object to contain the quantities we'll need: 1. According to the Spider-Man Wiki, Spider-Man weighs 76 kg. 2. Let's assume his terminal velocity is 60 m/s. 3. The length of the web is 100 m. 4. The initial angle of the web is 45 degrees to the left of straight down. 5. The spring constant of the web is 40 N / m when the cord is stretched, and 0 when it's compressed. Here's a Params object. In [3]: params = Params(height = 381 * m, g = 9.8 * m/s*2, mass = 75 kg, area = 1 * m*2, rho = 1.2 kg/m*3, v_term = 60 m / s, length = 100 * m, angle = (270 - 45) * degree, k = 40 * N / m, t_0 = 0 * s, t_end = 30 * s) Out[3]: values height 381 meter g 9.8 meter / second 2 mass 75 kilogram area 1 meter 2 rho 1.2 kilogram / meter ** 3 v_term 60.0 meter / second length 100 meter angle 225 degree k 40.0 newton / meter t_0 0 second t_end 30 second Compute the initial position In [4]: def initial_condition(params): """Compute the initial position and velocity. params: Params object """ height, length, angle = params.height, params.length, params.angle H⃗ = Vector(0, height) x, y = pol2cart(theta, length) L⃗ = Vector(x, y) P⃗ = H⃗ + L⃗ V⃗ = Vector(0, 0) * m/s return State(P⃗=P⃗, V⃗=V⃗) In [5]: initial_condition(params) Out[5]: values P⃗ [-70.71067811865477 meter, 310.28932188134524 ... V⃗ [0.0 meter / second, 0.0 meter / second] Now here's a version of make_system that takes a Params object as a parameter. make_system uses the given value of v_term to compute the drag coefficient C_d. In [6]: def make_system(params): """Makes a System object for the given conditions. params: Params object returns: System object """ init = initial_condition(params) mass, g = params.mass, params.g rho, area, v_term = params.rho, params.area, params.v_term C_d = 2 * mass * g / (rho * area * v_term2) return System(params, init=init, C_d=C_d) Let's make a System In [7]: system = make_system(params) Out[7]: values height 381 meter g 9.8 meter / second 2 mass 75 kilogram area 1 meter 2 rho 1.2 kilogram / meter 3 v_term 60.0 meter / second length 100 meter angle 225 degree k 40.0 newton / meter t_0 0 second t_end 30 second init P⃗ [-70.71067811865477 meter, 310.289321881... C_d 0.3402777777777778 dimensionless In [8]: system.init Out[8]: values P⃗ [-70.71067811865477 meter, 310.28932188134524 ... V⃗ [0.0 meter / second, 0.0 meter / second] Drag and spring forces Here's drag force, as we saw in Chapter 22. In [9]: def drag_force(V⃗, system): """Compute drag force. V⃗: velocity Vector system: System object returns: force Vector """ rho, C_d, area = system.rho, system.C_d, system.area mag = rho * V⃗.mag*2 C_d * area / 2 direction = -V⃗.hat() f_drag = direction * mag return f_drag In [10]: V⃗_test = Vector(10, 10) * m/s Out[10]: $\begin{pmatrix}10.0 & 10.0\end{pmatrix} meter/second$ In [11]: drag_force(V⃗_test, system) Out[11]: $\begin{pmatrix}-28.873526898450695 & -28.873526898450695\end{pmatrix} kilogram meter/second2$ And here's the 2-D version of spring force. We saw the 1-D version in Chapter 21. In [12]: def spring_force(L⃗, system): """Compute drag force. L⃗: Vector representing the webbing system: System object returns: force Vector """ extension = L⃗.mag - system.length if magnitude(extension) < 0: mag = 0 else: mag = system.k * extension direction = -L⃗.hat() f_spring = direction * mag return f_spring In [13]: L⃗_test = Vector(0, -system.length-1m) Out[13]: $\begin{pmatrix}0 & -101\end{pmatrix} meter$ In [14]: f_spring = spring_force(L⃗_test, system) Out[14]: $\begin{pmatrix}-0.0 & 40.0\end{pmatrix} newton$ Here's the slope function, including acceleration due to gravity, drag, and the spring force of the webbing. In [15]: def slope_func(state, t, system): """Computes derivatives of the state variables. state: State (x, y, x velocity, y velocity) t: time system: System object with g, rho, C_d, area, mass returns: sequence (vx, vy, ax, ay) """ P⃗, V⃗ = state g, mass = system.g, system.mass H⃗ = Vector(0, system.height) L⃗ = P⃗ - H⃗ a_grav = Vector(0, -g) a_spring = spring_force(L⃗, system) / mass a_drag = drag_force(V⃗, system) / mass A⃗ = a_grav + a_drag + a_spring return V⃗, A⃗ As always, let's test the slope function with the initial conditions. In [16]: slope_func(system.init, 0, system) Out[16]: (array([0., 0.]) <Unit('meter / second')>, array([ 5.35924893e-15, -9.80000000e+00]) <Unit('meter / second * 2')>) And then run the simulation. In [17]: results, details = run_ode_solver(system, slope_func) details Out[17]: values success True message The solver successfully reached the end of the... Visualizing the results We can extract the x and y components as Series objects. The simplest way to visualize the results is to plot x and y as functions of time. In [18]: def plot_position(P⃗): x = P⃗.extract('x') y = P⃗.extract('y') plot(x, label='x') plot(y, label='y') decorate(xlabel='Time (s)', ylabel='Position (m)') plot_position(results.P⃗) We can plot the velocities the same way. In [19]: def plot_velocity(V⃗): vx = V⃗.extract('x') vy = V⃗.extract('y') plot(vx, label='vx') plot(vy, label='vy') decorate(xlabel='Time (s)', ylabel='Velocity (m/s)') plot_velocity(results.V⃗) Another way to visualize the results is to plot y versus x. The result is the trajectory through the plane of motion. In [20]: def plot_trajectory(P⃗, options): x = P⃗.extract('x') y = P⃗.extract('y') plot(x, y, options) decorate(xlabel='x position (m)', ylabel='y position (m)') plot_trajectory(results.P⃗, label='trajectory') Letting go Now let's find the optimal time for Spider-Man to let go. We have to run the simulation in two phases because the spring force changes abruptly when Spider-Man lets go, so we can't integrate through it. Here are the parameters for Phase 1, running for 9 seconds. In [21]: params1 = Params(params, t_end=9s) system1 = make_system(params1) results1, details1 = run_ode_solver(system1, slope_func) plot_trajectory(results1.P⃗, label='Phase 1') The final conditions from Phase 1 are the initial conditions for Phase 2. In [22]: t_final = get_last_label(results1) s Out[22]: 8.999999999999991 second Here's the position Vector. In [23]: init = results1.last_row() init.P⃗ Out[23]: $\begin{pmatrix}42.09220704823149 & 273.0520143333356\end{pmatrix} meter$ And the velocity Vector. In [24]: init.V⃗ Out[24]: $\begin{pmatrix}14.625507683978038 & 7.937765075110924\end{pmatrix} meter/second$ Here is the System for Phase 2. We can turn off the spring force by setting k=0, so we don't have to write a new slope function. In [25]: system2 = System(system1, t_0=t_final, t_end=t_final+10s, init=init, k=0N/m) Out[25]: values height 381 meter g 9.8 meter / second 2 mass 75 kilogram area 1 meter 2 rho 1.2 kilogram / meter ** 3 v_term 60.0 meter / second length 100 meter angle 225 degree k 0.0 newton / meter t_0 8.999999999999991 second t_end 18.999999999999993 second init P⃗ [42.09220704823149 meter, 273.0520143333... C_d 0.3402777777777778 dimensionless Here's an event function that stops the simulation when Spider-Man reaches the ground. In [26]: def event_func(state, t, system): """Stops when y=0. state: State object t: time system: System object returns: height """ P⃗, V⃗ = state return P⃗.y Run Phase 2. In [27]: results2, details2 = run_ode_solver(system2, slope_func, events=event_func) Plot the results. In [28]: plot_trajectory(results1.P⃗, label='Phase 1') plot_trajectory(results2.P⃗, label='Phase 2') Now we can gather all that into a function that takes t_release and V_0, runs both phases, and returns the results. In [29]: def run_two_phase(t_release, V⃗_0, params): """Run both phases. t_release: time when Spider-Man lets go of the webbing V_0: initial velocity """ params1 = Params(params, t_end=t_release, V⃗_0=V⃗_0) system1 = make_system(params1) results1, details1 = run_ode_solver(system1, slope_func) t_0 = get_last_label(results1) * s t_end = t_0 + 10 * s init = results1.last_row() system2 = System(system1, t_0=t_0, t_end=t_end, init=init, k=0N/m) results2, details2 = run_ode_solver(system2, slope_func, events=event_func) results = results1.combine_first(results2) return TimeFrame(results) And here's a test run. In [30]: t_release = 9 s V⃗_0 = Vector(0, 0) * m/s results = run_two_phase(t_release, V⃗_0, params) plot_trajectory(results.P⃗) x_final = results.P⃗.last_value().x Out[30]: 143.42923899746137 meter Animation Here's a draw function we can use to animate the results. In [31]: xs = results.P⃗.extract('x') ys = results.P⃗.extract('y') def draw_func(state, t): set_xlim(xs) set_ylim(ys) x, y = state.P⃗ plot(x, y, 'bo') decorate(xlabel='x position (m)', ylabel='y position (m)') In [34]: animate(results, draw_func) Maximizing range To find the best value of t_release, we need a function that takes possible values, runs the simulation, and returns the range. In [ ]: def range_func(t_release, params): """Compute the final value of x. t_release: time to release web params: Params object """ V_0 = Vector(0, 0) * m/s results = run_two_phase(t_release, V_0, params) x_final = results.P⃗.last_value().x print(t_release, x_final) return x_final We can test it. In [ ]: range_func(9s, params) And run it for a few values. In [ ]: for t_release in linrange(3, 15, 3) s: range_func(t_release, params) Now we can use maximize_scalar to find the optimum. In [ ]: bounds = [6, 12] * s res = maximize_golden(range_func, bounds, params) Finally, we can run the simulation with the optimal value. In [ ]: best_time = res.x V⃗_0 = Vector(0, 0) * m/s results = run_two_phase(best_time, V⃗_0, params) plot_trajectory(results.P⃗) x_final = results.P⃗.last_value().x In [ ]:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7864267230033875, "perplexity": 12546.743185832202}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00544.warc.gz"}
http://mathoverflow.net/feeds/question/95925	What to call substructures in universal algebra in which we restrict the signature? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T09:02:17Z http://mathoverflow.net/feeds/question/95925 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95925/what-to-call-substructures-in-universal-algebra-in-which-we-restrict-the-signatur What to call substructures in universal algebra in which we restrict the signature? Andrej Bauer 2012-05-03T22:15:09Z 2012-05-03T22:28:45Z <p>Suppose \$\Sigma\$ is a signature in the sense of universal algebra and \$\Sigma' \subseteq \Sigma\$ a sub-signature. Every \$\Sigma\$-algebra is also a \$\Sigma'\$-algebra in a forgetful way. Suppose \$A\$ is a \$\Sigma\$-algebra and \$B \subseteq A\$ is a \$\Sigma'\$-subalgebra of \$A\$ viewed as a \$\Sigma'\$-algebra. Is there an accepted phrase which describes the relationship of \$B\$ to \$A\$? For example, we might say that \$B\$ is a \$\Sigma'\$-restriction of \$A\$, or something like that? It seems wrong to use the word "subalgebra" in this context.</p> <p>Here is an example: the semiring of natural numbers \$\mathbb{N}\$ is contained in the ring of real numbers \$\mathbb{R}\$. This makes \$\mathbb{N}\$ a what of \$\mathbb{R}\$? A subsemiring? What is the general phrase? A \$\Sigma'\$-subalgebra? I would prefer a word which does not refer to the signature explicitly.</p> <p>The concrete example which I need this for is when \$A\$ is the \$\Sigma\$-algebra freely generated by a set of generators \$X\$ and \$B\$ is the free \$\Sigma'\$-aglebr freely generated by the same set of generators \$X\$.</p> http://mathoverflow.net/questions/95925/what-to-call-substructures-in-universal-algebra-in-which-we-restrict-the-signatur/95927#95927 Answer by Joel David Hamkins for What to call substructures in universal algebra in which we restrict the signature? Joel David Hamkins 2012-05-03T22:19:27Z 2012-05-03T22:28:45Z <p>If the domain of \$B\$ is the same as \$A\$, but you only forget the interpretation of the extra language elements, then \$B\$ is called a <em>reduct</em> of \$A\$ to signature \$\Sigma'\$. But you don't merely have a reduct, since you are taking a substructure in the smaller language. Thus, what you have is that \$B\$ is a substructure of the reduct of \$A\$ to \$\Sigma'\$. Having needed this concept in a recent article, I used the term <em>reduct substructure</em> in exactly this situation, but I haven't seen this terminology elsewhere and I don't think there is an established terminology.</p>	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8767016530036926, "perplexity": 1931.757528509681}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705884968/warc/CC-MAIN-20130516120444-00014-ip-10-60-113-184.ec2.internal.warc.gz"}
http://g2s3.com/labs/notebooks/ImageDenoising.html	# Image Denoising: Tikhonov and Total Variation Regularization The problem of removing noise from an image without blurring sharp edges can be formulated as an infinite-dimensional minimization problem. Given a possibly noisy image $u_0(x,y)$ defined within a rectangular domain $\Omega$, we would like to find the image $u(x,y)$ that is closest in the $L_2$ sense, i.e. we want to minimize while also removing noise, which is assumed to comprise very rough components of the image. This latter goal can be incorporated as an additional term in the objective, in the form of a penalty, i.e., $\mathcal{R}_{TN} := \! \frac{\alpha}{2}\int_\Omega \nabla u \cdot \! \nabla u \; d\boldsymbol{x},$ where $\alpha$ acts as a diffusion coefficient that controls how strongly we impose the penalty, i.e. how much smoothing occurs. Unfortunately, if there are sharp edges in the image, this so-called Tikhonov (TN) regularization will blur them. Instead, in these cases we prefer the so-called total variation (TV) regularization, where (we will see that) taking the square root is the key to preserving edges. Since $\mathcal{R}_{TV}$ is not differentiable when $\nabla u = \boldsymbol{0}$, it is usually modified to include a positive parameter $\varepsilon$ as follows: $\mathcal{R}^{\varepsilon}_{TV} := \! \alpha \int_\Omega (\nabla u \cdot \! \nabla u + \varepsilon)^{\frac{1}{2}} \; d\boldsymbol{x}.$ We wish to study the performance of the two denoising functionals $\mathcal{F}_{TN}$ and $\mathcal{F}^{\varepsilon}_{TV}$, where $\mathcal{F}_{TN} := \mathcal{F}_{LS} + \mathcal{R}_{TN}$ and We prescribe the homogeneous Neumann condition $\nabla u \cdot \boldsymbol{n}=0$ on the four sides of the square, which amounts to assuming that the image intensity does not change normal to the boundary of the image. ## 1. Setup • We generate a rectangular mesh of size Lx by Ly. • We define a linear finite element space. • We generate two finite element functions u_true and u_0 that represent the true image and the noisy image respectively. from __future__ import print_function, division, absolute_import import matplotlib.pyplot as plt %matplotlib inline import dolfin as dl from hippylib import nb import math import numpy as np import logging from unconstrainedMinimization import InexactNewtonCG logging.getLogger('FFC').setLevel(logging.WARNING) logging.getLogger('UFL').setLevel(logging.WARNING) dl.set_log_active(False) np.random.seed(seed=1) noise_std_dev = .3 noise = noise_std_devnp.random.randn(data.shape[0], data.shape[1]) Lx = float(data.shape[1])/float(data.shape[0]) Ly = 1. class Image(dl.Expression): def __init__(self, Lx, Ly, data, kwargs): self.data = data self.hx = Lx/float(data.shape[1]-1) self.hy = Ly/float(data.shape[0]-1) def eval(self, values, x): j = int(math.floor(x[0]/self.hx)) i = int(math.floor(x[1]/self.hy)) values[0] = self.data[i,j] mesh = dl.RectangleMesh(dl.Point(0,0),dl.Point(Lx,Ly),200, 100) V = dl.FunctionSpace(mesh, "Lagrange",1) trueImage = Image(Lx,Ly,data,degree = 1) noisyImage = Image(Lx,Ly,data+noise, degree = 1) u_true = dl.interpolate(trueImage, V) u_0 = dl.interpolate(noisyImage, V) # Get min/max of noisy image, so that we can show all plots in the same scale vmin = np.min(u_0.vector().get_local()) vmax = np.max(u_0.vector().get_local()) plt.figure(figsize=(15,5)) nb.plot(u_true, subplot_loc=121, mytitle="True Image", vmin=vmin, vmax = vmax) nb.plot(u_0, subplot_loc=122, mytitle="Noisy Image", vmin=vmin, vmax = vmax) plt.show() ## 2. The misfit functional and the true error functional Here we describe the variational forms for the $L_2$ misfit functional $\mathcal{F}_{LS} := \frac{1}{2}\int_\Omega (u - u_0)^2 \; d\boldsymbol{x},$ and its first and second variations. Since we also know the true image u_true (this will not be the case for real applications) we can also write the true $L_2$ error functional $\mathcal{F}_{\rm true} := \frac{1}{2}\int_\Omega (u - u_{\rm true})^2 \; d\boldsymbol{x}.$ Finally, we define some values of $\alpha$ ($\alpha = 10^{-1}, 10^{-2}, 10^{-3}, 10^{-4}$) for the choice of the regularization paramenter. u = dl.Function(V) u_hat = dl.TestFunction(V) u_tilde = dl.TrialFunction(V) F_ls = dl.Constant(.5)dl.inner(u - u_0, u - u_0)dl.dx grad_ls = dl.inner(u - u_0, u_hat)dl.dx H_ls = dl.inner(u_tilde, u_hat)dl.dx trueError = dl.inner(u - u_true, u - u_true)dl.dx n_alphas = 4 alphas = np.power(10., -np.arange(1, n_alphas+1)) ## 3. Tikhonov regularization The function TNsolution computes the solution of the denoising inverse problem using Tikhonov regularization for a given amount a regularization $\alpha$. More specifically it minimizes the functional $\mathcal{F}_{TN}(u) = \frac{1}{2}\int_\Omega (u - u_0)^2 \; d\boldsymbol{x} + \frac{\alpha}{2}\int_\Omega \nabla u \cdot \nabla u d\boldsymbol{x}.$ The first variation of $\mathcal{F}_{TN}$ reads and the second variation is The best reconstruction of the original image is obtained for $\alpha = 10^{-3}$, however we notice that the sharp edges of the image are lost in the reconstruction. def TNsolution(alpha): F = F_ls + alphaR_tn H = H_ls + alphaH_tn print( "{0:15e} {1:15e} {2:15e} {3:15e} {4:15e}".format( alpha.values()[0], dl.assemble(F), dl.assemble(F_ls), dl.assemble(alphaR_tn), dl.assemble(trueError)) ) plt.figure() nb.plot(u, vmin=vmin, vmax = vmax) plt.show() print( "{0:15} {1:15} {2:15} {3:15} {4:15}".format("alpha", "F", "F_ls", "alphaR_tn", "True Error") ) for alpha in alphas: TNsolution(dl.Constant(alpha)) alpha F F_ls alphaR_tn True Error 1.000000e-01 1.888317e-01 1.687812e-01 2.005046e-02 2.520662e-01 1.000000e-02 2.034907e-01 1.864572e-01 1.703349e-02 2.893618e-01 1.000000e-03 1.012200e-01 9.155309e-02 9.666912e-03 1.052391e-01 1.000000e-04 1.479768e-01 1.412953e-01 6.681556e-03 2.304038e-01 ## 4. Total Variation regularization The function TVsolution computes the solution of the denoising inverse problem using Total Variation regularization for a given amount a regularization $\alpha$ and perturbation $\varepsilon$. More specifically it minimizes the functional $\mathcal{F}_{TV}(u) = \frac{1}{2}\int_\Omega (u - u_0)^2 \; d\boldsymbol{x} + \frac{\alpha}{2}\int_\Omega \left( \nabla u \cdot \nabla u + \varepsilon \right)^{\frac{1}{2}} d\boldsymbol{x}.$ The first variation of $\mathcal{F}_{TV}$ reads $\delta_u \mathcal{F}_{TV}(u, \hat{u}) = \int_\Omega (u - u_0)\hat{u} \; d\boldsymbol{x} + \alpha \int_\Omega \frac{1}{\left( \nabla u \cdot \nabla u + \varepsilon \right)^{\frac{1}{2}}}\nabla u \cdot \nabla \hat{u} d\boldsymbol{x},$ and the second variation is $\delta_u^2 \mathcal{F}_{TV}(u, \hat{u}, \tilde{u}) = \int_\Omega \tilde{u} \hat{u} \; d\boldsymbol{x} + \alpha \int_\Omega \frac{1}{\left( \nabla u \cdot \nabla u + \varepsilon \right)^{\frac{1}{2}}} \left[ \left( I - \frac{\nabla u \otimes \nabla u}{\nabla u \cdot \nabla u + \varepsilon}\right) \nabla \tilde{u}\right] \cdot \nabla \hat{u} d\boldsymbol{x}.$ The highly nonlinear term $\left( I - \frac{\nabla u \otimes \nabla u}{\nabla u \cdot \nabla u + \varepsilon}\right)$ in the second variation poses a substantial challange for the convergence of the Newton’s method. In fact, the converge radius of the Newtos’s method is extremely small. For this reason in the following we will replace the second variation with the variational form $H_{\rm approx} = \int_\Omega \tilde{u}\,\hat{u} \; d\boldsymbol{x} + \alpha \int_\Omega \frac{1}{\left( \nabla u \cdot \nabla u + \varepsilon \right)^{\frac{1}{2}}} \nabla \tilde{u} \cdot \nabla \hat{u} d\boldsymbol{x}.$ For small values of $\varepsilon$, there are more efficient methods for solving TV-regularized inverse problems than the basic Newton method we use here; in particular, so-called primal-dual Newton methods are preferred (see T.F. Chan, G.H. Golub, and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM Journal on Scientific Computing, 20(6):1964–1977, 1999). The efficient solution of TV-regularized inverse problems is still an active field of research. The resulting method will exhibit only a first order convergence rate but it will be more robust for small values of $\varepsilon$. The best reconstruction of the original image is obtained for $\alpha = 10^{-2}$. We also notice that Total Variation does a much better job that Tikhonov regularization in preserving the sharp edges of the original image. def TVsolution(eps, alpha): def TV(u, eps): R_tv = TV(u, eps)dl.dx F = F_ls + alphaR_tv H = H_ls + alphaH_tv solver = InexactNewtonCG() solver.parameters["rel_tolerance"] = 1e-5 solver.parameters["abs_tolerance"] = 1e-6 solver.parameters["gdu_tolerance"] = 1e-18 solver.parameters["max_iter"] = 1000 solver.parameters["c_armijo"] = 1e-5 solver.parameters["print_level"] = -1 solver.parameters["max_backtracking_iter"] = 10 print( "{0:15e} {1:15e} {2:5} {3:4d} {4:15e} {5:15e} {6:15e} {7:15e}".format( alpha.values()[0], eps.values()[0], solver.converged, solver.it, dl.assemble(F), dl.assemble(F_ls), dl.assemble(alphaR_tv), dl.assemble(trueError)) ) plt.figure() nb.plot(u, vmin=vmin, vmax = vmax) plt.show() print ("{0:15} {1:15} {2:5} {3:4} {4:15} {5:15} {6:15} {7:15}".format("alpha", "eps", "converged", "nit", "F", "F_ls", "alphaR_tn", "True Error") ) eps = dl.Constant(1e-4) for alpha in alphas: TVsolution(eps, dl.Constant(alpha)) alpha eps converged nit F F_ls alpha*R_tn True Error 1.000000e-01 1.000000e-04 1 688 2.208528e-01 2.134489e-01 7.403896e-03 3.419669e-01 1.000000e-02 1.000000e-04 1 332 9.018107e-02 5.045327e-02 3.972780e-02 1.619008e-02 1.000000e-03 1.000000e-04 1 100 4.384282e-02 2.895010e-02 1.489273e-02 1.173449e-02 1.000000e-04 1.000000e-04 1 13 9.558218e-03 1.026104e-03 8.532114e-03 6.968568e-02 ## Hands on #### Question 1 For both $\mathcal{R}_{TN}$ and $\mathcal{R}^\varepsilon_{TV}$, derive gradients and Hessians using calculus of variations, in both weak form and strong form. Hint: To derive the Hessian of $\mathcal{R}^\varepsilon_{TV}$, recall the identity $(\mathbf{a} \cdot \mathbf{b})\mathbf{c} = (\mathbf{c}\mathbf{a}^T )\mathbf{b}$, where $\mathbf{a}, \mathbf{b}, \mathbf{c} \in \mathbb{R}^n$, and $\mathbf{a} \cdot \mathbf{b} \in \mathbb{R}$ is the inner product and $\mathbf{c}\mathbf{a}^T \in \mathbb{R}^{n\times n}$ is a matrix of rank one. #### Question 2 Show that when $\nabla u$ is zero, $\mathcal{R}_{TV}$ is not differentiable, but $\mathcal{R}^\varepsilon_{TV}$ is. #### Question 3 Derive expressions for the two eigenvalues and corresponding eigenvectors of the tensor diffusion coefficient $A=\left( I - \frac{\nabla u \otimes \nabla u}{\nabla u \cdot \nabla u + \varepsilon}\right)$ that appears in the Hessian of the $\mathcal{R}^{\varepsilon}_{TV}$ functional. Based on these expressions, give an explanation of why $\mathcal{R}^{\varepsilon}_{TV}$ is effective at preserving sharp TV edges in the image, while $\mathcal{R}_{TN}$ is not. Consider a single Newton step for this argument. #### Question 4 Show that for large enough $\varepsilon$, $\mathcal{R}^{\varepsilon}_{TV}$ behaves like $\mathcal{R}_{TN}$, and for $\varepsilon = 0$, the Hessian of $\mathcal{R}^{\varepsilon}_{TV}$ is singular. This suggests that $\varepsilon$ should be chosen small enough that edge preservation is not lost, but not too small that ill-conditioning occurs. #### Question 5 Solve the denoising inverse problem defined above using TV regularization for $\alpha = 10^{-2}$ and different values of $\varepsilon$ (e.g., from $10$ to $10^{−4}$). How does the number of nonlinear iterations behave for decreasing $\varepsilon$? Try to explain this behavior based on your answer to Question 4. The number of nonlinear interations increases as we decrease $\varepsilon$. In fact, as we decrease $\varepsilon$ the the $\mathcal{R}^{\varepsilon}_{TV}$ becomes more nonlinear and its Hessian becomes more and more ill-conditioned. alpha = dl.Constant(1e-2) eps_s = [10., 1., 0.1, 1e-2, 1e-3, 1e-4] for eps in eps_s: TVsolution(dl.Constant(eps), alpha) 1.000000e-02 1.000000e+01 1 45 1.411075e-01 5.090067e-02 9.020687e-02 2.041545e-02 1.000000e-02 1.000000e+00 1 75 1.050705e-01 5.082861e-02 5.424194e-02 1.800654e-02 1.000000e-02 1.000000e-01 1 116 9.442521e-02 5.066080e-02 4.376441e-02 1.682353e-02 1.000000e-02 1.000000e-02 1 169 9.133863e-02 5.052624e-02 4.081239e-02 1.635375e-02 1.000000e-02 1.000000e-03 1 247 9.044518e-02 5.046918e-02 3.997599e-02 1.622075e-02 1.000000e-02 1.000000e-04 1 337 9.018107e-02 5.045326e-02 3.972781e-02 1.619008e-02	{"extraction_info": {"found_math": true, "script_math_tex": 63, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8301864862442017, "perplexity": 1560.8925406934707}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039749562.99/warc/CC-MAIN-20181121173523-20181121195523-00318.warc.gz"}
http://etna.ricam.oeaw.ac.at/volumes/2011-2020/vol42/abstract.php?vol=42&pages=1-12	## Revisiting the inverse field of values problem Natália Bebiano, João da Providência, Ana Nata, and João P. da Providência ### Abstract The field of values of a linear operator is the convex set in the complex plane comprising all Rayleigh quotients. For a given complex matrix, Uhlig proposed the inverse field of values problem: given a point inside the field of values, determine a unit vector for which this point is the corresponding Rayleigh quotient. In the present note we propose an alternative method of solution to those that have appeared in the literature. Our approach is based on the fact that the field of values can be seen as a union of ellipses under a compression to the two-dimensional case, in which case the problem has an exact solution. Refining an idea of Marcus and Pesce, we provide alternative algorithms to plot the field of values of a general complex matrix, which perform faster and more accurately than the existing ones. Full Text (PDF) [204 KB], BibTeX ### Key words field of values, numerical range, inverse problem, generating vector, compression 15A60, 47B35 < Back	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9000712037086487, "perplexity": 633.732946285614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738819.78/warc/CC-MAIN-20200811180239-20200811210239-00258.warc.gz"}
https://tohoku.pure.elsevier.com/en/publications/silicic-lava-effusion-controlled-by-the-transition-from-viscous-m	# Silicic lava effusion controlled by the transition from viscous magma flow to friction controlled flow Research output: Contribution to journalArticlepeer-review 5 Citations (Scopus) ## Abstract Silicic magma forms a vertical fault in volcanic conduits via the brittle-ductile transition. The formation of the fault changes flow type from viscous flow to friction controlled flow. Here we investigate flow dynamics of magma by coupling a one-dimensional conduit flow model with an experimentally calibrated brittle-ductile transition. The numerical simulation demonstrates that the length of magma plug at which friction controlled flow becomes the main flow type depends on magma flux, because of crystallization kinetics and the ductile-brittle transition. At high flux, a short plug forms, because nonequilibrium crystallization inhibits an increase of magma viscosity. This results in the effusion of less viscous lava and large shear stress at the shallow part of the conduit. In contrast, the long plug that forms under low flux cannot maintain large shear stress due to weakness of the magmatic fault, which causes the extrusion of a solidified lava spine. Original language English 3608-3614 7 Geophysical Research Letters 44 8 https://doi.org/10.1002/2017GL072875 Published - 2017 Apr 28 ## Keywords • brittle-ductile transition • friction controlled flow • lava effusion • magmatic fault • silicic magma • viscous flow ## ASJC Scopus subject areas • Geophysics • Earth and Planetary Sciences(all)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8332623839378357, "perplexity": 11082.294142529412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703507045.10/warc/CC-MAIN-20210116195918-20210116225918-00749.warc.gz"}
https://homepages.uc.edu/~bilman/project/spectral-singularities/	# A Robust Inverse Scattering Transform for Arbitrary Spectral Singularities ## Spectral Singularities Consider for example the Riemann-Hilbert problem satisfied by the Beals-Coifman eigenfunction matrix $\mathbf{M}(z;x,t)$ for the focusing nonlinear Schrödinger (NLS) equation with an oriented jump contour $\Sigma$ that is the continuous spectrum of the underlying non-self-adjoint Zakharov-Shabat operator. Spectral singularities in context of the Riemann-Hilbert problem satisfied by $\mathbf{M}(z;x,t)$ are values $s\in\Sigma$ for which $\mathbf{M}(z;x,t)$ fails to admit a continuous boundary value as $z \to s\in\Sigma$ non-tangentially from at least one side of $\Sigma$. Poles of $\mathbf{M}(z;x,t)$ in the complement of $\Sigma$ are associated with the discrete spectrum of the non-self-adjoint Zakharov-Shabat operator. As illustrated in an example constructed by Zhou, it is known that even for Schwartz-class potentials $\psi$, $\mathbf{M}(z;x,t)$ may have infinitely many poles accumulating to points on $\Sigma$ from its complement and these accumulation points can themselves accumulate from within to severe spectral singularities. There are also physical solutions that are associated with spectral singularities. ### Important examples of solutions associated with spectral singularities • Rogue wave solutions of the nonlinear Schrödinger equation (NLS), which are $L^1$-perturbations of a nonzero background field. Rogue waves (also referred to as “freak waves” – or even as “mad-dog waves”) are surface waves that appear from nowhere, disappear without a trace and can cause great damage to ships of other fixed structures (e.g. oil platforms). Therefore it is of practical importance to study dynamical stability properties of rogue waves, in other words, to determine conditions on initial data sufficient to generate one or more of these rogue wave solutions. A model proposed for rogue waves is the Peregrine breather $$\psi_\mathrm{P}(x,t) :=e^{\mathrm{i}t}\left(1-\frac{4(1+2\mathrm{i}t)}{1+4[(x-x_0)^2+(t-t_0)^2]}\right),$$ $(x_0,t_0)\in\mathbb{R}^2$, which is an exact solution of the focusing nonlinear Schrödinger equation $$\mathrm{i}\psi_t + \tfrac{1}{2}\psi_{xx} + \|\psi\|^2\psi =0.$$ • Algebraic solitons of the derivative nonlinear Schrödinger equation (DNLS) $$\mathrm{i}\psi_t + \psi_{xx} + \mathrm{i}(\|\psi\|^2\psi)_x =0,$$ which have slow (algebraic) decay rate to the zero background field. ## A Robust Inverse Scattering Transform To be able treat the Cauchy problem in context of inverse scattering transform (IST) techniques while allowing such solutions, one needs an IST that can handle, preferably arbitrary, spectral singularities. In A Robust IST for the Focusing NLS Equation we introduced a robust IST that deals with arbitrary-order poles and potentially severe spectral singularities in a simple and unified way. As an application, we used the robust IST to place the Peregrine solution and related higher-order rogue wave solutions in an inverse-scattering context for the first time. This allows one to directly study properties of these solutions such as their dynamical or structural stability, or their asymptotic behavior in the limit of high order singularity. Availability of an IST that can treat rogue waves opens the door to study questions such as: • Are rogue wave solutions stable to localized perturbations? If not, what kinds of perturbations excite instabilities, and what is the long-term nonlinear saturation of the instabilities? • Is it possible to make a prediction based on the computation of some relevant scattering data as to how many Peregrine-like peaks will be generated from a localized perturbation of the background? In other words, what kind of initial conditions generate rogue waves? • How do rogue waves interact with other coherent structures, such as the time-periodic Kuznetsov-Ma soliton and its Galilean-boosted generalization sometimes called the Tajiri-Watanabe soliton? How do they interact with more general waves that are not in the realm of “exact solutions”? • Since it is possible to define mathematically a “rogue wave of order $N$” for arbitrary $N$, what can be said quantitatively about the asymptotics for large $N$? The robust IST applies to other integrable models of wave propagation by natural generalizations. This project involves collaboration with Peter D. Miller. ##### Deniz Bilman ###### Assistant Professor Assistant Professor of Mathematics. Research interests include nonlinear waves, Riemann-Hilbert problems.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8985425233840942, "perplexity": 683.9110224479294}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989856.11/warc/CC-MAIN-20210511184216-20210511214216-00593.warc.gz"}
http://www.ck12.org/book/CK-12-Geometry-Second-Edition/r1/section/7.3/	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # 7.3: Similarity by AA Difficulty Level: At Grade Created by: CK-12 ## Learning Objectives • Determine whether triangles are similar. • Understand AA for similar triangles. • Solve problems involving similar triangles. ## Review Queue 1. Find the measures of x\begin{align}x\end{align} and y\begin{align}y\end{align}. 2. The two triangles are similar. Find w\begin{align}w\end{align} and z\begin{align}z\end{align}. 1. Use the true proportion 68=x28=27y\begin{align}\frac{6}{8}=\frac{x}{28}=\frac{27}{y}\end{align} to answer the following questions. 1. Find x\begin{align}x\end{align} and y\begin{align}y\end{align}. 2. Write another true proportion. 3. Is 288=6+x12\begin{align}\frac{28}{8}=\frac{6+x}{12}\end{align} true? If you solve for x\begin{align}x\end{align}, is it the same as in part a? Know What? George wants to measure the height of a flagpole. He is 6 feet tall and his shadow is 10 feet long. At the same time, the shadow of the flagpole was 85 feet long. How tall is the flagpole? ## Angles in Similar Triangles The Third Angle Theorem states if two angles are congruent to two angles in another triangle, the third angles are congruent too. Because a triangle has 180\begin{align}180^\circ\end{align}, the third angle in any triangle is 180\begin{align}180^\circ\end{align} minus the other two angle measures. Let’s investigate what happens when two different triangles have the same angle measures. We will use Investigation 4-4 (Constructing a Triangle using ASA) to help us with this. Investigation 7-1: Constructing Similar Triangles Tools Needed: pencil, paper, protractor, ruler 1. Draw a 45\begin{align}45^\circ\end{align} angle. Extend the horizontal side and then draw a 60\begin{align}60^\circ\end{align} angle on the other side of this side. Extend the other side of the 45\begin{align}45^\circ\end{align} angle and the 60\begin{align}60^\circ\end{align} angle so that they intersect to form a triangle. What is the measure of the third angle? Measure the length of each side. 2. Repeat Step 1 and make the horizontal side between the 45\begin{align}45^\circ\end{align} and 60\begin{align}60^\circ\end{align} angle at least 1 inch longer than in Step 1. This will make the entire triangle larger. Find the measure of the third angle and measure the length of each side. 3. Find the ratio of the sides. Put the sides opposite the 45\begin{align}45^\circ\end{align} angles over each other, the sides opposite the 60\begin{align}60^\circ\end{align} angles over each other, and the sides opposite the third angles over each other. What happens? AA Similarity Postulate: If two angles in one triangle are congruent to two angles in another triangle, the two triangles are similar. The AA Similarity Postulate is a shortcut for showing that two triangles are similar. If you know that two angles in one triangle are congruent to two angles in another, which is now enough information to show that the two triangles are similar. Then, you can use the similarity to find the lengths of the sides. Example 1: Determine if the following two triangles are similar. If so, write the similarity statement. Solution: Find the measure of the third angle in each triangle. mG=48\begin{align}m \angle G = 48^\circ\end{align} and \begin{align}m \angle M = 30^\circ\end{align} by the Triangle Sum Theorem. Therefore, all three angles are congruent, so the two triangles are similar. \begin{align}\triangle FEG \sim \triangle MLN\end{align}. Example 2: Determine if the following two triangles are similar. If so, write the similarity statement. Solution: \begin{align}m \angle C = 39^\circ\end{align} and \begin{align}m \angle F = 59^\circ\end{align}. The angles are not equal, \begin{align}\triangle ABC\end{align} and \begin{align}\triangle DEF\end{align} are not similar. Example 3: Are the following triangles similar? If so, write the similarity statement. Solution: Because \begin{align}\overline{AE} \ \|\| \ \overline{CD}, \angle A \cong \angle D\end{align} and \begin{align}\angle C \cong \angle E\end{align} by the Alternate Interior Angles Theorem. Therefore, by the AA Similarity Postulate, \begin{align}\triangle ABE \sim \triangle DBC\end{align}. ## Indirect Measurement An application of similar triangles is to measure lengths indirectly. The length to be measured would be some feature that was not easily accessible to a person, such as: the width of a river or canyon and the height of a tall object. To measure something indirectly, you would need to set up a pair of similar triangles. Example 4: A tree outside Ellie’s building casts a 125 foot shadow. At the same time of day, Ellie casts a 5.5 foot shadow. If Ellie is 4 feet 10 inches tall, how tall is the tree? Solution: Draw a picture. From the picture to the right, we see that the tree and Ellie are parallel, therefore the two triangles are similar to each other. Write a proportion. \begin{align}\frac{4ft, 10in}{xft}=\frac{5.5ft}{125ft}\end{align} Notice that our measurements are not all in the same units. Change both numerators to inches and then we can cross multiply. \begin{align}\frac{58in}{xft}=\frac{66in}{125ft} \longrightarrow 58(125) &= 66(x)\\ 7250 &= 66x\\ x & \approx 109.85 \ ft\end{align} Know What? Revisited It is safe to assume that George and the flagpole stand vertically, making right angles with the ground. Also, the angle where the sun’s rays hit the ground is the same for both. The two trianglesare similar. Set up a proportion. \begin{align}\frac{10}{85} = \frac{6}{x} \longrightarrow 10x &= 510\\ x &= 51 \ ft.\end{align} The height of the flagpole is 51 feet. ## Review Questions Use the diagram to complete each statement. 1. \begin{align}\triangle SAM \sim \triangle \underline{\;\;\;\;\;\;\;\;\;}\end{align} 2. \begin{align}\frac{SA}{?}=\frac{SM}{?}=\frac{?}{RI}\end{align} 3. \begin{align}SM = \underline{\;\;\;\;\;\;\;\;\;}\end{align} 4. \begin{align}TR = \underline{\;\;\;\;\;\;\;\;\;}\end{align} 5. \begin{align}\frac{9}{?}=\frac{?}{8}\end{align} Answer questions 6-9 about trapezoid \begin{align}ABCD\end{align}. 1. Name two similar triangles. How do you know they are similar? 2. Write a true proportion. 3. Name two other triangles that might not be similar. 4. If \begin{align}AB = 10, AE = 7,\end{align} and \begin{align}DC = 22\end{align}, find \begin{align}AC\end{align}. Be careful! 5. Writing How many angles need to be congruent to show that two triangles are similar? Why? 6. Writing How do congruent triangles and similar triangles differ? How are they the same? Use the triangles to the left for questions 5-9. \begin{align}AB = 20, DE = 15,\end{align} and \begin{align}BC = k\end{align}. 1. Are the two triangles similar? How do you know? 2. Write an expression for \begin{align}FE\end{align} in terms of \begin{align}k\end{align}. 3. If \begin{align}FE = 12\end{align}, what is \begin{align}k\end{align}? 4. Fill in the blanks: If an acute angle of a _______ triangle is congruent to an acute angle in another ________ triangle, then the two triangles are _______. Are the following triangles similar? If so, write a similarity statement. In order to estimate the width of a river, the following technique can be used. Use the diagram on the left. Place three markers, \begin{align}O, C,\end{align} and \begin{align}E\end{align} on the upper bank of the river. \begin{align}E\end{align} is on the edge of the river and \begin{align}\overline{OC} \bot \overline{CE}\end{align}. Go across the river and place a marker, \begin{align}N\end{align} so that it is collinear with \begin{align}C\end{align} and \begin{align}E\end{align}. Then, walk along the lower bank of the river and place marker \begin{align}A\end{align}, so that \begin{align}\overline{CN} \bot \overline{NA}\end{align}. \begin{align}OC = 50 \ feet, CE = 30 \ feet, NA = 80 \ feet\end{align}. 1. Is \begin{align}\overline{OC} \ \|\| \ \overline{NA}\end{align}? How do you know? 2. Is \begin{align}\triangle OCE \sim \triangle ANE\end{align}? How do you know? 3. What is the width of the river? Find \begin{align}EN\end{align}. 4. Can we find \begin{align}EA\end{align}? If so, find it. If not, explain. 5. Janet wants to measure the height of her apartment building. She places a pocket mirror on the ground 20 ft from the building and steps backwards until she can see the top of the build in the mirror. She is 18 in from the mirror and her eyes are 5 ft 3 in above the ground. The angle formed by her line of sight and the ground is congruent to the angle formed by the reflection of the building and the ground. You may wish to draw a diagram to illustrate this problem. How tall is the building? 6. Sebastian is curious to know how tall the announcer’s box is on his school’s football field. On a sunny day he measures the shadow of the box to be 45 ft and his own shadow is 9 ft. Sebastian is 5 ft 10 in tall. Find the height of the box. 7. Juanita wonders how tall the mast of a ship she spots in the harbor is. The deck of the ship is the same height as the pier on which she is standing. The shadow of the mast is on the pier and she measures it to be 18 ft long. Juanita is 5 ft 4 in tall and her shadow is 4 ft long. How tall is the ship’s mast? 8. Use shadows or a mirror to measure the height of an object in your yard or on the school grounds. Draw a picture to illustrate your method. Use the diagram below to answer questions 27-31. 1. Draw the three separate triangles in the diagram. 2. Explain why \begin{align}\triangle GDE \cong \triangle DFE \cong \triangle GFD\end{align}. Complete the following proportionality statements. 1. \begin{align}\frac{GF}{DF}=\frac{?}{FE}\end{align} 2. \begin{align}\frac{GF}{GD}=\frac{?}{GE}\end{align} 3. \begin{align}\frac{GE}{DE}=\frac{DE}{?}\end{align} 1. \begin{align}x=52^\circ, y=80^\circ\end{align} 2. \begin{align}\frac{w}{20} = \frac{15}{25} \qquad \qquad \qquad \quad \ \frac{15}{25} = \frac{18}{z}\!\\ 25w = 15(20) \qquad \quad 25(18) = 15z\!\\ 25w = 300 \qquad \qquad \quad \ \ 450=15z\!\\ {\;} \ \ w = 12 \qquad \qquad \qquad \ \ 30=z\end{align} 1. \begin{align}168 = 8x \qquad 6y = 216\!\\ {\;} \ \ x = 21 \qquad \ \ y = 36\end{align} 2. Answers will vary. One possibility: \begin{align}\frac{28}{8} = \frac{21}{6}\end{align} 3. \begin{align}28(12) = 8(6+x)\!\\ {\;} \ \ \ 336 = 48+8x\!\\ {\;} \ \ \ 288 = 8x\!\\ {\;} \quad \ 36 = x \quad \text{Because}\ x \neq 21, \ \text{like in part a, this is not a true proportion.}\end{align} Show Hide Details Description Tags: Subjects: Date Created: Feb 22, 2012	{"extraction_info": {"found_math": true, "script_math_tex": 70, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9008980393409729, "perplexity": 1733.1229549913544}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783404826.94/warc/CC-MAIN-20160624155004-00017-ip-10-164-35-72.ec2.internal.warc.gz"}
https://koreauniv.pure.elsevier.com/en/publications/study-of-the-top-quark-pair-production-in-association-with-a-bott	# Study of the top-quark pair production in association with a bottom-quark pair from fast simulations at the LHC Young Kwon Jo, Suyong Choi, Youn Jung Roh, Tae Jeong Kim Research output: Contribution to journalArticle 1 Citation (Scopus) ### Abstract A large number of top quarks will be produced at the Large Hadron Collider (LHC) during the Run II period. This will allow us to measure the rare processes from the top sector in great details. We present a study of top-quark pair production in association with a bottom-quark pair ($$t\bar tb\bar b$$) from fast simulations for the Compact Muon Solenoid (CMS) experiment. The differential distributions of $$t\bar tb\bar b$$ are compared with the top-quark pair production with two additional jets ($$t\bar tjj$$) and with the production in association with the Higgs ($$t\bar tH$$), where the Higgs decays to a bottom-quark pair. The significances of the $$t\bar tb\bar b$$ process in the dileptonic and the semileptonic decay modes are calculated with the data corresponding to an integrated luminosity of 10 fb<sup>-1</sup>, which is foreseen to be collected in the early Run II period. This study will provide an important input in searching for new physics beyond the standard model, as well as in searching for the $$t\bar tH$$ process where the Yukawa coupling with the top quark can be directly measured. Original language English 807-812 6 Journal of the Korean Physical Society 67 5 https://doi.org/10.3938/jkps.67.807 Published - 2015 Sep 26 • Delphes • Top physics ### ASJC Scopus subject areas • Physics and Astronomy(all)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9137722849845886, "perplexity": 1474.9084507470602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739370.8/warc/CC-MAIN-20200814190500-20200814220500-00445.warc.gz"}
https://undergroundmathematics.org/chain-rule/r6710/solution	Review question What can we say if a point $P$ on an ellipse is directly above the focus? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource Ref: R6710 Solution The point $S$ is a focus of the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, and $P$ is a point on the ellipse such that $PS$ is perpendicular to the axis of $x$. The tangent and normal to the ellipse at $P$ meet the axis of $y$ in $Q$ and $R$ respectively. If $H$ is the other focus of the ellipse prove that $QR=HP$. Firstly, we can work out the coordinates of $P$. It is a standard property of ellipses that the distance from the centre $O$ to either focus is $f=\sqrt{a^2-b^2}$ (with the convention that $a>b$). Thus at points $S$ and $P$ we have $x=\sqrt{a^2-b^2}$. Thus the $y$-coordinate of $P$ is \begin{align} \frac{y^2}{b^2} &= 1-\frac{a^2-b^2}{a^2} \\ &= \frac{b^2}{a^2}, \end{align} so $y^2 = \frac{b^4}{a^2}$ and so $y = \frac{b^2}{a},$ since we have picked $P$ to be in the top right quadrant. Thus $P$ has coordinates $\left(\sqrt{a^2-b^2},\dfrac{b^2}{a}\right)$. Now let’s work out the equation of the tangent to the ellipse at $P$. We differentiate the equation of the ellipse implicitly to find the gradient of the tangent at $P$: we have $\frac{2x}{a^2}+\frac{2y}{b^2}\frac{dy}{dx}=0,$ and so $\frac{dy}{dx} = -\frac{2x}{a^2}\times \frac{b^2}{2y} = -\frac{x}{y}\times\frac{b^2}{a^2}.$ Thus at point $P$ the derivative is \begin{align} \frac{dy}{dx} &= -\frac{\sqrt{a^2-b^2}}{b^2/a}\times\frac{b^2}{a^2} \\ &= -\frac{\sqrt{a^2-b^2}}{a}. \end{align} The equation of the tangent to the ellipse through $P$ therefore has the equation $y-\frac{b^2}{a}=-\frac{\sqrt{a^2-b^2}}{a}\left(x-\sqrt{a^2-b^2}\right).$ We can use this equation to work out the coordinates of $Q$. When $x=0$ we get point $Q$, where \begin{align} y &= \frac{b^2}{a}-\frac{\sqrt{a^2-b^2}}{a}\left(-\sqrt{a^2-b^2}\right)\\ &= \frac{b^2+(a^2-b^2)}{a}=a, \end{align} so $Q$ has coordinates $(0,a)$. (Without loss of generality we are assuming $a>b>0$.) Now let’s work out the equation of the normal at $P$ and the coordinates of $R$. Similarly, the equation of the normal at $P$ is $y-\frac{b^2}{a}=\frac{a}{\sqrt{a^2-b^2}}\left(x-\sqrt{a^2-b^2}\right).$ When $x=0$ we get the point $R$, where \begin{align} y&=\frac{b^2}{a}+\frac{a}{\sqrt{a^2-b^2}}\left(-\sqrt{a^2-b^2}\right)\\ y&=\frac{b^2}{a}-a=\frac{b^2-a^2}{a}, \end{align} so $R$ has coordinates $\left(0,\dfrac{b^2-a^2}{a}\right)$. Now we want to prove that $QR = HP$. The other focus of the ellipse, $H$, has coordinates $\left(-\sqrt{a^2-b^2},0\right)$. Therefore we have \begin{align} HP &= \sqrt{(2\sqrt{a^2-b^2})^2+\left(\frac{b^2}{a}\right)^2} \\ &= \sqrt{4(a^2-b^2)+\frac{b^4}{a^2}}\\ &= \frac{1}{a}\sqrt{4a^4-4a^2b^2+b^4} \\ &= \frac{1}{a}\sqrt{(2a^2-b^2)^2}=\frac{2a^2-b^2}{a}. \end{align} Similarly, $QR = a+\frac{a^2-b^2}{a}=\frac{2a^2-b^2}{a}$ since we know that $Q$ is above the $x$-axis and $R$ is below it (had we chosen the other focus as $S$ this would be reversed.) Thus $QR = HP$ as required. For an alternative solution using the geometry of the ellipse, look at Solution 2.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999896287918091, "perplexity": 155.78341203036175}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267163326.85/warc/CC-MAIN-20180926041849-20180926062249-00011.warc.gz"}