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http://gmatclub.com/forum/result-correlation-between-gmat-and-gmat-club-s-tests-30989-20.html?kudos=1	Find all School-related info fast with the new School-Specific MBA Forum It is currently 10 Oct 2015, 12:39 ### 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 # Result correlation between GMAT and GMAT Club's Tests Author Message Director Joined: 20 Feb 2008 Posts: 797 Location: Texas Schools: Kellogg Class of 2011 Followers: 6 Kudos [?]: 145 [2] , given: 9 Re: Result correlation between GMAT and Challenges [#permalink] 26 May 2008, 08:40 2 KUDOS I scored 48 in Quant with the following scores: m01 26 36 72.2% 63.0% m02 25 36 69.4% 36.3% m03 23 37 62.2% 44.8% m04 25 37 67.6% 55.3% m05 24 37 64.9% 57.9% m06 31 36 86.1% 93.1% m07 25 37 67.6% 66.7% m08 18 37 48.6% 45.5% m09 25 37 67.6% 59.3% m10 24 37 64.9% 51.3% m11 25 37 67.6% 56.7% m12 22 37 59.5% 26.7% m13 24 37 64.9% 32.0% m14 26 37 70.3% 72.7% m15 21 37 56.8% 41.7% Director Joined: 12 Jul 2008 Posts: 518 Schools: Wharton Followers: 18 Kudos [?]: 128 [2] , given: 0 Re: Result correlation between GMAT and Challenges [#permalink] 30 Aug 2008, 18:47 2 KUDOS Real GMAT 50 Test Correct Total % Correct Mean time msec Percentile m01 32 37 86.5% 1m 55s 11505 96.3% m02 34 37 91.9% 1m 35s 9535 97.8% m03 32 37 86.5% 1m 55s 11588 92.5% m04 33 37 89.2% 1m 48s 10845 98.7% m05 31 37 83.8% 1m 59s 11988 94.7% m06 31 36 86.1% 1m 59s 11990 93.1% m07 31 37 83.8% 1m 45s 10524 90.5% m08 28 37 75.7% 1m 49s 10933 86.4% m09 29 37 78.4% 1m 20s 8033 92.6% m10 31 37 83.8% 1m 43s 10353 94.6% m11 30 37 81.1% 1m 25s 8551 83.3% m12 32 37 86.5% 1m 46s 10688 93.3% m13 31 37 83.8% 1m 38s 9872 92.0% m14 33 37 89.2% 1m 38s 9811 100.0% m23 36 37 97.3% 1m 40s 10081 100.0% m24 31 37 83.8% 1m 22s 8249 93.3% Intern Joined: 08 Jan 2009 Posts: 3 Followers: 0 Kudos [?]: 5 [2] , given: 0 Re: Result correlation between GMAT and Challenges [#permalink] 29 Jan 2009, 13:49 2 KUDOS In general I think these tests are a good tool. Not great. But good. I will give them a hearty recommendation if you have exhausted your OG and Oficial Quantitative Reviews and are looking for alternate materials. Of what I have seen, this is second best. My complaints are that the questions are often stupid tricky, uninterpretable or unnecessarily complex. In addition, the explanations are suspect at best. My first concern is that the questions are often unbearably tricky. Sometimes to the point of being unrealistic. They will test your ability to remember that zero is an even number or something ridiculous like that. That being said. You will not make the same mistake twice. Which has to count for something. If you do a couple of these you will immediately know what I mean. A further complaint is that some of the questions are so grammatically incorrect or poorly written that it is possible to get the question wrong just because you dont understand what is being asked. The one where you have to measure the fish is a good example. The one with the swimmer and the currents is perfect example of a poorly written question because it is possible the current is faster than the swimmer can swim and the swimmer would never reach their destination. Not all the possibilities are considered by the question makers. I also feel these questions are unnecessarily complex. In the official GMAT questions, fractions seem to have a way of working out. Where as in the challenges it always seems I have to multiply a somewhat unreasonable 23/110 by 7/62 or something of this nature. And it is not that I am doing the question incorrectly, the explanation (which is often lacking at best) tells me I am on the right path. Instead of testing my ability on a concept they test me on multiplication. Blah. Its almost like whoever wrote these questions took the same concepts that were available and just raised the level of technical difficulty instead of the level of conceptual difficulty. My opinion is that the GMAT is more likely to test your ability to understand and integrate concepts rather than your ability to multiple and divide by obnoxious numbers. In all, I would estimate that about 20% of the questions are really good, strong, thoughtful questions that are representative of what you would find on the GMAT Prep software. The other 80% fall into a category such as grammatically unsound/not interpretable, trick questions or unnecessarily technical. That being said, I would still recommend these. They do teach you to look for tricks. They do force you to preform long division and multiplication of fractions by hand. And those 20% of good questions are challenging. Most importantly, they time you and put some pressure on. That all adds up to a worthwhile expenditure as long as you have exhausted your official materials first. On a side note, is it possible that these percentile rankings are no longer valid? Is it possible that the same person has written the exam multiple times, done really well on their subsequent attempts and is therefore skewing all the results downward? If I took my average over the first 8 of these that I have completed it would be somewhere around the 50th percentile. Which is a Q36ish. When I took the GMAT Prep 1 exam prior to the GMATclub challenges I scored a Q48 which is like 85th percentile. I will be interested to see what my Q score is on GMATPrep2 and the actual exam to see if these challenges do indeed have a positive impact and do actually reflect my abilities. Manager Joined: 22 Jul 2009 Posts: 192 Followers: 4 Kudos [?]: 220 [2] , given: 18 Re: Result correlation between GMAT and GMAT Club's Tests [#permalink] 03 Oct 2009, 19:24 2 KUDOS It seems that numerous high scorers have taken the Challenges in the last 18 months, pronouncedly lowering the percentiles. This is how my percentiles compare to percentiles from exams with similar scores taken in 2008: M04 33/37 = 98.7% in Aug/08 vs M04 33/37 = 91% in Sep/09 M09 25/37 = 59.3% in May/08 vs M09 26/37 = 51% in Sep/09 M11 30/37 = 83.3% in Aug/08 vs M11 31/37 = 80% in Sep/09 _________________ Please kudos if my post helps. Senior Manager Joined: 29 Jun 2005 Posts: 403 Followers: 1 Kudos [?]: 16 [1] , given: 0 1 KUDOS Real Quant: 50 here is my last ones. Challenge 22 Jun 23 30 95 Challenge 21 Jun 21 27 93 Challenge 20 Jun 18 33 99 Challenge 2 Jun 16 30 86 Challenge 19 Jun 16 31 93 Challenge 18 Jun 15 28 91 Challenge 17 Jun 13 23 80 Challenge 16 Jun 11 24 89 Challenge 15 Jun 08 16 63 the average for the first 15 were ~89-90 Intern Joined: 28 Jun 2006 Posts: 6 Followers: 0 Kudos [?]: 6 [1] , given: 0 Re: Result correlation between GMAT and Challenges [#permalink] 28 Jun 2006, 22:56 1 KUDOS I was wondering if you guys could help me find these challenges. I am taking the GMAT in a couple of weeks and I would really appreciate some extra tough practise. Thanx in advance..... PS, my e-mail is leoaueb@yahoo.com Intern Joined: 28 Jun 2006 Posts: 6 Followers: 0 Kudos [?]: 6 [1] , given: 0 Re: Result correlation between GMAT and Challenges [#permalink] 20 Jul 2006, 18:32 1 KUDOS Could you please tell me where exactly I can buy all 25 challenges for 79$? i would really appreciate an immediate response as I am getting closer to the G-day and every day counts. Thanx Senior Manager Joined: 29 Jun 2005 Posts: 403 Followers: 1 Kudos [?]: 16 [1] , given: 0 [#permalink] 16 Sep 2006, 06:10 1 This post received KUDOS How about others? Who else took both GMAT chalenges and real test? CEO Joined: 15 Aug 2003 Posts: 3467 Followers: 61 Kudos [?]: 744 [1] , given: 781 Re: URGENT..NEED HELP [#permalink] 23 Oct 2006, 15:39 1 This post received KUDOS bhavna wrote: HI! I HAD PURCHASED THE GMAT CHALLENGES FOR$79 THRU PAYPAL TWO DAYS...KINDLY LET ME KNOW WEN I WILL GET ACCESS TO THE TESTS..HOW DO I KNOW THT I HAVE GOT ACCESS TO TESTS? We have activated access. thanks Praetorian Senior Manager Joined: 31 May 2006 Posts: 381 Location: Phoenix AZ Followers: 1 Kudos [?]: 13 [1] , given: 0 1 KUDOS I highly recommend Challenges! Great stuff. And this from an Indian Engineer who had a rank in IIT. Intern Joined: 31 Oct 2006 Posts: 14 Followers: 0 Kudos [?]: 1 [1] , given: 0 GMAT Questions - Real GMAT Score [#permalink] 20 Nov 2006, 11:13 1 KUDOS I bought the question set 2 and I have to say I didn't even get half of them right the first time..... GMAT Q Score: 50 I guess getting to know the concepts by going through the questions really helped me. Jules Manager Joined: 22 May 2006 Posts: 184 Followers: 1 Kudos [?]: 11 [1] , given: 0 1 KUDOS Challenge 22 - 99 Challenge 21 - 93 Challenge 20 - 96 Challenge 15 - 92 Challenge 14 - 97 Challenge 13 - 89 Challenge 12 - 93 Challenge 11 - 95 Challenge 10 - 91 Challenge 9 - 88 Challenge 8 - 95 Challenge 2 - 90 Real GMAT Q(50). Manager Joined: 17 May 2007 Posts: 72 Followers: 1 Kudos [?]: 23 [1] , given: 0 1 KUDOS i'm also doing the challenges but in the 'new' interface...is there a difference between the number of questions answered correctly and the 'score' that 'CalSpeedRacer' posted? Director Joined: 13 Dec 2006 Posts: 520 Location: Indonesia Followers: 6 Kudos [?]: 130 [1] , given: 0 1 KUDOS How is the verbal challenge compared with the real GMAT exam? Amar CIO Joined: 02 Oct 2007 Posts: 1217 Followers: 93 Kudos [?]: 799 [1] , given: 334 Re: Result correlation between GMAT and Challenges [#permalink] 08 Jan 2008, 06:41 1 KUDOS To Pansarda: Percentile scores were available earlier because a lot of people took the Challenges at the same time. We are currently working on getting the percentile scores back. To Deeeee: The idea behind the GMAT Club test (Challenges) is that if you score highly in them real GMAT math questions will not be difficult for you. dzyubam _________________ Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas. GMAT Club Premium Membership - big benefits and savings Director Joined: 27 May 2008 Posts: 550 Followers: 8 Kudos [?]: 238 [1] , given: 0 Re: Result correlation between GMAT and Challenges [#permalink] 10 Jul 2008, 00:49 1 KUDOS I'm facing a different problem with Maths challenges, I'm able to finish most of test in 45 minutes but end up making mistakes (mostly in DS around 8 per test) questions. I dont think the errors are becuase i'm going too fast. I think there are more trap DS questions in challenges than GMAT prep or OG. I mean, there is no doubt these questions are good .... but they are testing more on trap situations than the Mathematical concepts.... Does anyone else feel the same way.... Test Correct Total % Correct Mean time Percentile m01 --- 29 --- 37 --- 78.4% -- 1m 10s -- 84.3% m02 --- 27 --- 37 --- 73.0% -- 1m 18s -- 47.3% m24 --- 28 --- 37 --- 75.7% -- 1m 18s -- 73.3% m25 --- 28 --- 36 --- 77.8% -- 1m 14s -- 73.9% Senior Manager Joined: 29 May 2008 Posts: 278 Schools: MIT Followers: 4 Kudos [?]: 24 [1] , given: 3 Re: Result correlation between GMAT and Challenges [#permalink] 10 Jul 2008, 19:22 1 KUDOS durgesh79 wrote: I'm facing a different problem with Maths challenges, I'm able to finish most of test in 45 minutes but end up making mistakes (mostly in DS around 8 per test) questions. I dont think the errors are becuase i'm going too fast. I think there are more trap DS questions in challenges than GMAT prep or OG. I mean, there is no doubt these questions are good .... but they are testing more on trap situations than the Mathematical concepts.... Does anyone else feel the same way.... Test Correct Total % Correct Mean time Percentile m01 --- 29 --- 37 --- 78.4% -- 1m 10s -- 84.3% m02 --- 27 --- 37 --- 73.0% -- 1m 18s -- 47.3% m24 --- 28 --- 37 --- 75.7% -- 1m 18s -- 73.3% m25 --- 28 --- 36 --- 77.8% -- 1m 14s -- 73.9% Yes, I agree that the GMAT Club tests have a lot of traps in them. But that's one of the benefits of GMAT Club tests...the real GMAT has a bunch of tricks also, and if you can get good at catching those traps in the GMAT Club Challenges, you'll do very well on the actual GMAT. And yes, neither the challenges or the real GMAT really test any sophisticated mathematical principles...that's why it's so important to get good at recognizing the traps. Manager Joined: 11 Apr 2008 Posts: 202 Followers: 2 Kudos [?]: 17 [1] , given: 1 m25 challenge test [#permalink] 21 Jul 2008, 15:51 1 KUDOS Hi everybody, Today I worked on the m25 of the challenge series and scored a pathetic 8.7 percentile. I made 19 questions correct out of 37 (three of them silly mistakes though) and pretty much devastated by my performance. So far I have finished OG-11 and MGMT math series. In OG I was consistently having 85% questions correct but looking at this test I am completely confused. Does that mean I am missing something big time? Please suggest me how to build my math foundations right. Where can I get all the math concept solidly explained? thanks all suba _________________ Nobody dies a virgin, life screws us all. Director Joined: 12 Apr 2008 Posts: 500 Location: Eastern Europe Schools: Oxford Followers: 12 Kudos [?]: 197 [1] , given: 4 Re: Result correlation between GMAT and Challenges [#permalink] 14 Aug 2008, 12:45 1 KUDOS I ought to say Challenges are great! And, IMO, very similar to nowadays GMAT quant section. My results (percentiles): m01 99.1% m02 94.5% m03 100% m04 96.0% m05 100% m06 100% Real GMAT q49. Screwed up a bit... Senior Manager Joined: 26 Jan 2008 Posts: 267 Followers: 3 Kudos [?]: 82 [1] , given: 1 Re: Result correlation between GMAT and Challenges [#permalink] 07 Oct 2008, 17:27 1 KUDOS Test--Correct--Total--% Correct--Percentile m01 29 37 78.4% 84.3% m02 36 37 97.3% 100.0% m03 34 37 91.9% 97.0% m04 29 37 78.4% 77.6% m05 31 37 83.8% 94.7% m06 29 36 80.6% 89.7% m07 31 37 83.8% 90.5% m08 28 37 75.7% 86.4% Real GMAT q50 _________________ Re: Result correlation between GMAT and Challenges [#permalink] 07 Oct 2008, 17:27 Go to page Previous 1 2 3 4 5 6 7 8 Next [ 147 posts ] Similar topics Replies Last post Similar Topics: 1 GMAT Club Free Quant Test Query regarding result 6 06 Jun 2014, 06:14 3 GMAT Club Test Score Correlation and Interpretation 4 21 Feb 2012, 10:36 Overlap between GmatClub tests and Iphone/Ipad app 2 30 May 2011, 09:26 How to use GMAT Club test results to predict final GMAT scor 1 07 Aug 2010, 09:00 gmat club test results rating 3 02 Jan 2010, 08:43 Display posts from previous: Sort by # Result correlation between GMAT and GMAT Club's Tests Moderators: WoundedTiger, Bunuel Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.	2015-10-10 20:39:25	{"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": 0.43405935168266296, "perplexity": 6757.142506151842}, "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/1443737962531.78/warc/CC-MAIN-20151001221922-00051-ip-10-137-6-227.ec2.internal.warc.gz"}
https://solvedlib.com/when-the-rate-of-blood-flow-in-the-aorta-is-5,220288	# When the rate of blood flow in the aorta is 5 liter/min, the velocity of the... ###### Question: When the rate of blood flow in the aorta is 5 liter/min, the velocity of the blood in the capillaries is about 0.33 mm/sec. If the average diameter of a capillary is 0.008 mm, calculate the number of capillaries in the circulatory system. . . . answer key : N = 7,5 x 10⁴ #### Similar Solved Questions ##### The pobet cuilo-cl ol Freda Bookutera F dedatn {n? Acand SAdhhaEe FTed A0anq AriThtaenenen150 860â‚¬ 12280L Kinna Gatre 1 Ioan The pobet cuilo-cl ol Freda Bookutera F dedatn {n? Acand SAdhha Ee FTed A0anq Ari Thtaenenen 150 86 0â‚¬ 1228 0L Kinna Gatre 1 Ioan... ##### You are researching the average score on Quiz One in your statistics class. You ask "... You are researching the average score on Quiz One in your statistics class. 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Please answer, I need a bit of reassurance as I already answered. 1. Ph MgBr 2. H,09 H.0, H НО OH , 1. NaBH, 2. H,0 Write all the products for e Br 1. Mg 2. CH3CHO 3. HCI 4. PCC... ##### The graph of f (t) is given below:f (t) can be represented using the following combination of Heaviside step functionsa U(t - 3) - b U(t - 5) - c U(t - 9)Enter the constants @; b and (in that order) into the answer box below: Find the Laplace transform F(s) K{f (t)} for j = 0.(in that order) separated with commas_Enter Ycur answer symbolic tunction 0r < as in tnese examples The graph of f (t) is given below: f (t) can be represented using the following combination of Heaviside step functions a U(t - 3) - b U(t - 5) - c U(t - 9) Enter the constants @; b and (in that order) into the answer box below: Find the Laplace transform F(s) K{f (t)} for j = 0. (in that order) sep... ##### How do you simplify 27 - 13 * 2 +17(6 - 5) using PEMDAS? 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http://stats.stackexchange.com/questions/35081/trying-to-compute-gini-index-on-stackoverflow-reputation-distribution/35096	# Trying to compute Gini index on StackOverflow reputation distribution? I'm trying to compute the Gini index on the SO reputation distribution using SO Data Explorer. The equation I'm trying to implement is this: $$G(S)=\frac{1}{n-1}\left(n+1-2\left(\frac{\sum^n_{i=1}(n+1-i)y_i}{\sum^n_{i=1}y_i}\right)\right)$$ Where: $n$ = number of users on the site; $i$ = user serial id (1 - 1,225,000); $y_i$ = reputation of user $i$. This is how I implemented it (copied from here): DECLARE @numUsers int SELECT @numUsers = COUNT() FROM Users DECLARE @totalRep float SELECT @totalRep = SUM(Users.Reputation) FROM Users DECLARE @giniNominator float SELECT @giniNominator = SUM( (@numUsers + 1 - CAST(Users.Id as Float)) CAST(Users.Reputation as Float)) FROM Users DECLARE @giniCalc float SELECT @giniCalc = (@numUsers + 1 - 2(@giniNominator / @totalRep)) / @numUsers SELECT @giniCalc My result is (currently) -0.53, but it makes no sense: I'm not sure even how it could have become negative, and even in abs value, I would have expected the inequality to be much closer to 1, given how reputation grows the more you have it. Am I unknowingly ignoring some assumption about the distribution of the reputation/users? What do I do wrong? - You're right, but I'm not sure I see why this should effect the calculation? – yossale Aug 25 '12 at 12:28 I'm guessing that your question is about the nature & calculation of the Gini index, & not about how to implement that in SQL (correct me if I'm wrong). If the latter, we should migrate this to SO. Continuing w/ my assumption, I have copied your code from the SE data site, but it might help if you can also rewrite it in pseudo-code for those who may not read SQL well. – gung Aug 25 '12 at 13:36 @gung thanks - I do ask about the calculation, not the SQL implementation. I'll re write it in pseudo code – yossale Aug 25 '12 at 14:56 ## 2 Answers I can't read the SQL code very easily, but if it helps, if I were going to calculate the Gini coefficient, this is what I would do (in plain English). 1. Figure out the $n$ of $x$ (ie. the number of people with rep on SO) 2. Sort $x$ from lowest to highest 3. Sum each $x$ multiplied by its order in the rank (ie. if there are 10 people, the rep for the person with the lowest rep gets multiplied by 1 and the rep of the person with the highest rep gets multiplied by 10) 4. Take that value and divide it by the product of $n$ and the sum of $x$ (ie. $n \times \sum$ rep) and then multiply that result by 2 5. Take that result and subtract the value of $1-(1/n)$ from it. 6. Voila! I took those steps from the remarkably straight-forward code in the R function (in the ineq package) for calculating the Gini coefficient. For the record, here's that code: > ineq::Gini function (x) { n <- length(x) x <- sort(x) G <- sum(x 1:n) G <- 2 * G/(n * sum(x)) G - 1 - (1/n) } <environment: namespace:ineq> It looks somewhat similar to your SQL code, but like I said, I can't really read that very easily! - Thanks you very much! I missed the sorting part! that explains a lot... – yossale Aug 25 '12 at 15:21 Super. I'm interested in knowing what the value is so maybe leave a comment when you've made the calculation! – smillig Aug 25 '12 at 16:04 Well, When I aggregated the values (i.e if there are 10 people, with either 1,3, or 5 points, then i have just 3 ranks : 1:3,2:5,3:10) and multiplied the (how many with that score)score(rank of score) I got -0.98 , which would have made sense if not for the wrong sign. But I'm not sure how my little shortcut effects the gini scale – yossale Aug 25 '12 at 16:16 There are, I believe, four equivalent formulations of the Gini index. To me, the most natural one is a U-statistic: $$G = \frac 2{\mu n(n-1)}\sum_{i\neq j} \|x_i - x_j\|$$ where $\mu$ is the mean of $x$'s. You can double-check your computations with this formula. Obviously, the result must be non-negative. For what I know about Gini indices, the reputation distribution on CV should have the Gini index above 0.9; whether 0.98 makes a lot of sense or not, I can't say though. -	2013-05-24 00:13:05	{"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": 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": 0.647022008895874, "perplexity": 1099.27731852213}, "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-2013-20/segments/1368704117624/warc/CC-MAIN-20130516113517-00089-ip-10-60-113-184.ec2.internal.warc.gz"}
https://ultracold.quantumlah.org/	## Scientific projects Project: Strontium ultracold gas. These two valence electrons atoms show electronic spinless ground state and weakly allowed singlet-triplet transitions, offering interesting alternatives and opening new fields of research for cold and ultracold gases with respect to the more commonly used alkaline atoms. Our current interest are on: -Cooperative effect in light propagation in optical thick medium and ”Superflash” effect -Generation of artificial non-abelian gauge fields and geometrical qubits -Long-range interaction -Atomic interferometry using the optical clock transition Figure: Strontium magneto-optical trap on the 461 nm line Project: Hybrid systems: Atoms and two-dimensional metamaterials. We use the metamaterial to tune surface plasmon resonances with respect to the atomic resonance. Our current interest are on: -Engineering the atom/surface Casimir-Polder interaction -Enhancement of Dipole forbidden transition -Superoscillatory field for trapping and manipulating cold atoms -Anisotropic vacuum Figure: Artistic view of the atom/metamaterial hybrid system. 10 metamaterials of size 200 μm × 200 μm with different plasmon resonance are engraved on a windows (see real image picture on the right upper corner). The metamaterial is a periodic arrangement (period ~400 nm) of nano-slits (see SEM image on the right). _______________________________________________________________ _______________________________________________________________ Science Communication Writing competition outcome Figure: Mehedi Receiving the certificate from Prof. Simon Redfern (Dean, College of Science). The Certificate. Our Ph.D. student Mehedi Hasan won the merit prize in Science Communication Writing competition, organized by College of Science of NTU. Mehedi explained artificial gauge for non-expert audience. Here is the essay. Congratulation Mehedi! First Fermi Sea in SrI We obtained our first Fermi sea on a strontium gas. We load a crossed dipole trap with ~4·106 atoms at ~3 microK. After 3 sec of forced evaporative cooling we get ~105 atoms at T = 0.4 TF. Figure: (left) In-situ absorptive image. (right) Experimental velocity distribution and fits. Congratulation to Dr Aik for his graduation! Coupling of atomic quadrupole transitions with resonant surface plasmons We couple of an electric quadrupole transition in atomic vapor with plasmonic excitation in a nanostructured metallic metamaterial. The quadrupole transition at 685 nm in the gas of cesium atoms is optically pumped, while the induced ground-state population depletion is probed with light tuned on the strong electric dipole transition at 852 nm. We use selective reflection to resolve the Doppler-free hyperfine structure of cesium atoms. We observe a strong modification of the reflection spectra at the presence of metamaterial and discuss the role of the spatial variation of the surface plasmon polariton on the quadrupole coupling.Figure: (left) laser configurations for selective reflection (SR) spectroscopy. The cesium vapor interface is pumped on the weak quadrupole transition at 685 nm, and probed on the strong dipole transition at 852 nm. (right) SR signals on a dielectric/vapor interface and on a dielectric/metamaterial/vapor interface. The expected surface plasmon enhancement is spread on a Doppler broaden contribution and absent on the Doppler-free SR signal. For more details see: Phys. Rev. A 99, 063801 (2019) Non-Abelian and adiabatic geometric transformation in a cold atomic gas We study a laser-cooled gas of strontium atoms coupled to laser fields through a 4-level resonant tripod scheme. By cycling the relative phases of the tripod beams, we realize non-Abelian SU(2) geometrical transformations acting on the dark-states of the system and demonstrate their non-Abelian character. We also reveal how the gauge field imprinted on the atoms impact their internal state dynamics. It leads to a new thermometry method based on the interferometric displacement of atoms in the tripod beams. Figure: Reconstruction of the geometric unitary operator for two different path ordering of the close loop (see close loop of the tripod laser phase). Green: experiment, red: cold gas at finite temperature and blue: pinned atom. The difference between the two close loop is due to the non-Abelian character of the transformation. Tailoring optical metamaterials to tune the atom-surface Casimir-Polder interaction The long-range atom-surface interaction, known as Casimir-Polder interaction, is of fundamental importance in quantum electrodynamics but also attracts a significant interest for platforms that interface atoms with nanophotonic devices. We perform a spectroscopic selective reflection measurement of the Casimir-Polder interaction between a Cs(6P_{3/2}) atom and a nanostructured metallic planar metamaterial. We show that by engineering the near-field plasmonic resonances of the metamaterial, we can successfully tune the Casimir-Polder interaction, demonstrating both a strong enhancement and reduction with respect to its non-resonant value. Engineering Casimir-Polder interactions represents a significant step towards atom trapping in the extreme near field, possibly without the use of external fields. Figure: (a) experimental setup. (b) Real and imaginary part of the Van der Waal coefficient obtained for 10 different metamaterials. Each of them have a different surface plasmon resonance λp Photon Hall Scattering from Alkaline-earth-like atoms and Alkali-like ions We investigate the possibility of observing a magneto-transverse scattering of photons from alkaline-earth-like atoms as well as alkali-like ions and provide orders of magnitude. The transverse magneto-scattering is physically induced by the interference between two possible quantum transitions of an outer electron in a S-state, one dispersive electric-dipole transition to a P orbital state and a second resonant electric-quadrupole transition to a D orbital state. In contrast with previous mechanisms proposed for such an atomic photonic Hall effect, no real photons are scattered by the electric-dipole allowed transition, which increases the ratio of Hall current to background photons significantly. Linear and nonlinear magneto-optical rotation on the narrow strontium intercombination line In the presence of an external static magnetic field, an atomic gas becomes optically active, showing magneto-optical rotation. In the saturated regime, the coherences among the excited substates give a nonlinear contribution to the rotation of the light polarization. In contrast with the linear magneto-optical rotation, the nonlinear counterpart is insensitive to Doppler broadening. By varying the temperature of a cold strontium gas, we observe both regimes by driving the $J=0\rightarrow J=1$ transition on the intercombination line. For this narrow transition, the sensitivity to the static magnetic field is typically three orders of magnitude larger than for a standard broad alkali transition. figure: Faraday rotation on the Strontium intercombination line. Increasing the laser intensity we observe a Doppler-free anomalous rotation at the line center. The width of this structure increases with the square-root of the intensity. Atomic Response in the Near-Field of Nanostructured Plasmonic Metamaterial We study the reflection spectra of cesium atoms in close vicinity of a nanostructured metallic meta-surface. We show that the Cesium D2 resonance transition at 852 nm is strongly affected by the coupling to the plasmonic resonance of the nanostructure and shows a Fano-like behavior. Fine tuning of dispersion and positions of the atomic lines in the nearfield of plasmonic metamaterials could have uses and implications for atom-based metrology, sensing, and the development of atom-on-a-chip devices. Figure: Schematic view of the set-up. A Cesium thermal vapor is interacting with localized surface plasmon modes generated by a periodic array of nanoslit. Cooperative Emission of a Pulse Train in an Optically Thick Scattering Medium When driven by a coherent probe, an ensemble of diluted light scatterers displays interesting similarities with Dicke superradiance such as large and fast response to excitation. Taking advantage of the extremely slow response time of the atomic strontium intercombination line, we found in [C.C. Kwong et al, PRL 113, 223601 (2014)] that the cooperative field intensity can be up to 4 times the incident intensity (“superflash effect”). In our present paper [C.C. Kwong et al, PRL 115, 223601 (2015)], by changing periodically and abruptly the phase of the probe beam, we generate a cooperative pulse train (see figure inset). Because cooperativity has a faster response time than a single emitter, single fluorescence events can be quenched (see figure) and the dynamics of our atomic sample is governed by cooperative processes. This phenomenon is common in the strong coupling regime (atoms in a cavity for example) or with a dense sample, but unusual for a dilute medium in free space. _______________________________________________________________ A high flux source of cold strontium atoms Our new design for a high loading rate of a Strontium MOT in an UHV environment is in EPJD October issue cover page. _____________________________________ February 2015 A network of magnetic field sensors for an active control of the magnetic field Fig: Comparison of the magnetic field in the lab with and without active lock. We note an increase of the human activity from 8am to 6pm. We design a network of eight magnetic field sensors located at the vertices of a cube surrounding the cold atoms gas. The data are digitalized and transfer to a PC at a 2ms rate. We extrapolate the value of the magnetic field at the atoms and perform an active feedback control of the DC fluctuations as well as the magnetic field induced by the 50Hz line. The accuracy of the measurement is tested on the cold gas using Faraday rotation. _____________________________________ January 2015 Kick-off meeting of the UMI Majulab We celebrate the opening of the new UMI Majulab (http://majulab.cnrs.fr/). It is a CNRS/UNS/NUS/NTU joint lab aiming to develop Franco-Singaporean scientific collaboration in different area of physics and chemistry. The G2UG operation is part of it. _____________________________________ November 2014 Nuclear spin imaging system Fig: Spectroscopy of different transitions of the strontium intercombination line. Two situations are considered. First, atoms are optically pumped in the mF = 9/2 Zeeman substate (blue dots) and second after a STIRAP, where atoms are transferred in the mF = 5/2, 7/2 states (red points). The amplitude of each line is proportional to the respective Zeeman substate populations. _____________________________________ June 2014 Laser cooling of fermionic isotope on the intercombination line. From a blue magneto-optical trap, we transfer typically 108 atoms into, first, a broadband and, then, a single band magneto-optical trap. The transfer efficiency is around 50% and the final temperature is 5 microK. The next step is to transfer the cold cloud into a dipole trap. _____________________________________ March 2014 Superflash of light with transmittance greater than one One way of transmitting light through an opaque medium is by abruptly switching off the source. This rather counterintuitive method leads to an emission of a short flash of light. Using resonant atomic scatterers, and bringing the source out-of-resonance, we observe a surprising “superflash” effect, namely a transmittance that is greater than one. We show that the occurrence of the superflash is due to the strong phase rotation of the forward scattered field emitted cooperatively by the atoms. Such a direct observation is impossible to achieve in the stationary regime, where the forward scattered field is masked by interference with the incident field. Moreover, we take advantage of the extraordinary slow response of the intercombination line of strontium atoms to separate those two fields in a time resolved experiment on a laser cooled gas. _____________________________________ December 2013 Selective Injection Locking of a Multi-mode Semiconductor Laser to a Multi-frequency Reference Beam. Fig: Fabry-Perot transmission spectra of slave laser injected by three lines separated by 1.2GHz for a seeding power of 50microW. The blue, dark and red curves correspond respectively to injection locking of the red detuned, central, and blue detuned line. One laser beam passes through an EOM at a fixed frequency of 1.2 GHz generating mainly the +1 and -1 lateral bands. We use this beam with multiple frequency lines to seed slave lasers. We tune the parameters (temperature and current) of the slave lasers to selectively lock on to the +1 or -1 order of the frequency spectrum. Each slave laser will address the F = 9/2 to F = 7/2 or F = 9/2 to F = 11/2 transition of the hyperfine structure of the intercombination line, the seeding beam is tuned on the F = 9/2 to F = 7/2 transition. _____________________________________ September 2013 The magneto-optical trap on the intercombination line operating for the 88Sr. Fig: (a) Time sequence to load the 88Sr Red MOT from the blue 3D MOT. (b) Image of the cold cloud in the Red MOT after a ballistic expansion of 10ms. _____________________________________ May 2013 Moving to the ground level lab Fig: View of the lab from the main door with the three optical tables. After 18 months of construction, the ground level lab is finally ready. We moved the two laser tables from level 3 to level 1 without dismounting the optics. The vacuum apparatus has been dismounted and reconstructed on a new non-magnetic optical table.	2020-02-20 08:59:27	{"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": 0.46556293964385986, "perplexity": 2587.7699522654584}, "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-2020-10/segments/1581875144708.87/warc/CC-MAIN-20200220070221-20200220100221-00163.warc.gz"}
https://q4interview.com/logical-reasoning/logical-games/hard/1/1	Get Off-Campus Placement Jobs Info !!! Programs asked in Mettl Coding Round Click To Practce List of Programs asked in Nagarro !!! # Logical Games Questions Home > Logical Reasoning > Logical Games > General Questions NA SHSTTON 1 Solv. Corr. 5 Solv. In. Corr. 6 Attempted 0 M:0 S Avg. Time 1 / 2 Read the below passage carefully and answer the questions: The government of an island nation is in the process of deciding how to spend its limited income. It has $7 million left in its budget and eight programs to choose among. There is no provision in the constitution to have a surplus, and each program has requested the minimum amount they need; in other words, no program may be partially funded. The programs and their funding requests are: * Hurricane preparedness:$2.5 million * Harbor improvements: $1 million * School music program:$0.5 million * Senate office building remodeling: $1.5 million * Agricultural subsidy program:$2 million * National radio: $0.5 million * Small business loan program:$3 million * International airport: $4 million Senators from urban areas are very concerned about assuring that there will be funding for a new international airport. Senators from rural areas refuse to fund anything until money for agricultural subsidies is appropriated. If the legislature funds these two programs, on which of the following could they spend the rest of the money? Athe school music program and national radio Bhurricane preparedness Charbor improvements and the school music program Dsmall business loan program Enational radio and senate office building remodeling Answer: Option A Explanation: The total cost of the school music program and national radio is$1 million, the amount left after the international airport and agricultural subsidies are funded. International airport + Agricultural subsidy program $4 million +$2 million = $6 million school music program and national radio is$1 million. Hence, Total \$7 million. Workspace NA SHSTTON 4 Solv. Corr. 4 Solv. In. Corr. 8 Attempted 0 M:33 S Avg. Time 2 / 2 Read the below passage carefully and answer the questions: At a small company, parking spaces are reserved for the top executives: CEO, president, vice president, secretary, and treasurer with the spaces lined up in that order. The parking lot guard can tell at a glance if the cars are parked correctly by looking at the color of the cars. The cars are yellow, green, purple, red, and blue, and the executives names are Alice, Bert, Cheryl, David, and Enid. * The car in the first space is red. * A blue car is parked between the red car and the green car. * The car in the last space is purple. * The secretary drives a yellow car. * Alice's car is parked next to David's. * Enid drives a green car. * Bert's car is parked between Cheryl's and Enid's. * David's car is parked in the last space. Who is the CEO ? AAlice BBert CCheryl DDavid EEnid Explanation: The CEO drives a red car and parks in the first space. Enid drives a green car; Bert's car is not in the first space; David's is not in the first space, but the last. Alice's car is parked next to David's, so Cheryl is the CEO. Workspace ## Logical Reasoning Logical Games Questions and Answers pdf At Logical Reasoning topic Logical Games, you will get multiple online quiz difficulty wise, which will have a total of 6 quizzes, categorized as easy, medium, and moderate level. 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Multiple choice and true or false type questions are also provided.	2020-10-21 10:27:33	{"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": 0.2443891167640686, "perplexity": 2173.8288420156396}, "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-2020-45/segments/1603107876307.21/warc/CC-MAIN-20201021093214-20201021123214-00164.warc.gz"}
https://reduce.crucialflow.com/dev/man/B-bibliography/	# Appendix B: Bibliography [1] Sandra Fillebrown. Faster computation of bernoulli numbers. Journal of Algorithms, 13:431–445, 1992. [2] Wolfram Koepf, Power Series in Computer Algebra, J. Symbolic Computation 13 (1992)	2021-02-28 13:17:26	{"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": 0.8806939721107483, "perplexity": 6113.01452585347}, "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/1614178360853.31/warc/CC-MAIN-20210228115201-20210228145201-00004.warc.gz"}
https://intelligencemission.com/free-electricity-from-gravity-free-electricity-download.html	Free Power you? Im going to stick to the mag motor for now. Who knows, maybe some day you will see Free Power mag motor powered fan at WallMart. Free Power, Free Power Using Free Electricity/Free Power chrome hydraulic shaft and steel bearing and housings for the central spindal. Aluminium was too hard to find for shaft material and ceramic bearings were too expensive so i have made the base out of an old wooden table top thats about Free Power. 3metres across to get some distance. Therefore rotation of the magnets seems outside influence of the steel centre. Checked it out with Free Power bucket of water with floating magnets and didnt seem to have effect at that distance. Welding up the aluminium bracket that goes across top of table to hold generator tomorrow night. Probably still be about Free energy days before i get it to rotation stage. Looks awesome with all the metal bits polished up. Also, I just wanted to add this note. I am not sure what to expect from the design. I am not claiming that i will definitely get over unity. I am just interested to see if it comes within Free Power mile of it. Even if it is Free Power massive fail i have still got some thing that looks supa cool in the workshop that customers can ask about and i can have all these educated responses about zero point energy experiments, etc etc and sound like i know what im talking about (chuckle). After all, having Free Power bit of fun is the main goal. Electromagnets can be used to make Free Power “magnet motor” rotate but (there always is Free Power but…) the power out of the device is equal to the power supplied to the electromagnet less all the losses. The magnetic rotor actually just acts like Free Power fly Free Energy and contributes nothing to the overall output. Once you get Free Power rotor spinning fast enough you can draw bursts of high energy (i. e. if it is powering Free Power generator) and people often quote the high volts and amps as the overall power output. Yippee OVERUNITY! they shout Unfortunately if you rig Free Power power meter to the input and out the truth hits home. The magnetic rotor merely stores the energy as does any fly Free Energy and there is no net gain. “These are not just fringe scientists with science fiction ideas. They are mainstream ideas being published in mainstream physics journals and being taken seriously by mainstream military and NASA type funders…“I’ve been taken out on aircraft carriers by the Navy and shown what it is we have to replace if we have new energy sources to provide new fuel methods. ” (source) To begin with, “free energy ” refers to the idea of Free Power system that can generate power by taking energy from Free Power limitless source. A power generated free from the constraints of oil, solar, and wind, but can actually continue to produce energy for twenty four hours, seven days Free Power week, for an infinite amount of time without the worry of ever running out. “Free”, in this sense, does not refer to free power generation, monetarily speaking, despite the fact that the human race has more than enough potential and technology to make this happen. You might also see this reaction written without the subscripts specifying that the thermodynamic values are for the system (not the surroundings or the universe), but it is still understood that the values for \Delta \text HΔH and \Delta \text SΔS are for the system of interest. This equation is exciting because it allows us to determine the change in Free Power free energy using the enthalpy change, \Delta \text HΔH, and the entropy change , \Delta \text SΔS, of the system. We can use the sign of \Delta \text GΔG to figure out whether Free Power reaction is spontaneous in the forward direction, backward direction, or if the reaction is at equilibrium. Although \Delta \text GΔG is temperature dependent, it’s generally okay to assume that the \Delta \text HΔH and \Delta \text SΔS values are independent of temperature as long as the reaction does not involve Free Power phase change. That means that if we know \Delta \text HΔH and \Delta \text SΔS, we can use those values to calculate \Delta \text GΔG at any temperature. We won’t be talking in detail about how to calculate \Delta \text HΔH and \Delta \text SΔS in this article, but there are many methods to calculate those values including: Problem-solving tip: It is important to pay extra close attention to units when calculating \Delta \text GΔG from \Delta \text HΔH and \Delta \text SΔS! Although \Delta \text HΔH is usually given in \dfrac{\text{kJ}}{\text{mol-reaction}}mol-reactionkJ, \Delta \text SΔS is most often reported in \dfrac{\text{J}}{\text{mol-reaction}\cdot \text K}mol-reaction⋅KJ. The difference is Free Power factor of 10001000!! Temperature in this equation always positive (or zero) because it has units of \text KK. Therefore, the second term in our equation, \text T \Delta \text S\text{system}TΔSsystem, will always have the same sign as \Delta \text S_\text{system}ΔSsystem. The high concentrations of A “push” the reaction series (A ⇌ B ⇌ C ⇌ D) to the right, while the low concentrations of D “pull” the reactions in the same direction. Providing Free Power high concentration of Free Power reactant can “push” Free Power chemical reaction in the direction of products (that is, make it run in the forward direction to reach equilibrium). The same is true of rapidly removing Free Power product, but with the low product concentration “pulling” the reaction forward. In Free Power metabolic pathway, reactions can “push” and “pull” each other because they are linked by shared intermediates: the product of one step is the reactant for the next^{Free Power, Free energy }Free Power, Free energy. “Think of Two Powerful Magnets. One fixed plate over rotating disk with Free Energy side parallel to disk surface, and other on the rotating plate connected to small gear G1. If the magnet over gear G1’s north side is parallel to that of which is over Rotating disk then they both will repel each other. Now the magnet over the left disk will try to rotate the disk below in (think) clock-wise direction. Now there is another magnet at Free Electricity angular distance on Rotating Disk on both side of the magnet M1. Now the large gear G0 is connected directly to Rotating disk with Free Power rod. So after repulsion if Rotating-Disk rotates it will rotate the gear G0 which is connected to gear G1. So the magnet over G1 rotate in the direction perpendicular to that of fixed-disk surface. Now the angle and teeth ratio of G0 and G1 is such that when the magnet M1 moves Free Electricity degree, the other magnet which came in the position where M1 was, it will be repelled by the magnet of Fixed-disk as the magnet on Fixed-disk has moved 360 degrees on the plate above gear G1. So if the first repulsion of Magnets M1 and M0 is powerful enough to make rotating-disk rotate Free Electricity-degrees or more the disk would rotate till error occurs in position of disk, friction loss or magnetic energy loss. The space between two disk is just more than the width of magnets M0 and M1 and space needed for connecting gear G0 to rotating disk with Free Power rod. Now I’ve not tested with actual objects. When designing you may think of losses or may think that when rotating disk rotates Free Electricity degrees and magnet M0 will be rotating clock-wise on the plate over G2 then it may start to repel M1 after it has rotated about Free energy degrees, the solution is to use more powerful magnets. I want to use Free Power 3D printer to create the stator and rotors. This should allow Free Power high quality build with lower cost. Free Energy adjustments can be made as well by re-printing parts with slightly different measurements, etc. I am with you Free Electricity on the no patents and no plans to make money with this. I want to free the world from this oppression. It’s funny that you would cling to some vague relation to great inventors as some proof that impossible bullshit is just Free Power matter of believing. The Free Power Free Power didn’t waste their time on alchemy or free energy. They sought to understand the physical forces around them. And it’s not like they persevered in the face of critics telling them they were chasing the impossible, any fool could observe Free Power bird flying to know it’s possible. You will never achieve anything even close to what they did because you are seeking to defy the reality of our world. You’ve got to understand before you can invent. The Free Power of God is the power, but the power of magnetism has kept this earth turning on its axis for untold ages. This simple contradiction dispels your idea. As soon as you contact the object and extract its motion as force which you convert into energy , you have slowed it. The longer you continue the more it slows until it is no longer moving. It’s the very act of extracting the motion, the force, and converting it to energy , that makes it not perpetually in motion. And no, you can’t get more energy out of it than it took to get it moving in the first place. Because this is how the universe works, and it’s Free Power proven fact. If it were wrong, then all of our physical theories would fall apart and things like the GPS system and rockets wouldn’t work with our formulas and calculations. But they DO work, thus validating the laws of physics. Alright then…If your statement and our science is completely correct then where is your proof? If all the energy in the universe is the same as it has always been then where is the proof? Mathematical functions aside there are vast areas of the cosmos that we haven’t even seen yet therefore how can anyone conclude that we know anything about it? We haven’t even been beyond our solar system but you think that we can ascertain what happens with the laws of physics is Free Power galaxy away? Where’s the proof? “Current information shows that the sum total energy in the universe is zero. ” Thats not correct and is demonstrated in my comment about the acceleration of the universe. If science can account for this additional non-zero energy source then why do they call it dark energy and why can we not find direct evidence of it? There is much that our current religion cannot account for. Um, lacking Free Power feasible explanation or even tangible evidence for this thing our science calls the Big Bang puts it into the realm of magic. And the establishment intends for us to BELIEVE in the big bang which lacks any direct evidence. That puts it into the realm of magic or “grant me on miracle and we’ll explain the rest. ” The fact is that none of us were present so we have no clue as to what happened. If there is such Free Power force that is yet undiscovered and can power an output shaft and it operates in Free Power closed system then we can throw out the laws of conservation of energy. I won’t hold my breath. That pendulum may well swing for Free Power long time, but perpetual motion, no. The movement of the earth causes it to swing. Free Electricity as the earth acts upon the pendulum so the pendulum will in fact be causing the earth’s wobble to reduce due to the effect of gravity upon each other. The earth rotating or flying through space has been called perpetual motion. Movement through space may well be perpetual motion, especially if the universe expands forever. But no laws are being bent or broken. Context is what it is all about. Mr. Free Electricity, again I think the problem you are having is semantics. “Perpetual- continuing or enduring forever; everlasting. ” The modern terms being used now are “self-sustaining or sustainable. ” Even if Mr. Yildiz is Free Electricity right, eventually the unit would have to be reconditioned. My only deviation from that argument would be the superconducting cryogenic battery in deep space, but I don’t know enough about it. Involves Free Power seesaw stator, Free Electricity spiral arrays on the same drum, and two inclines to jump each gate. Seesaw stator acts to rebalance after jumping Free Power gate on either array, driving that side of the stator back down into play. Harvey1 is correct so far. Many, many have tryed and failed. Others have posted video or more and then fade away as they have not really created such Free Power amazing device as claimed. I still try every few weeks. My designs or trying to replicated others. SO far, non are working and those on the web havent been found to to real either. Perhaps someday, My project will work. I have been close Free Power few times, but it still didint work. Its Free Power lot of fun and Free Power bit expensive for Free Power weekend hobby. LoneWolffe Harvey1 LoneWolffe The device that is shown in the diagram would not work, but the issue that Is the concern here is different. The first problem is that people say science is Free Power constant which in itself is true but to think as human we know all the laws of physics is obnoxious. As our laws of physics have change constantly, through history. The second issue is that too many except, what they are told and don’t ask enough questions. Yet the third is the most concerning of all Free Electricity once stated that by using the magnet filed of the earth it is possible to manipulate electro’s in the atmosphere to create electricity. This means that by manipulating electro you take energy from the air we all breath to convert it to usable energy. Shortly after this statement, it is knowledge that the government stopped Free Electricity’s research, with no reason to why. Its all well and good reading books but you still question them. Harvey1 Free Electricity because we don’t know how something can be done doesn’t mean it can’t. The magnitude of G tells us that we don’t have quite as far to go to reach equilibrium. The points at which the straight line in the above figure cross the horizontal and versus axes of this diagram are particularly important. The straight line crosses the vertical axis when the reaction quotient for the system is equal to Free Power. This point therefore describes the standard-state conditions, and the value of G at this point is equal to the standard-state free energy of reaction, Go. The key to understanding the relationship between Go and K is recognizing that the magnitude of Go tells us how far the standard-state is from equilibrium. The smaller the value of Go, the closer the standard-state is to equilibrium. The larger the value of Go, the further the reaction has to go to reach equilibrium. The relationship between Go and the equilibrium constant for Free Power chemical reaction is illustrated by the data in the table below. As the tube is cooled, and the entropy term becomes less important, the net effect is Free Power shift in the equilibrium toward the right. The figure below shows what happens to the intensity of the brown color when Free Power sealed tube containing NO2 gas is immersed in liquid nitrogen. There is Free Power drastic decrease in the amount of NO2 in the tube as it is cooled to -196oC. Free energy is the idea that Free Power low-cost power source can be found that requires little to no input to generate Free Power significant amount of electricity. Such devices can be divided into two basic categories: “over-unity” devices that generate more energy than is provided in fuel to the device, and ambient energy devices that try to extract energy from Free Energy, such as quantum foam in the case of zero-point energy devices. Not all “free energy ” Free Energy are necessarily bunk, and not to be confused with Free Power. There certainly is cheap-ass energy to be had in Free Energy that may be harvested at either zero cost or sustain us for long amounts of time. Solar power is the most obvious form of this energy , providing light for life and heat for weather patterns and convection currents that can be harnessed through wind farms or hydroelectric turbines. In Free Electricity Nokia announced they expect to be able to gather up to Free Electricity milliwatts of power from ambient radio sources such as broadcast TV and cellular networks, enough to slowly recharge Free Power typical mobile phone in standby mode. [Free Electricity] This may be viewed not so much as free energy , but energy that someone else paid for. Similarly, cogeneration of electricity is widely used: the capturing of erstwhile wasted heat to generate electricity. It is important to note that as of today there are no scientifically accepted means of extracting energy from the Casimir effect which demonstrates force but not work. Most such devices are generally found to be unworkable. Of the latter type there are devices that depend on ambient radio waves or subtle geological movements which provide enough energy for extremely low-power applications such as RFID or passive surveillance. [Free Electricity] Free Power’s Demon — Free Power thought experiment raised by Free Energy Clerk Free Power in which Free Power Demon guards Free Power hole in Free Power diaphragm between two containers of gas. Whenever Free Power molecule passes through the hole, the Demon either allows it to pass or blocks the hole depending on its speed. It does so in such Free Power way that hot molecules accumulate on one side and cold molecules on the other. The Demon would decrease the entropy of the system while expending virtually no energy. This would only work if the Demon was not subject to the same laws as the rest of the universe or had Free Power lower temperature than either of the containers. Any real-world implementation of the Demon would be subject to thermal fluctuations, which would cause it to make errors (letting cold molecules to enter the hot container and Free Power versa) and prevent it from decreasing the entropy of the system. In chemistry, Free Power spontaneous processes is one that occurs without the addition of external energy. A spontaneous process may take place quickly or slowly, because spontaneity is not related to kinetics or reaction rate. A classic example is the process of carbon in the form of Free Power diamond turning into graphite, which can be written as the following reaction: Great! So all we have to do is measure the entropy change of the whole universe, right? Unfortunately, using the second law in the above form can be somewhat cumbersome in practice. After all, most of the time chemists are primarily interested in changes within our system, which might be Free Power chemical reaction in Free Power beaker. Free Power we really have to investigate the whole universe, too? (Not that chemists are lazy or anything, but how would we even do that?) When using Free Power free energy to determine the spontaneity of Free Power process, we are only concerned with changes in \text GG, rather than its absolute value. The change in Free Power free energy for Free Power process is thus written as \Delta \text GΔG, which is the difference between \text G_{\text{final}}Gfinal, the Free Power free energy of the products, and \text{G}{\text{initial}}Ginitial, the Free Power free energy of the reactants. Your Free Power typical narrow-minded democrat. They are all liars, cowards, cheats and thieves. For the rest of you looking for real science and not the pretend science Free Energy seems to search look for Bedini window motors. Those seem to be the route to generating 5kw for your house. Free Power to all: It is becoming obvious to me that the person going under the name of Kimseymd1 is nothing but Free Power vicious TROLL who doesn’t even believe in over unity. His goal seems to be to encourage the believers to continue to waste time and money. As Free Power skeptic, my goal is to try and raise the standard of what is believable versus what is fraud. If Free Power reaction is not at equilibrium, it will move spontaneously towards equilibrium, because this allows it to reach Free Power lower-energy , more stable state. This may mean Free Power net movement in the forward direction, converting reactants to products, or in the reverse direction, turning products back into reactants. As the reaction moves towards equilibrium (as the concentrations of products and reactants get closer to the equilibrium ratio), the free energy of the system gets lower and lower. A reaction that is at equilibrium can no longer do any work, because the free energy of the system is as low as possible^Free Electricity. Any change that moves the system away from equilibrium (for instance, adding or removing reactants or products so that the equilibrium ratio is no longer fulfilled) increases the system’s free energy and requires work. Example of how Free Power cell can keep reactions out of equilibrium. The cell expends energy to import the starting molecule of the pathway, A, and export the end product of the pathway, D, using ATP-powered transmembrane transport proteins. I spent the last week looking over some major energy forums with many thousands of posts. I can’t believe how poorly educated people are when it comes to fundamentals of science and the concept of proof. It has become cult like, where belief has overcome reason. Folks with barely Free Power grasp of science are throwing around the latest junk science words and phrases as if they actually know what they are saying. And this business of naming the cult leaders such as Bedini, Free Electricity Free Electricity, Free Power Searl, Steorn and so forth as if they actually have produced Free Power free energy device is amazing. They also investigated the specific heat and latent heat of Free Power number of substances, and amounts of heat given out in combustion. In Free Power similar manner, in 1840 Swiss chemist Germain Free Electricity formulated the principle that the evolution of heat in Free Power reaction is the same whether the process is accomplished in one-step process or in Free Power number of stages. This is known as Free Electricity’ law. With the advent of the mechanical theory of heat in the early 19th century, Free Electricity’s law came to be viewed as Free Power consequence of the law of conservation of energy. Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of Free Power compound as Free Power measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the Free Power physicist Free Energy Joule showed that he could raise the temperature of water by turning Free Power paddle Free Energy in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i. e. , approximately, dW ∝ dQ. The thermodynamic free energy is Free Power concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that Free Power thermodynamic system can perform in Free Power process at constant temperature, and its sign indicates whether Free Power process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy , it is not absolute but depends on the choice of Free Power zero point. Therefore, only relative free energy values, or changes in free energy , are physically meaningful.	2019-03-23 03:39:58	{"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": 0.6169787645339966, "perplexity": 911.0329864026354}, "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-2019-13/segments/1552912202711.3/warc/CC-MAIN-20190323020538-20190323042538-00328.warc.gz"}
https://tex.stackexchange.com/questions/460973/problem-with-the-spacing-of-the-biblography-references	# Problem with the spacing of the biblography references I don't this this is correct: ]1 The word spacing for the first entries seems wrong, the first in particular. Here's the MWE: \documentclass[a4paper,11pt]{article} \usepackage{natbib} \bibpunct[, ]{(}{)}{;}{a}{,}{,} \usepackage[british]{babel} \usepackage{url} \usepackage{hyperref} \begin{document} \cite{stoptheclot:2008} \cite{wiki:xxx} \cite{stoptheclot2:2008} \pagebreak \bibliographystyle{apalike} \bibliography{bibfile} \end{document} The .bib file is: % Encoding: UTF-8 @misc{wiki:xxx, author = "{Wikipedia contributors}", title = "LaTeX --- {Wikipedia}{,} The Free Encyclopedia", year = "2011", howpublished = "\url{https://en.wikipedia.org/w/index.php?title=LaTeX&oldid=413720397}", note = "Viewed 12th November 2018." } @misc{stoptheclot:2008, author = "{stoptheclot contributors}", title = "Vitamin K and Coumadin - What you need to Know. [online]", year = "2008", note = "Viewed 12th November 2018.", } @misc{stoptheclot2:2008, author = "{Stoptheclot contributors}", title = "Vitamin K and Coumadin - What you need to", year = "2008", note = "Viewed 12th November 2018.", } Is there any way I can control the spacing of the references (preferably left justified)? • Try the xurl package – user36296 Nov 20 '18 at 15:13 • If you want your text left aligned, you could use \raggedright before your bibliography, but this will still give strange line breaks within the url, so I suggest the xurl package – user36296 Nov 20 '18 at 15:16 • xurl works a treat. – Paul Nov 20 '18 at 15:18 The xurl package can be used to add more possible breaking points to the urls: \documentclass[a4paper,11pt]{article} \usepackage{natbib} \bibpunct[, ]{(}{)}{;}{a}{,}{,} \usepackage[british]{babel} \usepackage{url} \usepackage{hyperref} \usepackage{filecontents} \begin{filecontents}{\jobname.bib} % Encoding: UTF-8 @misc{wiki:xxx, author = "{Wikipedia contributors}", title = "LaTeX --- {Wikipedia}{,} The Free Encyclopedia", year = "2011", howpublished = "\url{https://en.wikipedia.org/w/index.php?title=LaTeX&oldid=413720397}", note = "Viewed 12th November 2018." } @misc{stoptheclot:2008, author = "{stoptheclot contributors}", title = "Vitamin K and Coumadin - What you need to Know. [online]", year = "2008", note = "Viewed 12th November 2018.", } @misc{stoptheclot2:2008, author = "{Stoptheclot contributors}", title = "Vitamin K and Coumadin - What you need to", year = "2008", note = "Viewed 12th November 2018.", } \end{filecontents} \usepackage{xurl} \begin{document} \cite{stoptheclot:2008} \cite{wiki:xxx} \cite{stoptheclot2:2008} \pagebreak \bibliographystyle{apalike} \bibliography{\jobname} \end{document} • Replacing \usepackage{url} with \usepackage{xurl} works too. – Paul Nov 20 '18 at 15:33 • @Paul Even in the example in your question, you don't need the url package, because you load hyperref – user36296 Nov 20 '18 at 15:34	2019-05-23 07:37:39	{"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": 0.8055275678634644, "perplexity": 13700.475662294104}, "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/1558232257156.50/warc/CC-MAIN-20190523063645-20190523085645-00461.warc.gz"}
https://stats.stackexchange.com/questions/405355/does-the-jensen-shannon-divergence-maximise-likelihood	# Does the Jensen-Shannon divergence maximise likelihood? Minimising the KL divergence between your model distribution and the true data distribution is equivalent to maximising the (log-) likelihood. In machine learning, we often want to create a model with some parameter(s) $$\theta$$ that maximises the likelihood of some distribution. I have a couple of questions regarding how minimising other divergence measures optimise our model. In particular: 1. Does the Jensen Shannon Divergence also maximise the likelihood? If not what does it maximise? 2. Does the reverse KL divergence also maximise the likelihood? If not what does it maximise? Edit: As you can see from the figure below from this paper , the KL and JSD have different optimal solutions, so if minimising the KL is equivalent to optimising the likelihood, then the same cannot necessarily be the case for JSD. First, it is important to clarify a few things. 1. The KL divergence is a dissimilarity between two distributions, so it cannot maximize the likelihood, which is a function of a single distribution. 2. Given a reference distribution $$P(\cdot)$$, the value of $$\theta$$ that minimizes $$\text{KL}(P(\cdot)\|\|Q(\cdot\|\theta))$$ is not the one that maximizes the likelihood. Actually, there is no likelihood because there is no observed value. So, saying that minimizing the KL divergence is equivalent to maximizing the log-likelihood can only mean that choosing $$\hat{\theta}$$ so as to maximize $$Q(x_1, \ldots, x_n\|\theta)$$, ensures that $$\hat{\theta} \rightarrow \theta^$$, where $$\theta^ = \text{argmin}_\theta \text{ KL}(P(\cdot)\|\|Q(\cdot\|\theta)).$$ This is true under some usual regularity conditions. To see this, assume that we compute $$Q(x_1, \ldots, x_n\|\theta)$$, but the sample $$x_1, \ldots, x_n$$ is actually drawn from $$P(\cdot)$$. The expected value of the log-likelihood is then $$\int P(x_1, \ldots, x_n) \log Q(x_1, \ldots, x_n\|\theta) dx_1 \ldots dx_n.$$ Maximizing this value with respect to $$\theta$$ is he same as minimizing $$\text{KL}(P(\cdot)\|\|Q(\cdot\|\theta)) = \int P(x_1, \ldots, x_n) \log \frac{P(x_1, \ldots, x_n)}{Q(x_1, \ldots, x_n\|\theta)}dx_1 \ldots dx_n.$$ This is not an actual proof, but this gives you the main idea. Now, there is no reason why $$\theta^*$$ should also minimize $$\text{KL}(Q(\cdot\|\theta)\|\|P(\cdot)) = \int Q(x_1, \ldots, x_n\|\theta) \log \frac{Q(x_1, \ldots, x_n\|\theta)}{P(x_1, \ldots, x_n)}dx_1 \ldots dx_n.$$ Your question actually provides a counter-example of this, so it is clear that the value of $$\theta$$ that minimizes the reverse KL divergence is in general not the same as the maximum likelihood estimate (and thus the same goes for the Jensen-Shannon divergence). What those values minimize is not so well defined. From the argument above, you can see that the minimum of the reverse KL divergence corresponds to computing the likelihood as $$P(x_1, \ldots, x_n)$$ when $$x_1, \ldots, x_n$$ is actually drawn from $$Q(\cdot\|\theta)$$, while trying to keep the entropy of $$Q(\cdot\|\theta)$$ as high as possible. The interpretation is not straightforward, but we can think of it as trying to find a "simple" distribution $$Q(\cdot\|\theta)$$ that would "explain" the observations $$x_1, \ldots, x_n$$ coming from a more complex distribution $$P(\cdot)$$. This is a typical task of variational inference. The Jensen-Shannon divergence is the average of the two, so one can think of finding a minimum as "a little bit of both", meaning something in between the maximum likelihood estimate and a "simple explanation" for the data. • Thanks for your highly descriptive and informative answer. I am a little confused though by your last two sentences. If you look at the very first figure on arxiv.org/abs/1511.01844 you can see that the KLD and the JSD converge to different solutions so their optimal objectives can't be the same. I.e. they can't both be equivalent. Apr 27 '19 at 11:19 • Hi @gui11aume, I have updated my original post to add the figure. Apr 27 '19 at 11:54 • OK, I see your point. My answer is incomplete because it assumes that we have the same family of distributions in the KL divergence (in line with the blog post you linked to). I will update the answer. Apr 27 '19 at 12:01 • Thanks for your updated awesome answer. I think there's a small typo - I think the reverse KL tries to increase the entropy of Q, as $KL(Q\|\|P)$ = $E_Q[log Q] - E_Q[log P]$ = $-H[Q] - E_Q[log P]$. So minimising the KL would maximise the entropy of Q Apr 28 '19 at 9:35 • Yes of course. I wrote too fast. Simple distribution have high entropy, not low entropy. Thanks for spotting! Apr 28 '19 at 10:40	2021-09-22 18:30:31	{"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": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9170966744422913, "perplexity": 239.5205963439306}, "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/1631780057371.69/warc/CC-MAIN-20210922163121-20210922193121-00506.warc.gz"}
http://mathhelpforum.com/calculus/9079-finding-limits-2.html	Originally Posted by TD! That's just a matter of definition, see above I am aware of that. I liked what you posted. I was just pointing out what a text of mine said on the subject.	2015-11-25 18:30:27	{"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": 0.8027114272117615, "perplexity": 528.1196411959494}, "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-2015-48/segments/1448398445291.19/warc/CC-MAIN-20151124205405-00189-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.aidansean.com/projects/?tag=collaborative	# 91 map I played the game 91 and wanted to create a map of the world. What started out as a simple map to help keep track of the regions soon turned into a larger project which resulted in an A0 sized poster being produced. The creator of the game got in touch and at the time of writing the first poster has been printed and more will follow. The creator is going to publish and sell these posters online. ### Overview The game 91 is a tile based canvas game which is written entirely in Javascript (served up by PHP via AJAX requests). The game itself has a “fog” which means that only regions in a line of sight are visible. Given the way the game is organised means that in principle it should be easy to create a map. I adapted the code to make maps of each region, and then created a patchwork of all these small maps to create a larger map. ### Challenges Challenge: The code had to be reverse engineered to obtain all the maps. Solution: One of the most fun parts of this project was reverse engineering how the AJAX requests were handled and how the maps were parsed. Fortunately it was relatively straightforward to do. (Resolved.) Challenge: Small maps had to be combined with different drawing styles. Solution: To make the large map I had to combined many smaller maps. There’s no “cheap” way to do this, so I created an object that contained the smaller maps in a larger two dimensional array where each cell has its own drawing style flag, allowing non-trivial overlap of different drawing styles. (Resolved.) Challenge: A poster of very large dimensions needed to be created. Solution: There’s no easy way to manage an image of the size needed to make a large poster. I have made large posters before (for example, in the Marble Hornets project) so I was prepared for many of the problems. The sides of the map had to have relative sizes of $$\sqrt{2}$$, which fortunately was relatively easy (especially when compared to the Citadel project. In the end I opted to have a large .png file at $$\sim 500 ~\mathrm{dpi}$$ giving very fine print quality. The resulting file is just under 20 MB in size, which is rather impressive given its physical size. (Resolved.) ### Sample outputs The final version of the poster, as approved by the game’s creator, can be seen here: Poster version 2.	2019-01-21 00:24:51	{"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": 0.23311342298984528, "perplexity": 852.5605832233023}, "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-2019-04/segments/1547583743003.91/warc/CC-MAIN-20190120224955-20190121010955-00493.warc.gz"}
https://docs.itascacg.com/3dec700/3dec/block/doc/manual/block_manual/block_commands/block.contact/cmd_block.contact.local-stiffness.html	# block contact local-stiffness command Syntax block contact local-stiffness b Toggle flag to indicate that local contact stiffnesses should be used when calculating stabel timestep. Setting b to $$true$$ may yield larger timesteps for dynamic analysis. It will have no effect for non-dynamic analyses. The default is $$false$$.	2023-02-07 22:27:15	{"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": 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": 0.20551009476184845, "perplexity": 5672.3384934415035}, "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-2023-06/segments/1674764500641.25/warc/CC-MAIN-20230207201702-20230207231702-00735.warc.gz"}
https://nickhigham.wordpress.com/	## PCAM Authors Speaking About Their Work at SAMSI The Statistical and Applied Mathematical Sciences Institute (SAMSI) has just run a Workshop on the Interface of Statistics and Optimization. Among the speakers were four authors of articles in The Princeton Companion to Applied Mathematics (PCAM). In an earlier post I provided links to videos of PCAM authors giving talks related to the topics of their PCAM articles. To add to those, here are the four PCAM author talks from the SAMSI workshop. I have also included the talk by Margaret Wright, because it provides insight into a number of important topics covered in PCAM in a very lucid way. • John Burns, Parameter Identification for Dynamical Systems with Structured Uncertainty (author of PCAM article Optimal Sensor Location in the Control of Energy-Efficient Buildings) • Jack Dongarra, The Road to Exascale and Legacy Software for Dense Linear Algebra (author of PCAM article High-Performance Computing) • Yonina Eldar, Phase Retrieval and Analog to Digital Compression (author of PCAM article Compressed Sensing) • Stephen Wright, Randomness in Coordinate Descent (author of PCAM article Continuous Optimization (Nonlinear and Linear Programming) • Margaret Wright, Old, New, Borrowed, and Blue in the Marriage of Statistics and Optimization ## Preparing CMYK Figures for Book Printing All printing is done in CMYK, the color space based on the four colors cyan, magenta, yellow, and black. Figures that we generate in MATLAB and other systems are invariably saved in RGB format (red, green, blue). When we send a paper for publication we submit RGB figures and they are transformed to CMYK somewhere in the production process, usually without us realizing that it has been done. If you are one of those people who writes books and prefers to generate the final PDF yourself then you will need to convert any color figures to CMYK. The generation and use of CMYK files is something of a dark art. Here I report what I found out about it when producing the third edition (2017) of MATLAB Guide, co-authored with Des Higham. This is the first edition of the book to use color. CMYK produces a different range of colors than RGB. Since it is a subtractive color space, designed for inks, it cannot produce some of the brilliant colors that RGB can, especially in the blues. In other words, some RGB colors are out of gamut in CMYK. (Less importantly, the converse is true: some CMYK colors cannot be produced in RGB.) This is something we are used to, but usually do not notice. Whenever we print a document on a laser printer we view a CMYK representation of the colors. In many cases, a figure will look very similar in print and on screen, but there are plenty of exceptions. The following image shows an RGB image on the left, the result of converting that image to CMYK and then back to RGB in the middle, and a scan of a laser printer’s reproduction of the RGB image on the right. The differences between the RGB version and the other two versions may be shocking! Fortunately, when the CMYK version is viewed on a printed page in isolation from the RGB version (necessarily displayed on a monitor) it does not look so bad. [Of course, if you are reading a printed version of this post then the first two images will look essentially the same.] After some experimentation, I settled on the following procedure, which I describe for a PDF workflow. For a PostScript workflow, PDF files need to be replaced by EPS files. • Print the whole document from an RGB file. • Find figures that look very different in print than on screen and select from those any where the difference is not acceptable. In most cases an unacceptable difference will be one where contrast between colors, or saturation of colors, has been reduced. • Edit the selected figures in Photoshop, or some other image manipulation package that can save in CMYK form, in order to produce a better looking CMYK file. In Photoshop, Image-Mode-CMYK Color converts an image to CMYK form, but before using this command you should set the correct CMYK working space under Edit-Color Settings (see the Color Space section below). You can edit the RGB image (making use of View-Proof Color to see how the image will look in CMYK, and View-Gamut Warning to see colors that will be out of gamut in CMYK) and then convert to CMYK, or you can convert to CMYK and then edit the file. Save the CMYK image as a PDF file. • Generate the PDF file of the book using the edited CMYK figures and the RGB forms of all the other figures, that is, those that did not need special treatment. • Load the PDF file into Adobe Acrobat Pro and issue the command Tools - Print Production - Convert Colors This converts all objects in the file to CMYK. Of the well over 100 figures in MATLAB Guide, only two needed special treatment. However, there was one problem with this procedure. A handful of images are screen dumps that show a MATLAB window, and these are necessarily low resolution, at 72dpi. When converted to CMYK in Adobe Acrobat these images degraded badly. The solution was to resample the images to 150dpi in Photoshop via Image-Image Size and save to PDF; conversion in Acrobat then worked fine. (Such resampling is probably good practice anyway.) This is not quite the full story. Here are some more gory details, which are worth reading if you are actually producing a book. ## Color Spaces There is no unique CMYK or RGB color space: these spaces are device dependent. RGB spaces can have different white points and CMYK spaces are designed for particular combinations of paper and ink. Adobe Acrobat Pro offers “U.S. Web Coated (SWOP) v2”, “Uncoated FOGRA29 (ISO 12647-2:2004)” and many other inscrutably named CMYK profiles. So “convert to CMYK” is an ill-defined instruction unless the precise profile is specified. The conversion settings I used are shown in this screen dump of the dialog box, and were provided by the company who printed the book. Your settings might need to be different. There are a couple of things to note. First, Adobe Acrobat does not remember the settings in the dialog box, so they need to be re-entered every time. Second, since “Embed profile” is not selected with the settings shown, there is no way to tell which profile has been used once the conversion has been done. Does it really matter what CMYK profile you use? Yes, if you want the best possible results. Consider the following figure. On the left is the result of converting the original RGB image to “U.S. Web Coated (SWOP) v2” and on the right is the result of converting to “Photoshop 5 default CMYK” (and converting back to RGB in both cases, the latter conversion producing no visual difference in Photoshop). There is a significant difference between the two conversions in every color except white! In principle, both conversions will produce the same result when printed with the target ink and paper, but if you choose the profile without knowing the target you have little idea what the printed result will be. ## Photography Books An important assumption in the process described above is that the accuracy of the color reproduction is not vital. For photography books this assumption clearly does not hold and conversion to CMYK enters a new and frightening realm where images might need to be individually fine-tuned. Indeed high quality photography books typically undergo one or more proof stages using actual galley proofs from the ultimate printing device, sometimes with the author present at the printing press. ## Generating CMYK Files in MATLAB Most of the figures in MATLAB Guide are (naturally) produced in MATLAB. Figures saved with the print function are by default in RGB mode. CMYK is supported for EPS and PS files only, using the ‘-cmyk’ option. This is not very useful if you are using a PDF workflow, as I do. Instead of using the print function I experimented with export_fig, which is available on MathWorks File Exchange and can save in CMYK format to PDF, EPS, or TIFF files. export_fig creates a PDF file via an EPS file using Ghostscript. This sounds straightforward, but I found that many of the PDF files generated by export_fig were not fully in CMYK Mode. A PDF file can contain objects in different color spaces and I had files where a color plot was in CMYK but the colorbar was in RGB! The question arises of how one can check whether a given PDF file has any RGB objects. Unfortunately, there seems to be no simple way to do so in Adobe Acrobat Pro. What one can do is invoke Tools - Print Production - Preflight - PDF analysis - List objects using ICCbased CMYK - Analyze then open up Overview - color spaces (I am using Adobe Acrobat Pro XI, 11.0.18; usage could differ in other versions). This should contain “DeviceCMYK color space”, but if it contains “DeviceRGB color space” or “DeviceGray color space” then RGB or Grayscale objects are present. If the latter terms appear in a multi-page PDF file, double clicking on the corresponding icon should take you to the last such object. You can also open up Overview - Images to get a list of pages and object types on those pages. Double clicking on a page icon takes you to that page. ## Good Times in MATLAB: How to Typeset the Multiplication Symbol The MATLAB output >> A = rand(2); whos Name Size Bytes Class Attributes A 2x2 32 double will be familiar to seasoned users. Consider this, however, from MATLAB R2016b: >> s = string({'One','Two'}) s = 1×2 string array "One" "Two" At first sight, you might not spot anything unusual, other than the new string datatype. But there are two differences. First, MATLAB prints a header giving the type and size of the array. It does so for arrays of type other than double precision and char. Second, the times symbol is no longer an “x” but is now a multiplication symbol: “×”. The new “times” certainly looks better. There are still remnants of “x”, for example in whos s for the example above, but I presume that all occurrences of “x” will be changed to the new symbol in the next release However, there is a catch: the “×” symbol is a Unicode character, so it will not print correctly when you include the output in LaTeX (at least with the version provided in TeX Live 2016). Moreover, it may not even save correctly if your editor is not set up for Unicode characters. Here is how we dealt with the problem in the third edition (published in January 2017) of MATLAB Guide. We put the code \usepackage[utf8x]{inputenc} \DeclareUnicodeCharacter{0215}{\ensuremath{\times}} in the preamble of the master TeX file, do.tex. We also told our editor, Emacs, to use a UTF-8 coding, by putting the following code at the end of each included .tex file (we have one file per chapter): %%% Local Variables: %%% coding: utf-8 %%% mode: latex %%% TeX-master: "do" %%% End: With this setup we can cut and paste output including “×” into our .tex files and it appears as expected in the LaTeX output. ## Hyphenation of Compound Words Compound words are common in mathematical writing and it can be hard to remember how to hyphenate them. Unfortunately, there are no hard and fast rules. In this article I give some guidance and illustrative examples. The principle to keep in mind is that hyphenation should help to avoid ambiguity. In phrases of the form “adjective noun noun” or “noun adjective/participle noun” a hyphen is usually used: closed-form solution, nineteenth-century mathematics, error-correcting code. But if the adjective follows the noun then no hyphen is needed: solution in closed form, mathematics of the nineteenth century, code that is error correcting. Here are some other examples: • nearest-neighbor interpolation, • higher-dimensional discrete Fourier transforms, • large-scale optimization problem, • minimum-norm solution but solution of minimum norm, • first-order differential equation but differential equation of first order, • the parameter-dependent ODE but the ODE is parameter dependent, • rank-1 matrix but the matrix has rank 1. In examples such as finite-difference method and finite-element method it is a matter of convention and taste whether to hyphenate. Some authors do and some don’t. Most authors do not hyphenate singular value decomposition. Compounds beginning with adverbs ending in ly are not hyphenated, since they are usually unambiguous. Examples: slowly converging sequence, highly oscillatory integrand, continuously differentiable function, numerically oriented examples. An important special case is compounds beginning with ill, well, little, much, and best, the first two of which are particularly common in mathematical writing. Here, a hyphen is used for a compound of two words used adjectivally, but if the compound itself is modified then no hyphen is used. Examples (these also apply with ill replaced by well): • This is an ill-conditioned problem. • This is a very ill conditioned problem. • The problem is ill conditioned. • This problem is very ill conditioned. If the first example were to be written as This is an ill conditioned problem then it could be read as if ill were an adjective modifying the compound conditioned problem. Confusion is unlikely in this instance, but in ill-prepared contestant the hyphen is needed unless we are talking about a contestant who is prepared but not well. Here are two further examples that are complete sentences. • MATLAB allows a two-dimensional array to be subscripted as though it were one dimensional. • This approach is particularly well-suited to high-precision computation. The hyphen in well-suited in the last example is not essential, but is rather a matter of taste. I know from personal experience that it is hard to achieve good, consistent hyphenation when you are concentrating on all the other aspects of writing. This is where having the services of a copy editor is extremely valuable. To benefit, you need to publish with a journal or book publisher that takes copy editing seriously (SIAM, PUP, CUP, OUP, …). I give the final word to an Oxford University Press style manual, as quoted in the Economist Style Guide: If you take hyphens seriously, you will surely go mad. I am indebted to Sam Clark of T&T Productions for checking this post (and for saving me from many hyphenation blunders in my last two books). ## MATLAB Guide, Third Edition (2017) The third edition of MATLAB Guide, which I co-wrote with Des Higham, has just been published by SIAM. It is a major update of the second edition (2005) to reflect the many changes in MATLAB over the last twelve years, and is 25 percent longer. There are new sections and chapters, and almost every page has changed. The new chapters are • Object-Oriented Programming: presents an introduction to object-oriented programming in MATLAB through two examples of classes. • Graphs: describes the new MATLAB classes graph and digraph for representing and manipulating undirected graphs and directed graphs. • Large Data Sets: describes MATLAB features for handling data sets so large that they do not fit into the memory of the computer. • The Parallel Computing Toolbox: describes this widely used and increasingly important toolbox. The chapter The Symbolic Math Toolbox has been revised to reflect the change of the underlying symbolic engine from Maple (at the time of the second edition) to MuPAD. New sections include Empty Matrices, Matrix Properties, Argument Checking and Parsing, Fine Tuning the Display of Arrays, Live Editor, Unit Tests, String Arrays, Categorical Arrays, Tables and Timetables, and Timing Code. Two other big changes are that figures are now printed in color and there are thirteen “Asides”, highlighted in gray boxes, which contain discussions of MATLAB-related topics, such as anonymous functions, reproducibility, and color maps. The book was launched with a reception hosted by The Mathworks and SIAM at the SIAM booth at the Joint Mathematics Meetings in Atlanta on January 6, 2017. Jim Rundquist (Senior Education Technical Evangelist) represented MathWorks, and several SIAM staff, including SIAM Publisher David Marshall, were present. Two delicious cakes, one containing a representation of the cover of the book, were enjoyed by reception attendees. Inspired by MATLAB, the cakes were served using slice, deal, and input, and an occasional reshape or rotate, with a pool of workers consuming them asynchronously. ## Taking Up the SIAM Presidency I am honored to be taking over the reins from Pam Cook as president of the Society for Industrial and Applied Mathematics (SIAM) for the next two years, starting January 1, 2017. Pam remains as past-president during 2017. I look forward to helping to address the challenges facing SIAM and to working with the excellent SIAM officers and staff. Eighteen months ago I wrote a “candidate statement” for the fall 2015 SIAM elections. The comments I made then remain valid and so I thought it would be worth reproducing the statement here. The January/February 2017 issue of SIAM News will contain my first From the SIAM President column, in which I give further thoughts on SIAM’s future. I am happy to receive comments from SIAM members or potential members, either in the box below or by email. Candidate Statement: SIAM is the leading international organization for applied mathematics and has been an important part of my professional life since I joined as a PhD student, 31 years ago. SIAM is the first place that many people turn to for publications, conferences, and news about applied mathematics and it represents the profession nationally and internationally. I have been fortunate to be involved in the leadership for many years, having spent six years on the Council, eight years on the Board, and having recently served two terms as Vice President At Large (2010-2013). SIAM faces a number of challenges that, if elected as President, I relish helping to address, working with SIAM members, SIAM officers, and the excellent SIAM staff. SIAM’s publications remain strong, but are vulnerable to changes in the way scholarly journals operate (open access, article processing charges, etc.). SIAM needs to monitor the situation and respond appropriately, while striving to provide an even greater service to authors, referees and editors, for example by better use of web tools. SIAM’s membership is also healthy, but SIAM must continue to enhance membership benefits and work hard to attract and retain student members, who are the future of the society, and to provide value for its members in industry. Book sales are declining globally and in academic publishing it is becoming harder to find authors with the time to write a book. Nevertheless, the SIAM book program is in a strong position and the 2015 review of the program that I chaired has produced a list of recommendations that should help it to thrive. SIAM conferences are a terrific place to learn about the latest developments in the subject, meet SIAM staff, browse SIAM books, and attend a business meeting. Attendances continue to grow (the SIAM CSE meeting in Salt Lake City last March was the largest ever SIAM meeting, with over 1700 attendees), but in any given year, the majority of SIAM’s 14,000 members do not attend a SIAM conference. Audio and slide captures of selected lectures are made available on SIAM Presents, but we need to do more to help members engage in virtual participation. The SIAM web site has provided sterling service for a number of years, but is in need of a major redesign, which is underway. This is an excellent opportunity to integrate better the many services (conferences, journals, books, membership, activity groups, chapters, sections, etc.) in a responsive design. Beyond the core website, SIAM has a strong social media presence, posts a wide variety of videos on its YouTube channel, hosts SIAM Blogs (which I was involved in setting up in 2013), has recently made SIAM News available online, and has SIAM Connect and SIAM Unwrapped as further outlets. Optimizing the use of all these communication tools will be an ongoing effort. These are just some of the challenges facing SIAM in the future as it continues to play a global leadership role for applied mathematics. July 2015 Posted in miscellaneous \| Tagged \| 1 Comment ## Numerical Linear Algebra Group 2016 The Manchester Numerical Linear Algebra group (some of whom are in the photo below) was very active in 2016. This post summarizes what we got up to. Publications are not included here, but many of them can be found on MIMS EPrints under the category Numerical Analysis. ## Software The group has joined Jack Dongarra’s team at the University of Tennessee to become one of the two partners involved in the development of PLASMA: Parallel Linear Algebra Software for Multicore Architectures. We continue to make our research codes available, which is increasingly done on GitHub; see the repositories of Higham, Relton, Sego, Tisseur, Zhang. We also put MATLAB software on MATLAB Central File Exchange and on our own web sites, e.g., the Rational Krylov Toolbox (RKToolbox). Several algorithms have been incorporated in other software packages, such as, from Stefan Guettel, the NLEIGS solver which is now part of SLEPc, the Zolotarev quadrature approach which is now part of the FEAST eigenvalue solver package, and rational deferred correction which is now part of pySDC. ## PhD Students After defending her thesis in March 2016, Nataša Strabić (2012-2016) left in May to take up a position as Teacher of Mathematics at Sevenoaks School, Kent. Bahar Arslan defended her PhD thesis in December 2016. Mario Berljafa defended his PhD thesis in November 2016. In September he took up a postdoctoral position in the Department of Computer Science at KU Leuven. Weijian Zhang spent January-February visiting the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) Lab. New PhD students Jennifer Lau and Steven Elsworth joined the group in September 2016. ## Postdoctoral Research Associates (PDRAs) Pedro Valero Lara and Mawussi Zounon joined us in January 2016 to work on the Parallel Numerical Linear Algebra for Extreme Scale Systems (NLAFET) project. Sam Relton, who had previously been working on the Functions of Matrices: Theory and Computation project, moved onto this project in March. Jakub Sistek joined us in March 2016 to work on the Programming Model INTERoperability ToWards Exascale (INTERTWinE) project. Mary Aprahamian (2011-2016) left in May to take up a position as Data Scientist at Bloom Agency in Leeds. After several years as PhD student and then PDRA, James Hook left in April to take up a fellowship in the Institute for Mathematical Innovation at the University of Bath. Prashanth Nadukandi joined the group in September 2016, supported by a Marie Skłodowska-Curie Individual Fellowship. Timothy Butters (2013-2016), KTP Associate with Sabisu, has taken up a permanent position as Head of Research & Development with the company following the completion of the KTP in December 2016. Pedro Valero Lara left in October to take up a position as Senior Researcher on the Human Brain project at Barcelona Supercomputer Centre. David Stevens joined us in December 2016 to work on the Programming Model INTERoperability ToWards Exascale (INTERTWinE) project. ## Presentations Members of the group gave presentations (talks or posters) at the following conferences and workshops. SIAM UKIE Meeting 2016, January 7, 2016, University of Cambridge, UK: Strabic. Bath–RAL Numerical Analysis Day, January 11, 2016, Didcot, UK: Guettel. GAMM Annual Meeting, March 7-11, 2016, Braunschweig, Germany: Guettel SIAM Conference on Parallel Processing for Scientific Computing, April 12-15, 2016, Paris: Valero Lara, Zhang. University of Strathclyde SIAM Student Chapter Meeting, Glasgow, May 3, 2016: Higham. Workshop on Batched, Reproducible, and Reduced Precision BLAS, Innovative Computing Laboratory, University of Tennessee, May 18–19, 2016: Zounon. See the report on the workshop by Sven Hammarling. ESSAM School on Mathematical Modelling, Numerical Analysis and Scientific Computing, Czech Republic, May 29-June 3, 2016: Sistek. ECCOMAS Congress 2016, Crete, Greece, June 5-10, 2016: Sistek. Programs and Algorithms of Numerical Mathematics, Czech Republic June 19-24, 2-16: Sistek. SIAM Annual Meeting, Boston, USA, July 11-15, 2016: Fasi, Higham, Tisseur, Zemaityte, Zhang. Fifth IMA Conference on Numerical Linear Algebra and Optimization, University of Birmingham, UK, September 7-9, 2016: Gwynne, Relton, Tisseur, Zounon. GAMM Workshop on Applied and Numerical Linear Algebra, TU Hamburg–Harburg, Germany. September 15-16, 2016: Guettel 4th Workshop on Sustainable Software for Science: Practice and Experiences (WSSSPE4), University of Manchester, September 12-14, 2016: Relton. Chebyshev Day, University of Oxford, UK, November 14, 2016: Guettel. SIAM Annual Student Chapter Conference, University of Warwick, November 23, 2016: Zhang. ## Conference and Workshop Organization The Manchester SIAM Student Chapter organized their 6th Manchester SIAM Student Chapter Conference on May 4, 2016. Jakub Sistek was one of the organizers of Françoise Tisseur was on the organizing/scientific committees of Mario Berljafa, Jonathan Deakin, Nick Higham, Matthew Gwynne, Mante Zemaityte, and Weijian Zhang organized the Manchester Julia Workshop, September 19-20, 2016 at the University of Manchester. Videos of the talks are available on YouTube. Jakub Sistek and Maksims Abalenkovs were on the organizing committee of the European Exascale Applications Workshop held here in the School of Mathematics, October 11-12, 2016. ## Visitors Vedran Sego visited the group until May 2016. Peter Kandolf visited the group from September 2015 to March 2016. Tomáš Gergelits visited the group from October 2015 to March 2016. Meisam Sharify visited the group in September 2016. ## Knowledge Transfer The three-year Knowledge Transfer Partnership with Sabisu (a data analytics platform for the oil and gas industries), involving KTP Associate Tim Butters, Stefan Guettel, Nick Higham, and Jon Shapiro (School of Computer Science) was completed in December 2016. Among other achievements, an alarm management system has been developed and launched as a product. ## Recognition and Service Françoise Tisseur was elected SIAM Fellow. Stefan Guettel was elected Secretary/Treasurer of the SIAM UKIE section, 2016–2018, and has also taken on the role of vice-chair of the GAMM Activity Group on Applied and Numerical Linear Algebra. He joined the editorial board of the SIAM Journal on Scientific Computing in January 2016. Weijian Zhang won a bronze medal in the SET for Britain 2016 competition, which took place at the House of Commons, London, for his poster “Time-Dependent Network Modelling for Mining Scientific Literature”. Photo from LMS Newsletter. April 2016. (l to r) Dr Stephen Benn (Royal Society of Biology), Sylaja Srinivasan (Bank of England), Professor Nick Woodhouse (Clay Mathematics Institute), Weijian Zhang (Bronze Award Winner), Dr Philip Pearce (Gold Award Winner), Dr Tom Montenegro-Johnson (Silver Award Winner), Professor Sir Adrian Smith (CMS), Stephen Metcalfe MP Mario Berljafa won a SIAM Student Paper Prize for his work with Stefan Guettel entitled “Generalized Rational Krylov Decompositions with an Application to Rational Approximation”. A poster “The Math behind Alarm Redundancy Detection” by Mario Berljafa, Massimiliano Fasi, Matthew Gwynne, Goran Malic, Mante Zemaityte, and Weijian Zhang won a prize in SIAM’s “Math Matters” contest and is featured on the Math Matters, Apply It! website. Nick Higham served as president-elect of SIAM. He was also elected to Academia Europaea. Weijian Zhang won a SIAM Travel Award to attend the SIAM Conference on Parallel Processing for Scientific Computing in Paris in April 2016. Mario Berljafa, Massimiliano Fasi and Mante Zemaityte were awarded SIAM Student Travel Awards to attend the SIAM Annual Meeting 2016 in Boston. Weijian Zhang represented the Manchester Student Chapter at the meeting. Jakub Sistek was re-elected in Februrary as treasurer of the Czech Network for Mathematics in Industry EU-MATHS-IN.CZ. ## New Guidelines for DOI Linking and Display For sometime I have been collecting digital object identifiers (DOIs) in my BibTeX entries, as described in this blog post. When I use my own BST file to format the references BibTeX creates hyperlinks to the published source via the DOI. If I use the the SIAM BST file the DOI is instead displayed as part of the reference. The Crossref organization (which provides DOIs) has recently issued revised guidelines on the display of DOIs. Up until now, DOIs have typically been displayed as, for example, 10.1137/130920137, and linked to as http://dx.doi.org/10.1137/16M1057577. The new guidelines say that the link should be https://doi.org/10.1137/16M1057577 and that it should always be displayed in this form, as a full URL. Note that the “dx” part of the URL has gone, and “https” has replaced “http”. The main reason for the change is that the pure DOI on its own is not much use, as it can’t be clicked on or pasted into a browser address bar without first adding the https://doi.org/ prefix. Additionally, https provides more secure browsing than http, and Google gives a small ranking boost to sites that use https. Crossmark states that the old http://dx.doi.org/10.1137/16M1057577 form of URL will continue to work forever. I have updated my BST file myplain2-doi.bst in this GitHub repository, which contains a BibTeX bibliography for all my outputs, so that it produces links in the required form. SIAM has updated the BST file in its macro packages to implement the new guidelines. ## Hyphenation Question: Row-wise or Rowwise? Sam Clark of T&T Productions, the copy editor for the third edition of MATLAB Guide (co-authored with Des Higham and to be published by SIAM in December 2016), recently asked whether we would like to change “row-wise” to “rowwise”. A search of my hard disk reveals that I have always used the hyphen, probably because I don’t like consecutive w’s. Indeed, in 1999 I published a paper Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem . A bit more searching found recent SIAM papers containing “rowwise”, so it is clearly acceptable usage to omit the hyphen.. My dictionaries and usage guides don’t provide any guidance as far as I can tell. Here is what some more online searching revealed. • The Oxford English Dictionary does not contain either form (in the entry for “row” or elsewhere), but the entry for “column” contains “column-wise” but not “columnwise”. • The Google Ngram Viewer shows a great prevalence of the hyphenated form, which was about three time as common as the unhyphenated form in the year 2000. • A search for “row-wise” and “rowwise” at google.co.uk finds about 724,000 and 248,00 hits, respectively. • A Google Scholar search for “row-wise” and “rowwise” finds 31,600 and 18,900 results, respectively. For each spelling, there are plenty of papers with that form in the title. The top hit for “rowwise” is a 1993 paper The rowwise correlation between two proximity matrices and the partial rowwise correlation, which manages to include the word twice for good measure! Since the book is about MATLAB, it also seemed appropriate to check how the MATLAB documentation hyphenates the term. I could only find the hyphenated form: doc flipdim: When the value of dim is 1, the array is flipped row-wise down But for columnwise I found that MATLAB R2016b is inconsistent, as the following extracts illustrate, the first being from the documentation for the Symbolic Math Toolbox version of the function. doc reshape: The elements are taken column-wise from A ... Reshape a matrix row-wise by transposing the result. doc rmmissing: 1 for row-wise (default) \| 2 for column-wise doc flipdim: When dim is 2, the array is flipped columnwise left to right. doc unwrap: If P is a matrix, unwrap operates columnwise. So what is our conclusion? We’re sticking to “row-wise” because we think it is easier to parse, especially for those whose first language is not English. Posted in writing \| Tagged \| 1 Comment ## What’s New in MATLAB R2016b MATLAB R2016b was released in the middle of September 2016. In this post I discuss some of its new features (I will not consider the toolboxes). This is personal selection of highlights; for a complete overview see the Release Notes. The features below are discussed in greater detail in the third edition of MATLAB Guide, to be published by SIAM in December 2016. ## Live Editor The Live Editor, introduced in R2016a, provides an interactive environment for editing and running MATLAB code. When the code that you enter is executed the results (numerical or graphical) are displayed in the editor. The code is divided into sections that can be evaluated, and subsequently edited and re-evaluated, individually. The Live Editor works with live scripts, which have a .mlx extension. Live scripts can be published (exported) to HTML or PDF. R2016b adds more functionality to the Live Editor, including an improved equation editor and the ability to pan, zoom, and rotate axes in output figures. The Live Editor is particularly effective with the Symbolic Math Toolbox, thanks to the rendering of equations in typeset form, as the following image shows. The Live Editor is a major development, with significant benefits for teaching and for script-based workflows. No doubt we will see it developed further in future releases. ## Local Functions Local functions are what used to be called subfunctions: they are functions within functions or, to be more precise, functions that appear after the main function in a function file. What’s new in R2016b is that a script can have local functions. This is a capability I have long wanted. When writing a script I often find that a particular computation or task, such as printing certain statistics, needs to be repeated at several places in the script. Now I can put that code in a local function instead of repeating the code or having to create an external function for it. ## String Arrays MATLAB has always had strings, created with a single quote, as in s = 'a string' which sets up a 1-by-8 character vector. A new datatype string has been introduced. A string is an array for which each entry contains a character vector. The syntax str = string('a string') sets up a 1-by-1 string array, whereas str = string({'Boston','Manchester'}) sets up a 1-by-2 string array via a cell array. String arrays are more memory efficient than cell arrays and allow for more flexible handling of strings. They are particularly useful in conjunction with tables. According to this MathWorks video, string arrays “have a multitude of new methods that have been optimized for performance”. At the moment, support for strings across MATLAB is limited and it is inconvenient to have to set up a string array by passing a cell array to the string function. No doubt string arrays will be integrated more seamlessly in future releases. ## Tall Arrays Tall arrays provide a way to work with data that does not fit into memory. Calculations on tall arrays are delayed until a result is explicitly requested with the gather function. MATLAB optimizes the calculations to try to minimize the number of passes through the data. Tall arrays are created with the tall function, which take as argument an array (numeric, string, datetime, or one of several other data types) or a datastore. Many MATLAB functions (but not the linear algebra functions, for example) work the same way with tall arrays as they do with in-memory arrays. ## Timetables Tables were introduced in R2013b. They store tabular data, with columns representing variables of possibly different types. The newly introduced timetable is a table for which each row has an associated date and time, stored in the first column. The timerange function produces a subscript that can be used to select rows corresponding to a particular time interval. These new features make MATLAB an even more powerful tool for data analysis. ## Missing Values MATLAB has new capabilities for dealing with missing values, which are defined according to the data type: NaNs (Not-a-Number) for double and single data, NaTs (Not-a-Time) for datetime data, <undefined> for categorical data, and so on. For example, the function ismissing detects missing data and fillmissing fills in missing data according to one of several rules. ## Mac OS Version I have Mac OS X Version 10.9.5 (Mavericks) on my Mac. Although this OS is not officially supported, R2016b installed without any problem and runs fine. The pre-release versions of R2016a and R2016b would not install on Mavericks, so it seems that compatibility with older operating systems is ensured only for the actual release. At the time of writing, there are some compatibility problems with Mac OS Version 10.12 (Sierra) for certain settings of Language & Region.	2017-02-20 06:18:21	{"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": 0.34567490220069885, "perplexity": 2808.659940171647}, "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-2017-09/segments/1487501170425.26/warc/CC-MAIN-20170219104610-00540-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/number-theory-symbol.202703/	# Number Theory Symbol 1. Dec 5, 2007 ### jbowers9 What does the symbol Î mean in number theory? As in... Prove if r,s Î Z, then 4r + 6s is even... Also, where can I find a website with a comprehensive math symbol index? 2. Dec 5, 2007 ### cristo Staff Emeritus It should be $\in$. There's probably some conflict where they both use the same code or something like that. 3. Dec 5, 2007 ### Staff: Mentor Cristo is pointing out that what you see is a font translation/rendering problem, and quite correctly. I've had things like that happen and confuse the living ... out of me. 4. Dec 5, 2007 ### Gokul43201 Staff Emeritus	2017-04-24 15:30:50	{"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": 0.5435957908630371, "perplexity": 4635.517254639783}, "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-2017-17/segments/1492917119637.34/warc/CC-MAIN-20170423031159-00486-ip-10-145-167-34.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/31867/is-there-an-interactive-proof-system-for-factoring-with-the-perfect-zero-knowled?answertab=votes	# Is there an interactive proof system for factoring with the perfect zero knowledge property? Given the decision version of the factoring problem, is there an interactive proof system with the perfect zero knowledge property? I know there is for just the zero knowledge property, but is there without the assumption of one way functions? perfect zero knowledge property: Let P and V be randomized algorithms of an interactive proof system for the decision problem L. This proof system has the perfect zero knowledge property if for every polynomial time randomized algorithm V' that can replace V, there is a randomized algorithm A with polynomially bounded worst case expected runtime that for each $x\in L$ produces what is communicated between P and V' with the same probabilities. - ## 1 Answer If by the decision version of the factoring problem you mean: does this number have a non-trivial factorization (i.e. is this number prime?), that's primality testing, which is in P so it's automatically in PZK. Otherwise, I think "the decision version of the factoring problem" is ambiguous. You could mean questions like: "is the 10th digit of the largest factor 7?" or questions like "does this number have exactly k prime factors." I wouldn't be surprised if there were a PZK protocol for the second question, but I would be very surprised if there was one for the first. - To clarify, I was thinking along the lines of the second question, where one would ask "does this number have k prime factors". – Alexander Kalinowski Jul 15 '10 at 0:27 There's a paper that does something similar (in statistical zero knowledge): Camenisch and Michels: Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes. springerlink.com/content/blqm17fy9wr5n1xx – Peter Shor Jul 17 '10 at 13:24 I'll check that out, thank you! – Alexander Kalinowski Jul 19 '10 at 3:40	2015-01-26 04:39:11	{"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": 0.6700206995010376, "perplexity": 609.0335291185706}, "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-2015-06/segments/1422115858171.97/warc/CC-MAIN-20150124161058-00287-ip-10-180-212-252.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/nuclear-decay-semi-empirical-formula.809263/	# Nuclear Decay - Semi Empirical Formula Tags: 1. Apr 18, 2015 ### unscientific 1. The problem statement, all variables and given/known data (a) What processes changes atomic number by 1? What are the favourable conditions? How do you tell a neutrino is involved? How can we use this to understand the mass of this particle? (b) Use semi empirical mass formula to explain why odd-odd isobars are unlikely, while even-even isobars are possible. Why is $Tc$ the lightest odd-odd isobar? Show by mass difference $Mo$ is stable. (c) What is the other possible process and its $Q$ value? (d) What background is suppressed and what other background exists? What's the significance of T=Q? 2. Relevant equations 3. The attempt at a solution This question completely stumped me, as I have no idea how to proceed. Part (a) I suppose the two processes are neutron capturing: $_a ^b X + n \rightarrow _a ^{b+1} Y + \gamma$ and fission: $_a ^b Z + n \rightarrow _a ^{b-1} W + 2n + \gamma$. I think favourable conditions are an odd-even nucleus? Not sure what other conditions there are. When a neutrino is involved, I suppose we find leptons? How do we use leptonic decay to figure out the mass? Part (b) For an odd-odd configuration, $\delta_P < 0$ so lower binding energy compared to an even-even configuration where $\delta_P = 0$. Not sure why $(Z,N) = (43,57)$ is the lightest odd-odd isobar. What about $(41,59)$? It seems that $Mo$ has a higher binding energy than $Tc$, so I suppose it is more stable. Not sure for the other parts of this question.. 2. Apr 18, 2015 ### SteamKing Staff Emeritus For part a), it's the atomic number which changes. Which particle determines the atomic number of an atom? Does fission change the atomic number by 1? Or does fission do something entirely different to a nucleus? 3. Apr 18, 2015 ### unscientific Ok, the atomic number is the proton number. So instead of a neutron it would be a proton then. Fission actually breaks the nucleus into many parts + some other neutrons, so I don't think it will be applicable in this case. 4. Apr 18, 2015 ### SteamKing Staff Emeritus Is capturing a proton the only process which increases the atomic number of an atom? Think about the different types of radioactivity (there are three types). 5. Apr 18, 2015 ### unscientific Ok, I can think of 3 radiations: Beta decay: $_a X~ \rightarrow~ e^- + _{a+1}Y$ Alpha decay: Won't this change the atomic number by $2$? Gamma decay: $_a X~ \rightarrow~ _{a+1}Y + e^- + \nu_e + \gamma$. 6. Apr 18, 2015 ### SteamKing Staff Emeritus Does gamma emission always lead to a change in atomic number? What about beta decay? 7. Apr 18, 2015 ### unscientific Gamma emission doesn't always, but beta decay has to (conservation of charge). 8. Apr 18, 2015 ### SteamKing Staff Emeritus Can you answer question a) now? 9. Apr 18, 2015 ### unscientific What are the favourable conditions? How do we tell if a neutrino is involved? Even if a neutrino is involved, I can't see how that can be used to figure out the mass of the reactants... 10. Apr 18, 2015 ### SteamKing Staff Emeritus The question is not asking for the mass of the reactants ... 11. Apr 18, 2015 ### unscientific I suppose one of the experimental signature that the sum of the partial widths is less than it would be a peak/resonance in the cross-section where $E=m_Z$ due to the production of the $Z^0$ boson. The "missing" or "invisible" width belongs to the neutrino? 12. Apr 19, 2015 ### unscientific I suppose the mass of the neutrino can be calculated from the width $\Gamma_{\nu}$? 13. Apr 19, 2015 ### SteamKing Staff Emeritus The question is a bit vague. IMO, "understand" is not the same as "calculate", w.r.t. the mass of the neutrino. I think the question here is looking for a qualitative estimate of whether neutrinos are relatively massive particles, or if there is not much mass to one ... 14. Apr 19, 2015 ### unscientific True, I read it has a very low but non-zero mass. For part (b), why is the $Tc$ the lightest isobar? Why can't $Z=41, N=59$ be formed? 15. Apr 19, 2015 ### SteamKing Staff Emeritus I'm afraid my knowledge of atomic physics is pretty much exhausted after being able to tell the difference between atomic number and atomic mass ... 16. Apr 20, 2015 ### unscientific No problem, thanks alot for spending time on this problem. Would appreciate help from anyone else who have done atomic physics! 17. Apr 22, 2015 ### unscientific bumpp 18. Apr 25, 2015 ### unscientific bumpp 19. Apr 30, 2015 ### unscientific bumpp 20. May 4, 2015 ### unscientific bumpp would appreciate any help to start	2018-03-21 19:42:41	{"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": 0.5431303977966309, "perplexity": 1969.2787274063307}, "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/1521257647681.81/warc/CC-MAIN-20180321180325-20180321200325-00525.warc.gz"}
https://www.mail-archive.com/users@lists.scilab.org/msg10799.html	# Re: [Scilab-users] Bernoulli numbers calculation Hello Lester, Le 30/12/2021 à 08:59, Lester Anderson a écrit : Hello Samuel, Thanks for the solution. As pointed out it is best to show the equation being assessed (from www.bernoulli.org <http://www.bernoulli.org>). The one I looked at was the following: Explicit_formula.PNG Using nchoosek in the original code gives the same issue. The inner sum over v is very prone to cumulative rounding errors: The term v^n gets huge rapidly -- so is numerically truncated --, while the (-1)^v term makes the sum alternate, which enhances residues... that then mainly come from numerical truncations. With n_max = 20, the maximum value of nchoosek(20,10)=184756 and is definitely not an issue. While even only 13^13 --> 13^13 ans = 3.029D+14 is already not far from 1/%eps. The recurrent implementation proposed earlier and based on Bₘ = -∑_k=0_→ m-1 (C_^k _m+1 ).B_k /(m+1) \frac{-1}{m+1}{\sum _{{k=0}}^{{m-1}}{m+1 \choose k}B_k has neither alternate terms nor huge power values that make a direct computation numerically catastrophic. Regards Samuel _______________________________________________ users mailing list users@lists.scilab.org http://lists.scilab.org/mailman/listinfo/users	2023-03-21 23:04:02	{"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": 0.5146377682685852, "perplexity": 13645.529816956634}, "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-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00727.warc.gz"}
https://mattermodeling.stackexchange.com/questions/925/state-of-the-art-in-computational-materials-design/937	# State of the art in computational materials design With the advent of more computational power than ever in the recent years, interest in in silico design of interesting compounds has grown as well. I am wondering about the state of the art for the case of designing novel materials: • What methods are commonly used (DFT, semi-empirical, more / less expensive)? • What size of lattices is one able to treat in high-througput screening approaches? • What is the effort in terms of runtime one needs to put in? • Isn't this question a bit too broad? May 19, 2020 at 23:48 • I removed the last subpart of the question if you worry about that. It has actually been answered in materials.stackexchange.com/questions/157. The others really belong together for me, because if you talk about runtime you have to refer to the method which was used and the size of systems which can be treated. May 20, 2020 at 5:32 • May 21, 2020 at 4:50 After a little research I found a great article [1], which provides a good overview to what I asked above in Figure 2. Summarising in a table: Method effort reliability system size Interatomic potentials high high/low* $$10^8$$ Linear-scaling DFT high medium-high $$10^6$$ Tight binding high medium-high $$10^6$$ LDA DFT low medium-low $$10^3$$ GGA DFT low medium $$10^3$$ GGA+U DFT low medium-high $$10^3$$ Hybrid DFT low high $$10^2$$ GW high high $$10^1$$ * high for geometries and energetics, but low for excited states or the dielectric function where effort refers to the manual effort from the researcher, reliability gives the reliability of the method and system size is the typical system size in the number of atoms. In the table I am providing a condensed (and maybe biased) overview, focusing on properties such as geometry, energetics, dielectric function, excited states or bandgap. See [1] for the full details. ### References [1] K. T. Butler, J. M. Frost, J. M. Skelton, K. L. Svane and A. Walsh. Chem. Soc. Rev., 2016, 45, 6138. DOI 10.1039/c5cs00841g • Since this thread just got bumped, I want to point out GGA+U is definitely not low effort and I wouldn't say its more reliable than GGA or LDA. Jan 19, 2022 at 1:00 I am sure there are A LOT of authors publishing papers to answer this very question. Mainly because the theories employed have face a paradigm since "one-size-doesn't-fit-all". Here are the variables that affect this use of a certain method: (i) Molecular models or periodic solids (ii) Chemical Accuracy (energies with accuracy of < 1kcal/mol) - e.g. in polymorph stability such as crystal structure prediction or molecular solids (iii) Electronic structure (band gap/density of states/ band structure/excitonic effects) can be calculated using PBE+U (or PBE+D3+U) that is Fast vs Hybrid (PBE0/HSE06/etc.) or quasiparticle GW calculations that can be quite slow A good read on theoretical comparisons: (i) Philosophical+technical: https://science.sciencemag.org/content/355/6320/49/tab-figures-data (ii) Technical benchmarking of a recent density functional across various model solids: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041005	2023-03-26 17:51:16	{"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": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40688660740852356, "perplexity": 2749.363013108798}, "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-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00026.warc.gz"}
https://www.semanticscholar.org/paper/FORMING-DISK-GALAXIES-IN-WET-MAJOR-MERGERS.-I.-Athanassoula-Rodionov/bdd29a6dea5f9bb32cd3a9b584ffbfc1eb22b8f1	# FORMING DISK GALAXIES IN WET MAJOR MERGERS. I. THREE FIDUCIAL EXAMPLES @article{Athanassoula2016FORMINGDG, title={FORMING DISK GALAXIES IN WET MAJOR MERGERS. I. THREE FIDUCIAL EXAMPLES}, author={E. Athanassoula and S. A. Rodionov and N. Peschken and J. C. Lambert}, journal={The Astrophysical Journal}, year={2016}, volume={821} } • Published 9 February 2016 • Physics • The Astrophysical Journal Using three fiducial N-body+SPH simulations, we follow the merging of two disk galaxies that each have a hot gaseous halo component, and examine whether the merger remnant can be a spiral galaxy. The stellar progenitor disks are destroyed by violent relaxation during the merging and most of their stars form a classical bulge, while the remaining stars, as well as stars born during the merging times, form a thick disk and its bar. A new stellar disk forms subsequently and gradually in the… ## Figures and Tables from this paper • Physics Monthly Notices of the Royal Astronomical Society • 2020 We show how wet major mergers can create disc galaxies in a cosmological context, using the Illustris simulation. We select a sample of 38 disc galaxies having experienced a major merger in their • Physics • 2018 Most giant spiral galaxies have pseudo or disc-like bulges that are considered to be the result of purely secular processes. This may challenge the hierarchical scenario predicting about one major • Physics Monthly Notices of the Royal Astronomical Society • 2021 We investigate the formation history of massive disc galaxies in hydrodynamical simulation – the IllustrisTNG, to study why massive disc galaxies survive through cosmic time. 83 galaxies in the • Physics • 2017 Context. In a series of papers, we study the major merger of two disk galaxies in order to establish whether or not such a merger can produce a disk galaxy. Aims. Our aim here is to describe in • Physics • 2017 We perform controlled N-body simulations of disc galaxies growing within live dark matter (DM) haloes to present-day galaxies that contain both thin and thick discs. We consider two types of models: • Physics, Geology Astronomy & Astrophysics • 2020 Stellar populations in barred galaxies save an imprint of the influence of the bar on the host galaxy’s evolution. We present a detailed analysis of star formation histories (SFHs) and chemical • Physics Monthly Notices of the Royal Astronomical Society • 2019 We present a new version of the GalactICS code that can generate self-consistent equilibrium galaxy models with a two-component stellar disc and a gas disc as well as a centrally-concentrated bulge • Physics • 2018 We present the first results of applying Gaussian Mixture Models in the stellar kinematic space of normalized angular momentum and binding energy on NIHAO high-resolution galaxies to separate the The discs in galaxies are radially extended, rotationally supported, flattened systems. In the cosmological Lambda Cold Dark Matter model the formation of the discs is intimately connected with • Physics • 2017 Galaxy surveys have suggested that rapid and sustained decrease in the star-formation rate, "quenching", in massive disk galaxies is frequently related to the presence of a bar. Optical and near-IR ## References SHOWING 1-7 OF 7 REFERENCES • Physics • 2016 We use the Spitzer Survey of Stellar Structure in Galaxies (S$^{4}$G) 3.6 $\mu$m imaging to study the properties (length and strength) and fraction of bars at $z=0$. We use the maximum of • Physics • 1998 Induced Star Formation.- Observational Evidence for Interactions and Mergers.- Dynamics of Galaxy Interactions. • Physics, Biology • 2013 This chapter discusses secular evolution in disk galaxies, the evolution of star formation and gas in the interstellar medium, and the role of stellar populations in this evolution. • PhR, • 1984	2023-03-27 00:20:27	{"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": 0.4771488308906555, "perplexity": 4902.065386326562}, "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-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00042.warc.gz"}
https://indico.fysik.su.se/event/322/timetable/?view=standard_numbered_inline_minutes	# Origins of Homochirality Europe/Stockholm Nordita ### Nordita , , Description For a list of scheduled talks that are not part of the conference, click here on the page for Nordita talks. Most of the talks contain streaming video recordings. If you want to download an entire lecture (non-streaming), you need to replace the mms in the beginning by http, so you'd say, for example, http://videos.nordita.org/conference/Chirality2008/Soai.wmv Conference Schedule ===================== Monday, 25 February =================== chair: Axel Brandenburg 9:00- 9:50 Raphaël Plasson: Thermodynamics of chirality (video,pdf) 10:00-10:50 Cristobal Viedma: When "Left" and "Right" cannot coexist: chiral purity by thermodynamic-kinetic feedback near equilibrium (pdf,ppt) 11:00-11:30 coffee 11:30-12:20 Wim Noorduin: Explanation for the emergence of a single chiral solid state during grinding (video, video2) 12:30-14:00 lunch chair: Meir Lahav 14:00-14:50 Josep Ribo: Chemical constraints in spontaneous mirror symmetry breaking (video) 15:00-15:30 coffee 15:30-16:20 J. Michael McBride: A mechanism for deracemization by crystal grinding (video,video2) 16:30-17:30 discussion 17:30 reception Tuesday, 26 February ==================== chair: Commeyras 9:00- 9:50 Henri Kagan: Nonlinear effects in asymmetric catalysis (video,ppt) 10:00-10:50 Kenso Soai: Asymmetric autocatalysis and origins of homochirality (video) 11:00-11:30 coffee 11:30-12:20 Kouichi Asakura: Emergence of homochirality in chemical systems (video) 12:30-14:00 lunch chair: Ribo 14:00-14:50 Antonio Rizzo: The ab initio calculation of linear and nonlinear properties of chiral systems (video) 15:00-15:30 coffee 15:30-16:20 tba 16:30-17:20 Günter von Kiedrowski: Systems chemistry and the origin of life (video,ppt) 17:30-18:30 discussion 19:00 Conference Dinner (After Dinner Speach by J. Michael McBride ) Wednesday, 27 February ====================== chair: Asakura 9:00- 9:50 Laurence Barron: Structure and behaviour of the molecules of life from Raman optical activity (video,pdf,ppt) 10:00-10:50 discussion 11:00-11:30 coffee 11:30-12:20 Yukio Saito: Fluctuation effect on enantiomeric excess amplification and chiral symmetry breaking (video,ppt,ppt2) 12:30-14:00 lunch (free afternoon) Thursday, 28 February ===================== chair: Kagan 9:00- 9:50 Armando Cordova: Asymmetric amino acid catalysis (video) 10:00-10:50 Patrick Sandars: The relative handedness of nucleic acids and proteins (video) 11:00-11:30 coffee 11:30-12:20 Auguste Commeyras: Origin of life: the need of steps of concentration (video,ppt,anim1,anim2) 12:30-14:00 lunch chair: McBride 14:00-14:50 Meir Lahav: Racemic templates for stochastic mirror symmetry breaking (video) 15:00-15:30 coffee 15:30-16:20 Jonathan Wattis: Mathematical models for the emergence of homochirality (video) 16:30-17:30 discussion Friday, 29 February =================== chair: Plasson 9:00- 9:50 Ramadurai: Neutrino induced homochirality (video) 10:00-10:50 Peter Schmidt: Evolution of homochirality: a probabilistic process and epimerization (video,ppt,ppt2) 11:00-11:30 coffee 11:30-12:20 Sara Walker: Right versus left: why bigger is better (... but not always good enough) (video1,video2) 12:30-14:00 lunch chair: Barron 14:00-14:50 Axel Brandenburg: Homochirality in spatially extended systems (video,pdf,ppt,htm) 16:00 End of Conference #### Background and motivation: Homochirality is a unique property of living matter. It is a property that gradually disappears after the death of living matter. The origin of homochirality is therefore closely linked to the origin of life, which makes this topic a prominent research field in astrobiology. The problem of the possible origins of homochirality in living matter is frequently discussed in the literature. On the one hand, physical and external factors (e.g., the electroweak parity breaking, enhanced for example by heavy Cu complexes, as well as magnetic fields and polarized light) are hard to rule out. On the other hand, the possibility of a bifurcation process is quite plausible, but there is no unique mechanism. Possible candidates include autocatalysis combined with enantiomeric cross-inhibition in the RNA world (Sandars 2003) and the activation-polymerization-epimerization-depolymerization reaction of Plasson (2004). One purpose of this program is to establish the viability of these two different pathways, and to discuss the possibility of an interplay between them. Also the significance of crystallization experiments with stirring either for just demonstrating the effects of growth combined with competition, or as a primitive mechanism under prebiotic conditions should be discussed. Finally, quantitative aspects of approaches of involving physical and external factors should be discussed. Can some quantitative agreement be established regarding the subsequent role of amplification mechanisms and the enantiomeric excess that can be achieved? It is anticipated that such a program can be an important mile stone in this field, which is currently being attacked from the many different angles, without there being sufficient interaction between them. The program extends over four weeks, where the last week is devoted to a symposium. Although long-term participation is strongly encouraged, it is also possible to stay for shorter periods. The number of program participants is limited to a maximum of about 20 at any time. Funding will be available to accommodate program participants in apartments, whenever possible. Desks and shared office space will be available in the Nordita building. #### Program routine We expect to have only one regular review talk per week. Some of these talks can be oriented toward a broader audience. In addition, we plan to have one extensive discussion session once or twice a week, e.g. between 10:30 and 12:30. Each discussion will be started off by about 3 short presentations (20 min) by program participants talking on a related topic. There should be a vague idea about the topics of each session prior to the begin of the program (to be discussed with the participants via email), but revisions during the course of the program are anticipated. In addition, regular coffee session every morning at 10:00 and at 15:00 provide informal means of exchanging ideas and starting collaborations. Other than that, we try to keep the days open for doing regular work. #### Symposium For the last week (February 25-29) we consider organizing an open symposium that is available to a broader community and, in particular, to people that could not come for the full duration of the program. We are also considering to collect a number of papers for a special issue of Origins of Life and Evolution of the Biosphere. This would allow us to have a permanent record connected with the activities and discussions at the program and/or the open symposium. #### Participation Scientists interested in this progam are encouraged to apply by filling in the registration form. The deadline for applications is December 15, 2007. Schedule ========= Tue 5 Feb. 10-12:30: discussion (Jonathan, Susanne, Harry, ...) Fri 8 Feb Jonathan Wattis (Astrobiology seminar), with reception afterwards Tue 12 Feb. 10:30: Sara Walker (talk) Thu, 14 Feb, 14:15: Laurence Barron (talk) Thu, 15 Feb, 16:15: Meir Lahav (talk) Fri, 15 Feb, 10:30: Mark Green (talk) Fri, 15 Feb, 16:00: Guenter von Kiedrowski (Astrobiology seminar), + reception Sat, 16 Feb, 10:00: Mark Green (discussion) Sat, 16 Feb, 14:30: Meir Lahav (discussion) Tue, 19 Feb. 10-12:30: discussion (Asakura, Mashimo, Saito, ...) Fri, 22 Feb, 16:00: Kouichi Asakura (Astrobiology seminar), with reception Mon, 25 Feb, 9:00 start of conference (see below) Arrival/Departure times of Participants, pictures, roster. Final Report How to get here? (this link has a description and a map). The meeting takes place in the Nordita building, just next to the AlbaNova main building. Organizers: Axel Brandenburg, Raphaël Plasson, Anja C. Andersen Participants • Anja C. Andersen • Antonio Rizzo • Armando Cordova • Auguste Commeyras • Axel Brandenburg • Christina Moberg • Cristobal Viedma • David Hochberg • Günter von Kiedrowski • HANS Ågren • Harry Lehto • Henri Kagan • Hisanari Mashimo • J. Michael McBride • Jonathan Wattis • Josep M. Ribo • Kenso SOAI • Kouichi Asakura • Lars Samuelsson • Laurence Barron • Mark M. Green • Meir Lahav • Patrick Sandars • Peter Coveney • Peter Schmidt • Raphaël Plasson • Sara Walker	2022-01-26 19:36:19	{"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": 0.29450899362564087, "perplexity": 11358.068017211534}, "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-2022-05/segments/1642320304961.89/warc/CC-MAIN-20220126192506-20220126222506-00571.warc.gz"}
https://math.stackexchange.com/questions/2465737/i-need-help-understanding-a-few-things-regarding-least-squares-regression	# I need help understanding a few things regarding Least Squares Regression. First of all, I imagine that I will get many downvotes on this since the questions are probably considered "stupid." However, please understand that I'm taking a class that is way above my head, and I'm not allowed to drop it. I'm asking these questions so that I know exactly what I need to learn without wasting time. I'm taking a class in Big Data/Data Mining and I've been given an assignment to "do" least squares regression on a data set in Matlab. The problem is that I have never learned linear algebra before. I'm spending all my spare time catching up, but I feel like I will not make the deadline unless I focus only exactly on what the assignment requires. I took notes during the classes, but I didn't know linear algebra back then so I couldn't understand what exactly I was writing. After spending weeks learning about vectors, matrices and subspaces, I understand some of it, but it's not enough. Therefore, I ask you to help me understand the following: 1. If $x = [x(1), x(2), ... ,x(d)]$, then $\bar{x} = [1, x(1), x(2), ..., x(d)]$ (these are a column vectors, but I don't know the latex code). However, I watched a Khan Academy video on linear regression where $\bar{x}$ was described as the mean value of $x$. From what I know, 'mean value' refers to a single (scalar) value and not a vector, so that has me confused. So, what does $\bar{x}$ actually mean? 2. The dependent value (I know the difference between independent and dependent values) is defined as $y(x) = w0 + w1x(1)+w2x(2)+...+ wdx(d)$ What on earth does $w$ mean? It's defined as a column vector ranging from $w0$ to $wd$. 3. What does $w$ mean? 4. After doing the least squares regression, I'm asked to print the value of $w$ generated by the regression. Is this also a column vector or something completely different? 5. What am I actually trying to figure out with linear regression? A formula? A value? Nothing has been said about it in the class based on the notes I've taken, and I can't find any explanation in any book either. The closest I've gotten is that the objective is to "minimize the residuals." I understand what 'residual' means, but what is the output exactly? I mean, I have training data. I use the regression formula on that data set. What am I left with that I can use on the test data? 6. Do I need to know anything about Eigen-values or anything involving "Eigen" in order to solve this problem? Any help is greatly appreciated. Thank you. • 3. (w) is probably the transpose of the vector (w) but it depends on how it's defined in your class as () is used for many things. 5. The goal of linear regression to find the equation of a line which 'matches' your data the best. With this line you can predict values of (w) which you don't have data for. Oct 10, 2017 at 9:22 • The transpose of the matrix is defined as $x^T$. Also, in the notes I've taken, there's the equation $x^Ty = x^Txw^$. Edit: I'm not sure but I think it's actually $w^$ and not $w$ Oct 10, 2017 at 9:27 • @TonyS.F. I'm answering a second time on your comment. Isn't the goal to predict the $y$ value of $x$? I mean, if $x$ is the independent, and $y$ is the dependent. Where does $w$ come in exactly? edit: In my previous comment, I mean that the transpose of the vector is defined as $x^T$, not the matrix. Oct 10, 2017 at 9:31 • Yes you are correct, you want to predict the values of the dependent variable, my mistake. You are also correct that usually xbar is not a vector, but a scalar quantity representing the arithmetic average. It seems, though, that your text/class also uses xbar to denote an 'augemented vector' i.e. they put another entry with a '1' in it. Oct 10, 2017 at 9:37 • Thanks! That's one mystery sort of solved. Although, I just googled 'augmented vector' and it seems like they put the '1' at the end/bottom and not at the top/beginning. Is that relevant? Oct 10, 2017 at 9:45 You are given a bunch of vectors $x_i \in \mathbb R^d$ and corresponding scalars $y_i \in \mathbb R$. Your goal is to find a vector $w \in \mathbb R^{d+1}$ such that $\bar x_i^T w \approx y_i$ for all $i$. We select $w$ to be the vector that minimizes the objective function $$E(w) = \sum_i (\bar x_i^T w - y_i)^2.$$ But minimizing $E(w)$ is something that we learned how to do in multivariable calculus. Just set the gradient of $E$ equal to $0$, and solve for $w$. • @Lobs001 No, I don't mean that you should set $E(w)$ equal to $0$. In precalculus, you have learned to find the minimum point (vertex) on a parabola by the technique of completing the square. So, minimizing a quadratic function of one variable is something that you know how to do from precalculus. In calculus you will learn a different method for minimizing functions: you set the derivative equal to $0$. So, how do we minimize $E(w)$? Well, $E(w)$ is a quadratic function of several variables $w_0, w_1,\ldots, w_d$. You can either "complete the square" or "set the derivative to $0$". Oct 11, 2017 at 3:35 • It is difficult to understand the details without knowing some multivariable calculus and linear algebra. Multivariable calculus and linear algebra are prerequisites for machine learning. Here is an overview: it is possible to rewrite $E(w)$ using matrix notation as $E(w) = \\| X w - y \\|^2$. Here $X$ is the matrix whose $i$th row is $\bar x_i^T$, and $y$ is the column vector whose $i$th component is $y_i$. From multivariable calculus, the gradient of $E$ is $\nabla E(w) = 2 X^T (Xw - y)$. Set the gradient of $E$ equal to $0$ and we get $X^T Xw = X^T y$. Now solve for $w$. Oct 11, 2017 at 3:41 • The equations $X^T X w = X^T y$ are called the "normal equations". You can solve a least squares problem by writing down and then solving the normal equations. Oct 11, 2017 at 3:42	2022-09-29 11:21:05	{"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": 0.7738046050071716, "perplexity": 172.49811553750837}, "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/1664030335350.36/warc/CC-MAIN-20220929100506-20220929130506-00237.warc.gz"}
https://zbmath.org/?q=an%3A0951.47001	# zbMATH — the first resource for mathematics Linear operators sum and Kato-McIntosh’s conjecture. (Sommes d’opérateurs et conjecture de Kato-McIntosh.) (French) Zbl 0951.47001 The paper under review deals with regular (sectorial, closed and densely defined) forms on a fixed complex Hilbert space satisfying Kato’s condition. We recall that a regular form $$\psi$$ (or the $$m$$-sectorial operator $$A$$ uniquely associated with $$\psi$$) is said to satisfy Kato’s condition if the domain of $$A^{1/2}$$ equals the domain of $$(A^*)^{1/2}$$ and they coincide with the domain of the form $$\psi$$. The author proves that one can associate a maximal accretive operator satisfying Kato’s condition with the sum of two regular forms which satisfy some assumptions concerning the intersection of their domains. As a consequence, if $$A$$ and $$B$$ are two linear $$m$$-sectorial operators satisfying Kato’s condition then, in some additional hypotheses, there exists a unique $$m$$-sectorial operator $$A\oplus B$$ which satisfies the same condition and is the maximal accretive of the algebraic sum $$A+B$$. Under certain assumptions on two maximal accretive operators $$A$$ and $$B$$, more information is given on the numerical range of $$A\oplus B$$ in terms of numerical ranges of $$A$$ and $$B$$; in other words, $$A\oplus B$$ satisfies the spectral condition of McIntosh whenever $$A$$ and $$B$$ do. ##### MSC: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A07 Forms (bilinear, sesquilinear, multilinear) 47B44 Linear accretive operators, dissipative operators, etc. 47A12 Numerical range, numerical radius Full Text:	2021-06-16 02:08:35	{"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": 0.8953487873077393, "perplexity": 690.2826224924243}, "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/1623487621699.22/warc/CC-MAIN-20210616001810-20210616031810-00249.warc.gz"}
https://jech.bmj.com/content/61/8/665?ijkey=82f25dde4e1a96a9ce587c072111bb0f709ca7c2&keytype2=tf_ipsecsha	Article Text Effect of socioeconomic status on the relationship between atmospheric pollution and mortality 1. Olivier Laurent1, 2. Denis Bard1, 3. Laurent Filleul2, 4. Claire Segala3 1. 1LERES, Ecole Nationale de la Santé Publique, Rennes, France 2. 2CIRE Aquitaine, Institut de Veille Sanitaire, Bordeaux, France 3. 3Sepia-Santé, Melrand, France 1. Correspondence to:  Olivier Laurent  LERES, Ecole Nationale de la Santé Publique, Avenue du Professeur Léon Bernard, 35043 Rennes Cedex, France;olivier.laurent{at}ensp.fr ## Abstract Current knowledge about potential interactions between socioeconomic status and the short- and long-term effects of air pollution on mortality was reviewed. A systematic search of the Medline database through April 2006 extracted detailed information about exposure measures, socioeconomic indicators, subjects’ characteristics and principal results. Fifteen articles (time series, case-crossover, cohort) examined short-term effects. The variety of socioeconomic indicators studied made formal comparisons difficult. One striking fact emerged: studies using socioeconomic characteristics measured at coarser geographic resolutions (city- or county-wide) found no effect modification, but those using finer geographic resolutions found mixed results, and five of six studies using individually-measured socioeconomic characteristics found that pollution affected disadvantaged subjects more. This finding was echoed by the six studies of long-term effects (cohorts) identified; these had substantial methodological differences, which we discuss extensively. Current evidence does not yet justify a definitive conclusion that socioeconomic characteristics modify the effects of air pollution on mortality. Nevertheless, existing results, most tending to show greater effects among the more deprived, emphasise the importance of continuing to investigate this topic. • BMI, body mass index • CoH, coefficient of haze • NO2, nitrogen dioxide • O3, ozone • PM10, particulate matter with an aerodynamic diameter of up to 10 μm • PM2.5, particulate matter with an aerodynamic diameter of up to 2.5 μm • SES, socioeconomic status • SO2, sulfur dioxide • TSP, total suspended particulates • air pollution • mortality • effect modifier • socioeconomic factors • urban health ## Request Permissions If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways. An inverse gradient between socioeconomic status (SES) and mortality in Western countries has been solidly established.1 This gradient is well documented for all-cause mortality as well as for some specific causes of death, including cardiovascular diseases2–4 and several cancers.4–6 Although most pronounced during middle age, it is also observed among the elderly.7 The prevalence of numerous risk factors for potentially fatal diseases (again, cardiovascular diseases and cancers) also tends to be inversely associated with SES. Compared with populations with high SES, less advantaged populations tend to smoke more8 and to eat less fresh fruit and vegetables9 and more saturated fat.10 They also face more types of psychosocial stress (eg, financial strain, job insecurity, low control at work)11 and receive poorer healthcare (accessibility, use, quality of care).12 Nonetheless, it remains difficult to quantify the extent to which the unequal distribution of these risk factors in populations with divergent SES explains these socioeconomic mortality gradients. Moreover, relatively few studies have examined the contribution of environmental exposures, such as air pollution, to socioeconomic health inequalities.13 Several authors hypothesise that air pollution contributes to creating or accentuating the socioeconomic disparities seen in various diseases (including cancer,14 asthma15 and cardiovascular diseases16) and thus in premature death rates.17 Two types of potential mechanisms have been suggested. • Firstly, populations with low SES may be more frequently or more intensely exposed to air pollution than those with high SES.18,19 Nonetheless, Bowen concluded in 2002 that the results of studies documenting the distribution of exposure to air pollution in populations with different SES remain “mixed and inconclusive”.20 Later studies21–24 support this observation. The methodological diversity of these studies and the variety of their settings22 may partly explain the heterogeneity of their results. • Secondly, populations with low SES may be more susceptible to air pollution than those with high SES18 in that several factors which are more prevalent in less advantaged populations may be effect modifiers of the relationship between pollution and mortality. These include poor health status (for example, diabetes, obesity and chronic obstructive pulmonary disease),18 addictions (including smoking)25 and multiple pollutant exposures (passive smoking, occupational exposure) likely to act in addition to or in synergy with urban pollution,25 and difficulties with access to healthcare.19,26 Less obvious factors, such as psychosocial stress,17,19,26 low intake of proteins, vitamins and minerals,19 and even genetic make-up17 may also play a part. This review examines studies that tested this second hypothesis about mortality, by asking if SES is a sensitivity factor in the relationship between atmospheric pollution and mortality. ## METHODS We searched Medline from its inception to the end of April 2006, using three-MeSH term queries following the structure “Mortality AND Socioeconomic Factors AND Air Pollution”. The following alternative MeSH terms were also used: “Death” for mortality; “Social Class, Unemployment, Income, Poverty, Educational Status, Education, Occupations” for socioeconomic factors; and “Ozone, Nitrogen Dioxide, Sulphur Dioxide, Carbon Monoxide” for air pollution. Non-MeSH terms also used included “Socioeconomic Status”, “SES”, “Wealth” “Insurance Status” “Poverty” “Deprivation” and “Particulate Matter”. Studies were identified either because their abstract explicitly mentioned testing effect modification by socioeconomic indicators, or because they were cited in retrieved articles. Two unpublished studies27,28 were identified in this way, and detailed information was then obtained from the authors. Cross-sectional studies, considered to provide weaker evidence than other study designs, were excluded from the study report. We finally identified 21 studies. ## RESULTS We first present those studies that tested the influence of socioeconomic variables on the short-term (0–3 days) relationship between air pollution and mortality and then those studies that examined the influence of socioeconomic variables on the long-term (several years) relationship. Because the associations observed between mortality and exposure to air pollution are likely to be sensitive to how air pollution exposure is measured (ecological measurements at different geographic resolutions, individual measurements, time resolution of the measurement, lag time for health effects), we report in detail the exposure measures used in each study. SES is often a confounder in studies of long-term pollution health effects.29,30 It is also a multidimensional notion that no single socioeconomic variable (education, occupation, assets, income), considered alone, can capture.31 No socioeconomic variable can serve as another’s proxy.31 Accordingly, we also report the details of the socioeconomic variables used in each study. Careful examination of these factors showed that the studies identified were too heterogeneous in their exposure measurements, socioeconomic indicators and subjects’ ages for meta-analysis. ### Studies of short-term relationships Ten time-series studies (table 1), four case-crossover studies and one cohort study (table 2) of the short-term relationship between pollution and mortality were identified. Table 1 Time-series studies of short-term relationships between air pollution and mortality Table 2 Case-crossover and cohort studies of short-term relationships between air pollution and mortality Most estimated pollutant concentrations at the resolution of a city or county. Only two authors estimated concentrations at finer geographical resolutions. Jerrett et al divided Hamilton (Canada) into five zones based on Thiessen polygons (approximately 2×3 km to 8×7 km), defined around pollution monitors as the central nodal points.26 In Sao Paulo (Brazil), Martins et al defined six subcity zones within a 2-mile (3.2-km) perimeter around monitors, all of which were at sites of high traffic.32 In both cases, the pollutant concentrations attributed to each defined zone were those measured by the monitors in that zone. All but three28,32,33 of the studies identified examined non-trauma all-cause mortality in subjects aged 65 years and older or in subjects of all ages. As relatively few results were available for specific causes of death (respiratory,32,34,35 cardiovascular27,34,35 and cardiorespiratory36,37), we report and discuss only those results dealing with all-cause mortality. #### Mortality for those 65 years or older. Four studies examined PM10 (particulate matter with an aerodynamic diameter of up to 10 μm). In Mexico City (Mexico), O’Neill et al39 tested the influence of percentage of literate subjects, percentage of indigenous language speakers, percentage of homes with electricity, piped water or drainage, and a sociospatial development index, all measured at the resolution of a county. In Vancouver (Canada), Villeneuve et al34 tested the influence of mean family income, measured by “enumeration areas”. In Cook County, IL (USA), Bateson and Schwartz examined the influence of percentage with bachelor’s degrees, median household income and percentage of adults not speaking English at home, measured by ZIP codes.42 None of these studies showed any effect modification by the socioeconomic variables tested. In Sao Paulo (Brazil), Gouveia and Fletcher reported stronger associations for the populations with higher SES, measured by a composite deprivation index at a district resolution,40 but the differences in the associations observed according to the value of the deprivation index were not statistically significant. Three studies examined black smoke and individual socioeconomic variables. In four Polish cities, Wojtyniak et al observed statistically significant associations only in subjects who had not completed secondary school.27 In their case-crossover study in Bordeaux (France), Filleul et al observed statistically significant associations only in subjects who were blue-collar workers, but found no statistically significant association when the study population was stratified according to educational level.37 In a cohort study of the same population, which compared the characteristics of people who died on days when the highest and lowest black smoke concentrations were observed (that is, above the 90th and below the 10th percentile of observed concentrations), Filleul et al found that neither past occupational status nor educational level modified the effect of pollution on mortality.43 Villeneuve et al found no modification by mean family income, assessed by enumeration area, of the effect of either total suspended particulates (TSP) or PM2.5.34 Both Villeneuve et al34 and O’Neill et al39 studied ozone and found no modifying effect by any of the SES variables tested. #### All-age mortality Four studies examined PM10. In a study of 20 US cities, Samet et al found that the effect of PM10 was not modified by the percentage of high school graduates or by either of two income indicators (percentage with annual income <US$12 675, percentage with annual income >US$100 000), all measured city-wide.36 Similarly, Schwartz studied 10 US cities and found no effect modification by unemployment rate, percentage of the population below the poverty line or percentage of college degrees, all measured city-wide.38 In a study of four US cities, Zanobetti and Schwartz used individual data about educational level41 and found stronger associations for the subjects who had not completed high school (interaction not statistically significant). A study by Zeka et al of 20 US cities also used individual data and showed associations twice as strong for the subjects who had not attained high school as for those who went on to college. The trend was nonetheless not statistically significant.35 In Hamilton (Canada), Jerrett et al observed stronger associations (statistically significant interaction) for the coefficient of haze (CoH) in zones with more manufacturing employment and lower educational levels. There were no statistically significant interactions with the other SES variables tested (table 1).26 For black smoke, Wojtyniak et al reported statistically significant associations only for subjects who had not completed secondary school.27 ### Studies of long-term relationships Six cohort studies (table 3) tested the influence of socioeconomic variables on long-term relationships between pollution and mortality. Table 3 Studies of long-term relationships between air pollution and mortality The reanalysis of cohorts from the Six Cities Study (8111 subjects aged 25–74 years at recruitment, followed from 1974 through 1991)48 and the American Cancer Society (552 138 subjects aged 30 years or more at recruitment, followed from 1982 through 1989)49 tested the influence of subjects’ educational levels on the relationships between exposure to air pollutants (PM2.5 and sulfates) and mortality in 56 US cities. Pollutant concentrations were estimated city-wide. PM2.5 measurements were not available for the entire ACS cohort (only for 295 223 subjects). Several individual covariates were taken into account: direct and indirect smoking, occupational exposure to dust or fumes, body mass index (BMI) and alcohol consumption.44 For all-cause mortality, subjects who had not completed high school had stronger (and statistically significant) relative risks for PM2.5 than those who continued on to college (relative risks not statistically significant). A similar but less pronounced result was observed for cardiopulmonary mortality. Results were generally similar for sulfates. Follow-up of the ACS cohort, prolonged through 1998 and including additional covariates (fat intake, consumption of vegetables, citrus, high-fibre grains), confirmed these observations.50 In the PAARC study of seven French cities (14 284 subjects aged 25–59 years at recruitment and followed from 1974 through 2000), Filleul et al tested the influence of educational level on the relationship between mortality and exposure to black smoke, TSP and NO2.45 Pollutant concentrations were measured by monitors set up especially for this study in 24 residential areas 0.5–2.3 km in diameter. The covariates considered were smoking (by subjects and their spouses), BMI and occupational exposure to dust, gas and fumes (estimated dichotomously via a job exposure matrix). Manual labourers were excluded from this study. After the exclusion of six zones whose measurements were judged to be excessively influenced by main roads near the monitors, no gradient according to educational level (primary, secondary or university) was found for the associations between all-cause mortality and any of the three pollutants. In the Netherlands, Hoek et al tested the influence of educational level on the relationships between black smoke and mortality in the NLCS cohort (4492 subjects aged 55–69 years at recruitment, followed from 1986 to 1994).46 They used a three-component exposure measure that combined regional background (estimated by inverse distance squared weighted interpolation of regional background monitoring station measurements), additional urban background (estimated by regression analyses of the density of postal addresses and monitoring station measurements) and the influence of roadways near the subjects’ homes (<50 m for local roads, <100 m for major roads). Observed air pollution levels were lower among less educated subjects. The covariates studied were smoking (by subject and spouse), BMI (Quetelet index), fruit and vegetable consumption and total fat intake. The relative risk between black smoke and mortality was higher for subjects with only elementary school education than for those with intermediate vocational education. The relative risk for subjects with intermediate vocational education was itself higher than that for subjects who had at least completed high school. The differences in relative risks were not, however, statistically significant. In Hamilton (Canada), Finkelstein et al tested the influence of mean household income of the neighbourhood (enumeration area) on the relationships between TSP, SO2 and mortality.47 The cohort included 5228 subjects greater than 40 years of age at recruitment, who had been referred for pulmonary function testing and were followed from 1992 through 1999. The concentrations of these pollutants were estimated at the resolution of residences (postal address) by universal kriging of measurements from monitors (29 monitors for TSP, 19 for SO2). This study used a dichotomous exposure measure (above or below the median of the concentrations estimated for the study area). The covariates studied were BMI, chronic disease diagnoses (chronic pulmonary diseases, chronic ischaemic heart disease, diabetes mellitus) and lung function measures. Since no smoking data were available, the authors assumed that lung function was a proxy for smoking status. The relative risks of mortality associated with TSP and SO2 were higher for subjects living in enumeration areas with a mean household income less than the Hamilton median. Finkelstein et al replicated this study with the same pollution data and the same population, focusing specifically on mortality from cardiovascular causes.16 SES was estimated using a composite deprivation indicator (table 3), assessed at the resolution of an enumeration area. Two pollution indicators were estimated for each subject’s actual residence address: a background pollution index (sum of the standardised values of TSP and SO2) and a measure of proximity to roads (subjects considered exposed if they lived less than 50 m from a major urban road or less than 100 m from a highway). The deprivation indicator did not modify the associations between cardiovascular mortality and either of these two exposure measures. ## DISCUSSION ### Studies of short-term relationships All but one26 of the studies examining all-cause mortality used city-wide exposure measurements. They considered diverse pollutants, most often PM10.34–36,38–42 Given the very strong correlations between PM2.5 and PM10 reported by two studies of PM2.5 (0.83 for Villeneuve et al,34 0.96 for Cifuentes et al28), their results may also be related to PM10. None of the studies examined here provided information about correlation of black smoke, TSP and CoH with PM10, but earlier studies have shown that black smoke and TSP are often strongly correlated with PM10.51,52 Similar correlations for CoH and PM10 are less clear. Very few studies adjust for copollutants.26,28,36 The temporal resolution of exposure measurements (a day,43 mean of several days34) and delayed effects (lags) tested also differs slightly between studies. These studies use socioeconomic variables that are very diverse in both in their nature (eg, educational level, income, percentage of unemployed people in the neighbourhood, composite deprivation index) and their resolution (individuals,37 cities,36 districts,40 author-defined city subdivisions,26,32 enumeration areas,34 and ZIP codes33). Moreover, for the same type of socioeconomic variable, different studies sometimes use different cut-off points for defining deprivation (tables 1 and 2). All these differences make it difficult to summarise results from the available studies (eg, by meta-analysis) and to draw solid conclusions. Nonetheless, one point is striking: of the three studies that used socioeconomic variables at very coarse geographic resolutions (city-wide or county-wide), none found differences in associations according to these socioeconomic variables, despite very large populations. The studies using socioeconomic variables at finer geographic resolutions produced mixed results. And above all, five of the six studies that used individual socioeconomic variables (educational level27,28,35,37,41,43 or occupation43) reported stronger pollution–mortality associations for the populations with the more unfavourable socioeconomic variables. This observation does not justify a definitive conclusion that SES interacts with the short-term relationship between pollution and mortality, but it does highlight the importance of continuing to study the influence of socioeconomic variables (in particular individual variables) on this relationship. ### Studies of long-term relationships Studies focusing on long-term relationships generally encounter greater difficulties than those examining short-term relationships in documenting subjects’ precise exposures and in eliminating the influence of confounding factors (whereas in studies of short-term relationships, factors that remain stable during the lag period between exposure and event are not confounding factors). In all these studies, exposure was assessed when subjects entered the cohort. The authors assumed that those measurements were reasonable approximations of exposure for the years before and after study entry. On a city-wide scale, mean annual pollutant concentrations are generally stable from one year to the next. Substantial changes in concentrations occur over decades rather than years. It therefore seems reasonable to assume that this approximation resulted in little exposure misclassification.46 Another potential problem associated with long-term exposure measurements is people’s mobility. In the Six Cities Study, the difference in relative risk according to educational level was observed both for subjects who had changed city of residence during the follow-up period and for those who had not. The ACS cohort data, unfortunately, could not test this relationship.44 Hoek et al, Finkelstein et al and Filleul et al did not take into account their subjects’ changes of residence after study entry.16,45–47 Hoek et al justified this decision by pointing out that 90% of subjects had lived at their 1986 address for 10 years or more. Moreover, they did test relationships with black smoke and found relative risks (all education levels) were similar for the subjects who had lived for 10 years or more at their 1986 address and for the entire cohort.46 Accordingly, it appears implausible that changes in residence of members of the ACS, Six Cities and NLCS cohorts might explain the differences in relative risks observed according to educational level. This possibility cannot be ruled out for the Hamilton cohort,16,47 however, since the authors had no information about subjects changing accommodation. This is also the case for the PAARC cohort, where only 23.4% of the subjects lived in the same area during recruitment and 25 years later.45 Dockery and Pope et al presented city-wide measurements as an acceptable proxy for assessing residents’ long-term exposure to PM2.5.48,49 Finkelstein, however, considered that intra-urban variations in outdoor PM2.5 concentrations could cause differential exposure misclassification that might explain the differences in the relative risks observed according to educational level.53 Findings by Jerrett et al in Los Angeles54 and Rotko et al in Helsinki55 support this hypothesis. To avoid this potential problem, the NLCS, PAARC and Hamilton cohorts used intra-urban level exposure measurements.16,45–47 Several types of factors which are unequally distributed between populations with different SES may be effect modifiers of the relationship between pollution and mortality. In some cases, this might explain the variation in pollution–mortality associations observed between groups with different SES. The influence of some of these factors on the relationship between pollution and mortality were tested in some cohorts: • Smoking was considered in all cohorts, except that in Hamilton. In the Six Cities, ACS and NCLS cohorts, smoking was not an interaction factor between pollution and mortality.44,46 Nonetheless, when the ACS cohort was followed through 1998,50 relative risks associated with PM2.5 became stronger in non-smokers (since the cohort had aged, a healthy smoker effect may be suspected). In contrast, the relative risks associated with pollution in the PAARC study were stronger in smokers than in non-smokers. • Occupational exposure to dust, gas and fumes was considered only in the Six Cities, ACS and PAARC cohorts. In the first two, these exposures did not notably modify the relative risks observed between PM2.5 and mortality.44 In the PAARC study (not including manual labourers), subjects with these occupational exposures had higher pollution-related relative risks. • When they were considered, passive smoking,44 spouse’s smoking status45,46 and diet46,50 did not substantially modify the associations between pollution and mortality. No clear lessons can be drawn from the examination of these factors: smoking and occupational exposures do not seem to be effect modifiers except in the PAARC study, where the associations observed between pollution and mortality did not differ noticeably according to educational level.45 In contrast, in the studies where the associations observed between pollution and mortality differed substantially according to the value of the SES indicators,44,46 no covariate appeared to be a sufficiently important effect modifier to explain these differences. These six studies do not allow us to reach any definitive conclusions about the modifying effects of SES variables on the long-term relationships between pollution and mortality. It is nonetheless interesting that four of them showed associations that differed clearly in extent according to individual education level44,46,50 and neighbourhood household income.47 Nonetheless we cannot totally rule out the possibility of confounding factors that were measured poorly or not at all (indoor pollution, occupational exposure) or of differential exposure misclassification according to SES. ### Problems common to short- and long-term studies In an attempt to overcome this problem of potential differential exposure misclassification according to SES,53,56 several authors estimated pollutant concentrations at the resolution of city subdivisions. The exposure attributed to each subject was thus the prevalent concentration in his or her zone (as defined in each study: actual address16,46 or neighbourhood, at a more or less fine resolution26,32,45). It is difficult to appreciate to what extent these approaches really attenuate exposure misclassification relative to city-wide measurements. • Except for two studies documenting the proximity of roads,16,46 the intra-urban measurements used concern (local) urban background pollution. The quantity of pollutants added or subtracted to this local urban background may differ according to subjects’ SES for several reasons: very local effects of emission sources on pollutant concentrations, penetration of exterior air pollutants into buildings (depending on building characteristics, such as air conditioning), sources of indoor pollution, passive smoking, etc. • Simple measurement of concentrations inside or outside the home does not take into account the subjects’ time activity patterns57 including time spent at home, at work, in the neighbourhood, indoors or outdoors. Nonetheless, most people generally spend a substantial portion of their time at home (68% on average in the US58). The measurement of pollutant concentrations at home must therefore reflect at least part of the total exposure to pollutants, although more exhaustive and integrated exposure measurement would obviously be preferable. Unfortunately, the lack of available information about the possible differences in time activity patterns according to SES17 complicates the discussion of this aspect. Each of the studies tested effect modification by SES only for a limited portion of the dose–response relationship between pollutant concentration and mortality. That is, in these studies, the relative risk is generally measured for an increase in the concentration of a pollutant (from concentration x1 to concentration x2). Some populations may conceivably be more susceptible than others to concentrations that are generally considered “low”. Other populations, less susceptible to these “low” concentrations, may become increasingly susceptible as the pollutant concentration increases. Figure 1 illustrates a fictitious example: the slope of a dose–response curve corresponding to a population with low SES might be stronger than that of a population with high SES for some concentration ranges (between x1 and x2), and lower for a range of higher concentrations (between x3 and x4). The slopes of these curves may be considered equivalent to relative risks. This shows the importance of taking into account the range of pollutant concentrations tested for which SES might be an effect modifier. Figure 1 Fictitious example of dose–response relationships in populations with high and low SES. • This first review of potential interactions between socioeconomic status and the effects of air pollution on mortality shows that the resolution at which socioeconomic characteristics are measured influences the results. • There is no effect modification for coarser geographic resolutions (city- or county-wide) and there are mixed results for finer geographic resolutions, while such an interaction is relatively consistent when individual measures are used: poorer people tend to be more susceptible to the effects of air pollution. ### Policy implications • Further research on this topic should consider the largest possible number of SES indicators (both individual and contextual) to identify the most discriminating in terms of relative risks of mortality associated with pollution. ## CONCLUSION The available studies do not allow confirmation or exclusion of an influence of SES on the relationship between air pollution and mortality. More studies with comparable designs are necessary to achieve that aim. Future studies must, in so far as possible, use exposure measurements that minimise differential exposure misclassifications according to SES. They must also test the largest possible number of SES indicators (individual and contextual, at different geographic resolutions)31 simultaneously to identify the most discriminating in terms of relative risks of mortality associated with pollution. Additional multicentre studies would guarantee harmonisation of the indicators and statistical methods used.59 ## Acknowledgments Thanks to Jo Ann Cahn for her critical translation of this paper from the French. ## Footnotes • Funding: None. • Competing interests: None.	2022-08-15 05:10:05	{"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": 0.5269560217857361, "perplexity": 6353.876337679678}, "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-2022-33/segments/1659882572127.33/warc/CC-MAIN-20220815024523-20220815054523-00461.warc.gz"}
https://docs.duckietown.org/daffy/duckumentation/draft/markduck_basic.html	build details # Basic Markduck guide Modified 2019-09-22 by Andrea Censi The Duckiebooks are written in Markduck, a Markdown dialect. It supports many features that make it possible to create publication-worthy materials. ## Markdown Modified 2018-06-02 by Andrea Censi The Duckiebook are written in a Markdown dialect. Modified 2020-09-02 by Andrea Censi You can insert comments using the HTML syntax for comments: any text between “`<!–`” and “`–>`” is ignored. ``````# My section <!-- this text is ignored --> Let's start by... `````` ## Variables in command lines and command output Modified 2018-06-02 by Andrea Censi Use the syntax “`![name]`” for describing the variables in the code. For example, to obtain: ``````$ssh robot name.local `````` Use the following: ``````For example, to obtain:$ ssh ![robot name].local`````` Make sure to quote (with 4 spaces) all command lines. Otherwise, the dollar symbol confuses the LaTeX interpreter. ## Character escapes Modified 2019-10-01 by Rohit Suri Use the string `$` to write the dollar symbol `\$`, otherwise it gets confused with LaTeX math materials. Also notice that you should probably use “USD” to refer to U.S. dollars. Other symbols to escape are shown in Table 1.1. ## Keyboard keys Modified 2018-06-02 by Andrea Censi Use the `kbd` element for keystrokes. For example, to obtain: Press a then Ctrl-C. use the following: ``````Press <kbd>a</kbd> then <kbd>Ctrl</kbd>-<kbd>C</kbd>. `````` ## Figures Modified 2018-06-02 by Andrea Censi To create a figure, use the element `figure`: ``````<figure> <figcaption>Hello</figcaption> <img style='width:8em' src="duckietown-logo-transparent.png"/> </figure> `````` ### More attributes Modified 2018-06-02 by Andrea Censi Use `class="caption-left"` to have the caption show up on the left rather than on the bottom: ``````<figure class="caption-left"> <figcaption>Hello</figcaption> <img style='width:8em' src="duckietown-logo-transparent.png"/> </figure> `````` ## Subfigures Modified 2018-06-02 by Andrea Censi You can create subfigures by nesting `figure` elements: ``````<figure> <figcaption>Main caption</figcaption> <figure> <figcaption>Hello</figcaption> <img style='width:8em' src="duckietown-logo-transparent.png"/> </figure> <figure> <figcaption>second</figcaption> <img style='width:8em' src="duckietown-logo-transparent.png"/> </figure> </figure> `````` By default, they are displayed one per block. To make them flow horizontally, add `class="flow-subfigures"` to the external figure: ``````<figure class="flow-subfigures"> <figcaption>Main caption</figcaption> <figure> <figcaption>Hello</figcaption> <img style='width:8em' src="duckietown-logo-transparent.png"/> </figure> <figure> <figcaption>second</figcaption> <img style='width:8em' src="duckietown-logo-transparent.png"/> </figure> </figure> `````` For any element, adding an attribute called `figure-id` with value `fig:figure ID` or `tab:table ID` will create a figure that wraps the element. ## Shortcut for tables Modified 2020-09-02 by Andrea Censi The shortcuts `col2`, `col3`, `col4`, `col5` are expanded in tables with 2, 3, 4 or 5 columns. The following code: ``````<col2 figure-id="tab:mytable" figure-caption="My table"> <span>A</span> <span>B</span> <span>C</span> <span>D</span> </col2> `````` gives the following result: ### `labels-row1` and `labels-row1` Modified 2018-06-02 by Andrea Censi Use the classes `labels-row1` and `labels-row1` to make pretty tables like the following. `labels-row1`: the first row is the headers. `labels-col1`: the first column is the headers. Modified 2018-06-02 by Andrea Censi Modified 2020-09-02 by Andrea Censi You give IDs to headers using the format: ``````### header title {#topic ID} `````` For example, for this subsection, we have used: ``````### Establishing names of headers {#establishing} `````` With this, we have given this header the ID “`establishing`”. By convention, we use consistently dashes rather than underscores. For example, instead of using the ID `#my_cool_section`, use `#my-cool-section`. ### How to name IDs - and why it’s not automated Modified 2020-09-02 by Andrea Censi Some time ago, if there was a section called ``````## My section `````` then it would be assigned the ID “my-section”. This behavior has been removed, for several reasons. One is that if you don’t see the ID then you will be tempted to just change the name: ``````## My better section `````` and silently the ID will be changed to “my-better-section” and all the previous links will be invalidated. The current behavior is to generate an ugly link like “autoid-209u31j”. This will make it clear that you cannot link using the PURL if you don’t assign an ID. Also, I would like to clarify that all IDs are global (so it’s easy to link stuff, without thinking about namespaces, etc.). Therefore, please choose descriptive IDs, with at least two IDs. E.g. if you make a section called ``````## Localization {#localization} `````` that’s certainly a no-no, because “localization” is too generic. ``````## Localization {#intro-localization} `````` Also note that you don’t need to add IDs to everything, only the things that people could link to. (e.g. not subsubsections) ### Linking from the documentation to the documentation Modified 2020-09-02 by Andrea Censi You can use the syntax: ``````[](#topic ID) `````` You can also use some slightly more complex syntax that also allows to link to only the name, only the number or both (Table 1.5). Modified today by Liam Paull It is possible to link from one book to another. The syntax is a slightly extended syntax. Instead of using something like ``````See this [interesting section](#interesting-section). `````` You need to use add `+other-book-id` before the `#`: ``````See this [interesting section in another book](+other-book-id#interesting-section). `````` To find out what is the book ID, go to the current index of all the books, which, for `daffy`, is `https://docs.duckietown.org/daffy/`. Go to the book you want to link, and note the URL. The book ID is the part after `daffy`. For example, this book is published at ``````https://docs.duckietown.org/daffy/duckumentation/out/index.html `````` The book ID is `duckumentation`. To link to the entire book, use something like `+BOOKID#book`. (By convention, each book will have the main header assigned the header `#book:book`.) Here is a list of some of the books as of August 2020: ### (For developers) How to update the list of books that can be crossreferenced. Modified 2020-09-02 by Andrea Censi The dictionary between book ID and URL is maintained in the repo `docs-build` in the file `books.crossref.yaml`. When a new book is added, the list needs to be updated and the image `duckietown/docs-build` be updated.	2021-04-22 18:13:00	{"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": 0.5204849243164062, "perplexity": 5871.132671560898}, "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-2021-17/segments/1618039594341.91/warc/CC-MAIN-20210422160833-20210422190833-00356.warc.gz"}
https://math.stackexchange.com/questions/650045/general-approach-to-find-continuous-functions?noredirect=1	General approach to find continuous functions? I have two functions: 1. $f: \mathbb{R} \to \mathbb{R}: x \mapsto \|x\|$ 2. $f: \mathbb{R} \to \mathbb{R}: x \mapsto 3x^2-7x^2+11x-1$ I´m not really sure how to approach the question whether these functions are continuous or not. For the 1. because it is not differentiable at $0$ than its not continuous? For the 2. its continuous because its differentiable? • While what you say in 2. is true, this is not the appropriate argument. Rather, appeal to the facts that $f(x)=x$ is continuous, constant functions are continuous, and sums, products, and constant multiples of continuous functions are continuous. – David Mitra Jan 24 '14 at 15:52 On 1: The only problem is $x=0$. To see it is indeed continuous, you have to look at the limits $x\to0$ for $x<0$ and $x>0$. Both limites are $0$, so the function is continuous. In a metric space, like $\mathbb R$ (if it is equipped with its usual topology) it is enough to prove or check that $x_n\rightarrow x$ implies that $f(x_n)\rightarrow f(x)$.	2020-01-24 08:36:08	{"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": 0.9300382137298584, "perplexity": 152.1482769588436}, "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-2020-05/segments/1579250616186.38/warc/CC-MAIN-20200124070934-20200124095934-00119.warc.gz"}
https://geo.libretexts.org/Bookshelves/Sedimentology/Book%3A_Introduction_to_Fluid_Motions_and_Sediment_Transport_(Southard)/06%3A_Oscillatory_Flow/6.02%3A_The_Nature_of_Waves	# 6.2: The Nature of Waves ## Introduction In a very fundamental sense, the waves that are of interest to us here can be viewed as a manifestation of unsteady free-surface flow subjected to gravitational forces. That is, any unsteady flow with a deformable free surface can be considered to be a kind of wave. Do not let it bother you that real water waves involve changes in the water-surface geometry even when you follow along with the waves. You know from Physics I that a function of the form $$y = f (x - ct)$$ represents a wave traveling with speed $$c$$ in the positive $$x$$ direction—and the shape of the wave does not change if you just travel along with the wave. And $$c$$ could be a function of $$t$$, meaning that the speed of the wave changes everywhere with time but the shape of the wave train still stays the same. But now suppose that you took one additional step: let $$c$$ be a function of $$x$$ rather than $$t$$. Then the shape of the wave changes as it moves: there is no speed at which you can travel, along with the wave, to keep the wave shape looking the same. The best way to think about this situation is that each point on the wave (you could call such points wavelets) has its own speed, so that, as all of them move, the overall shape of the wave changes with time. In terms of the forces involved in wave motion, the motions of the water in the interior and the geometry of the free surface are an outcome of the interaction between pressure forces and gravity forces. Although it may or may not help you any, one way of thinking about waves is to consider that gravity tries to even out some initial nonplanarity of the water surface, and in doing so produces a usually complex unsteady flow in which the water-surface geometry changes as a function of time, but the characteristic amplitude of the water-surface disturbance has no way of actually decreasing unless viscous forces act also. Real waves do decrease in amplitude, of course, because of the slight shear and therefore viscous friction in the interior of the water. But unless the waves produce water motions at the bottom, the rate of viscous dissipation of the wave motion is very slight. Mathematically, this means that the viscous term in the equation of motion can be ignored. Only when an oscillatory boundary develops at the bottom is the viscous dissipation substantial. ## The Equations of Motion The equation of motion that describes water waves is just the Navier– Stokes equation without the viscous term but including a term for gravity. It turns out that this equation for inviscid flow affected by gravity can be put into the form of a wave equation, so you mathematically the existence of waves should not surprise you. If you had never fooled around with waves before, your natural inclination upon reading the foregoing paragraph would probably be to try to solve the equations to account for the observed behavior of water waves. And people have been doing this since the middle of the 1800s. But there are two serious impediments to simple solutions: 1. The equation is nonlinear, because of the presence of the convective acceleration term, which as you know from Chapter 3 involves products of velocities and spatial derivative of velocities. 2. An even more serious problem is that one of the boundary conditions— the geometry of the free surface—is itself one of the unknowns in the problem! So it is unfortunately true that there is no general solution to the problem. People have therefore tried to make various simplifying assumptions that allow some mathematical progress in certain ranges of conditions for water waves. Much mathematical effort has gone into developing these partial approaches and establishing their limits of approximate validity. ## Classification of Water Waves It is notoriously difficult to develop a rational classification of water waves, basically because of the mathematical complexity mentioned above. One way to classify water waves I already mentioned: does the water move with the waves (translatory waves), or does the water merely oscillate as the wave passes, to return to its original position after the wave has passed (oscillatory waves)? But I also mentioned a more fundamental approach: waves for which the convective inertia terms can be neglected are called linear waves, and those for which the convective inertia terms are at least in part included in the analysis are called nonlinear waves. Yet another fundamental approach to classification is on the basis of the relative magnitudes of the three important length scales in the problem: wave height $$H$$, wavelength $$L$$, and water depth $$d$$. Out of these three you can make three characteristic ratios: $$H/L$$, $$H/d$$, and $$L/d$$. In deep water, $$H/d$$ and $$L/d$$ are both small, and the most important parameter is $$H/L$$, called the wave steepness. In shallow water, on the other hand, neither $$H/d$$ nor $$L/d$$ is likely to be small, and the most important parameter is likely to be $$H/d$$, called the relative height. In an intermediate range of water depths, the situation is more complicated.	2021-02-25 21:59:52	{"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": 0.6736973524093628, "perplexity": 241.8418131283798}, "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/1614178355937.26/warc/CC-MAIN-20210225211435-20210226001435-00226.warc.gz"}
https://www.springerprofessional.de/logic-rationality-and-interaction/14961974	main-content ## Über dieses Buch This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan. The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning. ## Inhaltsverzeichnis ### A Logical Framework for Graded Predicates In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, we propose a general research program towards a logic-based account of reasoning with graded predicates. Petr Cintula, Carles Noguera, Nicholas J. J. Smith ### Evidence Logics with Relational Evidence We introduce a family of logics for reasoning about relational evidence: evidence that involves an ordering of states in terms of their relative plausibility. We provide sound and complete axiomatizations for the logics. We also present several evidential actions and prove soundness and completeness for the associated dynamic logics. Alexandru Baltag, Andrés Occhipinti ### Rational Coordination with no Communication or Conventions We study pure coordination games where in every outcome, all players have identical payoffs, ‘win’ or ‘lose’. We identify and discuss a range of ‘purely rational principles’ guiding the reasoning of rational players in such games and analyse which classes of coordination games can be solved by such players with no preplay communication or conventions. We observe that it is highly nontrivial to delineate a boundary between purely rational principles and other decision methods, such as conventions, for solving such coordination games. Valentin Goranko, Antti Kuusisto, Raine Rönnholm ### Towards a Logic of Tweeting In this paper we study the logical principles of a common type of network communication events that haven’t been studied from a logical perspective before, namely network announcements, or tweeting, i.e., simultaneously sending a message to all your friends in a social network. In particular, we develop and study a minimal modal logic for reasoning about propositional network announcements. The logical formalisation helps elucidate core logical principles of network announcements, as well as a number of assumptions that must be made in such reasoning. The main results are sound and complete axiomatisations. Zuojun Xiong, Thomas Ågotnes, Jeremy Seligman, Rui Zhu ### Multi-Path vs. Single-Path Replies to Skepticism In order to reply to the contemporary skeptic’s argument for the conclusion that we don’t have any empirical knowledge about the external world, several authors have suggested different fallibilist theories of knowledge that reject the epistemic closure principle. Holliday [8], however, shows that almost all of them suffer from either the problem of containment or the problem of vacuous knowledge. Furthermore, Holliday [9] suggests that the fallibilist should allow a proposition to have multiple sets of relevant alternatives, each of which is sufficient while none is necessary, if all its members are eliminated, for knowing that proposition. Not completely satisfied with Holliday’s multi-path reply to the skeptic, the author suggests a new single-path relevant alternative theory of knowledge and argues that it can avoid both the problem of containment and the problem of vacuous knowledge while rejecting skepticism. Wen-fang Wang ### An Extended First-Order Belnap-Dunn Logic with Classical Negation In this paper, we investigate an extended first-order Belnap-Dunn logic with classical negation. We introduce a Gentzen-type sequent calculus FBD+ for this logic and prove theorems for syntactically and semantically embedding FBD+ into a Gentzen-type sequent calculus for first-order classical logic. Moreover, we show the cut-elimination theorem for FBD+ and prove the completeness theorems with respect to both valuation and many-valued semantics for FBD+. Norihiro Kamide, Hitoshi Omori ### A Characterization Theorem for Trackable Updates The information available to some agents can be represented with several mathematical models, depending on one’s purpose. These models differ not only in their level of precision, but also in how they evolve when the agents receive new data. The notion of tracking was introduced to describe the matching of information dynamics, or ‘updates’, on different structures.We expand on the topic of tracking, focusing on the example of plausibility and evidence models, two central structures in the literature on formal epistemology. Our main result is a characterization of the trackable updates of a certain class, that is, we give the exact condition for an update on evidence models to be trackable by a an update on plausibility models. For the positive cases we offer a procedure to compute the other update, while for the negative cases we give a recipe to construct a counterexample to tracking. To our knowledge, this is the first result of this kind in the literature. Giovanni Cinà ### Convergence, Continuity and Recurrence in Dynamic Epistemic Logic The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps. Dominik Klein, Rasmus K. Rendsvig ### Dynamic Logic of Power and Immunity We present a dynamic logic for modelling legal competences, and in particular for the Hohfeldian categories of power and immunity. We argue that this logic improves on existing models by explicitly capturing the norm-changing character of legal competences, while at the same time providing a sophisticated reduction of the latter to static normative positions. The logic is shown to be completely axiomatizable; an analysis of its resulting dynamic normative positions is provided; and it is finally applied to a concrete case in German contract law to illustrate how the logic can distinguish legal ability and legal permissibility. Huimin Dong, Olivier Roy ### A Propositional Dynamic Logic for Instantial Neighborhood Models We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL and dynamic game logic. INL is a recently proposed modal logic, based on a richer extension of neighborhood semantics which permits both universal and existential quantification over individual neighborhoods. We show that a number of game constructors from game logic can be adapted to this setting to ensure invariance for instantial neighborhood bisimulations, which give the appropriate bisimulation concept for INL. We also prove that our extended logic IPDL is a conservative extension of dual-free game logic, and its semantics generalizes the monotone neighborhood semantics of game logic. Finally, we provide a sound and complete system of axioms for IPDL, and establish its finite model property and decidability. Johan van Benthem, Nick Bezhanishvili, Sebastian Enqvist ### Contradictory Information as a Basis for Rational Belief As agents faced with fallible information, we frequently find ourselves in situations where we are forced to base our beliefs on evidence which is in some way or another contradictory. We nevertheless want these beliefs to be rational. This paper presents a simple probabilistic model of what it means for a belief based on a contradictory body of evidence to be rational. In this approach, we model contradictions in the evidence available to us as resulting from random noise, and we model our task as rational agents as reconstructing the most likely states of affairs given the evidence available to us. Our main result consists in providing several equivalent descriptions of the non-reflexive and non-monotonic consequence relation which formalizes the notion that it is reasonable to accept that a proposition is true given good evidence supporting some set of propositions. ### Stability in Binary Opinion Diffusion The paper studies the stabilization of the process of diffusion of binary opinions on networks. It first shows how such dynamics can be modeled and studied via techniques from binary aggregation, which directly relate to neighborhood frames. It then characterizes stabilization in terms of such neighborhood structures, and shows how the monotone $$\mu$$μ-calculus can express relevant properties of them. Finally, it illustrates the scope of these results by applying them to specific diffusion models. Zoé Christoff, Davide Grossi ### Quotient Dynamics: The Logic of Abstraction We propose a Logic of Abstraction, meant to formalize the act of “abstracting away” the irrelevant features of a model. We give complete axiomatizations for a number of variants of this formalism, and explore their expressivity. As a special case, we consider the “logics of filtration”. Alexandru Baltag, Nick Bezhanishvili, Julia Ilin, Aybüke Özgün ### The Dynamics of Group Polarization Exchange of arguments in a discussion often makes individuals more radical about their initial opinion. This phenomenon is known as Group-induced Attitude Polarization. A byproduct of it are bipolarization effects, where the distance between the attitudes of two groups of individuals increases after the discussion. This paper is a first attempt to analyse the building blocks of information exchange and information update that induce polarization. I use Argumentation Frameworks as a tool for encoding the information of agents in a debate relative to a given issue a. I then adapt a specific measure of the degree of acceptability of an opinion (Matt and Toni 2008). Changes in the degree of acceptability of a, prior and posterior to information exchange, serve here as an indicator of polarization. I finally show that the way agents transmit and update information has a decisive impact on polarization and bipolarization. Carlo Proietti ### Doing Without Nature We show that every indeterministic n-agent choice model $$M^i$$Mi can be transformed into a deterministic n-agent choice model $$M^d$$Md, such that $$M^i$$Mi is a bounded morphic image of $$M^d$$Md. This generalizes an earlier result from Van Benthem and Pacuit [16] about finite two-player choice models. It further strengthens the link between STIT logic and game theory, because deterministic choice models correspond in a straightforward way to normal game forms, and choice models are generally used to interpret STIT logic. Frederik Van De Putte, Allard Tamminga, Hein Duijf ### Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus This paper positively solves an open problem if it is possible to provide a Hilbert system to Epistemic Logic of Friendship (EFL) by Seligman, Girard and Liu. To find a Hilbert system, we first introduce a sound, complete and cut-free tree (or nested) sequent calculus for EFL, which is an integrated combination of Seligman’s sequent calculus for basic hybrid logic and a tree sequent calculus for modal logic. Then we translate a tree sequent into an ordinary formula to specify a Hilbert system of EFL and finally show that our Hilbert system is sound and complete for an intended two-dimensional semantics. Katsuhiko Sano ### The Dynamic Logic of Stating and Asking: A Study of Inquisitive Dynamic Modalities Inquisitive dynamic epistemic logic (IDEL) extends public announcement logic incorporating ideas from inquisitive semantics. In IDEL, the standard public announcement action can be extended to a more general public utterance action, which may involve a statement or a question. While uttering a statement has the effect of a standard announcement, uttering a question typically leads to new issues being raised. In this paper, we investigate the logic of this general public utterance action. We find striking commonalities, and some differences, with public announcement logic. We show that dynamic modalities admit a set of reduction axioms, which allow us to turn any formula of IDEL into an equivalent formula of static inquisitive epistemic logic. This leads us to establish several complete axiomatizations of IDEL, corresponding to known axiomatizations of public announcement logic. Ivano Ciardelli ### The Stubborn Non-probabilist—‘Negation Incoherence’ and a New Way to Block the Dutch Book Argument We rigorously specify the class of nonprobabilistic agents which are, we argue, immune to the classical Dutch Book argument. We also discuss the notion of expected value used in the argument as well as sketch future research connecting our results to those concerning incoherence measures. Leszek Wroński, Michał Tomasz Godziszewski ### Conjunction and Disjunction in Infectious Logics In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. Hitoshi Omori, Damian Szmuc ### On the Concept of a Notational Variant In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic. Alexander W. Kocurek ### Conditional Doxastic Logic with Oughts and Concurrent Upgrades In this paper, we model the behavior of an epistemic agent that faces a deliberation against a background of oughts, beliefs and information. We do this by introducing a dynamic epistemic logic where ought operators are defined and release of information makes beliefs and oughts co-vary. The static part of the logic extends single-agent Conditional Doxastic Logic by combining dyadic operators for conditional beliefs and oughts that are interpreted over two distinct preorders. The dynamic part of the logic introduces concurrent upgrade operators, which are interpreted on operations that change the two preorders in the same way, thus generating the covariation of beliefs and oughts. The effect of the covariation is that, after receiving new information, the agent will change both her beliefs and her oughts accordingly, and in deliberating, she will pick up the best states among those she takes to be the most plausible. Roberto Ciuni ### On Subtler Belief Revision Policies This paper proposes three subtle revision policies that are not propositionally successful (after a single application the agent might not believe the given propositional formula), but nevertheless are not propositionally idempotent (further applications might affect the agent’s epistemic state). It also compares them with two well-known revision policies, arguing that the subtle ones might provide a more faithful representation of humans’ real-life revision processes. ### Topo-Logic as a Dynamic-Epistemic Logic We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announcements’ in the style of Bjorndahl [5]. We give a complete axiomatization for this “Dynamic Topo-Logic”, which is in a sense simpler than the standard axioms of topologic. Our completeness proof is also more direct (making use of a standard canonical model construction). Moreover, we study the relations between this extension and other known logical formalisms, showing in particular that it is co-expressive with the simpler (and older) logic of interior and global modality [1, 4, 10, 14]. This immediately provides an easy decidability proof (both for topologic and for our extension). Alexandru Baltag, Aybüke Özgün, Ana Lucia Vargas Sandoval ### Strategic Knowledge of the Past in Quantum Cryptography We propose an epistemic strategy logic with future and past time operators, called $$\text {SLKP}$$SLKP, for Strategy Logic with Knowledge of the Past. With $$\text {SLKP}$$SLKP we can model mutually observed moves/actions in strategic contexts. In a semantic game, agents may completely or partially observe other agents’ moves, their moves may depend on their knowledge of other players’ strategies, and their knowledge may depend on the history of their own or other’s moves. The logic $$\text {SLKP}$$SLKP also allows us to describe temporal properties involving past, future, and composed tenses such as future perfect or counterfactual assertions. We illustrate SLKP by formalising the quantum cryptography protocol BB84, with the purpose to initiate an integrated epistemic and strategic treatment of agent interactions in quantum systems. Christophe Chareton, Hans van Ditmarsch ### Enumerative Induction and Semi-uniform Convergence to the Truth I propose a new definition of identification in the limit, also called convergence to the truth, as a new success criterion that is meant to complement, but not replace, the classic definition due to Putnam (1963) and Gold (1967). The new definition is designed to explain how it is possible to have successful learning in a kind of scenario that the classic account ignores—the kind of scenario in which the entire infinite data stream to be presented incrementally to the learner is not presupposed to completely determine the correct learning target. For example, suppose that a scientists is interested in whether all ravens are black, and that she will never observe a counterexample in her entire life. This still leaves open whether all ravens (in the universe) are black. From a purely mathematical point of view, the proposed definition of convergence to the truth employs a convergence concept that generalizes net convergence and sits in between pointwise convergence and uniform convergence. Two results are proved to suggest that the proposed definition provides a success criterion that is by no means weak: (i) Between the proposed identification in the limit and the classic one, neither implies the other. (ii) If a learning method identifies the correct target in the limit in the proposed sense, any U-shaped learning involved therein has to be essentially redundant. I conclude that we should have (at least) two success criteria that correspond to two senses of identification in the limit: the classic one and the one proposed here. They are complementary: meeting any one of the two is good; meeting both at the same time, if possible, is even better. Hanti Lin ### How to Make Friends: A Logical Approach to Social Group Creation This paper studies the logical features of social group creation. We focus on the mechanisms which indicate when agents can form a team based on the correspondence in their set of features (behavior, opinions, etc.). Our basic approach uses a semi-metric on the set of agents, which is used to construct a network topology. Then it is extended with epistemic features to represent the agents’ epistemic states, allowing us to explore group-creation alternatives where what matters is not only the agent’s differences but also what they know about them. We use tools of dynamic epistemic logic to study the properties of different strategies to network formations. ### Examining Network Effects in an Argumentative Agent-Based Model of Scientific Inquiry In this paper we present an agent-based model (ABM) of scientific inquiry aimed at investigating how different social networks impact the efficiency of scientists in acquiring knowledge. The model is an improved variant of the ABM introduced in [3], which is based on abstract argumentation frameworks. The current model employs a more refined notion of social networks and a more realistic representation of knowledge acquisition than the previous variant. Moreover, it includes two criteria of success: a monist and a pluralist one, reflecting different desiderata of scientific inquiry. Our findings suggest that, given a reasonable ratio between research time and time spent on communication, increasing the degree of connectedness of the social network tends to improve the efficiency of scientists. AnneMarie Borg, Daniel Frey, Dunja Šešelja, Christian Straßer ### Substructural Logics for Pooling Information This paper puts forward a generalization of the account of pooling information – offered by standard epistemic logic – based on intersection of sets of possible worlds. Our account is based on information models for substructural logics and pooling is represented by fusion of information states. This approach yields a representation of pooling related to structured communication within groups of agents. It is shown that the generalized account avoids some problematic features of the intersection-based approach. Our main technical result is a sound and complete axiomatization of a substructural epistemic logic with an operator expressing pooling. Vít Punčochář, Igor Sedlár ### Logical Argumentation Principles, Sequents, and Nondeterministic Matrices The concept of “argumentative consequence” is introduced, involving only the attack relations in Dung-style abstract argumentation frames. Collections of attack principles of different strength, referring to the logical structure of claims of arguments, lead to new characterizations of classical and nonclassical consequence relations. In this manner systematic relations between structural constraints on abstract argumentation frames, sequent rules, and nondeterministic matrix semantics for corresponding calculi emerge. Esther Anna Corsi, Christian G. Fermüller ### Non-triviality Done Proof-Theoretically It is well known that naive theories of truth based on the three-valued schemes K3 and LP are non-trivial. Rohan French, Shawn Standefer ### Sette’s Logics, Revisited One of the simple approaches to paraconsistent logic is in terms of three-valued logics. Assuming the standard behavior with respect to the “classical"values, there are only two possibilities for paraconsistent negation, namely the negation of the Logic of Paradox and the negation of Sette’s logic P$$^1$$1. From a philosophical perspective, the paraconsistent negation of P$$^1$$1 is less discussed due to the lack of an intuitive reading of the third value. Based on these, the aim of this paper is to fill in the gap by presenting a semantics for P$$^1$$1 à la Jaśkowski which sheds some light on the intuitive understanding of Sette’s logic. A variant of P$$^1$$1 known as I$$^1$$1 will be also discussed. Hitoshi Omori ### Multi-agent Belief Revision Using Multisets Revising a belief set K with a proposition a results in a theory that entails a. We consider the case of a multiset of beliefs, representing the beliefs of multiple agents, and define its revision with a multiset of desired beliefs the group of agents should have. We give graph theoretic semantics to this revision operation and we postulate two classes of distance-based revision operators. Further, we show that this multiset revision operation can express the merging of the beliefs of multiple agents. Konstantinos Georgatos ### Boosting Distance-Based Revision Using SAT Encodings Belief revision has been studied for more than 30 years, and the theoretical properties of the belief revision operators are now well-known. Contrastingly, there are almost no practical applications of these operators. One of the reasons is the computational complexity of the corresponding inference problem, which is typically NP-hard and coNP-hard. Especially, existing implementations of belief revision operators are capable to solve toy instances, but are still unable to cope with real-size problem instances. However, the improvements achieved by SAT solvers for the past few years have been very impressive and they allow to tackle the solving of instances of inference problems located beyond NP. In this paper we describe and evaluate SAT encodings for a large family of distance-based belief revision operators. The results obtained pave the way for the practical use of belief revision operators in large-scale applications. Sébastien Konieczny, Jean-Marie Lagniez, Pierre Marquis ### Counterfactuals in Nelson Logic We motivate and develop an extension of Nelson’s constructive logic N3 that adds a counterfactual conditional to the existing setup. After developing the semantics, we will outline how our account will be able to give a nice analysis of natural language counterfactuals. In particular, the account does justice to the intuitions and arguments that have lead Alan Hájek to claim that most conditionals are false, but assertable, without actually forcing us to endorse that rather uncomfortable claim. Andreas Kapsner, Hitoshi Omori ### A Dynamic Approach to Temporal Normative Logic State commands refer to states, not actions. They have a temporal dimension explicitly or implicitly. They indirectly change what we are permitted, forbidden or obligated to do. This paper presents $${{\mathrm{\mathsf {DTNL}}}}{}$$DTNL, a deontic logic meant to handle state commands based on the branching-time temporal logic $$\mathsf {PCTL}^*$$PCTL∗. The models of $${{\mathrm{\mathsf {DTNL}}}}{}$$DTNL are trees with bad states, which are identified by a propositional constant $$\mathfrak {b}$$b introduced in the language. To model state commands, a dynamic operator that adds states to the extension of $$\mathfrak {b}$$b is introduced. Fengkui Ju, Gianluca Grilletti ### Labelled Sequent Calculus for Inquisitive Logic A contraction-free and cut-free labelled sequent calculus $$\mathsf {GInqL}$$GInqL for inquisitive logic is established. Labels are defined by a set-theoretic syntax. The completeness of $$\mathsf {GInqL}$$GInqL is shown by the equivalence between the Hilbert-style axiomatic system and sequent system. Jinsheng Chen, Minghui Ma ### Testing Minimax for Rational Ignorant Agents Richard Pettigrew [13, 14] defends the following theses: (1) epistemic disutility can be measured with strictly proper scoring rules (like the Brier score) and (2) at the beginning of their credal lives, rational agents ought to minimize their worst-case epistemic disutility (Minimax). This leads to a Principle of Indifference for ignorant agents. However, Pettigrew offers no argument in favour of Minimax, suggesting that the epistemic conservatism underlying it is a “normative bedrock.” Is there a way to test Minimax? In this paper, we argue that, since Pettigrew’s Minimax is impermissive, an argument against credence permissiveness constitutes an argument in favour of Minimax, and that arguments for credence permissiveness are arguments against Minimax. Marc-Kevin Daoust, David Montminy ### A Reconstruction of Ex Falso Quodlibet via Quasi-Multiple-Conclusion Natural Deduction This paper is intended to offer a philosophical analysis of the propositional intuitionistic logic formulated as $$\textit{NJ}$$NJ. This system has been connected to Prawitz and Dummett’s proof-theoretic semantics and its computational counterpart. The problem is, however, there has been no successful justification of ex falso quodlibet (EFQ): “From the absurdity ‘$$\bot$$⊥’, an arbitrary formula follows.” To justify this rule, we propose a novel intuitionistic natural deduction with what we call quasi-multiple conclusion. In our framework, EFQ is no longer an inference deriving everything from ‘$$\bot$$⊥’, but rather represents a “jump” inference from the absurdity to the other possibility. Yosuke Fukuda, Ryosuke Igarashi ### A Nonmonotonic Modal Relevant Sequent Calculus Motivated by semantic inferentialism and logical expressivism proposed by Robert Brandom, in this paper, I submit a nonmonotonic modal relevant sequent calculus equipped with special operators, □ and R. The base level of this calculus consists of two different types of atomic axioms: material and relevant. The material base contains, along with all the flat atomic sequents (e.g., Γ0, p \|~0 p), some non-flat, defeasible atomic sequents (e.g., Γ0, p \|~0 q); whereas the relevant base consists of the local region of such a material base that is sensitive to relevance. The rules of the calculus uniquely and conservatively extend these two types of nonmonotonic bases into logically complex material/relevant consequence relations and incoherence properties, while preserving Containment in the material base and Reflexivity in the relevant base. The material extension is supra-intuitionistic, whereas the relevant extension is stronger than a logic slightly weaker than R. The relevant extension also avoids the fallacies of relevance. Although the extended material consequence relation is defeasible and insensitive to relevance, it has local regions of indefeasibility and relevance (the latter of which is marked by the relevant extension). The newly introduced operators, □ and R, codify these local regions within the same extended material consequence relation. Shuhei Shimamura ### A Formalization of the Greater Fools Theory with Dynamic Epistemic Logic The greater fools explanation of financial bubbles says that traders are willing to pay more for an asset than they deem it worth, because they anticipate they might be able to sell it to someone else for an even higher price. As agents’ beliefs about other agents’ beliefs are at the heart of the greater fools theory, this paper comes to formal terms with the theory by translating the phenomenon into the language and models of dynamic epistemic logic. By presenting a formalization of greater fools reasoning, structural insights are obtained pertaining to the structure of its higher-order content and the role of common knowledge. Hanna S. van Lee ### On Axiomatization of Epistemic GDL The Game Description Language (GDL) has been introduced as an official language for specifying games in the AAAI General Game Playing Competition since 2005. It was originally designed as a declarative language for representing rules of arbitrary games with perfect information. More recently, an epistemic extension of GDL, called EGDL, has been proposed for representing and reasoning about imperfect information games. In this paper, we develop an axiomatic system for a variant of EGDL and prove its soundness and completeness with respect to the semantics based on the epistemic state transition model. With a combination of action symbols, temporal modalities and epistemic operators, the completeness proof requires novel combinations of techniques used for completeness of propositional dynamic logic and epistemic temporal logic. We demonstrate how to use the proof theory for inferring game properties from game rules. Guifei Jiang, Laurent Perrussel, Dongmo Zhang ### Putting More Dynamics in Revision with Memory We have proposed in previous works [14, 15] a construction that allows to define operators for iterated revision from classical AGM revision operators. We called these operators revision operators with memory and show that the operators obtained have nice logical properties. But these operators can be considered as too conservative, since the revision policy of the agent, encoded as a faithful assignment, does not change during her life. In this paper we propose an extension of these operators, that aims to add more dynamics in the revision process. Sébastien Konieczny, Ramón Pino Pérez ### An Empirical Route to Logical ‘Conventionalism’ The laws of classical logic are taken to be logical truths, which in turn are taken to hold objectively. However, we might question our faith in these truths: why are they true? One general approach, proposed by Putnam [8] and more recently Dickson [3] or Maddy [5], is to adopt empiricism about logic. On this view, logical truths are true because they are true of the world alone – this gives logical truths an air of objectivity. Putnam and Dickson both take logical truths to be true in virtue of the world’s structure, given by our best empirical theory, quantum mechanics. This assumes a determinate logical structure of the world given by quantum mechanics. Here, I argue that this assumption is false, and that the world’s logical structure, and hence the related ‘true’ logic, are underdetermined. This leads to what I call empirical conventionalism. Eugene Chua ### Beating the Gatecrasher Paradox with Judiciary Narratives A probabilistic model for the narrative approach to reasoning in legal fact-finding is developed and applied to the gatecrasher paradox. Rafal Urbaniak ### Distributed Knowledge Whether (Extended Abstract) As is known, by putting their knowledge together, agents can obtain distributed knowledge. However, by pooling their non-ignorance, agents can only obtain distributed knowledge as to whether something holds, rather than distributed knowledge (of something). Jie Fan ### A Note on Belief, Question Embedding and Neg-Raising The epistemic verb to believe does not embed polar questions, unlike the verb to know. After reviewing this phenomenon, I propose an explanation which connects the neg-raising behavior of belief with its embedding patterns (following [14]). I use dynamic epistemic logic to model the presuppositions and the effects associated with belief assertions. Michael Cohen ### Distributed Knowing Whether (Extended Abstract) Standard epistemic logic studies reasoning patterns about ‘knowing that’, where interesting group notions of ‘knowing that’ arise naturally, such as distributed knowledge and common knowledge. In recent research, other notions of knowledge are also studied, such as ‘knowing whether’, ‘knowing how’, and so on. It is natural to ask what are the group notions of these non-standard knowledge expressions. This paper makes an initial attempt in this line, by looking at the notion corresponding to distributed knowledge in the setting of ‘knowing whether’. We introduce the distributed know-whether operator, and give complete axiomatizations of the resulting logics over arbitrary or $$\mathcal {S}$$S5 frames, based on the corresponding axiomatizations of ‘knowing whether’. Xingchi Su ### A Causal Theory of Speech Acts In speech acts, a speaker utters sentences that might affect the belief state of a hearer. To formulate causal effects in assertive speech acts, we introduce a logical theory that encodes causal relations between speech acts, belief states of agents, and truth values of sentences. We distinguish trustful and untrustful speech acts depending on the truth value of an utterance, and distinguish truthful and untruthful speech acts depending on the belief state of a speaker. Different types of speech acts cause different effects on the belief state of a hearer, which are represented by the set of models of a causal theory. Causal theories of speech acts are also translated into logic programs, which enables one to represent and reason about speech acts in answer set programming. Chiaki Sakama ### An Axiomatisation for Minimal Social Epistemic Logic A two-dimensional modal logic, intended for applications in social epistemic logic, with one dimension for agents and the other for epistemic states is given. The language has hybrid logic devices for agents, as proposed in earlier papers by Seligman, Liu and Girard. We give an axiomatisation and a proof of its completeness. Liang Zhen ### Relief Maximization and Rationality This paper introduces the concept of relief maximization in decisions and games and shows how it can explain experimental behavior, such as asymmetric dominance and decoy effects. Next, two possible evolutionary explanations for the survival of relief-based behavior are sketched. Paolo Galeazzi, Zoi Terzopoulou ### Reason to Believe In this paper we study the relation between nonmonotonic reasoning and belief revision. Our main conceptual contribution is to suggest that nonmonotonic reasoning guides but does not determine an agent’s belief revision. To be adopted as beliefs, defeasible conclusions should remain stable in the face of certain bodies of information. This proposal is formalized in what we call a two-tier semantics for nonmonotonic reasoning and belief revision. The main technical result is a sound and complete axiomatization for this semantic. Chenwei Shi, Olivier Roy ### Justification Logic with Approximate Conditional Probabilities The importance of logics with approximate conditional probabilities is reflected by the fact that they can model non-monotonic reasoning. We introduce a new logic of this kind, $$\mathsf {CPJ}$$CPJ, which extends justification logic and supports non-monotonic reasoning with and about evidences. Zoran Ognjanović, Nenad Savić, Thomas Studer ### From Concepts to Predicates Within Constructivist Epistemology In this research constructivist epistemology provides a ground for conceptual analysis of concept construction, conception production, and concept learning processes. Relying on a constructivist model of knowing, this research will make an epistemological and logical linkage between concepts and predicates.	2021-05-09 01:29:19	{"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": 0.5769725441932678, "perplexity": 1542.638169475818}, "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/1620243988953.13/warc/CC-MAIN-20210509002206-20210509032206-00348.warc.gz"}
https://falumuzeum.eu/dio-remastered-pevso/b584ad-latex-highlight-paragraph	latex_engine: LaTeX engine for producing PDF output. 2020, Mar 04. Colours can be brought in the LaTeX document by importing the package color or xcolor. There are a many quoting environments with many different outputs. Hyphenation I. This is a paragraph of text. castersugar Fewdropsofvanillaessence 3largeeggs 6oz. ( \paragraph is a sectioning command and has nothing to do with text paragraphs.) If you want to delete the highlighted, crossed-out, or underlined formatting to your text, just click the … 2. Large $\LaTeX$ equations that do not fit inline within a paragraph may be written as display equations using a fenced code block with the "language" math as in the example below. See Lengths for more details. paper) 1. To do alternating row colors, you can also include the xcolor package with the table option (i.e. Feel free to sprinkle your LaTeX documents with all the multiline comments you need now. To unindent an indented paragraph: Click the Decrease Indent command button in the Home tab’s Paragraph group or press Ctrl+Shift+M. Syntax colouring will highlight commands in blue and can make it easier to spot mistakes. Unlike the paragraph and subparagraph styles, it is not merged with the subsequentparagraph. To use it, we include the following line in the preamble: \usepackage{graphicx} The command \graphicspath{ {./images/} } tells L a T e X that the images are kept in a folder named images under the directory of the main document.. \end{document} 3 Open an example in Overleaf. So if you add 10 blank lines, you’re still only going to have one paragraph. 2015] LaTeX fills lines and adjusts spacing between words to produce an aesthetically pleasing result. It works like a paragraph whose width is given by the user. LaTeX will classify anything preceeded by a blank line or defined with a \par marker to be a new paragraph. Includes index. Highlighting paragraphs in Latex June 08, 2011 When revising a document, I often want to highlight my changes, so my collaborators can easily see what I changed. \underline works for single words, but it puts everything in a horizontal box and long text isn't wrapped anymore. Everything from the percent symbol up to the end of line is ignored by LaTeX. Those purposes might be to color text or highlight text by changing its background color. LaTeX and quoting environments. You may recall from Tutorial 7 — Formatting 1 the intro- duction of font formatting commands, such as \textrm, \textit, \textbf, etc. The underline command doesn't really change your font, but it's sometimes used to highlight text anyway. The first one is … You may even want to do both, highlight colored text. Example to highlight the … A build command can be specified via the layer variable latex-build-command.This variable can be set to any of the entities in TeX-command-list, including any custom entries you may have added there.. Overfull and underfull boxes. A paragraph box is specially used when the user is working within a tabular environment. Unlike most LaTeX formatting, this one’s pretty simple. Select the text by clicking and holding the left mouse button and dragging the cursor over the text. Paper Writing with LaTeX Jia-Bin Huang Department of Electrical and Computer Engineering Virginia Tech jbhuang@vt.edu. \end{comment} That's all you need to do. 3.1.3 amsmath—Nonbreaking dashes The amsmath package, extensively discussed in Chapter 8, also oﬀers one com-mand for use within paragraphs. Manual spacing is a matter of macro writing and package creation. Open an example in Overleaf. While preparing a document in LaTeX, you may want to use colors for different purposes. L a T e X allows two writing modes for mathematical expressions: the inline mode and the display mode. Those commands enable you to use Bold, Italic, Underline, Typewriter fonts and much more in LaTeX. Font sizes. Paragraph Boxes. This syntax is paired with the inline syntax for Footnote references. \usepackage[table]{xcolor}), and immediately preceding the tabular environment use the command \rowcolors{start}{color1}{color2} — this will produce a table with colored rows, starting at the row indicated by start, with odd rows colored color1 and even rows colored color2. You can select both at once, and apply the List Bullet style to both at once. \section {The Next Section} Here is the second paragraph\footnote {with a footnote}. This is another paragraph of text. A brief document to illustrate how to use \LaTeX. margarine 6oz. This is very useful. Use default if neither package is to be used, which means citations will be processed … To do that, click anywhere in one paragraph. To indent a paragraph one tab stop from the left: Click the Increase Indent command button in the Home tab’s Paragraph group or press Ctrl+M. It is against LaTeX philosophy to insert spaces manually and will usually lead to bad formatting. Go ahead and open Word and enter in the text that you would like to highlight and transfer over to PowerPoint. The default settings highlight paragraph starts with indentation instead of vertical spacing, so the behavior you describe comes from using some package or document class option. \usepackage{moredefs}\usepackage[mla]{lips} Elsewhere \olips the dots are normally set with full word spaces between them \lips. An example would be this paragraph. Yet, there is an alternative that offers a little more ﬂexibility. The command \parbox typesets the content which is given in its second argument and its first argument gives the width of the box. You can use a simple tag to insert a line break. Latex to render mathematical and scientific writing. Math into LaTeX : an introduction to LaTeX and AMS-LaTeX / George Gr¨atzer p. cm. To this 3. That will give you a bullet at the beginning of the paragraph. This example shows how to use the smallest available font (tiny) in L a T e X and the small caps style. The highlight_languages option allows you to specify additional languages that are supported by highlight.js, but are not considered “common” and therefore are not supported by default. ò Type the following: \documentclass[a4paper,12pt]{article} \begin{document} A sentence of text. Once the text is selected, a pop-up window appears, and you can click the highlight button to add highlighting. Then when you want to create a multiline comment, just do this: \begin{comment} This is my comment. Completely blank lines in the input file break your text into paragraphs. From the Style box on the toolbar (Figure 1), select List Bullet. \end {abstract} \chapter {Introduction} \section {The First Section} This is a simple \LaTeX \␣document. The spaces between words and sentences, between paragraphs, sections, subsections, etc. any way you like to highlight the structure of your manuscript and make it easier to edit. Just end a line with two or more spaces, then type return. You often end up having to use a line break while writing text, there isn’t really a need to start a new paragraph by inserting two lines gap. self-raisingﬂour 1–2tblsp. Click in the first paragraph that you want bulleted. Ingredients 6oz. We have also used the backslash symbol \ which indicates that we are using a LaTeX command, as in \LaTeX or \today. example would be this paragraph. Computerized typesetting. citation_package: The LaTeX package to process citations, natbib or biblatex. First, you need to \includepackage[table]{xcolor} at the top of the LaTeX document. Note that it can span multiple lines. Writing Gatsby Articles in Markdown and LaTeX. math f(a) = \frac{1}{2\pi}\int_{0}^{2\pi} (\alpha+R\cos(\theta))d\theta Footnotes. In LaTeX there's not a single quoting environment. In this tutorial, we’re going to discuss how to color and highlight text, and how to define our own colors. To change the … How to make nice-looking framed boxes in LaTeX articlesExamples of framed, mdframed, fancybox and bclogo packages Vesa Linja-aho Metropolia July 29, 2011 Vesa Linja-aho How to make nice-looking framed boxes in LaTeX articles 2. This means you can have comments in your source code to remind you what a particular part of your code is doing. Apart from that, both the packages provide a common set of commands for colour manipulation. AMS-LaTeX. ... paragraph 1. paragragh 2. paragrah 1 blank line also means break to new line. This post focalizes on the basic quotation commands, perfect to highlight parts of the text without changing too … As you see, the way the equations are displayed depends on the delimiter, in this case and . The \parbox example demonstrates a much more general issue: when processing your LaTeX code the TeX engine being used to typeset your document (pdfTeX, XeTeX or LuaTeX) might consider that LaTeX’s requests result in typeset content that does not “fit nicely” within the confines of the box provided or requested. Latex can not manage images by itself, so we need to use the graphicx package. For example, if you want source code highlighting for Go and clojure in all pages, set highlight_languages = ["go", "clojure"] in params.toml . ... •DO use \paragraph \subsection{Datasets} \paragraph{Datatset A} \paragraph{Datatset B} ... •Examples that highlight the key idea of the paper [Parikh and Grauman 2011] [Huang et al. is determined automatically by LaTeX. Mathematics printing–Computer programs. Options are "pdflatex", "lualatex", and "xelatex". 3. Or leave an empty line. Ever want to highlight table rows in a LaTeX document? HTML equivalent: Output Result: Colab Notebook • Line breaks. Board index LaTeX Editors LyX Ask a question LaTeX Community Announcements Community talk Comments & Wishes New Members LaTeX Text Formatting Graphics, Figures & Tables Math & Science Fonts & Character Sets Page Layout Document Classes General LaTeX's Friends BibTeX, biblatex and biber MakeIndex, Nomenclature, Glossaries and Acronyms Here is the first paragraph. To turn this off, put the following at the top of the document or in a .sty file: \setlength{\parindent}{0in} Works wonders. As a default, LaTeX indents the first line of each paragraph. In the document, click Add-ons / LaTeX Syntax Highlight, which will format the whole document; Note: it is worth cutting and re-pasting the whole document without formatting first; Example From this. xcolor package is more flexible and supports a larger number of colour models. ò Go to the Format menu and select Syntax Coloring, then LaTeX. hotwater Method Beat margarine and caster sugar … Do that in the LaTeX document preamble. : alk. 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https://randompermutations.com/category/research/page/2/	# Babai’s conjecture for classical groups with random generators Yesterday Urban Jezernik and I uploaded to the arxiv our preprint Babai’s conjecture for high-rank classical groups with random generators. I want to use this space to explain what our work is about and where it fits in the literature. To try to cater for a possibly wide range of mathematical backgrounds, I will start friendly and informal and get progressively more precise and technical. Thanks in advance for your attention! The subject matter is diameters of groups. A familiar example is Rubik’s cube, which has ${n \approx 4 \times 10^{19}}$ (${40}$ billion billion) possible configurations. The set of all configurations of the cube can be viewed as a group ${R}$. (For the exact group structure, see wikipedia.) The standard generating set ${S}$ consists of rotations of any of the 6 faces, a set of size ${19}$ (including the do-nothing operation). The diameter is the maximum number of moves it takes to solve the cube from any configuration. Now the number of configurations a distance ${d}$ from the origin, denoted ${S^d}$, is at most ${19^d}$: at each step, choose one of the ${19}$ possible moves. Therefore the diameter cannot be smaller than $\displaystyle \left\lceil\frac{\log n}{\log 19}\right\rceil = 16.$ The exact answer is not that much larger: 20. The size of ${S^d}$ is plotted below, which exhibits almost perfect exponential growth, until the end when it runs out of space. In general, let ${G}$ be a finite group and ${S}$ a set of generators. Assume ${S = S^{-1}}$ and ${1 \in S}$. The Cayley graph ${\mathrm{Cay}(G, S)}$ is the graph with vertex set ${G}$ and an edge for every pair ${\{g, gs\}}$ with ${g\in G}$ and ${s \in S \setminus \{1\}}$. The diameter ${\mathrm{diam}\,\,\Gamma}$ of a graph ${\Gamma}$ is the “longest shortest path”: the distance between two vertices is the length of the shortest path between them, and the diameter is the greatest distance between any two vertices. The diameter of a Cayley graph ${\mathrm{Cay}(G, S)}$ is the same as the smallest ${d}$ such that ${S^d = G}$. One expects similar behaviour as we saw for the Rubik’s cube group ${R}$ for any group ${G}$ which is sufficiently nonabelian (so that most products of generators are different, causing the balls ${S^d}$ to expand at about the rate they do in a tree). The most ideal form of nonabelianness is simplicity, and Babai’s conjecture is a precise form of this intuition for finite simple groups. The conjecture states that $\displaystyle \mathrm{diam}\, \mathrm{Cay}(G, S) \leq (\log \|G\|)^{O(1)},$ uniformly over finite simple groups ${G}$ and generating sets ${S}$. The trivial lower bound is ${\log_2\|G\|}$, so the conjecture states that the truth is within a power of this trivial lower bound. By the classification of finite simple groups, Babai’s conjecture breaks naturally into three parts: 1. finite groups ${X(q)}$ of a fixed Lie type ${X}$ over a field of order ${q}$ with ${q \to \infty}$; 2. quasisimple classical groups of dimension ${n}$ with ${n \to \infty}$ and ${q}$ arbitrary: namely, the special linear group ${\mathrm{SL}_n(q)}$, the symplectic group ${\mathrm{Sp}_n(q)}$, the derived subgroup of the orthogonal group ${O_n(q)'}$, and the special unitary group ${\mathrm{SU}_n(q)}$; 3. alternating groups ${A_n}$. The first part is the “bounded rank” case, and the latter two parts make up the “unbounded rank” case (and you can loosely consider ${A_n}$ to be ${\mathrm{PSL}_n(1)}$, if you want). The bounded rank case of Babai’s conjecture is completely resolved, following breakthrough work of Helfgott, Pyber–Szabo, and Breuillard–Green–Tao. Even stronger conjectures can be made in this case. For instance, it may be that the graphs ${\mathrm{Cay}(G, S)}$ have a uniform spectral gap, and in particular that $\displaystyle \mathrm{diam}\,\,\mathrm{Cay}(G,S) \leq O(\log\|G\|),$ with the implicit constant depending only on the rank. This is true if the generators are random, by work of Breuillard–Green–Guralnick–Tao. Personally I am most interested in high-rank groups, such as the alternating group ${A_n}$ (cf. the name of this blog). In the case of ${A_n}$, Babai’s conjecture (a much older conjecture in this case) asserts simply that $\displaystyle \mathrm{diam}\, \mathrm{Cay}(A_n, S) = n^{O(1)}.$ For example, if the generating set consists just of the cycles ${(12)}$ and ${(12\cdots n)^{\pm1}}$, then the the diameter is comparable to ${n^2}$. A folklore conjecture asserts that this is the worst case up to a constant factor. The strongest results in this direction are the result of Helfgott–Seress (see also this later paper of Helfgott) which states that $\displaystyle \mathrm{diam}\, \mathrm{Cay}(A_n, S) \leq \exp O((\log n)^{4 + o(1)}),$ which is quasipolynomial rather than polynomial, and the result of Helfgott–Seress–Zuk which states that, if the generators are random, $\displaystyle \mathrm{diam}\, \mathrm{Cay}(A_n, S) \leq n^2 (\log n)^{O(1)}.$ Thus we are “almost there” with ${A_n}$. On the other hand, we are still a long way off for high-rank classical groups such as ${\mathrm{SL}_n(q)}$. Such a group has size comparable to ${q^{n^2}}$, and Babai’s conjecture asserts that $\displaystyle \mathrm{diam}\, \mathrm{Cay}(G, S) \leq (n \log q)^{O(1)}.$ In this case the best bound we have is one of Halasi–Maroti–Pyber–Qiao (building on Biswas–Yang), which states $\displaystyle \mathrm{diam}\, \mathrm{Cay}(G, S) \leq q^{O(n (\log n)^2)}.$ In many ways ${A_n}$ and, say, ${\mathrm{SL}_n(2)}$ behave similarly, but in other ways they are very different. For example, suppose your generating set for ${A_n}$ contains a ${3}$-cycle. Then because there are at most ${n^3}$ ${3}$-cycles in all, it is clear that every ${3}$-cycle has length at most ${n^3}$ in your generators, and hence every element of ${A_n}$ has length at most ${n^4}$, so the conjecture is trivial in this case. On other hand, suppose your generating set for ${\mathrm{SL}_n(2)}$ contains the closest analogue to a ${3}$-cycle, a transvection. Unfortunately, there is not a trivial argument in this case, because the number of transvections is roughly ${2^{2n-1}}$. Indeed this is a difficult problem that was solved only earlier this year by Halasi. However, if the size of the field ${q}$ is bounded, and you have at least ${q^C}$ random generators, then Urban and I know what to do. Under these conditions we show that $\displaystyle \mathrm{diam}\, \mathrm{Cay}(G, S) \leq n^{O(1)},$ as conjectured by Babai. Roughly, the recipe is the following. Let ${S}$ be your set of random generators. We want to show that we can reach everywhere in ${G}$ using ${n^{O(1)}}$ steps in ${S}$. 1. Start with a random walk of length ${n/10}$. All of the points you get to will have “large support”, in the sense that ${g-1}$ has no large eigenspace. 2. Use explicit character bounds and the second moment method to show that, within the first ${n/10}$ steps, you will reach any specified large normal subset ${\mathfrak{C}}$. 3. Choose ${\mathfrak{C}}$ so that every element of ${\mathfrak{C}}$ has a ${n^{O(1)}}$ power which has minimal support. Hence we can reach such an element with ${n^{O(1)}}$ steps. 4. Now act on that element by conjugation. This looks much like the standard action of ${G}$ on the natural module ${\mathbf{F}_q^n}$. We show that with high probability the Schreier graph of this action actually has a spectral gap, and in particular logarithmic diameter. Hence we can cover the entire conjugacy class. 5. Every element of ${G}$ can be written as the product of ${O(n)}$ such elements, so every element of ${G}$ has length ${n^{O(1)}}$ in ${S}$. Some of these ideas are recycled from my previous paper with Stefan Virchow (discussed in this earlier post). Probably the most interesting part is step 4, which generalizes a result of Friedman–Joux–Roichman–Stern–Tillich for the symmetric group. The Schreier graph of the usual action of ${S_n}$ on ${\{1, \dots, n\}}$ is one of the standard models for a random bounded-degree regular graph, and the spectral gap of this graph is well-studied. The graph we care about on the other hand has vertex set ${\mathbf{F}_q^n \setminus \{0\}}$, with ${v}$ joined to ${gv}$ for each ${g}$ in our set of random generators. We found experimentally that, spectrally, this graph is virtually indistinguishable from the random regular graph. In particular, there should be a spectral gap for at least ${2}$ random generators. Our method needs ${q^C}$ generators. The reason is that we have great difficulty saying anything about the behaviour of the random walk after about ${n}$ steps, or indeed somewhat fewer depending on the type (linear/symplectic/unitary/orthogonal) of the group. To get around this problem we need to ensure that the random walk covers the whole Schreier graph before this critical time, so we need enough generators so that the random walk spreads quickly enough. # Mixing time of a pseudorandom number generator Today I was due to speak at the Isaac Newton Institute’s workshop on “Interactions between group theory, number theory, combinatorics and geometry”, which has obviously been canceled. I was going to speak about my work on the Hall–Paige conjecture: see this earlier post. Meanwhile Péter Varjú was going to speak about some other joint work, which I’d like to share with you now. Consider (if you can consider anything other than coronaviral apocalapyse right now) the random process ${(X_n)}$ in ${\mathbf{Z}/p\mathbf{Z}}$ defined in the following way: ${X_0 = 1}$ (or any initial value), and for ${n\geq 1}$ $\displaystyle X_n = aX_{n-1} + b_n. \ \ \ \ \ (1)$ Here we take ${a}$ to be a fixed integer and ${b_1, b_2, \dots}$ a sequence of independent draws from some finitely supported measure ${\mu}$ on ${\mathbf{Z}}$. As a representative case, take ${a = 2}$ and ${\mu = u_{\{-1, 0, 1\}}}$ (uniform on ${\{-1, 0, 1\}}$). Question 1 What is the mixing time of ${(X_n \bmod p)}$ in ${\mathbf{Z}/p\mathbf{Z}}$? That is, how large must we take ${n}$ before ${X_n}$ is approximately uniformly distributed in ${\mathbf{Z}/p\mathbf{Z}}$? This question was asked by Chung, Diaconis, and Graham (1987), who were motivated by pseudorandom number generation. The best-studied pseudorandom number generators are the linear congruential generators, which repeatedly apply an affine map ${x\mapsto ax+b \bmod p}$. These go back to Lehmer (1949), whose parameters ${a}$ and ${b}$ were also subject to some randomness (from MathSciNet, “The author’s proposal for generating a sequence of `random’ 8 decimal numbers ${u_n}$ is to start with some number ${u_0\neq 0}$, multiply it by 23, and subtract the two digit overflow on the left from the two right hand digits to obtain a new number ${u_1}$.”) The process ${(X_n)}$ defined above is an idealized model: we assume the increment ${b}$ develops under some external perfect randomness, and we are concerned with the resulting randomness of the iterates. My own interest arises differently. The distribution of ${X_n}$ can be thought of as the image of ${a}$ under the random polynomial $\displaystyle P_n(X) = X^n + b_1 X^{n-1} + \cdots + b_n,.$ In particular, ${X_n \bmod p = 0}$ if and only if ${a}$ is a root of ${P_n}$. Thus the distribution of ${X_n \bmod p}$ is closely related to the roots of a random polynomial (of high degree) mod ${p}$. There are many basic and difficult questions about random polynomials: are they irreducible, what are their Galois groups, etc. But these are questions for another day (I hope!). Returning to Question 1, in the representative case ${a = 2}$ and ${\mu = u_{\{-1, 0, 1\}}}$, CDG proved the following results (with a lot of clever Fourier analysis): 1. The mixing time is at least $\displaystyle (1+o(1)) \log_2 p.$ This is obvious: ${X_n}$ is supported on a set of size ${O(2^n)}$, and if ${n \leq (1-\varepsilon) \log_2 p}$ then ${2^n \leq p^{1-\varepsilon}}$, so at best ${X_n}$ is spread out over a set of size ${p^{1-\varepsilon}}$. 2. The mixing time is never worse than $\displaystyle C \log p \log \log p.$ 3. Occasionally, e.g., if ${p}$ is a Mersenne prime, or more generally if ${a}$ has small order mod ${p}$ (or even roughly small order, suitably defined), the mixing time really is as bad as that. 4. For almost all odd ${p}$ the mixing time is less than $\displaystyle 1.02 \log_2 p.$ You would be forgiven for guessing that ${1.02}$ can be replaced with ${1+o(1)}$ with more careful analysis, but you would be wrong! In 2009, Hildebrand proved that for all ${p}$ the mixing time of ${X_n \bmod p}$ is at least $\displaystyle 1.004 \log_2 p.$ Therefore the mixing time of ${X_n \bmod p}$ is typically slightly more than ${\log_2 p}$. What is going on here? What is the answer exactly? In a word, the answer is entropy. Recall that entropy of a discrete random variable ${X}$ is defined by $\displaystyle H(X) = \sum_{x : \mu(x) > 0} \mathbf{P}(X = x) \log \mathbf{P}(X = x)^{-1}.$ Here are some basic facts about entropy: 1. If ${X}$ is uniform on a set of size ${k}$ then ${H(X) = \log k}$. 2. Entropy is subadditive: the entropy of the joint variable ${(X, Y)}$ is at most ${H(X) + H(Y)}$. 3. Entropy cannot be increased by a (deterministic) function: ${H(f(X)) \leq H(X)}$. By combining the second and third facts, we have the additive version (in the sense of adding the variables) of subadditivity: $\displaystyle H(X + Y) \leq H(X) + H(Y).$ In particular, it follows from (1) that $\displaystyle H(X_{m+n}) \leq H(X_m) + H(X_n),$ and hence by the subadditive lemma ${H(X_n)/n}$ converges. (We are thinking now of ${X_n}$ as a random variable in ${\mathbf{Z}}$, not reduced modulo anything.) Call the limit ${H = H(a, \mu)}$. It is easy to see in our model case ${a=2, \mu = u_{\{-1, 0, 1\}}}$ that ${H \leq \log 2}$ (because ${X_n}$ has support size ${O(2^n)}$). If ${H < \log 2}$, then it follows that the mixing time of ${X_n \bmod p}$ is strictly greater than ${\log_2 p}$ (as ${X_n}$ cannot approach equidistribution mod ${p}$ before its entropy is at least ${(1+o(1))\log p}$). Indeed it turns out that ${H < \log 2}$. This is "just a computation": since ${H = \inf_{n\geq 1} H(X_n) / n}$, we just need to find some ${n}$ such that ${H(X_n) / n < \log 2}$. Unfortunately, the convergence of ${H(X_n) / n}$ is rather slow, as shown in Figure 1, but we can take advantage of another property of entropy: entropy satisfies not just subadditivity but submodularity $\displaystyle H(X+Y+Z) + H(X) \leq H(X+Y) + H(X+Z),$ and it follows by a short argument that ${H(X_n) - H(X_{n-1})}$ is monotonically decreasing and hence also convergent to ${H}$; moreover, unlike the quotient ${H(X_n)/n}$, the difference ${H(X_n) - H(X_{n-1})}$ appears to converge exponentially fast. The result is that $\displaystyle H / \log 2 = 0.98876\dots,$ so the mixing time of ${X_n \bmod p}$ is not less than $\displaystyle H^{-1} \log p = (1.01136\dots ) \log_2 p.$ (We can also deduce, a posteriori, that we will have ${H(X_n) / n < \log 2}$ for ${n \geq 72}$, though it is out of the question to directly compute ${H(X_n)}$ for such large ${n}$.) This observation was the starting point of a paper that Péter and I have just finished writing. The preprint is available at arxiv:2003.08117. What we prove in general is that the mixing time of ${X_n \bmod p}$ is indeed just ${(H^{-1} + o(1)) \log p}$ for almost all ${p}$ (either almost all composite ${p}$ coprime with ${a}$, or alternatively almost all prime ${p}$). In other words, entropy really is the whole story: as soon as the entropy of ${X_n}$ is large enough, ${X_n \bmod p}$ should be close to equidistributed (with a caveat: see below). The lower bound is more or less clear, as above. Most of the work of the paper is involved with the upper bound, for which we needed several nontrivial tools from probability theory and number theory, as well as a few arguments recycled from the original CDG paper. However, just as one mystery is solved, another arises. Our argument depends on the large sieve, and it therefore comes with a square-root barrier. The result is that we have to assume ${H(a, \mu) > \frac12 \log a}$. This is certainly satisfied in our representative case ${a = 2, \mu = u_{\{-1, 0, 1\}}}$ (as the entropy is very close to ${\log 2}$), but in general it need not be, and in that case the problem remains open. The following problem is representative. Problem 2 Let ${a \geq 2}$ and let ${\mu = u_{\{0, 1\}}}$. Then ${X_n}$ is uniform on a (Cantor) set of size ${2^n}$, so ${H(a, \mu) = \log 2}$. Show that the mixing time of ${X_n \bmod p}$ is ${(1+o(1))\log_2 p}$ for almost all primes ${p}$. You might call this the “2–3–4–5 problem”. The case ${a=2}$ is trivial, as ${X_n}$ is uniform on ${\{1, \dots, 2^n\}}$. The case ${a=3}$ is covered by our main theorem, since ${\log 2 > \frac12 \log 3}$. The case ${a=4}$ is exactly borderline, as ${\log 2 = \frac12 \log 4}$, and this case is not covered by our main theorem, but we sketch how to stretch the proof to include this case anyway. For ${a \geq 5}$ we need a new idea.	2020-09-24 11:58:49	{"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": 228, "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": 0.9283159971237183, "perplexity": 180.99225930006784}, "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-2020-40/segments/1600400217623.41/warc/CC-MAIN-20200924100829-20200924130829-00318.warc.gz"}
https://proofwiki.org/wiki/Symbols:E/Experiment	# Symbols:E/Experiment $\mathcal E$ An experiment, which can conveniently be denoted $\EE$, is a probability space $\struct {\Omega, \Sigma, \Pr}$. The $\LaTeX$ code for $\mathcal E$ is \mathcal E or \EE.	2023-02-04 05:49:24	{"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": 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": 0.9999322891235352, "perplexity": 3018.547586088335}, "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-2023-06/segments/1674764500094.26/warc/CC-MAIN-20230204044030-20230204074030-00192.warc.gz"}
https://stacks.math.columbia.edu/tag/02XL	Lemma 4.32.2. Let $\mathcal{C}$ be a category. Let $p : \mathcal{S} \to \mathcal{C}$ be a category over $\mathcal{C}$. 1. The composition of two strongly cartesian morphisms is strongly cartesian. 2. Any isomorphism of $\mathcal{S}$ is strongly cartesian. 3. Any strongly cartesian morphism $\varphi$ such that $p(\varphi )$ is an isomorphism, is an isomorphism. Proof. Proof of (1). Let $\varphi : y \to x$ and $\psi : z \to y$ be strongly cartesian. Let $t$ be an arbitrary object of $\mathcal{S}$. Then we have \begin{align} & \mathop{Mor}\nolimits _\mathcal {S}(t, z) \\ & = \mathop{Mor}\nolimits _\mathcal {S}(t, y) \times _{\mathop{Mor}\nolimits _\mathcal {C}(p(t), p(y))} \mathop{Mor}\nolimits _\mathcal {C}(p(t), p(z)) \\ & = \mathop{Mor}\nolimits _\mathcal {S}(t, x) \times _{\mathop{Mor}\nolimits _\mathcal {C}(p(t), p(x))} \mathop{Mor}\nolimits _\mathcal {C}(p(t), p(y)) \times _{\mathop{Mor}\nolimits _\mathcal {C}(p(t), p(y))} \mathop{Mor}\nolimits _\mathcal {C}(p(t), p(z)) \\ & = \mathop{Mor}\nolimits _\mathcal {S}(t, x) \times _{\mathop{Mor}\nolimits _\mathcal {C}(p(t), p(x))} \mathop{Mor}\nolimits _\mathcal {C}(p(t), p(z)) \end{align} hence $z \to x$ is strongly cartesian. Proof of (2). Let $y \to x$ be an isomorphism. Then $p(y) \to p(x)$ is an isomorphism too. Hence $\mathop{Mor}\nolimits _\mathcal {C}(p(z), p(y)) \to \mathop{Mor}\nolimits _\mathcal {C}(p(z), p(x))$ is a bijection. Hence $\mathop{Mor}\nolimits _\mathcal {S}(z, x) \times _{\mathop{Mor}\nolimits _\mathcal {C}(p(z), p(x))} \mathop{Mor}\nolimits _\mathcal {C}(p(z), p(y))$ is bijective to $\mathop{Mor}\nolimits _\mathcal {S}(z, x)$. Hence the displayed map of Definition 4.32.1 is a bijection as $y \to x$ is an isomorphism, and we conclude that $y \to x$ is strongly cartesian. Proof of (3). Assume $\varphi : y \to x$ is strongly cartesian with $p(\varphi ) : p(y) \to p(x)$ an isomorphism. Applying the definition with $z = x$ shows that $(\text{id}_ x, p(\varphi )^{-1})$ comes from a unique morphism $\chi : x \to y$. We omit the verification that $\chi$ is the inverse of $\varphi$. $\square$ In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	2019-04-19 06:35:37	{"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": 2, "x-ck12": 0, "texerror": 0, "math_score": 1.0000085830688477, "perplexity": 1456.490453055083}, "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-2019-18/segments/1555578527148.46/warc/CC-MAIN-20190419061412-20190419083412-00317.warc.gz"}
http://mathhelpforum.com/algebra/129838-word-problem-equations.html	1. ## Word Problem Equation:1st try I'm completely lost with this one.... A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P is linear. If 300 units sold results in $4650 profit and 375 units results in$9000 profit write the equation that models the profit. What I got was 4350x-1300350 using the y-y1=m(x-x1) 2. I got $y=58x-12750$ 3. How did you get that answer? : ( 4. Originally Posted by Annb A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P is linear. If 300 units sold results in $4650 profit and 375 units results in$9000 profit write the equation that models the profit. What I got was 4350x-1300350 using the y-y1=m(x-x1) Huh? You have 2 points: (300,4650) and (375,9000) linear equation using 2 points - Google Search= 5. $y=ax+b$ $y_i=ax_i+b$ $ y=4650 $ $x=300$ $y_i=9000$ $x_i=375$ subtract both equations, cancel B out $y-y_i=a(x-x_i)$ $-4350=-75a$ $a=\frac{-4350}{-75}=58$ place a in an orig. equation $y=ax+b$ $ 4650=58(300)+b=17400+b$ $4650-17400=b$ $b=-12750$ plug in $y=58x-12750$ 6. Most simple way: $\frac{y-y_{1}}{x-x_{1}} = \frac {y_{2}-y_{1}}{x_{2}-x_{1}}$ Substitute values in to get $75y-348750=4350x-1631250$ Divide 75 to get $y-4650=58x-21750$ $y+17100=58x$ $y=58x-17100$ In the form of $y=mx+c$ My answer is different to integrals's but this is just to let you know you can use the 2 point formula. 7. Originally Posted by jgv115 Most simple way: $\frac{y-y_{1}}{x-x_{1}} = \frac {y_{2}-y_{1}}{x_{2}-x_{1}}$ Substitute values in to get $75y-348750=4350x-1631250$ Divide 75 to get $y+8550-19x$ You've lost a "="! 8. corrected =]	2017-06-28 02:52:57	{"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": 24, "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": 0.5969456434249878, "perplexity": 3761.528729149834}, "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-2017-26/segments/1498128322275.28/warc/CC-MAIN-20170628014207-20170628034207-00407.warc.gz"}
https://mathsgee.com/36696/initial-nonzero-overrightarrow-terminal-mathbb-direction	# arrow_back Find an initial point $P$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with terminal point $Q(3,0,-5)$ and such that $\mathbb{u}$ has the same direction as $\mathbf{v}=(4,-2,-1)$. 54 views Find an initial point $P$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with terminal point $Q(3,0,-5)$ and such that $\mathbb{u}$ has the same direction as $\mathbf{v}=(4,-2,-1)$. ## Related questions Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a terminal point $Q$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with initial point $P(-1,3,-5)$ and such that Find a terminal point $Q$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with initial point $P(-1,3,-5)$ and such thatFind a terminal point $Q$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with initial point $P(-1,3,-5)$ and such that (a) $\mathbf{u}$ has the ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The components of the vector $\mathbf{v}=\overrightarrow{P_{1} P_{2}}$ with initial point $P_{1}(2,-1,4)$ and terminal point $P_{2}(7,5,-8)$ are The components of the vector $\mathbf{v}=\overrightarrow{P_{1} P_{2}}$ with initial point $P_{1}(2,-1,4)$ and terminal point $P_{2}(7,5,-8)$ areThe components of the vector $\mathbf{v}=\overrightarrow{P_{1} P_{2}}$ with initial point $P_{1}(2,-1,4)$ and terminal point $P_{2}(7,5,-8)$ are ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the unit vector $\mathbf{u}$ that has the same direction as $\mathbf{v}=(2,2,-1)$. Find the unit vector $\mathbf{u}$ that has the same direction as $\mathbf{v}=(2,2,-1)$.Find the unit vector $\mathbf{u}$ that has the same direction as $\mathbf{v}=(2,2,-1)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let $\mathbf{u}=(1,-1,3,5)$ and $\mathbf{v}=(2,1,0,-3)$. Find scalars $a$ and $b$ so that $a \mathbf{u}+b \mathbf{v}=(1,-4,9,18)$. Let $\mathbf{u}=(1,-1,3,5)$ and $\mathbf{v}=(2,1,0,-3)$. Find scalars $a$ and $b$ so that $a \mathbf{u}+b \mathbf{v}=(1,-4,9,18)$.Let $\mathbf{u}=(1,-1,3,5)$ and $\mathbf{v}=(2,1,0,-3)$. Find scalars $a$ and $b$ so that $a \mathbf{u}+b \mathbf{v}=(1,-4,9,18)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,2)$ and whose terminal point is $B(2,0)$. Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,2)$ and whose terminal point is $B(2,0)$.Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,2)$ and whose terminal point is $B(2,0)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,1,3)$ and whose terminal point is $B(-1,-1,2)$. Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,1,3)$ and whose terminal point is $B(-1,-1,2)$.Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,1,3)$ and whose terminal point is $B(-1,-1,2)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let $\mathbf{u}=(4,-1), \mathbf{v}=(0,5)$, and $\mathbf{w}=(-3,-3)$. Find the components of Let $\mathbf{u}=(4,-1), \mathbf{v}=(0,5)$, and $\mathbf{w}=(-3,-3)$. Find the components ofLet $\mathbf{u}=(4,-1), \mathbf{v}=(0,5)$, and $\mathbf{w}=(-3,-3)$. Find the components of (a) $\mathbf{u}+\mathbf{w}$ (b) $\mathbf{v}-3 \mathbf{u}$ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a unit vector that is orthogonal to both $\mathbf{u}=(1,0,1)$ and $\mathbf{v}=(0,1,1)$ Find a unit vector that is orthogonal to both $\mathbf{u}=(1,0,1)$ and $\mathbf{v}=(0,1,1)$Find a unit vector that is orthogonal to both $\mathbf{u}=(1,0,1)$ and $\mathbf{v}=(0,1,1)$ ... Let $\mathbf{u}=(-3,1,2), \mathbf{v}=(4,0,-8)$, and $\mathbf{w}=(6,-1,-4)$. Find the components of Let $\mathbf{u}=(-3,1,2), \mathbf{v}=(4,0,-8)$, and $\mathbf{w}=(6,-1,-4)$. Find the components ofLet $\mathbf{u}=(-3,1,2), \mathbf{v}=(4,0,-8)$, and $\mathbf{w}=(6,-1,-4)$. Find the components of (a) $\mathbf{v}-\mathbf{w}$ (b) $6 \mathrm{u}+2 \ma ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the terminal point of the vector that is equivalent to$\mathbf{u}=(1,2)$and whose initial point is$A(1,1)$. 0 answers 83 views Find the terminal point of the vector that is equivalent to$\mathbf{u}=(1,2)$and whose initial point is$A(1,1)$.Find the terminal point of the vector that is equivalent to$\mathbf{u}=(1,2)$and whose initial point is$A(1,1)$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 In relation to the points$P_{1}$and$P_{2}$, what can you say about the terminal point of the following vector if its initial point is at the origin? 0 answers 40 views In relation to the points$P_{1}$and$P_{2}$, what can you say about the terminal point of the following vector if its initial point is at the origin?In relation to the points$P_{1}$and$P_{2}$, what can you say about the terminal point of the following vector if its initial point is at the origin ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the norm of the vector$\mathbf{v}=(2,-1,3,-5)$in$R^{4}$? 1 answer 56 views What is the norm of the vector$\mathbf{v}=(2,-1,3,-5)$in$R^{4}$?What is the norm of the vector$\mathbf{v}=(2,-1,3,-5)$in$R^{4}$? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the components of the vector$\overrightarrow{P_{1} P_{2}}$when$P_1(3,5)$and$P_2(2,8)$0 answers 45 views Find the components of the vector$\overrightarrow{P_{1} P_{2}}$when$P_1(3,5)$and$P_2(2,8)$Find the components of the vector$\overrightarrow{P_{1} P_{2}}$when$P_1(3,5)$and$P_2(2,8)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$\mathbf{u}=\frac{1}{\\|\mathbf{v}\\|} \mathbf{v}$is a unit vector 1 answer 149 views Show that$\mathbf{u}=\frac{1}{\\|\mathbf{v}\\|} \mathbf{v}$is a unit vectorShow that$\mathbf{u}=\frac{1}{\\|\mathbf{v}\\|} \mathbf{v}$is a unit vector ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (1, -1, 2)$0 answers 79 views Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (1, -1, 2)$Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (1, -1, 2)\$ ...	2022-05-16 08:10:53	{"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": 0.8245438933372498, "perplexity": 313.8449232489606}, "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-2022-21/segments/1652662510097.3/warc/CC-MAIN-20220516073101-20220516103101-00655.warc.gz"}
https://www.impan.pl/en/publishing-house/banach-center-publications/all/42/0/110271/the-p-1-central-extension-of-the-mapping-class-group-of-orientable-surfaces	# Publishing house / Banach Center Publications / All volumes ## The $p_1$-central extension of the Mapping Class Group of orientable surfaces ### Volume 42 / 1998 Banach Center Publications 42 (1998), 111-117 DOI: 10.4064/-42-1-111-117 #### Abstract Topological Quantum Field Theories are closely related to representations of Mapping Class Groups of surfaces. Considering the case of the TQFTs derived from the Kauffman bracket, we describe the central extension coming from this representation, which is just a projective extension. #### Authors • Sylvain Gervais ## Search for IMPAN publications Query phrase too short. Type at least 4 characters. Reload image	2019-12-08 06:29:40	{"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": 0.3906116187572479, "perplexity": 1732.3328658802623}, "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-2019-51/segments/1575540506459.47/warc/CC-MAIN-20191208044407-20191208072407-00202.warc.gz"}
https://quantumcomputing.stackexchange.com/questions/21608/how-to-choose-beta-in-gaussian-derivative-component-of-drag-pulse	# How to choose $\beta$ in Gaussian derivative component of DRAG pulse? From definition of the DRAG pulse it is: $$f(x)=Gaussian+1j\beta(-(x-duration/2)/\sigma^2)Gaussian,$$ where $$Gaussian(x, amp, \sigma)=ampe^{-(1/2)(x-duration/2)^2/\sigma^2}$$. If I try it in Python (for $$\beta=$$1e-6): import numpy as np import matplotlib.pyplot as plt t = np.arange(0,8e-6,10e-9) amp = 1 sigma=1e-6 tc = 8e-6 gaussian = ampnp.exp(-0.5(t-tc/2)2/sigma2) beta = 1e-6 drag_component = beta(-(t-tc/2)/sigma2)gaussian I get: but if I try to set the amplitude of derivative part equaled to the Gaussian ($$\beta$$=1): the result is strange. How to choose $$\beta$$, what it's meaning and on what it depends?	2021-12-01 09:20:35	{"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8610290288925171, "perplexity": 1808.6756064588983}, "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-2021-49/segments/1637964359976.94/warc/CC-MAIN-20211201083001-20211201113001-00126.warc.gz"}
https://global.ihs.com/doc_detail.cfm?document_name=ISO%202039-2&item_s_key=00037699	# Plastics - Determination of Hardness - Part 2: Rockwell Hardness Detail Summary Active, Most Current ENGLISH * SAME AS BS 2782 P3 METH 365C Format Details Price (USD) PDF Single User \$45.00 Print In Stock \$45.00 This part of ISO 2039 specifies a method for determining the indentation hardness of plastics by means of the Rockwell hardness tester using the Rockwell M, L and R hardness scales. A Rockwell hardness number is directly related to the indentation hardness of a plastic material; the higher the Rockwell hardness number, the harder the material. Due to a short overlap of Rockwell hardness scales by this procedure, two different Rockwell hardness numbers of different scales may be obtained on the same material, both of which may be technically correct. For materials having high creep and recovery, the time-factors involved in application of the major and minor loads have a considerable effect on the results of the measurements. An alternative method of using the apparatus to give hardness on the Rockwell-α hardness scale is specified in the annex which shows how this scale may be related to the hardness measurement of ISO 2039-l.	2019-03-23 06:24:25	{"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": 0.8665394186973572, "perplexity": 1924.423738636282}, "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-2019-13/segments/1552912202728.21/warc/CC-MAIN-20190323060839-20190323082839-00079.warc.gz"}
https://physics.stackexchange.com/tags/electrical-engineering/new	# Tag Info 1 Assuming it's not deliberate, two things come to mind: light-sensitive switches will have significant hysteresis to avoid flickering on and off in dim light. So they will require brighter light to switch on in the morning than to switch off in the evvening. human vision perceives a given light level as being brighter during a transition from dark to ... 0 If we measure the voltage between the terminals of a diode in an open circuit, the outcome is zero. The E-field of the junction in only internal. When a forward voltage is applied, but there is also a big resistance in series in the circuit, there is a tension between the ends of the diode but below 0.7V. Even below the threshold a small current flows. When ... 2 A diode in its grounded state is an insulator. Start with that. The way we build the diode is, we take two insulators that are very close to being conductors but not quite there, and we make them conductors, in one case by inserting atoms which have extra electrons to give (N-doping) and in the other case by inserting atoms which have a tendency to instead ... 1 Now, when a voltage is applied in the right direction, free electrons flow to the part where the holes are. This happens independently of an external voltage, because the electrons in the n-doped part feel the urge to fill the holes in the p-doped part. But because electrons move from the n-doped part to the p-doped part, the n-doped part becomes positively ... 2 I also think the effect is cogging. This torque is position dependent and its periodicity per revolution depends on the number of magnetic poles and the number of teeth on the stator. Cogging torque is an undesirable component for the operation of such a motor. It is especially prominent at lower speeds, with the symptom of jerkiness. Cogging torque results ... 1 Hi Reading this is interesting. The reason that the fan goes backwards is simple. It is a Direct Current motor which has a capacitor across the power terminals to keep the power factor near to unity. A motor is a wound component which will produce a lagging current so a capacitor is added to bring that current nearer to unity (A capacitor creates leading ... 1 I think by "simple" you mean Linear, which would consist of Source, R/L/C, and Transformers. Or as Engineers tend to label them "Electrical Circuits" as opposed to "Electronic Circuits" which have transistors/diodes. These circuits can have their responses written in terms of Linear ODEs. The definitions get tricky, because as ... 4 Did the fan really rotate backwards, or merely appear to? You may be looking at a Wagon-Wheel Effect. Basically, when a wheel or propeller rotates at a certain speed, particularly if you're using fluorescent lighting, which has a natural flicker to it that isn't always obvious, the object can appear to stop or rotate in the opposite direction. All the ... 0 How do i calculate output resistance if i have the corresponding table for it? There are two output resistances here: 1)total AC, and 2)differential (dynamic) output resistances. The second one causes the incremental variation of the first. AC output resistance is the total instantaneous resistance for a given output voltage Vcb. Althu this is the parallel ... 4 On balance, I think @nielsneilsen's answer is likely the correct one. But there is another possibility. Is there a control loop in play? Almost universally, practical control systems for hitting a desired position, velocity, flow rate or whatever use a PID control loop, sometimes omitting the P or D element depending on the application. Other control ... 142 The overshoot behavior you noticed is called cogging and occurs when the magnet arrangement in the motor "catches" the rotating magnetic core of the motor during shutdown and jerks it back to one of the local strong spots in the field. You can demonstrate this yourself by carefully rotating the fan blade around with your finger when the motor is ... 0 I just have guesses. Is there any sort of spring in the motor, or anything spring like? For example a fan belt could stretch if it was trying to turn a stiff bearing. You might discover this by trying to spin the fan by hand and seeing if it turns the other way when it stops. Another source of springiness could be electrical. A power smooths variations in ... 6 Your PC is a box with limited vents for air to enter/exit. Especially if these clog up with dust, the fan could create a noticeable pressure differential between inside and outside of the box. After the fan turns off, that equalizes, forcing some air backward through the fan, and causing it to rotate backward. Maybe. Another possibly, as pointed out in ... 1 Here is the most basic answer with regards to why we use ultrasound for imaging rather than sound in the human range of hearing. Ultrasound, by nature, is high frequency. The higher the frequency, the denser the sound traveling through the medium, which, in turn, provides a higher resolution image. You could certainly create an image using sound waves ... 0 This is kind of like asking "how hot is too hot?" It will depend on how fast a battery can be charged and discharged- weakest link. You can always connect through a resistor, let it sit for some time so they equalize (current through resistor drops to zero or voltage across resistor becomes zero), then connect directly. Practically it doesn't have ... 0 I interpret the question as being about cooling. In a thought experiment you may scale up the A64FX ARM CPU powering FUGAKU by a linear factor of 10.000 or 100.000 and then replace its integrated solid state electronic components by discrete ones. Cooling will not be a theoretical problem as the device is essentially 2D and you have the third dimension to ... 1 Ohmic would mean means it follows Ohm's law $\ I= {\mathcal{E} \over R}$ It's non-ohmic so it does not, the current passed is not proportional to the EMF. Symmetric would mean that for negative EMF the the exact opposite current would flow. Being asymmetic, (in this case) it means that current flows more readily in one direction than in the opposite ... 0 If "switches and wires" means transistors, then yes, you could build a supercomputer out of individual transistors instead of microchips. The Atlas was an early supercomputer from 1962 built from germanium transistors. Although it was considered a supercomputer at the time, it was very slow by modern standards. It performed 700,000 instructions per ... Top 50 recent answers are included	2021-02-27 10:16:52	{"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": 0.6413193941116333, "perplexity": 905.8936356174021}, "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-2021-10/segments/1614178358798.23/warc/CC-MAIN-20210227084805-20210227114805-00141.warc.gz"}
https://leanprover-community.github.io/archive/stream/217875-Is-there-code-for-X%3F/topic/linear.20image.20of.20segment.html	## Stream: Is there code for X? ### Topic: linear image of segment #### Bhavik Mehta (Mar 01 2021 at 20:32): import analysis.convex.basic open linear_map universes u v variables {E : Type u} {F : Type v} lemma segment_image (f : E →ₗ[ℝ] F) (a b : E) : f '' segment a b = segment (f a) (f b) := begin end Is something like this in mathlib somewhere? #### Eric Wieser (Mar 01 2021 at 21:17): docs#mem_segment_translate was the closest I could find #### Eric Wieser (Mar 01 2021 at 21:18): Which I guess you want to generalize from (+ a) to any affine map? #### Adam Topaz (Mar 01 2021 at 21:20): Shouldn't there be a lemma saying that an affine map sends segments to segments, and something which constructs an affine map out of a linear map? #### Bhavik Mehta (Mar 01 2021 at 23:09): Turned out it just has a one line proof - perhaps it should be there for affine maps though Last updated: May 16 2021 at 05:21 UTC	2021-05-16 11:57:03	{"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": 0.487185537815094, "perplexity": 3826.8704129843777}, "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/1620243991269.57/warc/CC-MAIN-20210516105746-20210516135746-00521.warc.gz"}
https://quant.stackexchange.com/questions/34902/distributional-assumptions-in-priips/35598	# Distributional assumptions in PRIIPs And yet another question to discuss the assumptions in PRIIPs. It is remarkable that in these legal documents a Cornish-Fisher expansion including skewness and kurtosis is used. Looking at the very recent version of the document we find on page 27 the following formula for the moderate scenario (Which is, if I read it correctly, supposed to be the 50% quantile): $$\exp(M_1 \cdot N - \sigma \mu_1/6 - 0.5 \sigma^2 N ),$$ where $N$ is the number of days (more details are not necessary here), $M_1$ is the first moment of the log returns observed, $\sigma$ is the standard deviation and $\mu_1$ is the skewness measured. I have one question: I see that $- \sigma \mu_1/6$ enters if we put in $0$ for the "z-value". Thus there is something that remains from skewness. But is it ok to have the average return $M_1$ if we model in a risk-neutral world? If $M_1$ is the average of log-returns then we have $M_1 = \tilde{\mu} + \sigma^2/2$ where $\tilde{\mu}$ is the "true" mean and $\sigma^2/2$ is the convexity that we have in the log-normal case. This is corrected in the last part of the formula by the term $- 0.5 \sigma^2 N$. This formula is different from the others where there is usually just an expected return of $-\sigma^2/2 N$ which makes the expected growth zero (see e.g. page 28 point 11). In short: is it really consistent to have the $M_1$ term above? Any comments are really appreciated!	2020-06-02 14:58:35	{"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": 0.8998079299926758, "perplexity": 248.00097958933824}, "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-2020-24/segments/1590347425148.64/warc/CC-MAIN-20200602130925-20200602160925-00144.warc.gz"}
http://www.real-statistics.com/linear-algebra-matrix-topics/linear-independent-vectors/	# Linear Independent Vectors Definition 1: Vectors X1, …, Xk of the same size and shape are independent if for any scalar values b1, … bk, if b1 X1 +⋯+ bXk = 0, then b1 = … = bk = 0. Vectors X1, …, Xk are dependent if they are not independent, i.e. there are scalars b1, … bk, at least one of which is non-zero, such that b1 X1 +⋯+ bk Xk = 0. Observation: If X1, …, Xk are independent, then Xj ≠ 0 for all j. Property 1X1, …, Xk are dependent if and only if at least one of the vectors can be expressed as a linear combination of the others. Proof: Suppose X1, …, Xk are dependent. Then there are scalars b1, … bk, at least one of which is non-zero such that b1 X1 +⋯+ bk Xk = 0. Say bi ≠ 0. Then Now suppose that Xi = $\sum_{j \neq i} b_j X_j$. Then b1 X1 +⋯+ bk Xk = 0, where b= -1, and so X1, …, Xk are dependent. Definition 2: The span of independent vectors X1, …, Xk consists of all the vectors which are a linear combination of these vectors. If W is any set of vectors, then the vectors X1, …, Xk are said to be a basis of W if they are independent and their span equals W. We call a set of vectors W closed if W is the span of some set of vectors. Since we will only consider finite sets of vectors, henceforth we will assume that any closet set is finite. Property 2: If X1, …, Xk is a basis of W, then every element in W has a unique representation as a linear combination of X1, …, Xk. Proof: That one such representation exists follows from the definition of span. We now show uniqueness. Suppose there are two such representations, as follows: $\sum_{j = 1}^k b_j X_j$ = $\sum_{j = 1}^k c_j X_j$ Then $\sum_{j = 1}^k (b_j - c_j) X_j$ = 0. But since X1, …, Xk are independent, bj – cj = 0 for all j, i.e. bj = cj for all j, and so the two representations are equal. Property 3: If B is a set of independent vectors such that the span of B is a subset of a closed (finite) set of vectors W, then B can be expanded to be a (finite) basis for W. Proof: Let W = {X1, …, Xn}. We now build a finite set of vectors recursively as follows. Start with B0 = B. For each k from 0 to n–1, define Bk+1 = Bk ∪ {Xk} if Xk is not already in the span of Bk and Bk+1 = Bk otherwise. Clearly each Bk is an independent set of vectors and the span of Bn is W. Corollary 1: Every closed set of vectors W has a (finite) basis. Proof: The corollary is Property 3 with B = Ø. Property 4: If Y1,…,Yn is a basis for W and X1, …, Xm is a set of independent vectors in W, then m ≤ n. Proof: We now show by induction that for each k, 1 ≤ km, there are vectors Z1,…,Zk such that {Z1,…,Zk} ⊆ {Y1,…,Yn} and Z1, …, ZkXk+1, …, Xm are independent. We now assume the assertion is true for all values less than k and show it is true for k, where km, i.e. we need to prove that for at least one jZ1,…,Z, YjXk+1,…, Xm are independent. If there is no such j then by Property 1, each Yj can be expressed as a linear combination of Z1,…,ZXk+1,…, Xm. But since Xk is in and Y1,…,Yn, is a basis for W, we can express Xk as a linear combination of the Y1,…,Yn and therefore as a linear combination of Z1,…,ZXk+1,…, Xm. Thus by Property 1, Z1,…,Z, XkXk+1,…, Xare not independent, a violation of the induction hypothesis. We conclude there is some j for which Z1, …, ZYjXk+1,…, Xm are independent. We set Zequal to any such Yjwhich yields the desired result, namely that Z1, …, ZXk+1,…, Xm are independent. Where k = m, we conclude that {Z1, …, Zm} ⊆ {Y1, …, Yn} and that Z1, …, Zm are independent. Since Z1, …, Zare independent, they are all distinct, but since {Z1, …, Zm} ⊆ {Y1, …, Yn}, it follows that ≤ n. Corollary 2: Any two bases for a finite set of vectors have the same number of elements. Proof: Suppose X1, …, Xm and Y1, …, Yn are bases for W. By Property 4, m ≤ n and also nm, and so m = n. Corollary 3: Let Y1, …, Ym be a basis for W and let X1, …, Xm be a set of independent vectors in W. Then X1, …, Xm is also basis for W. Proof: Suppose X1, …, Xm is not a basis for W. By Property 3, it can be expanded to become a basis for W. This basis has n elements for some n > m, but this contradicts Property 4 since Y1, …, Ym is a basis for W. Thus X1, …, Xm must also be a basis for W. Corollary 4: Any set of n linearly independent n × 1 column vectors is a basis for the set of n × 1 column vectors. Similarly, any set of n linearly independent 1 × n row vectors is a basis for the set of 1 × n row vectors. Proof: Let Cj be the jth column of the identity matrix In. It is easy to see that for any n, C1, …, Cn forms a basis for the set of all n × 1 column vectors. The result for column vectors now follows by Corollary 3. The proof for row vectors is similar. Definition 3: The dimension of a closed set of vectors W is the size of any basis of W. Observation: This definition makes sense since, as we have seen from the above, any closed set of vectors has a basis, and any two bases have the same number of elements. Further, note that any element in W can be expressed uniquely as a linear combination of the elements in any basis. ### 2 Responses to Linear Independent Vectors 1. Michael says: I just discovered your site. It is very instructive! Quick question: in the summation as part of the first proof on this page, should the b(j) term be -b(j)? • Charles says: Michael, Yes, you are right. Thanks for catching this error. I have now updated the referenced webpage. Charles	2018-01-17 05:30:44	{"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": 4, "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": 0.9416916966438293, "perplexity": 380.4077837849976}, "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-2018-05/segments/1516084886815.20/warc/CC-MAIN-20180117043259-20180117063259-00736.warc.gz"}
https://codereview.stackexchange.com/questions/158688/calculating-speed-from-a-pandas-dataframe-with-time-x-and-y-columns/158774#158774	# Calculating speed from a Pandas Dataframe with Time, X, and Y columns I'm trying to calculate speed between consecutive timepoints given data that is in a '.csv' file with the following columns: "Time Elapsed", "x", and "y". The ultimate goal is to get the data into a format where I can plot "Time Elapsed" vs. "speed" I'm fairly sure that my implementation is doing what I want, but it's certainly possible (and likely) that I overlooked something. I'm also wondering whether there are faster/more efficient ways (in Python) to perform these calculations? import pandas as pd import numpy as np def calculate_speeds(path_to_csv): xy = data_df[['x', 'y']] b = np.roll(xy, -1, axis=0)[:-1] a = xy[:-1] dxy = np.linalg.norm(a - b, axis=1) dt = (np.roll(data_df['Time Elapsed'], -1) - data_df['Time Elapsed'])[:-1] speeds = np.divide(dxy, dt) speed_df = pd.DataFrame(data={'Time Elapsed':data_df['Time Elapsed'][:-1],'Speed':speeds}) return speed_df The code reads good enough and is pretty straightforward; you should consider improving its quality by adding documentation in the form of a docstring explaining what kind of data it expects. Speaking as such, you should extract the I/O part out of the function and have it being fed the required data, for better reusability and testing. One other thing to note is that you perform the same roll twice on different columns of the same dataframe. You can combine these operations and write the equation in a more ... equationy-ish way: import pandas as pd import numpy as np def calculate_speeds(positions_over_time): time = 'Time Elapsed' movements_over_timesteps = ( np.roll(positions_over_time, -1, axis=0) - positions_over_time)[:-1] speeds = np.sqrt( movements_over_timesteps.x 2 + movements_over_timesteps.y 2 ) / movements_over_timesteps[time] return pd.DataFrame({ time: positions_over_time[time][:-1], 'Speed': speeds, }) if __name__ == '__main__': • +1, in the OP's code it took me quite some time to find the actual velocity calculation, because it is split and partially hidden behind the np.linalg.norm... Mar 25, 2017 at 11:31	2022-06-25 11:41:37	{"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": 0.3083529472351074, "perplexity": 2230.434874214225}, "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-2022-27/segments/1656103034930.3/warc/CC-MAIN-20220625095705-20220625125705-00665.warc.gz"}
http://math.eretrandre.org/tetrationforum/showthread.php?tid=168&pid=2162	• 0 Votes - 0 Average • 1 • 2 • 3 • 4 • 5 Iteration by Ramanujan 05/27/2008, 08:12 AM Post: #1 Gottfried Long Time Fellow Posts: 731 Joined: Aug 2007 Iteration by Ramanujan Hi, just today I found this msg in the sci.math newsgroup, which may be of interest here. Especially the second function of Ramanujan, which combines (a somehow inverse to) Andrew's E()-function and the ("Tetra-")series of increasing heigths. Maybe, you like this Gottfried subject: yeah sure!! author: galathaea@gmail.com Code: ```i've already pointed out in this thread that ramanujan worked on continuous iteration in his quarterly reports these were written between august 5th, 1913 and march 9th, 1914 ramanujan actually expands the notion of iteration into a power series oo j --- psi (x) n \ j (f)^n(x) = / ----------- --- (1) j=0 j where because n could be any value in the convergence radius there is a potential continuous definition but ramanujan was by no means the first either i've also mentioned comtet's book which even berndt's coverage recommends to put this on a rigorous foundation this has been around since before euler fractional differentiation for instance was developed from several different transform approaches from the very early transform studies it's natural that if (-ik)^n corresponds to n-th differentiation in the transform language then there is a clear generalisation of differentiation that allows real orders .. to show some of the other cool things in ramanujan's reports and to connect to the tetration threads ramanujan studies x x e x e e e e e f(x) = 1 + -- + --- + ---- + ... 3 4 5 2 3 4 2 3 2 ramanujan shows that this function is enitre and yet grows faster than any x . . e e finitely iterated exponential (...) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar``` Gottfried Helms, Kassel 05/27/2008, 08:23 AM Post: #2 bo198214 Administrator Posts: 1,366 Joined: Aug 2007 RE: Iteration by Ramanujan galthaea Wrote: Code: ```i've already pointed out in this thread that ramanujan worked on continuous iteration in his quarterly reports these were written between august 5th, 1913 and march 9th, 1914 ramanujan actually expands the notion of iteration into a power series oo j --- psi (x) n \ j (f)^n(x) = / ----------- --- (1) j=0 j where because n could be any value in the convergence radius there is a potential continuous definition but ramanujan was by no means the first either i've also mentioned comtet's book which even berndt's coverage recommends to put this on a rigorous foundation this has been around since before euler fractional differentiation for instance was developed from several different transform approaches from the very early transform studies it's natural that if (-ik)^n corresponds to n-th differentiation in the transform language then there is a clear generalisation of differentiation that allows real orders .. to show some of the other cool things in ramanujan's reports and to connect to the tetration threads ramanujan studies x x e x e e e e e f(x) = 1 + -- + --- + ---- + ... 3 4 5 2 3 4 2 3 2 ramanujan shows that this function is enitre and yet grows faster than any x . . e e finitely iterated exponential``` Wow thats amazing, can you give any references? @Gottfried: can you point galthaea to our forum? 05/27/2008, 09:39 AM Post: #3 Gottfried Long Time Fellow Posts: 731 Joined: Aug 2007 RE: Iteration by Ramanujan bo198214 Wrote:@Gottfried: can you point galthaea to our forum? Henryk - I'll try to send him a personal mail; hope his adress is valid. Gottfried Gottfried Helms, Kassel 05/27/2008, 11:03 AM (This post was last modified: 05/27/2008 03:37 PM by Ivars.) Post: #4 Ivars Long Time Fellow Posts: 366 Joined: Oct 2007 RE: Iteration by Ramanujan Are those 2^3,2^3^4, 2^3^4^5... = 2^3^4^...n what Andrew calls E factorial as E(n) ? Does it have generalization to x? Obviously they can not start at 1. The smallest integer is 2, unlike ordinary factorial. What if its turned around, so 2^1, 3^2^1, 4^3^2^1, 5^4^3^2^1.. n^..3^2^1. It is also a fast growing number. x^(x-1)^(x-2)..1, but much slower then the other. This slower one has been called exponential factorial: Exponential Factorial Wolfram MathWorld It is given by recurence relation: $a_n=n^{a_{n-1}}$ $a_1=1$ Ramanujan's factorial would be bigger. Do I understand right that by applying some transformation involving such factorials the summation of many divergent series can be brought to some sort of convergence-if their speed of growth is slower than these factorials? Then these perhaps can be applied to power series of extremely slow functions directly, like e.g. 1/h(z). Ivars 05/27/2008, 06:23 PM Post: #5 andydude Long Time Fellow Posts: 505 Joined: Aug 2007 RE: Iteration by Ramanujan First of all, that is not the exponential factorial. The EF is (5^4^3^2) whereas this is (2^3^4^5). Secondly, I found this on JSTOR, so I'm going to make a trip to the local library soon... Andrew Robbins 05/27/2008, 08:38 PM Post: #6 Ivars Long Time Fellow Posts: 366 Joined: Oct 2007 RE: Iteration by Ramanujan andydude Wrote:Secondly, I found this on JSTOR, so I'm going to make a trip to the local library soon... Andrew Robbins One place Ramanujan considers infinite exponentials is Notebook 5: At Amazon.com The pages 490-492 which speaks about convergence criteria for iterated exponentials can be read there by LookInside, but do not contain the formulas mentioned by Gottfried. Ivars 05/27/2008, 09:35 PM Post: #7 Gottfried Long Time Fellow Posts: 731 Joined: Aug 2007 RE: Iteration by Ramanujan Ivars Wrote:mentioned by Gottfried. ... just cited. I don't know anything about them (don't have JSTOR-access either). Source is the poster galaethea... Gottfried Helms, Kassel 05/28/2008, 03:47 AM Post: #8 andydude Long Time Fellow Posts: 505 Joined: Aug 2007 RE: Iteration by Ramanujan Ivars Wrote:One place Ramanujan considers infinite exponentials is Notebook 5: At Amazon.com Yes indeed, this book can also be found on http://scholar.google.com/ but sadly they require money or something for pages 410 and 490 which are where Ramanujan's iterated exponential formulas are... but luckily the surrounding pages talk about how Bachman recently proved this formula to be true. Bachman's article can be found here. Andrew Robbins 05/28/2008, 06:52 AM Post: #9 bo198214 Administrator Posts: 1,366 Joined: Aug 2007 RE: Iteration by Ramanujan andydude Wrote:...but luckily the surrounding pages talk about how Bachman recently proved this formula to be true. Haha, ya Ramanujan was the guy who wildly wrote down a lot a formulas, which mostly could be shown to be true. « Next Oldest \| Next Newest » Possibly Related Threads... Thread: Author Replies: Views: Last Post Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 1,401 09/04/2011 05:59 AM Last Post: Gottfried Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 10 7,914 06/09/2011 05:56 AM Last Post: bo198214 ramanujan and tetration galathaea 11 4,785 05/30/2008 12:38 PM Last Post: Ivars User(s) browsing this thread: 1 Guest(s)	2016-10-24 03:24:21	{"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": 2, "/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": 0.5703451633453369, "perplexity": 14151.187071327286}, "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-2016-44/segments/1476988719465.22/warc/CC-MAIN-20161020183839-00249-ip-10-171-6-4.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/300707/underfull-hbox-badness-10000-in-sty	# Underfull \hbox (badness 10000) in .sty I reasearched a lot of advice on the undefull box problem. But nothing I tried solved the problem. I wrote a .sty file for a certain formatting and get this warning for every occurrence of this markup: \newcommand{\recordsAffected}[2]{% \noindent This problem affects #1 record\s{#1}: \vspace{3pt} \setlength\parindent{0pt}{\tiny #2} } The code inside the .tex file looks like this, no linebreak anywhere, but it can contain many hundreds of numbers: \recordsAffected{39}{123, 456, 789, 123, 456, 789, 123, 456, 789, 123, 456, 789, 123, 456}% What am I doing wrong? Minimal example: \documentclass[a4paper]{scrartcl} \sloppy %improves justification, problem occured also without \usepackage{my_possibly_dumb_package} \begin{document} \recordsAffected{39}{a43278/008, a43942/008, a45969/008, a46754/008, a49221/008, a49581/008, a49622/008, a52060/008, a52125/008, a52127/008, a52435/008, a55814/008, a56445/008, a57540/008, a57622/008, a57624/008, a57808/008, a60025/008, a61589/008, a61966/008, a69208/008, ocm02999106/008, ocm30263703/008, a40465/008, a40629/008, ocm02573713/008, ocm27892685/008, ocm04943922/008, ocm09696410/008, ocm08401480/008, ocm19374238/008, ocm04445359/008, ocm10964101/008, ocm12302731/008, ocm06112303/008, ocm08717325/008, ocm23645394/008, ocm23400177/008, a69971/008}% \end{document} Warning: Underfull \hbox (badness 4647) in paragraph at lines 7--8 []\T1/ptm/m/n/6 a43278/008, a43942/008, a45969/008, a46754/008, a49221/008, a49 581/008, a49622/008, a52060/008, a52125/008, a52127/008, a52435/008, a55814/008 , [] • No. No \\ anywhere. But I will try to provide the full example, should have already. The warning refers to this tag though. – ena Mar 24 '16 at 20:03 • @ena: How about using a \raggedright output rather than justified? Here's a suggested output. – Werner Mar 24 '16 at 20:39 The posted example gives an error for \s but I guessed a definition for that. I used \raggedright here to avoid over/underfull boxes. I added a missing \par at the end of the scope for \tiny so that the matching baselineskip is used, rather than the normal baselineskip. \usepackage{my_possibly_dumb_package} \begin{document} \recordsAffected{39}{a43278/008, a43942/008, a45969/008, a46754/008, a49221/008, a49581/008, a49622/008, a52060/008, a52125/008, a52127/008, a52435/008, a55814/008, a56445/008, a57540/008, a57622/008, a57624/008, a57808/008, a60025/008, a61589/008, a61966/008, a69208/008, ocm02999106/008, ocm30263703/008, a40465/008, a40629/008, ocm02573713/008, ocm27892685/008, ocm04943922/008, ocm09696410/008, ocm08401480/008, ocm19374238/008, ocm04445359/008, ocm10964101/008, ocm12302731/008, ocm06112303/008, ocm08717325/008, ocm23645394/008, ocm23400177/008, a69971/008}% \end{document} \def\s#1{% \ifnum#1>1 s\fi } \newcommand{\recordsAffected}[2]{% \noindent This problem affects #1 record\s{#1}:% \vspace{3pt}% {\raggedright\tiny#2\par}% } Or if you want justified paragraph with inter word spaces allowed to stretch to cope then replace {\raggedright\tiny#2\par}% by {\parindent0pt \spaceskip .3em plus\textwidth \tiny#2\par}% • Thank you very much! (And sorry for forgetting the \s definition.) Though, I really prefer the aligned version, visually. At the moment, I just ignore warnings with -interaction=nonstopmode (but this is a messy copout). – ena Mar 25 '16 at 14:03 • @ena tex doesn't stop on warnings so -interaction not really doing anything in that case. If you prefer stretching the white space to maintain alignment then TeX will not complain so long as you tell it that you want the white space to stretch. None of the constraints are built in they are user-set. I updated the answer with a version for justified paragraph setting. Mar 25 '16 at 14:12 • Thank you for the idea. I think, the problem is that my record lists are very long (sometimes several pages, didn't want to clutter the minimal example like that) and then the badness 1000 does stop the processing (many many times, always giving line numbers of this very command). If whitespace stretching is the problem, shouldn't this already be gone using \sloppy (aka 3em)? I will experiment a bit more around whitespace, the suggestion still outputs warnings. Thanks again. – ena Mar 27 '16 at 13:28 • @ena No. TeX does not stop on badness warnings or pause for user interaction in any way, they are simply warning messages sent to the terminal and log file. You can not possibly get underfull warnings with that space setting unless some of your numbers are more than half the text width, so that you can only fit one on a line, in which case you can not do a justified setting so a warning is approprate, or use the ragged setting. Mar 27 '16 at 13:44	2022-01-17 16:49:02	{"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": 0.8708438277244568, "perplexity": 8752.145902555005}, "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-2022-05/segments/1642320300574.19/warc/CC-MAIN-20220117151834-20220117181834-00071.warc.gz"}
http://www.maplesoft.com/support/help/Maple/view.aspx?path=StringTools/Random	StringTools - Maple Programming Help Home : Support : Online Help : Programming : Names and Strings : StringTools Package : Random Strings : StringTools/Random StringTools Random return a random string Calling Sequence Random( len, alphabet ) Parameters len - positive integer; length of string to generate alphabet - (optional) string or symbol; restricts the characters that form the string seed - (optional) integer; seed for the random number generator Description • The Random(len, alphabet) calling sequence generates a random string of a given length, with the option of restricting the characters that form the returned string. The Random(len) calling sequence returns a string of length len whose characters are randomly distributed and in the numeric range $1..255$. That is, any non-zero 8-bit character can appear, and all appear with equal likelihood. If the second optional argument, alphabet, is included in the calling sequence, it specifies the "alphabet" upon which the random string is generated. This option can assume one of two forms. If it is of type string, then the characters in that string are taken to be the alphabet from which to randomly draw characters in the output string. The alphabet characters must appear in US-ASCII order and cannot contain repetitions. If the alphabet parameter is a symbol, then it must be one of the following recognized character class names. Symbol Range of Characters alpha A-Z or a-z ascii ASCII code 1 through 127 alnum A-Z, a-z, or 0-9 binary 0 or 1 cntrl FF, NL, CR, HT, VT, BEL, or BS digit 0-9 dna A,C,G or T graph alnum or punct xdigit 0-9, a-f, or A-F ident A-Z, a-z, 0-9, or _ ident1 A-Z, a-z, or _ lower a-z octal 0-7 print punct, alnum, or space character (" ") punct ascii and not in alnum, space, or cntrl space tab ("\t"), newline ("\n"), vertical tab ("\v") form-feed ("\f"), or space (" ") upper A-Z Examples > $\mathrm{with}\left(\mathrm{StringTools}\right):$ > $\mathrm{length}\left(\mathrm{Random}\left(100000\right)\right)$ ${100000}$ (1) > $\mathrm{length}\left(\mathrm{Select}\left(\mathrm{IsAlphaNumeric},\mathrm{Random}\left(100000\right)\right)\right)$ ${24412}$ (2) > $\left(\mathrm{min},\mathrm{max}\right)\left(\mathrm{op}\left(\mathrm{convert}\left(\mathrm{Random}\left(100000\right),'\mathrm{bytes}'\right)\right)\right)$ ${1}{,}{255}$ (3) > $\mathrm{dna}≔\mathrm{Random}\left(20,"ACGT"\right)$ ${\mathrm{dna}}{≔}{"CAGGAAGTTTCTCCTATGTC"}$ (4) > $\mathrm{Random}\left(20,'\mathrm{binary}'\right)$ ${"11000100001000110101"}$ (5) > $\mathrm{Random}\left(20,'\mathrm{upper}'\right)$ ${"FUWAOGIXUXHQIFZXZUQA"}$ (6) > $\mathrm{IsDigit}\left(\mathrm{Random}\left(1000,'\mathrm{digit}'\right)\right)$ ${\mathrm{true}}$ (7)	2017-02-26 03:20:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 16, "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": 0.5737022161483765, "perplexity": 4742.965296954574}, "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-2017-09/segments/1487501171933.81/warc/CC-MAIN-20170219104611-00169-ip-10-171-10-108.ec2.internal.warc.gz"}
http://www.csc.kth.se/~fpokorny/publications/abstracts/stork2013a/index.html	Towards Postural Synergies for Caging Grasps Johannes A. Stork, Florian T. Pokorny, Danica Kragic In Hand Synergies - how to tame the complexity of grapsing, Workshop, IEEE International Conference on Robotics and Automation (ICRA), 2013 Abstract Postural synergies have in recent years been successfully used as a low-dimensional representation for the control of robotic hands and in particular for the synthesis of force-closed grasps. This work proposes to study caging grasps using synergies and reports on an initial analysis of postural synergies for such grasps. Caging grasps, which have originally only been analyzed for simple planar objects, have recently been shown to be useful for certain manipulation tasks and are now starting to be investigated also for complicated object geometries. In this workshop contribution, we investigate a synthetic data-set of caging grasps of four robotic hands on several every-day objects and report on an analysis of synergies for this data-set. Files @inproceedings{stork2013a, author = {Stork, Johannes A. and Pokorny, Florian T. and Kragic, Danica}, booktitle = {Hand Synergies - how to tame the complexity of grapsing, Workshop, IEEE International Conference on Robotics and Automation (ICRA)}, title = {Towards Postural Synergies for Caging Grasps}, year = {2013}, address = {Karlsruhe, Germany}, url = {http://www.csc.kth.se/~fpokorny/static/publications/stork2013a.pdf} }	2017-10-18 02:05:36	{"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": 0.32697513699531555, "perplexity": 5377.995235257055}, "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-2017-43/segments/1508187822668.19/warc/CC-MAIN-20171018013719-20171018033719-00106.warc.gz"}
https://www.physicsforums.com/threads/help-with-physics-signs-and-directions.665353/	# Help with Physics signs and directions 1. Jan 19, 2013 ### love2learn1 The acceleration due to gravity is -9.8m.s^2 , so what does the up mean, and what does the negative mean? I thought that the negative sign always means down and you don't need to put the direction in brackets. 2. Jan 19, 2013 ### Simon Bridge The author wrote to tell you that "up" is the positive direction. This means that -9.8m.s-2 could mean the object is going down and gaining speed or it is going up and losing speed (or momentarily stationary). The sign convention is arbitrary - you don't have to call "up" positive and in many situations it makes the math easier to make down positive. You don't have to make the x axis horizontal either, or the y axis vertical. But you do have to say somewhere what convention you are using, and you have to be consistent within the problem. 3. Jan 20, 2013 ### love2learn1 But if it says - and [up] doesn't that mean that up is the negative direction 4. Jan 20, 2013 ### Staff: Mentor That seems an odd bit of notation. Where did you see it? Since you know that the acceleration due to gravity is always down, if it's given as negative that means you are taking up as positive. 5. Jan 20, 2013 ### flatmaster The notation does seem odd. He's using where a unit vector would be used. Unit vectors have multiple conventions, but I've never seen x hat, y hat, z hat i, j, k, e1, e2, e3 6. Jan 20, 2013 ### nasu They use similar notations in high school physics. In US and Canada. [E], [N], [W], . 7. Jan 20, 2013 ### BruceW What the author wrote makes sense to me. That is how I would say it, if I were explaining it with words. "In SI units, g equals minus nine point eight in the 'up' direction". And then if I define 'down' to be the negative of 'up', then it is equivalent to saying: "In SI units, g equals nine point eight in the 'down' direction" 8. Jan 20, 2013 ### Staff: Mentor Yep, it looks like they are using to represent a unit vector in the up direction, like flatmaster pointed out. Makes sense to me, though I don't recall seeing that. 9. Jan 20, 2013 ### love2learn1 So does this mean that up was not chosen as the positive direction? I'm really confused on the sign conventions in physics. Why do you need the ? 10. Jan 20, 2013 ### Staff: Mentor It means that "up" is the positive direction. Therefore "down" is the negative direction, and since the number given has a - sign, it indicates a downward acceleration. If they had written it as "9.8 m/s^2 [D]" it would have meant the same thing. I've never seen this particular notation either, but it's been more than forty years since I was in high school. The textbooks I've used and taught from at college level would say something like $$\vec a = -9.8 \hat y \text{ m/s^2}$$ where $\hat y$ is a unit vector that points upwards. Some books use $\hat x$, $\hat y$ and $\hat z$ for the unit vectors, others use $\hat i$, $\hat j$ and $\hat k$. Or they use boldface instead of the caret ("hat"). 11. Jan 21, 2013 ### Simon Bridge Beginning students often get confused when a negative sign is used with a positive direction. The sign convention is the same in physics as it is in mathematics. It indicates a deficit of something. -10m is a deficit of 10m in the upwards direction ... which is the same as saying "10m downwards". You could just say, "well why not just say so then?" The reason is because it makes the math easier when you refer to only one positive direction. If you went 10m and then 20m [D] you'd end up 10m [D] ... which you did intuitively. In math you'd have to convert one of the or [D] first so you can say (taking [D] as positive) (-10m[D]) + 20m[D] = (20-10)m[D] = 10m[D] In math, 10m[D] is "ten meters multiplied by the direction [downwards]". Unless it says something else in the book (or wherever you saw the notation) then .. no. Treat the indicator in brackets as the positive direction. In the case of - that would indicate that "upwards" is the positive direction. A negative value of a positive direction is the same as the positive value on the negative direction. Using math notation we can say "down is the opposite of up" like this: [D] = - so: -9.9 = -1x9.8x =9.8x(-1)x = 9.8(-) = 9.8[D] Because the direction of the positive axis is entirely arbitrary - if a direction is not specified, then the reader could get confused about what was intended. Maybe it seems obvious to you know, which direction things like gravity should be? Why bother saying it? Isn't it just being pedantic? But if the problem is, say, a box sliding down a slope, then it makes the math easier to put the +x axis pointing down along the slope. This means the -y axis does not point in the direction of gravity. If the author did not tell the reader that the +x axis was taken to be "down along the slope" then the reader may not realize that and get confused. Somewhere where the reader can see it there has to be some indicator. You could write: the initial velocity is -23m/s [down along the slope] with acceleration +9.8/2m/s/s [down along the slope] or just say +x dir = [down along the slope] (I'd use the last one personally.) Whatever you use - it has to be clear to the reader, which is why I suspect the author of the notation you are referring to has actually explained it someplace and maybe you just missed it? Whatever - it is a failure to communicate. Learn from it. Last edited: Jan 21, 2013 12. Jan 21, 2013 ### sophiecentaur It's all a matter of context. Anyone starting on any calculation of this sort is free to use either convention they want - as long as they stick to it throughout. If we do calculations about falling bodies (down mineshafts and off cliffs) we often choose 'downward motion' to be positive and, hence the acceleration due to gravity will be a positive value. We state (or strongly imply) that this is what we mean and then we stick with that convention and get the right answer (how far down, etc.). If we do calculations on a ballistics problem, we would (instinctively) be pointing the gun in a direction we would call Positive (UP = positve this time) and then our initial velocity would be positive and the acceleration would be negative.	2018-02-24 02:39:00	{"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": 0.7928324341773987, "perplexity": 961.5444284875726}, "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-2018-09/segments/1518891815034.13/warc/CC-MAIN-20180224013638-20180224033638-00727.warc.gz"}
https://www.physicsforums.com/threads/confused-about-ohms-law.310101/	1. Apr 27, 2009 ### suhasm After seeing contradictory posts on many forums , and getting differing opinions from my teachers , i'm completely lost with the ohms law.... I have a number of questions. Can someone please answer them for me? 1) Do semiconductors obey Ohms law? and why do they obey/not obey? if they obey , then why is the drop across a ideal diode constant even when the current in it changes? 2) I heard someone say in another thread "semiconductors obey ohms law , but semiconductor junctions dont". why is it so? 3) A thread in another forum said that liquids dont obey ohms law as ions are the current carriers... true or false? 4) Is ohm's law a special case of V=IR or is V=IR a special case of ohms law? 5) Is Ohms law a law at all? 6) Is there any theory in physics which explains why ohms law works the way it does? 2. May 2, 2009 ### Xezlec Believe it or not, you're asking a fairly deep and interesting question. It's a great question, but getting a coherent answer that makes sense to you (and is correct!) might take a lot of tries. :) I'd love to be the one who finally answers it right... we'll see. Someone will probably stop me if I say something wrong. Normally, yes. If you have nothing more complicated than a lump of silicon, it obeys the law pretty well, I believe. Well, uhh... err.... they just do. Okay, there are reasons, but they are complicated. Basically, the idea (warning: classical approximation, not really valid in quantum physics) is that the electrons just move in the direction that the applied electric field tells them to, until they hit an atom, and then they bounce off in some random direction, until the field starts pulling them back around again to the direction it wants them to travel in, etc. After lots of math (I can elaborate if you're interested) you get Ohm's Law (under certain conditions). The thing you need to know is that there are "ohmic" metrials and "non-ohmic" materials. Ohmic materials obey Ohm's Law. Non-ohmic materials do not. Of course, really, for high enough values of V and/or I, pretty much everything becomes non-ohmic eventually. So Ohm's Law is an approximation that holds in certain regions of voltage and current, for certain materials. Because a diode is not a semiconductor any more than a house is a brick. It is made out of semiconductor materials, but a diode is a device. It is a machine constructed from different materials such that the junction between them has special properties (because of quantum physics). Quick way to think about it: N-type and P-type silicon are both fairly ohmic by themselves, but when you put them together, crazy quantum junk happens at the boundary between them and all the normal rules fly out the window. At that point, right at the junction, you can kiss Ohm's Law (and a few other "laws" you may be used to!) goodbye. Well, the answer requires you to be able to think of a doped semiconductor as having more "holes" than "free electrons" or vice-versa. Start with http://en.wikipedia.org/wiki/P-n_junction" [Broken]. But be warned: these things are sometimes hard to get a firm grasp on without a quantum mechanics background. Hmmm, I think that sometimes they obey Ohm's Law. V=IR is a special case of Ohm's Law, I suppose, but not very special. Basically, that is Ohm's Law exactly. No, not if the word "law" means something that is always true for anything. It's a rule that some materials follow sometimes. Another (better) way to look at it is that it is just the definition of "resistance". Anything not following that law doesn't have a well-defined "resistance". Heh. I think electrical conduction is pretty well understood in normal cases. Last edited by a moderator: May 4, 2017 3. May 2, 2009 ### ImAnEngineer I would like to add a question. When a material doesn't 'obey Ohm's law', does that mean U/I isn't constant but the equation is still valid to calculate a third variable if you know two? E.g. V=5V, R=10 Ohm for a non-Ohmic material, is: I= 5 / 10 = 0,5A anyway ? 4. May 2, 2009 ### Xezlec Huh? Non-ohmic means that the resistance isn't defined. 5. May 3, 2009 ### ImAnEngineer So if there's a current of 1A, and a voltage of 2V, the resistance isn't 2/1=2Ohm if it's a non-ohmic material? So then what is the resistance? Is there any way to figure that out? 6. May 3, 2009 ### Xezlec Not sure what you're trying to figure out. Sure, if you want you can just define a resistance over a smaller range, and say something like, "oh, this material is ohmic over the range of 1.99 to 2.01 volts, and in that range it has a resistance of 2 ohms." Here, tell me what you would consider to be the resistance is of the non-ohmic device with this I-V relationship: http://www.utc.edu/Faculty/Tatiana-Allen/IVfig6.gif [Broken] Last edited by a moderator: May 4, 2017 7. May 3, 2009 ### dE_logics At certain values (of current or V) they do, and at certain they don't. Not obeying ohms law is a property of the material, usually metals (i.e kernels in a sea of electrons) obey ohms law. Here is a section of my notes, might be of some help - "Ohm's law - V = IR. This relation is experimentally derived. Explain in terms of K.E of electrons - The resistance offered by a conductor is a final function of the no. of kernels it encounters through the conductor. If a circuit is in a constant voltage source, and the length of the is resistance suppose x, and if the length is reduced to half; the resistance is also reduced to half and so each electron will have to dissipate more energy per unit length so as to give out all the energy it possesses. So finally; what determines the energy generated throughout the circuit per electron? The only thing can be is current, that's the only reason; if energy dissipation is seen by the resistance, it should decrease on decrement of the resistance since the no. of kernels will reduce resulting in lesser kernels on which the electron can dissipate energy on, but this is not so; it remains a constant. Answer -- As the current increases the velocity of each electron also increases, and so the momentum, thereby reduction of the kernels is compensated by increase in momentum of the electrons and if the length or resistance is made half, the momentum will increase 2 folds maintaining energy dissipation per electron. In the case of a constant current source, the potential decreases 2 folds cause the momentum of the election is maintained at a constant and so the energy released per kernel changes; since the total no. of kernels each election encounter has been reduced to half (the resistance has been reduced to half) the energy dissipated will too be half." na na na...many people are wrong. We have nothing called kernels in fluids, considering that, it cant be compared. Same thing. As said before, this is practically derived, but we can prove it using drift velocity and all. 8. May 4, 2009 ### Mapes What do you mean by "kernels"? Ohm's Law can be useful whenever charge carriers exist and respond linearly to an electric field. Electrolytes (liquids containing ions) certainly are modeled with Ohm's Law. 9. May 4, 2009 ### Caesar_Rahil i always thought that ohm's law is the actual definition of resistance. Like Ohm did a number of experiments and found out V/I=constant and called it resistance. I also heard that Ohm didn't give the law as V=IR, but in some terms of current density and electric field. like E=pJ something where p is resistivity From all i know, ohm's law can be derived as a special case. One way to do it is by assuming something called as drift velocity of electrons My text book has some explanations but it uses statistics assuming a large number of electron collide but on average they move with constant velocity, but couldn't grasp it well 10. May 7, 2009 ### TheorPhys Actually, in the case of non-ohmic materials We can speak about resistance, but not as a quotient of voltage and current, but the derivative U'(I). This is a so called differential resistance. It was widely used for radio lamps - very old radioelemnts based on electron emissions from heated cathode. 11. May 7, 2009 ### chroot Staff Emeritus All electrical currents always obey Ohm's law. Always. Always always. The trouble is that the resistance is rarely a simple number, fixed, for all time. Much more often, the resistance is a complex function of voltage, distance, time, capacitance, doping ratios, the Lotto numbers, etc. - Warren 12. May 7, 2009 ### diazona Which is practically the definition of not obeying Ohm's law...:uhh: 13. May 7, 2009 ### chroot Staff Emeritus According to whom? - Warren 14. May 7, 2009 ### ImAnEngineer Well, I got confused with this 'definition'. Never heard about it. 15. May 7, 2009 ### nasu Maybe we should first agree what is "Ohm's law". If you allow for "resistance" to vary with current, voltage and other things, what would you say Ohm's law means? Definitely the voltage won't be proportional with the current (if "resistance" depends on the current). 16. May 8, 2009 ### atyy 17. May 8, 2009 ### chroot Staff Emeritus Uh, atyy, your book reference supports me. -Warren 18. May 8, 2009 ### atyy Well, the reference first says that Ohm's law is RI=V where R is constant. Then it says RI=V can be used to define resistance even if R is not constant. 19. May 8, 2009 ### Born2bwire The more fundamental form of Ohm's Law is: $$\mathbf{J} = \sigma \mathbf{E}$$ You can get the circuit form by taking the spatial integral across the cross-section and path of the wire/device. Conductivity/resistivity do not have to be constants for this relation to hold. There is nothing in Ohm's Law that requires a linear relationship between voltage and current. Another way of putting it, in the circuit model, would be $$R = \frac{\partial V}{\partial I}$$ While these forms are not as useful when the device is non-linear, like a diode or transistor, you can still use the derivative form to find the resistance to calculate the ohmic loss in power or to find the effective resistance. Taylor series expansions of the voltage-current relationship in non-linear devices can result in estimates of effective linear resistances that are used to create a small-signal model for easier circuit analysis. For example, the turn on state of the diode can be estimated as a voltage source in series with a resistor in the small-signal realm. Taking more terms of the Taylor's series would allow you to expand the range of voltage signals the model would be valid across. 20. May 8, 2009 ### nasu This is just an approximation. In general the current is some function of E. j=f(E) You can expand the function in Taylor series in powers of E. If all the powers higher than 1 are negligible then we have j=sigmaE . I think that this is what is called an ohmic case and this is Ohm law. You may say that j=f(E) in general is Ohm's law but then is just a matter of definition. One reason the formula j=sigmaE with sigma=constant is that sigma contains the relaxation time. This is considered constant and it is a very good assumption at low fields. But higher field may change the relaxation time and then sigma is not a constant, it depend on the field.	2018-01-20 15:36:02	{"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": 0.6907961368560791, "perplexity": 1011.0819909842571}, "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-2018-05/segments/1516084889660.55/warc/CC-MAIN-20180120142458-20180120162458-00241.warc.gz"}
https://puzzling.stackexchange.com/questions/50096/2-aliens-walk-on-a-line-meeting-probability	# 2 aliens walk on a line meeting probability [closed] 2 aliens walk on a line randomly. At each timestep they walk independently either left or right (1 meter) with equal probability. They start 10 meters apart. What's the probability that after 7 time steps they have met (passed through the same point)? Hello, I'm trying to solve this puzzle but I'm struggling. I know that there are $4^7$ states in the tree. If we imagine them being on a number line. Alien $A$ starting at $0$ and Alien $B$ starting at $10$. I know that they can only meet at points $3$-$7$. I know that the probability of Alien $A$ getting to $3$ after $3$ time steps is $\frac{1}{8}$. I don't really know where to go from here. Thank you for your suggestions. • they walk sideways? Or ahead and they go left/right after each step ? – Marius Mar 17 '17 at 20:36 • Sideways. Like this ______<-A->_________________<-B->______ – Rupert Gatwick Mar 17 '17 at 20:49 • this does not look much as a puzzle. Maybe you have more luck with it here: math.stackexchange.com – Marius Mar 17 '17 at 21:37 Let's start by tracing the probabilities with a single alien: At the 1st step, he might be at positions $+1$ or $-1$ with $1/2$ probability each. At the 2nd step, $-2$ ($1/4$), $0$ ($2/4$) or $+2$ ($1/4$). At the 3rd step, $-3$ ($1/8$), $-1$ ($3/8$), $+1$ ($3/8$), $+3$ ($1/8$). At the 4th step, $-4$ ($1/16$), $-2$ ($4/16$), $0$ ($6/16$), $+2$ ($4/16$), $+4$ ($1/16$). At the 5th step, $-5$ ($1/32$), $-3$ ($5/32$), $-1$ ($10/32$), $+1$ ($10/32$), $+3$ ($5/32$), $+5$ ($1/32$). At the 6th step, $-6$ ($1/64$), $-4$ ($6/64$), $-2$ ($15/64$), $0$ ($20/64$), $+2$ ($15/64$), $+4$ ($6/64$), $+6$ ($1/64$). At the 7th step, $-7$ ($1/128$), $-5$ ($7/128$), $-3$ ($21/128$), $-1$ ($35/128$), $+1$ ($35/128$), $+3$ ($21/128$), $+5$ ($7/128$), $+7$ ($1/128$). This can easily be seen when you build: a triangle with a number 1 in the top and filling each row below it with the sum of the two numbers above. Like this: Each line has a position from $-7$ to $+7$ (the horizontal positions) and the probability of the alien being in that position is expressed as $\frac{x}{2^y}$, where $x$ is the number in the table for the step $y$. Blanks should be considered as $x = 0$. Now, let's see where the two aliens might meet: • [a] At the 5th step with $+5$ and $-5$, coming from $+4$ and $-4$ with a probability of $\frac{1}{32} \times \frac{1}{32} = \frac{1}{1024}$. Note that: At the 6th step with $+6$ and $-6$, coming from $+5$ and $-5$ they would already had met at the 5th step; • [b] At the 6th step with $+6$ and $-4$ coming from $+5$ and $-3$. This gives a probability of $\frac{1}{64} \times \frac{5}{64} = \frac{5}{4096}$; • [c] The opposite of [b]; • [d] At the 7th step, having the 5th as $+5$ and $-3$, 6th as $+6$ and $-2$ and 7th as $+7$ and $-3$; • [e] At the 7th step, having the 5th as $+5$ and $-3$, 6th as $+4$ and $-4$ and 7th as $+5$ and $-5$; • [f] At the 7th step, having the 5th as $+3$ and $-3$, 6th as $+4$ and $-4$ and 7th as $+5$ and $-5$; • [g] opposite of [d]; • [h] opposite of [e]. For cases d, e, g and h, the probabilities of reaching the 5th step are calculated as: $\frac{1}{32} \times \frac{5}{32} = \frac{5}{1024}$ for each. For case f, the proability of reaching the 5th step is: $\frac{5}{32} \times \frac{5}{32} = \frac{25}{1024}$ Each one of the cases d to h depend on exacts two steps performed by each of the aliens, so... ... we multiply each of those probabilities by $\frac{1}{16}$, because we have four steps to do, each one having $\frac{1}{2}$ of probability of happening. This gives the probabilities as: $P = p_a + p_b + p_c + p_d \times \frac{1}{16} + p_e \times \frac{1}{16} + p_f \times \frac{1}{16} + p_g \times \frac{1}{16} + p_h \times \frac{1}{16}$ However... Given that $p_b = p_c$ and that $p_d = p_e = p_g = p_h$, then $p_b + p_c = 2 p_b$ and $p_d + p_e + p_g + p_h = 4 p_d$ and we can simplify the formula to: $P = p_a + 2 p_b + 4 p_d \times \frac{1}{16} + p_f$ Now, we can solve this as... \begin{align} P & = p_a + 2 p_b + 4 p_d \times \frac{1}{16} + p_f \\ & = \frac{1}{1024} + 2 \times \frac{5}{4096} + 4 \times \frac{5}{1024} \times \frac{1}{16} + \frac{25}{1024} \times \frac{1}{16} \\ & = \frac{16}{16384} + \frac{40}{16384} + \frac{20}{16384} + \frac{25}{16384} \\ & = ... \end{align} And the final result is... $$P = \frac{101}{16384}$$ And a final curiosity: The aliens are always separated by an even number of meters. This also ensures that if they meet, they will collide and not pass one through the other swapping their positions. • Oh, you typed all that math on phone? :-O Cool! – Techidiot Mar 18 '17 at 2:57 • @Techidiot Yes. And posting answers in SE using cellphones is an exercise of torture, specially when they feature math. Now that I am at my notebook, I edited the answer severely to put it in a more adequate format. – Victor Stafusa Mar 18 '17 at 11:08	2020-01-19 10:39:38	{"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9974607825279236, "perplexity": 526.9040822472393}, "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-2020-05/segments/1579250594391.21/warc/CC-MAIN-20200119093733-20200119121733-00243.warc.gz"}
https://itectec.com/superuser/windows-7-alttab-transparent-windows-effect-delay/	# Windows 7 Alt+Tab transparent windows effect delay aero-peekalt-tabwindows 7 In windows 7 when browsing through the alt+tab thumbnails, lingering on one thumbnail for a second will engage the Aero-Peek effect causing every window to be transparent except for the chosen window. This effect is slightly delayed before starting for the first time of each alt+tab “session”, and afterwards will be applied quicker as you browse through the thumbnails. Is there a way to change the value of that initial delay? And maybe even that of the subsequent faster delays? Okay I've found the answer. Someone was kind to share some knowledge on my post at the Microsoft forum: Open Registry Editor and create the following registry key: HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\AltTab. In that key, create the following DWORD value: LivePreview_ms and set it to the delay (in milliseconds) of the first live preview. Restart Explorer to see the changes. Other Aero-peek related registry entries that I've found on the net are: HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\Advanced • DesktopLivePreviewHoverTime • ThumbnailLivePreviewHoverTime • ExtendedUIHoverTime These control the delay of other components of Aero-peek.	2021-09-20 18:09:10	{"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": 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": 0.4842526316642761, "perplexity": 4459.015872428977}, "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/1631780057083.64/warc/CC-MAIN-20210920161518-20210920191518-00046.warc.gz"}
https://www.studysmarter.us/textbooks/math/precalculus-enhanced-with-graphing-utilities-6th/counting-and-probability/q-19-use-the-information-given-in-the-figure-how-many-are-in/	Suggested languages for you: Americas Europe Q 19. Expert-verified Found in: Page 847 ### Precalculus Enhanced with Graphing Utilities Book edition 6th Author(s) Sullivan Pages 1200 pages ISBN 9780321795465 # Use the information given in the figure. How many are in A but not C? $18$. See the step by step solution ## Step 1. Given Information. The given figure is : ## Step 2. Counting values. The values are $n\left(A\cap C\text{'}\right)=15+3\phantom{\rule{0ex}{0ex}}n\left(A\cap C\text{'}\right)=18$.	2023-03-25 10:51:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "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": 0.8171929121017456, "perplexity": 12739.988745697001}, "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-2023-14/segments/1679296945323.37/warc/CC-MAIN-20230325095252-20230325125252-00138.warc.gz"}
http://www.koreascience.or.kr/article/JAKO199711919539062.page	다공성 방풍펜스 후방에 놓인 삼각프리즘의 표면압력특성에 관한 풍공학적 연구 DOI QR Code 박철우;이상준 Park, Cheol-U;Lee, Sang-Jun • 발행 : 1997.11.01 • 15 3 초록 The effects of porous wind fence on the pressure characteristics around a 2-dimensional prism model of triangular cross-section were investigated experimentally. The fence and prism model were embedded in a neutral atmospheric surface boundary layer over the city suburb. In this study, various fences of different porosity, back fence, inclination angle of prism and location of additional back prisms were tested to investigate their effects on the pressure and wall shear stress of the prism surface. The fence and prism had the same height of 40 mm and Reynolds number based on the model height was Re=3.9*10$^{4}$. The porous fence with porosity 40% was found to be the best wind fence for decreasing the mean and pressure fluctuations on the prism surface. By installing the fence of porosity 40%, the wall shear stress on the windward surface of prism was largely decreased up to 1/3 of that without the fence. This indicates that the porous fence is most effective to abate the wind erosion. Pressure fluctuations on the model surface were decreased more than half when a back fence was located behind the prism in addition to the front fence. With locating several back prisms and decreasing the inclination angle of triangular prism, the pressure fluctuations on the model surface were increased on the contrary. 키워드 다공벽;삼각프리즘;풍공학;대기경계층	2018-12-11 00:53:38	{"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": 0.5383726358413696, "perplexity": 2791.9547933709387}, "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-2018-51/segments/1544376823516.50/warc/CC-MAIN-20181210233803-20181211015303-00334.warc.gz"}
https://drchristiansalas.com/2017/01/15/a-closer-look-at-how-the-principal-orbital-and-magnetic-quantum-numbers-arise-in-schrodingers-theory-of-the-hydrogen-atom/	# A closer look at how the principal, orbital and magnetic quantum numbers arise in Schrödinger’s theory of the hydrogen atom In this note I want to explore some aspects of the solution of Schrödinger’s three-dimensional wave equation in spherical polar coordinates which pertain to the three main quantum numbers characterising the electron in a hydrogen atom: the electron’s principal, orbital and magnetic quantum numbers. In particular, I have noticed that many physics and mathematics sources tend to gloss over some (or all) of the mathematical details of how permissibility conditions on the three quantum numbers emerge naturally from validity constraints on the relevant underlying differential equations. I want to bring out these details clearly in the present note. In general, four quantum numbers are needed to fully describe atomic electrons in many-electron atoms. These four numbers and their permissible values are: Principal quantum number $\tilde{n} = 1, 2, 3, \ldots$ Orbital quantum number $l = 0, 1, 2, \ldots, (\tilde{n} - 1)$ Magnetic quantum number $m_l = 0, \pm 1, \pm 2, \ldots, \pm l$ Spin magnetic quantum number $m_s = -\frac{1}{2}, +\frac{1}{2}$ The principal quantum number determines the electron’s energy, the orbital quantum number its orbital angular-momentum magnitude, the magnetic quantum number its orbital angular-momentum direction, and the spin magnetic quantum number its spin direction. I have noticed that it is often not explained clearly why, for example, the orbital quantum number cannot exceed the principal quantum number minus one, or why the magnitude of the magnetic quantum number cannot exceed that of the orbital quantum number. I will explore issues like these in depth in the context of the time-independent Schrödinger equation for the hydrogen atom, which only involves the first three quantum numbers. I will not discuss the spin magnetic quantum number in the present note. Schrödinger’s wave equation for the hydrogen atom In Cartesian coordinates, Schrödinger’s three-dimensional equation for the electron in the hydrogen atom is $\frac{\partial^2 \psi}{\partial x^2} + \frac{\partial^2 \psi}{\partial y^2} + \frac{\partial^2 \psi}{\partial z^2} + \frac{2m_e}{\hbar^2}(E - U) \psi = 0$ where $m_e$ denotes the electron mass. The potential energy $U$ is the electric potential energy of a charge $-e$ given that it is at distance $r$ from another charge $+e$, namely $U = -\frac{e^2}{4 \pi \epsilon_0 r}$ It is necessary to change variables in Schrödinger’s equation since the potential energy is a function of radial distance $r$ rather than the Cartesian coordinate variables $x$, $y$ and $z$. Given the spherical symmetry of the atom, it is sensible to proceed by changing the variables in Schrödinger’s equation to those of spherical polar coordinates (rather than changing the $r$ variable in $U$ to Cartesian coordinates using $r = \sqrt{x^2 + y^2 + z^2}$). Only the variables in the Laplacian part of Schrödinger’s equation need to be changed, so we can use the approach in my previous note on changing variables in Laplace’s equation to get $\frac{1}{r^2} \frac{\partial }{\partial r}\big( r^2 \frac{\partial \psi}{\partial r}\big) + \frac{1}{r^2 \sin \theta}\frac{\partial }{\partial \theta}\big( \sin \theta \frac{\partial \psi}{\partial \theta} \big) + \frac{1}{r^2 \sin^2 \theta}\frac{\partial^2 \psi}{\partial \phi^2} + \frac{2m_e}{\hbar^2}(E - U) \psi = 0$ I will now temporarily simplify things by using the representation of the square of the angular momentum operator in spherical polar coordinates which I obtained in another previous note, namely $L^2 = - \hbar^2 \big( \frac{1}{\sin \theta}\frac{\partial}{\partial \theta} \big( \sin \theta \frac{\partial}{\partial \theta}\big) + \frac{1}{\sin^2 \theta}\frac{\partial^2}{\partial \phi^2} \big)$ $= - \hbar^2 r^2 \big( \frac{1}{r^2 \sin \theta}\frac{\partial}{\partial \theta} \big( \sin \theta \frac{\partial}{\partial \theta}\big) + \frac{1}{r^2 \sin^2 \theta}\frac{\partial^2}{\partial \phi^2} \big)$ Using this to replace the two middle terms in Schrödinger’s equation and rearranging we get $\frac{1}{r^2} \frac{\partial }{\partial r}\big( r^2 \frac{\partial \psi}{\partial r}\big) + \frac{2m_e}{\hbar^2}(E - U) \psi = \frac{L^2}{\hbar^2 r^2} \psi$ This equation can now be solved by the usual separation of variables approach. We assume that the $\psi$ function can be expressed as a product $\psi(r, \theta, \phi) = R(r) Y(\theta, \phi)$ and then substitute this back into the wave equation to get $\frac{Y}{r^2} \frac{d}{ d r}\big( r^2 \frac{d R}{d r}\big) + \frac{2m_e}{\hbar^2}(E - U) R Y = \frac{R}{\hbar^2 r^2} L^2 Y$ Dividing through by $\frac{R Y}{r^2}$ we get $\frac{1}{R} \frac{d}{d r}\big( r^2 \frac{d R}{d r}\big) + \frac{2m_e r^2}{\hbar^2}(E - U) = \frac{1}{\hbar^2 Y} L^2 Y$ Since the left-hand side of this equation depends only on $r$ while the right-hand side depends only on $\theta$ and $\phi$, both sides must be equal to some constant which we can call $\lambda$. Setting the left and right-hand sides equal to $\lambda$ in turn and rearranging slightly we finally get the radial equation $\frac{1}{r^2} \frac{d}{d r}\big( r^2 \frac{d R}{d r}\big) + \big[ \frac{2m_e}{\hbar^2}(E - U) - \frac{\lambda}{r^2} \big] R = 0$ and the angular equation $L^2 Y = \lambda \hbar^2 Y$ We can now apply separation of variables again to the angular equation. Rewriting the operator $L^2$ in full the angular equation becomes $- \hbar^2 \big( \frac{1}{\sin \theta}\frac{\partial}{\partial \theta} \big( \sin \theta \frac{\partial Y}{\partial \theta}\big) + \frac{1}{\sin^2 \theta}\frac{\partial^2 Y}{\partial \phi^2} \big) = \lambda \hbar^2 Y$ which simplifies to $\frac{1}{\sin \theta}\frac{\partial}{\partial \theta} \big( \sin \theta \frac{\partial Y}{\partial \theta}\big) + \frac{1}{\sin^2 \theta}\frac{\partial^2 Y}{\partial \phi^2} + \lambda Y = 0$ We assume that the $Y$ function can be written as the product $Y(\theta, \phi) = \Theta (\theta) \Phi (\phi)$ Substituting this into the angular equation gives $\frac{\Phi}{\sin \theta}\frac{d}{d \theta} \big( \sin \theta \frac{d \Theta}{d \theta}\big) + \frac{\Theta}{\sin^2 \theta}\frac{d^2 \Phi}{d \phi^2} + \lambda Y \Theta \Phi = 0$ Multiplying through by $\frac{\sin^2 \theta}{\Theta \Phi}$ and rearranging we get $-\frac{1}{\Phi} \frac{d^2 \Phi}{d \phi^2} = \frac{\sin^2 \theta}{\Theta}\big[ \frac{1}{\sin \theta}\frac{d}{d \theta}\big(\sin \theta \frac{d \Theta}{d \theta}\big) + \lambda \Theta\big]$ Since the left-hand side of this equation depends only on $\phi$ while the right-hand side depends only on $\theta$, both sides must be equal to some constant which we can provisionally call $k$. Setting the left and right-hand sides equal to $k$ in turn and rearranging we get $\frac{d^2 \Phi}{d \phi^2} + k \Phi = 0$ and $\frac{1}{\sin \theta}\frac{d}{d \theta}\big(\sin \theta \frac{d \Theta}{d \theta}\big) + \big( \lambda - \frac{k}{\sin^2 \theta}\big) \Theta = 0$ We now have three ordinary differential equations that need to be solved, one for $\Phi$, one for $\Theta$ and one for $R$. We will solve each of them in turn. The equation for $\Phi$ The equation for $\Phi$ is a straightforward second-order differential equation with auxiliary equation $\zeta^2 + k = 0$ implying $\zeta = \pm \sqrt{-k}$ if $k < 0$ and $\zeta = \pm i \sqrt{k}$ if $k > 0$. Therefore it has a general solution of the form $\Phi(\phi) = Ae^{\sqrt{-k} \phi} + Be^{- \sqrt{-k} \phi}$ if $k < 0$ and $\Phi(\phi) = Ae^{i \sqrt{k} \phi} + Be^{- i \sqrt{k} \phi}$ if $k > 0$, where $A$ and $B$ are arbitrary constants. Now, the azimuth angle $\phi$ can take any value in $(-\infty, \infty)$ but the function $\Phi$ must take a single value at each point in space (since this is a required property of the quantum wave function which $\Phi$ is a constituent of). It follows that the function $\Phi$ must be periodic since it must take the same value at $\phi$ and $\phi + 2\pi$ for any given $\phi$. This imposes two constraints on the form of the general solution: (1) it cannot consist only of exponential functions with real arguments since these are not periodic (thus ruling out the first general solution above and thereby implying that the separation constant $k$ must be nonnegative); (2) $\sqrt{k}$ must be an integer. Given these constraints, it is customary in quantum mechanics to denote $\pm \sqrt{k}$ by the letter $m$ (it is called the magnetic quantum number) and to specify the separation constant in the angular equations as $m^2$, which guarantees its nonnegativity. We then state the general solution of the equation for $\Phi$ as $\Phi(\phi) = Ae^{i m \phi} + Be^{- i m \phi}$ In practice, a particular electron wave function will involve only a single value of $m$ so only the first of the two terms in the general solution will be necessary. We can therefore state the general solution of the equation for $\Phi$ for a given magnetic quantum number $m$ as $\Phi(\phi) \propto e^{i m \phi}$ The equation for $\Theta$ Given that we now know the separation constant for the angular equations is either zero or a positive square number $k = m^2$, we can write the equation for $\Theta$ as $\frac{1}{\sin \theta}\frac{d}{d \theta}\big(\sin \theta \frac{d \Theta}{d \theta}\big) + \big( \lambda - \frac{m^2}{\sin^2 \theta}\big) \Theta = 0$ Expanding the first term we get $\frac{1}{\sin \theta} \cos \theta \frac{d \Theta}{d \theta} + \frac{d^2 \Theta}{d \theta^2} + \big( \lambda - \frac{m^2}{\sin^2 \theta}\big) \Theta = 0$ I am now going to multiply and divide the first two terms by $\sin^2 \theta$ to get $\sin^2 \theta \big(\frac{\cos \theta}{\sin^3 \theta} \frac{d \Theta}{d \theta} + \frac{1}{\sin^2 \theta} \frac{d^2 \Theta}{d \theta^2} \big) + \big( \lambda - \frac{m^2}{\sin^2 \theta}\big) \Theta = 0$ $\iff$ $\sin^2 \theta \big(- \frac{\cos \theta}{\sin^3 \theta} \frac{d \Theta}{d \theta} + \frac{1}{\sin^2 \theta} \frac{d^2 \Theta}{d \theta^2} + \frac{2 \cos \theta}{\sin^3 \theta} \frac{d \Theta}{d \theta}\big) + \big( \lambda - \frac{m^2}{\sin^2 \theta}\big) \Theta = 0$ Now we can make the change of variable $x = \cos \theta$ which implies $dx = - \sin \theta d \theta$ and therefore $\frac{d \theta}{dx} = - \frac{1}{\sin \theta}$ $\frac{d \Theta}{d x} = \frac{d \Theta}{d \theta} \frac{d \theta}{d x} = - \frac{1}{\sin \theta} \frac{d \Theta}{d \theta}$ $\frac{d^2 \Theta}{d x^2} = \frac{d}{d \theta} \big[ - \frac{1}{\sin \theta} \frac{d \Theta}{d \theta} \big] \frac{d \theta}{d x} = - \frac{\cos \theta}{\sin^3 \theta} \frac{d \Theta}{d \theta} + \frac{d^2 \Theta}{d \theta^2}$ Using these in the amended form of the $\Theta$ equation together with the fact that $\sin^2 \theta$ = $1 - x^2$, the $\Theta$ equation becomes $(1 - x^2) \big(\frac{d^2 \Theta}{d x^2} - \frac{2x}{1 - x^2} \frac{d \Theta}{d x} \big) + \big(\lambda - \frac{m^2}{1 - x^2} \big) \Theta = 0$ $\iff$ $(1 - x^2) \frac{d^2 \Theta}{d x^2} - 2x \frac{d \Theta}{d x} + \big(\lambda - \frac{m^2}{1 - x^2} \big) \Theta = 0$ We will solve this equation first for the case $m = 0$ (the solutions will be Legendre polynomials) and use these results to construct solutions for the case $m \neq 0$ (the solutions here will be the associated Legendre functions). Setting $m = 0$ we get $(1 - x^2) \frac{d^2 \Theta}{d x^2} - 2x \frac{d \Theta}{d x} + \lambda \Theta = 0$ which has the form of a well known differential equation known as Legendre’s equation. It can be solved by assuming a series solution of the form $\Theta = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + \cdots + a_n x^n + \cdots$ and then differentiating it term by term twice to get $\Theta^{\prime} = a_1 + 2 a_2 x + 3 a_3 x^2 + 4 a_4 x^3 + \cdots + n a_n x^{n-1} + \cdots$ and $\Theta^{\prime \prime} = 2 a_2 + 6 a_3 x + 12 a_4 x^2 + 20 a_5 x^3 + \cdots + n (n - 1) a_n x^{n-2} + \cdots$ We now substitute these into Legendre’s equation and set the coefficient of each power of $x$ equal to zero (because $\Theta$ must satisfy Legendre’s equation identically). We find that the coefficient of the $x^n$ term satisfies $(n + 2)(n + 1) a_{n + 2} + (\lambda - n(n + 1)) a_n = 0$ which implies $a_{n + 2} = - \frac{(\lambda - n(n + 1))}{(n + 2)(n + 1)} a_n$ This formula makes it possible to find any even coefficient as a multiple of $a_0$ and any odd coefficient as a multiple of $a_1$. The general solution of our Legendre equation is then a sum of two series involving two arbitrary constants $a_0$ and $a_1$: $\Theta = a_0 \bigg \{1 - \frac{\lambda}{2!} x^2 + \frac{\lambda (\lambda - 6)}{4!} x^4 - \frac{\lambda(\lambda - 6)(\lambda - 20)}{6!} x^6 + \cdots \bigg \}$ $+ a_1 \bigg \{x - \frac{(\lambda - 2)}{3!} x^3 + \frac{(\lambda - 2)(\lambda - 12)}{5!} x^5 - \frac{(\lambda - 2)(\lambda - 12)(\lambda - 30)}{7!} x^7 + \cdots \bigg \}$ Both of the series in this sum converge for $x^2 < 1$ but in general they do not converge for $x^2 = 1$. This is a problem for us because in our change of variables we set $x = \cos \theta$ and we want solutions that converge for all possible values of $\theta$ including those that result in $x^2 = 1$. It turns out that the only way to get such solutions is to choose integer values of $\lambda$ that make either the $a_0$ or the $a_1$ series in the above sum terminate (the other series will generally be divergent so we remove it by setting the corresponding arbitrary constant equal to zero). This requires $\lambda$ to take values in the quadratic sequence $0$, $2$, $6$, $12$, $20$, $30$, $42$, $56 \ldots$ The $l$-th term of this sequence is $l(l + 1)$, so the separation constant $\lambda$ must be of this form, i.e., $\lambda = l(l + 1)$ for some $l = 0, 1, 2, 3, \dots$. When $l$ takes an even value the $a_0$ series will terminate and we can set $a_1 = 0$ to make the other series vanish. Conversely, when $l$ takes an odd value the $a_1$ series will terminate and we can set $a_0 = 0$ to make the other series vanish. From the eigenvalue equation for $L^2$ given earlier ($L^2 Y = \lambda \hbar^2 Y$) it is clear that the magnitude of the orbital angular momentum is $L = \sqrt{l(l + 1)} \hbar$. It is interesting to see how the form of this arises mathematically from considering series solutions to Legendre’s equation above. The parameter $l$ is called the orbital angular momentum quantum number. Note that negative integral values of $l$ are allowed but they simply give solutions already obtained for positive values. For example, $l = -2$ gives $\lambda = 2$ and this makes the $a_1$ series terminate, yielding the polynomial solution $\Theta = a_1 x$ This is exactly the same solution as the one that would be obtained if $l = 1$. It is therefore customary to restrict $l$ to nonnegative values. Each possible value of $l$ gives a polynomial solution to Legendre’s equation. For $l = 0$ we get $\Theta = a_0$, for $l = 1$ we get $\Theta = a_1 x$, for $l = 2$ we get $\Theta = a_0 - 3 a_0 x^2$, and so on. If the value of $a_0$ or $a_1$ in each polynomial equation is selected so that $\Theta = 1$ when $x = 1$ the resulting polynomials are called Legendre polynomials, denoted by $P_l(x)$. Given that for each $l$ we have $P_l(1) = 1$ the first few Legendre polynomials are $P_0(x) = 1$ $P_1(x) = x$ $P_2(x) = \frac{1}{2}(3 x^2 - 1)$ $P_3(x) = \frac{1}{2}\big(5 x^3 - 3x \big)$ These are the physically acceptable solutions to Legendre’s equation for $\Theta$ above. We now consider the solutions for $m \neq 0$ of the equation $(1 - x^2) \frac{d^2 \Theta}{d x^2} - 2x \frac{d \Theta}{d x} + \big(\lambda - \frac{m^2}{1 - x^2} \big) \Theta = 0$ We now know that $\lambda = l(l + 1)$ so we can write this in and we can also add the subscript $l$ to $m$ as the solutions to this equation will involve a link the between the values of the orbital angular momentum and magnetic quantum numbers. The equation we need to solve becomes $(1 - x^2) \frac{d^2 \Theta}{d x^2} - 2x \frac{d \Theta}{d x} + \big[l(l + 1) - \frac{m_l^2}{1 - x^2} \big] \Theta = 0$ The link between $l$ and $m_l$ arises from the fact that we are constrained in trying to solve this equation: it encompasses the case $m_l = 0$ for which the physically acceptable solutions are the Legendre polynomials $P_l(x)$. Therefore the physically allowable solutions for the above equation must include the Legendre polynomials as a special case. We can find these by using the series approach again and it turns out that the physically acceptable solutions are the so-called associated Legendre functions which take the form $P_l^{m_l}(x) = (1 - x^2)^{m_l/2}\frac{d^{m_l}}{d x^{m_l}}P_l(x)$ Now, each Legendre polynomial $P_l(x)$ is a polynomial of degree $l$. Therefore the $m_l$-th order derivative in $P_l^{m_l}$ will equal zero if $\|m_l\| > l$, so for physically acceptable solutions we must impose the constraint $\|m_l\| \leq l$ in the differential equation for $\Theta$. This is where the link between the quantum numbers $l$ and $m_l$ comes from in the quantum theory of the hydrogen atom: given a value of $l$ the acceptable values of $m_l$ are integers in the range $-l \leq m_l \leq l$. Finally, note two things: (1) $P_l^{m_l}(x)$ reduces to the Legendre polynomial $P_l(x)$ when $m_l = 0$, which is what we needed. (2) A negative value for $m_l$ does not change $m_l^2$ in the original differential equation so a solution for positive $m_l$ is also a solution for the corresponding negative $m_l$. Thus many references define the associated Legendre function $P_l^{m_l}(x)$ for $-l \leq m_l \leq l$ as $P_l^{\|m_l\|}(x)$. To conclude, given values for the quantum numbers $l$ and $m_l$, the general solution of the equation for $\Theta$ can be written as $\Theta(\theta) \propto P_l^{m_l}(\cos \theta)$ To clarify where the principal quantum number comes from, the final equation we need to deal with is the radial equation $\frac{1}{r^2} \frac{d}{d r}\big( r^2 \frac{d R}{d r}\big) + \big[ \frac{2m_e}{\hbar^2}(E - U) - \frac{\lambda}{r^2} \big] R = 0$ Writing $\lambda = l(l + 1)$ and replacing $U$ with the formula for the potential energy we get $\frac{1}{r^2} \frac{d}{d r}\big( r^2 \frac{d R}{d r}\big) + \big[ \frac{2m_e}{\hbar^2}\big(\frac{e^2}{4 \pi \epsilon_0 r} + E\big) - \frac{l(l + 1)}{r^2} \big] R = 0$ $\iff$ $\frac{d^2 R}{d r^2} + \frac{2}{r} \frac{d R}{d r} + \frac{2m_e}{\hbar^2} \big[ E + \frac{e^2}{4 \pi \epsilon_0 r} - \frac{l(l + 1) \hbar^2}{2 m_e r^2} \big] R = 0$ We are only interested in solutions for which the electron is bound within the atom, so we take $E < 0$ (the negative energy of the electron is the amount of energy that must be supplied to it to free it from the atom). In order to solve the above equation it is customary to make the change of variable $\rho = \big(-\frac{8 m_e E}{\hbar^2}\big)^{1/2} r$ and define the dimensionless constant $\tau = \frac{e^2}{4 \pi \epsilon_0 \hbar} \big(-\frac{m_e}{2 E} \big)^{1/2}$ If we then specify $R = R(\rho)$ we have $\frac{d R}{d r} = \frac{d R}{d \rho} \frac{d \rho}{d r} = \big(-\frac{8 m_e E}{\hbar^2}\big)^{1/2} \frac{d R}{d \rho}$ $\frac{2}{r} \frac{d R}{d r} = \big(-\frac{8 m_e E}{\hbar^2}\big) \frac{2}{\rho} \frac{d R}{d \rho}$ $\frac{d^2 R}{d r^2} = \big(-\frac{8 m_e E}{\hbar^2}\big)^{1/2} \frac{d^2 R}{d \rho^2} \frac{d \rho}{d r} = \big(-\frac{8 m_e E}{\hbar^2}\big) \frac{d^2 R}{d \rho^2}$ $\frac{2 m_e}{\hbar^2} E + \frac{2 m_e}{\hbar^2} \frac{e^2}{4 \pi \epsilon_0 r} = \big(-\frac{8 m_e E}{\hbar^2}\big) \big \{\frac{1}{4}\frac{e^2}{4 \pi \epsilon_0 r} \big(-\frac{1}{E}\big) - \frac{1}{4}\big \} = \big(-\frac{8 m_e E}{\hbar^2}\big) \big(\frac{\tau}{\rho} - \frac{1}{4}\big)$ $\frac{l(l + 1)}{r^2} = \big(-\frac{8 m_e E}{\hbar^2}\big) \frac{l(l + 1)}{\rho^2}$ Using these results we can rewrite the differential equation as $\big(-\frac{8 m_e E}{\hbar^2}\big) \bigg \{\frac{d^2 R}{d \rho^2} + \frac{2}{\rho} \frac{d R}{d \rho} + \big[\frac{\tau}{\rho} - \frac{1}{4} - \frac{l(l + 1)}{\rho^2}\big] R(\rho) \bigg \} = 0$ $\iff$ $\frac{d^2 R}{d \rho^2} + \frac{2}{\rho} \frac{d R}{d \rho} + \big[\frac{\tau}{\rho} - \frac{1}{4} - \frac{l(l + 1)}{\rho^2}\big] R(\rho) = 0$ To make further progress we consider the behaviour of this differential equation as $\rho \rightarrow \infty$. It reduces to $\frac{d^2 R}{d \rho^2} - \frac{1}{4} R = 0$ which is a straightforward second-order differential equation with auxiliary equation $\zeta^2 - \frac{1}{4} = 0$ $\implies \zeta = \pm \frac{1}{2}$ The positive solution to the auxiliary equation implies a term in the general solution of the form $e^{\rho/2}$ which is unacceptable since it explodes as $\rho \rightarrow \infty$. Therefore we only accept the negative solution to the auxiliary equation and the general solution for $R$ as $\rho \rightarrow \infty$ must be of the form $R \propto e^{-\rho/2}$ This suggests we can try an exact solution of the full differential equation of the form $R = e^{-\rho/2} F(\rho)$ Differentiating this twice we get $\frac{d R}{d \rho} = -\frac{1}{2} e^{-\rho/2} F(\rho) + e^{-\rho/2} F^{\prime} (\rho)$ $\frac{d^2 R}{d \rho^2} = \frac{1}{4} e^{-\rho/2} F(\rho) - \frac{1}{2} e^{-\rho/2} F^{\prime}(\rho) - \frac{1}{2} e^{-\rho/2} F^{\prime}(\rho) + e^{-\rho/2} F^{\prime \prime} (\rho)$ Substituting these into the differential equation $\frac{d^2 R}{d \rho^2} + \frac{2}{\rho} \frac{d R}{d \rho} + \big[\frac{\tau}{\rho} - \frac{1}{4} - \frac{l(l + 1)}{\rho^2}\big] R(\rho) = 0$ gives $F^{\prime \prime}(\rho) + \frac{(2 - \rho)}{\rho} F^{\prime}(\rho) + \big[\frac{(\tau - 1)}{\rho} - \frac{l(l + 1)}{\rho^2}\big] F(\rho) = 0$ $\iff$ $\rho^2 F^{\prime \prime}(\rho) + \rho (2 - \rho) F^{\prime}(\rho) + \big[\rho (\tau - 1) - l(l + 1)\big] F(\rho) = 0$ We can now try to solve this latest version of the differential equation by the method of Frobenius, which involves assuming a generalised power series solution of the form $F(\rho) = a_0 \rho^s + a_1 \rho^{s + 1} + a_2 \rho^{s + 2} + \cdots$ Differentiating twice we get $F^{\prime}(\rho) = s a_0 \rho^{s-1} + (s + 1) a_1 \rho^s + (s + 2) a_2 \rho^{s + 1} + \cdots$ $F^{\prime \prime}(\rho) = (s - 1) s a_0 \rho^{s-2} + s (s + 1) a_1 \rho^{s-1} + (s + 1) (s + 2) a_2 \rho^s + \cdots$ Then the terms appearing in the differential equation have the generalised power series forms $\rho^2 F^{\prime \prime}(\rho) = (s - 1) s a_0 \rho^s + s (s + 1) a_1 \rho^{s+1} + (s + 1) (s + 2) a_2 \rho^{s+2} + \cdots$ $2 \rho F^{\prime}(\rho) = 2 s a_0 \rho^s + 2 (s + 1) a_1 \rho^{s+1} + 2 (s + 2) a_2 \rho^{s + 2} + \cdots$ $-\rho^2 F^{\prime}(\rho) = - s a_0 \rho^{s+1} - (s + 1) a_1 \rho^{s+2} - (s + 2) a_2 \rho^{s + 3} - \cdots$ $(\tau - 1) \rho F(\rho) = (\tau - 1) a_0 \rho^{s+1} + (\tau - 1) a_1 \rho^{s + 2} + (\tau - 1) a_2 \rho^{s + 3} + \cdots$ $-l(l + 1) F(\rho) = -l(l + 1) a_0 \rho^s - l(l + 1) a_1 \rho^{s + 1} - l(l + 1) a_2 \rho^{s + 2} - \cdots$ Summing these terms (remembering that the sum must be identically equal to zero) we find the coefficient of $\rho^s$ to be $[s(s - 1) + 2s - l(l+1)]a_0 = 0$ $\implies$ $s(s + 1) - l(l+1) = 0$ $\implies$ $s = l$ or $s = -l - 1$ Now, when $s = -l - 1$ the first term of the power series for $F(\rho)$ is $a_0/\rho^{l+1}$ which explodes as $\rho \rightarrow 0$. This is unacceptable so we discard this solution and set $s = l$. For the coefficient of $\rho^{s + n}$ we get $[(s+n)(s+n-1) + 2(s+n) - l(l+1)]a_n + [(\tau - 1) - (s+n-1)]a_{n-1} = 0$ Setting $s = l$ and rearranging gives us the recurrence equation $a_n = \frac{(l + n - \tau)}{(l+n+1)(l+n) - l(l+1)} a_{n-1}$ From this recurrence equation we observe that $a_n \rightarrow \frac{1}{n}a_{n-1} = \frac{1}{n!}a_0$ as $n \rightarrow \infty$. We deduce from this that the series for $F(\rho)$ becomes like $a_0 \rho^l \sum \frac{\rho^n}{n!}$ as $n \rightarrow \infty$ and therefore $R = e^{-\rho/2} F(\rho)$ becomes like $a_0 \rho^l e^{\rho/2}$. However, this diverges as $\rho \rightarrow \infty$ which is unacceptable, so we conclude that the series for $F(p)$ must terminate at some value of $n$ which we will call $N$. In this case we have $a_{N+1} = 0$ which the recurrence equation tells us can only happen if $\tau = l + N + 1 \equiv \tilde{n}$ This is how the principal quantum number $\tilde{n}$ first appears. Now, we have $\tau = \frac{e^2}{4 \pi \epsilon_0 \hbar} \big(-\frac{m_e}{2 E} \big)^{1/2} = \tilde{n}$ $\iff$ $\big(\frac{e^2}{4 \pi \epsilon_0}\big)^2 \big(-\frac{m_e}{2 \hbar^2}\big) \frac{1}{E} = \tilde{n}^2$ $\iff E_{\tilde{n}} = \big(-\frac{m_e}{2 \hbar^2}\big) \big(\frac{e^2}{4 \pi \epsilon_0}\big)^2 \frac{1}{\tilde{n}^2}$ These are the famous bound-state energy eigenvalues for $\tilde{n} = 1, 2, \ldots$. This is the same formula for the energy levels of the hydrogen atom that Niels Bohr obtained by intuitive means in his 1913 ‘solar system’ model of atomic structure. As stated above, the integer $\tilde{n}$ is called the principal quantum number. Recall that $\tilde{n} = l + N + 1$ and $N$ cannot be smaller than zero. It follows that $\tilde{n} - l - 1 \geq 0$ $\iff$ $l \leq \tilde{n} - 1$ This explains why for a given value of $\tilde{n}$ the allowable values of $l$ are $l = 0, 1, 2, \dots, (\tilde{n}-1)$. Returning to the solution of $\rho^2 F^{\prime \prime}(\rho) + \rho (2 - \rho) F^{\prime}(\rho) + \big[\rho (\tau - 1) - l(l + 1)\big] F(\rho) = 0$ the above discussion suggests that we should look for a solution of the form $F(\rho) = a_0 \rho^l L(\rho)$ where $L(\rho)$ is a polynomial (rather than an infinite series). Differentiating this twice gives $F^{\prime}(\rho) = a_0 l \rho^{l-1}L(\rho) + a_0 \rho^l L^{\prime}(\rho)$ $F^{\prime \prime} (\rho) = a_0 (l-1) l \rho^{l-2}L(\rho) + 2 a_0 l \rho^{l-1} L^{\prime}(\rho) + a_0 \rho^l L^{\prime \prime}(\rho)$ Substituting these into the differential equation and setting $\tau = \tilde{n}$ we get $\rho^{l+2} L^{\prime \prime}(\rho) + (2l + 2 - \rho) \rho^{l+1}L^{\prime}(\rho) + (\tilde{n} - 1 - l)\rho^{l+1}L(\rho) = 0$ $\iff$ $\rho L^{\prime \prime}(\rho) + (2l + 2 - \rho) L^{\prime}(\rho) + (\tilde{n} - 1 - l) L(\rho) = 0$ $\iff$ $\rho L^{\prime \prime}(\rho) + (\alpha + 1 - \rho) L^{\prime}(\rho) + \tilde{n}^{} L(\rho) = 0$ where $\alpha \equiv 2l + 1$ and $\tilde{n}^{} \equiv \tilde{n} - 1 - l$. This last form is a well known differential equation whose physically acceptable solutions in the present context are associated Laguerre polynomials given by the formula $L_{\tilde{n}^{}}^{(\alpha)} = \sum_{j = 0}^{\tilde{n}^{}} (-1)^j \frac{(\tilde{n}^{} + \alpha)!}{(\tilde{n}^{}-j)!(\alpha + j)!}\frac{\rho^j}{j!}$ For given quantum numbers $\tilde{n}$ and $l$, the solution of the radial equation for $R$ is then $R_{\tilde{n}l}(r) \propto e^{-\rho/2}p^l L_{\tilde{n} - l - 1}^{(2l + 1)}$ Final form of the electron wave function $\psi$ Putting everything together, for given principal quantum number $\tilde{n}$, orbital quantum number $l$ and magnetic quantum number $m_l$, the wave function of the electron in the hydrogen atom is $\psi_{\tilde{n} l m_l}(r, \theta, \phi) \propto e^{-\rho/2}p^l L_{\tilde{n} - l - 1}^{(2l + 1)} P_l^{m_l}(\cos \theta) e^{i m_l \phi}$ where $\rho = \big(-\frac{8 m_e E_{\tilde{n}}}{\hbar^2}\big)^{1/2} r$ and $E_{\tilde{n}} = \big(-\frac{m_e}{2 \hbar^2}\big) \big(\frac{e^2}{4 \pi \epsilon_0}\big)^2 \frac{1}{\tilde{n}^2}$	2019-02-16 15:47:52	{"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": 328, "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": 0.9424770474433899, "perplexity": 112.46129688216038}, "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-2019-09/segments/1550247480622.9/warc/CC-MAIN-20190216145907-20190216171907-00438.warc.gz"}
http://physics.stackexchange.com/tags/time-reversal/new	# Tag Info 0 No. A single measurement can't tell you if the state was in a superposition or it was a pure state. In order to be able to do that you must have knowledge of how the state was prepared, which means you must have gauged your apparatus and therefore performed a statistically relevant number of measurements on the very same state many times and taken note of ... 0 check this http://www.birs.ca/workshops/2014/14w5147/files/breannan_smith_reflections_slides.pdf i made it!this contains a think part of the answer you are seeking 0 The laws of classical physics are strictly symmetric under time reversal. So given the backwards motion of every single point particle (which allows you to know convectional/conduction flow of heat, as well as longitudinal sound waves), as well as every single light ray (radiational flow of heat), you must be able to run a simulation backwards in time and ... 0 In solid state physics: Any transition to ferro- or antiferro-magnetically ordered state breaks the time inversion symmetry (1'), because the spontaneous magnetic moment on each atom changes the sign at 1'-operation. 1 I don't know if this is standard, but consider a pendulum that can swing a full circle in a plane. Vibrate the point of suspension up and down at the appropriate frequency. The pendulum will gain energy and spin either clockwise or counterclockwise. 2 You're confusing many different things together, and I'll try to clarify and separate them to make the problem clear. The problem you're facing isn't a time reversal issue. It's lack of information. So let's go through this one by one. Classical physics is 100% symmetric in time. This is the concept of determinism. There's no doubt in that. The ... -1 Inelastic collisions are so that kinetic energy is not conserved, for example, collision of macroscopic objects in real life. Part of kinetic energy is transformed in heat (atomic motion in participants). In order to write time-reversible, symmetrical equations, you have to include losses of kinetic energy. Briefly, "a set of objects with positions and ... 2 The problem here arises because the 4-current in the OP is assumed to be a 1-form, and after many years of accumulated rust on the subject I completely forgot that this is, strictly speaking, not the right geometrical object that can describe current density. Indeed, being a density, it must be a 3-form, and therefore the correct geometrical object is J = ... 1 Conservation of momentum! Force × Time = Impulse = Δ Momentum Since the average force is the same going up and down, and since the momentum change is the same going up and down as well, the time during which the force is applied must also be the same. 1 When one throws a stone.... Your arm is capable of propelling an object at up to around 150km/h (and that's with some practice). At that speed the many factors like air resistance are negligible. Let’s load a 16-inch shell into a gun (you will find several on the ISS Iowa), aim it 45 degrees up and press the button. The shell is going to go up at ... 4 A lot of things have to hold to get that symmetry. You have to neglect air resistance. You either have to throw it straight up, or the ground over there has to be at the the same altitude as the ground over here. You have to through it slowly enough that it comes back down (watch out for escape velocity) But if you have that, then the simplest explanation ... 0 Assuming that the only forces acting on the stone are the initial force exerted by the hand on the stone AND the force of gravity, we have the following situation: Immediately after throwing, the stone has a kinetic energy in the x-direction that never changes (conservation of energy) and the stone has a kinetic energy in the y-direction that is constantly ... 7 I would consider that since acceleration is a constant vector pointing downward, that the time the projectiles downward component takes to accelerate from V(initial) to 0 would be the same as the time it takes to accelerate the object from 0 to V(final) 2 (Non-kinematics math attempt but just some principles) It is a partial observation in that It hits the ground with same speed. Angle by which it hits the ground is the same (maybe a direction change) It takes equal time to reach to the peak and then hit the ground They are equally strange coincidences. Which are more fundamental? Consider the following ... 1 Asking "Why" in physics often leads out of physics and into philosophy. Why is there light? Because God said so. Physics only answers questions about how the universe behaves and how to describe that behavior. If a why question can be answered with physics, the answer is "because it follows from a law of physics." A law is just a mathematical description of ... 3 One could say that this is an experimental observation; after one could envisage, hypothetically, where this is not the case. This is not hypothetical once you take air resistance into account. One could say that the curve that the stone describes is a parabola; and the two halves are symmetric around the perpendicular line through its apex. But ... 4 I think its because both halves of a projectile's trajectory are symmetric in every aspect. The projectile going from its apex position to the ground is just the time reversed version of the projectile going from its initial position to the apex position. 14 I would say that it is a result of time reversal symmetry. If you consider the projectile at the apex of its trajectory then all that changes under time reversal is the direction of the horizontal component of motion. This means that the trajectory of the particle to get to that point and its trajectory after that point should be identical apart from a ... Top 50 recent answers are included	2015-03-07 01:54:09	{"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": 0.687711775302887, "perplexity": 362.8891060182142}, "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-2015-11/segments/1424937406179.50/warc/CC-MAIN-20150226075646-00306-ip-10-28-5-156.ec2.internal.warc.gz"}
https://www.vedantu.com/question-answer/question-the-kinetic-energy-of-an-electron-in-class-11-chemistry-jee-main-5f4818a02b8d06442522c1a8	Question # Question: The kinetic energy of an electron in the second Bohr’s orbit of a hydrogen atom is: [${a_0}$ is the Bohr’s radius](A) $\dfrac{{{h^2}}}{{4{\pi ^2}m{a_0}^2}}$ (B) $\dfrac{{{h^2}}}{{16{\pi ^2}m{a_0}^2}}$ (C) $\dfrac{{{h^2}}}{{32{\pi ^2}m{a_0}^2}}$ (D) $\dfrac{{{h^2}}}{{64{\pi ^2}m{a_0}^2}}$ Hint: Before attempting this question one should have prior knowledge of Bohr model, working on it and basic formulas given by Bohr’s model, using the given information will help you to approach towards the solution to the question. Complete step by step solution: Niels Bohr introduced an atomic hydrogen model, in which he describes a positively charged nucleus, inside which are protons and neutrons which are then surrounded by negatively charged electron clouds. Since, Bohr describes that the electron orbits the nucleus in an atomic shell. Hence, according to the question we are asked the kinetic energy of an electron in the second Bohr’s orbit of a hydrogen atom. So, according to Bohr, the angular momentum is given as follows. $mvr = \dfrac{{nh}}{{2\pi }}$ From here, mv=$\dfrac{{nh}}{{2\pi r}}$ (equation 1) Since, we have to find out the kinetic energy, So kinetic energy =$\dfrac{1}{2}m{v^2}$ (equation 2) By equating these two equations we get, $(mv) = \dfrac{{nh}}{{2\pi r}}$ By squaring the above equation we get, $(m{v^2}) = \dfrac{{{n^2}{h^2}}}{{({2^2}){\pi ^2}{r^2}}}$ Which is then equal to ${m^2}{v^2} = \dfrac{{{n^2}{h^2}}}{{4{\pi ^2}{r^2}}}$ Now, let us move m towards left side then, we will get the equation as: $m{v^2} = \dfrac{1}{m} \times \dfrac{{{n^2}{h^2}}}{{4{\pi ^2}{r^2}}}$ (equation 3) Now, let us put equation 3 in equation 1 Then, kinetic energy = $\dfrac{1}{2} \times \dfrac{1}{m} \times \dfrac{{{n^2}{h^2}}}{{4{\pi ^2}{r^2}}}$ Now, as we have given in the question that radius of the Bohr’s=${a_0}$ and the electron is in the second shell, so n=2 and ${r_1} = {a_0}$ (given). As the electron is in the second shell Thus, ${r_2} = {a_0} \times {(2)^2} = 4{a_0}$ Let us put the final values to the above equation: $K.E = \dfrac{1}{2} \times \dfrac{{{2^2}{h^2}}}{{4{\pi ^2}{{(4{a_0})}^2}m}}$ =$\dfrac{{{h^2}}}{{32{\pi ^2}{a_0}^2m}}$ Hence, Option C is correct. Note: As we all know, the Bohr’s model was an important step in development of atomic theory, but it has several limitations too which are as follows: According to Bohr’s model the electrons have both a known radius and orbit, but this concept causes violation of the Heisenberg uncertainty principle which says that it is impossible to simultaneously determine the momentum and position of an electron. The Bohr model does not predict the spectra when larger atoms are in question. It also cannot predict the intensities of several lines. The Bohr model does not tell us about the fact that when an electron is in acceleration, it emits electromagnetic radiation.	2020-10-29 19:40:10	{"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": 0.8508016467094421, "perplexity": 355.28998858393845}, "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-2020-45/segments/1603107905777.48/warc/CC-MAIN-20201029184716-20201029214716-00100.warc.gz"}
http://www.maplesoft.com/support/help/Maple/view.aspx?path=Database/ConnectionBuilder	Database - Maple Help Home : Support : Online Help : Connectivity : Database Package : Database/ConnectionBuilder Database ConnectionBuilder launch Connection Builder Assistant Calling Sequence ConnectionBuilder( opts ) Database( opts ) Parameters opts - (optional) equation of the form filename=file Description • The ConnectionBuilder command opens a Assistant to help you create a database connection. You can enter driver and connection parameters in the interface. The parameters correspond to the arguments you can specify for the LoadDriver and OpenConnection commands. The Assistant opens a connection to the specified database. You can also use the Database package name as a top-level command to launch the Connection Builder Assistant. • If a connection is successfully established by the Assistant, it returns an expression sequence of length 2. The first element is the driver module and the second is the connection module. • To facilitate specifying the files required for the connection, the Assistant allows you to search the file system. • The Connection Builder Assistant can also load and save connection settings to files. These files are compatible with those used by the Save and LoadConnection commands. It is recommended that you save connection settings. This allows you to easily re-establish connections. • Each connection stored in a file is associated with an identifier. This identifier allows multiple connections to be stored in a single file. To specify the identifier for connection settings, use the Connection combination box. • The ConnectionBuilder command accepts the optional filename=file equation, which allows you to specify the connection file (as a string) to use when opening the Assistant. If not specified, the Assistant opens $HOME/maple/toolbox/Database/data/default.con, where$HOME is the value returned by kernelopts( homedir ). If this file does not exist, no file is loaded. If a file is successfully loaded, the connection with the identifier default is displayed by default. If no connection has the identifier default, the Assistant displays the connection properties for the connection with the alphabetically first identifier. • For more detailed information, see the Help menu in the Connection Builder Assistant. Examples The Connection Builder Assistant can be opened either by using the top-level Database command, as shown below, or by calling Database:-ConnectionBuilder. > $\mathrm{driver},\mathrm{conn}≔\mathrm{Database}\left(\right):$ > $\mathrm{result}≔\mathrm{conn}:-\mathrm{ExecuteQuery}\left("SELECT * FROM animals"\right)$ ${\mathrm{result}}{:=}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{option}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{unload}}{=}{\mathrm{Close}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{local}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{handle}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{export}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{Next}}{,}{\mathrm{Previous}}{,}{\mathrm{Last}}{,}{\mathrm{First}}{,}{\mathrm{GetRowNumber}}{,}{\mathrm{GotoRow}}{,}{\mathrm{GetRowCount}}{,}{\mathrm{InsertRow}}{,}{\mathrm{DeleteRow}}{,}{\mathrm{UpdateRow}}{,}{\mathrm{GetData}}{,}{\mathrm{UpdateData}}{,}{\mathrm{GetType}}{,}{\mathrm{GetName}}{,}{\mathrm{GetColumnCount}}{,}{\mathrm{SetOptions}}{,}{\mathrm{GetOptions}}{,}{\mathrm{Close}}{,}{\mathrm{ToMaple}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (1) Show the results. > $\mathbf{while}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}r:-\mathrm{Next}\left(\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{do}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}r:-\mathrm{GetData}\left("id"\right),r:-\mathrm{GetData}\left("name"\right),r:-\mathrm{GetData}\left("number"\right),r:-\mathrm{GetData}\left("mass"\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end do}$ ${1}{,}{"fish"}{,}{100}{,}{0.0100000000000000002}$ ${2}{,}{"dog"}{,}{10}{,}{20.5000000000000000}$ ${3}{,}{"cat"}{,}{10}{,}{5.50000000000000000}$ ${4}{,}{"rat"}{,}{50}{,}{0.500000000000000000}$ ${5}{,}{"horse"}{,}{3}{,}{400.300000000000011}$ ${6}{,}{"snake"}{,}{1}{,}{7.75000000000000000}$ ${7}{,}{"lizard"}{,}{5}{,}{0.100000000000000004}$ ${8}{,}{"parrot"}{,}{20}{,}{2.}$ ${9}{,}{"pig"}{,}{4}{,}{10.}$ ${10}{,}{"hamster"}{,}{30}{,}{0.200000000000000012}$ (2) Perform a more complex SELECT and convert the output to a Maple table. > $c:-\mathrm{ExecuteQuery}\left("SELECT id, name FROM animals WHERE mass > 5",'\mathrm{output}'='\mathrm{table}'\right)$ ${\mathrm{table}}{}\left(\left[\left({2}{,}{"id"}\right){=}{3}{,}\left({4}{,}{"id"}\right){=}{6}{,}\left({3}{,}{"name"}\right){=}{"horse"}{,}\left({1}{,}{"id"}\right){=}{2}{,}\left({5}{,}{"id"}\right){=}{8}{,}\left({4}{,}{"name"}\right){=}{"snake"}{,}\left({3}{,}{"id"}\right){=}{5}{,}\left({2}{,}{"name"}\right){=}{"cat"}{,}\left({1}{,}{"name"}\right){=}{"dog"}{,}\left({5}{,}{"name"}\right){=}{"pig"}\right]\right)$ (3) Perform another SELECT and convert the output to a Maple Array. > $c:-\mathrm{ExecuteQuery}\left("SELECT name, mass FROM animals WHERE number BETWEEN 10 and 50",'\mathrm{output}'='\mathrm{Array}'\right)$ $\left[\begin{array}{cc}{"dog"}& {20.5000000000000000}\\ {"cat"}& {5.50000000000000000}\\ {"rat"}& {0.500000000000000000}\\ {"parrot"}& {2.}\\ {"hamster"}& {0.200000000000000012}\end{array}\right]$ (4)	2016-05-01 13:36:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 18, "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": 0.45724305510520935, "perplexity": 1952.9562548217666}, "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-2016-18/segments/1461860116173.76/warc/CC-MAIN-20160428161516-00212-ip-10-239-7-51.ec2.internal.warc.gz"}
https://learn.microsoft.com/en-us/dotnet/visual-basic/language-reference/modifiers/default	# Default (Visual Basic) Identifies a property as the default property of its class, structure, or interface. ## Remarks A class, structure, or interface can designate at most one of its properties as the default property, provided that property takes at least one parameter. If code makes a reference to a class or structure without specifying a member, Visual Basic resolves that reference to the default property. Default properties can result in a small reduction in source code-characters, but they can make your code more difficult to read. If the calling code is not familiar with your class or structure, when it makes a reference to the class or structure name it cannot be certain whether that reference accesses the class or structure itself, or a default property. This can lead to compiler errors or subtle run-time logic errors. You can somewhat reduce the chance of default property errors by always using the Option Strict Statement to set compiler type checking to On. If you are planning to use a predefined class or structure in your code, you must determine whether it has a default property, and if so, what its name is. Because of these disadvantages, you should consider not defining default properties. For code readability, you should also consider always referring to all properties explicitly, even default properties. The Default modifier can be used in this context: Property Statement	2023-02-03 05:14:37	{"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": 0.38411563634872437, "perplexity": 1148.8596938013766}, "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/1674764500042.8/warc/CC-MAIN-20230203024018-20230203054018-00077.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Avolkwein.stefan	## Volkwein, Stefan Compute Distance To: Author ID: volkwein.stefan Published as: Volkwein, Stefan; Volkwein, S. External Links: MGP Documents Indexed: 81 Publications since 1997 1 Contribution as Editor Co-Authors: 64 Co-Authors with 68 Joint Publications 1,388 Co-Co-Authors all top 5 ### Co-Authors 14 single-authored 8 Kunisch, Karl 5 Mechelli, Luca 4 Hinze, Michael 4 Kahlbacher, Martin 4 Lass, Oliver 3 Hintermüller, Michael 3 Iapichino, Laura 3 Sachs, Ekkehard W. 3 Tröltzsch, Fredi 3 Urban, Karsten 2 Alla, Alessandro 2 Beermann, Dennis 2 Borzì, Alfio 2 Diwoky, Franz 2 Falcone, Maurizio 2 Gubisch, Martin 2 Herzog, Roland 2 Hömberg, Dietmar 2 Leibfritz, Friedemann 2 Tonn, Timo 2 Weiser, Martin 2 Wesche, Andrea 1 Bachmann, Freya 1 Banholzer, Stefan 1 Benner, Peter 1 Bernreuther, Marco 1 Dellnitz, Michael 1 Düring, Bertram 1 Fabrini, Giulia 1 Fuertinger, Doris H. 1 Gänzler, Tobias 1 Gräßle, Carmen 1 Grüne, Lars 1 Jäkle, Christian 1 Jehle, Jonas Siegfried 1 Jüngel, Ansgar 1 Kammann, Eileen 1 Kappel, Franz 1 Keil, Tim 1 Keiper, Winfried 1 Kopacka, Ian 1 Kotanko, Peter 1 Lu, Jianjie 1 Makarov, Eugen 1 Mancini, Roberta 1 Milde, Anja 1 Neitzel, Ira 1 Ohlberger, Mario 1 Peitz, Sebastian 1 Pirkelmann, Simon 1 Posch, C. 1 Rogg, S. 1 Salomon, Julien 1 Scharrer, G. 1 Schindler, Felix 1 Spasov, Yulian 1 Studinger, Alina 1 Trenz, Stefan 1 Ulbrich, Stefan 1 Unterrreiter, A. 1 von Winckel, Gregory 1 Vossen, Georg 1 Xie, Lei 1 Zeeb, Oliver all top 5 ### Serials 8 Computational Optimization and Applications 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 SIAM Journal on Control and Optimization 4 Optimization Methods & Software 3 Journal of Optimization Theory and Applications 3 SIAM Journal on Scientific Computing 2 Control and Cybernetics 2 SIAM Journal on Numerical Analysis 2 Advances in Computational Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Mathematical and Computer Modelling of Dynamical Systems 2 PAMM. Proceedings in Applied Mathematics and Mechanics 1 International Journal for Numerical Methods in Fluids 1 Journal of Mathematical Biology 1 Journal of Computational and Applied Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 COMPEL 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Linear Algebra and its Applications 1 SIAM Review 1 Grazer Mathematische Berichte 1 Numerical Linear Algebra with Applications 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Discussiones Mathematicae. Differential Inclusions, Control and Optimization 1 SIAM Journal on Applied Dynamical Systems 1 Communications in Mathematical Sciences 1 GAMM-Mitteilungen 1 Numerical Algebra, Control and Optimization 1 Mathematical Control and Related Fields all top 5 ### Fields 61 Calculus of variations and optimal control; optimization (49-XX) 46 Numerical analysis (65-XX) 41 Partial differential equations (35-XX) 27 Operations research, mathematical programming (90-XX) 14 Systems theory; control (93-XX) 7 Classical thermodynamics, heat transfer (80-XX) 5 Fluid mechanics (76-XX) 5 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) ### Citations contained in zbMATH Open 75 Publications have been cited 1,187 times in 650 Documents Cited by Year Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. Zbl 1075.65118 Kunisch, K.; Volkwein, S. 2002 Galerkin proper orthogonal decomposition methods for parabolic problems. Zbl 1005.65112 Kunisch, K.; Volkwein, S. 2001 Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition. Zbl 0949.93039 Kunisch, K.; Volkwein, S. 1999 Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control. Zbl 1079.65533 Hinze, Michael; Volkwein, Stefan 2005 Proper orthogonal decomposition for optimality systems. Zbl 1141.65050 Kunisch, Karl; Volkwein, Stefan 2008 POD a-posteriori error estimates for linear-quadratic optimal control problems. Zbl 1189.49050 Tröltzsch, F.; Volkwein, S. 2009 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061 Kunisch, K.; Volkwein, S.; Xie, L. 2004 Optimal control of a phase-field model using proper orthogonal decomposition. Zbl 1007.49019 Volkwein, S. 2001 Analysis of instantaneous control for the Burgers equation. Zbl 1022.49001 Hinze, M.; Volkwein, S. 2002 Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition. Zbl 1191.49040 Hinze, M.; Volkwein, S. 2008 Optimal snapshot location for computing POD basis functions. Zbl 1193.65113 Kunisch, Karl; Volkwein, Stefan 2010 Model order reduction for PDE constrained optimization. Zbl 1327.49043 Benner, Peter; Sachs, Ekkehard; Volkwein, Stefan 2014 Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition. Zbl 1044.49028 Hömberg, D.; Volkwein, S. 2003 Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation. Zbl 0974.49020 Volkwein, S. 2000 The SQP method for control constrained optimal control of the Burgers equation. Zbl 1001.49035 Tröltzsch, Fredi; Volkwein, Stefan 2001 A primal-dual active set strategy for optimal boundary control of a nonlinear reaction-diffusion system. Zbl 1090.49024 Griesse, R.; Volkwein, S. 2005 Distributed control problems for the Burgers equation. Zbl 0976.49001 Volkwein, S. 2001 Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems. Zbl 1156.35020 Kahlbacher, Martin; Volkwein, Stefan 2007 POD-Galerkin approximations in PDE-constrained optimization. Zbl 1205.35011 Sachs, Ekkehard W.; Volkwein, Stefan 2010 A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD. Zbl 1282.49021 Kammann, Eileen; Tröltzsch, Fredi; Volkwein, Stefan 2013 Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming. Zbl 1149.90183 Leibfritz, F.; Volkwein, S. 2006 Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem. Zbl 1302.49045 Tonn, Timo; Urban, K.; Volkwein, S. 2011 POD Galerkin schemes for nonlinear elliptic-parabolic systems. Zbl 1272.49060 Lass, O.; Volkwein, S. 2013 Formulation and numerical solution of finite-level quantum optimal control problems. Zbl 1143.65048 Borzì, A.; Salomon, J.; Volkwein, S. 2008 A globalized Newton method for the accurate solution of a dipole quantum control problem. Zbl 1206.35211 Von Winckel, G.; Borzì, A.; Volkwein, S. 2009 Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach. Zbl 1378.49025 Alla, A.; Falcone, M.; Volkwein, S. 2017 Multiobjective PDE-constrained optimization using the reduced-basis method. Zbl 1386.35068 Iapichino, L.; Ulbrich, S.; Volkwein, Stefan 2017 Greedy sampling using nonlinear optimization. Zbl 1322.65070 Urban, Karsten; Volkwein, Stefan; Zeeb, Oliver 2014 Lagrange-SQP techniques for the control constrained optimal boundary control for the Burgers equation. Zbl 1077.49024 Volkwein, S. 2003 Dynamical systems-based optimal control of incompressible fluids. Zbl 1081.76016 Hintermüller, Michael; Kunisch, Karl; Spasov, Yulian; Volkwein, Stefan 2004 POD a-posteriori error analysis for optimal control problems with mixed control-state constraints. Zbl 1302.49039 Gubisch, Martin; Volkwein, Stefan 2014 Optimal and suboptimal control of partial differential equations: Augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition. Zbl 1005.49029 Volkwein, Stefan 2001 POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems. Zbl 1272.49059 Kahlbacher, Martin; Volkwein, Stefan 2012 Numerical analysis of POD a-posteriori error estimation for optimal control. Zbl 1275.49050 Studinger, Alina; Volkwein, Stefan 2013 Parametric sensitivity analysis for optimal boundary control of a 3D reaction-diffusion system. Zbl 1104.49033 Griesse, Roland; Volkwein, Stefan 2006 Mesh-independence for an augmented Lagrangian-SQP method in Hilbert spaces. Zbl 0945.49024 Volkwein, S. 2000 Second-order conditions for boundary control problems of the Burgers equation. Zbl 1001.93033 Volkwein, Stefan 2001 Optimal control of parameter-dependent convection-diffusion problems around rigid bodies. Zbl 1216.49006 Tonn, Timo; Urban, Karsten; Volkwein, Stefan 2010 Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling. Zbl 1342.49055 Lass, Oliver; Volkwein, Stefan 2015 Nonlinear conjugate gradient methods for the optimal control of laser surface hardening. Zbl 1062.49034 Volkwein, Stefan 2004 Affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods. Zbl 1029.49026 Volkwein, S.; Weiser, M. 2002 Nonlinear boundary control for the heat equation utilizing proper orthogonal decomposition. Zbl 0999.49019 Diwoky, Franz; Volkwein, Stefan 2001 Set-oriented multiobjective optimal control of PDEs using proper orthogonal decomposition. Zbl 1418.65165 Beermann, Dennis; Dellnitz, Michael; Peitz, Sebastian; Volkwein, Stefan 2018 Reduced-order multiobjective optimal control of semilinear parabolic problems. Zbl 1352.65166 Iapichino, Laura; Trenz, Stefan; Volkwein, Stefan 2016 Asymptotic stability of POD based model predictive control for a semilinear parabolic PDE. Zbl 1329.93072 Alla, Alessandro; Volkwein, Stefan 2015 The reduced basis method applied to transport equations of a lithium-ion battery. Zbl 1358.78076 Volkwein, Stefan; Wesche, Andrea 2013 Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location. Zbl 1302.49040 Lass, Oliver; Volkwein, Stefan 2014 Estimation of regularization parameters in elliptic optimal control problems by POD model reduction. Zbl 1189.93036 Kahlbacher, Martin; Volkwein, Stefan 2009 Augmented Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates. Zbl 1027.49027 Sachs, E.; Volkwein, S. 2002 POD-based economic model predictive control for heat-convection phenomena. Zbl 1425.93133 Mechelli, Luca; Volkwein, Stefan 2018 Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems. Zbl 1254.49018 Vossen, Georg; Volkwein, Stefan 2012 Admittance identification from point-wise sound pressure measurements using reduced-order modelling. Zbl 1205.49032 Volkwein, S. 2010 A-posteriori error estimation of discrete POD models for PDE-constrained optimal control. Zbl 06861101 Gubisch, Martin; Neitzel, Ira; Volkwein, Stefan 2017 An inverse scattering problem for the time-dependent Maxwell equations: nonlinear optimization and model-order reduction. Zbl 1313.78032 Mancini, Roberta; Volkwein, Stefan 2013 Optimality system POD and a-posteriori error analysis for linear-quadratic problems. Zbl 1318.49067 Volkwein, Stefan 2011 Fast solution techniques in constrained optimal boundary control of the semilinear heat equation. Zbl 1239.49039 Hintermüller, M.; Volkwein, S.; Diwoky, F. 2007 Optimal control of the stationary quantum drift-diffusion model. Zbl 1152.35096 Unterrreiter, A.; Volkwein, S. 2007 Estimation of diffusion coefficients in a scalar Ginzburg-Landau equation by using model reduction. Zbl 1157.65473 Kahlbacher, M.; Volkwein, S. 2008 Augmented Lagrangian-SQP techniques and their approximations. Zbl 0913.49018 Kunisch, K.; Volkwein, S. 1997 Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach. Zbl 1430.92039 Rogg, S.; Fuertinger, D. H.; Volkwein, S.; Kappel, F.; Kotanko, P. 2019 Coupling MPC and HJB for the computation of POD-based feedback laws. Zbl 07136779 Fabrini, Giulia; Falcone, Maurizio; Volkwein, Stefan 2018 POD-based economic optimal control of heat-convection phenomena. Zbl 1416.49026 Mechelli, Luca; Volkwein, Stefan 2018 Numerical feedback controller design for PDE systems using model reduction: techniques and case studies. Zbl 1226.93069 Leibfritz, Friedemann; Volkwein, Stefan 2007 SQP methods for parameter identification problems arising in hyperthermia. Zbl 1113.65067 Gänzler, T.; Volkwein, S.; Weiser, M. 2006 Mesh-independence of Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates. Zbl 1079.90166 Volkwein, S. 2002 Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints. Zbl 1167.49027 Hintermüller, Michael; Kopacka, Ian; Volkwein, Stefan 2009 Sequential quadratic programming method for volatility estimation in option pricing. Zbl 1159.91389 Düring, B.; Jüngel, A.; Volkwein, S. 2009 Boundary control of the Burgers equation: Optimality conditions and reduced-order approach. Zbl 1024.49024 Volkwein, Stefan 2002 POD-based mixed-integer optimal control of the heat equation. Zbl 1430.49023 Bachmann, Freya; Beermann, Dennis; Lu, Jianjie; Volkwein, Stefan 2019 POD-based multiobjective optimal control of time-variant heat phenomena. Zbl 1425.90145 Banholzer, Stefan; Makarov, Eugen; Volkwein, Stefan 2018 Condition number of the stiffness matrix arising in POD Galerkin schemes for dynamical systems. Zbl 1354.65199 Volkwein, Stefan 2004 Reduced-order modeling (ROM) for simulation and optimization. Powerful algorithms as key enablers for scientific computing. Zbl 1402.65010 2018 Model order reduction by proper orthogonal decomposition. Zbl 1467.35021 Gräßle, Carmen; Hinze, Michael; Volkwein, Stefan 2021 Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084 Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan 2021 A non-conforming dual approach for adaptive trust-region reduced basis approximation of PDE-constrained parameter optimization. Zbl 07405597 Keil, Tim; Mechelli, Luca; Ohlberger, Mario; Schindler, Felix; Volkwein, Stefan 2021 Model order reduction by proper orthogonal decomposition. Zbl 1467.35021 Gräßle, Carmen; Hinze, Michael; Volkwein, Stefan 2021 Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084 Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan 2021 A non-conforming dual approach for adaptive trust-region reduced basis approximation of PDE-constrained parameter optimization. Zbl 07405597 Keil, Tim; Mechelli, Luca; Ohlberger, Mario; Schindler, Felix; Volkwein, Stefan 2021 Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach. Zbl 1430.92039 Rogg, S.; Fuertinger, D. H.; Volkwein, S.; Kappel, F.; Kotanko, P. 2019 POD-based mixed-integer optimal control of the heat equation. Zbl 1430.49023 Bachmann, Freya; Beermann, Dennis; Lu, Jianjie; Volkwein, Stefan 2019 Set-oriented multiobjective optimal control of PDEs using proper orthogonal decomposition. Zbl 1418.65165 Beermann, Dennis; Dellnitz, Michael; Peitz, Sebastian; Volkwein, Stefan 2018 POD-based economic model predictive control for heat-convection phenomena. Zbl 1425.93133 Mechelli, Luca; Volkwein, Stefan 2018 Coupling MPC and HJB for the computation of POD-based feedback laws. Zbl 07136779 Fabrini, Giulia; Falcone, Maurizio; Volkwein, Stefan 2018 POD-based economic optimal control of heat-convection phenomena. Zbl 1416.49026 Mechelli, Luca; Volkwein, Stefan 2018 POD-based multiobjective optimal control of time-variant heat phenomena. Zbl 1425.90145 Banholzer, Stefan; Makarov, Eugen; Volkwein, Stefan 2018 Reduced-order modeling (ROM) for simulation and optimization. Powerful algorithms as key enablers for scientific computing. Zbl 1402.65010 2018 Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach. Zbl 1378.49025 Alla, A.; Falcone, M.; Volkwein, S. 2017 Multiobjective PDE-constrained optimization using the reduced-basis method. Zbl 1386.35068 Iapichino, L.; Ulbrich, S.; Volkwein, Stefan 2017 A-posteriori error estimation of discrete POD models for PDE-constrained optimal control. Zbl 06861101 Gubisch, Martin; Neitzel, Ira; Volkwein, Stefan 2017 Reduced-order multiobjective optimal control of semilinear parabolic problems. Zbl 1352.65166 Iapichino, Laura; Trenz, Stefan; Volkwein, Stefan 2016 Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling. Zbl 1342.49055 Lass, Oliver; Volkwein, Stefan 2015 Asymptotic stability of POD based model predictive control for a semilinear parabolic PDE. Zbl 1329.93072 Alla, Alessandro; Volkwein, Stefan 2015 Model order reduction for PDE constrained optimization. Zbl 1327.49043 Benner, Peter; Sachs, Ekkehard; Volkwein, Stefan 2014 Greedy sampling using nonlinear optimization. Zbl 1322.65070 Urban, Karsten; Volkwein, Stefan; Zeeb, Oliver 2014 POD a-posteriori error analysis for optimal control problems with mixed control-state constraints. Zbl 1302.49039 Gubisch, Martin; Volkwein, Stefan 2014 Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location. Zbl 1302.49040 Lass, Oliver; Volkwein, Stefan 2014 A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by POD. Zbl 1282.49021 Kammann, Eileen; Tröltzsch, Fredi; Volkwein, Stefan 2013 POD Galerkin schemes for nonlinear elliptic-parabolic systems. Zbl 1272.49060 Lass, O.; Volkwein, S. 2013 Numerical analysis of POD a-posteriori error estimation for optimal control. Zbl 1275.49050 Studinger, Alina; Volkwein, Stefan 2013 The reduced basis method applied to transport equations of a lithium-ion battery. Zbl 1358.78076 Volkwein, Stefan; Wesche, Andrea 2013 An inverse scattering problem for the time-dependent Maxwell equations: nonlinear optimization and model-order reduction. Zbl 1313.78032 Mancini, Roberta; Volkwein, Stefan 2013 POD a-posteriori error based inexact SQP method for bilinear elliptic optimal control problems. Zbl 1272.49059 Kahlbacher, Martin; Volkwein, Stefan 2012 Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems. Zbl 1254.49018 Vossen, Georg; Volkwein, Stefan 2012 Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem. Zbl 1302.49045 Tonn, Timo; Urban, K.; Volkwein, S. 2011 Optimality system POD and a-posteriori error analysis for linear-quadratic problems. Zbl 1318.49067 Volkwein, Stefan 2011 Optimal snapshot location for computing POD basis functions. Zbl 1193.65113 Kunisch, Karl; Volkwein, Stefan 2010 POD-Galerkin approximations in PDE-constrained optimization. Zbl 1205.35011 Sachs, Ekkehard W.; Volkwein, Stefan 2010 Optimal control of parameter-dependent convection-diffusion problems around rigid bodies. Zbl 1216.49006 Tonn, Timo; Urban, Karsten; Volkwein, Stefan 2010 Admittance identification from point-wise sound pressure measurements using reduced-order modelling. Zbl 1205.49032 Volkwein, S. 2010 POD a-posteriori error estimates for linear-quadratic optimal control problems. Zbl 1189.49050 Tröltzsch, F.; Volkwein, S. 2009 A globalized Newton method for the accurate solution of a dipole quantum control problem. Zbl 1206.35211 Von Winckel, G.; Borzì, A.; Volkwein, S. 2009 Estimation of regularization parameters in elliptic optimal control problems by POD model reduction. Zbl 1189.93036 Kahlbacher, Martin; Volkwein, Stefan 2009 Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints. Zbl 1167.49027 Hintermüller, Michael; Kopacka, Ian; Volkwein, Stefan 2009 Sequential quadratic programming method for volatility estimation in option pricing. Zbl 1159.91389 Düring, B.; Jüngel, A.; Volkwein, S. 2009 Proper orthogonal decomposition for optimality systems. Zbl 1141.65050 Kunisch, Karl; Volkwein, Stefan 2008 Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition. Zbl 1191.49040 Hinze, M.; Volkwein, S. 2008 Formulation and numerical solution of finite-level quantum optimal control problems. Zbl 1143.65048 Borzì, A.; Salomon, J.; Volkwein, S. 2008 Estimation of diffusion coefficients in a scalar Ginzburg-Landau equation by using model reduction. Zbl 1157.65473 Kahlbacher, M.; Volkwein, S. 2008 Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems. Zbl 1156.35020 Kahlbacher, Martin; Volkwein, Stefan 2007 Fast solution techniques in constrained optimal boundary control of the semilinear heat equation. Zbl 1239.49039 Hintermüller, M.; Volkwein, S.; Diwoky, F. 2007 Optimal control of the stationary quantum drift-diffusion model. Zbl 1152.35096 Unterrreiter, A.; Volkwein, S. 2007 Numerical feedback controller design for PDE systems using model reduction: techniques and case studies. Zbl 1226.93069 Leibfritz, Friedemann; Volkwein, Stefan 2007 Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming. Zbl 1149.90183 Leibfritz, F.; Volkwein, S. 2006 Parametric sensitivity analysis for optimal boundary control of a 3D reaction-diffusion system. Zbl 1104.49033 Griesse, Roland; Volkwein, Stefan 2006 SQP methods for parameter identification problems arising in hyperthermia. Zbl 1113.65067 Gänzler, T.; Volkwein, S.; Weiser, M. 2006 Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control. Zbl 1079.65533 Hinze, Michael; Volkwein, Stefan 2005 A primal-dual active set strategy for optimal boundary control of a nonlinear reaction-diffusion system. Zbl 1090.49024 Griesse, R.; Volkwein, S. 2005 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061 Kunisch, K.; Volkwein, S.; Xie, L. 2004 Dynamical systems-based optimal control of incompressible fluids. Zbl 1081.76016 Hintermüller, Michael; Kunisch, Karl; Spasov, Yulian; Volkwein, Stefan 2004 Nonlinear conjugate gradient methods for the optimal control of laser surface hardening. Zbl 1062.49034 Volkwein, Stefan 2004 Condition number of the stiffness matrix arising in POD Galerkin schemes for dynamical systems. Zbl 1354.65199 Volkwein, Stefan 2004 Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition. Zbl 1044.49028 Hömberg, D.; Volkwein, S. 2003 Lagrange-SQP techniques for the control constrained optimal boundary control for the Burgers equation. Zbl 1077.49024 Volkwein, S. 2003 Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. Zbl 1075.65118 Kunisch, K.; Volkwein, S. 2002 Analysis of instantaneous control for the Burgers equation. Zbl 1022.49001 Hinze, M.; Volkwein, S. 2002 Affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods. Zbl 1029.49026 Volkwein, S.; Weiser, M. 2002 Augmented Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates. Zbl 1027.49027 Sachs, E.; Volkwein, S. 2002 Mesh-independence of Lagrange-SQP methods with Lipschitz-continuous Lagrange multiplier updates. Zbl 1079.90166 Volkwein, S. 2002 Boundary control of the Burgers equation: Optimality conditions and reduced-order approach. Zbl 1024.49024 Volkwein, Stefan 2002 Galerkin proper orthogonal decomposition methods for parabolic problems. Zbl 1005.65112 Kunisch, K.; Volkwein, S. 2001 Optimal control of a phase-field model using proper orthogonal decomposition. Zbl 1007.49019 Volkwein, S. 2001 The SQP method for control constrained optimal control of the Burgers equation. Zbl 1001.49035 Tröltzsch, Fredi; Volkwein, Stefan 2001 Distributed control problems for the Burgers equation. Zbl 0976.49001 Volkwein, S. 2001 Optimal and suboptimal control of partial differential equations: Augmented Lagrange-SQP methods and reduced-order modeling with proper orthogonal decomposition. Zbl 1005.49029 Volkwein, Stefan 2001 Second-order conditions for boundary control problems of the Burgers equation. Zbl 1001.93033 Volkwein, Stefan 2001 Nonlinear boundary control for the heat equation utilizing proper orthogonal decomposition. Zbl 0999.49019 Diwoky, Franz; Volkwein, Stefan 2001 Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation. Zbl 0974.49020 Volkwein, S. 2000 Mesh-independence for an augmented Lagrangian-SQP method in Hilbert spaces. Zbl 0945.49024 Volkwein, S. 2000 Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition. Zbl 0949.93039 Kunisch, K.; Volkwein, S. 1999 Augmented Lagrangian-SQP techniques and their approximations. Zbl 0913.49018 Kunisch, K.; Volkwein, S. 1997 all top 5 ### Cited by 977 Authors 49 Luo, Zhendong 32 Volkwein, Stefan 26 Rozza, Gianluigi 23 Kunisch, Karl 16 Iliescu, Traian 15 Benner, Peter 13 Karasözen, Bülent 13 Navon, Ionel Michael 13 Tröltzsch, Fredi 12 Teng, Fei 11 Singler, John R. 11 Stabile, Giovanni 10 Borzì, Alfio 10 Efendiev, Yalchin R. 10 Gugercin, Serkan 10 Manzoni, Andrea 10 Willcox, Karen E. 9 Alla, Alessandro 9 Haasdonk, Bernard 9 Hinze, Michael 9 Li, Hong 9 Ohlberger, Mario 9 Patera, Anthony T. 9 Quarteroni, Alfio M. 9 Uzunca, Murat 9 Wang, Zhu 8 Chaturantabut, Saifon 8 Shen, Chunyu 7 Chen, Jing 7 Chung, Tsz Shun Eric 7 San, Omer 6 Borggaard, Jeff T. 6 Grepl, Martin A. 6 Veroy, Karen 6 Xie, Zhenghui 6 Zhou, Yanjie 5 Amsallem, David 5 Beattie, Christopher A. 5 Ciaramella, Gabriele 5 Fang, Fangxin 5 Gao, Anna 5 Gildin, Eduardo 5 Kalise, Dante 5 Karatzas, Efthymios N. 5 Peitz, Sebastian 5 Pinnau, René 5 Rebholz, Leo G. 5 Schneier, Michael 5 Sun, Ping 5 Tian, Lixin 5 Yücel, Hamdullah 4 Ballarin, Francesco 4 Barone, Matthew F. 4 Bordas, Stéphane Pierre Alain 4 Breiten, Tobias 4 Choi, Youngsoo 4 Falcone, Maurizio 4 Gunzburger, Max D. 4 Heinkenschloss, Matthias 4 Herzog, Roland 4 Hintermüller, Michael 4 Hömberg, Dietmar 4 Jiang, Lijian 4 Kalashnikova, Irina 4 Kärcher, Mark 4 Kerfriden, Pierre 4 Küçükseyhan, Tuğba 4 Lass, Oliver 4 Lee, Hyung-Chun 4 Maday, Yvon 4 Mola, Andrea 4 Nguyen, Ngoc Cuong 4 Nouy, Anthony 4 Pain, Christopher C. 4 Perotto, Simona 4 Piao, Guangri 4 Reese, Stefanie 4 Rubino, Samuele 4 Ştefănescu, Răzvan 4 Stoll, Martin 4 Ulbrich, Stefan 4 Weiser, Martin 3 Akman, Tuğba 3 Benosman, Mouhacine 3 Chen, Yanlai 3 Di, Zhenhua 3 Dihlmann, Markus A. 3 Dolgov, Sergey V. 3 Du, Juan 3 Fareed, Hiba 3 Farhat, Charbel H. 3 Feng, Lihong 3 Gao, Junqiang 3 Ghattas, Omar N. 3 Grüne, Lars 3 Hamdouni, Aziz 3 Herty, Michael Matthias 3 Hijazi, Saddam 3 Hoang, K. C. 3 Huang, Ting-Zhu ...and 877 more Authors all top 5 ### Cited in 153 Serials 46 Computer Methods in Applied Mechanics and Engineering 37 Journal of Computational Physics 34 SIAM Journal on Scientific Computing 30 Journal of Computational and Applied Mathematics 24 International Journal for Numerical Methods in Engineering 19 Advances in Computational Mathematics 17 Computational Optimization and Applications 15 Computers & Mathematics with Applications 14 Applied Mathematics and Computation 14 Journal of Scientific Computing 13 Computers and Fluids 13 Journal of Mathematical Analysis and Applications 10 Applied Numerical Mathematics 9 SIAM Journal on Control and Optimization 9 SIAM Journal on Numerical Analysis 9 Optimization Methods & Software 8 Applied Mathematical Modelling 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Mathematical and Computer Modelling of Dynamical Systems 7 International Journal for Numerical Methods in Fluids 7 Journal of Optimization Theory and Applications 6 International Journal of Control 6 Numerische Mathematik 5 Numerical Functional Analysis and Optimization 5 Numerical Methods for Partial Differential Equations 5 Mathematical and Computer Modelling 5 Computational Geosciences 5 Optimization and Engineering 5 Nonlinear Analysis. 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(English Edition) 2 Computer Physics Communications 2 Inverse Problems 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Journal of Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Mathematics of Computation 2 Applied Mathematics and Optimization 2 Systems & Control Letters 2 Optimization 2 COMPEL 2 Japan Journal of Industrial and Applied Mathematics 2 SIAM Review 2 Computational and Applied Mathematics 2 Discrete and Continuous Dynamical Systems 2 International Journal of Computational Fluid Dynamics 2 Vietnam Journal of Mathematics 2 New Journal of Physics 2 Journal of Dynamical and Control Systems 2 Mathematical Modelling and Analysis 2 Discrete and Continuous Dynamical Systems. Series B 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Thai Journal of Mathematics 2 Inverse Problems in Science and Engineering 2 GAMM-Mitteilungen 2 Discrete and Continuous Dynamical Systems. Series S 2 Advances in Applied Mathematics and Mechanics 2 Numerical Algebra, Control and Optimization 2 Communications in Applied and Industrial Mathematics 2 East Asian Journal on Applied Mathematics 2 SIAM/ASA Journal on Uncertainty Quantification 2 Iranian Journal of Numerical Analysis and Optimization 2 Research in the Mathematical Sciences 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Applicable Analysis 1 International Journal of Heat and Mass Transfer 1 Journal of Engineering Mathematics 1 Mathematical Biosciences 1 Bulletin of Mathematical Biology 1 Theoretical and Computational Fluid Dynamics 1 Calcolo 1 Journal of Differential Equations 1 Zeitschrift für Analysis und ihre Anwendungen 1 Applied Mathematics and Mechanics. (English Edition) 1 Bulletin of the Iranian Mathematical Society 1 Physica D 1 Science in China. Series A 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. 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Matematica e Applicazioni ...and 53 more Serials all top 5 ### Cited in 34 Fields 395 Numerical analysis (65-XX) 234 Partial differential equations (35-XX) 193 Calculus of variations and optimal control; optimization (49-XX) 170 Fluid mechanics (76-XX) 118 Systems theory; control (93-XX) 55 Operations research, mathematical programming (90-XX) 48 Mechanics of deformable solids (74-XX) 31 Biology and other natural sciences (92-XX) 26 Optics, electromagnetic theory (78-XX) 23 Dynamical systems and ergodic theory (37-XX) 18 Classical thermodynamics, heat transfer (80-XX) 17 Probability theory and stochastic processes (60-XX) 16 Statistics (62-XX) 16 Computer science (68-XX) 14 Geophysics (86-XX) 11 Quantum theory (81-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Ordinary differential equations (34-XX) 9 Approximations and expansions (41-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Operator theory (47-XX) 4 Mechanics of particles and systems (70-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Combinatorics (05-XX) 2 Functional analysis (46-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mathematics education (97-XX)	2022-05-17 13:15:24	{"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": 0.5891903042793274, "perplexity": 8284.731186728555}, "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/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00105.warc.gz"}
https://getpractice.com/questions/1090640	$AL,BM$ and $CN$ are perpendiculars from angular points of a triangle $ABC$ on the opposite sides $BC,CA$ and $AB$ respectively.$\triangle$ is the areas of triangle $ABC, r$ and $R$ are the inradius and circumradius . On the basis of the above information,answer the following questions:	2020-10-24 02:44:14	{"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": 0.9193836450576782, "perplexity": 125.16561343972168}, "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/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00191.warc.gz"}
https://physics.stackexchange.com/questions/665141/finiteness-of-maxwell-gauge-field-symplectic-form	# Finiteness of Maxwell gauge field symplectic form? The symplectic form for a Maxwell $$U(1)$$ gauge field is $$\omega = \int_\Sigma d \Sigma^\mu \delta F_{\mu \nu} \wedge \delta A^\nu$$ where $$\wedge$$ acts on field space. (In this notation, $$\delta$$ is like the exterior derivative $$\mathrm{d}$$ but for field variations instead of spacetime variations.) Here, our phase space is solutions to the Maxwell e.o.m.. Remember that the symplectic form will take in two "tangent vectors" in phase space, i.e. two field variations $$\delta A$$ which are "based" at a point, and output a number. In particular, the 'point' we're basing this at is an on-shell solution $$A$$, and the variations $$A+\delta A$$ must also be on-shell at the linearized level. For instance, unwrapping the notation a bit, we have $$\omega[A; \delta_1 A, \delta_2 A] = \int_\Sigma d \Sigma^\mu \big( \delta_1 F_{\mu \nu} \delta_2 A^\nu - \delta_2 F_{\mu \nu} \delta_1 A^\nu \big).$$ Here $$\Sigma$$ is a Cauchy slice. My question concerns the finiteness of the symplectic form $$\omega$$ given some reasionable boundary conditions. If we take a simple Cauchy slice $$t = 0$$, then the integrand will roughly be $$\sim \int d^2\Omega r^2 dr F_{t i} A^i$$ where $$i=1,2,3$$ are the spatial directions. (Here I dropped the variations $$\delta$$ because all I care about is the fall offs.) Now, $$F_{ti}$$ is the electric field, and if we assume that there is no radiation at infinitely far distances, then we can assume it falls off as $$F_{ti} \sim r^{-2}$$. Furthermore, let's assume that $$A^i$$ takes the form of the Leonard-Wiechert potential, in which case it will fall off as $$A^i \sim r^{-1}$$. Our $$r$$ integral is then $$\int dr r^2 \frac{1}{r^2} \frac{1}{r}$$ which seems to diverge as $$\log(r)$$ for large radius. Isn't this a problem? Shouldn't the symplectic form be finite for these very reasonable fall off conditions? Yes, the symplectic form should be finite in order to be mathematically well-defined. The main idea is to impose appropriate asymptotic fall-off conditions at spatial infinity as OP already writes. The solution involves (i) imposing parity conditions and (ii) adding boundary terms to the symplectic form, see Ref. 1 for details. References: 1. M. Henneaux & C. Troessaert, Asymptotic symmetries of electromagnetism at spatial infinity, arXiv:1803.10194 ; section 3. • Thank you very much for this reference! I see how the parity conditions will make the action finite. However, the boundary term seems a bit different. In the paper they say it is necessary to make the action Poincare invariant. However, they are not using the covariant phase space formalism as I am here, which is manifestly covariant-- so maybe adding a boundary term is not necessary for my $\omega$? Sep 10 at 4:13 • The use of one valid formalism over another should in principle not substantively alter the underlying physics. Sep 10 at 4:58 I accepted Qmechanic's answer for pointing me to the right answer, but will give more details here. The retarded vector potential in Lorenz gauge $$(\partial_\mu A^\mu = 0)$$ for a charge of constant velocity $$\vec{\beta}$$ which passes through the origin is $$$$A_\mu^{\rm ret}(t, \vec{r}) = \frac{e}{4 \pi \epsilon_0} \frac{(-1, \vec{\beta})}{\sqrt{ (\vec{r} - \vec{\beta} t)^2 + (\vec{r} \cdot \vec{\beta} )^2 - \beta^2 r^2 }}.$$$$ Notice that the components of the gauge field fall off as $$A_\mu \sim r^{-1}$$. Let's now look at the symplectic form on a $$t = \mathrm{const}$$ slice. $$$$\label{omega_large_r} \omega = \int_0^\infty r^2 dr \; \int_{S^2} d^2 \Omega \left( \delta_1 F^{t i} \delta_2 A_i - \delta_2 F^{t i} \delta_1 A_i \right).$$$$ If $$F \sim r^{-2}$$, and $$A \sim r^{-1}$$, then the $$r$$ integral is $$\int \frac{dr}{r}$$ which diverges logarithmically. However, let's take a closer look at our vector potential $$A_\mu^{\rm ret}$$. Notice that if we hold $$t$$ fixed and send $$\|\vec{r}\| \to \infty$$, then it is even under sending $$\vec{r} \mapsto - \vec{r}$$. $$$$\label{Aantipodal} A_\mu^{\rm ret}(t, \vec{r}) = A_\mu^{\rm ret}(t, - \vec{r}) \hspace{0.5 cm} (\text{for large }r).$$$$ This fact, that the vector potential takes the same value at antipodal points at spatial infinity, gives us another key boundary condition we need to adopt in order to make $$\omega$$ well defined. Let's now figure out what antipodal condition $$F_{ti}$$ satisfies. From the equation $$A_\mu^{\rm ret}(-t, \vec{r}) = A_\mu^{\rm ret}(t, -\vec{r})$$, we can see that $$F_{ti} = \partial_t A_i - \partial_i A_t$$ satisfies $$$$\label{Fantipodal} F_{ti}(t, -\vec{r}) = -F_{ti}(t, - \vec{r}) \hspace{0.5 cm} (\text{for large }r).$$$$ So while $$A_\mu$$ is even, $$F_{\mu \nu}$$ is odd. These are our final boundary conditions. Using them, we can see that the $$\int d^2 \Omega$$ integral in the expression for $$\omega$$ at large $$r$$ vanishes identically.	2021-12-07 23:44:57	{"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": 47, "wp-katex-eq": 0, "align": 0, "equation": 4, "x-ck12": 0, "texerror": 0, "math_score": 0.97196364402771, "perplexity": 278.46951819317917}, "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-2021-49/segments/1637964363420.81/warc/CC-MAIN-20211207232140-20211208022140-00327.warc.gz"}
https://www.groundai.com/project/network-coding-with-modular-lattices/	Network coding with modular lattices # Network coding with modular lattices Andreas Kendziorra Claude Shannon Institute University College Dublin Stefan E. Schmidt Institut für Algebra Technische Universität Dresden ###### Abstract In [13], Kötter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map . In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map , where is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a singleton bound for codes, which are subsets of modular lattices. 2010 Mathematics Subject Classification: 06C05, 68P30, 94B65, 05A15, 20K27. ## 1 Introduction Network coding is a tool for information transmission in networks. A network is considered to be a directed graph, where an edge from a vertex to a vertex is drawn, if is able to send information directly to (cf. [11]). A subset of the vertices is the set of senders and another subset is the set of receivers. Each sender is interested in sending his information to every receiver (broadcasting). The information is transmitted over several vertices to the receivers. With network coding a vertex is allowed to combine received information and forward these combinations. Usually the information is represented by vectors of the -vector space for a prime power and a positive integer (cf. [7]). The combinations are then -linear combinations. In random network coding the coefficients of these linear combinations are randomly chosen. For basic properties, advantages and further information on random network coding the reader is referred to [10, 11, 13]. Regarding general network coding see [1]. Kötter and Kschischang presented in [13] a new model for error correcting codes in random network coding. A sender transmits vectors of the , spanning a subspace of . A receiver receives vectors, which will span a subspace of . In the error free case thes subspaces are equal. Thus the alphabet in this model is the subspace lattice of the -vector space and a code is a subset of this lattice. To transmit a codeword a sender injects a basis of this codeword. The metric on this alphabet is the map . In this paper we generalize this model to modular lattices. So we will consider codes as subsets of modular lattices with finite length and we use the metric , where is the height function of the lattice. This generalization is used to apply submodule lattices for random network coding. As in coding theory codes over (see e.g. [5, 6, 14]) came out to be useful we place emphasis to -modules of the form for a prime and positive integers and . We introduce so called enumerable lattices, which are a generalization of the submodule lattices of these modules with certain combinatorial properties. We derive a method to compute the cardinalities of spheres in these lattices. We present a sphere packing, a sphere covering, and a singleton bound for codes in modular lattices. These bounds are stated for arbitrary (finite) modular lattices and for enumerable lattices. In the latter case the bounds can be computed explicitly. This paper is not meant to present concrete code constructions with encoding and decoding algorithms. It is rather a beginning or an introduction into a research topic. Basically we wish to explore modular lattices as metric spaces. Furthermore, we want to show, that the model presented in [13] is also applicable to submodule lattices of arbitrary finite modules and not only to subspace lattices. For concrete codes and algorithms further research will be required. The outline of the paper is as follows. In chapter 2 we give all necessary definitions. Chapter 3 describes how network coding with modular lattices and especially submodule lattices can work. In chapter 4 we introduce enumerable lattices. The main part of this chapter describes a method to compute sizes of spheres in enumerable lattices. Bounds for codes in modular lattices are presented in chapter 5. ## 2 Preliminaries For basic notations in lattice theory the reader is referred to [3] and [8]. For technical reasons we will consider a lattice mostly as an algebraic structure, instead as an ordered set. So a lattice is an algebraic structure with a set and two binary operations (join) and (meet), which are both associative, commutative and satisfy the absorption laws x∧(x∨y)=xandx∨(x∧y)=x for all . Every lattice gives rise to an ordered set where for . For the set is called the interval between and . Note that it is again a lattice. If the lattice is bounded then we denote the least element by (zero) and the greatest element by (one). A totally ordered set is called a chain. The length of a chain is its cardinality minus one. The length of a lattice is the least upper bound of the lengths of chains in . If is finite, then is said to be of finite length. A lattice of finite length is complete, thus it has a zero and an one. If is finite, then has finite length. In a lattice of finite length the height function gives for an element the greatest length of the chains between and . is called the height of . For we denote by the set of elements in with height . ### 2.1 Modular lattices and submodule lattices ###### Definition 2.1. A lattice is called modular if for all holds: u≤w⇒u∨(v∧w)=(u∨v)∧w. For a modular lattice of finite length the map d:L×L→N, (u,v)↦h(u∨v)−h(u∧v) (1) is a metric (see [3] chapter X §1 and §2). Further, the height function satisfies the equality h(u)+h(v)=h(u∨v)+h(u∧v) (2) for every (see [3] chapter IV §4). For this reason one obtains for the metric also d(u,v)=h(u)+h(v)−2h(u∧v)=2h(u∨v)−h(u)−h(v) for every . We briefly recall the definitions of ring and module, which we take from [2]. ###### Definition 2.2. A ring is an algebra consisting of a set , two binary operations and and two elements of such that is an abelian group, is a monoid (i.e. a semigroup with identity ) and is both left and right distributive over . ###### Definition 2.3. Let be a ring. An abelian group together with a map (”left scalar multiplication”) via is called a left -module if for all and the equations a(x+y)=ax+ay,(a+b)x=ax+bx,(ab)x=a(bx)and1x=x hold. A subgroup of is called left -submodule of if holds for every and . For the submodule of generated by is denoted by . Accordingly, one can define right -module and right -submodule by a ”right scalar multiplication”. If is commutative this distinction will be obsolete. We will consider from now on just left -modules and we will say just “-modules” instead of “left -modules”. For further information on modules see e.g. [2]. For any ring and a -module we will denote the set of all -submodules by . This set with the operations , which is defined by , and is a modular lattice (see [3] chapter VII §1 Theorem 1; note that this Theorem uses a more general definition of module, which covers the definition used here). We will call this lattice the submodule lattice of and denote it by . Because of the modularity of this lattice, we have the metric d:L(M)×L(M)→N, (U,V)↦h(U+V)−h(U∩V). (3) ###### Example 1. For a prime power and a positive integer the submodule lattice (here the subspace lattice) of the -vector space is a finite modular lattice. The height of a subspace is exactly the dimension of . The metric on this lattice is which was presented in [13]. ###### Example 2. Consider the abelian -group for a prime and positive integers . This group is a -module. The set of all -submodules equals the set of all subgroups of . If , then there exists such that is isomorphic to . For the height function there holds . With this height function one obtains again a metric with the function defined in (3). ### 2.2 Partitions of nonnegative integers We will shortly introduce partitions of nonnegative integers. The notations are done as in [15]. We will use partitions later for semi-primary lattices. A partition of a nonnegative integer is a finite monotonically decreasing sequence of nonnegative integers with . Zeros in this sequences are permitted and if two partitions differ only in the number of zeros, then they are considered to be equal. If is a partition of , then it is denoted by . With we denote the set of all partitions of . For a partition with times the entry we write also . One can define an order on the set of all partitions by μ≤λ:⇔μi≤λi for all i for two partitions and . For a partition the set is called the Ferrers diagram of . The partition with the Ferrers diagram is called the conjugated partition of and is denoted by . Note that is the number of sequence elements in , which are distinct from zero. For the partitions and we define the partition , where we set for . Note that implies . ### 2.3 Semi-primary lattices Definitions and results in this chapter are mostly taken from [12]. An element in a lattice is called cycle if the interval is a chain and dual cycle if the interval is a chain. A modular lattice of finite length is called semi-primary if every element in is the join of cycles and the meet of dual cycles. The elements of a modular lattice of finite length are called independent if the equation holds for every . If are independent, then we write also instead of . For semi-primary lattices we now state Theorem 4.9. of [12]. ###### Theorem 2.4. Every element of a semi-primary lattice is the join of independent cycles. Moreover, if has the two representations u=x1\veedot...\veedotxkandu=y1\veedot...\veedotyn with cycles , and , which are distinct from , then , and there exists a permutation such that for . Because of this theorem we can agree on the following definition. ###### Definition 2.5. Let be a semi-primary lattice, , cycles distinct from with , and , such that . Then is called the type of . The type of is also called the type of and also denoted by . Types of elements in semi-primary lattices can be considered as partitions of nonnegative integers. For a partition and a semi-primary lattice we denote by the set of elements in , which have type . If an element of a semi-primary lattice has type , then it is easy to see, that this element has height (see Lemma 4.3). Note that if is a semi-primary lattice and an interval in , then is also semi-primary (see [12] Corollary 4.4.) and it holds (see [9] Lemma 2.4.). It follows for every the implication , because is an interval in . As in [12] we call a Ring completely primary uniserial if there exists a two-sided ideal of such that every left or right ideal of is of the form (where ). Theorem 6.7. of [12] says, that every submodule lattice of a finitely generated module over a completely primary uniserial ring is semi-primary (in fact the theorem says more than that). ###### Example 3. The field is completely primary uniserial, because the only ideals of are and . So the subspace lattice of the -vector space is semi-primary. If has dimension , then has the type . ###### Example 4. The Ring is completely primary uniserial, because every ideal is of the form for some and with we have . So the submodule lattice of the -module is semi-primary. If , then there exists with such that is isomorphic to . Then has the type . ## 3 Network coding with modular lattices In this chapter, we will generalize the notion of operator channel, which was presented in [13]. Similar to the discussion in [13] we can here decompose the metric distance between two elements in an error and an erasure part. We consider the signal transmission from a single sender to a single receiver with an arbitrary finite modular lattice as the alphabet. In this context it is not important, whether the channel is a network or not. For an input the channel will deliver an output . The metric on this alphabet is the function defined in (1). We define the functions era :L×L→N, (u,v)↦h(u)−h(u∧v) and err :L×L→N, (u,v)↦h(v)−h(u∧v). It is easy to see that d(u,v)=era(u,v)+err(u,v) holds for every . For an input and an output we call the erasure and the error from to . Roughly speaking is a measure for the information, which was contained in but after the transmission not anymore in , and is a measure for the information, which was not contained in but after the transmission is contained in . If for there exists such that has the representation v=(u∧v)\veedote, then we have and and so the intervals and are isomorphic (see [3] chapter I, §7, corollary 2). If follows err(u,v)=h(v)−h(u∧v)=h(e)−h(0L)=h(e). If the chosen lattice is the subspace lattice of the -vector space , then such an e exists for every and corresponds to the definition of errors in Definition 1 in [13]. corresponds also to the definition of erasures in Definition 1 in [13], independently of the existence of such an . Such an does not exist in general for modular lattices. More precisely: For every exists an , such that (choose for example ), but an , such that and holds, does not exist in general. Let now , such that . Then . Because of holds . Thus, the intervals and are isomorphic (see again [3] chapter I, §7, corollary 2). It follows err(u,v)=h(v)−h(u∧v)=h(e)−h(u∧e). Roughly speaking is also a measure for the information which is contained in , but not in . A code is in this paper a subset of a finite modular lattice . We denote the minimum distance of by . If every codeword in has the same height, then we call a constant height code. If is moreover semi-primary and every codeword in has the same type, then we call a constant type code. Clearly every constant type code is a constant height code. ### 3.1 Random network coding with submodule lattices Now we consider the case that the information is transmitted through a network and that the alphabet for the signal transmission is a submodule lattice of a finite -module for a ring . As in [13] we consider the case of the communication between a single sender and a single receiver (single unicast). The generalization to multicast is straightforward. If the sender wishes to transmit a submodule , then he sends a generating set of into the network. A node in the network, which receives module elements , sends to the node a -linear combination yb=k∑i=1rb,imi with random ring elements for if there is a link from to . If the sender sends the generating set into the network and a receiver receives the elements , then has in the error free case the representation vj=k∑i=1rj,iui for some elements for and . is a submodule of . If the receiver collects sufficiently many module elements, then equals . In the case that errors appear, that means that module elements , which are not contained in , are transmitted through the network, then has the representation vj=k∑i=1rj,iui+m∑t=1sj,tet for some elements for , and . Let , and . Then there exists a submodule of , such that has the representation V=(U∩V)+E′. The intersection of and must not necessarily be trivial. The erasure in this case is . The error is , or if we wish to express it in terms of , it is . If the intersection of and is trivial (and so the intersection of and as well), then the error is . ## 4 Enumerable lattices and spheres Let be the subgroup lattice of a finite abelian -group and a partition. If two subgroups in this lattice are isomorphic, i.e. they have the same type, then they have the same number of subgroups of type . More precisely, if have the same type, then holds. But if we consider the number of groups in this lattice, which are greater or equal than or instead of less or equal, then the statement does not hold in general. More precisely, if have the same type, then does not necessarily follow. E.g. if we consider the subgroup lattice of in Figure 1, then the black colored element of type is covered by two elements of type and the other two elements of type by none. If we define for and the sphere with radius centered at , then we have as a consequence that the spheres with radius 1 centered at the elements of type have not the same cardinality. The sphere centered at the black colored element has the cardinality and the other two spheres have cardinality . More general, if have the same type, then does not necessarily follows. But that might be a desired property. If we restrict now to be of the form for some integers and , then for follows if and have the same type (see Theorem 4.2 and Example 6). For example, this can be seen in the subgroup lattice of in Figure 1. Consequently for follows if and have the same type (see chapter 4.2). In the following we will generalize the subgroup lattices of finite abelian -groups to down-enumerable lattices and subgroup lattices of finite abelian -groups of the form to enumerable lattices. Enumerable lattices are semi-primary lattices with the desired property described above. In chapter 4.1 we will present a result, which shows that down-enumerable lattices are under certain circumstances even enumerable, which is a generalization of the group case described above. Since we know that two spheres in an enumerable lattice with same radius and centered at two elements with the same type have the same cardinality, we would like to compute the size of these spheres dependent on the radius and the type of the element in the center. This will be described in chapter 4.2. ###### Definition 4.1. A finite semi-primary lattice is called down-enumerable if for every and every partition the implication tp(u)=tp(v)⇒\|{w∈Lμ∣w≤u}\|=\|{w∈Lμ∣w≤v}\| holds. Then for an element of type and a partition we denote . is called up-enumerable if for every and every partition the implication tp(u)=tp(v)⇒\|{w∈Lμ∣w≥u}\|=\|{w∈Lμ∣w≥v}\| holds. Then for an element of type and a partition we denote . If is down-enumerable and up-enumerable, then it is called enumerable. ### 4.1 A duality result This section is devoted to a proof of the following theorem. ###### Theorem 4.2. Let be a self-dual down-enumerable lattice and for some positive integers . Assume further, that for every cycle there exists a cycle with and . Then is enumerable and for every two partitions holds β(μ,φ)=α(λ−μ,λ−φ). (4) ###### Lemma 4.3. Let be a modular lattice of finite length and . Then there holds h(u1∨...∨un)≤h(u1)+...+h(un). Furthermore we have the equivalence: u1,...,un are independent ⇔h(u1∨...∨un)=h(u1)+...+h(un). ###### Proof. See [3] chapter IV §1 and §4. ∎ ###### Lemma 4.4. The type of a semi-primary lattice is equal to the type of its dual lattice. ###### Proof. See [12] Corollary 4.11. ∎ For the next Lemma, we need another notation from [12]. Let be a semi-primary lattice, and a positive integer. The join of all cycles with and is denoted by . ###### Lemma 4.5. Let be a semi-primary lattice and . Then the following equivalence holds: u1,...,un are independent⇔u1[1],...,un[1] are independent. ###### Proof. See [12] Theorem 4.14. ∎ ###### Lemma 4.6. Let be a semi-primary lattice, and . Then there exists an element with . ###### Proof. Let . There exist independent cycles distinct from zero with , such that is the join of . Since , there exists a cycle with for . Because are independent cycles, also the cycles must be independent. Hence, we conclude and . ∎ An element of a bounded lattice is called atom if it has height 1. ###### Lemma 4.7. Let be a semi-primary lattice, , and with and , such that . Furthermore let be independent cycles distinct from zero, such that is the join of . Then there exists an atom , such that are independent. ###### Proof. Let be the uniquely determined atom with for . Let be an atom such that are not independent. By Lemma 4.3 it follows that m = h(a1∨...∨am)≤h(a1∨...∨am∨~a) < h(a1)+...+h(am)+h(~a)=m+1. So we have and finally . Let be the set of atoms in . Assume that for every the elements are not independent. Then it follows that a1∨...∨am=a1∨...∨am∨(⋁(A∖{a1,...,am}))=⋁A, and so . It follows that there exists no element in with type and . But that is a contradiction to Lemma 4.6, because holds for . It follows, that there exists an atom , such that are independent. With Lemma 4.5, it follows that are independent, because of for and . ∎ ###### Corollary 4.8. Let be a semi-primary lattice, , , and independent cycles distinct from zero, such that is the join of . If , then there exist atoms , such that are independent. Let be a semi-primary lattice and . With we denote the type of in the dual lattice of and call it the dual type of . ###### Lemma 4.9. Let be a semi-primary lattice, for some positive integers , and . Further assume, that for every cycle , there exists a cycle with and . Then there holds tpD(u)=λ−μ. ###### Proof. Let be independent cycles distinct from zero, such that is the join of . If then there exist by Corollary 4.8 atoms , such that are independent. By our premise, there exist cycles with for , for and for . If is the uniquely determined atom with for , then are independent. By Lemma 4.5, it follows that are independent, because of . It follows , because has type and is the only element in with type . We define for (it holds ) and . So is a cycle in . We will show, that are independent in . That means, that holds for every . We define for and so are independent and is the join of . Let be fixed. Then we have z1∨...∨zi−1∨zi+1∨...∨zn= (x1∨u)∨...∨(xi−1∨u)∨(xi+1∨u)∨... ...∨(xn∨u) = u∨x1∨...∨xi−1∨xi+1∨...∨xn = u1∨...∨un∨x1∨...∨xi−1∨xi+1∨...∨xn = x1∨...∨xi−1∨ui∨xi+1∨...∨xn. The last equality holds because of for . are independent. It follows h(z1∨...∨zi−1∨zi+1∨...∨zn) =h(x1∨...∨xi−1∨ui∨xi+1∨...∨xn) =h(x1∨...∨xn)−h(xi)+h(ui)=sn−s+μi. For the second equality we used Lemma 4.3. Because of , we have h(zi) =h(u1∨...∨ui−1∨xi∨ui+1∨...∨un) =h(u1∨...∨un)−h(ui)+h(xi)=\|μ\|−μi+s. We used again Lemma 4.3 for the second equality. By equation (2), there follows h((z1∨...∨zi−1∨zi+1∨...∨zn)∧zi)= h(z1∨...∨zi−1∨zi+1∨...∨zn) +h(zi)−h(z1∨...∨zn) = (sn−s+μi)+(\|μ\|−μi+s)−sn=\|μ\|. From this, we obtain , because of and . So, are independent cycles in and there holds . We denote by the height of in . There holds for . It follows that has in the type and since we have . By Lemma 4.4, it follows that also the dual lattice of has type . The one-element of this dual lattice is exactly , and it follows, that has dual type in and so in . ∎ Now we can state the proof of Theorem 4.2. ###### Proof of Theorem 4.2. Let and be fixed and let by and . Further let with and . Because of the self-duality we have α(ϑ,ω)=\|{v∈L∣v≤u,tp(v)=ω}\|=\|{v∈L∣u′≤v,tpD(v)=ω}\|. By Lemma 4.9, it follows that an element in with dual type has the type	2020-10-22 14:51:54	{"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": 0.9425952434539795, "perplexity": 465.6523430581857}, "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/1603107879673.14/warc/CC-MAIN-20201022141106-20201022171106-00064.warc.gz"}
http://mathhelpforum.com/differential-geometry/140560-very-interesting-question-about-sets.html	# Math Help - Very interesting question about sets 1. ## Very interesting question about sets A = (a,b) B = [a,b) C = [a,b] D = (a,b] , a,b are real numbers Which one of these sets is the biggest? (Proof is not necessary, I only need to know the correct answer) 2. Originally Posted by Kiki A = (a,b) B = [a,b) C = [a,b] D = (a,b] , a,b are real numbers Which one of these sets is the biggest? (Proof is not necessary, I only need to know the correct answer) Bad question: there's no biggest nor smallest. All of them have the same cardinality (assuming, of course, $a...) Tonio 3. Originally Posted by tonio Bad question: there's no biggest nor smallest. All of them have the same cardinality (assuming, of course, $a...) Tonio Ok, thank you. Another question: I have prooved that a function converges in all these 4 sets. I would just like to use the "biggest" of them to show that it converges in the a larger area (like trying to include all the 4 of them, in a sentence) and I am wondering which one to use. Maybe the set "C" ? (assuming , $a...) 4. Originally Posted by Kiki A = (a,b) B = [a,b) C = [a,b] D = (a,b] , a,b are real numbers Which one of these sets is the biggest? Here is a hint. Define $f:[0,1]\to (0,1)$ by $f(0)=\frac{1}{2},~ f(1)=\frac{1}{3}, f(1/n)=\frac{1}{n+1}, n\ge3,~x\text{ otherwise}$. It is easy to show that $f$ is a bijection. Thus we see that $[0,1]~\&~(0,1)$ are ‘same size’. 5. Originally Posted by Kiki I have prooved that a function converges in all these 4 sets. I would just like to use the "biggest" of them to show that it converges in the a larger area (like trying to include all the 4 of them, in a sentence) and I am wondering which one to use. Use set $C$ because each of the others are subsets. 6. Originally Posted by Plato Use set $C$ because each of the others are subsets. Ok thank you, my question is answered now. 7. But it sounds weird to me that A,B,D are subsets of C, but C is not "bigger" than them. (My major is not mathematics so I havent studied pure topology) 8. Originally Posted by Kiki But it sounds weird to me that A,B,D are subsets of C, but C is not "bigger" than them. In this case what matters is being the supper-set. That is, if I understand what you mean by “a function converges”. For example: If $f$ is continuous on $[a,b]$ then it is continuous on $(a,b)$. "Bigger than" has not meaning in this context. 9. Originally Posted by Plato what you mean by “a function converges”. btw I wanted to say "a series of function converges", sorry Originally Posted by Plato In this case what matters is being the supper-set. That is, if I understand what you mean by “a function converges”. For example: If $f$ is continuous on $[a,b]$ then it is continuous on $(a,b)$. "Bigger than" has not meaning in this context. Now its pretty clear, thank you for helping me	2015-11-27 19:46:21	{"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": 15, "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": 0.8349176645278931, "perplexity": 1586.2021636773284}, "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-2015-48/segments/1448398450559.94/warc/CC-MAIN-20151124205410-00339-ip-10-71-132-137.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-simplify-xsqrt-16x-3y-ysqrt-27xy-2	# How do you simplify xsqrt(16x^3y) + ysqrt(27xy^2)? $4 {x}^{2} \sqrt{x y} \text{ "+" } 3 {y}^{2} \sqrt{3 x}$ $x \sqrt{{4}^{2} {x}^{2} \times x \times y} \text{ " +" } y \sqrt{3 \times {3}^{2} \times x \times {y}^{2}}$ $\text{ "4x^2sqrt(xy)" "+" } 3 {y}^{2} \sqrt{3 x}$	2021-09-17 18:32:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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": 0.7621087431907654, "perplexity": 14457.170201431632}, "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-2021-39/segments/1631780055775.1/warc/CC-MAIN-20210917181500-20210917211500-00291.warc.gz"}
https://codegolf.meta.stackexchange.com/questions/630/how-to-make-code-golf-more-enjoyable-winners-by-language	# How to Make Code Golf More Enjoyable: Winners by Language? So, I was reading the related question here, when I went off on a tangent. The point of the given post, as I read it, is that certain languages like GolfScript, K, and some other extremely-high level languages can trivialize Code Golf by taking problems (for the sake of discussion, determining whether some string is a palindrome), and creating a solution in likely less than 15-20 characters, which totally blows other more verbose languages out of the water; they simply can't compete! A potential solution I want to discuss is probably not a real shocker, and might seem a tad obvious: winners can be tallied by language. To return to the palindrome example, say User A creates a 65-character Python solution and a 15 character GolfScript solution, while User B creates a 45-character K solution and a 25 character GolfScript solution. In categories, User A would be the winner for GolfScript, while User B would be the winner for K (at least, until some challenger comes to take their title away.) The major point I can see against this idea is that there's only one Green Checkmark of Victory. This idea is imperfect because splitting things up by category raises the question of what it really means to win at Code Golf. Dividing by language means the possibility of multiple winners, which is thoroughly incompatible with the format of a Q/A site. So, the Meta-Question: A) How can we compartmentalize these competitions such that users of arcane, high-level languages can recieve recognition alongside users of more verbose languages, and B) If we accept a multi-winner paradigm, how can we crown the One True Winner? I thought of (some form of) this question probably since the first day I checked out the site. And my view is that this is something the platform is supposed to provide, but afaik support for this kind of features is missing (in stackexchange). The way I imagine it is this: each answer can specify a language and a score (in separate fields from the main textarea), then the system automatically shows the list of languages used, and for each language it provides some info about the best answer (perhaps the user's name with a link to the answer) and a filter to show only answers in that language. Also, there should be an option to sort answers by score (both when filtered and globally), and sort languages in the list by score and by number of answers (not just alphabetically). So that would answer question A. For question B, I think we can either remove the option to have a global winner, or (better) let the asker choose whichever winner they desire (including none), perhaps even having an option to automatically select the answer with the best score. I think voting just doesn't cut it, except for challenges where there is no objective score and the winner is actually determined by voting. So yes, some questions will have no objective score (e.g. the recent code-trolling ones) and others will have no direct language association (e.g. polyglot challenges) but generally they have both. If this kind of system can't be done on stackexchange, then what about making a separate site for it? The point of the given post, as I read it, is that certain languages like GolfScript, K, and some other extremely-high level languages can trivialize Code Golf by taking problems (for the sake of discussion, determining whether some string is a palindrome), and creating a solution in likely less than 15-20 characters, which totally blows other more verbose languages out of the water I disagree with that analysis. Trivial questions get trivial answers. Non-trivial questions may sometimes get very short answers, but at the cost of substantial effort. A) How can we compartmentalize these competitions such that users of arcane, high-level languages can recieve recognition alongside users of more verbose languages Why is it necessary to compartmentalise? Upvotes are recognition. Is the question that interests you how to get people to upvote answers in verbose languages? I don't think it is necessary to have language specific winners. For example, I know python better than most languages, and know that in most challenges it isn't really a contender. How ever, I can appreciate the terseness of some responses. However, when I see a ridiculously short python answer I almost always up-vote it as I know how hard it must have been. I'd like to think the community will always acknowledge good golfing, regardless of language. languages like GolfScript, K, and some other extremely-high level languages can trivialize Code Golf by taking problems While it is true that those languages are in fact made for expressing simple tasks with very short code everybody seems to miss a certain point: • It is by far NOT easy to golf in those languages It may be easy to write a shorter program than Java in those languages but still, finding the shortest solution requires the same amount of skill (or even more) as golfing in any other language. If you take 'The Burlesque Programming Language' as an example: It has many built-ins. The idea is, that stuff you have to do often should be accessible very easy. Therefore it has a built-in function to do X etc. Obviously when it comes to EXACTLY DO X you CAN'T beat it with another language. However, when it comes to array manipulation you don't stand a chance with Burlesque. But that's not really the point. The point is, that it's still difficult to golf in Burlesque. When golfing in Burlesque you do exactly the same process as golfing in any other language: You start with an idea, write it, shorten the code. Start with another idea, write it shorten the code. Try to abuse test cases. Abuse bugs, abuse undocumented stuff. Abuse weird behaviour. I'll attach a documentation about a solution of mine for a problem to calculate binomial coefficients with the input format " , " wd{-]}[M^pnr [12B] ","""r~penr [11B] psShra^pnr [10B] psRT[-p^nr [10B] ps^p/vnr [8B] Removing the ',' is the tricky part. wd{-]}[M^pnr does this by splitting into words and then calling Head inside MapParse. ","""r~penr obviously uses a regex to remove the ',' from the input psShra^pnr uses Parse and then converts to Pretty and back to a string obtaining a format parsable by read array which has a weird behaviour that skips over the ',' psRT[-p^nr uses Parse and then rotates and tails the block to remove the ',' ps^p/vnr uses Parse and pushes all elements to the stack and uses SwapPop to remove the ',' As you hopefully will see, it really still takes skill, time and endurance to find the shortest solution. And that's what golfing is about as far as my opinion goes. Saying: "Oh no. It's too easy to golf in golfscript" is just wrong. • The problem isn't that golfing in the language is easy; the problem is that these minimalistic, esoteric languages consistently beat everything else, which makes them an obvious choice to win the competition, and are hard to read (unless you already know the language, in which case you're fine.) I assert that these languages, while requiring skill, remove the sportsmanship from Code Golf, which is what I want to find a way around. Sep 9 '13 at 13:45 • If you happen to do 'language agnostic' golfing than obviously the language you're using is a huge factor. The language becomes a tool(and with any competitions that use tools)you can't win if your tool is not the best choice. Obviously my chances of winning a archery competition where those high-tec bows are allowed with my own plain bow is not an option because it's just the wrong tool for these competitions. As for sportmanship: If you do language agnostic competitions and you are aware that your language can't win you have to consider learning how to use better tools. Sep 12 '13 at 8:31 • Or you can choose to ignore that and keep using a tool even if you know that it's obsolete and a bad choice. You can't play soccerr without the right shoes, it's just too slippery when wet. Not using the right shoes doesn't make you a good sportsman, it makes you a bad and ignorant one. Sep 12 '13 at 8:34 • Also the definition of "esoteric" is somewhat subjective. APL and J are not actually considered esoteric but they really rock at code golfing. You can't ban them just because they are good. That's also not good sportsmanship. Other languages like awk, vi(m script), sed also allow to write very short code. What about those? Also, what's your definition of "unreadable"? Can you read haskell code without knowing haskell? You can't really do that either. Sep 12 '13 at 8:39 • I mean seriously: What does pythons Sep 12 '13 at 8:40 • Sorry. I pressed ENTER to early. My point is: What's unreadable anyway? If I wouldn't know python then foo[::-1] is unreadable. And perl at codegolf level is unreadable in my eyes too. Maybe you can't read Burlesque (or Flogscript, or Golfscript) code but that's only because you don't know a single command. If you knew, you'd understand code like ln)XXtp\[\[sh at ease. It's just print.concat.concat.transpose.map explode.lines in haskell terms (where explode converts a String to a list of characters). Sep 12 '13 at 8:50 • Why not create divisions? Have a winner for terse languages (APL, J, Golfscript, etc.). Then crown a winner for the non-terse languages. I occasionally golf in Python. My personally goal is to beat other Python, ruby, javascript, and perl answers. But it stinks that I can almost never win with my chosen language. Sep 20 '13 at 17:25	2021-12-04 17:09:37	{"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": 0.3506580591201782, "perplexity": 1600.018068594457}, "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-2021-49/segments/1637964362999.66/warc/CC-MAIN-20211204154554-20211204184554-00403.warc.gz"}
https://undergroundmathematics.org/hyperbolic-functions/square-wheels/solution	Under construction Resources under construction may not yet have been fully reviewed. Food for thought Solution (This resource is still in draft form.) This applet shows a square with slide length $2$ rolling over an upside-down catenary with equation $y=-\cosh x$. When the square is horizontal, the centre of its base touches the vertex of the catenary. Move the slider to roll the square. Brief solutions (require more detail): • What is the locus of the centre of the square? The locus of the centre of the square is a straight line along the $x$-axis. • How far can the square roll with the same side still touching the catenary? The square can rotate until the vertex of the square touches the catenary. At this point, the arc length of the catenary from the vertex of the catenary to this point equals half of the square’s side length, which is $1$. The arc length from $(0,-1)$ to $(x, -\cosh x)$ is $\sinh x$, so this occurs when $\sinh x=1$, or $x=\arsinh 1$. Using the formula for $\arsinh$ or solving $\sinh x=1$ directly gives an alternative expression for this: $x=\ln(1+\sqrt{2})$. Furthermore, at this point, the gradient of the catenary is $y'=-\sinh x=-1$. This means that the square has rotated by $45^\circ$, and thus the centre of the square is also at $x=\arsinh 1$.	2018-01-23 23:16:41	{"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": 0.8376332521438599, "perplexity": 304.72018418193846}, "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-2018-05/segments/1516084892802.73/warc/CC-MAIN-20180123231023-20180124011023-00482.warc.gz"}
https://tex.stackexchange.com/questions/415289/double-tip-arrow-with-upper-symbol-in-tikz	# Double tip arrow with upper symbol in Tikz How can I write this diagram in Tikz: Here is my try: \begin{tikzcd} x \arrow{leftrightarrow}{r}{} \arrow[dashed]{dr}{} & & y \arrow[dashed]{dl}{} \\ & z & \end{tikzcd} Possible solution: \documentclass[tikz]{standalone} \usepackage{tikz-cd} \begin{document} \begin{tikzcd} x \arrow[rr, leftrightarrow, ""] \arrow[dr, dashrightarrow, ""'] & & y \arrow[dl, dashrightarrow, ""] \\ & z & \end{tikzcd} \end{document} Edit: Another solution with pure TikZ: \documentclass[tikz]{standalone} \begin{document} \begin{tikzpicture} \node (x) at (0,0) {$x$}; \node (y) at (2,0) {$y$}; \node (z) at (1,-1) {$z$}; \draw[<->] (x) -- node[above] {$\ast$} (y); \draw[->,dashed] (x) -- node[below left] {$\ast$} (z); \draw[->,dashed] (y) -- node[below right] {$\ast$} (z); \end{tikzpicture} \end{document} \documentclass{article} \usepackage{tikz} \usepackage{tikz-cd} \begin{document} \begin{tikzcd} x \arrow[dashed,""']{dr}\arrow[leftrightarrow]{rr}{} & & y \arrow[dashed]{dl}{}\\ & z & \end{tikzcd} \end{document} • OK, this is almost a bit silly. Two very similar solutions posted at almost the same time … If yours gets accepted, I will delete mine. – Jasper Habicht Feb 14 '18 at 13:45 • @JasperHabicht No, leave it. It's a different syntax. Someone will find it useful. P.S.: I tried to see which answer was the first one but it's easier to see if Han shot first :P – Phelype Oleinik Feb 14 '18 at 13:52 A simple tikz solution: \documentclass[tikz]{standalone} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture} \draw[<->] (0,0) node[left] {$x$}--(4,0) node[midway, above]{$$} node[right]{$y$}; \draw[->,dashed] (0,0)--(2,-1.7) node[midway,below left]{$$} node[below]{$z$}; \draw[->,dashed] (4,0)--(2,-1.7) node[midway,below right]{}; \end{tikzpicture} \end{document} Output: • The arrow heads collide. This could be prevented using shorten >. – Jasper Habicht Feb 14 '18 at 15:21 • @JasperHabicht it is an option, but it would be solved easier by another arrowhead like "-latex" instead of "->" – koleygr Feb 14 '18 at 21:09	2019-08-20 19:17:46	{"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": 0.9827297925949097, "perplexity": 6795.515400066868}, "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-2019-35/segments/1566027315558.25/warc/CC-MAIN-20190820180442-20190820202442-00305.warc.gz"}
https://www.ilnuovosaggiatore.sif.it/article/258	# Muon Collider: a window to the future ### Maria Enrica Biagini, Donatella Lucchesi 1 The proposed future collider projects The last decade has seen the consolidation of some fundamental open questions in our understanding of the Universe, such as the nature of dark matter, the origin of the observed matter-antimatter imbalance, the role of gravity with the discovery of the gravitational waves and the neutrino oscillations. Particle accelerators have been and currently are one of the best tools to investigate the new phenomena confirming theoretical models, like the standard model, or disproving them. The study of the Higgs boson properties at the LHC experiments completes what is expected by the standard model and, in order to answer the aforementioned questions, a major leap forward is needed. As of today, it is not obvious what kind of accelerator will be the LHC successor. In fact, the recent document “Update of the European Strategy for Particle Physics” sees the High-Luminosity LHC (HL-LHC) with the upgraded experiments as the next step in high-energy physics. According to the current schedule, the LHC collider will be in use until 2036, and in the meanwhile the successor of LHC has to be defined. Consequently, the same document proposes to study several possible options, notably including high-intensity electron-positron colliders and an extreme energy proton-proton collider. The document also suggests investigating the possibility of having bright muon beams. There are different proposals of electron-positron colliders: • Circular machines: Circular Electron-Positron Collider (CepC) in China at maximum center-of-mass energy of 240 GeV and Future Circular Collider $e^+ e^–$ (FCC-ee) at CERN at 350 GeV center-of-mass energy. They have a limited reach in the center-of-mass energy due to synchrotron-radiation losses. • Linear machines: International Linear Collider (ILC) in Japan and Compact Linear Collider at CERN where the electric bill constitutes an important expense if center-of- mass energies above few TeV have to be reached. The proposed proton-proton colliders at present are the Future Circular Collider (FCC-hh) at CERN that aims to reach a center-of-mass energy of the order of 100 TeV, and the SppC in China, both needing a ring of the order of 100 km. This implies a huge civil engineering work and cost. In this scenario, the Muon Collider (MC) is becoming a more concrete possibility. In order to study and solve the many technical challenges of a Muon Collider, an International Collaboration (MC Design Study) is being established, based at CERN, to propose a feasible design and define the needed R&D. The Collaboration shall provide a baseline concept for a Muon Collider, well-supported performance expectations, and assess the associated key risks as well as the cost in particular for the electricity consumption. It shall focus on the high-energy frontier and consider options with a center-of-mass energy of 3 TeV and of 10 TeV or more, identify an R&D path to demonstrate its feasibility and support its performance claims. The different R&D topics will be addressed by several dedicated working groups. Colliding muons imply a change of paradigm: a different way of thinking about accelerator, detector and machine- detector-interface is required, as will be discussed in the following. 2 Why the Muon Collider Muons are elementary particles, over 200 times heavier than the electrons, therefore much less subject to synchrotron radiation emission than the electron/positron beams. For this reason, Muon Colliders are the ideal accelerators to reach multi-TeV center-of-mass energies, otherwise forbidden in conventional $e^+ e^–$ linear colliders because of the cost. Moreover, muons can be accelerated to very high energy in a circular ring of the dimension of the currently available ones. The electric power necessary to operate the full complex has not been calculated yet, however a preliminary evaluation classifies the Muon Collider as a “green” machine. In fact, this is demonstrated in fig. 1 where the yearly integrated luminosity per energy consumption in Terawatt-hour is plotted as a function of the center-of-mass energy. The Muon Collider, in red, is compared to the future $e^+ e^–$ linear collider ILC and CLIC and to the circular machine, FCC-ee. The figure includes also p-p colliders, the present LHC, the possible high-energy LHC (HE-LHC) and the future FCC-hh. The Muon Collider performs just as well as the proton-proton machine in terms of power consumption. Moreover, in this collider the delivered number of useful collisions (referred to in the following as luminosity) increases as the center-of-mass energy grows. In summary, operating a Muon Collider at high energy is convenient with respect to other accelerators. Another very important parameter to consider, when comparing with a proton collider, is the physics discovery potential. Electron-positron colliders and Muon Collider at the same energy have roughly the same potential, while comparing proton-proton collider and Muon Collider is complex. Protons are particles made of quarks and gluons, they carry only a fraction of the energy carried by the accelerated protons. When protons beams collide, the interaction is between their constituents therefore at an energy lower than the protons one. In the case of muons the full energy can be exploited in the interaction. Figure 2 illustrates the center-of-mass energy at which a proton collider equals that one of a Muon Collider to produce with the same cross section two heavy new particles with mass approximately equal to half the Muon Collider energy (blue curve). The vertical dashed line indicates 100 TeV, the center-of-mass energy proposed for the FCC-hh machine, that corresponds to 14 TeV for the Muon Collider. The advantages of working with muon collisions are many more and they will be discussed in the next section. The reason why there are no Muon Colliders as of today is that building such a machine is very challenging. Muons are unstable particles, differently from protons and electrons. They decay with a lifetime of 2.2∙10–6 s if at rest, while in a machine with a center-of-mass energy of 3 TeV each beam has an energy of 1.5 TeV and the muons have a longer lifetime, 3.1∙10–2 s. In this very short time, the produced muons have to be accelerated and transferred in the collider to make them interact, possibly several times. The recent technological developments are opening the door to the possibility of designing such a facility even though there are challenges to face before declaring victory. 3 The Muon Collider facility A Muon Collider is indeed a complete accelerator facility. Three stages are needed: muons have to be produced, accelerated and finally brought to collision in such a way to have enough interactions useful for physics measurements. Most of the facility designs are based on muons production as tertiary particles by decay of pions created with an intense, typically several MW, proton beam interacting with a heavy material target. In order to achieve high luminosity in the collider, the muon beam, produced with low energy and hence a limited lifetime, and with very large transverse and longitudinal emittances, has to be cooled by approximately five orders of magnitude in the six-dimensional (6D) transverse and longitudinal phase space. Then the beam has to be accelerated rapidly to avoid muon decays. Production, acceleration and collision of muon beams is an amazing technical challenge, due to the muon short lifetime and to the difficulties of their production. A MC accelerator complex has been studied for several years by the MAP (Muon Accelerator Project) collaboration in the US, established in order to develop the concepts and address the feasibility of novel technologies required for MC and neutrino factories based on a proton driver source. Figure 3 shows a schematic layout of the MAP accelerator complex. In the following a short overview of the different stages will be given. The cooling stage: since muons are not free in nature, they need to be produced by interaction of pions with a target. However, the muons are produced with large angular deviations and then large beam emittances, hence they have to be collected, cooled and focused in order to become high-quality beams suitable for a high-luminosity collider. The process studied by MAP to damp the muon 6D emittance is quite complex. The main ingredients are: • a proton driver, an intense proton source able to create pions which will decay into muons. Protons are produced and accelerated through a superconducting (SC) Linac, accumulated in an accumulator ring, bunched in a buncher ring to build 2 ns bunches, and finally compressed in a bunch compressor, which provides a 90° rotation in the longitudinal phase space; • a front-end, where pions are produced by interaction of the proton beam with a MW class target which must stand the proton high power, immersed in a high solenoidal field to capture and guide pions into the decay channel, where muons are captured in a bunches train, with a time-dependent acceleration due to their different energies; • several cooling stages: muon cooling is achieved by a process called “ionization cooling” to reduce the 6D phase space by 5 orders of magnitude, so the muon beam will fit inside the first acceleration stage acceptance. This process is critical to achieve the muon beam characteristics needed for a high-luminosity MC. The challenge of the cooling process is the short muon lifetime, so cooling must take place more quickly than any of the cooling methods presently in use. For a description of the method see Box 1. A transverse ionization cooling proof-of-principle experiment, MICE (Muon Ionization Cooling Experiment), has been carried out at RAL, UK. A solenoidal cooling channel was built (without RF cavities) and the ionization cooling of muons was demonstrated by using both liquid hydrogen and lithium hydride absorbers. The cooling effect has been observed through the measurement of both an increase in the number of small-amplitude particles and an increase in the phase-space density of the beam. The results agree with the simulations. The acceleration stage: after muons are produced, due to their short lifetime at rest, a very fast acceleration chain is needed to bring the beams to the required collider energy. The acceleration can be achieved in stages. The key issues driving the design are: to limit the number of decays and avoid longitudinal emittance growth; to have good power efficiency; to limit the cost (RF cavities being the driving cost factor). Since RF cavities are expensive, as many passes as possible should be done through them: small circumference of acceleration stages are preferred, with high dipole fields and a large dipole packing factor. The acceleration gradient should be large due to the short lifetime. To reduce the emittance growth, an increase in circumference, with a small momentum compaction factor, could help. Several kinds of accelerators have been considered for the fast acceleration process: Linac, Recirculating Linear Accelerator (RLA), Fixed Field Alternating Gradient (FFAG), or Rapid Cycling Synchrotron (RCS). Linac are single-pass, so they are quite inefficient and also expensive. In the multi-pass Recirculating Linear Accelerator the beam goes through separate passes (arcs) depending on its energy. This solution is preferred at low energy, its main limitation being the geometry of the in/out of the different arcs. A “dogbone” layout, with one Linac and several arcs at both ends, would help. To preserve the longitudinal emittance, relatively long arcs are needed and focusing of the beam and matching between Linac and arcs will be necessary. Fixed Field Alternating Gradient are rings where magnetic fields do not vary with time, so there is a single beamline for many energies. This means that the dipole magnets need to have a very large aperture. The tolerated decay and emittance growth determine the circumference overturns ratio. Finally, Rapid Cycling Synchrotrons are pulsed synchrotrons where magnet fields are proportional to the beam momentum. They are preferred to Fixed Field Alternating Gradient accelerators, since higher RF frequencies and/or more turns can be chosen. The RF cavities, as many as possible, should be distributed uniformly. The magnet field increases rapidly (less than 1 ms), however the average field available is low (around 1.5 T), so a hybrid solution was proposed. In a hybrid pulsed synchrotron, the average bend field is increased by interleaving fixed-field superconducting dipoles and bipolar pulsed warm dipoles, so that more RF passes, and a shorter circumference is possible, however a larger magnet aperture is needed. At higher energies this solution may be preferred because of the longer beam lifetime. At the moment, a choice on which method is best has not been made and will be one of the crucial subjects of the International Muon Collaboration studies. The collider stage: the final stage of the MC facility is the collider ring, where the physics data are collected. In a collider, a high collision frequency, a small beam emittance and a high number of particles per bunch are needed to reach high luminosity. These requirements are quite challenging in the case of a MC, where a luminosity of the order of 1035 cm–2s–1 is desired on a wide range of energies. The design of the rings needs to cope with several requirements in order to maximize luminosity: low beta-functions (see Box 2) at the interaction point (few mm in the range of 3–6 TeV center-of-mass energy), small emittances, short bunch lengths, small ring circumference to increase the collision rate in the short muon lifetime. At present there is a limitation on the maximum magnetic field achievable in the superconducting dipoles, which also need to be protected from the backgrounds produced by muon decay particles. The short lifetime has consequences in the high rate of decay backgrounds, therefore a careful design of the interaction region is needed, together with the detector protection design: machine-detector-interface is a key issue in this case. Since beam emittance and energy spread in the MAP production scheme are quite large, the rings need to be designed with large physical, dynamic and momentum apertures and also a small momentum compaction factor to obtain a short bunch length with a reasonable RF voltage. Moreover, since the energy range of operation should be very large, spanning from 3 to 14 TeV center-of-mass energy, a lattice design optimized for all energies is quite difficult to achieve. The design of the rings has been done in the past for several different energies, with different ring circumferences. In the framework of the International Muon Collider Collaboration this topic will be the subject of a dedicated study group. The muon decay $\mu^{-} \rightarrow e^{-}\bar{\nu}_{e}\nu_{\mu}$ and its charge conjugate are the major source of background in a Muon Collider. It can be so high that it could make it impossible to perform any physics measurement. Electrons, positrons and synchrotron photons, successively radiated, interact with the machine components and the surrounding environment producing secondary particles, mainly charged and neutral hadrons, Bethe-Heitler muons, electrons and photons, that eventually may reach the detector. Studies performed by the MAP Collaboration demonstrated that two tungsten cone- shaped shields (nozzles) in proximity of the interaction point, accurately designed and optimized for each specific beam energy, can mitigate the background arriving at the detector. Figure 7 shows a simulation obtained with FLUKA of a muon beam of 1.5 TeV circulating in a realistic ring with a realistic nozzle and the support structures of the experimental hall. The detector is represented by the black box and the decay products are not traced into the detector. The figure clearly shows the amount of background that reaches the detector. The optimization of the machine-detector-interface is an activity that sees accelerator and detector physicists working together to balance the level of the background in the detector region and the luminosity for each center-of-mass option. The decay neutrinos coming from muon decays do not affect the detector design due to the low interaction cross section, but the secondary radiation, hadrons, muons and electrons produced by the neutrino interaction with the earth could constitute a radiological hazard. Preliminary studies, conducted with simulations in the MAP facility configuration, show that the neutrino radiation from a muon beam with an energy in the order of TeV is concentrated in the machine plane. Therefore, if the collider is installed underground, the neutrinos interact with a certain length of earth depending on the collider depth, before escaping on the surface. Assuming the MAP muon beam parameters, the dose-equivalent rate for different hypotheses of the machine depth, and muon beam energy, has been roughly estimated. Along the collider arcs this dose-equivalent does not represent a hazard if the beam energy is below about 1.5 TeV, while in the straight sections, where the neutrinos from muon decay are much more collimated, the radiation induced by the interaction with the material can create hazards if the beam energy is above 1 TeV. Methods to mitigate the effects, like introducing small oscillations to the beam orbit (beam wobbling) to name one, have been proposed and seem very effective. They have to be studied in detail taking in consideration the site configuration. The International Muon Collider Collaboration proposes to evaluate the possibility of locating the accelerator at CERN and therefore the Radiation and Safety Office is conducting the study. 4 A new idea for a muon source To avoid the rather complicated and technically difficult cooling process needed with the proton-based MAP muon source, the idea to create muon pairs from the interaction of a high-energy positron beam with a high-density target was conceived at Snowmass in 2013. In the following years a Low Emittance Muon Accelerator (LEMMA) concept was developed at the INFN Frascati National Laboratories (Italy). The scheme is based on the muon production from a 45 GeV $e^+$ beam annihilating with the electrons of a target close to threshold for $\mu^{+}\mu^{-}$ pair creation, thus generating muon beams with low enough transverse emittance for a high-energy collider. The advantage of this scheme is that small emittance muon bunches can be created, without the need for a complicated cooling process. Since the bunches have lower emittance, a relatively lower number of muons is required to achieve high luminosity, this lowers also the background rates due to the muons decays, and in particular the boundary radiation limitations due to the neutrino-induced hazard. The initial design foresaw an $e^{+}$ storage ring with an internal target, in order to allow for multiple interactions of the $e^+$ with the electrons at rest in the target, and the subsequent formation of a muon bunch. However, this layout has encountered several limiting difficulties. An alternative design was conceived, where $e^{+}$ bunches are extracted to impinge on multiple targets in one or more dedicated straight sections. This scheme could release the impact of the average power on the target and also reduce the number of $e^{+}$ required from the positron source. The facility layout is schematically shown in fig. 8. The complex consists of a chain of several components. A Positron Source (PS) at 300 MeV produces positrons which are accelerated in a 5 GeV Linac and then stored in a 5 GeV Damping Ring (DR) to reduce the beam emittances. A SC Linac (or an Energy Recovery Linac (ERL)) is used to accelerate positrons to 45 GeV and inject them into a 45 GeV Positron Ring (PR) to accumulate the 1000 bunches needed for muon production. Some delay loops will synchronize the positron bunches extracted before passing through one or more Target Lines (TL) for the muon production. After the production muons are collected in two Accumulation Rings (AR), where they are stored until the bunch has a suitable number of particles, the same bunch will pass the same TL (and the AR) several times until it reaches the required number of muons. To restore the initial positron-beam current and to release the stress on the PS, which has to produce a number of positrons above the current state-of-the-art sources, an “embedded” positron source, where positrons are produced by the photons coming from the interaction $e^+$ /target, can be envisaged. Another option under study is to recuperate the “spent” positron beam, with a large energy spread, at the exit of the TL after the muon production and inject it back into the 45 GeV ring. The LEMMA scheme poses several technical challenges and has some issues. First of all, a high-rate positron source is needed, one order of magnitude larger than the ILC and CLIC ones. The muon production rate at the moment is quite lower than in the MAP scheme, solutions to recombine muons into one bunch should be studied. Moreover, the target material choice is critical, since the target needs to have a high density for a high production rate, to stand the heat load and mechanical stress from the interaction of the intense positron beam for many pulses, and at the same time to have a low density to avoid multiple scattering which would increase the muon bunch emittance. Some R&D is ongoing worldwide, also as a number of proposals for the next US Snowmass process due by summer 2022. Examples of future R&D topics are the target studies, as well as the design of a powerful positron source, the latest in synergy with the future $e^{+}e^{–}$ colliders FCC-ee and CepC. 5 The guaranteed physics discovery The possibility to reach very high energy with muon collisions has motivated several theoretical studies that are demonstrating that a Muon Collider would perform much better than other proposed machines, extending the reach of the searches for new particles and new phenomena. But even if the answers to the main open questions through the direct searches sat at energies much higher than the ones reachable by any future machine, the Muon Collider would nonetheless offer a unique possibility: the precise determination of the Higgs field potential. The Higgs boson, discovered at LHC in 2012, was introduced in the standard model as a consequence of the mechanism by which the elementary particles were assumed to acquire mass. Its discovery was a tremendous success of both the model for its predictive power and the experiments for being able to catch such an elusive particle. Elementary fermions and bosons interact with the Higgs field, a process by which they acquire mass, and the strength of these couplings predicted by the theory will be evaluated by the LHC experiments and could be precisely measured at any of the future colliders, while the determination of the shape of the Higgs field will not be possible. Why is it so important to determine it? In the current understanding of the Universe and its evolution, before the electroweak symmetry breaking, all the elementary bosons and fermions were massless, the potential of the Higgs field was symmetric with respect to the vacuum. At a certain moment, or better at a given temperature, the Higgs field potential assumed the so-called “Mexican” hat form with infinite possible minimum configurations, the bottom of the hat. The choice of one configuration is referred to as the spontaneously breaking of the electroweak symmetry. In the standard model, this potential configuration is parametrized in terms of the expectation value on the vacuum, $\nu = 1 / (\sqrt{2}G_{F})^{1/2} \sim 246$ GeV, with $G_F$ the Fermi constant, $\lambda$ the strength of the coupling of the Higgs to itself and the Higgs mass $m_{H} = \sqrt{2\lambda} \nu$. Processes where a virtual Higgs boson produces two or three Higgs bosons, governed by the so-called trilinear and quadrilinear Higgs self-couplings, are of paramount importance to verify if the Higgs potential corresponds to the one predicted by the standard model. In order to be as general as possible and to include deviations from the standard model, the Higgs potential is written assuming two different values for trilinear ($\lambda_{3}$) and quadrilinear ($\lambda_{3}$) self-couplings: $V ( h ) = \frac{1}{2} m^{2}_{H} h^{2} + \lambda_{3}\nu h^{3} \frac{1}{2}\lambda_{4}h^{4}$, where $\lambda_{3} = \lambda_{4} = \lambda ( m^{2}_{H} ) / (2\nu^{2})$ in the standard model and the scalar field, $h$ an expansion around $\nu / \sqrt{2}$, describes a physical Higgs boson. The direct measurement of $\lambda_{3}$ and $\lambda_{4}$ will verify the actual nature of the observed Higgs particle and the determination of the shape of the Higgs potential could dramatically affect the knowledge of cosmology being related to the spontaneous symmetry breaking. Experimentally $\lambda_{3} ( \lambda_{4} )$ can be measured by counting events where a virtual Higgs boson produces two (three) Higgs bosons. These processes are expected to have extremely small cross sections and to require collisions at very high energy, reachable only by the muon collisions. The next question is if an experiment at a Muon Collider will be able to detect and reconstruct events where two (three) Higgs bosons decay in two b-jets, the most probable process, given the high level of beam-induced background. A dedicated machine-detector-interface has been designed for 1.5 TeV center-of-mass energy and used with the full simulation of the detector to find new strategies that exploit new technologies in order to mitigate the effect of the background. Recent studies have demonstrated that high granularity silicon-based tracking detectors and calorimeters combined with the arrival time of each particle give very good performance in physics object reconstruction including b-jets. The expectations for 3 TeV center-of-mass energy are similar even though we should have a lower level of background since at higher energies muons live longer. Figure 9 shows the decay of two Higgs bosons into b-quark jets, produced by muon collision at 3 TeV center-of-mass energy as they appear in the detector. The reconstructed four b-jets are clearly visible, here the beam-induced background is not shown. In four years of data taking at an instantaneous luminosity of 4.4·1034 cm-2s-1 around 70 events fully reconstructed are expected with a ratio of signal-to-physics background of about 1 to 10. Already at 3 TeV, considered as low energy for a Muon Collider, it would be possible to extract information on the Higgs boson potential, unique to the Muon Collider. The goal of the Muon Collider project is to reach energies higher than 3 TeV, 10 TeV are currently explored. At this energy a sizable number of double and triple Higgs bosons will be produced allowing the full determination of the Higgs potential. 6 Synergies with other physics fields and social impact The studies for a Muon Collider will have a huge impact on the state-of-the-art technologies for new accelerators. Most of the future programs to explore nature are based on the extrapolation of the conventional approach used at LEP and at LHC. Powerful lepton colliders are proposed to perform precision measurements of the Higgs properties and of other key parameters of the standard model. ILC, CepC, FCC-ee are gigantic infrastructures with dimensions in the range of 30–100 km, investments of several billion euros and construction times of about 10 years. New hadron machines are proposed to push forward the energy frontier deep into the multi-TeV region. Colliders like SppC and FCC-hh imply rings of 100 km circumference, a new generation of superconducting magnets to be developed, costs exceeding 20 billion euros and very long construction time scales. A Muon Collider would be a serious alternative to some of these programs, providing access to the most important measurements with a smaller and substantially cheaper machine, a new generation of particle colliders capable of performing precision studies, with the flexibility to be scaled to the multi-TeV regime. Furthermore, the complex of accelerators necessary to implement a Muon Collider would allow for a rich program of physics measurements, as, for example, neutrino physics. The huge amount of R&D involved in this project would be extremely useful for the accelerator and high-energy physics communities. For example, if the studies could prove it feasible, the LEMMA scheme at low energy could be used for intense photon beam production empowering many applied fields, including material studies, medical science, and lithography. Italy, in particular, has a glorious history of design, construction and operation of accelerators for the study of the fundamental constituents of matter and their interactions, since the construction of the first machine in the '60s at the INFN Frascati National Laboratories. In recent years, due to the increasing size of the projects and the larger costs, it became more difficult to build national accelerators, therefore the training and the interest of young researchers on colliders design has diminished. The Muon Collider study, being a completely new and challenging field of research, can renew the interest of many students and young researchers in this field, for a new generation of accelerator physicists and engineers. Looking at the applications aspect, the Muon Collider can be dreamed of as the door to a new era. For example, muon tomography is a technique that uses cosmic-ray muons to reconstruct the three-dimensional image of a given volume that can be hidden under the earth or a heavy material given the highly penetrating power of these particles. In Italy the project Mu-Ray aims at mapping the inside of Vesuvius volcano. Muon tomography is also used to monitor nuclear reactors. The earthquake of 2011 in Japan caused serious damage to the Fukushima Daiichi power plant. The direct evaluation of the real damage to the cores of the reactor was very dangerous given the high level of radiation in the site. The Toshiba Corporation has for the very first time used a muon tomography detector to analyze the cosmic- ray muons scattered by the reactor and evaluate the conditions of the cores. Data was collected for about four weeks in order to have enough muons impinging on the reactor, due to the low rate of high-energy cosmic muons. While it is clear that the present Muon Collider proposals are for a facility of large dimensions, in the future a dream to have Muon Collider technology so advanced to build tools based on muon beams and perform much faster analyses as the ones mentioned, could be envisaged. The present Muon Collider status is very similar to the beginning of the era of electron and hadron accelerators, when it was difficult to imagine that nowadays compact accelerators are used in hospitals for cancer treatment, or table-top accelerators could have been built for industrial applications. If a compact muon beam were available, it could be used for example in the harbors or at the borders, to monitor the nuclear waste and the nuclear weapons illegal trade, methods which are already in use but that take time given the cosmic-ray muon rate. Concluding in one sentence, the Muon Collider is a chance not to be missed. Acknowledgments The authors thank Susanna Guiducci, Nadia Pastrone, Lorenzo Sestini, Laura Buonincontri and Massimo Casarsa for the useful and constructive discussions. Thanks to Paola Sala, Camilla Curatolo, Francesco Collamati and Alessio Mereghetti for preparing the material on the machine-detector-interface.	2021-09-19 13:47:08	{"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": 0.7314066886901855, "perplexity": 999.0736248380507}, "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/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00009.warc.gz"}
https://www.research.unipd.it/handle/11577/3270448	A vector bundle on a smooth projective variety, if it is generically generated by global sections, yields a rational map to a Grassmannian, called Kodaira map. We investigate the asymptotic behavior of the Kodaira maps for the symmetric powers of a vector bundle, and we show that these maps stabilize to a map dominating all of them, as it happens for a line bundle via the Iitka fibration. Through this Iitaka-type construction, applied to the cotangent bundle, we give a new characterization of Abelian varieties. ### Iitaka Fibrations for Vector Bundles #### Abstract A vector bundle on a smooth projective variety, if it is generically generated by global sections, yields a rational map to a Grassmannian, called Kodaira map. We investigate the asymptotic behavior of the Kodaira maps for the symmetric powers of a vector bundle, and we show that these maps stabilize to a map dominating all of them, as it happens for a line bundle via the Iitka fibration. Through this Iitaka-type construction, applied to the cotangent bundle, we give a new characterization of Abelian varieties. ##### Scheda breve Scheda completa Scheda completa (DC) File in questo prodotto: Non ci sono file associati a questo prodotto. ##### Pubblicazioni consigliate Caricamento pubblicazioni consigliate I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione. Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11577/3270448` • ND • 8 • 7	2022-10-07 02:28:47	{"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": 0.8218240141868591, "perplexity": 2133.7247690717013}, "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/1664030337906.7/warc/CC-MAIN-20221007014029-20221007044029-00557.warc.gz"}
https://proofwiki.org/wiki/Category:Restrictions	# Category:Restrictions This category contains results about Restrictions. Definitions specific to this category can be found in Definitions/Restrictions. Let $\mathcal R$ be a relation on $S \times T$. Let $X \subseteq S$, $Y \subseteq T$. The restriction of $\mathcal R$ to $X \times Y$ is the relation on $X \times Y$ defined as: $\mathcal R {\restriction_{X \times Y} }: = \mathcal R \cap \paren {X \times Y}$ If $Y = T$, then we simply call this the restriction of $\mathcal R$ to $X$, and denote it as $\mathcal R {\restriction_X}$. ## Subcategories This category has the following 3 subcategories, out of 3 total.	2020-01-20 23:31:30	{"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": 0.9945252537727356, "perplexity": 297.9371575066864}, "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-2020-05/segments/1579250601040.47/warc/CC-MAIN-20200120224950-20200121013950-00377.warc.gz"}
http://mathhelpforum.com/differential-geometry/195024-riemann-integral-print.html	# Riemann Integral • January 8th 2012, 04:34 AM younhock Riemann Integral Suppose i have $f(x)=0$ for $x \neq \frac{1}{n},n=1,2,3,.....$ and $f(\frac{1}{n})=1$. how to show that $f$ is Riemann Integrable and the riemann sum is 0 by using definition? • January 8th 2012, 05:23 AM girdav Re: Riemann Integral Fix $\varepsilon>0$, and $n_0$ such that $n_0^{-1}\leq \varepsilon$. Put $s_2(x):=\begin{cases} 1&\mbox{ if } x\leq n_0^{-1}\\0&\mbox{ otherwise}\end{cases}$ and $s_1(x)=0$. Choose a good subdivision and you are done. • January 8th 2012, 08:59 AM younhock Re: Riemann Integral Quote: Originally Posted by girdav Fix $\varepsilon>0$, and $n_0$ such that $n_0^{-1}\leq \varepsilon$. Put $s_2(x):=\begin{cases} 1&\mbox{ if } x\leq n_0^{-1}\\0&\mbox{ otherwise}\end{cases}$ and $s_1(x)=0$. Choose a good subdivision and you are done. Why we construct $s_2 (x)$ and $s_1 (x)?$ Can it related to $f?$ • January 8th 2012, 09:21 AM girdav Re: Riemann Integral It's just a definition. $s_1$ and $s_2$ are step functions. Using the subdivision $0, you can check the definition of Riemann integrable.	2014-03-13 19:54:24	{"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": 20, "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": 0.9445903301239014, "perplexity": 879.3881729031273}, "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-2014-10/segments/1394678680766/warc/CC-MAIN-20140313024440-00066-ip-10-183-142-35.ec2.internal.warc.gz"}
https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2/share/doc/Macaulay2/QuaternaryQuartics/html/___Type_sp%5B441b%5D_cm_sp__C__Y_spof_spdegree_sp16.html	# Type [441b], CY of degree 16 -- lifting to a 3-fold with components of degrees 8, 8 We construct via linkage an arithmetically Gorenstein 3-fold $X = X_{8} \cup X_{8}' \subset \bf{P}^7$, of degree 16, having Betti table of type [441], on component [441b]. For an artinian reduction $A_F$, the quadratic part of the ideal $F^\perp$ is the ideal of two skew lines, and $F^\perp$ contains pencils of ideals of three points on one line and three fix points on the other. So we construct $X_{8}$ in the intersection of two cubics in a P5 and $X_{8}'$ in the intersection of two cubics in another P5. In the construction the intersection $X\cup X'$ of a component $X$ with the other is an anticanonical divisor on $X$. The Betti table is $\phantom{WWWW} \begin{matrix} &0&1&2&3&4\\ \text{total:}&1&9&16&9&1\\ \text{0:}&1&\text{.}&\text{.}&\text{.}&\text{.}\\ \text{1:}&\text{.}&4&4&1&\text{.}\\ \text{2:}&\text{.}&4&8&4&\text{.}\\ \text{3:}&\text{.}&1&4&4&\text{.}\\ \text{4:}&\text{.}&\text{.}&\text{.}&\text{.}&1\\ \end{matrix}$ i1 : kk=QQ; i2 : U=kk[y0,y1,y2,y3,y4,y5,y6,y7]; i3 : P5a=ideal(y0,y1);--a P5 containing P3c o3 : Ideal of U i4 : P5b=ideal(y2,y3);--another P5 containing P3c o4 : Ideal of U i5 : P3=P5a+P5b;--the common P3 of P5a and P5b o5 : Ideal of U i6 : F0=matrix{{random(2,U),random(2,U)},{random(2,U),random(2,U)}};--a 2x2 matrix of quadrics, 2 2 o6 : Matrix U <--- U i7 : F1=matrix{{y2},{y3}}\|F0;--a 2x3 matrix, one columns of linear forms, and two of quadrics, 2 3 o7 : Matrix U <--- U i8 : X8a=P5a+minors(2,F1);--a 3-fold of degree 8 in P5a linked (1,1,3,3) to P3 o8 : Ideal of U i9 : F2=matrix{{y0},{y1}}\|F0;--a 2x3 matrix, one columns of linear forms, and two of quadrics, 2 3 o9 : Matrix U <--- U i10 : X8b=P5b+minors(2,F2);--a 3-fold of degree 8 in P5b linked (1,1,3,3) to P3 o10 : Ideal of U i11 : X16=intersect(X8a,X8b);-- a 3-fold of degree 16 in P7 with betti table of type 441b o11 : Ideal of U i12 : betti res X16 0 1 2 3 4 o12 = total: 1 9 16 9 1 0: 1 . . . . 1: . 4 4 1 . 2: . 4 8 4 . 3: . 1 4 4 . 4: . . . . 1 o12 : BettiTally	2022-07-05 09:16:53	{"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": 0.6681947708129883, "perplexity": 882.7324516680787}, "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/1656104542759.82/warc/CC-MAIN-20220705083545-20220705113545-00607.warc.gz"}
https://www.stats4stem.org/r-boxplots	R: Boxplot I. Basic Boxplot An electric car manufacturer asked engineers to do nine seperate endurance tests on two of their car models. One model is called the Electra and the second is called the # create wind variable to be used to construct boxplots wind = airquality$Wind boxplot(wind) II. horizontal and col parameters An electric car manufacturer asked engineers to do nine seperate endurance tests on two of their car models. One model is called the Electra and the second is called the boxplot(wind, horizontal = TRUE, col = "blue") III. main and xlab parameters An electric car manufacturer asked engineers to do nine seperate endurance tests on two of their car models. One model is called the Electra and the second is called the boxplot(wind, horizontal = TRUE, col = "blue", main = "Boxplot of Wind Speed", xlab = "Wind Speed (mpg)") IV. Side-by-side Boxplots Side-by-side boxplots are an excellent graphical tool to help discern the relationship between a categorical and numerical variables. Example 1: For this example, we will use the preinstalled airquality dataset that contains data for New York City. For this specific example we will be analyzing the relationship between the maximum New York City daily temperature and month. Before we can begin our analysis, for simplicity, we first will define two new variables as shown below. temp = airquality$Temp month = airquality$Month Next, let's analyze the relationship between maximum daily temperature and month. To do this, we will construct a side-by-side boxplots using the R code shown below: boxplot(temp ~ month, col = rainbow(5), names = c("May", "June", "July", "Auguest", "September"), main = "Maximum New York City Daily Temperature by Month", xlab = "Month", ylab = "Temperature (F)") Example 2: For this example, we will use the cats dataset found in the MASS library. To access this dataset, we will first need to load the MASS library first. Once the library has been loaded, one can view a small portion of the dataset, to get a feel for the dataset, by using the head(cars) command as shown below. > # Load MASS library > library(MASS) > > head(cats) Sex Bwt Hwt 1 F 2.0 7.0 2 F 2.0 7.4 3 F 2.0 9.5 4 F 2.1 7.2 5 F 2.1 7.3 6 F 2.1 7.6 Once the data has been loaded, let's analyze the relationship between sex and body weight, which is represented by the Bwt variable. To do this, we will construct a side-by-side boxplot using the R code shown below: # define two variables to be analyzed in boxplot sex = cats$Sex weight = cats\$Bwt boxplot(weight ~ sex, col = c("blue", "green"), main = "Cat Weight by Sex", xlab = "Sex", ylab = "Body Weight (kg)")	2018-12-18 14:15:53	{"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": 0.3735080659389496, "perplexity": 14787.871310825707}, "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-2018-51/segments/1544376829399.59/warc/CC-MAIN-20181218123521-20181218145521-00022.warc.gz"}
https://www.atmos-chem-phys.net/19/1059/2019/	Journal topic Atmos. Chem. Phys., 19, 1059–1076, 2019 https://doi.org/10.5194/acp-19-1059-2019 Atmos. Chem. Phys., 19, 1059–1076, 2019 https://doi.org/10.5194/acp-19-1059-2019 Research article 28 Jan 2019 Research article \| 28 Jan 2019 # Heterogeneous ice nucleation on dust particles sourced from nine deserts worldwide – Part 2: Deposition nucleation and condensation freezing Heterogeneous ice nucleation on dust particles sourced from nine deserts worldwide – Part 2: Deposition nucleation and condensation freezing Yvonne Boose1,a, Philipp Baloh2, Michael Plötze3, Johannes Ofner4, Hinrich Grothe2, Berko Sierau1, Ulrike Lohmann1, and Zamin A. Kanji1 Yvonne Boose et al. • 1Institute for Atmospheric and Climate Science, ETH Zürich, Zürich, Switzerland • 2Institute for Materials Chemistry, TU Wien, Vienna, Austria • 3Institute for Geotechnical Engineering, ETH Zürich, Zürich, Switzerland • 4Institute for Chemical Technologies and Analytics, TU Wien, Vienna, Austria • anow at: Institute of Atmospheric Physics, German Aerospace Center, Wessling, Germany Correspondence: Yvonne Boose (yvonne.boose@alumni.ethz.ch) and Zamin A. Kanji (zamin.kanji@env.ethz.ch) Abstract Mineral dust particles from deserts are amongst the most common ice nucleating particles in the atmosphere. The mineralogy of desert dust differs depending on the source region and can further fractionate during the dust emission processes. Mineralogy to a large extent explains the ice nucleation behavior of desert aerosol, but not entirely. Apart from pure mineral dust, desert aerosol particles often exhibit a coating or are mixed with small amounts of biological material. Aging on the ground or during atmospheric transport can deactivate nucleation sites, thus strong ice nucleating minerals may not exhibit their full potential. In the partner paper of this work, it was shown that mineralogy determines most but not all of the ice nucleation behavior in the immersion mode found for desert dust. In this study, the influence of semi-volatile organic compounds and the presence of crystal water on the ice nucleation behavior of desert aerosol is investigated. This work focuses on the deposition and condensation ice nucleation modes at temperatures between 238 and 242 K of 18 dust samples sourced from nine deserts worldwide. Chemical imaging of the particles' surface is used to determine the cause of the observed differences in ice nucleation. It is found that, while the ice nucleation ability of the majority of the dust samples is dominated by their quartz and feldspar content, in one carbonaceous sample it is mostly caused by organic matter, potentially cellulose and/or proteins. In contrast, the ice nucleation ability of an airborne Saharan sample is found to be diminished, likely by semi-volatile species covering ice nucleation active sites of the minerals. This study shows that in addition to mineralogy, other factors such as organics and crystal water content can alter the ice nucleation behavior of desert aerosol during atmospheric transport in various ways. 1 Introduction The ice phase in clouds causes one of the largest uncertainties for understanding the role of clouds in the present climate and for projecting future climate . While it is known that for the initial formation of ice in clouds warmer than 235 K certain aerosol particles, so-called ice nucleating particles (INPs), are necessary, many aspects of heterogeneous ice nucleation remain poorly understood . Mineral dust is thought to be the most prevalent INP type in the atmosphere . found naturally occurring mineral dust particles to nucleate ice at temperatures T<258 K. and detected mineral dust in ice crystal residuals in mixed-phase clouds. In these clouds the most common ice nucleating mechanisms are likely immersion and contact freezing. Both mechanisms require a cloud droplet to form first and an INP to either initiate freezing from the inside of the droplet (immersion) or via contact with the surface of the droplet (contact freezing). observed mineral dust also in ice crystal residuals in cirrus clouds. When the relative humidity (RH) with respect to ice is high enough (e.g., RHi>140 % at 238 K), ice forms via homogeneous freezing of solution droplets without the help of an INP . At lower RH ice may form via immersion freezing on INPs in solution droplets or via the deposition mode, where ice nucleation occurs on an INP directly from the vapor phase . Condensation freezing is understood as freezing occurring during the formation of a liquid phase, when water saturation is exceeded but before a droplet has formed. Recently, the differentiation between condensation and immersion freezing has been questioned . Furthermore, it has been suggested that freezing at water subsaturated (RHw<100 %) conditions, referred to as deposition nucleation, may in some cases be explained by condensation and subsequent freezing of water in pores on the particles' surface (pore condensation and freezing – PCF; Marcolli2017). Mineral dust is thought to have an influence on cloud microphysical processes on a global scale, with global dust emission rate estimates of up to 5 Pg yr−1 (Engelstaedter et al.2006, and references therein). found increased concentrations of INPs in air masses over Florida which carried Saharan dust, while observed precipitation in California to be influenced by dust from Asia and the Sahara. Over Europe, and found periods of Saharan dust advection to coincide with increased INP concentrations under mixed-phase cloud conditions. Even at the South Pole, identified about 60 % of ice crystal residuals to be clay minerals. For several decades, clay minerals were believed to be responsible for the ice activity of mineral dust, mainly due to their high mass fraction in airborne dust. Recently, K-feldspars have been identified to nucleate ice at warmer temperatures or lower relative humidity than all other minerals, both in the immersion mode as well as in the deposition and condensation modes . found the K-feldspar content to correlate well with the ice nucleation activity of dust at temperatures between 238 and 243 K for three dust samples from Iceland, China, and the Himalayas. While found K-feldspar in only one out of eight dust samples collected in potential atmospheric dust source regions in South America, Asia, and Africa, we observed K-feldspar to be present in all but one sample from a collection of 21 samples from deserts around the world . Furthermore, feldspars are prone to chemical weathering processes in acids or water which may passivate certain active sites and decrease the feldspar's ice nucleation activity . The nature of these active sites is still under debate. It is suspected that they are associated with high energy defects in the lattice structure such as steps, cracks, and impurities or crystal boundaries in twinned crystals where a (100) crystal plane is exposed to water or vapor . found that feldspars with perthitic microtexture, i.e., intergrowth of sodic alkali feldspar into a host of K-feldspar, have the highest ice nucleating ability. observed weathering to occur primarily at excess energy sites on the feldspar surface. During atmospheric transport, such chemical weathering processes or aging could alter the ice nucleation activity of feldspar particles compared to those on the ground or freshly cleaved crystals used in laboratory studies . By implementing parameterizations for marine organics and feldspar INPs into their global model, found indications that terrestrial INP concentrations could be dominated by feldspar. However, atmospheric aging effects were not taken into account. Thus, feldspar has the potential to be the most important ice nucleating mineral in the atmosphere, but its atmospheric relevance is yet to be confirmed. Atmospheric aging processes are challenging to observe in situ, thus several laboratory studies have mimicked potential aging processes. These processes often modify the surface of dust particles and, as such, the ice nucleation ability of mineral dust. could block and unblock surface ice nucleation sites with selected organic molecules. Sulfuric acid coating leads to a reduction in the ice nucleation ability of mineral dust , the exposure to low amounts of ozone increases it , and coatings of organic aerosol make no difference to it in condensation mode . The presence of ammonium sulfate has been suggested to improve the ice nucleation ability of Saharan dust advected to Tenerife . Recently, and confirmed that very dilute ammonium salt solutions (<1 mol kg−1) increase the ice nucleation temperature of microcline by 3 to 4.5 K. While surface-collected dust particles from the Sahara were found to have negligible amounts of nitrate or sulfate, a high degree of mixing of nitrate and/or sulfate with mineral dust was observed after advection to Cape Verde, Tenerife, or Ireland . Residues from ice nucleating biological material such as fungal proteins or nanoscale pollenaceous INPs have been observed to adsorb to mineral dust while retaining their ice nucleation ability . Even though desert soils contain typically <1 % organic matter due to the low average annual precipitation , long-range transport of dust has been suggested to efficiently disperse bacteria on a global scale . Enriched fluorescent particle concentrations, an indication for enriched biological material, were found in long-range transported Saharan dust by in ice crystal residuals from mixed-phase clouds in the Swiss Alps and in condensation-mode INPs at 241 K by on the Canary Islands. In contrast to biological material, secondary organic aerosol coatings have been observed to decrease the ice nucleation ability of dust particles in the laboratory in deposition mode but not in condensation mode . In a partner paper to this work we investigated the immersion-mode ice nucleation activity of airborne dust samples, which were collected after atmospheric transport or sampled from the surface in deserts. We showed that the K-feldspar fraction, i.e., the fraction of microcline plus orthoclase, of these dust samples correlates well with the ice-active surface site density in the immersion mode at T=253 K. At T≤245 K the best correlation of the ice nucleation activity was found for the bulk quartz plus feldspar (microcline, orthoclase, and plagioclase) content in the dust samples, while the fraction of clays was negatively correlated with the ice nucleation activity. Quartz alone has been found to show various immersion-mode ice nucleation activities in laboratory studies. found quartz being active at temperatures comparable to microcline, while measured ice nucleation activity below feldspar temperatures but above those of clay. , in contrast, only observed ice nucleation activity at temperatures comparable to or lower than those of clays. These differences in ice nucleation ability can be related to the history of the quartz samples and different ways of pre-processing them . Milling quartz samples leads to a breakup of $\mathrm{Si}-\mathrm{O}-\mathrm{Si}$ bridges on the surface, leading to the formation of Si−OH and $\mathrm{Si}-\mathrm{O}-\mathrm{OH}$ in the presence of water vapor, which increases the ice nucleation activity of the quartz particles . Quartz is the most abundant mineral on Earth and is widely spread in various soils. It is highly resistant to chemical and mechanical weathering (Goldich1938), the latter leading to its abundance increasing with particle size. But quartz is also found, to a lower degree, in smaller sized dust particles (e.g., 11 % volume fraction of 1.6 µm sized particles over Morocco; Kandler et al.2009). The current paper focuses on the ice nucleation behavior at 238–242 K of airborne and surface-collected dust samples. We investigate ice nucleation at a constant temperature while RH is increased from ice saturation to above water saturation. While the partner paper showed that mineralogy explains most but not all of the observed ice nucleation behavior of desert dust, this paper focuses on the role of compounds other than the pure minerals for ice nucleation. We use thermogravimetric analysis and chemical imaging methods to highlight the effect of other entities mixed with the dust, such as organic material or soot, on the ice nucleation behavior. In addition to the samples studied in the partner paper , three more airborne Saharan samples are investigated. Comparing the in total seven airborne Saharan samples to in situ measurements in the Saharan Air Layer, we find low variability in the ice nucleation behavior of dust from different sources. Furthermore, we show that airborne samples containing orthoclase are similarly active at the studied temperatures to those containing microcline. 2 Methods ## 2.1 Dust sample origins and processing In this part of the series we present ice nucleation measurements of 18 dust samples. Seven airborne samples were collected after advection from the Sahara. Four of the airborne samples were collected directly from the air in August 2013 and 2014 at the Izaña observatory in Tenerife, Spain, using a custom-made large cyclone (Advanced Cyclone Systems, S.A.: flow rate of 200 m3 h−1 and D50=1.3µm, the diameter at which the collection efficiency is 50 %). The remaining three airborne samples were collected by deposition on solar panels or roofs in April 2014 (Crete and Peloponnese, Greece) and on 10 May 2010 (Aburdees, Egypt). Nine samples were collected from the surface in the following deserts: (i) the Atacama desert in Chile; (ii) a location approximately 70 km from Uluru in Australia; (iii) the Great Basin in Nevada and (iv) the Mojave desert in California, USA; (v) a Wadi in the Negev desert, approximately 5 km from Sde Boker in Israel; (vi) dunes in the Sahara, close to Merzouga in Morocco; (vii) dunes in the Arabian desert in Dubai; (viii) the Etosha pan in Namibia, a dry salt pan; and (ix) the Taklamakan desert in China. A map showing the locations is provided in . Before arriving to the laboratory, samples were stored in various ways: Samples collected from the surface were typically stored for several weeks in PET bottles or other plastic containers. Airborne samples were stored in polypropylene tubes and sealed with paraffin wax tape. In the laboratory, all samples were stored in the dark at room temperature in polypropylene tubes after pre-processing (sieving and milling, see below). While changes in the ice nucleating ability due to water uptake, loss of volatile material, or growth of biological material which may occur during storage cannot be excluded, they are assumed to be minor, because the samples were collected and stored under dry conditions, hardly exposed to air, and kept at a lower temperature than at which they were collected. The Israel sample and the Etosha sample are from the same batch as those studied in . The surface-collected samples were sieved with a cascade of dry sieves (Retsch Vibratory Sieve Shaker AS 200) with 32 µm diameter being the smallest cutoff size. Most samples only contained a few weight percent in this size range. The Australia and Morocco samples were milled using a vibratory disc mill (Retsch, model RS1), as the fraction of particles in the sub-32 µm size range was too low for ice nucleation experiments. Particles in the lowest available size bin (32–64 µm) of the Morocco sample were milled. The Australia sample was first sieved with a coarse, millimeter-range sieve to separate any large material, and the remaining smaller fraction was milled. For the Israel and the Atacama dusts, a sieved and a milled sample were included in the study. The Israel sample was first sieved, and part of a sub-32 µm fraction was milled, while in case of the Atacama sample part of the initial, unsieved batch was milled. To investigate if the ice nucleation activity of the samples is influenced by biological particles internally or externally mixed with the dust or by organic coatings on the dust particle surface, selected samples were heated to 300 C and stayed at this temperature for 10 h before the ice nucleation experiments. At this temperature proteinaceous material, such as bacterial and fungal INPs, should be denatured , and the majority of organic material, such as glucose, is combusted and evaporated (Kristensen1990, and references therein). ## 2.2 Dust particle generation and size distribution Dust particles were dry dispersed using a rotating brush generator (RBG, Palas, model RBG 1000) with N2 (5.0) as carrier gas into a 2.78 m3 stainless steel aerosol reservoir tank via a cyclone that confined the dust size distribution to below D50=2.5µm. Total particle concentration was monitored using a condensation particle counter (CPC; TSI model 3772). The tank was filled with particles up to a concentration of 1200 cm−3, which decreased steadily to about 300 cm−3 over approximately 10 h. The tank was cleaned before an experiment by repeatedly evacuating and purging it with N2 until the particle concentration decreased to 30–90 cm−3. The particle size distribution of all samples was measured with a scanning mobility particle sizer (SMPS; TSI; DMA model 3081, CPC model 3010) for mobility diameters (dm) between 12 and 615 nm and an aerodynamic particle sizer (APS; TSI; model 3321) for aerodynamic diameters (daer) between 0.5 and 20 µm. The mobility and aerodynamic diameters were converted to volume equivalent diameter (dve) by assuming a typical dust particle density of ρ=2.65 g cm−3 and optimizing the shape factor χ to receive the best overlap of two size distributions measured by the SMPS and APS. This yielded χ=1.36, which is in the range of earlier studies . Assuming spherical particles, the area size distribution was calculated and fitted with a bimodal log-normal distribution. The mean particle surface area ($\stackrel{\mathrm{‾}}{{A}_{\mathrm{ve},\mathrm{w}}}$) was calculated from the resulting fit for each sample. Four size distributions and the fit parameters for all samples are provided in . During an experiment $\stackrel{\mathrm{‾}}{{A}_{\mathrm{ve},\mathrm{w}}}$ was reduced by between 6 % to 24 % due to a faster sedimentation of larger particles in the aerosol tank. The Great Basin sample was coarser than the other samples and settled out faster. Therefore two refills were necessary, and $\stackrel{\mathrm{‾}}{{A}_{\mathrm{ve},\mathrm{w}}}$ varied by 64 %. Table 1Mineralogical composition in wt % of airborne Saharan dust samples. Crete, Egypt, Tenerife2013 (Tenerife in Part 1), and Peloponnese as in . Results were rounded to the nearest integer from the original Rietveld fit results, thus total composition ≠100 wt % may occur. ## 2.3 Mineralogical, thermogravimetric, and morphology analysis The quantitative mineralogical composition of the bulk dust samples was investigated with the X-ray diffraction (XRD) Rietveld method (Rietveld1969) using a Bragg–Brentano diffractometer (Bruker AXS D8 Advance with Cu Ka radiation). The qualitative-phase composition was determined with the software DIFFRACplus (Bruker AXS). On the basis of the peak positions and their relative intensities, the mineral phases were identified in comparison to the PDF-2 database (International Centre for Diffraction Data). The quantitative composition was calculated by means of Rietveld analysis of the XRD pattern (Rietveld program AutoQuan, GE SEIFERT; Bergmann et al.1998; Bish and Plötze2011). Due to the small amount of the dust sample, it was not possible to do a mineralogical analysis of the identical size fraction as in the tank (<2.5µm). Instead, the entire size fraction of the airborne and the milled samples, and the sub-32 µm fraction of the sieved samples, was used. The measured mineralogical composition is provided in , and that of the additional Tenerife samples is provided in Table 1. The Tenerife2014_1 sample was additionally measured by Powder XRD (Panalytical XPert Pro) in Bragg–Brentano geometry, equipped with a copper anode providing Cu Ka radiation. A diffractogram was recorded before and after heating the sample to 300 C for 10 h on a silicon sample carrier. Thermogravimetric analysis (TGA) of six of the dust samples was conducted by gradually heating the dust samples from 40 to 300 C at 10 K min−1 and continuously recording the mass of the samples in a thermogravimetric analyzer (Model Pyris 1 TGA, PerkinElmer). During the temperature scan, the samples were under a constant nitrogen flow of 20 mL min−1. The morphology of one sample was investigated using scanning electron microscopy (SEM; FEI Quanta 250 FEG, ThermoFisher Scientific). ## 2.4 Chemical imaging: ATR spectrometry and Raman mapping Attenuated total reflection infrared (ATR-IR) spectroscopy was carried out on an FTIR (Bruker Vertex 80v) equipped with an ATR cell (Pike GladiATR, diamond ATR crystal). The beam path of the spectrometer and the optical parts of the ATR cell are under a vacuum (1.65 mbar) to minimize the influence of water vapor and CO2. The crystal where the sample is placed sits in a cell that is flushed with nitrogen gas before and through the measurement for the same reason. A liquid-nitrogen-cooled MCT detector is used for spectra acquisition. Spectra of the samples were recorded before and after a heat treatment. For the heat treatment the samples were placed for 10 h into a laboratory oven at 300 C. The spectral window was set between 700 and 4000 cm−1, with a resolution of 1 cm−1. Spectra for the Tenerife2014_1, Etosha, and Australia samples were recorded this way. Raman images were recorded on a confocal Raman spectrometer (WITec alpha300 RSA+) using a 488 nm laser, 50× magnification, grating of 600 lines per millimeter, and a laser power of 4.7 mW. For Raman imaging the dust was impacted on a clean aluminium surface as described in and subsequently mapped with the aid of a Piezo XY stage. Raman mappings were carried out before and after the same heat treatment as that for the ATR-IR measurements. The Etosha and Australia samples were mapped with this method. ## 2.5 Deposition and condensation nucleation experiments and data treatment Ice nucleation experiments were conducted with the portable ice nucleation chamber (PINC; Chou et al.2011; Boose et al.2016a). Aerosol particles are sampled from the tank, dried, and introduced into the chamber, where they are layered between two particle-free sheath air flows. Before an experiment, the two chamber walls are coated with a thin layer of ice. During an experiment a temperature gradient is applied between the walls, leading to diffusion of water vapor and heat. A linear gradient of temperature and the partial pressure of water vapor between the walls leads to supersaturation with respect to ice. At a constant aerosol layer temperature, the RH is raised at a constant rate until supersaturation with respect to water of a few percent (RHw=103 %–105 %) is reached. If ice nucleation occurs under these conditions, ice crystals grow on the INPs and are detected in the lower part of the chamber by an optical particle counter. As the ice nucleation mechanisms cannot be identified visually in the PINC we refer to the deposition mode at RHw<100 % and to condensation freezing at RHw>100 %. We use these relative-humidity-based thermodynamic regimes as an operational definition, which does not exclude the possibility of PCF to occur at RHw<100 % (Marcolli2017). Condensation mode refers here to the conditions above water saturation where full droplet activation prior to freezing cannot be guaranteed. In the deterministic concept ice nucleation is assumed to take place at so-called ice nucleation active sites on the particle's surface (Vali1966). The probability of such a site being present on a particle and thus of the particle to nucleate ice at a certain temperature scales with the particle's surface area . To account for this dependency and compare the ice nucleation ability of the different dust samples the ice-active surface site density ns was calculated: $\begin{array}{}\text{(1)}& {n}_{\mathrm{s}}=-\frac{\mathrm{ln}\left(\mathrm{1}-\text{AF}\right)}{\stackrel{\mathrm{‾}}{{A}_{\mathrm{ve},\mathrm{w}}}}\approx \frac{\text{INP}}{{N}_{\mathrm{tot}}\stackrel{\mathrm{‾}}{{A}_{\mathrm{ve},\mathrm{w}}}},\end{array}$ with the total particle concentration Ntot and the activated fraction AF given by INP∕Ntot. The approximation is only valid for AF<0.1, which is the case in this study. As aerosol particles larger than 1 µm were in the size range of the ice crystals and could not be differentiated based on size in the optical particle counter spectra, the ns was corrected by subtracting the average ns at RHi=100 % to 103 %. At these low RHi values no ice nucleation is expected, thus counts in the size range of ice crystals are assumed to be large dust particles. The ice nucleation activity of the Australia, Atacama milled, Etosha, Tenerife2014_1, Peloponnese, and Morocco samples was additionally measured after they had been exposed to 300 C for 10 h. For these experiments the tank was not used. Instead, dust was dry dispersed using particle-free air from a sonicated flask via a cyclone with a cutoff of 2.5 µm and a diffusion dryer into a PINC, a CPC, an APS, and a SMPS. The unheated samples were additionally measured with the same setup to allow direct comparison. The ns measured with the tank setup, in comparison to the sonicated flask setup for the unheated samples, varied between a factor of 1∕3 to 3, which is a good agreement given the limitations of ns as a comparison parameter . Possible reasons for the differences are the sonicated flask breaking up larger entities, thus leading to a different mineralogy per size bin than the rotating brush generator or uncertainties stemming from the use of a different measurement setup. This shows the limits of using ns for such complex, polydisperse samples, which should ideally remove any size dependency. To reduce setup dependent uncertainty, only results measured with the same measurement setup are compared in the following discussion. Figure 1Ice-active surface site density at (a) 238 K, (b) 240 K, and (c) 242 K of samples collected airborne at the Izaña observatory on Tenerife in 2013 and 2014 (circles), in Egypt, Crete, and Peloponnese (triangles), and ns measured in situ during the CALIMA 2013 and 2014 campaigns which took place at the Izaña observatory. Figure 2Natural log of the ice-active surface site density as a function of the sum of quartz and feldspar content of the samples. Square symbols indicate surface-collected samples, stars indicate milled samples, and circles indicate airborne samples. For clarity, the Tenerife samples are not named individually and are instead shown as open circles. The asterisk in the legend indicates that the correlation is significant at the 0.05 level. 3 Results and discussion ## 3.1 Ice nucleation in the deposition and condensation mode and dust mineralogy Ice-active surface site density was determined for 18 dust samples, of which four are from the Sahara and were collected after atmospheric transport at the Izaña observatory in Tenerife and three were from after atmospheric transport in the Peloponnese, in Crete, and the Sinai Peninsula in Egypt. Figure 1 shows RH scans at three temperatures for these Saharan samples together with RH scans measured online at the Izaña observatory during the Cloud Affecting particLes In Mineral dust from the sAhara (CALIMA) campaigns in August 2013 and 2014, when the observatory was located in the Saharan Air Layer. The data and description of the location and campaigns are given in . The online and offline measured ns values agree well. Most of the ns curves of the different Saharan samples span an order of magnitude. In Fig. 2 a scatter plot of ln(ns) at RHw=102 % against the quartz plus feldspar content of the dust samples is shown, which is discussed in more details below. It reveals that the airborne Saharan samples are similar in ns and their quartz plus feldspar fraction (20 wt %–30 wt %). This holds true for most other mineral components, as shown in Table 1. The biggest differences are found for smectite and calcite, the latter accounting for 25 wt %–33 wt % in the Crete, Egypt, and Peloponnese samples but only for 4 wt %–7 wt % in the Tenerife samples. Smectite, in contrast, was only found in the Tenerife samples (23 wt %–32 wt %) and not in dust from the other three locations. Smectite and calcite are both known to have low ice nucleation activity . Thus, the similar amount of one or the other mineral in all Saharan dust samples is in line with the observed similar ns. Differentiating between microcline and orthoclase and comparing the bulk mineralogy to the surface-dependent ice nucleation ability introduces uncertainty. Within this uncertainty, there is no detectable effect from the presence of microcline versus orthoclase in the airborne samples at the studied temperatures. This is in line with the findings by that there is no correlation between ice nucleating ability and the level of ordering in the aluminosilicate framework, which determines if orthoclase (less ordered) or microcline (more ordered) is present. Table 2Overview of the Pearson correlation coefficients of the sum of selected mineral fractions and ln(ns) at different temperatures. An asterisk indicates that the correlation was significant at the 0.05 level. K-feldspar comprises microcline and orthoclase, while feldspar refers to the sum of microcline, orthoclase, and plagioclase. The number of samples included in each correlation varies, because the ns of the Mojave, Peloponnese, and Tenerife2014_2 samples was below the detection limit at 242 K, and the size distribution measurements of the Tenerife2014_1 sample were corrupted for the RH scan at 238 K. Figure 3Ice-active surface site density at (a) 240 K and (b) 242 K of samples before (filled symbols) and after (open symbols) heat treatment. Error bars include the Poisson error of the INP measurements and the maximum variation of $\stackrel{\mathrm{‾}}{{A}_{\mathrm{ve},\mathrm{w}}}$. Square symbols indicate surface-collected samples, stars indicate milled samples, and circles indicate airborne samples. To determine how well the dust mineralogy can overall predict the ice nucleation activity, the correlation of ln(ns) with the fractions of the most common minerals in the dust samples was compared in the partner paper . This comparison showed that the immersion-mode ice nucleation activity correlates best with the K-feldspar fraction alone at T=253 K, a temperature where only feldspar minerals are found to have significant ice nucleation activity . At T≤245 K, the ice nucleation activity correlates best with the quartz and quartz + feldspar fractions of the dust samples . At these lower temperatures, quartz as well as, to a lower degree, clay minerals were found to nucleate ice efficiently . Before investigating the role of other compounds, here we do a similar correlation analysis of the ln(ns) at T=238, 240, and 242 K and RHw=97 % and 102 % with the fraction of various minerals contained in the dust samples. Figure 2 exemplarily shows a scatter plot of ln(ns) at RHw=102 % against the quartz plus feldspar content of the dust samples. The Etosha sample was excluded from the correlation, as it does not contain any significant amount of these minerals. The surface-collected samples with a high ratio of quartz and feldspar tend to have a higher ns than the airborne samples. This trend is similar at the three investigated temperatures. The resulting correlation coefficients for the investigated mineral fractions are provided in Table 2. The findings by for the immersion mode ns are confirmed in the deposition and condensation mode: at all three tested temperatures, the highest correlation of ns is found for the fraction of quartz, followed by the quartz + feldspar fraction. The correlation with quartz alone is dominated by the Australia sample, which consists of 91 wt % quartz and is by far the most ice nucleation active dust sample. The remaining samples, which consist of, at most, 64 wt % of quartz, correlate only weakly with quartz alone (e.g., R=0.29, p=0.27, at T=238 K and RHw=102 %) and better with quartz plus feldspar (R=0.41, p=0.08). Adding illite to the quartz + feldspar fraction leads to insignificant changes of the correlation coefficient while adding kaolinite reduces it. Calcite and kaolinite alone are always negatively correlated with ns in both deposition and condensation mode. These observations are reasonable when compared to the findings of , who found a higher ns for quartz over clay minerals at T>236 K but lower ns for quartz than for feldspars for T>242 K. Generally, the correlations are lower in this study compared to the immersion-mode data from . A possible reason for this is that the only partial activation of INPs at these measurement conditions in the PINC due to an inhomogeneous RH profile along the particle trajectories inside the chamber weakens the effect of differences in mineralogy. Another reason could be that surface coatings play a more prominent role at lower RH values, because they are less diluted than in immersion mode. Correlating mineralogy, which is based on the bulk fraction, with the surface property ns, leads to additional uncertainty, as described above. Effects by non-mineral substances such as coatings are discussed in the following. Figure 4Relative mass loss (a) and its derivative (b) under heating of the different dust samples. ## 3.2 Ice nucleation and heat labile material In this section, the role of heat labile material on the surface of dust particles is investigated. A representative subset of the samples was selected to reduce the number of experiments necessary. The Australia and Morocco sample were selected because of their exceptional high ns, the Etosha sample because its mineralogy did not explain the observed ns, the Atacama milled sample because we expected a higher ns from the mineralogy, and finally the Tenerife2014_1 and Peloponnese samples as representatives for two airborne samples from different locations. Figure 3 shows the ns at 240 and 242 K of the unheated and the heated samples. In case of the Tenerife2014_1 sample the heat treatment led to an increase of ns at RHw<100 %, while it had no effect above water saturation. In contrast, the maximum ns of the Etosha sample decreased by 1 order of magnitude at 240 K after heating. At 242 K the ns was below the detection limit, as can be seen by a scattered flat ns curve in Fig. 3b. The heating had a small decreasing effect on the ns of the Peloponnese sample at all RH values and little to no significant effect on the ns of the remaining samples. A change in ice nucleation ability due to the heating gives an indication of the nature of the active sites, i.e., if they are inherent to the minerals themselves or a semi-volatile coating material or are due to biological particles, which are impacted by the heating. An RH dependency of the change in ice nucleation ability may suggest that the material which contains or coats the active sites is susceptible to dissolution. We investigated these possible implications further by thermogravimetric analysis, ATR-IR, and Raman spectroscopy of the samples. The relative mass loss under increasing temperature is shown in Fig. 4a and its first derivative in Fig. 4b. If pure samples of single minerals or organic species were studied, the TGA would show discrete steps in mass loss, indicated by spikes in the derivative plot. However, the complexity of the dust samples in this study, which consist of several minerals and likely also various other components, cause the spikes to widen, thus reducing the possibility to observe discrete steps. For example, showed that the mixture of a montmorillonite with varying concentrations of organic surfactant shifts the peak in the derivative mass between the higher temperature of the montmorillonite and the lower temperature of the surfactant, depending on the concentration of the surfactant. This makes it impossible to identify exactly which species are evaporated at which temperature. However, taking into account the temperature range, a qualitative analysis is possible. The Morocco, Australia, and Atacama milled samples, which all showed no change in ns after heating, exhibit a small, gradual decrease in mass of, at maximum, 0.5 % between 40 and 300 C. In the case of the three samples whose ns changed after heating, i.e., the Etosha, Peloponnese, and Tenerife2014_1 samples, a larger mass loss is found. A first decrease in mass of about 1 % (Etosha) to 2 % (both airborne samples) is observed between 40 and 110 C. The Etosha sample shows a second graduate mass release from 220 C onwards (1 %). The two airborne samples, Peloponnese and Tenerife2014_1, show small steps in mass release between 110 and 225 C and 110 and 170 C, respectively, and a continuous reduction in mass above these temperatures, reaching a total loss of 3 % and 8 % at 300 C, respectively. The temperature ranges where the mass loss occurs can be related to different materials which were evaporated and potentially altered the ice nucleation behavior. The first decrease in mass at 40 to 110 C is mostly due to the evaporation of adsorbed water on the surface of the dust particles or of volatile material such as volatile organics. At temperatures between 110 and 300 C the mass loss is mainly related to decomposition of organic matter, e.g., amides, carboxylic, and phenolic functional groups or the combustion of certain organic compounds such as cellulose . studied various biogenic organic materials, such as cellulose, glucose, bacteria (Escherichia coli and bacillus subtilis), and humic and glutamic acid, which showed either a bimodal or trimodal pattern in the TGA derivative. For all samples, they observed a first peak at 160–180 C, which accounted for 10 %–42 % of the mass loss and a second mass loss peak between 340 and 490 C. Most minerals present in the dust samples are stable at T≤300C, apart from smectite and gypsum (Földvári2011), as further discussed below. Figure 5Attenuated total reflectance infrared (ATR-IR) spectra for the (a) Australia, (b) Etosha, and (c) Tenerife2014_1 samples before (blue) and after heating (red). We performed ATR-IR spectroscopy on the Etosha and Tenerife2014_1 to investigate the nature of the material responsible for the respective decrease and increase in ns with heating. Furthermore, we chose the Australia sample as representative for most other cases where the ns stayed the same. Figure 5 shows the ATR-IR spectra of the three samples before and after heating. The bands between wavenumber 700 to 1200 cm−1 are related to the dominant minerals in the (bulk) samples: quartz in case of the Australia sample; dolomite, calcite, and ankerite in the case of Etosha; and kaolinite and smectite in case of the Tenerife2014_1 sample. Kaolinite also has signals at 3619, 3650, and 3685 cm−1 . No significant differences are observed between the unheated and the heated Australia and Etosha samples. The intensity differences in the mineral bands are likely related to single grains not representatively amplifying the signal during sampling. The Tenerife2014_1 sample, in contrast, shows clear differences before and after heating. A loss of intensity in the OH stretch region between 3500 and 3100 cm−1 is observed, which is too pronounced to be from adsorbed water only. Further intensity loss is observed in the C–H aliphatic region, with decreasing bands between 3000 and 2850 cm−1. This points to volatile organics being present on the unheated sample which were released during heating. Figure 6Raman mapping results for the Australia (a, b) and the Etosha sample (c, d). In each panel, (1) and (2) show the location of particles from clusters with spectra similar to those shown in (3) and (4). In (d1) the particle is encircled for which the filter (d3) found a spectrum. Raman mapping was performed on the Etosha, Tenerife2014_1, and Australia samples. Due to strong fluorescence, however, the Tenerife2014_1 spectra did not yield any information and are thus not presented here. The Raman maps for the Etosha and Australia samples are shown in Fig. 6. They reveal bands between 1200 and 1700 cm−1 with a distinctive pattern related to soot and carbonaceous material being present on many particles in the Australia sample (Fig. 6a2 and a4) and on some in the Etosha sample (Fig. 6c2 and c4). The carbonaceous material is not affected by the heating (Fig. 6b and d). A cluster with a strong broad signal at 3180 cm−1 and a secondary band at around 1080 cm−1 is observed for the unheated Etosha sample, which is present on most particles (Fig. 6c1 and c3). After the heat treatment, no cluster is identified anymore containing the broad 3180 cm−1 band, yet the signal at 1080 cm−1 remains. This supports the interpretation that the band at 1080 cm−1 can be attributed to calcite. Furthermore, the band at 1080 cm−1 does not correlate with the 3180 cm−1 band, therefore they belong to two different compounds. The cluster analysis groups these signals for the unheated sample due to the spatial proximity of the materials on the dust. It is likely that on mineral dust grains with a high calcite content a compound was absorbed. During the heat treatment this absorbed compound disappeared and the calcite remained. Afterwards, the cluster analysis showed no group containing the 3180 cm−1 band. A filter (3180±175 cm−1) was applied to search specifically for this signal. This revealed only very few particles carrying the related material after heating (Fig. 6d1 and d3). Identification of the material which was released or decomposed during the heating was hampered by fluorescence inherent to the minerals in the samples and also possibly due to biological material if present in the unheated samples. The ratio of signal to noise (fluorescence) was optimized by impacting small amounts of the samples on a pure aluminum surface and by adjusting the laser power, but the fluorescence could not be entirely suppressed. This, together with the complexity of the samples, inhibited an unambiguous identification of the species which were altered by the heating and may affect the ice nucleation ability. We suggest three possible candidates for the cluster with a strong Raman signal at 3180 cm−1 in the Etosha sample. (a) Amides typically show a Raman signal between 3300 and 3100 cm−1 (Socrates2001), as observed in the Etosha sample, but distinct peaks are usually also observed for amides between 1700 and 1600 cm−1, which are absent in the Etosha sample. (b) Pure ammonium sulfate has a broad band above 3000 cm−1 and a sharp peak at around 990 cm−1 . While the broad band at 3180 cm−1 agrees well with the observed signal, a second band is found at 1080 cm−1 in the Etosha sample. Ammonium sulfate has a band at 990 cm−1, which is significantly different from 1080 cm−1. Thus, the signal can be attributed to the calcite which has a very prominent band at this position. In addition, the XRD measurements confirmed calcite to be present in the sample. (c) Cellulose shows a broad band between 3575 and 3125 cm−1 and numerous bands between 1320 and 1030 cm−1 (Socrates2001). Additional bands at 1750 and 1725 cm−1, 1635 and 1600 cm−1, and 1480 and 1435 cm−1 are not distinguishable in the Etosha Raman spectrum. For the Etosha sample an effect of organic or other heat labile material on the ice nucleation behavior appears likely. The main minerals contained in the Etosha sample (i.e., ankerite, calcite, dolomite, and muscovite) are not known to be particularly ice nucleation active at the investigated temperatures. In case of ankerite the ice nucleation ability is unknown. Based on its similarity with dolomite, a carbonate known not to be ice nucleation active, it is assumed that ankerite is also not active. Thus, one of the suggested candidates with the strong Raman signal at 3180 cm−1 is likely responsible for the ice nucleation activity of the Etosha sample. Being part of proteins, amides are ubiquitous in nature. Similarly, cellulose is the most abundant organic compound on Earth (Kamide2005) amongst others as a structural component of algae. Both cellulose and some proteins have been identified to cause ice nucleation at the studied temperatures. Ammonium sulfate has been observed to correlate with higher INP concentration in Saharan dust and to increase the freezing onset temperature of microcline and various other minerals by up to 3 K. According to a study on the Ntwetwe Pan in Botswana by , the organic carbon concentration in a salt pan is about 1 wt % at the surface and consists of cyanobacteria and algae. We assume that similar values apply also for the Etosha pan. The Etosha sample was collected from the edge of the salt pan, a few hundred meters away from a fertile soil area containing the highest organic carbon content of the national park . As wind erosion was identified in these nearby fertile soils, aeolian transport potentially led to higher organic matter concentration at the edge of the pan compared to farther towards the center of the pan. Overall, this suggests that the Etosha sample's ice nucleation ability is almost entirely caused by organic matter, potentially cellulose or proteins which were mixed with or adsorbed onto the mineral dust on the ground, explaining the almost complete suppression of ice nucleation of the heated samples. In contrast to the Etosha sample, the Tenerife2014_1 sample consists of a number of minerals ice nucleation active at the studied temperatures, e.g., orthoclase, plagioclase, and quartz (Table 1). The sample shows the largest mass loss in the TGA analysis. The rather steep step in the TGA loss curve at about 120 C suggests a certain species to be released at this temperature, probably containing aliphatic compounds as suggested by the ATR-IR measurements. The complexity of the airborne Saharan samples is indicated by , who studied organic material in the Saharan Air Layer. They collected 42 PM2.5 and PM10 filters at the Izaña observatory in parallel to the Tenerife2013 sample collection and the CALIMA 2013 campaign in August 2013. Organic matter accounted for about 1.5 wt % of the aerosol composition in the Saharan Air Layer and was determined to mainly consist of saccharides, related to organic material in soils, biogenic secondary organic aerosol particles resulting from isoprene and α-pinene oxidation, and organic compounds from natural and anthropogenic sources such as vegetation and engine emissions. During daytime, the boundary layer reaches the altitude of the Izaña observatory and organic matter can originate from local sources. During nighttime the observatory is located in the free troposphere and aerosol sources are distant. Anthropogenic and natural emissions can originate from the North African coast or be advected from Europe . As the dust collection took place over several days and nights, an influence of organic matter from local sources cannot be excluded. Figure 7XRD diffractogram of unheated and heated Tenerife2014_1 sample. Vertical text indicates changes in peak height which were used to identify the decrease in gypsum and increase in anhydrite with heating. Horizontal text indicates peaks associated with other minerals in the sample. Another explanation for the reduction in mass at temperatures below 300 C is the release of free water molecules from the crystal lattice as indicated also in the ATR-IR spectra between 3600 and 3100 cm−1. In some cases, this affects the crystal lattice: Smectite, a swelling mineral, collapses under decreasing water vapor pressure as experienced during the heating. This decreases the interlayer spacing (for an overview of the effect of layer charge on smectite swelling see ). It is unknown if the change in crystal lattice has an effect on the ice nucleation ability of the otherwise only weakly ice nucleation active smectite . An effect cannot be excluded as the lattice match with ice is believed to be one of the factors promoting ice nucleation . In the studied samples, smectite was present in the Tenerife2014_1 sample (23 wt %), and traces were found in the Etosha sample (1 wt %). Thus, the collapse of the smectite lattice should only influence the Tenerife2014_1 sample. In case it has an influence, this would be related to an increase in ice nucleation ability. XRD analysis of the unheated and heated Tenerife2014_1 sample show the conversion of gypsum to anhydrite (Fig. 7). Gypsum has a low ice nucleation ability, similar to the clay minerals kaolinite and illite . found anhydrite to have a higher ice nucleation activity than quartz in the immersion mode at temperatures below 243 K when dry generated but a much lower ns when particles were generated from an aqueous solution. Anhydrite transforms back to gypsum when exposed to a relative humidity higher than 97 % at room temperature . However, this process occurs on the order of hours to days, in line with the observed differences in ns between wet and dry generated particles in . Potentially, the transformation to anhydrite during heating explains the higher ns of the heated Tenerife2014_1 sample compared to the unheated one at subsaturated conditions. In this case, a partial conversion of anhydrite back to gypsum during RH conditions above water saturation might explain the unchanged ns of the unheated and heated Tenerife2014_1 sample above water saturation. It should be kept in mind that the bulk mineralogy as determined by XRD is not necessarily representative of the particle surface where ice nucleation takes place. As needle formation has been observed in the transformation of gypsum to anhydrite , we use the occurrence of needles in our sample as an indication that the gypsum–anhydrite transformation took place on the surface of particles and thus might be responsible for the change in ice nucleation behavior of the sample. In SEM images of the unheated Tenerife2014_1 sample (Fig. 8a), hardly any needles are visible. A small number of needles is observed at the center of the image of the heated sample (Fig. 8b), while no needles are found in other SEM images of the heated sample (see the Supplement). The apparently limited needle formation and the fact that only about 1 wt % gypsum is contained in the sample suggests that gypsum transformation under heat treatment should only have a small effect on the ice nucleation behavior of the Tenerife2014_1 sample. However, given that, at maximum, only about 10 % of the particles act as INPs in case of the Tenerife2014_1 sample, the gypsum–anhydrite transformation might be non-negligible. Additionally, we suggest that the increase in the ns found under subsaturated RHw conditions for the Tenerife2014_1 sample is caused by the volatilization of aliphatic compounds containing matter, as indicated by the ATR-IR and TGA measurements, which inhibited the active sites of the mineral dust itself. Figure 8Scanning electron microscopy images of the (a) unheated and (b) heated Tenerife2014_1 sample. Note the different scales in the two images. 4 Conclusions In this study we showed that the fractions of quartz and the sum of quartz and feldspars in desert dust samples correlate better than all other mineral fractions with the ice nucleation active surface site density of the dust in deposition and the condensation mode at temperatures between 238 and 242 K. This is in line with the observations for the immersion mode presented in Part 1 of this study. The high abundance of quartz in soils worldwide, its resistance to chemical weathering processes, and its presence in particles of all sizes make it a potentially widely spread atmospheric INP type. According to a recent study by , the variation in quartz ice nucleation ability found in laboratory studies and the superior ice nucleation ability of the quartz-rich samples from Australia and Morocco in this study and its partner paper may be explained by the pre-processing of the samples. Milling of quartz samples, as done in our study, increases the ice nucleation ability of quartz by creating $\mathrm{Si}-\mathrm{O}\cdot$ and Si⋅ radical sites, which can then react with water vapor . However, milling may not be the only reason for formation of the silanol (Si−OH) groups on the surface of quartz, because exposure to water molecules in ambient humidity could also result in passively converting surface siloxane groups ($\mathrm{Si}-\mathrm{O}-\mathrm{Si}$) to silanol groups . As such quartz samples may still exhibit high ice nucleation activity in the absence of milling due to the chemical history of the particles. Thus, how much quartz contributes to the ice nucleation ability of (unmilled) atmospheric dust remains an open question. Apart from mineralogy, the ice nucleation activity of desert dust is found to be influenced by organic material mixed with the dust. In a carbonaceous sample from the Etosha salt pan, where less than 1 wt % quartz and no feldspar were present, the ice-active surface site density is found to be almost entirely due to organic matter, likely cellulose or proteins, which are mixed with the dust. In contrast, the deposition-mode ice nucleation activity of an airborne Saharan dust sample was found to increase after heating. Three potential explanations are found, two of them related to changes in the mineralogy; while it cannot be excluded that the increase in the ns was caused by a change in lattice spacing due to interlayer water release, it seems more likely that gypsum transforming into anhydrite made the sample more ice nucleation active. The Tenerife2014_1 sample is the only gypsum-containing sample that was investigated after heating, thus it remains an open question if and how much anhydrite contributed to the increase in ns. Another reason for the increase could be that the ice nucleation active sites of the unheated sample were blocked by volatile organic material. The volatilization of the aliphatic compounds during the heating recovered these active sites. This is further supported by the observation that no difference was found for the same sample in the condensation-freezing mode, indicating that the water condensing on the surface may also recover the active sites. As this change in ice-active surface site density was not observed for a second airborne Saharan dust sample, it suggests that different aging processes or the mixing of Saharan dust with organic material during atmospheric transport can influence the dust's ice nucleation ability in both directions. Data availability Data availability. Ice nucleation data from this study are available from . Additional SEM images can be found in the Supplement. Additional data are available upon request. Supplement Supplement. Author contributions Author contributions. YB collected the Tenerife and Israel samples, conceived and lead the measurement campaign, performed the ice nucleation measurements and analysis, performed and analyzed the XRD measurements, analyzed the TGA measurements, and wrote the paper. PB performed and analyzed the SEM, ATR-IR, and Raman measurements, and contributed to the paper. JO contributed to the Raman measurements. HG supervised the ATR-IR and Raman measurements and analysis and contributed to the paper. MP performed and analyzed the XRD measurements. ZAK performed the TGA measurements. BS, ZAK, and UL supervised the project and contributed to the paper. All authors contributed to the interpretation of data. Competing interests Competing interests. The authors declare no competing interests. Acknowledgements Acknowledgements. We thank the two anonymous reviewers for their helpful comments. The various dust samples in this paper have been collected by a number of people who the authors are very thankful to Maria Kanakidou and her team (Peloponnese, Crete); Felix Lüönd (Atacama); Paolo D'Odorico and Christopher Hoyle (Etosha); Lukas Kaufmann, Konrad Kandler, and Lother Schütz (Taklamakan); André Welti (Australia, Mojave); Monika Kohn (Dubai); Joel Corbin (Morocco); Sergio Rodríguez (Tenerife); and Hamza Mohamed Hamza (Egypt). The authors would like to thank Joanna Wong for her assistance with the TGA measurements and the Laboratory of Composite Materials and Adaptive Structures at ETH Zurich for the use of their thermal analysis equipment. We thank Hannes Wydler for his technical support with the PINC. Philipp Baloh would like to thank Karin Wieland and Rita Wiesinger for helpful discussions concerning the interpretation of the Raman spectra. Hinrich Grothe and Philipp Baloh would like to thank the Analytical Instrumentation Center and the X-Ray Center at TU Wien for the use of the Raman and XRD equipment and the University Service Centre for Transmission Electron Microscopy at TU Wien for recording the SEM images in this work. Yvonne Boose and Zamin A. Kanji gratefully acknowledge support by the Swiss National Science Foundation (grant 200020 150169/1). The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-797 2013) under grant agreement no. 603445 (BACCHUS). Hinrich Grothe and Philipp Baloh gratefully acknowledge support by the FFG (Austrian Research Promotion Agency) for funding under project no. 850689. Edited by: Eliza Harris Reviewed by: two anonymous referees References Alexander, J. 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https://codedocs.xyz/gammasoft71/xtd/group__xtd__drawing.html	xtd - Reference Guide 0.2.0 Modern c++17/20 framework to create console, GUI and unit test applications on Windows, macOS, Linux, iOS and android. xtd.drawing ## Classes class xtd::drawing::bitmap Encapsulates a GDI+ bitmap, which consists of the pixel data for a graphics image and its attributes. A bitmap is an object used to work with images defined by pixel data. More... class xtd::drawing::brush Defines objects used to fill the interiors of graphical shapes such as rectangles, ellipses, pies, polygons, and paths. More... class xtd::drawing::brushes brushes for all the standard colors. This class cannot be inherited. More... class xtd::drawing::color Represents an ARGB (alpha, red, green, blue) color. More... class xtd::drawing::colors colors for all the standard colors. This class cannot be inherited. More... Encapsulates a xtd::drawing::brush with a conical gradient. This class cannot be inherited. More... class xtd::drawing::drawing2d::graphics_path Defines an object used to draw lines and curves. This class cannot be inherited. More... class xtd::drawing::drawing2d::graphics_state Represents the state of a xtd::drawing::graphics object. This object is returned by a call to the xtd::drawing::graphics::save() methods. This class cannot be inherited. More... class xtd::drawing::drawing2d::hatch_brush Defines a rectangular xtd::drawing::brush with a hatch style, a foreground color, and a background color. This class cannot be inherited. More... Encapsulates a xtd::drawing::brush with a linear gradient. This class cannot be inherited. More... class xtd::drawing::drawing2d::matrix Encapsulates a 3-by-3 affine matrix that represents a geometric transform. This class cannot be inherited. More... Encapsulates a xtd::drawing::brush with a radial gradient. This class cannot be inherited. More... class xtd::drawing::font Defines a particular format for text, including font face, size, and style attributes. This class cannot be inherited. More... class xtd::drawing::font_family Defines a group of type faces having a similar basic design and certain variations in styles. This class cannot be inherited. More... class xtd::drawing::graphics Defines an object used to draw lines and curves. This class cannot be inherited. More... class xtd::drawing::icon Represents a Windows icon, which is a small bitmap image that is used to represent an object. Icons can be thought of as transparent bitmaps, although their size is determined by the system. More... class xtd::drawing::image An abstract base class that provides functionality for the bitmap and metafile descended classes. More... class xtd::drawing::imaging::color_palette Defines an array of colors that make up a color palette. The colors are 32-bit ARGB colors. Not inheritable. More... class xtd::drawing::imaging::encoder An Encoder object encapsulates a globally unique identifier (GUID) that identifies the category of an image encoder parameter. More... class xtd::drawing::imaging::encoder_parameter Used to pass a value, or an array of values, to an image encoder. More... class xtd::drawing::imaging::encoder_parameters Encapsulates an array of EncoderParameter objects. More... class xtd::drawing::imaging::frame_dimension Provides properties that get the frame dimensions of an image. Not inheritable. More... class xtd::drawing::imaging::image_format Specifies the file format of the image. Not inheritable. More... class xtd::drawing::imaging::property_item Encapsulates a metadata property to be included in an image file. Not inheritable. More... class xtd::drawing::pen Defines an object used to draw lines and curves. This class cannot be inherited. More... class xtd::drawing::pens pens for all the standard colors. This class cannot be inherited. More... class xtd::drawing::point Represents an ordered pair of integer x- and y-coordinates that defines a point in a two-dimensional plane. More... class xtd::drawing::point_f Represents an ordered pair of floating-point x- and y-coordinates that defines a point in a two-dimensional plane. More... class xtd::drawing::rectangle Stores a set of four integers that represent the location and size of a rectangle. More... class xtd::drawing::rectangle_f Stores a set of four floating-point numbers that represent the location and size of a rectangle. For more advanced region functions, use a xtd::drawing::region object. More... class xtd::drawing::region Describes the interior of a graphics shape composed of rectangles and paths. This class cannot be inherited. More... class xtd::drawing::size Stores an ordered pair of integers, which specify a height and width. More... class xtd::drawing::size_f Stores an ordered pair of floating-point, which specify a height and width. More... class xtd::drawing::solid_brush Defines a xtd::drawing::brush of a single color. Brushes are used to fill graphics shapes, such as rectangles, ellipses, pies, polygons, and paths. This class cannot be inherited. More... class xtd::drawing::string_format Encapsulates text layout information (such as alignment, orientation and tab stops) display manipulations (such as ellipsis insertion and national digit substitution) and OpenType features. This class cannot be inherited. More... class xtd::drawing::system_brushes Each property of the xtd::drawing::system_brushes class is a xtd::drawing::solid_brush that is the color of a Windows display element. More... class xtd::drawing::system_colors Each property of the xtd::drawing::system_colors class is a xtd::drawing::color structure that is the color of a Windows display element. More... class xtd::drawing::system_fonts Specifies the fonts used to display text in Windows display elements. More... class xtd::drawing::system_icons Each property of the xtd::drawing::system_icons class is an xtd::drawing::icon object for Windows system-wide icons. This class cannot be inherited. More... class xtd::drawing::system_images Each property of the xtd::drawing::system_images class is an xtd::drawing::image object for Windows system-wide images. This class cannot be inherited. More... class xtd::drawing::system_pens Each property of the xtd::drawing::system_pens class is a xtd::drawing::xtd::drawing::pen that is the color of a Windows display element and that has a width of 1 pixel. More... class xtd::drawing::text::font_collection Provides a base class for installed and private font collections. More... class xtd::drawing::text::installed_font_collection Represents the fonts installed on the system. This class cannot be inherited. More... class xtd::drawing::text::private_font_collection Provides a collection of font families built from font files that are provided by the client application. More... class xtd::drawing::texture_brush Each property of the xtd::drawing::texture_brush class is a xtd::drawing::brush object that uses an image to fill the interior of a shape. This class cannot be inherited. More... ## Enumerations enum xtd::drawing::drawing2d::compositing_mode { xtd::drawing::drawing2d::compositing_mode::source_over = 0, xtd::drawing::drawing2d::compositing_mode::source_copy = 1 } Specifies how the source colors are combined with the background colors. More... enum xtd::drawing::drawing2d::compositing_quality { xtd::drawing::drawing2d::compositing_quality::invalid = -1, xtd::drawing::drawing2d::compositing_quality::default_value = 0, xtd::drawing::drawing2d::compositing_quality::high_speed = 1, xtd::drawing::drawing2d::compositing_quality::high_quality = 2, xtd::drawing::drawing2d::compositing_quality::gamma_corrected = 3, xtd::drawing::drawing2d::compositing_quality::assume_linear = 4 } Specifies the quality level to use during compositing. More... enum xtd::drawing::copy_pixel_operation { xtd::drawing::copy_pixel_operation::blackness = 66, xtd::drawing::copy_pixel_operation::capture_blt = 1073741824, xtd::drawing::copy_pixel_operation::destination_invert = 5570569, xtd::drawing::copy_pixel_operation::merge_copy = 12583114, xtd::drawing::copy_pixel_operation::merge_paint = 12255782, xtd::drawing::copy_pixel_operation::no_mirror_bitmap = -2147483648, xtd::drawing::copy_pixel_operation::not_source_copy = 3342344, xtd::drawing::copy_pixel_operation::not_source_erase = 1114278, xtd::drawing::copy_pixel_operation::pat_copy = 15728673, xtd::drawing::copy_pixel_operation::pat_invert = 5898313, xtd::drawing::copy_pixel_operation::pat_paint = 16452105, xtd::drawing::copy_pixel_operation::source_and = 8913094, xtd::drawing::copy_pixel_operation::source_copy = 13369376, xtd::drawing::copy_pixel_operation::source_erase = 4457256, xtd::drawing::copy_pixel_operation::source_invert = 6684742, xtd::drawing::copy_pixel_operation::source_paint = 15597702, xtd::drawing::copy_pixel_operation::whiteness = 16711778 } Determines how the source color in a copy pixel operation is combined with the destination color to result in a final color. More... enum xtd::drawing::dash_style { xtd::drawing::dash_style::solid = 0, xtd::drawing::dash_style::dash, xtd::drawing::dash_style::dot, xtd::drawing::dash_style::dash_dot, xtd::drawing::dash_style::dash_dot_dot, xtd::drawing::dash_style::custom } Specifies the style of dashed lines drawn with a xtd::drawing::pen object. More... enum xtd::drawing::imaging::encoder_parameter_value_type { xtd::drawing::imaging::encoder_parameter_value_type::value_type_byte = 1, xtd::drawing::imaging::encoder_parameter_value_type::value_type_ascii = 2, xtd::drawing::imaging::encoder_parameter_value_type::value_type_short = 3, xtd::drawing::imaging::encoder_parameter_value_type::value_type_long = 4, xtd::drawing::imaging::encoder_parameter_value_type::value_type_rational = 5, xtd::drawing::imaging::encoder_parameter_value_type::value_type_long_range = 6, xtd::drawing::imaging::encoder_parameter_value_type::value_type_undefined = 7, xtd::drawing::imaging::encoder_parameter_value_type::value_type_rational_range = 8, xtd::drawing::imaging::encoder_parameter_value_type::value_type_rational_pointer = 9 } Specifies the data type of the xtd::drawing::imaging::encoder_parameter used with the xtd::drawing::image::save or xtd::drawing::image::save_add method of an image. More... enum xtd::drawing::drawing2d::fill_mode { xtd::drawing::drawing2d::fill_mode::alternate, xtd::drawing::drawing2d::fill_mode::winding } Specifies how the interior of a closed path is filled. More... enum xtd::drawing::drawing2d::flush_intention { xtd::drawing::drawing2d::flush_intention::flush = 0, xtd::drawing::drawing2d::flush_intention::sync = 1 } Specifies whether commands in the graphics stack are terminated (flushed) immediately or executed as soon as possible. More... enum xtd::drawing::font_style { xtd::drawing::font_style::regular = 0, xtd::drawing::font_style::bold = 0b1, xtd::drawing::font_style::italic = 0b10, xtd::drawing::font_style::underline = 0b100, xtd::drawing::font_style::strikeout = 0b1000 } Specifies style information applied to text. This enumeration has a flags attribute that allows a bitwise combination of its member values. More... enum xtd::drawing::text::generic_font_families { xtd::drawing::text::generic_font_families::serif = 0, xtd::drawing::text::generic_font_families::sans_serif = 1, xtd::drawing::text::generic_font_families::monospace = 2 } Specifies a generic font_family object. More... enum xtd::drawing::graphics_unit { xtd::drawing::graphics_unit::world = 0, xtd::drawing::graphics_unit::display = 1, xtd::drawing::graphics_unit::pixel = 2, xtd::drawing::graphics_unit::point = 3, xtd::drawing::graphics_unit::inch = 4, xtd::drawing::graphics_unit::document = 5, xtd::drawing::graphics_unit::millimeter = 6 } Specifies the unit of measure for the given data. This enumeration has a flags attribute that allows a bitwise combination of its member values. More... enum xtd::drawing::drawing2d::hatch_style { xtd::drawing::drawing2d::hatch_style::horizontal = 0, xtd::drawing::drawing2d::hatch_style::vertical = 1, xtd::drawing::drawing2d::hatch_style::forward_diagonal = 2, xtd::drawing::drawing2d::hatch_style::backward_diagonal = 3, xtd::drawing::drawing2d::hatch_style::cross = 4, xtd::drawing::drawing2d::hatch_style::diagonal_cross = 5, xtd::drawing::drawing2d::hatch_style::percent_05 = 6, xtd::drawing::drawing2d::hatch_style::percent_10 = 7, xtd::drawing::drawing2d::hatch_style::percent_20 = 8, xtd::drawing::drawing2d::hatch_style::percent_25 = 9, xtd::drawing::drawing2d::hatch_style::percent_30 = 10, xtd::drawing::drawing2d::hatch_style::percent_40 = 11, xtd::drawing::drawing2d::hatch_style::percent_50 = 12, xtd::drawing::drawing2d::hatch_style::percent_60 = 13, xtd::drawing::drawing2d::hatch_style::percent_70 = 14, xtd::drawing::drawing2d::hatch_style::percent_75 = 15, xtd::drawing::drawing2d::hatch_style::percent_80 = 16, xtd::drawing::drawing2d::hatch_style::percent_90 = 17, xtd::drawing::drawing2d::hatch_style::light_downward_diagonal = 18, xtd::drawing::drawing2d::hatch_style::light_upward_diagonal = 19, xtd::drawing::drawing2d::hatch_style::dark_downward_diagonal = 20, xtd::drawing::drawing2d::hatch_style::dark_upward_diagonal = 21, xtd::drawing::drawing2d::hatch_style::wide_downward_diagonal = 22, xtd::drawing::drawing2d::hatch_style::wide_upward_diagonal = 23, xtd::drawing::drawing2d::hatch_style::light_vertical = 24, xtd::drawing::drawing2d::hatch_style::light_horizontal = 25, xtd::drawing::drawing2d::hatch_style::narrow_vertical = 26, xtd::drawing::drawing2d::hatch_style::narrow_horizontal = 27, xtd::drawing::drawing2d::hatch_style::dark_vertical = 28, xtd::drawing::drawing2d::hatch_style::dark_horizontal = 29, xtd::drawing::drawing2d::hatch_style::dashed_downward_diagonal = 30, xtd::drawing::drawing2d::hatch_style::dashed_upward_diagonal = 31, xtd::drawing::drawing2d::hatch_style::dashed_horizontal = 32, xtd::drawing::drawing2d::hatch_style::dashed_vertical = 33, xtd::drawing::drawing2d::hatch_style::small_confetti = 34, xtd::drawing::drawing2d::hatch_style::large_confetti = 35, xtd::drawing::drawing2d::hatch_style::zig_zag = 36, xtd::drawing::drawing2d::hatch_style::wave = 37, xtd::drawing::drawing2d::hatch_style::diagonal_brick = 38, xtd::drawing::drawing2d::hatch_style::horizontal_brick = 39, xtd::drawing::drawing2d::hatch_style::weave = 40, xtd::drawing::drawing2d::hatch_style::plaid = 41, xtd::drawing::drawing2d::hatch_style::divot = 42, xtd::drawing::drawing2d::hatch_style::dotted_grid = 43, xtd::drawing::drawing2d::hatch_style::dotted_diamond = 44, xtd::drawing::drawing2d::hatch_style::shingle = 45, xtd::drawing::drawing2d::hatch_style::trellis = 46, xtd::drawing::drawing2d::hatch_style::sphere = 47, xtd::drawing::drawing2d::hatch_style::small_grid = 48, xtd::drawing::drawing2d::hatch_style::small_checker_board = 49, xtd::drawing::drawing2d::hatch_style::large_checker_board = 50, xtd::drawing::drawing2d::hatch_style::outlined_diamond = 51, xtd::drawing::drawing2d::hatch_style::solid_diamond = 52, xtd::drawing::drawing2d::hatch_style::wide_checker_board = 53 } Specifies the different patterns available for xtd::drawing::drawing2d::hatch_brush objects. More... enum xtd::drawing::text::hotkey_prefix { xtd::drawing::text::hotkey_prefix::none = 0, xtd::drawing::text::hotkey_prefix::show = 1, xtd::drawing::text::hotkey_prefix::hide = 2 } Specifies the type of display for hot-key prefixes that relate to text. More... enum xtd::drawing::imaging::image_flags { xtd::drawing::imaging::image_flags::none = 0, xtd::drawing::imaging::image_flags::scalable = 0b1, xtd::drawing::imaging::image_flags::has_alpha = 0b10, xtd::drawing::imaging::image_flags::has_translucent = 0b100, xtd::drawing::imaging::image_flags::partially_scalable = 0b1000, xtd::drawing::imaging::image_flags::color_space_rgb = 0b10000, xtd::drawing::imaging::image_flags::color_space_cmyk = 0b100000, xtd::drawing::imaging::image_flags::color_space_gray = 0b1000000, xtd::drawing::imaging::image_flags::color_space_ycbcr = 0b10000000, xtd::drawing::imaging::image_flags::color_space_ycck = 0b100000000, xtd::drawing::imaging::image_flags::has_real_dpi = 0b1000000000000, xtd::drawing::imaging::image_flags::has_real_pixel_size = 0b10000000000000, xtd::drawing::imaging::image_flags::caching = 0b100000000000000000 } Specifies the attributes of the pixel data contained in an xtd::drawing::image object. The xtd::drawing:iImage::flags property returns a member of this enumeration. More... enum xtd::drawing::drawing2d::interpolation_mode { xtd::drawing::drawing2d::interpolation_mode::invalid = -1, xtd::drawing::drawing2d::interpolation_mode::default_value = 0, xtd::drawing::drawing2d::interpolation_mode::low = 1, xtd::drawing::drawing2d::interpolation_mode::hight = 2, xtd::drawing::drawing2d::interpolation_mode::bilinear = 3, xtd::drawing::drawing2d::interpolation_mode::bicubic = 4, xtd::drawing::drawing2d::interpolation_mode::nearest_neighbor = 5, xtd::drawing::drawing2d::interpolation_mode::high_quality_bilinear = 6, xtd::drawing::drawing2d::interpolation_mode::high_quality_bicubic = 7 } The xtd::drawing::drawing2d::interpolation_mode enumeration specifies the algorithm that is used when images are scaled or rotated. More... enum xtd::drawing::known_color { xtd::drawing::known_color::active_border = 1, xtd::drawing::known_color::active_caption, xtd::drawing::known_color::active_caption_text, xtd::drawing::known_color::app_workspace, xtd::drawing::known_color::control, xtd::drawing::known_color::control_dark, xtd::drawing::known_color::control_dark_dark, xtd::drawing::known_color::control_light, xtd::drawing::known_color::control_light_light, xtd::drawing::known_color::control_text, xtd::drawing::known_color::desktop, xtd::drawing::known_color::gray_text, xtd::drawing::known_color::highlight, xtd::drawing::known_color::highlight_text, xtd::drawing::known_color::hot_track, xtd::drawing::known_color::inactive_border, xtd::drawing::known_color::inactive_caption, xtd::drawing::known_color::inactive_caption_text, xtd::drawing::known_color::info, xtd::drawing::known_color::info_text, xtd::drawing::known_color::scroll_bar, xtd::drawing::known_color::window, xtd::drawing::known_color::window_frame, xtd::drawing::known_color::window_text, xtd::drawing::known_color::transparent, xtd::drawing::known_color::alice_blue, xtd::drawing::known_color::antique_white, xtd::drawing::known_color::aqua, xtd::drawing::known_color::aquamarine, xtd::drawing::known_color::azure, xtd::drawing::known_color::beige, xtd::drawing::known_color::bisque, xtd::drawing::known_color::black, xtd::drawing::known_color::blanched_almond, xtd::drawing::known_color::blue, xtd::drawing::known_color::blue_violet, xtd::drawing::known_color::brown, xtd::drawing::known_color::burly_wood, xtd::drawing::known_color::chartreuse, xtd::drawing::known_color::chocolate, xtd::drawing::known_color::coral, xtd::drawing::known_color::cornflower_blue, xtd::drawing::known_color::cornsilk, xtd::drawing::known_color::crimson, xtd::drawing::known_color::cyan, xtd::drawing::known_color::dark_blue, xtd::drawing::known_color::dark_cyan, xtd::drawing::known_color::dark_goldenrod, xtd::drawing::known_color::dark_gray, xtd::drawing::known_color::dark_green, xtd::drawing::known_color::dark_khaki, xtd::drawing::known_color::dark_magenta, xtd::drawing::known_color::dark_olive_green, xtd::drawing::known_color::dark_orange, xtd::drawing::known_color::dark_orchid, xtd::drawing::known_color::dark_red, xtd::drawing::known_color::dark_salmon, xtd::drawing::known_color::dark_sea_green, xtd::drawing::known_color::dark_slate_blue, xtd::drawing::known_color::dark_slate_gray, xtd::drawing::known_color::dark_turquoise, xtd::drawing::known_color::dark_violet, xtd::drawing::known_color::deep_pink, xtd::drawing::known_color::deep_sky_blue, xtd::drawing::known_color::dim_gray, xtd::drawing::known_color::dodger_blue, xtd::drawing::known_color::firebrick, xtd::drawing::known_color::floral_white, xtd::drawing::known_color::forest_green, xtd::drawing::known_color::fuchsia, xtd::drawing::known_color::gainsboro, xtd::drawing::known_color::ghost_white, xtd::drawing::known_color::gold, xtd::drawing::known_color::goldenrod, xtd::drawing::known_color::gray, xtd::drawing::known_color::green, xtd::drawing::known_color::green_yellow, xtd::drawing::known_color::honeydew, xtd::drawing::known_color::hot_pink, xtd::drawing::known_color::indian_red, xtd::drawing::known_color::indigo, xtd::drawing::known_color::ivory, xtd::drawing::known_color::khaki, xtd::drawing::known_color::lavender, xtd::drawing::known_color::lavender_blush, xtd::drawing::known_color::lawn_green, xtd::drawing::known_color::lemon_chiffon, xtd::drawing::known_color::light_blue, xtd::drawing::known_color::light_coral, xtd::drawing::known_color::light_cyan, xtd::drawing::known_color::light_goldenrod_yellow, xtd::drawing::known_color::light_gray, xtd::drawing::known_color::light_green, xtd::drawing::known_color::light_pink, xtd::drawing::known_color::light_salmon, xtd::drawing::known_color::light_sea_green, xtd::drawing::known_color::light_sky_blue, xtd::drawing::known_color::light_slate_gray, xtd::drawing::known_color::light_steel_blue, xtd::drawing::known_color::light_yellow, xtd::drawing::known_color::lime, xtd::drawing::known_color::lime_green, xtd::drawing::known_color::linen, xtd::drawing::known_color::magenta, xtd::drawing::known_color::maroon, xtd::drawing::known_color::medium_aquamarine, xtd::drawing::known_color::medium_blue, xtd::drawing::known_color::medium_orchid, xtd::drawing::known_color::medium_purple, xtd::drawing::known_color::medium_sea_green, xtd::drawing::known_color::medium_slate_blue, xtd::drawing::known_color::medium_spring_green, xtd::drawing::known_color::medium_turquoise, xtd::drawing::known_color::medium_violet_red, xtd::drawing::known_color::midnight_blue, xtd::drawing::known_color::mint_cream, xtd::drawing::known_color::misty_rose, xtd::drawing::known_color::moccasin, xtd::drawing::known_color::navajo_white, xtd::drawing::known_color::navy, xtd::drawing::known_color::old_lace, xtd::drawing::known_color::olive, xtd::drawing::known_color::olive_drab, xtd::drawing::known_color::orange, xtd::drawing::known_color::orange_red, xtd::drawing::known_color::orchid, xtd::drawing::known_color::pale_goldenrod, xtd::drawing::known_color::pale_green, xtd::drawing::known_color::pale_turquoise, xtd::drawing::known_color::pale_violet_red, xtd::drawing::known_color::papaya_whip, xtd::drawing::known_color::peach_puff, xtd::drawing::known_color::peru, xtd::drawing::known_color::pink, xtd::drawing::known_color::plum, xtd::drawing::known_color::powder_blue, xtd::drawing::known_color::purple, xtd::drawing::known_color::rebecca_purple, xtd::drawing::known_color::red, xtd::drawing::known_color::rosy_brown, xtd::drawing::known_color::royal_blue, xtd::drawing::known_color::salmon, xtd::drawing::known_color::sandy_brown, xtd::drawing::known_color::sea_green, xtd::drawing::known_color::sea_shell, xtd::drawing::known_color::sienna, xtd::drawing::known_color::silver, xtd::drawing::known_color::sky_blue, xtd::drawing::known_color::slate_blue, xtd::drawing::known_color::slate_gray, xtd::drawing::known_color::snow, xtd::drawing::known_color::spring_green, xtd::drawing::known_color::steel_blue, xtd::drawing::known_color::tan, xtd::drawing::known_color::teal, xtd::drawing::known_color::thistle, xtd::drawing::known_color::tomato, xtd::drawing::known_color::turquoise, xtd::drawing::known_color::violet, xtd::drawing::known_color::wheat, xtd::drawing::known_color::white, xtd::drawing::known_color::white_smoke, xtd::drawing::known_color::yellow, xtd::drawing::known_color::yellow_green, xtd::drawing::known_color::button_face, xtd::drawing::known_color::button_highlight, xtd::drawing::known_color::accent, xtd::drawing::known_color::accent_text, xtd::drawing::known_color::text_box, xtd::drawing::known_color::text_box_text } Specifies the known system colors. More... enum xtd::drawing::drawing2d::line_cap { xtd::drawing::drawing2d::line_cap::flat = 0, xtd::drawing::drawing2d::line_cap::square = 1, xtd::drawing::drawing2d::line_cap::round = 2 } Specifies the available cap styles with which a xtd::drawing::pen object can end a line. More... enum xtd::drawing::drawing2d::line_join { xtd::drawing::drawing2d::line_join::miter = 0, xtd::drawing::drawing2d::line_join::bevel = 1, xtd::drawing::drawing2d::line_join::round = 2, xtd::drawing::drawing2d::line_join::miter_clipped = 3 } Specifies how to join consecutive line or curve segments in a figure (subpath) contained in a xtd::drawing::drawing2d::graphics_path object. More... } Specifies the direction of a linear gradient. More... enum xtd::drawing::drawing2d::matrix_order { xtd::drawing::drawing2d::matrix_order::prepend = 0, xtd::drawing::drawing2d::matrix_order::append = 1 } Specifies the order for matrix transform operations. More... enum xtd::drawing::drawing2d::pen_alignment { xtd::drawing::drawing2d::pen_alignment::center = 0, xtd::drawing::drawing2d::pen_alignment::inset = 1, xtd::drawing::drawing2d::pen_alignment::outset = 2, xtd::drawing::drawing2d::pen_alignment::left = 3, xtd::drawing::drawing2d::pen_alignment::right = 4 } SSpecifies the alignment of a xtd::drawing::pen object in relation to the theoretical, zero-width line. More... enum xtd::drawing::drawing2d::pen_type { xtd::drawing::drawing2d::pen_type::solid_color = 0, xtd::drawing::drawing2d::pen_type::hatch_fill = 1, xtd::drawing::drawing2d::pen_type::texture_fill = 2, } Specifies the type of fill a xtd::drawing::pen object uses to fill lines. More... enum xtd::drawing::imaging::pixel_format { xtd::drawing::imaging::pixel_format::undefined = 0, xtd::drawing::imaging::pixel_format::dont_care = 0, xtd::drawing::imaging::pixel_format::max = 0x0000000F, xtd::drawing::imaging::pixel_format::indexed = 0x00010000, xtd::drawing::imaging::pixel_format::gdi = 0x00020000, xtd::drawing::imaging::pixel_format::format16bpp_rgb555 = 0x00021005, xtd::drawing::imaging::pixel_format::format16bpp_rgb565 = 0x00021006, xtd::drawing::imaging::pixel_format::format24bpp_rgb = 0x00021808, xtd::drawing::imaging::pixel_format::format32bpp_rgb = 0x00022009, xtd::drawing::imaging::pixel_format::format1bpp_indexed = 0x00030101, xtd::drawing::imaging::pixel_format::format4bpp_indexed = 0x00030402, xtd::drawing::imaging::pixel_format::format8bpp_indexed = 0x00030803, xtd::drawing::imaging::pixel_format::alpha = 0x00040000, xtd::drawing::imaging::pixel_format::format16bpp_argb1555 = 0x00061007, xtd::drawing::imaging::pixel_format::palpha = 0x00080000, xtd::drawing::imaging::pixel_format::format32bpp_pargb = 0x000E200B, xtd::drawing::imaging::pixel_format::extended = 0x00100000, xtd::drawing::imaging::pixel_format::format16bpp_gray_scale = 0x00101004, xtd::drawing::imaging::pixel_format::format48bpp_rgb = 0x0010300C, xtd::drawing::imaging::pixel_format::format64bpp_pargb = 0x001C400E, xtd::drawing::imaging::pixel_format::canonical = 0x00200000, xtd::drawing::imaging::pixel_format::format32bpp_argb = 0x0026200A, xtd::drawing::imaging::pixel_format::format64bpp_argb = 0x0034400D } Specifies the format of the color data for each pixel in the image. More... enum xtd::drawing::drawing2d::pixel_offset_mode { xtd::drawing::drawing2d::pixel_offset_mode::invalid = -1, xtd::drawing::drawing2d::pixel_offset_mode::default_value = 0, xtd::drawing::drawing2d::pixel_offset_mode::high_speed = 1, xtd::drawing::drawing2d::pixel_offset_mode::high_quality = 2, xtd::drawing::drawing2d::pixel_offset_mode::none = 3, xtd::drawing::drawing2d::pixel_offset_mode::half = 4 } Specifies how pixels are offset during rendering. More... enum xtd::drawing::rotate_flip_type { xtd::drawing::rotate_flip_type::rotate_none_flip_none = 0, xtd::drawing::rotate_flip_type::rotate_90_flip_none = 1, xtd::drawing::rotate_flip_type::rotate_180_flip_none = 2, xtd::drawing::rotate_flip_type::rotate_270_flip_none = 3, xtd::drawing::rotate_flip_type::rotate_none_flip_x = 4, xtd::drawing::rotate_flip_type::rotate_90_flip_x = 5, xtd::drawing::rotate_flip_type::rotate_180_flip_x = 6, xtd::drawing::rotate_flip_type::rotate_270_flip_x = 7, xtd::drawing::rotate_flip_type::rotate_none_flip_y = rotate_180_flip_x, xtd::drawing::rotate_flip_type::rotate_90_flip_y = rotate_270_flip_x, xtd::drawing::rotate_flip_type::rotate_180_flip_y = rotate_none_flip_x, xtd::drawing::rotate_flip_type::rotate_270_flip_y = rotate_90_flip_x, xtd::drawing::rotate_flip_type::rotate_none_flip_xy = rotate_180_flip_none, xtd::drawing::rotate_flip_type::rotate_90_flip_xy = rotate_270_flip_none, xtd::drawing::rotate_flip_type::rotate_180_flip_xy = rotate_none_flip_none, xtd::drawing::rotate_flip_type::rotate_270_flip_xy = rotate_90_flip_none } Specifies how much an image is rotated and the axis used to flip the image. More... enum xtd::drawing::drawing2d::smoothing_mode { xtd::drawing::drawing2d::smoothing_mode::invalid = -1, xtd::drawing::drawing2d::smoothing_mode::default_value = 0, xtd::drawing::drawing2d::smoothing_mode::high_speed = 1, xtd::drawing::drawing2d::smoothing_mode::high_quality = 2, xtd::drawing::drawing2d::smoothing_mode::none = 3, xtd::drawing::drawing2d::smoothing_mode::anti_alias = 4 } Specifies whether smoothing (antialiasing) is applied to lines and curves and the edges of filled areas. More... enum xtd::drawing::string_alignment { xtd::drawing::string_alignment::near = 0, xtd::drawing::string_alignment::center = 1, xtd::drawing::string_alignment::far = 2 } Specifies the alignment of a text string relative to its layout rectangle. More... enum xtd::drawing::string_format_flags { xtd::drawing::string_format_flags::direction_right_to_left = 0b1, xtd::drawing::string_format_flags::direction_vertical = 0b10, xtd::drawing::string_format_flags::fit_black_box = 0b100, xtd::drawing::string_format_flags::display_format_control = 0b100000, xtd::drawing::string_format_flags::no_font_fallback = 0b10000000000, xtd::drawing::string_format_flags::measure_trailing_spaces = 0b100000000000, xtd::drawing::string_format_flags::no_wrap = 0b1000000000000, xtd::drawing::string_format_flags::line_limit = 0b10000000000000, xtd::drawing::string_format_flags::no_clip = 0b100000000000000 } Specifies the display and layout information for text strings. This enumeration allows a bitwise combination of its member values. More... enum xtd::drawing::string_trimming { xtd::drawing::string_trimming::none = 0, xtd::drawing::string_trimming::character = 1, xtd::drawing::string_trimming::word = 2, xtd::drawing::string_trimming::ellipsis_character = 3, xtd::drawing::string_trimming::ellipsis_word = 4, xtd::drawing::string_trimming::ellipsis_path = 5 } Specifies how to trim characters from a string that does not completely fit into a layout shape. More... enum xtd::drawing::text::text_rendering_hint { xtd::drawing::text::text_rendering_hint::system_default = 0, xtd::drawing::text::text_rendering_hint::single_bit_per_pixel_grid_fit = 1, xtd::drawing::text::text_rendering_hint::single_bit_per_pixel = 2, xtd::drawing::text::text_rendering_hint::anti_alias_grid_fit = 3, xtd::drawing::text::text_rendering_hint::anti_alias = 4, xtd::drawing::text::text_rendering_hint::clear_type_grid_fit = 5 } Specifies the quality of text rendering. More... ## ◆ compositing_mode strong #include <xtd.drawing/include/xtd/drawing/drawing2d/compositing_mode.h> Specifies how the source colors are combined with the background colors. Namespace xtd::drawing::drawing2d Library xtd.drawing Enumerator source_over Specifies that when a color is rendered, it is blended with the background color. The blend is determined by the alpha component of the color being rendered. source_copy Specifies that when a color is rendered, it overwrites the background color. ## ◆ compositing_quality strong #include <xtd.drawing/include/xtd/drawing/drawing2d/compositing_quality.h> Specifies the quality level to use during compositing. Namespace xtd::drawing::drawing2d Library xtd.drawing Remarks Compositing is done during rendering when the source pixels are combined with the destination pixels to produce the resultant pixels. The quality of compositing directly relates to the visual quality of the output and is inversely proportional to the render time. The higher the quality, the slower the render time. This is because the higher the quality level, the more surrounding pixels need to be taken into account during the composite. The linear quality setting (AssumeLinear) compromises by providing better quality than the default quality at a slightly lower speed. Enumerator invalid Invalid quality. default_value Default quality. high_speed High speed, low quality. high_quality High quality, low speed compositing. gamma_corrected Gamma correction is used. assume_linear Assume linear values. ## ◆ copy_pixel_operation strong #include <xtd.drawing/include/xtd/drawing/copy_pixel_operation.h> Determines how the source color in a copy pixel operation is combined with the destination color to result in a final color. Namespace xtd::drawing Library xtd.drawing Remarks The xtd::drawing::copy_pixel_operation enumeration is used by the xtd::drawing::graphics::copy_from_screen method of the xtd::drawing::graphics class. Enumerator blackness The destination area is filled by using the color associated with index 0 in the physical palette. (This color is black for the default physical palette.) capture_blt Windows that are layered on top of your window are included in the resulting image. By default, the image contains only your window. Note that this generally cannot be used for printing device contexts. destination_invert The destination area is inverted. merge_copy The colors of the source area are merged with the colors of the selected brush of the destination device context using the Boolean AND operator. merge_paint The colors of the inverted source area are merged with the colors of the destination area by using the Boolean OR operator. no_mirror_bitmap The bitmap is not mirrored. not_source_copy The inverted source area is copied to the destination. not_source_erase The source and destination colors are combined using the Boolean OR operator, and then resultant color is then inverted. pat_copy The brush currently selected in the destination device context is copied to the destination bitmap. pat_invert The colors of the brush currently selected in the destination device context are combined with the colors of the destination are using the Boolean XOR operator. pat_paint The colors of the brush currently selected in the destination device context are combined with the colors of the inverted source area using the Boolean OR operator. The result of this operation is combined with the colors of the destination area using the Boolean OR operator. source_and The colors of the source and destination areas are combined using the Boolean AND operator. source_copy The source area is copied directly to the destination area. source_erase The inverted colors of the destination area are combined with the colors of the source area using the Boolean AND operator. source_invert The colors of the source and destination areas are combined using the Boolean XOR operator. source_paint The colors of the source and destination areas are combined using the Boolean OR operator. whiteness The destination area is filled by using the color associated with index 1 in the physical palette. (This color is white for the default physical palette.) ## ◆ dash_style strong #include <xtd.drawing/include/xtd/drawing/dash_style.h> Specifies the style of dashed lines drawn with a xtd::drawing::pen object. Namespace xtd::drawing Library xtd.drawing Remarks To define a custom dash_style, set the dash_pattern property of the xtd::drawing::pen. Enumerator solid Specifies a solid line. dash Specifies a line consisting of dashes. dot Specifies a line consisting of dots. dash_dot Specifies a line consisting of a repeating pattern of dash-dot. dash_dot_dot Specifies a line consisting of a repeating pattern of dash-dot-dot. custom Specifies a user-defined custom dash style. ## ◆ encoder_parameter_value_type strong #include <xtd.drawing/include/xtd/drawing/imaging/encoder_parameter_value_type.h> Specifies the data type of the xtd::drawing::imaging::encoder_parameter used with the xtd::drawing::image::save or xtd::drawing::image::save_add method of an image. Namespace xtd::drawing::imaging Library xtd.drawing Enumerator value_type_byte An 8-bit unsigned integer. value_type_ascii An 8-bit ASCII value. This field specifies that the array of values is a null-terminated ASCII character string. value_type_short A 16-bit, unsigned integer. value_type_long A 32-bit unsigned integer. value_type_rational A pair of 32-bit unsigned integers. Each pair represents a fraction, the first integer being the numerator and the second integer being the denominator. value_type_long_range Two long values that specify a range of integer values. The first value specifies the lower end, and the second value specifies the higher end. All values are inclusive at both ends. value_type_undefined A byte that has no data type defined. The variable can take any value depending on field definition. value_type_rational_range A set of four 32-bit unsigned integers. The first two integers represent one fraction, and the second two integers represent a second fraction. The two fractions represent a range of rational numbers. The first fraction is the smallest rational number in the range, and the second fraction is the largest rational number in the range. The values are inclusive at both ends. value_type_rational_pointer A pointer to a block of custom metadata. ## ◆ fill_mode strong #include <xtd.drawing/include/xtd/drawing/drawing2d/fill_mode.h> Specifies how the interior of a closed path is filled. Namespace xtd::drawing Library xtd.drawing Remarks An application fills the interior of a path using one of two fill modes: alternate or winding. The mode determines how to fill and clip the interior of a closed figure. The default mode is xtd::drawing::drawin2d::fill_mode::alternate. To determine the interiors of closed figures in the alternate mode, draw a line from any arbitrary start point in the path to some point obviously outside the path. If the line crosses an odd number of path segments, the starting point is inside the closed region and is therefore part of the fill or clipping area. An even number of crossings means that the point is not in an area to be filled or clipped. An open figure is filled or clipped by using a line to connect the last point to the first point of the figure. The xtd::drawing::drawin2d::fill_mode::winding mode considers the direction of the path segments at each intersection. It adds one for every clockwise intersection, and subtracts one for every counterclockwise intersection. If the result is nonzero, the point is considered inside the fill or clip area. A zero count means that the point lies outside the fill or clip area. A figure is considered clockwise or counterclockwise based on the order in which the segments of the figure are drawn. Enumerator alternate Specifies the alternate fill mode. winding Specifies the winding fill mode. ## ◆ flush_intention strong #include <xtd.drawing/include/xtd/drawing/drawing2d/flush_intention.h> Specifies whether commands in the graphics stack are terminated (flushed) immediately or executed as soon as possible. Namespace xtd::drawing::drawing2d Library xtd.drawing Enumerator flush Specifies that the stack of all graphics operations is flushed immediately. sync Specifies that all graphics operations on the stack are executed as soon as possible. This synchronizes the graphics state. ## ◆ font_style strong #include <xtd.drawing/include/xtd/drawing/font_style.h> Specifies style information applied to text. This enumeration has a flags attribute that allows a bitwise combination of its member values. Namespace xtd::drawing Library xtd.drawing Enumerator regular Normal text. bold Bold text. italic Italic text. underline Underline text. strikeout Text with a line through the middle. ## ◆ generic_font_families strong #include <xtd.drawing/include/xtd/drawing/text/generic_font_families.h> Specifies a generic font_family object. Namespace xtd::drawing::text Library xtd.drawing Enumerator serif A generic Serif font_family object. sans_serif A generic Sans Serif font_family object. monospace A generic Monospace font_family object. ## ◆ graphics_unit strong #include <xtd.drawing/include/xtd/drawing/graphics_unit.h> Specifies the unit of measure for the given data. This enumeration has a flags attribute that allows a bitwise combination of its member values. Namespace xtd::drawing Library xtd.drawing Enumerator world Specifies the world coordinate system unit as the unit of measure. display Specifies 1/75 inch as the unit of measure. pixel Specifies a device pixel as the unit of measure. point Specifies a printer's point (1/72 inch) as the unit of measure. inch Specifies the inch as the unit of measure. document Specifies the document unit (1/300 inch) as the unit of measure. millimeter Specifies the millimeter as the unit of measure. ## ◆ hatch_style strong #include <xtd.drawing/include/xtd/drawing/drawing2d/hatch_style.h> Specifies the different patterns available for xtd::drawing::drawing2d::hatch_brush objects. Namespace xtd::drawing::drawing2d Library xtd.drawing Enumerator horizontal A pattern of horizontal lines. vertical A pattern of vertical lines. forward_diagonal A pattern of lines on a diagonal from upper left to lower right. backward_diagonal A pattern of lines on a diagonal from upper right to lower left. cross Specifies horizontal and vertical lines that cross. diagonal_cross A pattern of crisscross diagonal lines. percent_05 Specifies a 5-percent hatch. The ratio of foreground color to background color is 5:95. percent_10 Specifies a 10-percent hatch. The ratio of foreground color to background color is 10:90. percent_20 Specifies a 20-percent hatch. The ratio of foreground color to background color is 20:80. percent_25 Specifies a 25-percent hatch. The ratio of foreground color to background color is 25:75. percent_30 Specifies a 30-percent hatch. The ratio of foreground color to background color is 30:70. percent_40 Specifies a 40-percent hatch. The ratio of foreground color to background color is 40:60. percent_50 Specifies a 50-percent hatch. The ratio of foreground color to background color is 50:50. percent_60 Specifies a 60-percent hatch. The ratio of foreground color to background color is 60:40. percent_70 Specifies a 70-percent hatch. The ratio of foreground color to background color is 70:30. percent_75 Specifies a 75-percent hatch. The ratio of foreground color to background color is 75:25. percent_80 Specifies a 80-percent hatch. The ratio of foreground color to background color is 80:20. percent_90 Specifies a 90-percent hatch. The ratio of foreground color to background color is 90:10. light_downward_diagonal Specifies diagonal lines that slant to the right from top points to bottom points and are spaced 50 percent closer together than forward_diagonal, but are not antialiased. light_upward_diagonal Specifies diagonal lines that slant to the left from top points to bottom points and are spaced 50 percent closer together than backward_diagonal, but they are not antialiased. dark_downward_diagonal Specifies diagonal lines that slant to the right from top points to bottom points, are spaced 50 percent closer together than, and are twice the width of forward_diagonal. This hatch pattern is not antialiased. dark_upward_diagonal Specifies diagonal lines that slant to the left from top points to bottom points, are spaced 50 percent closer together than backward_diagonal, and are twice its width, but the lines are not antialiased. wide_downward_diagonal Specifies diagonal lines that slant to the right from top points to bottom points, have the same spacing as hatch style forward_diagonal, and are triple its width, but are not antialiased. wide_upward_diagonal Specifies diagonal lines that slant to the left from top points to bottom points, have the same spacing as hatch style backward_diagonal, and are triple its width, but are not antialiased. light_vertical Specifies vertical lines that are spaced 50 percent closer together than vertical. light_horizontal Specifies horizontal lines that are spaced 50 percent closer together than horizontal. narrow_vertical Specifies vertical lines that are spaced 75 percent closer together than hatch style vertical (or 25 percent closer together than light_vertical). narrow_horizontal Specifies horizontal lines that are spaced 75 percent closer together than hatch style horizontal (or 25 percent closer together than light_horizontal). dark_vertical Specifies vertical lines that are spaced 50 percent closer together than vertical and are twice its width. dark_horizontal Specifies horizontal lines that are spaced 50 percent closer together than horizontal and are twice the width of horizontal. dashed_downward_diagonal Specifies dashed diagonal lines, that slant to the right from top points to bottom points. dashed_upward_diagonal Specifies dashed diagonal lines, that slant to the left from top points to bottom points. dashed_horizontal Specifies dashed horizontal lines. dashed_vertical Specifies dashed vertical lines. small_confetti Specifies a hatch that has the appearance of confetti. large_confetti Specifies a hatch that has the appearance of confetti, and is composed of larger pieces than small_confetti. zig_zag Specifies horizontal lines that are composed of zigzags. wave Specifies horizontal lines that are composed of tildes. diagonal_brick Specifies a hatch that has the appearance of layered bricks that slant to the left from top points to bottom points. horizontal_brick Specifies a hatch that has the appearance of horizontally layered bricks. weave Specifies a hatch that has the appearance of a woven material. plaid Specifies a hatch that has the appearance of a plaid material. divot Specifies a hatch that has the appearance of divots. dotted_grid Specifies horizontal and vertical lines, each of which is composed of dots, that cross. dotted_diamond Specifies forward diagonal and backward diagonal lines, each of which is composed of dots, that cross. shingle Specifies a hatch that has the appearance of diagonally layered shingles that slant to the right from top points to bottom points. trellis Specifies a hatch that has the appearance of a trellis. sphere Specifies a hatch that has the appearance of spheres laid adjacent to one another. small_grid Specifies horizontal and vertical lines that cross and are spaced 50 percent closer together than hatch style cross. small_checker_board Specifies a hatch that has the appearance of a checkerboard. large_checker_board Specifies a hatch that has the appearance of a checkerboard with squares that are twice the size of small_checker_board. outlined_diamond Specifies forward diagonal and backward diagonal lines that cross but are not antialiased. solid_diamond Specifies a hatch that has the appearance of a checkerboard placed diagonally. wide_checker_board Specifies a hatch that has the appearance of a checkerboard with squares that are twice the size of large_checker_board and Four times the size of small_checker_board. ## ◆ hotkey_prefix strong #include <xtd.drawing/include/xtd/drawing/text/hotkey_prefix.h> Specifies the type of display for hot-key prefixes that relate to text. Namespace xtd::drawing::text Library xtd.drawing Remarks A hot-key prefix allows you to use a keyboard combination (usually CTRL+HotKey or ALT+HotKey) to access functionality represented by text displayed on the screen. Enumerator none No hot-key prefix. show Display the hot-key prefix. hide Do not display the hot-key prefix. ## ◆ image_flags strong #include <xtd.drawing/include/xtd/drawing/imaging/image_flags.h> Specifies the attributes of the pixel data contained in an xtd::drawing::image object. The xtd::drawing:iImage::flags property returns a member of this enumeration. Namespace xtd::drawing::imaging Library xtd.drawing Enumerator none There is no format information. scalable The pixel data is scalable. has_alpha The pixel data contains alpha information. has_translucent Specifies that the pixel data has alpha values other than 0 (transparent) and 255 (opaque). partially_scalable The pixel data is partially scalable, but there are some limitations. color_space_rgb The pixel data uses an RGB color space. color_space_cmyk The pixel data uses a CMYK color space. color_space_gray The pixel data is grayscale. color_space_ycbcr Specifies that the image is stored using a YCBCR color space. color_space_ycck Specifies that the image is stored using a YCCK color space. has_real_dpi Specifies that dots per inch information is stored in the image. has_real_pixel_size Specifies that the pixel size is stored in the image. caching The pixel data can be cached for faster access. ## ◆ interpolation_mode strong #include <xtd.drawing/include/xtd/drawing/drawing2d/interpolation_mode.h> The xtd::drawing::drawing2d::interpolation_mode enumeration specifies the algorithm that is used when images are scaled or rotated. Namespace xtd::drawing::drawing2d Library xtd.drawing Enumerator invalid Equivalent to the xtd::drawing::drawing2d::quality_mode::invalid element of the xtd::drawing::drawing2d::quality_mode enumeration. default_value Specifies default mode. low Specifies low quality interpolation. hight Specifies high quality interpolation. bilinear Specifies bilinear interpolation. No prefiltering is done. This mode is not suitable for shrinking an image below 50 percent of its original size. bicubic Specifies bicubic interpolation. No prefiltering is done. This mode is not suitable for shrinking an image below 25 percent of its original size. nearest_neighbor Specifies nearest-neighbor interpolation. high_quality_bilinear Specifies high-quality, bilinear interpolation. Prefiltering is performed to ensure high-quality shrinking. high_quality_bicubic Specifies high-quality, bicubic interpolation. Prefiltering is performed to ensure high-quality shrinking. This mode produces the highest quality transformed images. ## ◆ known_color strong #include <xtd.drawing/include/xtd/drawing/known_color.h> Specifies the known system colors. Namespace xtd::drawing Library xtd.drawing xtd::drawing::color Enumerator active_border The system-defined color of the active window's border. active_caption The system-defined color of the background of the active window's title bar. active_caption_text The system-defined color of the text in the active window's title bar. app_workspace The system-defined color of the application workspace. The application workspace is the area in a multiple-document view that is not being occupied by documents. control The system-defined face color of a 3-D element. control_dark The system-defined shadow color of a 3-D element. The shadow color is applied to parts of a 3-D element that face away from the light source. control_dark_dark The system-defined color that is the dark shadow color of a 3-D element. The dark shadow color is applied to the parts of a 3-D element that are the darkest color. control_light The system-defined color that is the light color of a 3-D element. The light color is applied to parts of a 3-D element that face the light source. control_light_light The system-defined highlight color of a 3-D element. The highlight color is applied to the parts of a 3-D element that are the lightest color. control_text The system-defined color of text in a 3-D element. desktop The system-defined color of the desktop. gray_text The system-defined color of dimmed text. Items in a list that are disabled are displayed in dimmed text. highlight The system-defined color of the background of selected items. This includes selected menu items as well as selected text. highlight_text The system-defined color of the text of selected items. hot_track The system-defined color used to designate a hot-tracked item. Single-clicking a hot-tracked item executes the item. inactive_border The system-defined color of an inactive window's border. inactive_caption The system-defined color of the background of an inactive window's title bar. inactive_caption_text The system-defined color of the text in an inactive window's title bar. info The system-defined color of the background of a ToolTip. info_text The system-defined color of the text of a ToolTip. The system-defined color of a menu's background. The system-defined color of a menu's text. scroll_bar The system-defined color of the background of a scroll bar. window The system-defined color of the background in the client area of a window. window_frame The system-defined color of a window frame. window_text The system-defined color of the text in the client area of a window. transparent A system-defined color. alice_blue A system-defined color. antique_white A system-defined color. aqua A system-defined color. aquamarine A system-defined color. azure A system-defined color. beige A system-defined color. bisque A system-defined color. black A system-defined color. blanched_almond A system-defined color. blue A system-defined color. blue_violet A system-defined color. brown A system-defined color. burly_wood A system-defined color. A system-defined color. chartreuse A system-defined color. chocolate A system-defined color. coral A system-defined color. cornflower_blue A system-defined color. cornsilk A system-defined color. crimson A system-defined color. cyan A system-defined color. dark_blue A system-defined color. dark_cyan A system-defined color. dark_goldenrod A system-defined color. dark_gray A system-defined color. dark_green A system-defined color. dark_khaki A system-defined color. dark_magenta A system-defined color. dark_olive_green A system-defined color. dark_orange A system-defined color. dark_orchid A system-defined color. dark_red A system-defined color. dark_salmon A system-defined color. dark_sea_green A system-defined color. dark_slate_blue A system-defined color. dark_slate_gray A system-defined color. dark_turquoise A system-defined color. dark_violet A system-defined color. deep_pink A system-defined color. deep_sky_blue A system-defined color. dim_gray A system-defined color. dodger_blue A system-defined color. firebrick A system-defined color. floral_white A system-defined color. forest_green A system-defined color. fuchsia A system-defined color. gainsboro A system-defined color. ghost_white A system-defined color. gold A system-defined color. goldenrod A system-defined color. gray A system-defined color. green A system-defined color. green_yellow A system-defined color. honeydew A system-defined color. hot_pink A system-defined color. indian_red A system-defined color. indigo A system-defined color. ivory A system-defined color. khaki A system-defined color. lavender A system-defined color. lavender_blush A system-defined color. lawn_green A system-defined color. lemon_chiffon A system-defined color. light_blue A system-defined color. light_coral A system-defined color. light_cyan A system-defined color. light_goldenrod_yellow A system-defined color. light_gray A system-defined color. light_green A system-defined color. light_pink A system-defined color. light_salmon A system-defined color. light_sea_green A system-defined color. light_sky_blue A system-defined color. light_slate_gray A system-defined color. light_steel_blue A system-defined color. light_yellow A system-defined color. lime A system-defined color. lime_green A system-defined color. linen A system-defined color. magenta A system-defined color. maroon A system-defined color. medium_aquamarine A system-defined color. medium_blue A system-defined color. medium_orchid A system-defined color. medium_purple A system-defined color. medium_sea_green A system-defined color. medium_slate_blue A system-defined color. medium_spring_green A system-defined color. medium_turquoise A system-defined color. medium_violet_red A system-defined color. midnight_blue A system-defined color. mint_cream A system-defined color. misty_rose A system-defined color. moccasin A system-defined color. navajo_white A system-defined color. navy A system-defined color. old_lace A system-defined color. olive A system-defined color. olive_drab A system-defined color. orange A system-defined color. orange_red A system-defined color. orchid A system-defined color. pale_goldenrod A system-defined color. pale_green A system-defined color. pale_turquoise A system-defined color. pale_violet_red A system-defined color. papaya_whip A system-defined color. peach_puff A system-defined color. peru A system-defined color. pink A system-defined color. plum A system-defined color. powder_blue A system-defined color. purple A system-defined color. rebecca_purple A system-defined color. red A system-defined color. rosy_brown A system-defined color. royal_blue A system-defined color. A system-defined color. salmon A system-defined color. sandy_brown A system-defined color. sea_green A system-defined color. sea_shell A system-defined color. sienna A system-defined color. silver A system-defined color. sky_blue A system-defined color. slate_blue A system-defined color. slate_gray A system-defined color. snow A system-defined color. spring_green A system-defined color. steel_blue A system-defined color. tan A system-defined color. teal A system-defined color. thistle A system-defined color. tomato A system-defined color. turquoise A system-defined color. violet A system-defined color. wheat A system-defined color. white A system-defined color. white_smoke A system-defined color. yellow A system-defined color. yellow_green A system-defined color. button_face The system-defined face color of a 3-D element. button_highlight The system-defined color that is the highlight color of a 3-D element. This color is applied to parts of a 3-D element that face the light source. The system-defined color that is the shadow color of a 3-D element. This color is applied to parts of a 3-D element that face away from the light source. The system-defined color of the lightest color in the color gradient of an active window's title bar. The system-defined color of the lightest color in the color gradient of an inactive window's title bar. The system-defined color of the background of a menu bar. accent The system-defined color of the accent color (macos specific. On other platform is same as menu_highlight). accent_text The system-defined color of the accent text color (macos specific. On other platform is same as highlight_text). text_box The system-defined color of the accent color (macos specific. On other platform is same as window). text_box_text The system-defined color of the accent text color (macos specific. On other platform is same as window_text). ## ◆ line_cap strong #include <xtd.drawing/include/xtd/drawing/drawing2d/line_cap.h> Specifies the available cap styles with which a xtd::drawing::pen object can end a line. Namespace xtd::drawing::drawing2d Library xtd.drawing Enumerator flat Specifies a flat line cap. square Specifies a square line cap. round Specifies a round line cap. ## ◆ line_join strong #include <xtd.drawing/include/xtd/drawing/drawing2d/line_join.h> Specifies how to join consecutive line or curve segments in a figure (subpath) contained in a xtd::drawing::drawing2d::graphics_path object. Namespace xtd::drawing::drawing2d Library xtd.drawing Remarks Compositing is done during rendering when the source pixels are combined with the destination pixels to produce the resultant pixels. The quality of compositing directly relates to the visual quality of the output and is inversely proportional to the render time. The higher the quality, the slower the render time. This is because the higher the quality level, the more surrounding pixels need to be taken into account during the composite. The linear quality setting (AssumeLinear) compromises by providing better quality than the default quality at a slightly lower speed. Enumerator miter Specifies a mitered join. This produces a sharp corner or a clipped corner, depending on whether the length of the miter exceeds the miter limit. bevel Specifies a beveled join. This produces a diagonal corner. round Specifies a circular join. This produces a smooth, circular arc between the lines. miter_clipped Specifies a mitered join. This produces a sharp corner or a beveled corner, depending on whether the length of the miter exceeds the miter limit. strong #include <xtd.drawing/include/xtd/drawing/drawing2d/linear_gradient_mode.h> Specifies the direction of a linear gradient. Namespace xtd::drawing::drawing2d Library xtd.drawing Enumerator horizontal Specifies a gradient from left to right. vertical Specifies a gradient from top to bottom. forward_diagonal Specifies a gradient from upper left to lower right. backward_diagonal Specifies a gradient from upper right to lower left. ## ◆ matrix_order strong #include <xtd.drawing/include/xtd/drawing/drawing2d/matrix_order.h> Specifies the order for matrix transform operations. Namespace xtd::drawing::drawing2d Library xtd.drawing Remarks Matrix transform operations are not necessarily commutative. The order in which they are applied is important. Enumerator prepend The new operation is applied before the old operation. append The new operation is applied after the old operation. ## ◆ pen_alignment strong #include <xtd.drawing/include/xtd/drawing/drawing2d/pen_alignment.h> SSpecifies the alignment of a xtd::drawing::pen object in relation to the theoretical, zero-width line. Namespace xtd::drawing::drawing2d Library xtd.drawing Remarks A xtd::drawing::pen object has width. The center point of this pen width is aligned relative to the line being drawn depending on the alignment value. A xtd::drawing::pen object can be positioned to draw inside of a line or centered over the line. xtd::drawing::pen Enumerator center Specifies that the xtd::drawing::pen object is centered over the theoretical line. inset Specifies that the xtd::drawing::pen is positioned on the inside of the theoretical line. outset Specifies the xtd::drawing::pen is positioned on the outside of the theoretical line. left Specifies the xtd::drawing::pen is positioned to the left of the theoretical line. right Specifies the xtd::drawing::pen is positioned to the right of the theoretical line. ## ◆ pen_type strong #include <xtd.drawing/include/xtd/drawing/drawing2d/pen_type.h> Specifies the type of fill a xtd::drawing::pen object uses to fill lines. Namespace xtd::drawing::drawing2d Library xtd.drawing Remarks The pen type is determined by the brush property of the xtd::drawing::pen object. Enumerator solid_color Specifies a solid fill. hatch_fill Specifies a hatch fill. texture_fill Specifies a bitmap texture fill. ## ◆ pixel_format strong #include <xtd.drawing/include/xtd/drawing/imaging/pixel_format.h> Specifies the format of the color data for each pixel in the image. Namespace xtd::drawing::imaging Library xtd.drawing Remarks The pixel format defines the number of bits of memory associated with one pixel of data. The format also defines the order of the color components within a single pixel of data. PixelFormat48bppRGB, PixelFormat64bppARGB, and PixelFormat64bppPARGB use 16 bits per color component (channel). GDI+ version 1.0 and 1.1 can read 16-bits-per-channel images, but such images are converted to an 8-bits-per-channel format for processing, displaying, and saving. Each 16-bit color channel can hold a value in the range 0 through 2^13. Some of the pixel formats contain premultiplied color values. Premultiplied means that the color values have already been multiplied by an alpha value. Enumerator undefined The pixel format is undefined. dont_care No pixel format is specified. max The maximum value for this enumeration. indexed The pixel data contains color-indexed values, which means the values are an index to colors in the system color table, as opposed to individual color values. gdi The pixel data contains GDI colors. format16bpp_rgb555 Specifies that the format is 16 bits per pixel; 5 bits each are used for the red, green, and blue components. The remaining bit is not used. format16bpp_rgb565 Specifies that the format is 16 bits per pixel; 5 bits are used for the red component, 6 bits are used for the green component, and 5 bits are used for the blue component. format24bpp_rgb Specifies that the format is 24 bits per pixel; 8 bits each are used for the red, green, and blue components. format32bpp_rgb Specifies that the format is 32 bits per pixel; 8 bits each are used for the red, green, and blue components. The remaining 8 bits are not used. format1bpp_indexed Specifies that the pixel format is 1 bit per pixel and that it uses indexed color. The color table therefore has two colors in it. format4bpp_indexed Specifies that the format is 4 bits per pixel, indexed. format8bpp_indexed Specifies that the format is 8 bits per pixel, indexed. The color table therefore has 256 colors in it. alpha The pixel data contains alpha values that are not premultiplied. format16bpp_argb1555 The pixel format is 16 bits per pixel. The color information specifies 32,768 shades of color, of which 5 bits are red, 5 bits are green, 5 bits are blue, and 1 bit is alpha. palpha The pixel format contains premultiplied alpha values. format32bpp_pargb Specifies that the format is 32 bits per pixel; 8 bits each are used for the alpha, red, green, and blue components. The red, green, and blue components are premultiplied, according to the alpha component. extended Reserved. format16bpp_gray_scale The pixel format is 16 bits per pixel. The color information specifies 65536 shades of gray. format48bpp_rgb Specifies that the format is 48 bits per pixel; 16 bits each are used for the red, green, and blue components. format64bpp_pargb Specifies that the format is 64 bits per pixel; 16 bits each are used for the alpha, red, green, and blue components. The red, green, and blue components are premultiplied according to the alpha component. canonical The default pixel format of 32 bits per pixel. The format specifies 24-bit color depth and an 8-bit alpha channel. format32bpp_argb Specifies that the format is 32 bits per pixel; 8 bits each are used for the alpha, red, green, and blue components. format64bpp_argb Specifies that the format is 64 bits per pixel; 16 bits each are used for the alpha, red, green, and blue components. ## ◆ pixel_offset_mode strong #include <xtd.drawing/include/xtd/drawing/drawing2d/pixel_offset_mode.h> Specifies how pixels are offset during rendering. Namespace xtd::drawing::drawing2d Library xtd.drawing By offsetting pixels during rendering, you can improve render quality at the cost of render speed. Enumerator invalid Specifies the default mode. default_value Specifies default mode. high_speed Specifies high speed, low quality rendering. high_quality Specifies high quality, low speed rendering. none Specifies no pixel offset. half Specifies that pixels are offset by -.5 units, both horizontally and vertically, for high speed antialiasing. ## ◆ rotate_flip_type strong #include <xtd.drawing/include/xtd/drawing/rotate_flip_type.h> Specifies how much an image is rotated and the axis used to flip the image. Namespace xtd::drawing Library xtd.drawing Remarks The xtd::drawing::image::rotate_flip method rotates the image clockwise. If you wish to draw on an image once it has been rotated, you should always retrieve a new graphics object from the image, otherwise an exception could occur. Enumerator rotate_none_flip_none Specifies no clockwise rotation and no flipping. rotate_90_flip_none Specifies a 270-degree clockwise rotation followed by a horizontal and vertical flip. rotate_180_flip_none Specifies a 180-degree clockwise rotation without flipping. rotate_270_flip_none Specifies a 270-degree clockwise rotation without flipping. rotate_none_flip_x Specifies no clockwise rotation followed by a horizontal flip. rotate_90_flip_x Specifies a 90-degree clockwise rotation followed by a horizontal flip. rotate_180_flip_x Specifies a 180-degree clockwise rotation followed by a horizontal flip. rotate_270_flip_x Specifies a 270-degree clockwise rotation followed by a horizontal flip. rotate_none_flip_y Specifies no clockwise rotation followed by a vertical flip. rotate_90_flip_y Specifies a 90-degree clockwise rotation followed by a vertical flip. rotate_180_flip_y Specifies a 180-degree clockwise rotation followed by a vertical flip. rotate_270_flip_y Specifies a 270-degree clockwise rotation followed by a vertical flip. rotate_none_flip_xy Specifies no clockwise rotation followed by a horizontal and vertical flip. rotate_90_flip_xy Specifies a 90-degree clockwise rotation followed by a horizontal and vertical flip. rotate_180_flip_xy Specifies a 180-degree clockwise rotation followed by a horizontal and vertical flip. rotate_270_flip_xy Specifies a 90-degree clockwise rotation without flipping. ## ◆ smoothing_mode strong #include <xtd.drawing/include/xtd/drawing/drawing2d/smoothing_mode.h> Specifies whether smoothing (antialiasing) is applied to lines and curves and the edges of filled areas. Namespace xtd::drawing::drawing2d Library xtd.drawing Remarks Dxtd::drawing::drawing2d::smoothing_mode::dfault_value, xtd::drawing::drawing2d::smoothing_mode::none, and xtd::drawing::drawing2d::smoothing_mode::xtd::drawing::drawing2d::smoothing_mode::high_speed are equivalent and specify rendering without smoothing applied. xtd::drawing::drawing2d::smoothing_mode::anti_alias and xtd::drawing::drawing2d::smoothing_mode::high_quality are equivalent and specify rendering with smoothing applied. Note When the xtd::drawing::graphics::smoothing_mode property is specified by using the xtd::drawing::drawing2d::smoothing_mode enumeration, it does not affect text. To set the text rendering quality, use the xtd::drawing::graphics::text_rendering_hint property and the xtd::drawing::drawing2d::text_rendering_hint enumeration. When the xtd::drawing::graphics::smoothing_mode property is specified by using the xtd::drawing::drawing2d::smoothing_mode enumeration, it does not affect areas filled by a path gradient brush. Areas filled by using a xtd::drawing::drawing2d::path_gradient_brush object are rendered the same way (aliased) regardless of the setting for the xtd::drawing::graphics::smoothing_mode property. Enumerator invalid Specifies an invalid mode. default_value Specifies default mode. high_speed Specifies high speed, low quality rendering. high_quality Specifies high quality, low speed rendering. none Specifies no pixel offset. anti_alias Specifies that pixels are offset by -.5 units, both horizontally and vertically, for high speed antialiasing. ## ◆ string_alignment strong #include <xtd.drawing/include/xtd/drawing/string_alignment.h> Specifies the alignment of a text string relative to its layout rectangle. Namespace xtd::drawing Library xtd.drawing Remarks When used with the line_alignment property, this enumeration sets the vertical alignment for a drawn string. When used with the alignment property, this enumeration sets the horizontal alignment. Enumerator near Specifies the text be aligned near the layout. In a left-to-right layout, the near position is left. In a right-to-left layout, the near position is right. center Specifies that text is aligned in the center of the layout rectangle. far Specifies that text is aligned far from the origin position of the layout rectangle. In a left-to-right layout, the far position is right. In a right-to-left layout, the far position is left. ## ◆ string_format_flags strong #include <xtd.drawing/include/xtd/drawing/string_format_flags.h> Specifies the display and layout information for text strings. This enumeration allows a bitwise combination of its member values. Namespace xtd::drawing Library xtd.drawing Enumerator direction_right_to_left Text is displayed from right to left. text. direction_vertical Text is vertically aligned. fit_black_box Parts of characters are allowed to overhang the string's layout rectangle. By default, characters are repositioned to avoid any overhang. display_format_control Control characters such as the left-to-right mark are shown in the output with a representative glyph. no_font_fallback Fallback to alternate fonts for characters not supported in the requested font is disabled. Any missing characters are displayed with the fonts missing glyph, usually an open square. measure_trailing_spaces Includes the trailing space at the end of each line. By default the boundary rectangle returned by the MeasureString method excludes the space at the end of each line. Set this flag to include that space in measurement. no_wrap Text wrapping between lines when formatting within a rectangle is disabled. This flag is implied when a point is passed instead of a rectangle, or when the specified rectangle has a zero line length. line_limit Only entire lines are laid out in the formatting rectangle. By default layout continues until the end of the text, or until no more lines are visible as a result of clipping, whichever comes first. Note that the default settings allow the last line to be partially obscured by a formatting rectangle that is not a whole multiple of the line height. To ensure that only whole lines are seen, specify this value and be careful to provide a formatting rectangle at least as tall as the height of one line. no_clip Overhanging parts of glyphs, and unwrapped text reaching outside the formatting rectangle are allowed to show. By default all text and glyph parts reaching outside the formatting rectangle are clipped. ## ◆ string_trimming strong #include <xtd.drawing/include/xtd/drawing/string_trimming.h> Specifies how to trim characters from a string that does not completely fit into a layout shape. Namespace xtd::drawing Library xtd.drawing Enumerator none Specifies no trimming. character Specifies that the text is trimmed to the nearest character. word Specifies that text is trimmed to the nearest word. ellipsis_character Specifies that the text is trimmed to the nearest character, and an ellipsis is inserted at the end of a trimmed line. ellipsis_word Specifies that text is trimmed to the nearest word, and an ellipsis is inserted at the end of a trimmed line. ellipsis_path The center is removed from trimmed lines and replaced by an ellipsis. The algorithm keeps as much of the last slash-delimited segment of the line as possible. ## ◆ text_rendering_hint strong #include <xtd.drawing/include/xtd/drawing/text/text_rendering_hint.h> Specifies the quality of text rendering. Namespace xtd::drawing::text Library xtd.drawing Remarks The quality ranges from text (fastest performance, but lowest quality) to antialiased text (better quality, but slower performance) to ClearType text (best quality on an LCD display). Enumerator system_default Each character is drawn using its glyph bitmap, with the system default rendering hint. The text will be drawn using whatever font-smoothing settings the user has selected for the system. single_bit_per_pixel_grid_fit Each character is drawn using its glyph bitmap. Hinting is used to improve character appearance on stems and curvature. single_bit_per_pixel Each character is drawn using its glyph bitmap. Hinting is not used. anti_alias_grid_fit Each character is drawn using its antialiased glyph bitmap with hinting. Much better quality due to antialiasing, but at a higher performance cost. anti_alias Each character is drawn using its antialiased glyph bitmap without hinting. Better quality due to antialiasing. Stem width differences may be noticeable because hinting is turned off. clear_type_grid_fit Each character is drawn using its glyph ClearType bitmap with hinting. The highest quality setting. Used to take advantage of ClearType font features.	2022-07-07 10:04:06	{"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": 0.24785779416561127, "perplexity": 6093.227873072622}, "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/1656104690785.95/warc/CC-MAIN-20220707093848-20220707123848-00475.warc.gz"}
http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=96-323	96-323 Daniel Bessis, Giorgio Mantica, G. Andrei Mezincescu, and Daniel Vrinceanu Electron Wave Filters from Inverse Scattering Theory (56K, postscript file (4 pages)) Jul 2, 96 Abstract , Paper (src), View paper (auto. generated ps), Index of related papers Abstract. Semiconductor heterostructures with prescribed energy dependence of the transmittance can be designed by combining: {\em a)} Pad\'e approximant reconstruction of the S-matrix; {\em b)} inverse scattering theory for Schro\"dinger's equation; {\em c)} a unitary transformation which takes into account the variable mass effects. The resultant continuous concentration profile can be digitized into an easily realizable rectangular-wells structure. For illustration, we give the specifications of a 2 narrow band-pass 12 layer $Al_cGa_{1-c}As$ filter with the high energy peak more than {\em twice narrower} than the other. Files: 96-323.src( desc , 96-323.uu )	2019-05-22 19:23:48	{"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": 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": 0.9799493551254272, "perplexity": 10057.781605178487}, "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/1558232256948.48/warc/CC-MAIN-20190522183240-20190522205240-00275.warc.gz"}
https://www.physicsforums.com/threads/screw-the-gas-company.6678/	# Screw the gas company I only use gas for heating water, so I'm considering a solar water heater. It seems dumb not to go solar here in Arizona. I was wondering do any of you have a solar water heater? How do you like it? Do you have any plans on how to build one? russ_watters Mentor I've never looked, but there are commecially available solar water heaters. No need to build one yourself (though it could be fun). Google it. Something to consider: If you have an attic, I have seen plans for a water heater that uses a fan to move attic air through a coil. Attics get pretty warm depending on the insulation arrangement. If the insulation is on the attic floor, the attic gets warm. If it's on the underside of the roof, the attic may not be too warm. If you do have a warm attic, this kind of system can have two positive effects, cools the attic and warms the water in the coil. This may not provide enough heat to completely heat the water, but the combined effect of reducing air conditioning load, and preheating domestic water may allow for electric or gas backup for the water heating and still allow for savings. This kind of system also works good for a swimming pool heater. russ_watters Mentor I'd never heard that, Aartman, but its a lose-lose catch-22. In the summer you want to keep your attic as cool as possible to reduce your a/c bill. Ivan Seeking Staff Emeritus Gold Member Originally posted by Artman Something to consider: If you have an attic, I have seen plans for a water heater that uses a fan to move attic air through a coil. Attics get pretty warm depending on the insulation arrangement. If the insulation is on the attic floor, the attic gets warm. If it's on the underside of the roof, the attic may not be too warm. If you do have a warm attic, this kind of system can have two positive effects, cools the attic and warms the water in the coil. This may not provide enough heat to completely heat the water, but the combined effect of reducing air conditioning load, and preheating domestic water may allow for electric or gas backup for the water heating and still allow for savings. This kind of system also works good for a swimming pool heater. One needs to be careful with ideas like this since the costs can exceed the lifetime benefit. The problem is the heat exchange efficiency. The rate of heat transfer through a separating wall increases as the velocity, density, specific heat, and the thermal conductivity of the fluids increase. The state of the fluids inside and outside of the thermal conductor is also significant. For example, liquid to liquid transfers are more efficient that gas to liquid. Here are some numbers from an old engineering book that I use; Refrigeration, Air Conditioning, and Cold Storage; by Gunther, 1969 [it was old when I got it]. This was long considered the bible of heat transfer applications. For a well designed industrial heat exchanger, using clean copper pipes and with low rates of fluid flow [e.g. < 1 gpm liquid flow per foot of linear contact between the media and the copper pipes, with air moving by a low power fan - air to water transfers], we typically get something like 2 BTU per hr per sq. ft of contact per degree F – a best case scenario. So if we use some typical 3/4" copper pipe, we get about 0.19 sq ft of contact per ft of pipe. We might expect a temperature differential of no more than 30 degrees F at the inlet, and 10 degrees at the outlet in order to be useful at the other end. So we can loosely assume an average of a 20 degree difference [not really but the error works in your favor]. Thus we get about 0.4 BTU per hr per linear foot of 3/4" pipe. The pipe size was chosen to make the system practical. Smaller pipe requires greater length; stay tuned. Next, 1 BTU per hr is about 0.29 watts [CRC]; which yields about 0.12 watts per linear foot of exchange. So in order to rival the contribution of a 100 watt light bulb, we need at least 830 feet of 3/4” copper tubing. The current price of type L copper [common] is about $2.25 per foot. So for only$1,900.00, just for the pipe mind you, you still need a pump, controls, wiring, a fan, these need to then be powered which may take more than 100 watts, you can have the heat of a 100 watt light bulb for about half the day. At ten cents per KWH, this would only require 43 years to pay for the pipe. My point: If these types of systems are to be of use they must be properly engineered. Last edited: Ivan Seeking Staff Emeritus Gold Member One thing that I have done is to use the cool air from underneath my house for free A/C. This can be dangerous if any molds or toxins are present, and the smell requires the use of good carbon filters, but I did this for several years. I found it to be effective in my house for up to 5 days running, in 100 degree F weather. Edit: Note that in fact we are using the heat capacity of the earth, the footer(s), and the structure of the house itself for heat storage. For every 1000 sq feet of house, we get about 2500 sq ft of heat exchange surfaces for heat storage. I blocked all but one vent [located on the NE corner of the house] for the crawlspace. Then, using a window style box fan, I just blew the air from under the house through some good filters, and directly into the house. Every day the temp under the house rose - after a week of very hot weather it ceases to be very effective - but for 5 days the blowing air stayed pretty close to 70 degrees most of the day. I estimated that this all equated to a 5000 BTU A/C unit [1500 watts] running for 6 hours a day. In moderate weather – in Oregon – this can work all summer long. Note that the air was (fortuitously) forced to travel a long path under the house before getting to the fan. This is very important. Also, by continuing to run the fan all evening, the cool night air helps to "recharge" the crawl space for the next day. If it never cools down at night the effectiveness tapers off very quickly. The elimination of heat exchangers can increase the efficiency of a system tremendously; sometimes even making something once useless, practical. A properly designed building could increase the effectiveness of this concept. Last edited: In a 105 deg F attic these type units exchange approximately 3 tons of heat (depending on the attic size and inlet water temperature) @ 2500 CFM. Also, an attic in Arizona is going to be closer to 110 or 115 deg F much of the year, giving a wider temperature difference for a better rate of exchange. I suggest this as a preheater, with the cooling of the attic as a side benefit raising the overall efficiency, but with 115 deg F or higher air temperatures, water circulating through this fan coil system will continue to rise in temperature until it reaches equilibrium with the air temperature at 115 deg F, which is hot enough for most domestic uses. A quick look at the ratings of a fan coil unit will verify that a 20 deg F rise in water temperature is easily optainable over 2 or 3 gpm even at as low as 1000 CFM using just a 2 row cooling coil and a small fractional HP fan with a difference in entering air to entering water temperture of only 35 deg F. (80 deg F DB EAT and 45 deg F EWT) We have that with 75 EWT and 110 EAT increase the air flow and the water temperature rise will increase (the air temp drop will decrease). So how long will the payback take with 36,000 btu gained by the water, AND 36,000 btu removed from the attic minus a 1/25 hp circulator (at most) and a 1/8 hp fan (at most)? By my calculations, 29 watts for the circulator and 93 watts for the fan is only about 122 watts according to your figures 1 btu is .29 watts so 36,000 is 10440 watts saved per hour x 2 (we are saving 36000 in AC and gaining 36000 in water heat) for a total of 20880 x say 75% eff loss (won't be this high, but it works in your favor) = 15660 watts per hour (during peak attic heat). At 10 cents per KWH this arrangement saves roughly $1.50 every hour it runs. If it costs$5000.00 to install the entire payback will be 3333.3 hrs of operation or probably a year or two of water heater operation. These things are already in use in areas with warm climates. They can completely cover the water heating load during summer months. Ivan Seeking Staff Emeritus Gold Member Originally posted by Artman In a 105 deg F attic these type units exchange approximately 3 tons of heat (depending on the attic size and inlet water temperature) @ 2500 CFM. Also, an attic in Arizona is going to be closer to 110 or 115 deg F much of the year, giving a wider temperature difference for a better rate of exchange. I suggest this as a preheater, with the cooling of the attic as a side benefit raising the overall efficiency, but with 115 deg F or higher air temperatures, water circulating through this fan coil system will continue to rise in temperature until it reaches equilibrium with the air temperature at 115 deg F, which is hot enough for most domestic uses. A quick look at the ratings of a fan coil unit will verify that a 20 deg F rise in water temperature is easily optainable over 2 or 3 gpm even at as low as 1000 CFM using just a 2 row cooling coil and a small fractional HP fan with a difference in entering air to entering water temperture of only 35 deg F. (80 deg F DB EAT and 45 deg F EWT) We have that with 75 EWT and 110 EAT increase the air flow and the water temperature rise will increase (the air temp drop will decrease). So how long will the payback take with 36,000 btu gained by the water, AND 36,000 btu removed from the attic minus a 1/25 hp circulator (at most) and a 1/8 hp fan (at most)? By my calculations, 29 watts for the circulator and 93 watts for the fan is only about 122 watts according to your figures 1 btu is .29 watts so 36,000 is 10440 watts saved per hour x 2 (we are saving 36000 in AC and gaining 36000 in water heat) for a total of 20880 x say 75% eff loss (won't be this high, but it works in your favor) = 15660 watts per hour (during peak attic heat). At 10 cents per KWH this arrangement saves roughly $1.50 every hour it runs. If it costs$5000.00 to install the entire payback will be 3333.3 hrs of operation or probably a year or two of water heater operation. These things are already in use in areas with warm climates. They can completely cover the water heating load during summer months. I don't see how this is possible. Where do you get this information? Also, your numbers are only good a few months out of the year. Even using these numbers, the two years is probably more like 8 or 10. Next, if we consider the total heat stored in that attic air at any moment, say at 115 degrees F, using 0.017 BTU per cu ft per degree F for dry 100 degree air, and using a 2000 sq foot house with an average of 4 ft overhead - 8000 cu ft - over the span of 100 to 115 degrees, we have a maximum of 2040 BTUs available. Last edited: Ivan, It is basically how a chilled water coil works. The fan draws entering air aproximately 80 DB across a coil holding 45 deg water and lowers the air temperature down to 55 or 56 DB and raises the temperature of the water 10 deg or more based on the flow rate. As long as the temperature differences are similar, and the fluid properties are similar, the amount of btu's exchanged will be similar. LAT = (Mbh/(CFM * .00108)) +EAT GPM = ((MBH1000) / ((EWT-LWT) SpHtW * 60 * 8.33)) Even a standard hot water baseboard with no fan gets about 300 btu/LF using 1 gpm of 140 deg F water and 65 deg air with only convection moving the air. You get much higher exchange rate with a fan. I may be over-estimating the savings a bit, but I think you may be under-estimating a bit more. Ivan Seeking Staff Emeritus Gold Member Originally posted by Artman Ivan, It is basically how a chilled water coil works. The fan draws entering air aproximately 80 DB across a coil holding 45 deg water and lowers the air temperature down to 55 or 56 DB and raises the temperature of the water 10 deg or more based on the flow rate. As long as the temperature differences are similar, and the fluid properties are similar, the amount of btu's exchanged will be similar. LAT = (Mbh/(CFM * .00108)) +EAT GPM = ((MBH1000) / ((EWT-LWT) SpHtW * 60 * 8.33)) Even a standard hot water baseboard with no fan gets about 300 btu/LF using 1 gpm of 140 deg F water and 65 deg air with only convection moving the air. You get much higher exchange rate with a fan. I may be over-estimating the savings a bit, but I think you may be under-estimating a bit more. First, I would need some convincing to believe this is really effective as indicated. I have no doubt that people think it is, but still, I'm skeptical. On the other hand, don't misunderstand; I was speaking to the need for caution. I have seen people lose a lot of money by slapping these kind of systems together. Note that I purposely did not even allow for radiator fins. I presented a typical scenario similar to examples that I have seen. If these systems are properly engineered, I am the biggest fan [forgive the pun] of alternative approaches. Unfortunately, there are many systems sold and used that are a waste of time; and way too much money! I don't mean to be too cynical [or skeptical], but when it comes to thousands of dollars potentially wasted, I get pretty cynical. Obviously in Arizona you enjoy much of a best case scenario. Here in Oregon, I did a lot of research on low head hydro. [I have a creek that ranges from 20 to 100 cfs; about 8 months of the year]. Since I had an interest in tapping this energy, if practical, I did a lot of research. My wife ran across a retired gentleman, then I would guess in his late sixties, who had build a pontoon, put it in the river, and sat a giant undershot paddle wheel on top. This was to power his house. It was absolutely huge; I am thinking it was about 10 feet in diameter, and 20 feet long.. He of course expected to sell these things to everyone in who lives near a river. He effectively spent his life’s savings on this device – he had to buy a small crane in order to move it around. He wanted to show it off, but also see why he could only get a couple hundred watts out of this monster. I could hear the 4x8 ft sheets of plywood slapping the water as I approached his house. I didn’t have the heart to tell this guy that his $20,000 was mostly wasted. . This is where a halfssed approach can get you. If good science and engineering are used in developing these systems, then you’ll find me leading the parade. Ivan Seeking Staff Emeritus Science Advisor Gold Member Originally posted by Artman Even a standard hot water baseboard with no fan gets about 300 btu/LF using 1 gpm of 140 deg F water and 65 deg air with only convection moving the air. You get much higher exchange rate with a fan. using the 2 BTU per sq ft per degrees F, we get 150 BTU per sq ft. Since a baseboard goes as about 1 sq ft per ft, we might expect 150 BTU per ft by this estimate. Also the exchange is more effecient due to the relative increase in water velocity. I think this accounts for the rest. Edit: I just checked my Lakewood oil radiator. The surfaces have nearly exactly 1 sq ft per ft. At full throttle, the oil temp is about 200 degrees F. The total surface area is 14 sq ft [and linear feet]. The heat transfer is about 1500 watts x 0.8 = 1200 [you don't get to count the electrical heat loss ], giving 4100 BTU per hour. (2 BTU/sqft/F)x(14 sq ft)x(130 degrees F) = 3640 BTU /hr Looks pretty close. These systems have a very low volume to surface area ratio, this also affects the results. I would agree that this number of 2 BTU does appear a bit conservative when it comes to a properly designed radiator. Last edited: Originally posted by Ivan Seeking First, I would need some convincing to believe this is really effective as indicated. I have no doubt that people think it is, but still, I'm skeptical. On the other hand, don't misunderstand; I was speaking to the need for caution. I have seen people lose a lot of money by slapping these kind of systems together. Note that I purposely did not even allow for radiator fins. I presented a typical scenario similar to examples that I have seen. If these systems are properly engineered, I am the biggest fan [forgive the pun] of alternative approaches. Unfortunately, there are many systems sold and used that are a waste of time; and way too much money! I don't mean to be too cynical [or skeptical], but when it comes to thousands of dollars potentially wasted, I get pretty cynical. Obviously in Arizona you enjoy much of a best case scenario. Here in Oregon, I did a lot of research on low head hydro. [I have a creek that ranges from 20 to 100 cfs; about 8 months of the year]. Since I had an interest in tapping this energy, if practical, I did a lot of research. My wife ran across a retired gentleman, then I would guess in his late sixties, who had build a pontoon, put it in the river, and sat a giant undershot paddle wheel on top. This was to power his house. It was absolutely huge; I am thinking it was about 10 feet in diameter, and 20 feet long.. He of course expected to sell these things to everyone in who lives near a river. He effectively spent his life’s savings on this device – he had to buy a small crane in order to move it around. He wanted to show it off, but also see why he could only get a couple hundred watts out of this monster. I could hear the 4x8 ft sheets of plywood slapping the water as I approached his house. I didn’t have the heart to tell this guy that his$20,000 was mostly wasted. . This is where a halfssed approach can get you. If good science and engineering are used in developing these systems, then you’ll find me leading the parade. I agree. There are also code issues, plumbing codes, building codes, lifesafety questions (the attic system is weighty and may be considered a pressure vessel), and should not be rushed into without research and study. I have thought about using the attic heater approach to heat a small pool, but there are many dangers with putting chlorinated water in such a system and then putting it into your attic (many corrosion factors to consider)and I don't want to put out the cost just to heat my pool. Doc Don't sit around arguing about it, go here: http://www.otherpower.com/ They have alot of alternative energy solutions and are very informative. There is a water wheel device shown also. russ_watters Mentor Originally posted by Ivan Seeking One thing that I have done is to use the cool air from underneath my house for free A/C. This can be dangerous if any molds or toxins are present, and the smell requires the use of good carbon filters, but I did this for several years. Interesting idea, but you have to be VERY careful. Besides mold, the humidity itself can cause you to INCREASE the cooling load on the house even if the air entering the house is below room temp. The vast majority of the energy your air conditioner uses (depending on climate of course - and the northwest is humid) goes toward DE-HUMIDIFICATION, not simply cooling. I'd have to do the psychometrics to know for sure what the maximum temp/humidity you could benefit from would be. At 10 cents per KWH this arrangement saves roughly $1.50 every hour it runs. Even a standard hot water baseboard.... I just checked my Lakewood oil radiator. Whoa, whoa, whoa, easy there guys. Radiators? Boilers? Fan coils? You're missing the big picture here. Usage rates and thermodynamics are interesting, but the savings realized is based on hours of use. You guys are assuming it is always running flat out. A heat recovery system of this type may very well save$1.50 an hour - but only for that hour right after you take your shower and run the dishwasher. The rest of the day, your hot water heater uses only about 100W. ~$.015 / hr. THAT is why it is not economically viable. Think about it - saving you$1.50 an hour is $1080 a month. What is your electric bill these days? Last edited: Ivan Seeking Staff Emeritus Science Advisor Gold Member Originally posted by russ_watters Interesting idea, but you have to be VERY careful. Besides mold, the humidity itself can cause you to INCREASE the cooling load on the house even if the air entering the house is below room temp. The vast majority of the energy your air conditioner uses (depending on climate of course - and the northwest is humid) goes toward DE-HUMIDIFICATION, not simply cooling. I'd have to do the psychometrics to know for sure what the maximum temp/humidity you could benefit from would be. True. Still, in my case it worked great within the limits cited. Whoa, whoa, whoa, easy there guys. Radiators? Boilers? Fan coils? You're missing the big picture here. Usage rates and thermodynamics are interesting, but the savings realized is based on hours of use. You guys are assuming it is always running flat out. A heat recovery system of this type may very well save$1.50 an hour - but only for that hour right after you take your shower and run the dishwasher. The rest of the day, your hot water heater uses only about 100W. ~$.015 / hr. THAT is why it is not economically viable. Think about it - saving you$1.50 an hour is $1080 a month. What is your electric bill these days? Well, I don't recall anyone citing$1000 per month benefit. Also, if the system is properly designed, which requires the use of a second insulated water tank, the practical problems that you cite can be accomodated...at least mostly. Again though, this gets into more cost with a longer period for your return on investment. This is the trap that many people and systems fall into. Have I mentioned the Hydrogen alternative? russ_watters Mentor Originally posted by Ivan Seeking Well, I don't recall anyone citing $1000 per month benefit. Aartman said$1.50 /hr. Actually though he also said 1-2 year payback for 3333 hrs use. At 2 years, thats 9hr/day or $410 / month. In any case, that way off how a water heater is actually used - an order of magnitude at least. I only use water for 1 person in an apartment, but my TOTAL electric bill for a month in the spring is <$20. Thats hot water, refrigerator, my computer, and my entertainment center. The hot water can't be more than $5 of that (which would be an average of 55W). And I average about 1.5 showers a day since I work out. I also have the thermostat on the water heater all the way up. Last edited: Ivan Seeking Staff Emeritus Science Advisor Gold Member Originally posted by russ_watters Aartman said$1.50 /hr. Actually though he also said 1-2 year payback for 3333 hrs use. At 2 years, thats 9hr/day or $410 / month. In any case, that way off how a water heater is actually used - an order of magnitude at least. posted by IvanEven using these numbers, the two years is probably more like 8 or 10. I agree...maybe more like 20 years. I only use water for 1 person in an apartment, but my TOTAL electric bill for a month in the spring is <$20. Thats hot water, refrigerator, my computer, and my entertainment center. The hot water can't be more than $5 of that (which would be an average of 55W). And I average about 1.5 showers a day since I work out. I also have the thermostat on the water heater all the way up. This brings up an interesting point. The maximum momentary energy demand is often quite different - by up to 5 times or more - from the average demand. Distribution of demand makes alternative sources much more viable. I have played with PWM on the heating coils for a full sized space heater. Instead of running the 20,000 watt heat load for a few minutes 10 times a day, the idea was to modulate one of the four coils as a variable load. This would ensure the maximum power transfer from the hydro generator [about 3000 watts continuous edit: but widely variable over days and weeks]. The regular coils and increased fan speed would kick in as needed. Also, by increasing the max temp on the water heater, we could dump excess energy into this system; if properly coupled. I have been playing with the hydro stuff for years but I have been afraid to spend the money for a dam. It is a risky investment. By the way, if I run electric heat, I can easily spend$150 a month on heat and hot water. For a time we had a large house, in excess of 2800 sq ft, that could fetch a $300 electric bill each month in mid winter. In very cold areas of the US, the equivalent cost of electric heat is hidden in the prices of cheap oil heat. Have I mentioned the real energy costs in a gallon of oil? Last edited: Originally posted by russ_watters Aartman said$1.50 /hr. Actually though he also said 1-2 year payback for 3333 hrs use. At 2 years, thats 9hr/day or $410 / month. In any case, that way off how a water heater is actually used - an order of magnitude at least. I only use water for 1 person in an apartment, but my TOTAL electric bill for a month in the spring is <$20. Thats hot water, refrigerator, my computer, and my entertainment center. The hot water can't be more than $5 of that (which would be an average of 55W). And I average about 1.5 showers a day since I work out. I also have the thermostat on the water heater all the way up. True, the most you could save has to be less than you spend for water heating now. However, I believe I overestimated the cost as well. Insulated storage tank, fan coil unit, circulator, some piping and valves, electrical connections, controls, if he installs it all himself shouldn't cost$5000.00. Also, the projected savings reduce as the attic cools and the water gets hotter (the temperature difference reduces between the EWT and EAT). I should have worked a few of the numbers before posting the response. However, you do get the benefit of "free cooling" of the attic space. This was included in my savings number. I like this system because you are transferring your heat from an unwanted heat source and in the process possibly decreasing the load on the home's AC system. With Solar panels, you block some of the sun from striking the roof, if your panels are mounted on the roof, but probably not significantly effecting the cooling load on the house. I like systems that provide multiple benefits. Actually another way to look at this is that you are air conditioning your attic and in the process getting some free hot water.	2021-05-14 07:14:57	{"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": 0.41004714369773865, "perplexity": 1552.189136552883}, "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-20210514060536-20210514090536-00292.warc.gz"}
https://communitydata.science/~ads/teaching/2019/stats/r_lectures/w09-R_lecture.html	For all of the examples this week, I’ll work with the population.tsv dataset from back in Week 5. The following lines of code load it and clean it a bit. Since we’ve worked with this dataset before I will not revisit the process of “getting to know” it. d <- read.delim(url("https://communitydata.science/~ads/teaching/2019/stats/data/week_05/population.tsv")) d$j <- as.logical(d$j) d$l <- as.logical(d$l) d$k <- factor(d$k, levels=c(1,2,3), labels=c("some", "lots", "all")) d <- d[complete.cases(d),] ## Transformations It is often necessary to transform variables for modeling (we’ll discuss some reasons why in class). Here are some common transformations with example code to perform them in R. Keep in mind that you also know some others (e.g., you know how to standardize a variable or take the square root). ### Interaction terms Interaction terms are best handled using the I() function (note the capitalization). I start with a “base” model and update it to add the interaction. m.base <- formula(y ~ x + j) summary(lm(m.base, data=d)) ## ## Call: ## lm(formula = m.base, data = d) ## ## Residuals: ## Min 1Q Median 3Q Max ## -4.9986 -2.4964 0.0199 2.5803 5.1769 ## ## Coefficients: ## Estimate Std. Error t value Pr(>\|t\|) ## (Intercept) -0.07040 0.12358 -0.570 0.569 ## x 2.98853 0.03016 99.103 <2e-16 * ## jTRUE 0.06583 0.13818 0.476 0.634 ## --- ## Signif. codes: 0 '' 0.001 '' 0.01 '' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.01 on 1897 degrees of freedom ## Multiple R-squared: 0.8383, Adjusted R-squared: 0.8381 ## F-statistic: 4917 on 2 and 1897 DF, p-value: < 2.2e-16 m.i <- update.formula(m.base, . ~ . + I(xj)) summary(lm(m.i, data=d)) ## ## Call: ## lm(formula = m.i, data = d) ## ## Residuals: ## Min 1Q Median 3Q Max ## -5.0670 -2.5254 -0.0188 2.5669 5.4437 ## ## Coefficients: ## Estimate Std. Error t value Pr(>\|t\|) ## (Intercept) 0.02816 0.14742 0.191 0.849 ## x 2.94958 0.04380 67.340 <2e-16 ** ## jTRUE -0.12630 0.20894 -0.604 0.546 ## I(x * j) 0.07402 0.06039 1.226 0.220 ## --- ## Signif. codes: 0 '*' 0.001 '' 0.01 '' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.01 on 1896 degrees of freedom ## Multiple R-squared: 0.8384, Adjusted R-squared: 0.8382 ## F-statistic: 3279 on 3 and 1896 DF, p-value: < 2.2e-16 ### Polynomial (square, cube, etc.) terms Polynomial terms can easily be created using I() as well: m.poly <- update.formula(m.base, . ~ . + I(x^2)) summary(lm(m.poly, data=d)) ## ## Call: ## lm(formula = m.poly, data = d) ## ## Residuals: ## Min 1Q Median 3Q Max ## -5.1627 -2.5549 0.0013 2.5957 5.1762 ## ## Coefficients: ## Estimate Std. Error t value Pr(>\|t\|) ## (Intercept) -0.004589 0.147378 -0.031 0.975 ## x 2.922286 0.086249 33.882 <2e-16 ## jTRUE 0.062671 0.138247 0.453 0.650 ## I(x^2) 0.008989 0.010965 0.820 0.412 ## --- ## Signif. codes: 0 '' 0.001 '' 0.01 '' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.01 on 1896 degrees of freedom ## Multiple R-squared: 0.8383, Adjusted R-squared: 0.8381 ## F-statistic: 3277 on 3 and 1896 DF, p-value: < 2.2e-16 Need higher order polynomials? Try including I(x^3) and so on… Creating polynomials this way is intuitive, but can also create a little bit of a messy situation for reasons that go beyond the scope of our course. In these circumstances, using the poly() function is useful (look up “orthogonalized polynomials” online to learn more). Generally speaking, creating polynomials in this way impacts the interpretation as well as the model estimates, so you should only use it if you need to and once you’ve taken the time to actually learn what is happening. That said, here’s what the code could look like: m.poly2 <- formula(y ~ j + poly(x,2)) summary(lm(m.poly2, data=d)) ## ## Call: ## lm(formula = m.poly2, data = d) ## ## Residuals: ## Min 1Q Median 3Q Max ## -5.1627 -2.5549 0.0013 2.5957 5.1762 ## ## Coefficients: ## Estimate Std. Error t value Pr(>\|t\|) ## (Intercept) 7.69671 0.09725 79.143 <2e-16 * ## jTRUE 0.06267 0.13825 0.453 0.650 ## poly(x, 2)1 298.44632 3.01172 99.095 <2e-16 * ## poly(x, 2)2 2.46880 3.01155 0.820 0.412 ## --- ## Signif. codes: 0 '*' 0.001 '' 0.01 '' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.01 on 1896 degrees of freedom ## Multiple R-squared: 0.8383, Adjusted R-squared: 0.8381 ## F-statistic: 3277 on 3 and 1896 DF, p-value: < 2.2e-16 Higher order (to the nth degree) terms can be created by using higher values of n as an argument to (e.g. poly(x, n)). ### Log-transformations We covered log transformations (usually natural logarithms) before, but just in case, here they are again. I usually default to using log1p() because it is less prone ot fail in the event your data (like mine) contains many zeroes. That said, if you have a lot of -1 values you may need something else: m.log <- update.formula(m.base, . ~ log1p(x) + j) summary(lm(m.log, data=d)) ## ## Call: ## lm(formula = m.log, data = d) ## ## Residuals: ## Min 1Q Median 3Q Max ## -7.1239 -2.8823 -0.1261 2.5982 13.4045 ## ## Coefficients: ## Estimate Std. Error t value Pr(>\|t\|) ## (Intercept) -2.9937 0.1813 -16.52 <2e-16 ## log1p(x) 9.8895 0.1288 76.79 <2e-16 * ## jTRUE 0.2134 0.1694 1.26 0.208 ## --- ## Signif. codes: 0 '*' 0.001 '' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 3.691 on 1897 degrees of freedom ## Multiple R-squared: 0.7569, Adjusted R-squared: 0.7566 ## F-statistic: 2953 on 2 and 1897 DF, p-value: < 2.2e-16 Keep in mind that you can use other bases for your logarithmic transformations. Check out the documentation for log() for more information. ## Interpreting regression results with model-predicted values When you report the results of a regression model, you should provide a table summarizing the model as well as some interpretation that renders the model results back into the original, human-intelligible measures and units specific to the study. This was covered in one of the resources I distributed last week (the handout on logistic regression from Mako Hill), but I wanted to bring it back because it is important. Please revisit that handout to see a worked example that walks through the process. The rest of this text is a bit of a rant about why you should bother to do so. When is a regression table not enough? In textbook/homework examples, this is not an issue, but in real data it matters all the time. Recall that the coefficient estimated for any single predictor is the expected change in the outcome for a 1-unit change in the predictor holding all the other predictors constant. What value are those other predictors held constant at? Zero! This is unlikely to be the most helpful or intuitive way to understand your estimates (for example, what if you have a dichotomous predictor, what does it mean then?). Once your models get even a little bit complicated (quick, exponentiate a log-transformed value and tell me what it means!), the regression-table-alone approach becomes arguably worse than useless. What is to be done? Provide predicted estimates for real, reasonable examples drawn from your dataset! For instance, if you were regressing lifetime earnings on a bunch of different predictors including years of education, gender, race, age, and height, you would, of course, start by showing your readers the table that includes all of the coefficients, standard errors, etc. Then you chould also provide some specific predicted values for “prototypical” individuals in your dataset. Regression models usually incorporate earnings as a square-root or log-transformed measure, so the table of raw model results won’t be easy to interpret. It is probably far more helpful to translate the model results into estimates of how much more/less you would we estimate 30 year old woman of average height with a college degree to change if they were white vs. asian/pacific islander. These prototypical predicted values (also sometimes referred to as “marginal effects”) may be presented as specific point-estimates in the text and/or using a visualization of some sort (e.g., lines plotting the predicted lifetime earnings by race over the observed range of age…). You can (and should!) even generate confidence intervals around them (But that’s a whole separate rant…). The point that I hope you take away is that just because you produced a regression table with some p-values and stars in it, your job is not done. You should always do the work to convey your results in a human-intelligible manner by translating the model back into some model-predicted estimates for reasonable combinations of your predictor variables. Once you’ve got the hang of that, you should also work on conveying the uncertainty/confidence around your predictions given the data/model.	2019-12-15 02:39:35	{"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": 0.5006354451179504, "perplexity": 2590.010082601635}, "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-2019-51/segments/1575541301014.74/warc/CC-MAIN-20191215015215-20191215043215-00212.warc.gz"}
http://www.math.gatech.edu/seminars-and-colloquia-by-series?series_tid=55&page=5	## Seminars and Colloquia by Series Friday, January 30, 2009 - 12:30 , Location: Skiles 269 , Jinyong Ma , School of Mathematics, Georgia Tech , Organizer: I plan to give a simple proof of the law of iterated logarithm in probability, which is a famous conclusion relative to strong law of large number, and in the proof I will cover the definition of some important notations in probability such as Moment generating function and large deviations, the proof is basically from Billingsley's book and I made some. Friday, January 23, 2009 - 12:30 , Location: Skiles 269 , Linwei Xin , School of Mathematics, Georgia Tech , Organizer: In this talk, I will focus on some interesting examples in the conditional expectation and martingale, for example, gambling system "Martingale", Polya's urn scheme, Galton-Watson process, Wright-Fisher model of population genetics. I will skip the theorems and properties. Definitions to support the examples will be introduced. The talk will not assume a lot of probability, just some basic measure theory.	2018-05-22 19:33:07	{"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": 0.8191781640052795, "perplexity": 728.5691487588421}, "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-2018-22/segments/1526794864872.17/warc/CC-MAIN-20180522190147-20180522210147-00511.warc.gz"}
https://physics.stackexchange.com/questions/177621/charge-conservation-in-the-complex-klein-gordon-field	# Charge conservation in the complex Klein-Gordon Field This is an extremely naive question (based on a knowledge of chapter 2 of peskin and schroeder) so apologies for any things that seem obvious. The complex scalar field, when quantized, has a conserved charge $$Q \propto\int d^3x\left(\phi^(x)\dot\phi(x)-\dot\phi^(x)\phi(x)\right)=\int\frac{d^3p} {(2\pi)^3}\Big(a^\dagger(\vec p)a(\vec p)-b^\dagger(\vec p)b(\vec p)\Big)$$ (up to an infinite constant, etc). We interpret the $a$ particles as positively charged and the $b$ particles as equally negatively charged, and further we see that $$Q\propto N(a)-N(b)$$ where $N(a,b)$ are the number operators. According to this, charge conservation predicts that if we create an $a$ particle then a $b$ particle must be created also to cancel out charge (and similarly for destruction). 1. In general, does this mean that no charged particles can be created in a QFT without a corresponding antiparticle appearing also (and is this the mathematical apparatus usually used to display this?) 2. Also, if this is all true, how is it even possible that there are more electrons in the universe than positrons?	2020-10-30 02:06:52	{"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": 0.6958136558532715, "perplexity": 310.32480467009117}, "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/1603107906872.85/warc/CC-MAIN-20201030003928-20201030033928-00707.warc.gz"}
https://www.physicsforums.com/threads/math-question-need-help-badly.66381/	# Math Question, need help badly. 1. Mar 7, 2005 ### lvlastermind I've been stuck on this question for awhile. Q: Square numbers 1, 4, 9, 16, 25.... are the values of the function s(n)=n^2, when n is a positive integer. The triangular numbers t(n)=(n(n+1))/2 are the numbers t(1)=1, t(2)=3, t(3)=6, t(4)=10. Prove: For all positive integers n, s(n+1) = t(n) + t(n+1) I've tride alot of things and come to the conclusion that I cant get my answer by using polynomials. I think that if you subsitiute t(n)=(n(n+1))/2 into the equation and simplify to get (n+1)^2 I will be done. My problem is that I'm having troubles doing this. Any sugestions??? 2. Mar 7, 2005 ### TsunamiJoe $$( \frac{1} {2} ( n - 1 ) n ) ^ 2$$ is most similiar to what your talking about, personaly i prefer the: $$( \frac{n} {2} ( n + 1 ) ) ^ 2$$ orr this could also be it: $$S_N = \frac{N}{2} ( A_1 + A_N)$$ and again im only regurgitating equations on you that look like what you could be searching for Last edited: Mar 7, 2005 3. Mar 7, 2005 ### vincentchan expand the right hand side and rearrange it into the form of (n+1)^2 = s(n+1) note: RHS = t(n)+t(n+1) = n(n+1)/2 + (n+1)((n+1)+1)/2 4. Mar 7, 2005 ### vitaly After changing n to (n+1), you get: (n+1)^2 = n(n+1)/2 + (n+1)((n+1)+1)/2) = (n+1)^2 = (n^2+n)/2 + (n+1)(n+2)/2 = (n+1)^2 = (n^2+n)/2 + (n^2+3n+2)/2 Since they have common denominators, we can add the right side together: = (n+1)^2 = (2n^2 + 4n + 2)/2 = (n+1)^2 = (2n+2)(n+1)/2 = (n+1)^2 = 2(n+1)(n+1)/2 The two's cancel out, which gives the needed proof: = (n+1)^2 = (n+1)(n+1) 5. Mar 7, 2005 ### lvlastermind how did you go from = (n+1)^2 = (2n^2 + 4n + 2)/2 to = (n+1)^2 = (2n+2)(n+1)/2 6. Mar 7, 2005 ### lvlastermind Thanks for the help all, I got it.	2017-11-20 19:21:09	{"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": 0.6233192682266235, "perplexity": 3907.187241614983}, "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-2017-47/segments/1510934806124.52/warc/CC-MAIN-20171120183849-20171120203849-00646.warc.gz"}
https://tex.stackexchange.com/questions/428456/variable-argument-macro-to-define-splitting-polynomial	# Variable argument macro to define splitting polynomial I need a macro that behaves the following: \mpoly{x}{1}{2} outputs (x+1)(x+2) \mpoly{x}{1}{2}{3} outputs (x+1)(x+2)(x+3) \mpoly{x}{1}{2}{3}{5} outputs (x+1)(x+2)(x+3)(x+5) and so on. I am not at all confident with the variable length argument processing by tex. Could anyone help me with this? • Will the arguments of \mpoly always be either a single letter or a single number, or could they be more general inputs? And how is LaTeX supposed to "know" if some argument in curly braces is (a) still another argument of \mpoly or (b) some other document element? – Mico Apr 25 '18 at 10:59 I streamline the syntax by putting all the term data in a comma separated list in the 2nd argument. I use listofitems to parse the list (the default list separtor is a comma, but that could be changed). The package's \foreachitem macro allows easy regurgitation. \documentclass{report} \usepackage{listofitems} \newcommand\mpoly[2]{% \foreachitem\x\in\myterms{(#1+\x)}% } \begin{document} $y_1 =\mpoly{x}{1,2}$ $y_2 =\mpoly{x}{1,2,3}$ $y_3 = \mpoly{x}{1,2,3,5}$ \end{document} This can be generalized to a more inclusive format, with the use of nested parsing, to allow multiple variables as well as setting the +/- operation: \documentclass{report} \usepackage{listofitems} \newcommand\mpoly[1]{% \setsepchar{/+\|\|-/,} \foreachitem\x\in\myterms[]{ \foreachitem\y\in\myterms[\xcnt,2]{(\myterms[\xcnt,1]\mytermssep[\xcnt,1]\y)}% }% } \begin{document} $y_1 =\mpoly{x+1,2 y-3,4}$ $y_2 =\mpoly{x+2,3 * x-4,5,6,7}$ $y_3 = \mpoly{x-1,2 * y+3,5 * z-6}$ \end{document} • +1. Very nice use of the listofitems package! – Mico Apr 25 '18 at 11:03 • @mxant I have generalized the solution. – Steven B. Segletes Apr 25 '18 at 11:21 • @Mico I made it even nicer. – Steven B. Segletes Apr 25 '18 at 11:32 Different syntax could be more flexible: \usepackage{pgffor} \newcommand\mpoly[2]{\foreach\x in{#2}{(#1\x)}} That would let you do \mpoly{x-}{1,2,3} or \mpoly{x+}{2,...,5}. Another option could be \newcommand\mpolyn[3]{\foreach\x in{#3}{(#1#2\x)}} That would let you do \mpolyn x-{1,2,3} or \mpolyn x+{2,...,5}. Or may be cleaner definition for this last synax \newcommand\mpolyn{} \protected\def\mpolyn#1#{\mpolynaux{#1}} \protected\def\mpolynaux#1#2{\foreach\x in{#2}{(#1\x)}} And that way you can \mpolyn xyz - {1,2,3} or \mpolyn \ln(x) + {2,...,5} for instance.	2019-06-18 17:00:14	{"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": 0.7976851463317871, "perplexity": 3323.014084325416}, "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/1560627998808.17/warc/CC-MAIN-20190618163443-20190618185443-00531.warc.gz"}
https://solvedlib.com/n/2020-fall-main-suno-general-cher-coutses-420201-sche-132n,13410800	2020 FALL Main (SUNO) General Cher coutses 420201 SCHE-132N-01 Topic Gases Homework 5sample 0f 35.1 Of methane gas has Tolume Question: 2020 FALL Main (SUNO) General Cher coutses 420201 SCHE-132N-01 Topic Gases Homework 5 sample 0f 35.1 Of methane gas has Tolume of 4.24L at = pressure of 2.70 AMn Calculate the temperature: Select one; le tion 47,-K 3.9-K 3376 63.8 K searcn 0 0 a 5 5 Similar Solved Questions Independent random samples of n1 = 150 and n2 = 150 observationswere randomly selected from binomial populations 1 and 2,respectively. Sample 1 had 98 successes, and sample 2 had 103successes. (a) Suppose you have no preconceived idea as to whichparameter, p1 or p2, is the larger, but you want to detect only adifference between the two parameters if one exists. What shouldyou choose as the alternative hypothesis for a statistical test?The null hypothesis? H0: (p1 âˆ’ p2) = 0 versus Ha: (p1 âˆ’ p Independent random samples of n1 = 150 and n2 = 150 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 98 successes, and sample 2 had 103 successes. (a) Suppose you have no preconceived idea as to which parameter, p1 or p2, is the larger, but you want t... Proton Is acted on by uniform electric field of magnitude 223 N/C pointing the positive direction_ The panticle In what direction wlll the Initially at rest charge move? Seleci _(b) Determine the work done by the electric feld when the particle has moved through distance of 3.55 cm from Its initial position.(c) Detenmine the change in electric potential energy ot the charged particle.(d) Determine the speed of tho charged particle. mis proton Is acted on by uniform electric field of magnitude 223 N/C pointing the positive direction_ The panticle In what direction wlll the Initially at rest charge move? Seleci _ (b) Determine the work done by the electric feld when the particle has moved through distance of 3.55 cm from Its initial... How will the role of RT Educator affect healthcare outcomes in the future? How will the role of RT Educator affect healthcare outcomes in the future?... Prepare journal entries to record the following merchandising transactions of Thompson's, which uses the perpetual inventory... Prepare journal entries to record the following merchandising transactions of Thompson's, which uses the perpetual inventory system and the gross method. (Hint: It will help to identify each receivable and payable; for example, record the purchase on July 1 in Accounts Payable—Knight.) ... Car with mass of 1500 kg travels around G0Om . The friction corner at 105 Kr/hr: The radius of the curve oetficlent between the pavement and the tires 035 The superelevation (bank) of the road is 7% (4") &Hi=_What is the centripetal acceleration of the vehicle? get At the current speed, does the car slide going around the corner? (show the FBD and proof of your answer to oints) car with mass of 1500 kg travels around G0Om . The friction corner at 105 Kr/hr: The radius of the curve oetficlent between the pavement and the tires 035 The superelevation (bank) of the road is 7% (4") &Hi=_ What is the centripetal acceleration of the vehicle? get At the current speed, do... 7. tinea versicolor 8. genital herpes 9. ringworm Herpes simplex virusa Tirnea corporis SKIN CANCER Under... 7. tinea versicolor 8. genital herpes 9. ringworm Herpes simplex virusa Tirnea corporis SKIN CANCER Under each photograph, list at least three facts for each type of skin cancer Basal cell carcinoma Chapter 11 Disorders and Diseases of the Skin Squamous cell carcinoma Malignant melanoma 11 Disorders... 1 8 8 8 8... Find the triple scalar product u .W ) of the vectors u(13,0,0),v = (-16,-3,-2) , and w (-11,-15,-1) .Provide your answer below: Find the triple scalar product u . W ) of the vectors u (13,0,0),v = (-16,-3,-2) , and w (-11,-15,-1) . Provide your answer below:... You are a manager of Nvidia and your only significant competitor in the mainstream graphics card... You are a manager of Nvidia and your only significant competitor in the mainstream graphics card market is the ATI subsidiary of Advanced Micro Devices. ATI and Nvidia both expect to select their output of the next generation of graphics card in July of next year. Nvidia’s graphics cards and A... (10%) For patients with schizophrenia there significant difference of concentrations between Oh and Zh? Please answer the queston with tne t test ofu=0.US. You should provide the following five paru of the test: (i) Hypotheses and any assumptions required for vour statement: (ii) Testing statistics (iii) Null distribution. teshng statistics (iv) Calculation with the Stabstical conclusion and practica conclusion (b) (S%3) what the non parametric test YDU can use answer the same question (a)? Just (10%) For patients with schizophrenia there significant difference of concentrations between Oh and Zh? Please answer the queston with tne t test ofu=0.US. You should provide the following five paru of the test: (i) Hypotheses and any assumptions required for vour statement: (ii) Testing statistics ...	2023-03-20 10:24:34	{"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": 2, "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": 0.46627676486968994, "perplexity": 6088.440964842146}, "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-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00792.warc.gz"}
https://physics.stackexchange.com/questions/257427/according-to-einstein-brian-greene-does-the-photon-remain-stationary-in-the-f	# According to Einstein & Brian Greene, does the photon remain stationary in the fourth dimension? [duplicate] According to Einstein and Brian Greene, does it logically follow that the photon remains stationary in the fourth dimension? In An Elegant Universe, Brian Greene writes: “Einstein found that precisely this idea—the sharing of motion between different dimensions—underlies all of the remarkable physics of special relativity, so long as we realize that not only can spatial dimensions share an object’s motion, but the time dimension can share this motion as well. In fact, in the majority of circumstances, most of an object’s motion is through time, not space. Let’s see what this means.” Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49 Brian Greene and Albert Einstein also state that there is one and only one velocity for all entities through the four dimensions--the velocity of light or c. A photon travels at c through the three spatial dimensions. All of its velocity is directed through the three spatial dimensions. Thus Brian and Einstein are stating that a photon must be stationary in the fourth dimension. For if the photon had any velocity component in the the fourth dimension, its velocity would be different from c, which is not the case. On the other hand, if an object is stationary in the three spatial dimensions, it must be moving at c through the fourth dimension. We can summarize this as: Axiom: All entities have one velocity through the four dimensions--c. (Einstein & Brian Greene). Axiom: The velocity of light (photons) is c through the three spatial dimensions. (Einstein) Theorem: The photon remains stationary in the fourth dimension, as all of its velocity c is through the three spatial dimensions. Does this logic make sense? Also, do you prefer using the word "Axiom" or "Postulate"? An Axiom or a Postulate is a Truth. A Theorem is that which follows logically from Axioms.	2019-08-17 11:27:16	{"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": 0.6905179619789124, "perplexity": 559.0645917219847}, "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-2019-35/segments/1566027312128.3/warc/CC-MAIN-20190817102624-20190817124624-00424.warc.gz"}
https://planetmath.org/RealTree	# real tree A metric space $X$ is said to be a real tree or $\mathbb{R}$-tree, if for each $x,y\in X$ there is a unique arc from $x$ to $y$, and furthermore this arc is an isometric http://planetmath.org/node/429embedding. Every real tree is a hyperbolic metric space; moreover, every real tree is 0 hyperbolic. The Cayley graph of any free group is considered to be a real tree. Note that its graph is a tree in the graph theoretic sense. To make it a real tree, we view the edges as isometric (http://planetmath.org/Isometric) to the line segment $[0,1]$ under a (surjective) isometry (http://planetmath.org/Isometry) and attach the edges to the tree. The resulting 1-complex is then a locally finite real tree. Because of this result, every free group is a hyperbolic group. Title real tree Canonical name RealTree Date of creation 2013-03-22 15:16:55 Last modified on 2013-03-22 15:16:55 Owner GrafZahl (9234) Last modified by GrafZahl (9234) Numerical id 10 Author GrafZahl (9234) Entry type Definition Classification msc 54E99 Classification msc 54E40 Synonym $\mathbb{R}$-tree Related topic MetricSpace Related topic Arc Related topic Curve Related topic SNCFMetric Related topic Isometry Related topic FreeGroup Related topic HyperbolicGroup	2018-11-17 21:40:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 7, "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": 0.4957751929759979, "perplexity": 1556.2217051452633}, "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/1542039743854.48/warc/CC-MAIN-20181117205946-20181117231946-00133.warc.gz"}
https://newproxylists.com/reductions-reduction-of-the-exact-coverage-to-the-total-sum-in-practice/	# reductions – Reduction of the exact coverage to the total sum in practice! The reduction of the exact coverage to the sum of subset has already been discussed at this forum. What interests me is the practical aspect of this reduction, which I will discuss in section 2 of this post. For you who do not know these problems, I will define them and show the reduction Exact Cover $$leq_p$$ Sum of subset in section 1. For readers already familiar with these issues, the reduction can move forward. section 2. ## section 1 the Exact coverage defined as follows: Given a family $${S_j }$$ of subsets of a set $${u_i, i = 1,2, ldots, t }$$ (often called the Universe), find a subfamily $${T_h } subseteq {S_j$$ such as sets $$T_h$$ are disjoint and $$cup T_h = cup S_j = {u_i, i = 1,2, ldots, t }$$. the Sum of subset is defined as follows: Given a set of positive integers $$A = {a_1, a_2, ldots, a_r }$$ and another positive integer $$b$$ find a subset $$A subseteq A$$ such as $$sum_ {i in A a_i = b$$. For the reduction Exact coverage $$leq_p$$ Subset Sum I followed that of Karp R.M. (1972) Reducibility among combinatorial problems Let $$d = \| {S_j } \| + 1$$and let $$epsilon_ {ji} = begin {cases} 1 & text {if} & u_i in S_j, \ 0 & text {if} & u_i notin S_j, end {cases}$$ then $$a_j = sum_ {i = 1} ^ {t} epsilon_ {ji} d ^ {i-1}, tag {1}$$ and $$b = frac {d ^ t-1} {d-1}. tag {2}$$ ## section 2 In practice (meaning real-world problems), the size of the universe for the exact coverage problem can be very large, for example. $$t = 100$$. This would mean that if you reduce the problem of exact coverage to the problem of the sum of the subsets, the numbers $$a_j$$ content in the set $$A$$ for the sum of subset could be extremely large, and the gap between $$min {A }$$ and $$max {A }$$ can be huge. For example, let's say $$t = 100$$ and $$d = 10$$, then it is possible to have a $$a_j propto 10 ^ {100}$$ and another $$a_i propto 10$$. Implementing on a computer can be very difficult because adding large numbers with small numbers largely ignores the small number. $$10 ^ {16} + 1 – 10 ^ {16} = 0$$. You can probably see why this could be a problem. Is it then possible to reduce the exact coverage to the subset sum more conveniently, avoiding large numbers, and having the integers in $$A$$ are of a more reasonable size? I know that it is possible to multiply both $$A$$ and $$b$$ by an arbitrary factor $$c$$ to resize the problem, but the fact remains this gap between the smallest and the largest integer possible $$A$$ is astronomical.	2019-04-25 20:46:04	{"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": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.825021505355835, "perplexity": 229.6845810102479}, "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-2019-18/segments/1555578733077.68/warc/CC-MAIN-20190425193912-20190425215912-00414.warc.gz"}
https://www.groundai.com/project/geant4-and-phits-simulations-of-the-shielding-of-neutrons-from-252cf-source/	GEANT4 and PHITS simulations of the shielding of neutrons from {}^{252}Cf source # GEANT4 and PHITS simulations of the shielding of neutrons from $^{252}$Cf source ## Abstract Monte Carlo simulations by using GEANT4 and PHITS are performed for studying neutron shielding abilities of several materials, such as graphite, iron, polyethylene, NS-4-FR and KRAFTON-HB. As a neutron source Cf is considered. For the Monte Carlo simulations by using GEANT4, high precision (G4HP) models with G4NDL 4.2 based on ENDF/B-VII data are used. For the simulations by using PHITS, JENDL-4.0 library are used. The neutron dose equivalent rates with or without five different shielding materials are estimated and compared with the experimental values. It is found that the differences between the shielding abilities calculated by using GEANT4 with G4NDL 4.2 and PHITS with JENDL-4.0 library are not significant for all the cases considered in this work. We investigate the accuracy of the neutron dose equivalent rates obtained by GEANT4 and PHITS by comparing our simulation results with experimental data and other values calculated earlier. The calculated neutron dose equivalent rates agree well with the experimental dose equivalent rates within 20% errors except for polyethylene. For polyethylene material, discrepancy between our calculations and the experiments are up to 40%, but all simulations show consistent features. Neutron shielding, Cf, GEANT4, PHITS, G4NDL 4.2, JENDL-4.0 ###### pacs: 07.05.Tp, 28.20.Fc, 02.70.Uu, 87.53.Bn ## I Introduction Accurate estimations of the neutron shielding abilities are essential for safety requirement in the design of facilities such as accelerators and nuclear reactors or a shielding container of neutron emitting sources. In determining the shielding abilities, characteristics of the materials is a major factor. Many studies have been done for neutron shielding abilities for various shielding materials ueki1 (); ueki2 (); ueki3 (); ueki4 (), shielding designs int0 (); int1 (); phits_ex_shield3 (), further development of new neutron shielding materials int3 (); int4 () and etc. Also, benchmark simulations by using different Monte Carlo codes bench1 (); bench2 (); bench3 (); bench4 (); bench5 (); bench6 (); bench7 (); bench8 () have been done with MCNP, MCNP4B2, SAS, SCALE and GEANT4. Effectiveness of various shielding materials for neutrons from a Cf source were experimentally evaluated in ueki4 (). In Ref. bench8 (), the neutron shielding was studied with GEANT4 code g4n1 (). For neutron interactions, both high precision (G4HP) models with G4Neutron Data Library (G4NDL) 3.13 based on ENDF/B-VI library and low energy parameterized (G4LEP) models were used and tested. Relative neutron dose equivalent rates were calculated and the results were compared with the experimental data ueki4 (). It was shown that G4HP models were a good candidate for accurate simulations of neutron shieldings. As an extension of these previous studies bench1 (); bench2 (); bench3 (); bench4 (); bench5 (); bench6 (); bench7 (); bench8 (), we have performed in this work Monte Carlo simulations for neutron shielding by using GEANT4 and PHITS phits1 (); phits2 (); phits3 (). In Ref. bench8 () G4NDL 3.13 based on ENDF/B-VI was used for GEANT4 v9.3, but the latest version of nuclear data available for GEANT4 is now G4NDL 4.X based on ENDF/B-VII. In this work, we also used different Monte Carlo code PHITS for a benchmark purpose. For neutron interactions, G4HP models with G4NDL 4.2 based on ENDF/B-VII library and JENDL-4.0 library are used for GEANT4 v9.6 and PHITS v2.52 simulations, respectively. As a neutron source, Cf is assumed. Cf emits neutrons with an average energy of 2.2 MeV by spontaneous fission. In Ref. ueki3 (); ueki4 () the neutron dose equivalent rates are extracted instead of measuring neutron spectrum. Thus, we also estimated the neutron dose equivalent rates for comparison with the experimental results ueki3 (); ueki4 (). The neutron dose equivalent rates with and without the shield are estimated for shielding materials such as graphite, iron, polyethylene, NS-4-FR and KRAFTON-HB. Graphite is used in reactor design as a moderator and reflector. Iron is commonly used for the high energy neutron shielding in accelerator facilities. Polyethylene is a popular neutron shielding material that highly contains hydrogen. NS-4-FR is an epoxy resin containing heavy elements together with boron to reduce the production of secondary -rays due to thermal neutron absorption. KRAFTON-HB also contains boron for the same purpose, and was developed as an advanced shielding material for fast breeder reactors. By comparing our results with the experimental data ueki3 (); ueki4 () and the previous simulation results bench1 (); bench3 (); bench5 (), we can compare the accuracy of the neutron dose equivalent rates obtained by GEANT4 and PHITS with new nuclear data libraries. The outline of the paper is as follows. In Sec. II, simulation tools and simulation set up are described. In Sec. III, the calculated neutron energy distributions scored in the detector region and the corresponding neutron dose equivalent rates are shown. The resulting neutron dose equivalent rates are compared with experimental data. A summary is given in Sec. IV. ## Ii Method ### ii.1 Simulation tools As Monte Carlo simulation tools, we use GEANT4 and PHITS and compare the results from them. For the low energy neutron interactions in material, G4HP models with G4NDL based on ENDF library endf () and JENDL library jendl () are used in GEANT4 and PHITS simulations, respectively. Here we list some key features of the simulation tools. GEANT4 : GEANT4 (GEometry ANd Tracking) is a simulation tool kit written in C++ language, which allows microscopic simulations of the propagation of particles interacting with materials. It is being widely used in many different fields, such as neutron shielding studies bench8 (); G4shield2 (), medical physics G4Med1 (); G4Med2 (); Shin1 (); Shin1a (), accelerator based single event upset studies ShinAcc1 (); Shin2 (), environment radiation detection studies G4Det2 (); G4Det3 (); Shin4 (), and etc. In our previous work bench8 (), we showed that G4HP models with G4NDL 3.13 were better than G4LEP models. For this reason, G4HP models with G4NDL 4.2 are used in this work. Both G4HP models and G4LEP models include cross sections for elastic, inelastic scattering, capture, fission and isotope production. The energy range of these classes are from thermal energies to 20 MeV. Data of G4NDL 4.2 come largely from the ENDF/B-VII library. The validations and the detailed descriptions of the GEANT4, G4HP models and G4NDL can be found on the GEANT4 website g4_web (). PHITS : PHITS (Particle and Heavy-Ion Transport code System) is a multi-purpose Monte Carlo transport code system for heavy ions and all particles with the energies from meV up to 200 GeV. It was developed by the collaboration of Japan Atomic Energy Agency (JAEA), Research Organization for Information Science Technology (RIST), High Energy Accelerator Research Organization (KEK), and several other institutes. PHITS is also used for many scientific studies such as space technology phits_ex_space1 (); phits_ex_space2 (), medical physics phits_ex_mp1 (); phits_ex_mp2 (); phits_ex_mp3 (), shielding designs phits_ex_shield1 (); phits_ex_shield2 (); phits_ex_shield3 (), accelerator applications phits_ex_acc1 (); phits_ex_acc2 () and etc. Neutron simulations can be done by using various evaluated nuclear data libraries in PHITS code. JENDL-4.0 library, which is the latest version of JENDL, is used in this work. Additional information and detailed descriptions of PHITS can be found on the web phits_web (). ### ii.2 Simulation set up In this work, we consider the neutron shielding experiments in Ref. ueki3 (); ueki4 (), where the experiments were done to evaluate the effectiveness of various shielding materials for neutrons from a Cf source. Cf emits neutrons with an average energy of 2.2 MeV. For the generation of neutrons from Cf source, Watt fission spectrum watt_1 (); watt_2 (); x5 () are used in our simulations. The spontaneous fission neutron spectrum given by the Watt fission spectrum is expressed as f(E)=exp(−E1.025)sinh(2.926E)1/2, (1) where E is the neutron energy in MeV x5 (). The geometry of the shield and the detector is drawn in Fig. 1. The Cf source is surrounded by a 50 50 50 cm paraffin container block. There is a conical shape of an opening in the paraffin so that the neutrons from the Cf can pass freely and propagate through the air to reach the detector behind the shield. The neutron detector has a cylindrical shape of radius 5.25 cm and length 10 cm. It is assumed that all the neutrons that reach the detector are scored. Shielding materials, source strengths of Cf, d1, d2 and the thicknesses (t) of the shielding materials are tabulated in Table 1. Five different shielding materials such as graphite, iron, polyethylene, NS-4-FR and KRAFTON-HB are considered. The components of these materials and their mass fractions are tabulated in Table 2. Typical simulation snap shots drawn by using OpenGL library are shown in Fig. 2. Figures 2 (a) and 2 (b) show the propagation of neutrons and gammas without and with the shielding material, respectively. It can be seen that a large number of neutrons fly through the opening but are mostly blocked by the shielding material. With this geometry, the energy distributions of the neutrons scored in the detector after escaping through the shielding materials are calculated. To make a comparison with the experimental results given in terms of dose equivalent rates ueki3 (); ueki4 (), we need to calculate dose equivalent rates. To estimate the human biological dose equivalent rates, one often uses a conversion factor which converts the neutron flux to human biological dose equivalent rate. In this work, neutron dose equivalent rates are calculated by using the flux to dose conversion factor from the National Council on Radiation Protection and Measurements (NCRP-38) standard ncrp (). ## Iii Results Simulations are performed by using GEANT4 v9.6 with G4NDL 4.2 and PHITS v2.52 with JENDL-4.0. First, the calculated neutron energy spectra scored in the detector region for various shielding materials are shown. The scored numbers of neutrons are normalized by the number of neutrons generated by the source. We refer to these values as ”counts”. In Ref. bench8 (), the neutron shielding simulations were done by using GEANT4 v9.3 with G4NDL 3.13. The data of G4NDL 3.13 are based on the ENDF/B-VI library. For the comparison between the results of Ref. bench8 () and the present work, the calculations by using GEANT4 v9.3 with G4NDL 3.13 have been also performed and the results are compared. The results from GEANT4 v9.6 with G4NDL 4.2 and PHITS v2.52 with JENDL-4.0 are also compared with each other. The calculated the neutron dose equivalent rates by using the flux to dose conversion factor from NCRP-38 are compared with those from the experiments ueki3 (); ueki4 () and other values calculated earlier bench1 (); bench3 (); bench5 (). ### iii.1 Neutron spectra scored in the detector region Neutron spectra scored in the detector region obtained from GEANT4 with G4NDL 3.13 and G4NDL 4.2 and those from PHITS with JENDL-4.0 are compared with each other. However, differences among the simulation results are not significant for all the cases. For this reason, we show only the results from GEANT4 v9.6 with G4NDL 4.2 and PHITS v2.52 with JENDL-4.0. For brevity, we refer to the calculations by using GEANT4 v9.6 with G4NDL 4.2 and PHITS v2.52 with JENDL-4.0 as simply GEANT4 and PHITS, respectively. Figure 3 shows the energy distributions of the neutrons scored in the detector region after passing through the shielding materials. The results for five different shielding materials with 15 and 25 cm of thicknesses are plotted in Fig. 3 (a) and 3 (b), respectively. It can be seen that graphite and iron reduce the number of neutrons at high energies but not at low energies in comparison with the counts without any shielding material. Also, graphite and iron do not reduce the neutron flux as much as other shielding materials. For polyethylene, NS-4-FR and KRAFTON-HB, which contain the hydrogen element, similar shapes of the spectrum and neutron shielding abilities are observed. It can be seen that those materials reduce the counts by up to two orders of magnitudes in comparison with the counts without any shielding material. Peak and valley structures are observed for both graphite and iron materials in Fig. 3, which can be understood from the total cross sections of the neutron on the elements. Figure 4 shows the energy distributions of the neutrons and the total cross sections of the neutron on the elements of the shielding materials. Total cross sections of the neutron on C, Fe, Fe, Fe and Fe are taken from ENDF/B-VII.1 endf (). Figure 4 (a) shows the energy distributions of the neutrons scored in the detector region with and without graphite materials and the total cross section of the neutron on C. As the thickness of the graphite material increases, the valley of the neutron spectrum near 3.5 MeV becomes pronounced. This feature can be understood by the total cross section of the neutron on C plotted in the lower panel. A broad peak, which mainly comes from the elastic cross section of the neutron on C, is shown near 3.5 MeV endf (). As a result, the neutrons with these energies are more reduced than those with other neutrons. For iron, drastic changes are observed in Fig. 4 (b). Two distinct valleys (at 0.008 and 0.03 MeV) and one peak (0.024 MeV) are shown. One can see that the energy distribution looks similar to a mirror image of the total cross section of the neutron on Fe. The peaks at 0.008 and 0.03 MeV in the lower panel mainly come from the contributions from elastic cross section of the neutron on Fe and Fe, respectively endf (). Also, a very sharp peak at 0.00115 MeV which comes from the contribution of capture cross section of the neutron on Fe endf () is shown in the lower panel. However, the probability that neutrons reach the energies of those sharp peak is very low because the peak has a very narrow width 10 eV. For this reason, this sharp peak at 0.00115 MeV does not produce a visible effect on the neutron counts. ### iii.2 Neutron dose equivalent rates With the energy distributions of the neutrons scored in the detector region and the conversion factors from NCRP-38, we can obtain neutron dose equivalent rates. Figures 5 9 show our results for the experimental dose equivalent rates for five different shielding materials. The upper and lower panels of each figure represent the dose equivalent rates in units of Sv/hr and the ratio of the calculated values to the experimental values (C/E) ueki3 (); ueki4 (), respectively. Figures 5 and 6 show the neutron dose equivalent rates for graphite and iron shielding materials, respectively. One can see that all the calculations agree with the experiments within 20% errors. C/E from both GEANT4 and PHITS are almost independent of thicknesses of the shielding materials. It means that the calculated neutron dose attenuations are very close to those from the experiments. For polyethylene, discrepancies between the experimental values and the simulations values are up to 40% as shown in Fig. 7. All simulations overestimate the experimental dose equivalent rates. Similar features can be seen in Ref. bench6 (). In Ref. bench6 (), even though differences between the calculated dose equivalent rates and the measured one for NS-4-FR and KRAFTON-HB were less than 20%, the calculated dose equivalent rates overestimated the experimental values up to 50% for polyethylene. Neutron dose equivalent rates for NS-4-FR and KRAFTON-HB are plotted in Fig. 8 and Fig. 9, respectively. One can see that the calculated neutron dose equivalent rates agree well with the experimental dose equivalent rates within 10% errors. Also, differences among the calculations are not significant. Figure 10 shows the neutron dose attenuations for five shielding materials considered in this work. The filled symbols and open symbols with lines denote the experimental and the calculated neutron dose attenuations, respectively. Only the results from GEANT4 are denoted in this figure, because differences between the results from GEANT4 and PHITS are not significant. Both the experiments and our simulations show the same trend in this figure. As mentioned before, the calculated and the experimental values for both graphite and iron almost overlap with each other within 5% errors. The differences between the calculated and the experimental values for polyethylene, NS-4-FR and KRAFTON-HB are within 30%, 10% and 10% errors, respectively. In Fig. 10, it can be seen that both graphite and iron materials reduce the neutron dose up to one order of magnitude when the thickness is 35 cm. Even though the energy distributions of the neutrons for graphite differ from those for iron as can be seen in Fig. 4, the neutron dose attenuation for graphite is almost the same as that for iron at t = 5 cm and 15 cm. As the thickness of the shield increases, however, difference between the attenuations for graphite and iron become significant. When polyethylene, NS-4-FR and KRAFTON-HB shielding materials are used, doses are reduced very effectively compared to graphite and iron. Shielding abilities of polyethylene, NS-4-FR and KRAFTON-HB with 15 cm of thickness are comparable to or better than those of graphite and iron with 35 cm of thickness. When the thickness of the shielding materials is larger than 25 cm, neutron doses are reduced by two orders of magnitudes. ## Iv Summary Neutron dose equivalent rates for various shielding materials are calculated by using GEANT4 and PHITS code. As a neutron source, Cf is assumed. Five different shielding materials such as graphite, iron, polyethylene, NS-4-FR and KRAFTON-HB are considered. For low energy neutron interactions, G4HP models with G4NDL 4.2 based on ENDF/B-VII and JENDL-4.0 library are used for GEANT4 and PHITS calculations, respectively. First, the neutron energy distributions scored in the detector region with and without shielding materials are calculated. The results obtained from GEANT4 and PHITS are compared with each other. Also, an old version of GEANT4 and G4NDL 3.13 based on ENDF/B-VI as in bench8 () are considered and the results are compared. It is found that differences between the calculations from GEANT4 and PHITS and the difference between the old and new versions of GEANT4 are not significant for all the cases considered in this work, which shows reliability of these Monte Carlo simulations. Second, the neutron dose equivalent rates with the calculated neutron spectra and conversion factors are obtained. The results are compared with the experimental dose equivalent rates ueki3 (); ueki4 () and the values calculated earlier bench1 (); bench3 (); bench5 (). From the comparison, it is found that GEANT4 and PHITS results based on nuclear data libraries describe the experimental dose equivalent rates quite well for the graphite, iron, NS-4-FR and GRAFTON-HB with the discrepancy between the experimental dose equivalent rates and the calculated values less than 20%. However, in the case of polyethylene, the discrepancy is up to 40%. Other studies bench1 (); bench3 (); bench6 () as well as the present study show consistent features. Neutron dose attenuations for the shields are also obtained. For graphite or iron shielding materials, the simulation results are consistent with the experiments within 5% errors. The differences between the simulations and the experiments for polyethylene, NS-4-FR and KRAFTON-HB are less than 30%, 10% and 10%, respectively. ###### Acknowledgements. This work was supported in part by the Basic Science Research Program through the Korea Research Foundation (NRF-2011-0025116, NRF-2012R1A1A2007826, NRF-2012M2B2A4030183). ### References 1. K. Ueki and Y. Namito, Nucl. Sci. Eng. 96, 30 (1987). 2. K. Ueki and Y. Namito, J. Nucl. Sci. Technol. 26, 411 (1989). 3. K. Ueki, A. Ohashi and Y. Anayma, in Proceedings of New Horizons in Radiation Protection and Shielding Topical Meeting, (Pasco, Washington, USA, April 26-May 1, 1992), p. 130-137. 4. K. Ueki et al., Nucl. Sci. Eng. 124, 455 (1996). 5. J. C. Liu and T. T. Ng, Radiat. Prot. Dosim. 83, 257 (1999). 6. A. X. da Silva and V. R. Crispim, Radiat. Prot. Dosim. 95, 333 (2001). 7. D. Satoh et al., J. Nucl. Sci. Technol. 49, 1097 (2012). 8. K. Okuno, Radiat. Prot. Dosim. 115, 258 (2005). 9. A. M. Sukegawa et al., J. Nucl. Sci. Technol. 48, 585 (2011). 10. H. Taniuchi and B. L. Broadhead, in ANS 8th International Conference on Radiation Shielding, (Arlington, Texas, USA, April 24-27, 1994). 11. B. L. Broadhead, J. S. Tang, R. L. Childs, C. V. Parks and H. Taniuchi, Nucl. Technol. 117, 206 (1997). 12. ”SOFTWARE QUALIFICATION REPORT for MCNP Version 4B2 - A General Monte Carlo N-Particle Transport Code”, 30033-2003 Rev 01, 1998. 13. M. Bace, R. Jecmenica and T. Smuc, in International Conference Nuclear Energy in Central Europe ’99, (Portoroz, Slovenia, September 6-9, 1999), p. 75-81. 14. D. A. Torres, R. D. Mosteller and J. E. Sweezy, LA-UR-04-0122, Los Alamos National Lab., 2004. 15. D. Wiarda, M. E. Dunn, D. E. Peplow, T. M. Miller and H. Akkurt, NUREG/CR-6990, Oak Ridge National Laboratory, 2009. 16. D. E. Peplow, Nucl. Technol. 174, 289 (2011). 17. S. I. Bak, T. S. Park, S. W. Hong, J. W. Shin and I. S. Hahn, J. Korean Phys. Soc. 59, 2071 (2011). 18. S. Agostinelli et al., Nucl. Instrum. Methods Phys. Res. Sect. A 506, 250 (2003). 19. H. Iwase, K. Niita and T. Nakamura, J. Nucl. Sci. Technol. 39, 1142 (2002). 20. K. Niita et al., Radiat. Meas. 41, 1080 (2006). 21. T. Sato et al., J. Nucl. Sci. Technol. 50, 913 (2013). 22. http://www.nndc.bnl.gov/csewg/. 23. http://wwwndc.jaea.go.jp/jendl/jendl.html. 24. S. Avery, C. Ainsley, R. Maughan and J. McDonough, Radiat. Protect. Dosim. 131, 167 (2008). 25. G. Barca et al., Nucl. Phys. B Proc. Suppl. 125, 80 (2003). 26. M. U. Bug et al., Eur. Phys. J. D 60, 85 (2010). 27. J. W. Shin, S. W. Hong, C. I. Lee and T. S. Suh, J. Korean Phys. Soc. 59, 12 (2011). 28. arXiv:1401.0692v1. 29. J. K. Park et al., J. Korean Phys. Soc. 58, 1511 (2011). 30. J. W. Shin et al., J. Korean Phys. Soc. 59, 2022 (2011). 31. S. Hurtado, M. Garcia-Leon and R. Garcia-Tenorio, Nucl. Instr. and Meth. A 518, 764 (2004). 32. K. Banerjee et al., Nucl. Instr. and Meth. A 608, 440 (2009). 33. P. M. Joshirao et al., Appl. Radiat. Isot. 81, 184 (2013). 34. http://geant4.web.cern.ch/. 35. T. Sato and K. Niita, Radiat. Res. 166, 544 (2006). 36. A. A Bahadori et al., Phys. Med. Biol. 58, 7183 (2013). 37. H. Nose, Y. Kase, N. Matsufuji and T. Kanai, Med. Phys. 36, 870 (2009). 38. T. Sato, Y. Kase, R. Watanabe, K. Niita and L. Sihver, Radiat. Res. 171, 107 (2009). 39. E. Seravalli et al., Phys. Med. Biol. 57, 1659 (2012). 40. Y. Iwamoto and R. M. Ronningen, Nucl. Instr. and Meth. B 269, 353 (2011). 41. A. M. Sukegawa, H. Kawasaki and K. Okuno, Prog. Nucl. Sci. Technol. 2, 375 (2011). 42. A. N. Golovchenko et al., Radiat. Meas. 45, 856 (2010). 43. Y. Iwamoto et al., Nucl. Instr. and Meth. A 629, 43 (2011). 44. http://phits.jaea.go.jp/. 45. B. E. Watt, Phys. Rev. 87, 1037 (1952). 46. A. B. Smith, P. R. Fields and J. H. Roberts, Phys. Rev. 108, 411 (1957). 47. X-5 MONTE CARLO TEAM, LA-UR-03-1987, Los Alamos National Lab., 2003. 48. National Council on Radiation Protection and Measurements Protection Against Neutron Radiation NCRP Report 38. Comments 0 You are adding the first comment! 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How to quickly get a good answer: • Keep your question short and to the point • Check for grammar or spelling errors. • Phrase it like a question Test Test description	2019-03-24 06:37:10	{"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": 0.7573404908180237, "perplexity": 3845.2160796262165}, "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-2019-13/segments/1552912203378.92/warc/CC-MAIN-20190324063449-20190324085449-00193.warc.gz"}
https://nebusresearch.wordpress.com/tag/stone-soup/	## Reading the Comics, April 25, 2020: Off Brand Edition Comic Strip Master Command decided I should have a week to catch up on things, and maybe force me to write something original. Of all the things I read there were only four strips that had some mathematics content. And three of them are such glancing mentions that I don’t feel it proper to include the strip. So let me take care of this. Mark Anderson’s Andertoons for the 20th is the Mark Anderson’s Andertoons for the week. Wavehead apparently wants to know whether $\frac{3}{4}$ or $\frac{6}{8}$ is the better of these equivalent forms. I understand the impulse. Rarely in real life do we see two things that are truly equivalent; there’s usually some way in which one is better than the other. There may be two ways to get home for example, both taking about the same time to travel. One might have better scenery, though, or involve fewer difficult turns or less traffic this time of day. This is different, though: $\frac{3}{4}$ or $\frac{6}{8}$ are two ways to describe the same number. Which one is “better”? The only answer is, better for what? What do you figure to do with this number afterwards? I admit, and suppose most people have, a preference for $\frac{3}{4}$. But that’s trained into us, in large part, by homework set to reduce fractions to “lowest terms”. There’s honest enough reasons behind that. It seems wasteful to have a factor in the numerator that’s immediately divided out by the denominator. If this were 25 years ago, I could ask how many of you have written out a check for twenty-two and 3/4 dollars, then, rather than twenty-two and 75/100 dollars? The example is dated but the reason to prefer an equivalent form is not. If I know that I need the number represented by $\frac{3}{4}$, and will soon be multiplying it by eight, then $\frac{6}{8}$ may save me the trouble of thinking what three times two is. Or if I’ll be adding it to $\frac{5}{8}$, or something like that. If I’m measuring this for a recipe I need to cut in three, because the original will make three dozen cookies and I could certainly eat three dozen cookies, then $\frac{3}{4}$ may be more convenient than $\frac{6}{8}$. What is the better depends on what will clarify the thing I want to do. A significant running thread throughout all mathematics, not just arithmetic, is finding equivalent forms. Ways to write the same concept, but in a way that makes some other work easier. Or more likely to be done correctly. Or, if the equivalent form is more attractive, more likely to be learned or communicated. It’s of value. Jan Eliot’s Stone Soup Classics rerun for the 20th is a joke about how one can calculate what one is interested in. In this case, going from the number of days left in school to the number of hours and minutes and even seconds left. Personally, I have never had trouble remembering there are 24 hours in the day, nor that there are 86,400 seconds in the day. That there are 1,440 minutes in the day refuses to stick in my mind. Your experiences may vary. Thaves’s Frank and Ernest for the 22nd is the Roman Numerals joke for the week, shifting the number ten to the representation “X” to the prefix “ex”. Harry Bliss’s Bliss for the 23rd speaks of “a truck driver with a PhD in mathematical logic”. It’s an example of signifying intelligence through mathematics credentials. (It’s also a bit classicist, treating an intelligent truck driver as an unlikely thing.) I’m caught up! This coming Sunday I hope to start discussingthis week’s comics in a post at this link. And for this week? I don’t know; maybe I’ll figure something to write. We’ll see. Thanks for reading. ## Reading the Comics, January 13, 2020: The State Pinball Championships Were Yesterday Edition I am not my state’s pinball champion, although for the first time I did make it through the first round of play. What is important about this is that between that and a work trip I needed time for things which were not mathematics this past week. So my first piece this week will be a partial listing of comic strips that, last week, mentioned mathematics but not in a way I could build an essay around. … It’s not going to be a week with long essays, either, though. Here’s a start, though. Henry Scarpelli’s Archie rerun for the 12th of January was about Moose’s sudden understanding of algebra, and wish for it to be handy. Well, every mathematician knows the moment when suddenly something makes sense, maybe even feels inevitably true. And then we do go looking for excuses to show it off. Art Sansom and Chip Sansom’s The Born Loser for the 12th has the Loser helping his kid with mathematics homework. And the kid asking about when they’ll use it outside school. Jason Chatfield’s Ginger Meggs for the 13th has Meggs fail a probability quiz, an outcome his teacher claims is almost impossible. If the test were multiple-choice (including true-or-false) it is possible to calculate the probability of a person making wild guesses getting every answer wrong (or right) and it usually is quite the feat, at least if the test is of appreciable length. For more open answers it’s harder to say what the chance of someone getting the question right, or wrong, is. And then there’s the strange middle world of partial credit. My love does give multiple-choice quizzes occasionally and it is always a source of wonder when a student does worse than blind chance would. Everyone who teaches has seen that, though. Jan Eliot’s Stone Soup Classics for the 13th just mentions the existence of mathematics homework, as part of the morning rush of events. Ed Allison’s Unstrange Phenomenon for the 13th plays with optical illusions, which include several based on geometric tricks. Humans have some abilities at estimating relative areas and distances and lengths. But they’re not, like, smart abilities. They can be fooled, basically because their settings are circumstances where there’s no evolutionary penalty for being fooled this way. So we can go on letting the presence of arrow pointers mislead us about the precise lengths of lines, and that’s all right. There are, like, eight billion cognitive tricks going on all around us and most of them are much more disturbing. That’s a fair start for the week. I hope to have a second part to this Tuesday. Thanks for reading. ## Reading the Comics, July 27, 2019: July 27, 2019 Edition Last week was busy enough in mathematically themed comic strips. Some of these are pretty slight topics. But including them lets me do one of my favorite things, to have an essay that’s all comics from a single day. It’s my blog, I can use it to amuse myself. Marcus Hamilton and Ron Ferdinand’s Dennis the Menace for the 27th shows the kind of slightness I’m dealing with. ‘Statistic’ has some nasty connotations in this sense. It suggests something dehumanizing has happened. But the word was maybe doomed to that. The word came about in the 18th century, to describe the systematic collection and study of information about whole populations. They started out being the gathering of information about the state. But gathering information about a whole state implies, first, that the thing one finds interesting about a people are some measured and recorded aspect. Not the whole of their person-hood. Second, it implies that you wish to approximate the diversity of a whole people with some smaller set of numbers. There’s compelling reasons for a state to want to have statistics. They make it more plausible to know what the state can do. They make it plausible to forecast the results of a policy. Ideally, this encourages wisdom in policy-making. If the tools are used well. Jan Eliot’s Stone Soup Classics for the 27th is the slightest of the comic strips I’m featuring this week. Really it should have been just a mention, but I wanted to have at least three comics shown for today’s essay. Making and counting change is constantly held up as the supreme purpose of teaching arithmetic. This though most any shop has a cash register that will calculate change faster and more accurately than even someone skilled in arithmetic will. I understand the crankiness of people who give the cashier $15.13 for their$12.38 bill, and get the thirteen cents handed back to them before it’s rung up. It’s not evidence that civilization is collapsing. It’s loose change. Paul Trap’s Thatababy for the 27th continues the strip’s thread of turning geometry figures into jokes. This one is less useful than the comic featured Tuesday, which might help one remember what a scalene triangle or a rhombus looks like. Still might be fun. And with that, last week’s mathematically-themed comic strips are fully discussed. This week’s comics will get discussion at an essay linked from here. Please visit soon and we’ll see what I have to say, and about what.	2021-03-02 18:09:11	{"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": 10, "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": 0.4901180565357208, "perplexity": 1330.5742187216422}, "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/1614178364027.59/warc/CC-MAIN-20210302160319-20210302190319-00254.warc.gz"}
https://gmatclub.com/forum/if-y-2x-1-what-is-the-value-of-x-in-terms-of-y-290176.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 21 Mar 2019, 00:55 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 If y = 2x - 1, what is the value of x in terms of y? Author Message TAGS: Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 53748 If y = 2x - 1, what is the value of x in terms of y? [#permalink] Show Tags 07 Mar 2019, 00:04 00:00 Difficulty: 25% (medium) Question Stats: 78% (00:21) correct 22% (00:26) wrong based on 9 sessions HideShow timer Statistics If $$y = 2x - 1$$, what is the value of x in terms of $$y$$? A. $$\frac{y}{2} - 1$$ B. $$\frac{y}{2} - \frac{1}{2}$$ C. $$\frac{y}{2} + \frac{1}{2}$$ D. $$\frac{y}{2} + 1$$ E. $$y + \frac{1}{2}$$ _________________ Intern Joined: 15 Dec 2018 Posts: 30 If y = 2x - 1, what is the value of x in terms of y? [#permalink] Show Tags 07 Mar 2019, 00:08 IMO C (Y+1)/2 can also be written as (Y/2)+(1/2) Posted from my mobile device If y = 2x - 1, what is the value of x in terms of y? [#permalink] 07 Mar 2019, 00:08 Display posts from previous: Sort by	2019-03-21 07:55:17	{"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": 0.5490759015083313, "perplexity": 2393.0319944999737}, "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-2019-13/segments/1552912202506.45/warc/CC-MAIN-20190321072128-20190321094128-00359.warc.gz"}
https://www.mathplanet.com/education/sat/section-2-questions-13-24/16-what-is-the-value-of-m-n	# 16. What is the value of m/n? $\begin{array}{lcl} 16.\: If\:m\:and\:n\:are\:positive,\:m=-2+n,\:\\ and\:m\cdot n=24,\: what\:is\:the\:value\:of\:\frac{m}{n}\:?\\ \\ \end{array}$	2023-02-04 12:50:11	{"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": 0.22284841537475586, "perplexity": 1219.5530989717554}, "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-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00472.warc.gz"}
https://tex.stackexchange.com/questions/422222/simple-color-environment-for-htlatex	# Simple Color Environment for htlatex I have a class I originally used for PDF output, but now want to also have an option for HTML. I have a very basic environment where the block of text is a different color. For example: \documentclass{article} \usepackage{xcolor} \newenvironment{specialtext} {\begin{color}{blue}} {\end{color}} \begin{document} This is normal text. \begin{specialtext} This is a first paragraph of special text. This is a second paragraph of special text. \end{specialtext} It works fine for pdflatex, but if I process with htlatex, there is no color. I have spent hours searching forums, and have found that \color and \begin{color} do not work with htlatex (for reasons that are over my head). Unfortunately, \textcolor{blue}{TEXT} is not an option, because the input spans multiple lines. My knowledge of htlatex and CSS are pretty limited. I tried just defining the environment in my .cfg file, and that didn't work. I also tried making a .4ht file with the same name as the class that has the environment definition (I just cribbed this from a forum; don't actually know what I'm doing): \ConfigureEnv{specialtext}{\NoFonts}{\EndNoFonts}{}{} \Css{.specialtext{font-color: blue;}} \endinput And this line then showed up in my .css file: ./specialtext{font-color: blue;} But the paragraphs that are supposed to be "specialtext" aren't tagged with it. Is there something really obvious I'm missing? This seems like it should be easy. TIA! UPDATE: My tex4ht.cfg file is minimal. I just use it to set the margins so the text is more readable. \Preamble{html} \begin{document} \Css{body { max-width : 600px; }} \Css{body { text-align : justify; }} \Css{body { margin : auto; }} \Css{img {max-width : 500px; height : auto;}} \EndPreamble "myclass.4ht" consists entirely of what I typed above. I created it solely to try to deal with this issue. (Like I said, I have pretty minimal knowledge, but everything except this has more or less worked out of the box). • it would be helpful if you posted your cfg file as well but I think that you need something like\ConfigureEnv{specialtext}{\HCode{<p class="specialtext">}}{\HCode{</p>}}{}{} – Andrew Mar 20 '18 at 23:18 • Thank you! I added the content of my .cfg file (such as it is) above responsive to your comment. I will add your suggestiong (I assume to the .4ht file) and see if that works. – Sean Mar 21 '18 at 5:51 I moved your environment to a custom package, in order to make it possible to configure it using a .4ht file: \ProvidesPackage{specialtext} \RequirePackage{xcolor} \definecolor{specialtextcolor}{rgb}{0,0,1} \newenvironment{specialtext} {\par\begin{color}{specialtextcolor}} {\end{color}} \endinput I made two changes: I defined specialtextcolor color. We will use it in the .4ht file to pass information about color to the CSS file. The second change is explicit \par command. I suppose that you want it and it is necessary in order to avoid HTML tag mismatch that would be produced otherwise. The configuration file specialtext.4ht may look like this: \def\get:xcolorcss#1#2{% \expandafter\extractcolorspec\expandafter{#1}{\tsf:color}% \expandafter\convertcolorspec\tsf:color{HTML}\tsf:color% \edef#2{\#\tsf:color}% } \ConfigureEnv{specialtext}{\ifvmode\IgnorePar\fi\EndP\HCode{<div class="specialtext">}}{\ifvmode\IgnorePar\fi\EndP\HCode{</div>}}{}{} \AtBeginDocument{% \get:xcolorcss{specialtextcolor}{\color:specialtext} \Css{.specialtext{color:\color:specialtext;}} } The \ifvmode\IgnorePar\fi\EndP commands are necessary for correct paragraph handling. The <div class="specialtext"> is used for styling it's contents. The code in \AtBeginDocument command is more interesting: \AtBeginDocument{% \get:xcolorcss{specialtextcolor}{\color:specialtext} \Css{.specialtext{color:\color:specialtext;}} } The \get:xcolorcss command extracts color name or specification in the CSS form and saves it in a command for a later use. We can use this command in the \Css command directly. It produces following code: .specialtext{color:#0000FF;} It is necessary to use it inside \AtBeginDocument, because it is defined in xcolor.4ht file, which is loaded after specialtext.4ht (the .4ht files are loaded in order they were used in the document). This is the resulting HTML: • Thank you so much! I tried this. Just to be sure I'm not dealing with collisions, I put the above text verbatim into specialtext.sty and specialtext.4ht in my local texmf path. Then I made a test.tex with just the three paragraphs. On my output, I get !Undefined control sequence. \@begindocumenthook ...t\endcsname \get:xcolorcss{specialtextcolor}{\color:...} Any thoughts on this? – Sean Mar 21 '18 at 14:53 • @Sean which TeX distribution do you use? The \get:xcolorcss is quite recent addition to tex4ht, so you may need to update it – michal.h21 Mar 21 '18 at 14:57 • My html output looks just like yours, except the first line is specialtextcolor And the two lines of specialtext are indented but not colored. – Sean Mar 21 '18 at 14:57 • This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=latex) restricted \write18 enabled. entering extended mode LaTeX2e <2016/02/01> Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. I'll see if updating to a newer version helps. Thanks again! – Sean Mar 21 '18 at 15:06 • @sean texlive 2015 is really old, you should try to update. I've updated my answer with definition for \get:xcolorcss so it should work anyway. – michal.h21 Mar 21 '18 at 16:43	2020-07-08 08:42:59	{"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": 0.812426745891571, "perplexity": 2476.1806618945766}, "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-2020-29/segments/1593655896905.46/warc/CC-MAIN-20200708062424-20200708092424-00114.warc.gz"}
https://klementtan.com/leetcodes/maximum-number-of-events-that-can-be-attended-ii/	## Problem Problem ID: 1851 Title: Maximum Number of Events That Can Be Attended II Difficulty: Hard Description: You are given an array of events where events[i] = [startDayi, endDayi, valuei]. The ith event starts at startDayi and ends at endDayi, and if you attend this event, you will receive a value of valuei. You are also given an integer k which represents the maximum number of events you can attend. You can only attend one event at a time. If you choose to attend an event, you must attend the entire event. Note that the end day is inclusive: that is, you cannot attend two events where one of them starts and the other ends on the same day. Return the maximum sum of values that you can receive by attending events. Example 1: Input: events = [[1,2,4],[3,4,3],[2,3,1]], k = 2 Output: 7 Explanation: Choose the green events, 0 and 1 (0-indexed) for a total value of 4 + 3 = 7. Example 2: Input: events = [[1,2,4],[3,4,3],[2,3,10]], k = 2 Output: 10 Explanation: Choose event 2 for a total value of 10. Notice that you cannot attend any other event as they overlap, and that you do not have to attend k events. Example 3: Input: events = [[1,1,1],[2,2,2],[3,3,3],[4,4,4]], k = 3 Output: 9 Explanation: Although the events do not overlap, you can only attend 3 events. Pick the highest valued three. Constraints: • 1 <= k <= events.length • 1 <= k * events.length <= 106 • 1 <= startDayi <= endDayi <= 109 • 1 <= valuei <= 106 ## Thoughts I had difficulty solving this problem as initially I was not sure how to optimise for value and end time for the DP transition. Knowing that k*events.length < 1e6 was a big hint as it implies that the problem should be solved using a 2DP of n times k. ## Solution General Idea We will use bottom up DP to solve this problem with the following state and transitions. The reason we have to use DP instead of greedy is because choosing event i could result in later overlapping events with large value(INF) being passed on but passing on event i could result in a wrong answer if event i has (INF) value. DP State - dp[i][j] • Represents the maximum score at the end of events[i]’s end time with j events selected. DP Transition - when processing event i we could: • Choosing current event: • Logically, this means choosing the current events with the maximum valid combination of previous events that do not overlap with the current event. • The value will be equals to events[i]’s value sum with dp[k][j-1] where k is the event with end time strictly less than the current event start time. • dp[k][j-1]: represents a combination of j-1 previous events that has the maximum value and do not overlap with the current event • Passing on the current event: • Value Equals to dp[i-1][j] as it represents the combination of previous j events • Final dp transition: dp[i][j] = max(dp[i-1][j], events[i][2] + dp[k][j-1]) ### Implementation class Solution { public: int maxValue(vector<vector<int>>& events, int k) { events.push_back({0,0,0}); int n = events.size(); sort(events.begin(), events.end(), [](const auto& a, const auto& b){return a[1] < b[1];}); vector<int> end_times(n,0); for (int i = 0; i < n; i++) end_times[i] = events[i][1]; vector<vector<int>> dp(n, vector<int>(k+1, 0)); int ret = 0; for (int i = 1; i < n; i++) { for (int j = 1; j < k+1; j++) { auto it = lower_bound(end_times.begin(), end_times.end(), events[i][0]); assert(it != end_times.end()); assert(it != end_times.begin()); it--; int k = std::distance(end_times.begin(), it); dp[i][j] = max(events[i][2] + dp[k][j-1], dp[i-1][j]); ret = max(ret, dp[i][j]); } } return ret; } };	2022-07-06 13:00:23	{"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": 0.42045167088508606, "perplexity": 2727.1455407308176}, "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/1656104672585.89/warc/CC-MAIN-20220706121103-20220706151103-00057.warc.gz"}
https://zbmath.org/?q=an:1012.20068	# zbMATH — the first resource for mathematics On finite loops whose inner mapping groups are Abelian. (English) Zbl 1012.20068 Given a loop $$(Q,\cdot)$$, for any $$a\in Q$$ let $$L_a$$ and $$R_a$$ be the left and the right translations by $$a$$ and let $$M(Q):=\langle\{L_a,R_a\mid a\in Q\}\rangle$$ be the multiplication group of $$(Q,\cdot)$$. If we denote by $$I(Q):=\{\gamma\in M(Q)\mid\gamma(e)=e\}$$ (where $$e$$ is the neutral element of the loop), then $$I(Q)$$ is the so-called inner mapping group of the loop $$(Q,\cdot)$$ (if $$(Q,\cdot)$$ is a group $$I(Q)$$ coincides with the inner automorphism group of $$Q$$). In this paper the author investigates the structure of $$I(Q)$$ in particular, he addresses the problem of finding classes of finite Abelian groups possibly isomorphic to $$I(Q)$$, generalizing the analogous problem for groups which has been completely solved by Baer (see the reference quoted in the note). The author reaches the following results: For a finite loop $$(Q,\cdot)$$: 1. $$I(Q)$$ is never isomorphic to the direct product $$C_{p^k}\times C_p$$, where $$p$$ is an odd prime number and $$k\geq 2$$ ($$C_n$$ denotes the cyclic group of order $$n$$). 2. $$I(Q)$$ is never isomorphic to $$(C_{p^k}\times C_p)\times D$$ where $$D$$ is an Abelian $$q$$-group and $$p$$ and $$q$$ are two prime numbers such that $$p$$ is odd and $$q$$ does not divide $$\|Q\|$$, and $$k\geq 2$$. These results are obtained by resorting to general group theoretical techniques via a crucial link provided by a theorem which allows a group $$G$$ to be isomorphic to the multiplication group of a loop if and only if there exists a subgroup $$H$$ satisfying some particular conditions (see Theorem 2.1). ##### MSC: 20N05 Loops, quasigroups 20K01 Finite abelian groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 20F29 Representations of groups as automorphism groups of algebraic systems Full Text: ##### References: [1] Foguel, Pacific J. Math. 197 pp 1– (2001) [2] Huppert, Endliche Gruppen I 134 (1967) · Zbl 0217.07201 [3] DOI: 10.2307/1990147 · Zbl 0061.02201 [4] DOI: 10.1007/BF01170643 · Zbl 0009.01101 [5] DOI: 10.1006/jabr.1996.0098 · Zbl 0853.20050 [6] Smith, Comment. Math. Univ. Carolin. 41 pp 415– (2000) [7] Phillips, Proceedings of the Groups (Korea 1998) pp 305– (2000) [8] Pflugfelder, Comment. Math. Univ. Carolin. 41 pp 359– (2000) [9] Niemenmaa, Bull. Austral. Math. Soc. 49 pp 121– (1994) [10] DOI: 10.1080/00927879608825558 · Zbl 0853.20049 [11] DOI: 10.1016/0021-8693(90)90152-E · Zbl 0706.20046 [12] DOI: 10.1006/jcss.1999.1673 · Zbl 0955.68053 [13] DOI: 10.1007/BF01198806 · Zbl 0789.20080 [14] DOI: 10.1080/00927879808826169 · Zbl 0913.20043 [15] DOI: 10.1016/0012-365X(92)90543-O · Zbl 0755.94006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.	2021-12-03 01:17:08	{"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": 0.8815315365791321, "perplexity": 676.362943574375}, "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-2021-49/segments/1637964362571.17/warc/CC-MAIN-20211203000401-20211203030401-00353.warc.gz"}
https://archive.lib.msu.edu/crcmath/math/math/i/i215.htm	## Inversive Distance The inversive distance is the Natural Logarithm of the ratio of two concentric circles into which the given circles can be inverted. Let be the distance between the centers of two nonintersecting Circles of Radii and . Then the inversive distance is (Coxeter and Greitzer 1967). The inversive distance between the Soddy Circles is given by and the Circumcircle and Incircle of a Triangle with Circumradius and Inradius are at inversive distance (Coxeter and Greitzer 1967, pp. 130-131). References Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 123-124 and 127-131, 1967.	2021-12-03 19:55:30	{"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": 0.9124259352684021, "perplexity": 852.9778566182835}, "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-2021-49/segments/1637964362918.89/warc/CC-MAIN-20211203182358-20211203212358-00598.warc.gz"}
https://eccc.weizmann.ac.il/report/2020/096/	Under the auspices of the Computational Complexity Foundation (CCF) REPORTS > DETAIL: ### Paper: TR20-096 \| 22nd June 2020 15:49 #### On the asymptotic complexity of sorting TR20-096 Authors: Igor Sergeev Publication: 24th June 2020 20:41	2020-09-28 16:14:30	{"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": 0.9299492239952087, "perplexity": 10161.76289514393}, "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/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00053.warc.gz"}
https://jordanbell.info/euler/euler-algebra-I-I-20.html	### Part I. Section I. Chapter 20. “Of the different Methods of Calculation, and of their mutual Connection.” 206 Hitherto we have only explained the different methods of calculation: namely, addition, subtraction, multiplication, and division; the involution of powers, and the extraction of roots. It will not be improper, therefore, in this place, to trace back the origin of these different methods, and to explain the connection which subsists among them; in order that we may satisfy ourselves whether it be possible or not for other operations of the same kind to exist. This inquiry will throw new light on the subjects which we have considered. In prosecuting this design, we shall make use of a new character, which may be employed instead of the expression that has been so often repeated, is equal to; this sign is =, which is read is equal to: thus, when I write $$a = b$$, this means that $$a$$ is equal to $$b$$: so, for example, 3 · 5=15. 207 The first mode of calculation that presents itself to the mind, is undoubtedly addition, by which we add two numbers together and find their sum: let therefore $$a$$ and $$b$$ be the two given numbers, and let their sum be expressed by the letter $$c$$, then we shall have $$a + b = c$$; so that when we know the two numbers $$a$$ and $$b$$, addition teaches us to find the number $$c$$. 208 Preserving this comparison $$a + b = c$$, let us reverse the question by asking, how we are to find the number $$b$$, when we know the numbers $$a$$ and $$c$$. It is here required therefore to know what number must be added to $$a$$, in order that the sum may be the number $$c$$: suppose, for example, $$a = 3$$ and $$c = 8$$; so that we must have $$3 + b = 8$$; then $$b$$ will evidently be found by subtractlng 3 from 8: and, in general, to find $$b$$, we must subtract $$a$$ from $$c$$, whence arises $$b = c - a$$; for by adding $$a$$ to both sides again, we have $$b+a=c - a + a$$, that is to say, $$=c$$, as we supposed. 209 Subtraction therefore takes place, when we invert the question which gives rise to addition. But the number which it is required to subtract may happen to be greater than that from which it is to be subtracted; as, for example, if it were required to subtract 9 from 5: this instance therefore furnishes us with the idea of a new kind of numbers, which we call negative numbers, because 5-9=-4. 210 When several numbers are to be added together, which are all equal, their sum is found by multiplication, and is called a product. Thus, $$ab$$ means the product arising from the multiplication of $$a$$ by $$b$$;, or from the addition of the number $$a$$, $$b$$ number of times; and if we represent this product by the letter $$c$$, we shall have $$ab = c$$; thus multiplication teaches us how to determine the number $$c$$, when the numbers $$a$$ and $$b$$ are known. 211 Let us now propose the following question: the numbers $$a$$ and $$c$$ being known, to find the number $$b$$. Suppose, for example, $$a = 3$$, and $$c = 15$$; so that $$3b = 15$$, and let us inquire by what number 3 must be multiplied, in order that the product may be 15; for the question proposed is reduced to this. This is a case of division; and the number required is found by dividing 15 by 3; and, in general, the number $$b$$ is found by dividing $$c$$ by $$a$$; from which results the equation $$b=\frac{c}{a}$$. 212 Now, as it frequently happens that the number $$c$$ cannot be really divided by the number $$a$$, while the letter $$b$$ must however have a determinate value, another new kind of numbers present themselves, which are called fractions. For example, suppose $$a = 4$$, and $$c =3$$, so that $$4b = 3$$; then it is evident that $$b$$ cannot be an integer, but a fraction, and that we shall have $$b = \frac{3}{4}$$. 213 We have seen that multiplication arises from addition; that is to say, from the addition of several equal quantities: and if we now proceed farther, we shall perceive that, from the multiplication of several equal quantities together, powers are derived; which powers are represented in a general manner by the expression $$a^b$$. This signifies that the number $$a$$ must be multiplied as many times by itself, minus 1, as is indicated by the number $$b$$. And we know from what has been already said, that, in the present instance, $$a$$ is called the root, $$b$$ the exponent, and $$a^b$$ the power. 214 Farther, if we represent this power also by the letter $$c$$, we have $$a^b = c$$, an equation in which three letters $$a$$, $$b$$, $$c$$, are found; and we have shown in treating of powers, how to find the power itself, that is, the letter $$c$$, when a root $$a$$ and its exponent $$b$$ are given. Suppose, for example, $$a = 5$$, and $$b= 3$$, so that $$c=5^3$$: then it is evident that we must take the third power of 5, which is 125, so that in this case $$c = 125$$. 215 We have now seen how to determine the power $$c$$, by means of the root $$a$$ and the exponent $$b$$; but if we wish to reverse the question, we shall find that this may be done in two ways, and that there are two different cases to be considered: for if two of these three numbers $$a$$, $$b$$, $$c$$, were given, and it were required to find the third, we should immediately perceive that this question would admit of three different suppositions, and consequently of three solutions. We have considered the case in which $$a$$ and $$b$$ were the given numbers, we may therefore suppose farther that $$c$$ and $$a$$, or $$c$$ and $$b$$, are known, and that it is required to determine the third letter. But, before we proceed any farther, let us point out a very essential distinction between involution and the two operations which lead to it. When, in addition, we reversed the question, it could be done only in one way; it was a matter of indifference whether we took $$c$$ and $$a$$, or $$c$$ and $$b$$, for the given numbers, because we might indifferently write $$a + b$$, or $$b + a$$; and it was also the same with multiplication; we could at pleasure take the letters $$a$$ and $$b$$ for each other, the equation $$ab = c$$ being exactly the same as $$ba = c$$: but in the calculation of powers, the same thing does not take place, and we can by no means write $$b^a$$ instead of $$a^b$$; as a single example will be sufficient to illustrate: for let $$a = 5$$, and $$b = 3$$; then we shall have $$a^b = 5^3 = 125$$; but $$b^a = 3^5 = 243$$: which are two very different results. 216 It is evident then, that we may propose two questions more: one, to find the root $$a$$ by means of the given power $$c$$, and the exponent $$b$$; the other, to find the exponent $$b$$, supposing the power $$c$$ and the root $$a$$ to be known. 217 It may be said, indeed, that the former of these questions has been resolved in the chapter on the extraction of roots; since if $$b= 2$$, for example, and $$a^2 =c$$, we know by this means, that $$a$$ is a number whose square is equal to $$c$$, and consequently that $$a = \surd c$$. In the same manner, if $$b = 3$$ and $$a^3 = c$$, wc know that the cube of $$a$$ must be equal to the given number $$c$$, and consequently that $$a = \sqrt[3]{\vphantom{c}}{c}$$. It is therefore easy to conclude, generally, from this, how to determine the letter $$a$$ by means of the letters $$c$$ and $$b$$; for we must necessarily have $$a = \sqrt[b]{\vphantom{c}}{c}$$. 218 We have already remarked also the consequence which follows, when the given number is not a real power; a case which very frequently occurs; namely, that then the required root, $$a$$, can neither be expressed by integers, nor by fractions; yet since this root must necessarily have a determinate value, the same consideration led us to a new kind of numbers, which, as we observed, are called surds, or irrational numbers; and which we have seen are divisible into an infinite number of different sorts, on account of the great variety of roots. Lastly, by the same inquiry, we were led to the knowledge of another particular kind of numbers, which have been called imaginary numbers. 219 It remains now to consider the second question, which was to determine the exponent; the power $$c$$, and the root $$a$$, both being known. On this question, which has not yet occurred, is founded the important theory of Logarithms, the use of which is so extensive through the whole compass of mathematics, that scarcely any long calculation can be carried on vathout their assistance; and we shall find, in the following chapter, for which we reserve this theory, that it will lead us to another kind of numbers entirely new, as they cannot be ranked among the irrational numbers before mentioned. #### Editions 1. Leonhard Euler. Elements of Algebra. Translated by Rev. John Hewlett. Third Edition. Longmans, Hurst, Rees, Orme, and Co. London. 1822. 2. Leonhard Euler. Vollständige Anleitung zur Algebra. Mit den Zusätzen von Joseph Louis Lagrange. Herausgegeben von Heinrich Weber. B. G. Teubner. Leipzig and Berlin. 1911. Leonhardi Euleri Opera omnia. Series prima. Opera mathematica. Volumen primum.	2023-03-22 05:19:19	{"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": 0.841952383518219, "perplexity": 281.7938638952281}, "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-2023-14/segments/1679296943750.71/warc/CC-MAIN-20230322051607-20230322081607-00314.warc.gz"}
https://stats.stackexchange.com/questions/29990/identifying-outliers-for-non-linear-regression	# Identifying outliers for non linear regression I am doing research on the field of functional response of mites. I would like to do a regression to estimate the parameters (attack rate and handling time) of the Rogers type II function. I have a dataset of measurements. How can I can best determine outliers? For my regression I use the following script in R (a non linear regression): (the dateset is a simple 2 column text file called data.txt file with N0 values (number of initial prey) and FR values (number of eaten prey during 24 hours): library("nlstools") #Rogers type II model a <- c(0,50) b <- c(0,40) plot(FR~N0,main="Rogers II normaal",xlim=a,ylim=b,xlab="N0",ylab="FR") rogers.predII <- function(N0,a,h,T) {N0 - lambertW(ahN0exp(-a(T-hN0)))/(ah)} params1 <- list(attackR3_N=0.04,Th3_N=1.46) RogersII_N <- nls(FR~rogers.predII(N0,attackR3_N,Th3_N,T=24),start=params1,data=dat,control=list(maxiter= 10000)) hatRIIN <- predict(RogersII_N) lines(spline(N0,hatRIIN)) summary(RogersII_N)$parameters For plotting the calssic residuals graphs I use following script: res <- nlsResiduals (RogersII_N) plot (res, type = 0) hist (res$resi1,main="histogram residuals") qqnorm (res$resi1,main="QQ residuals") hist (res$resi2,main="histogram normalised residuals") qqnorm (res$resi2,main="QQ normalised residuals") par(mfrow=c(1,1)) boxplot (res$resi1,main="boxplot residuals") boxplot (res\$resi2,main="boxplot normalised residuals") ### Questions • How can I best determine which data points are outliers? • Are there tests I can use in R which are objective and show me which data points are outliers? Several tests for outliers, including Dixon's and Grubb's, are available in the outliers package in R. For a list of the tests, see the documentation for the package. References describing the tests are given on the help pages for the corresponding functions. In case you were planning to remove the outliers from your data, bear in mind that this isn't always advisable. See for instance this question for a discussion on this (as well as some more suggestions on how to detect outliers). Neither am I a statistician. Therefore I use my expert knowledge about the data to find outliers. I.e. I look for physical/biological/whatever reasons that made some measurements different from the others. In my case that is e.g. • cosmic rays messing up part of the measured signal • someone entering the lab, switching on the light • just the whole spectrum somehow looks different • the first measurement series was taken during normal work hours and is an order of magniture more noisy than the 10 pm series Surely you could tell us similar effects. Note that my 3rd point is different from the others: I don't know what happened. This may be the kind of outlier you're asking about. However, without knowing what caused it (and that this cause invalidates the data point) it is difficult to say that it shouldn't appear in the data set. Also: your outlier may be my most interesting sample... Therefore, I often do not speak of outliers, but of suspicious data points. This reminds everyone that they need to be double checked for their meaning. Whether it is good or not to exclude data (who wants to find outliers just for the sake of having them?) depends very much on what the task at hand is and what the "boundary conditions" for that task are. Some examples: • you just discovered the new outlierensis Joachimii subspecies ;-) no reason to exclude them. Exclude all others. • you want to predict preying times of mites. If it is acceptable to restrict the prediction to certain conditions, you could formulate these and exclude all other samples and say your predictive model deals with this or that situation, though you already know other situations (describe outlier here) do occur. • Keep in mind that excluding data with the help of model diagnostics can create a kind of a self-fulfilling prophecy or an overoptimistic bias (i.e. if you claim your method is generally applicable): the more samples you exclude because they don't fit your assumptions, the better are the assumptions met by the remaining samples. But that's only because of exclusion. • I currently have a task at hand where I have a bunch of bad measurements (I know the physical reason why I consider the measurement bad), and a few more that somehow "look weird". What I do is that I exclude these samples from trainig of a (predicitve) model, but separately test the model with these so I can say something about the robustness of my model against outliers of those types which I know will occur every once in a while. Thus, the application somehow or other needs to deal with these outliers. • Yet another way to look at outliers is asking: "How much do they influence my model?" (Leverage). From this point of view you can measure robustness or stability with respect to weird training samples. • Whatever statistical procedure you use, it will either not identify any outliers, or also have false positives. You can characterize an outlier testing procedure like other diagnostic tests: it has a sensitivity and a specificity, and - more important for you - they correspond (via the outlier proportion in your data) to a positive and negative predictive value. In other words, particularly if your data has very few outliers, the probablility that a case identified by the outlier test really is an outlier (i.e. shouldn't be in the data) can be very low. I believe that expert knowledge about the data at hand is usually much better at detecting outliers than statistical tests: the test is just as good as the assumptions behind it. And one-size-fits-all is often not really good for data analysis. At least I frequently deals with a kind of outliers, where experts (about that type of measurement) have no problem identifying the exact part of the signal that is compromised while automated procedures often fail (it is easy to get them detecting that there is a problem, but very difficult to get them finding where the problem begins and where it ends). • There's a lot of good information here. I especially like bullet points #4 & 5. – gung - Reinstate Monica Jun 8 '12 at 18:47 For univariate outliers there is Dixon's ratio test and Grubbs' test assuming normality. To test for an outlier you have to assume a population distribution because you are trying to show that the observed value is extreme or unusual to come from the assumed distribution. I have a paper in the American Statistician in 1982 that I may have referenced here before which shows that Dixon's ratio test can be used in small samples even for some non-normal distributions. Chernick, M.R. (1982)"A Note on the Robustness of Dixon's Ratio in Small Samples" American Statistician p 140. For multivariate outliers and outliers in time series, influence functions for parameter estimates are useful measures for detecting outliers informally (I do not know of formal tests constructed for them although such tests are possible). Look at Barnett and Lewis' text "Outliers in Statistical Data" for detailed treatment of outlier detection methods. See http://www.waset.org/journals/waset/v36/v36-45.pdf, "On the outlier Detection in Nonlinear Regression" [sic]. ### Abstract The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers. • +1 Despite the obvious problems with English (and in the mathematical typesetting), this paper appears to be a useful contribution to the question. – whuber Oct 5 '12 at 12:23 An outlier is a point that is "too far" from "some baseline". The trick is to define both those phrases! With nonlinear regression, one can't just use univariate methods to see if an outlier is "too far" from the best-fit curve, because the outlier can have an enormous influence on the curve itself. Ron Brown and I developed a unique method (which we call ROUT -- Robust regression and Outlier removal) for doing detecting outliers with nonlinear regression, without letting the outlier affect the curve too much. First fit the data with a robust regression method where outliers have little influence. That forms the baseline. Then use the ideas of the False Discovery Rate (FDR) to define when a point is "too far" from that baseline, and so is an outlier. Finally, it removes the identified outliers, and fits the remaining points conventionally. The method is published in an open access journal: Motulsky HJ and Brown RE, Detecting outliers when fitting data with nonlinear regression – a new method based on robust nonlinear regression and the false discovery rate, BMC Bioinformatics 2006, 7:123. Here is the abstract: Background. Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results. We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion. Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives. It has not (as far as I know) been implemented in R. But we implemented it in GraphPad Prism. and provide a simple explanation in the Prism help. Your question is too general. There is no single best method to exclude the "outliers". You had to know some properties on the "outliers". or you do not know which method is the best. After deciding which method you want to use, you need to calibrate the parameters of the method carefully.	2020-02-19 12:35:16	{"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": 0.6572467088699341, "perplexity": 885.976013859309}, "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-2020-10/segments/1581875144150.61/warc/CC-MAIN-20200219122958-20200219152958-00226.warc.gz"}
http://www.physicsforums.com/showthread.php?t=112187	## Calc 3 questions concerning Normal and Tangent unit Vectors... heres is one problem i did, i photo'd it so i wouldnt have to worry about it... Am I doing it right? any problems can you see :-/ on like the 8th/9th line, I dont think I can do what I did.... http://img130.imageshack.us/img130/1332/test076ze.jpg Sooo PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire Recognitions: Homework Help Since you have $$\vec{T} (t) = \frac{1}{\sqrt{5t^2+1}} \left< 1,t,2t\right>= \left< \frac{1}{\sqrt{5t^2+1}},\frac{t}{\sqrt{5t^2+1}},\frac{2t}{\sqrt{5t^2+1} }\right>$$ $$\vec{T} ^{\mbox{ }\prime} (t)$$ will require the quotient rule, the result is $$\vec{T} ^{\mbox{ }\prime} (t) = \frac{1}{(5t^2+1)\sqrt{5t^2+1}}\left< -5t,1,2\right> = \frac{1}{(5t^2+1)^{\frac{3}{2}}}\left< -5t,1,2\right>$$ So I do the quotient rule to each of the components of T(t)? How did you get your answer for T'(t)? Recognitions: Homework Help ## Calc 3 questions concerning Normal and Tangent unit Vectors... Yep, differentiate each component of T(t) according to the quotient rule and simplify. How did I do it? Simple, I used Maple v10 Recognitions: Gold Member Science Advisor Staff Emeritus Instead of the quotient rule, I think I would be inclined to write the components as $$(5t^2+1)^{-\frac{1}{2}}$$ $$t(5t^2+1)^{-\frac{1}{2}}$$ $$2t(5t^2+1)^{-\frac{1}{2}}$$ and use the product and chain rules. Why not just differentiate the un-normalised tangent vector then normalise it afterwards? Seems computationally simpler to me. Edit: Hm, doesn't work. I don't understand why differentiating a normalised tangent vector vs. a tangent vector should change the direction in which the resulting vector points. I also don't understand why the derivative of the normalised tangent vector will always be normal, seems to me that would be an acceleration and should therefore only be normal if the particle isn't picking up any kinetic energy. Guess I'm gonna have to break out my calculus book and do some reading	2013-05-19 20:08:07	{"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": 0.6862155795097351, "perplexity": 722.8011748590412}, "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/1368698063918/warc/CC-MAIN-20130516095423-00042-ip-10-60-113-184.ec2.internal.warc.gz"}
https://ai.stackexchange.com/questions/30170/in-the-neat-algorithm-what-is-the-purpose-of-treating-disjoint-and-excess-genes	# In the NEAT algorithm, what is the purpose of treating disjoint and excess genes differently? In the NEAT algorithm, what is the purpose of treating disjoint and excess genes differently? They are treated so (or may be treated potentially) at least when calculating the distance between 2 individuals when dividing the population into species (c1 and c2 coefficients). • Look. Let our 2 genomes are g1=[1, 2, 3, 4, 6] and g2=[1, 2, 5, 7, 8] (here numbers are innovation numbers). Then if g1 is the first parent, then disjoint gene is 5 and excess genes are 7,8. If g2 is the first one, then 3,4,6 are all the disjoint genes and there are no excess genes. So distances become different: d(g1, g2) ≠ d(g2, g1) because c11+c22+c3W ≠c13+c20+c3W. Do I understand something wrong? Aug 16 at 19:34	2021-10-24 16:32:56	{"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": 0.8725436329841614, "perplexity": 2642.9657803709956}, "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/1634323586043.75/warc/CC-MAIN-20211024142824-20211024172824-00033.warc.gz"}
https://brilliant.org/problems/find-the-region/	# Find the region Calculus Level 4 Let $$2{ \left( f\left( x \right) \right) }^{ 2 }-\frac { { d }^{ 2 }f\left( x \right) }{ d{ x }^{ 2 } } f\left( x \right) +{ \left( \frac { df\left( x \right) }{ dx } \right) }^{ 2 }=0$$ and $$f\left( 0 \right) =f\left( 1 \right) =-1$$ Then the area of the region bounded by y=0, x=0, x=1 and $$y=\left( 2x-1 \right) f\left( x \right)$$ is $$2\left( 1-\frac { 1 }{ { e }^{ { 1 }/{ a } } } \right)$$ Then the value of a is??? ×	2017-01-21 21:47:35	{"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": 0.6354525685310364, "perplexity": 415.73896965503087}, "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-2017-04/segments/1484560281226.52/warc/CC-MAIN-20170116095121-00072-ip-10-171-10-70.ec2.internal.warc.gz"}
https://bintanvictor.wordpress.com/2012/04/	# #1 driver of long term FX #my take Q: what is the #1 fundamental driver of long term FX rate between 2 currencies? Is it PPP? I don’t think so. Is it supply/demand? Short term yes; long term … this seems less relevant %%A: “gold” backing. In the beginning, every pound issued by the British monarch is as good as an ounce of gold (or whatever fixed amount of gold). Therefore anyone holding a pound note can exchange it for the equivalent amount of gold. The monarch then decided to print more pound notes. Logically, all the existing and new pounds devalue. But the country also exports and, in a world of universal gold standard, earns gold. In a more realistic world, What is earned is foreign currency. I believe Every Singapore dollar issued is backed by some amount of “gold” which in modern context means foreign reserve in a basket of hard currencies. By the way, there’s nothing harder than gold. As the national economy expands, more goods are produced domestically so the CB could issue more SGD, but I guess the CB waits until the goods are exported[2] and foreign currency earned. Such a prudent practice helps ensure every SGD is fully backed by sufficient “gold”. [2] incoming tourists also spend their own currency like JPY, therefore contributing to the Singapore foreign reserve. If tourists sell their JPY for SGD outside Singapore, the JPY amounts tend to flow into the global banking systems and back to Singapore banks. I think non-Singapore banks don’t want to go long or short SGD for large amounts, so they would eventually exchange with Singapore banks including Citibank, HSBC, SCB, BOC. In general, a hard currency is more deeply backed by gold than a weak currency. Alternatively, the issuing central bank has other capabilities (besides gold reserve) to maintain the strength of her currency. This strength depends on Current Account and economic growth — the 2 fundamentals. Another factor is global competitiveness, but this is often measured by the capacity to export and compete on global markets. After all, it still seems to boil down to earning enough foreign currency to back our own currency — “gold” backing in disguise. # insert() — more versatile than assign() and range-ctor [[effSTL]] P31 points out that range-iterators are used consistently across containers — – Every (yes both sequence/associative) container supports a ctor taking a couple of range iterators – All sequence (not associative) containers support assign() method taking a couple – Every (yes both sequence/associative) container supports erase() method taking a couple However, I’d argue the most versatile is the insert() method in Every Sequence and Associative containers. * insert() can emulate the range-ctor * insert() can emulate assign() This is also more versatile than operator=(). This member function is also simpler than the free function copy(). # y create custom STL iterators, briefly Q: when would you write your own STL iterator? I think if you create your own customized container, you probably need custom iterator Objects. You probably need to return such an Object from rbegin() etc. In python, c# and (less commonly) in java, many data structures can be made iterable. There’s an implicit iterator. [[STL tutorial]] has a 3-page chapter showing a debuggable-iterator that reveals interesting details of the inner workings of STL containers and STL algorithms. # libor vs gov bond — 2 benchmarks Most credit instruments, all (secured/unsecured) loans, all IR products, most derivatives based on FX, IR or credit (I'd say virtually all derivatives) need to apply a spread on a reference yield. If the deal has a “maturity date” or “delivery date”, “call date” [1], then we look for that date on the reference yield curve and read a yield number like (222 bps pa) off that curve. That number is the reference yield, a.k.a reference spot rate. You can convert that to a discount factor easily. There are also straightforward and well-defined conversions to/from fwd rates, driven by arbitrage principles. [1] perhaps among a series such dates. Question is which reference yield curve to use. Most companies use a single, consolidated curve for each currency. One of the biggest muni security trading desks in the world has just one yield curve for USD, which is typical. Another megabank has a single live Libor curve for the entire bank, updated by the minute. If you use more than one yield curve built from different data sources, then for any maturity date, you would read 2 yield numbers off them. If sufficiently different, you create arbitrage opportunity and your valuations are inconsistent. On the short end of the IR space the reference curves are 1) Libor 2) Fed Funding (USD only). Libor is more popular. On the long end, T-bond dominates the USD market. Many governments issue similar bonds to create a reference riskless rate. However, the most liquid IR instruments are probably more realistic and reliable as a reflection of market sentiment. ED futures, Bund futures, T-bond inter-dealer market rates are examples. # c++highly parallel numerical programmIV(smart ptr, threading… These are mostly QQ type. Jap firm https://www.numtech.com Q: What are the differences between win32 and linux threading Implementation? I probably won’t spend time reading this. Q: given a bunch of 10-year old linear algebra c++ functions (using many VD or MD templates as function inputs), how would you go about extracting and packaging them into a DLL? No experience. Not on my Tier 1/2. %%A: stateless %%A: pure functions. %%A: remove code duplication %%A: for each function, there should usually be default parameters, so we can call it with 2 args, 3 args, 4 args etc A: function parameters should not be templates. Ints, double are probably fine. DLL interface is defined by the platform, not the language. Q: what’s wrong with boost libraries? AA: (STL is fine) many of them aren’t proven — just 10 years Q: Since you said shared_ptr is the most popular boost module, how is reference count done in heavily parallel programming %%A: for regular shared_ptr, thread safety is a big design goal, so probably fine[1]. For intrusive_ptr, the pointee class must expose certain mutator methods, which must be made thread-safe by the pointee class author, not boost authors [1] isn’t correct. The testing on shared_ptr thread safety isn’t sufficient for large number (thousands) of threads. See https://bintanvictor.wordpress.com/2017/07/09/shared_ptr-thread-safety-take/ # RTTI compiler-option enabled by default All modern compilers have RTTI enabled by default. If you disable it via a compiler option, then typeid, typeinfo and dynamic_cast may fail, but virtual functions continue to work. Here’s the g++ option -fno-rtti— Disable generation of information about every class with virtual functions for use by the C++ runtime type identification features (dynamic_cast‘ and typeid‘). If you don’t use those parts of the language, you can save some space by using this flag. Note that exception handling uses the same information, but it will generate it as needed. The dynamic_cast‘ operator can still be used for casts that do not require runtime type information, i.e. casts to void * or to unambiguous base classes. # double-ptr usage #2b — swap 2 pointers (Note this is a special case of “special reseating” — http://bigblog.tanbin.com/2011/04/double-pointer-usage-2-special.html) Q1: write a utility function to swap 2 pointer’s content. %%A: swap(int a, int b) {….} Obviously, the 2 pointer Variables must be declared to be compatible — to be elaborated [1], such as int* a1, b1; …. swap(&a1, &b1); To really understand why we need double pointers, consider Q2: function to swap 2 nonref variables. In other words, after i call swap(..), x should have the value of y. If y used to be -17.2, x now has that value. Note this number isn’t an address. In this case, you need to pass the address of x like &x…. To understand this Q2, it’s actually important to be be thoroughly familiar with Q3: what does swap(char i, char j) do? %%A: something other than swapping. I doubt it does anything meaningful at all. It receives two 8-bit chars by value. It doesn’t know where the original variables are physically, so it can’t put new values into those original variables, so it can’t swap them. Any swap must use some form of pass-by-reference. Q1b: function to swap 2 arrays. After the swap, array1 is still a pointer but it points to the physical location of array2 %%A: same signature as Q1. [1] void ** is probably a feasible idea but may require casting. Usually the 2 arguments a1 and b1 should have the same declaration. If a1 is Animal* and b1 is Dog* (Note the single asterisks), then such a polymorphic swap is no longer straight-forward and fool-proof. # Forex trading is Singapore’s strength (A personal blog.) I think for the past few months in the Singapore job market (java or c++), i didn't notice any fixed income, credit, equity domain roles. There are some cross-asset system positions, and there are commodities and FX positions. I feel FX is roughly half (up to 66%) of all the roles that pays a reasonable salary. This is a hard lesson learned — I have to deepen my FX knowledge and track record otherwise the biggest chunk of jobs stay beyond my reach. I feel in terms of domain knowledge, FX is more relevant (to high-end software jobs in Singapore) than volatility, bond math, exchange trading, structured products, etc But why does FX pay above other fields. Here's what I came up with – equity is small, less active in S'pore than HK. The high-paying eq-related jobs are usually in HK – FX is perhaps more profitable at this moment – FX is Singapore's traditional strength for decades. #4 behind Ldn, Nyk, Tky – FX is high speed and high volume (in terms of market-data) so this places some stringent criteria on developer skill – FX is more electronic, more standardized, more inter-connected than FI, commodities or derivative markets, on par with cash equities. More technical skills required. It's interesting that FixedIncome has more complexity and has more profit potential but doesn't really pay comparable salary. # real/fake market-order + limit order in FX ECN Some popular institutional ECN’s offer 3 main types of orders. Taking buy orders for example, you can place – limit order – to buy at or below a specified price. It might match some offers immediately. All remaining amounts on the order remain in the market – IOC – fake mkt order – buy at or below a specified price. All unfilled amount is cancelled. This is more popular than the real mkt order – real mkt order – order without a price # secDB — helps drv more than cash traders@@ (Personal speculations only) Now I feel secDB is more useful to prop traders or market makers with persistent positions in derivatives. There are other target users but I feel they get less value from SecDB. In an investment bank, equity cash and forex spot desks (i guess ED futures and Treasury too) have large volume but few open positions at end of day [1]. In one credit bond desk, average trade volume is 5000, and open positions number between 10,000 to 15,000. An ibank repo desk does 3000 – 20,000 trades/day In terms of risk, credit bonds are more complex than eq/fx cash positions, but simpler than derivative positions. Most credit bonds have embedded options, but Treasury doesn't. In 2 European investment banks, eq derivative risk (real time or EOD) need server farm with hundreds of nodes to recalculate market risk. That's where secDB adds more value. [1] word of caution — Having many open positions intra-day is dangerous as market often jumps intra-day. However, in practice, most risk systems are EOD. I was told only GS and JPM have serious real time risk systems. # island rainfall problem – C array/pointer algo #include <cstdlib> #include <cstdio> #include <iostream> #include <iterator> #include <algorithm> #include <assert.h> using namespace std; int const island[] = { 54, 50, 54, 54, 52, 55, 51, 59, 50, 56, 52, 50 }; /////////////// Pos # 0 1 2 3 4 5 6 7 8 9 10 11 int const size = sizeof(island) / sizeof(int); int accu = 0; template<class ForwardIterator> ForwardIterator max_element_last(ForwardIterator first, ForwardIterator last) { ForwardIterator ret = first; if (first == last) return last;//empty range while (++first != last) if (ret <= first) ret = first; return ret; } void print1(int const* const a, char const * const label) { printf("%s=%d/%d ", label, a, a - island); } void printAll(int const const L, int const* const l, int const* const h, int const* const H) { if (l < h) { print1(L, "wallL"); print1(l, "ptr"); printf(" "); print1(h, "ptr"); print1(H, "wallH"); } else { print1(H, "wallH"); print1(h, "ptr"); printf(" "); print1(l, "ptr"); print1(L, "wallL"); } printf("%d=accumulated\n", accu); } void onePassAlgo(){ intwallLo, wallHi; intl, h; //moving pointers wallLo = l = const_cast<int> (island); wallHi = h = const_cast<int> (island) + size - 1; if (l > h) { std::swap(l, h); std::swap(wallLo, wallHi); } printAll(wallLo,l,h,wallHi); printf("All pointers initialized\n"); while (l != h) { if (l > wallHi) { wallLo = wallHi; wallHi = l; std::swap(l, h); //printf("new wallHi:"); } else if (l >= wallLo) { wallLo = l; //printf("new wallLo:"); } else { accu += wallLo - l; printf("adding %d liter of water at Pos#%d (T=%d)\n", wallLo - l, l - island, accu); } printAll(wallLo,l,h,wallHi); //now move the scanner if (l < h) ++l; else --l; } } void twoPassAlgo() { int const* const peak = max_element_last(island, island + size); printf("highest peak (last if multiple) is %d, at Pos %d\n", peak, peak - island); //(island, island + size, ostream_iterator<int> (cout, " ")); //forward scan towards peak int pos = const_cast<int> (island); //left edge of island int wall = pos; for (++pos; pos < peak; ++pos) { if (wall > pos) { accu += wall - pos; // accumulate water printf("adding %d liter of water at Pos#%d (T=%d)\n", wall - pos, pos - island, accu); continue; } //ALL new walls must match or exceed previous wall. printf("found new wall of %d^ at Pos#%d\n", pos, pos - island); wall = pos; } cout << "^^^ end of fwd scan ; beginning backward scan vvv\n"; //backward scan pos = const_cast<int> (island) + size - 1; wall = pos; for (--pos; pos > peak; --pos) { if (wall > pos) { accu += wall - pos; // accumulate water printf("adding %d liter of water at Pos#%d (T=%d)\n", wall - pos, pos - island, accu); continue; } //Note all new walls must match or exceed previous wall. printf("found new wall of %d^ at Pos#%d\n", pos, pos - island); wall = pos; } } int main(int argc, char argv[]) { onePassAlgo(); } /* Requirement -- an island is completely covered with columns of bricks. If between Column A(height 9) and Column B(10) all columns are lower, then we get a basin to collect rainfall. Watermark level will be 9. We can calculate the amount of water. If I give you all the columns, give me total rainfall collected. Code showcasing - stl algo over raw array - array/pointer manipulation - array initialization - array size detection - std::max_element modified - std::swap / # c# ReferenceEquals() on value types int ten=10; System.Console.WriteLine(object.ReferenceEquals(ten, ten)) ; // prints False —- Why? ten is an int32, i.e. a struct instance. Copy-by-value. So 2 new instances of the struct instance are created on stack, with obviously different addresses. # const – zero runtime (or space) cost http://www.parashift.com/c++-faq-lite/const-correctness.html points out that the “const” access check “….is done entirely at compile-time: there is no run-time space or speed cost for the const”. I feel the private/protected and final access modifiers are similarly compile-time only. Further, I guess template instantiation is also runtime-cost free. # kurtosis — thick tail AND slender All normal distributions have kurtosis == 3.000. Any positive “excess kurtosis” is known as leptokurtic and is a sign of thick tail. The word leptokurtic initially means slender — in a histogram, the center bar is higher, i.e. higher concentration towards the mean. To my surprise, the extreme left/right bars are also __higher___, indicating thick tails. To compensate, the rest of the bars must be shorter, since all the bars in a histogram must add up to 100%. In short, excess kurtosis means 1) slender and 2) thick tail. Thick tail is more important to many users as thick tail means more unexpected extreme deviations (from mean) than in the Normal distribution. Thick tail is unexplainable by Normal distribution and indicates a different, unidentified distribution. However, the “Slender” feature is more visible and is the meaning of “leptokurtic”. The thick tail is almost invisible unless plotted logarithmically — see http://en.wikipedia.org/wiki/Kurtosis # island rainfall problem: my code #include #include #include #include #include #include using namespace std; int const island[] = { 54, 50, 54, 54, 52, 55, 51, 59, 50, 56, 52, 50 }; /////////////// Pos # 0 1 2 3 4 5 6 7 8 9 10 11 int const size = sizeof(island) / sizeof(int); int accu = 0; template ForwardIterator max_element_last(ForwardIterator scanner, ForwardIterator const end) { ForwardIterator ret = scanner; if (scanner == end) return ret;//empty range, with zero element! while (++scanner != end) if (ret <= scanner) //"=" means find LAST ret = scanner; return ret; } //print height and address of a column void print1(int const const pos, char const * const label) { //int const height = pos; printf(“%s=%d/%d “, label, pos, pos – island); } void printAll(int const* const L, int const* const l, int const* const h, int const* const H) { if (l < h) { print1(L, “wallL”); print1(l, “ptr”); printf(” “); print1(h, “ptr”); print1(H, “wallH”); } else { print1(H, “wallH”); print1(h, “ptr”); printf(” “); print1(l, “ptr”); print1(L, “wallL”); } printf(“%d=Accu\n”, accu); } //Rule: move the lo-side pointer only void onePassAlgo(){ intloptr; //moving pointer, moving-inward. intwallLo, wallHi; //latest walls inth; //1st we ASSUME the first left side wall will be lower than the first right side wall wallLo = loptr = const_cast (island); wallHi = h = const_cast (island) + size – 1; //2nd, we validate that assumption if (wallLo > wallHi) { std::swap(wallLo, wallHi); std::swap(loptr, h); } // now lo is confirmed lower than the hi side printAll(wallLo,loptr,h,wallHi); printf(“All pointers initialized (incl. 2 walls\n”); while (loptr != h) { if (loptr > wallHi) { wallLo = wallHi; wallHi = loptr; std::swap(loptr, h); //printf(“new wallHi:”); } else if (loptr >= wallLo) {//see the >= wallLo = loptr; //printf(“wallLo updated:”); } else { assert (loptr < wallLo); accu += (wallLo – loptr); printf(“adding %d liter of water at Pos_%d (%d=A\n”, wallLo – loptr, loptr – island, accu); } printAll(wallLo,loptr,h,wallHi); // only by moving the loptr (not h) can we confidently accumulate water if (loptr < h) ++loptr; //lo side is on the left, move loptr right else –loptr; //lo side is on the right, move loptr left } } void twoPassAlgo() {//less convoluted int const* const peak = max_element_last(island, island + size); printf(“highest peak (last if multiple) is %d, at Pos %d\n”, peak, peak – island); //(island, island + size, ostream_iterator (cout, ” “)); //forward scan towards peak int pos = const_cast (island); //left edge of island int* wall = pos; for (++pos; pos < peak; ++pos) { if (wall > pos) { accu += wall – pos; // accumulate water printf(“adding %d liter of water at Pos#%d (T=%d)\n”, wall – pos, pos – island, accu); continue; } //ALL new walls must match or exceed previous wall. printf(“found new wall of %d^ at Pos#%d\n”, pos, pos – island); wall = pos; } cout << "^^^ end of fwd scan ; beginning backward scan vvv\n"; //backward scan pos = const_cast (island) + size – 1; wall = pos; for (–pos; pos > peak; –pos) { if (wall > pos) { accu += wall – pos; // accumulate water printf(“adding %d liter of water at Pos#%d (T=%d)\n”, wall – pos, pos – island, accu); continue; } //Note all new walls must match or exceed previous wall. printf(“found new wall of %d^ at Pos#%d\n”, pos, pos – island); wall = pos; } } int main(int argc, char argv[]) { twoPassAlgo(); accu = 0; cout<<"—————————–\n"; onePassAlgo(); } / Requirement — a one-dimentional island is completely covered with columns of bricks. If between Column A(height 9) and Column B(10) all columns are lower, then we get a basin to collect rainfall. Watermark height (absolute) will be 9. We can easily calculate the amount of water. If I give you all the column heights, give me total rainfall collected. Code showcasing – stl algo over raw array – array/pointer manipulation – array initialization – array size detection – std::max_element modified – std::swap / # object DB + built-in language -> secDB I have noticed at least 2 original creators (U/ML) describing secDB as a 2-piece suite [1] — an OODB (secDB) + a built-in language (Slang). [1] that's my own language, not theirs. (By the way, different secDB users* refer to it using different terms. End-developers who build business apps atop secDB mostly talk about __Slang__, perhaps because that's what they express business logic, then debug/test every day. End-developers don't modify secDB core engine at all, so they see secDB as a data store. Business users talk about __secDB__, because they don't care about Slang programming. Generally, Business users are more interested in data, and application features, not implementations.) But let's come back to the 2-piece suite. Initial motivation is characterized by a small number of key-keywords — Positions, market-risk, what-if, chain-reaction, object-graph… — keep these key concepts in focus. I think the OODB idea came first. Loading all Positions across all desks into one virtualized memory is valuable to risk scenario analysis. Obviously a position's risk profile depends on many variables (product/account, interest rates, FX rates, index vol, credit spread, product characteristics) so all of these must be represented as objects in the same virtualized memory. A big object graph. In each SecDB-alike system, there's a dedicated team building an in-house customized OODB. In some cases, the OODB being built is quite similar to Gemfire or Tangosol. I was skeptical but one of the original SecDB creators confirmed “that particular OODB project” is indeed part of the SecDB challenger system. The other part — the language — will be another blog post. For now, I'll just mention that in each secDB-derivative system, there's a dedicated team creating a customized language to manipulate the object graph. In some cases, python is chosen, with DAG features added. In other cases, some of the secDB core team members were hired to create a new language. FMD is somewhat similar in purpose to Slang. # %%top 3 tips on unix permissions Scripts must be readable AND executable [1] but compiled programs need only be executable. [1] exception — It is possible to run a script without execute permission by entering sh myscript You don’t have to be the owner of a file or have write permission on it to rename or delete it! You only need write permission on the directory that contains the file. a directory isn’t really a program that you can run even if it has execute permission. The execute bit is reused (like C++ union) rather than waste space with additional permission bits. Besides controlling a user’s ability to cd into some directory, the execute permission is required on a directory to use the stat() system call on files within that directory. This stat() returns file inode details. Therefore, to use ls -l file (i.e., to use stat() system call), you must have execute on the directory, the directory’s parent, and all ancestor directories up to and including “/” (the root directory). If execute permission is required for a directory, it is usually required for each enclosing directory component on the full path to that directory. ———- The tips below are less understood — The execute bit on a directory is sometimes called search permission. For example, to read a file /foo/bar, before the file can be accessed you must first search the directory foo for the inode of file bar. This requires search (“x”) permission on the directory /foo. (Note you don’t[2] need read permission on the directory to search in this case! You would need read permission on a directory if you were to list its contents.) [2] With execute but not read permission on a directory, users cannot list the contents of the directory but can access files within it if they know about them. # binomial tree: y identical diamonds The standard CRR btree is always drawn with all straight lines, equally spaced vertically and equally spaced horizontally. Therefore you always see nothing but a strict pattern of identical diamonds. Let’s zoom into this “geometry”. First, let’s set the stage for the discussion. In this conceptual “world”, a price (say IBM) can only be observed/sampled at periodic discrete moments, either once a second, or once a day, though the interval should be small relative to time to maturity. Price may change mid-interval, but we can’t observe that. Further, during each interval, the price either moves up or down. It can remain unchanged only in a trinomial tree — not popular in industry. Why diamonds? Because of interlocking/recombinant. See http://bigblog.tanbin.com/2011/06/option-pricing-recombinant-binomial.html Why equally spaced horizontally? Because the intervals are fixed and constant — at each clock tick, the variable must either rise or fall, never stay flat like a trinomial. Why equally spaced vertically? Because the y-axis is log(price). An interesting feature of the CRR btree. If after n-1 intervals you plot the n price values in a bar chart, they don’t fit a straight line — but try plotting log(price). Why are all the diamonds identical? Because the nodes are equally spaced both vertically and horizontally. I feel the regularity is a great simplification and helps us focus on the real issue — the probability of an upswing at each node — the transition probability function, which is individually determined at each node position. # dev-cpp and mingw integration My dev-cpp used to work. I later installed minGW and dev-cpp stopped working even when I compile the simplest program 1. Download new MINGW compiler at http://www.mingw.org/ and install it in C:MinGW 2. in Dev c++. right click on menu Tools>Compiler options. 3. in tab “Directory”, right click on “Libraries” and change “C:Program FilesDev-CppLib” to “C:MinGWlib” 4. Compile! # sequence-container≠array-based My blog http://bigblog.tanbin.com/2009/04/4-basic-foundations-of-all-collection.html claims all java/c#/STL structures are based on 4 basic data structures – array …. Official STL documentation uses the term “sequence containers”. Now, Sequence-container can be non-array-backed. Linked list is one example. The deque is not completely array-based. See ObjectSpace manual. A more detailed description of the HP implementation of STL deque is on P139 [[stl tutorial]]. It consists of multiple mini-arrays (segments) linked to a lookup construct. Therefore deque combines array and linked graph. Deque is one of the few random-access containers. # STL algos and their _if() and _copy() derivatives Note all the _if() accept only Unary predicates i.e. filters. Often, you start with a binary predicate like less … then you use bind2nd() to convert binary to unary predicate —-These algos have both _if and _copy derivatives– remove remove_if remove_copy remove_copy_if replace replace_if replace_copy replace_copy_if —-These algos have an _if derivative– count count_if find find_if —-These algos have an _copy derivative– partial_sort partial_sort_copy rotate rotate_copy unique unique_copy # windowless GUI WPF is a windowless gui; winform is different. Swing is probably windowless. In a windowless, each button is an image. In winform, each button is a first class native window with a “handle”. # smart_ptr{double* }i.e. smart ptr of ptr Should or can we ever put ptr-to-ptr into a smart ptr like smart_ptr? My problem is the delete in the smart_ptr dtor — “delete ptr2ptr2dbl” where ptr2ptr2dbl is pointing at a 32-bit object (let’s call it “Dog123”). Dog123 is a 32-bit pointer to a double object. Is Dog123 on heap or on stack or in global area? If dog123 is not in heap, the delete will crash (UndefinedBehavior) — deleting a pointer to stack (or global) if dog123 is in heap, then how is it allocated? (Now it’s best to draw memory layout.) I feel it is almost always a field in a class/struct. Supposed the 32-bit object dog123 is also referred to as student1.pointerToFee, like class student{ double * pointerToFee; // in this case, our smart pointer is perhaps set up like smart_ptr sptr( &(student1.pointerToFee) ) } Now, if our “delete ptr2ptr2dbl” works, then the memory location occupied by Dog123 is reclaimed. – that means the 64-bit double object is never reclaimed — memory leak – also, student1.pointerToFee is in trouble. It’s not a wild pointer (its 64-bit pointee is ok), but the 32-bit memory location holding pointerToFee is reclaimed. On the real estate of student1instance, there’s now a 32-bit hole — 4 bytes de-allocated. Q: how can we safely use this kind of smart pointer? %%A: I guess we must use a custom deleter Q: When would you need this kind of smart poitner? %%A: I don’t think we need it at all. # self-rating in java GTD+theory/zbs #halos#YH Hi YH, Self-rating is subjective, against one’s personal yardsticks. My own yard stick doesn’t cover those numerous add-on packages (swing, spring, hibernate, JDBC, xml, web services, jms, gemfire, junit, jmock, cglib, design patterns …) but does include essential core jdk packages such as — • – anything to do with java concurrency, • – anything to do with java data structures, • – [2017] Garbage collection • memory profiling (jvm tools) • GC log analysis • – [2017] java.lang.instrument, mostly for memory • – networking/socket, file/stream I/O • [!2017] generics, esp. type erasure • – RMI, • – reflection, dynamic proxy, AOP • – serialization, • – JNI, esp. related to memory • – JMX, jconsole, • – difference between different JDK vendors, • – real time java (The highlighted areas are some of my obvious weaknesses.) Now I feel my self-rating should be 8/10, but i still feel no one in my circle knows really more about the areas outlined above. I guess that’s because we don’t need to. Many of these low-level implementation details are needed only for extreme latency, where c++ has a traditional advantage. Another purpose of this list — answer to this Q: what kind of java (theoretical) knowledge would give you the halos in a Wall St interview? # fail fast:fundamental+Practical principle #java Fail-fast is one of those low-level coding habits that deserve its place among the valuable habits to be adopted by practicing app developers in industry. In contrast, library developers (including open-source authors) generally adopt fail-fast by default. Principle — prefer crashing the entire program. Don’t keep going. Don’t hope the dubious condition will be tolerated. Don’t hope the corrupted data will be left alone and left untouched. Sooner or later what you fear will happen. In such a case it can be very hard to find the root cause. The crash site might be far away from the buggy code. Example — when dealing with DAM issues, there are specific tools to make the program crash as soon as detected. I think they intercept, replace or integrate with malloc/free. Example — if null pointer can cause problem then check as early as possible. In java and c#, a lot of error messages simply say null pointer (like “unknown exception”) . It can take hours to find out the real cause. Example — fail-fast iterators. # vol surface wings, briefly Deep ITM/OTM part of a smile curve is sensitive to Skew and Tail values. By the way, if you have a bunch of smile curves forming a surface, then those parts are known as the __wings__. (You are judged by your knowledge of the jargon.) # beta, briefly Beta is calculated using regression analysis, and you can think of beta as the tendency of a security’s percentage Returns (not the continuously compounded return) to respond to swings in the market (represented by a benchmark). A beta of 1 indicates that the security’s price will move at the same magnitude with the market. A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security’s price will be more volatile than the market. For example, if a stock’s beta is 1.2, it’s theoretically 20% more volatile than the market. For example, many utilities stocks have a beta of less than 1. Conversely, most high-tech stocks have a beta of greater than 1, offering the possibility of a higher rate of return, but also posing more risk. Zero beta means 0 correlation with the index (i.e. the market), i.e. independent, insulated. Negative beta means anti-correlation, or bucking the market. If the market is always up 10% and a stock is always up 20%, the correlation is one (correlation measures direction, not magnitude). However, beta takes into account both direction and magnitude, so in the same example the beta would be 2 (the stock is up twice as much as the market). I feel Beta is more important to the buy-side than the sell-side. Note many sell-side megabanks have buy-side units too. Beside the standard beta on Return, there’s also what I call “vol-space” beta — where a beta of 1 means IBM realized vol over the past 2 years has identical magnitude of ups and downs as s&p (the benchmark) realized vol. This vol-space beta is calculated using 2 years of historical volatility numbers. # fitting cost vs Local-Vol cost (I think this applies to any vol surface fitting — Eq, FX, IR…) As a concept, fitting-cost is part of fitting, not validation, not extrapolation. Extrapolation has no fitting-cost since there’s no fitting. LV-cost is different from fitting-cost. LV-cost measures smoothness in LV — there’s an LV value at each point on the vol surface. Extrapolation calibration tries to minimize LV-cost. – High fitting-cost means fitted curve deviates too much from targets i.e. input data. – High LV-cost means some LV values are too high (or too low!!) compared to other LV values. Bump check is one of the many post-fitting checks on the new surface. # max-thruput quote distribution: 6designs#CAS,socket Update — fastest would require single-threaded model with no shared mutable Suppose a live feed of market quotes pumps in messages at the max speed of the network (up to 100gigabit/sec). We have (5) thousands of hedge fund clients, each with some number (not sure how large, perhaps hundreds) of subscriptions to these quotes. Each subscription sets up a filter that may look like some combination of “Symbol = IBM”, “bid/ask spread < 0.2…”, or “size at the best bid price….”. All the filters only reference fields of the quote object such as symbol, size and price. We need the fastest distribution system. Bottleneck should be network, not our application. –memory allocation and copying– If an IBM /quote/ matches 300 filters, then we need to send it to 300 destinations, therefore copying 300 times, but not 300 allocations within JVM. We want to minimize allocation within JVM. I believe the standard practice is to send just one copy as a message and let the receiver (different machine) forward it to those 300 hedge funds. Non-certified RV is probably efficient, but unicast JMS is fine too. Given the messaging rate, socket reader thread should be as lean as possible. I suggest it should blindly drop each msg into a buffer, without looking at it. Asynchronously consumer threads can apply the filters and distribute the quotes. A fast wire format is fixed-width. Socket reader takes 500bytes and assume it’s one complete quote object, and blindly drops this 500-long byte array into the buffer. –multicast rather than concurrent unicast– –cpu dedication– Each thread is busy and important enough to deserve a dedicated cpu. That CPU is never given to another thread. ————- Now let me introduce my design. One thread per filter. Buffer is a circular array — bounded but efficient pre-allocation. Pre-allocation requires fixed-sized nodes, probably byte arrays of 500 each. I believe de-allocation is free — recycling. Another friend (csdoctor) suggested an unbounded linked list of arrays . Total buffer capacity should exceed the temporary queue build-up. Slowest consumer thread must be faster than producer, though momentarily the reverse could happen. —-garbage collection—- Note jvm gc can’t free the memory in our buffer. –Design 3– Allocate a counter in each quote object. Each filter applied will decrement the counter. The thread that hits zero will free it. But this incurs allocation cost for that counter. –Design 6– Each filter thread records in a global var its current position within the queue. Each filter thread advances through the queue and increments it’s global var. One design is based on the observation that given the dedicated CPU, the slowest thread is always the slowest in the wolfpack. This designated thread would free the memory after applying its filter. However, it’s possible for 2 filters to be equally slow. –design 8–We can introduce a sweeper thread that periodically wakes up to sequentially free all allocations that have been visited by all filters. –Design 9– One thread to apply all filters for a given HF client. This works if filter logic is few and simple. –Design A (CAS)– Create any # of “identical” consumer threads. Any time we can expand this thread pool. while(true){ 2) examine the Taken boolean flag. If already set, then simply “continue” the loop. This step might be needed if CAS is costly. 3) CAS to set this flag 4a) if successful, apply ALL filters on the quote. Then somehow free up the memory (without the GC). Perhaps set another boolean flag to indicate this fixed-length block is now reusable storage. 4b) else just “continue” since another thread will process and free it. } # steps in pricing a vanilla European option using implied vol These steps are observed for a vanilla European call/put. Not sure about other options. ) prepare funding information — interest rates … ) prepare dividend information ) derive the greeks All input data fields are represented as a sturct. You can also use a data holder class, a DTO, or a property set. # Stoch volatility ^ local-volatility SV doesn’t refer to the random walk of a stock price (or an forex rate). SV refers to the random walk of instant volatility value [2]. This instant volatility (IV) can take on a value of 10%pa now, and 11.5%pa an hour later [1]. If a stock price were to fluctuate constantly by the micro second, then we would be able to record these movements during each second and compute realized/historical IV values for each interval. [1] Note all volatility values are annualized, just as we compare different rice brands by per-kg price. [2] realized vol or implied vol? Irrelevant. In the BS theory, volatility is a concept related to Brownian motion. Both r-vol and i-vol are indications of that theoretical volatility. I feel in this /context/, there’s no differentiation of implied vs realized vol. I feel many people agree that it’s a sound assumption to assume IV follows a random walk, but there are very different random walks. For example, the stock price itself also follows a random walk, but that random walk is carefully modeled by the drift + the Brownian motion. That’s one type of random walk. The IV random walk is different and I call it a special random walk (SRW), for want of a better word. Basically, SV models assume 1) the stock price follows a random walk characterized by an IV variable, along with a drift 2) this variable doesn’t assume a constant value as BS suggested, but follows a SRW. This SRW is described by a state variable, which depends on current stock price and has a mean-reverting tendency. I find the mean-reversion assumption quite convincing (yes I do). In reality, if we measure the realized IBM volatility over each trading day and write down those realized-vol values on a table top calendar, we will see it surges and drops but always stays within a range instead of growing steadily. The stock price may grow steadily (drift) but the realized vol doesn’t. SABR and local vol were said to be 2 models describing stochastic volatility, but veterans told me LV isn’t stochastic at all. I believe LV doesn’t include a dB term in sigma_t i.e the Instantaneous volatility. LV — when IV is described merely as a function of underlier price St and of time t, we have a local volatility model. The local volatility model is a useful and simple SV model, according to some. Another veteran in Singapore told me that local vol (like SV) is designed to explain skew. During the diffusion, IV is assumed to be deterministic, and a function of 2 inputs only — spot price at that “instant” i.e. St and t. I guess what he means is, after 888888 discrete steps of diffusion, the underlier could be at any of 888888 levels (in a semi-continuous binomial tree). At each of those levels, the IV for the next step is a function of 2 inputs — that level of underlier price and the TTL. # inputIterator category — unneeded@@ Q: why there's a category “Input Iterator” at all, where is it used? (Output iterator is a similar story, so this post will omit it.) I think the only major use is input stream. There are some algorithms like std::merge(…) that require a tiny subset of a C pointer's full capabilities. To make merge() useful on an input stream, STL authors put the Dummy type name “InputIterator” into merge() template declaration as a hint — a hint that in the implementation, only that subset of pointer capabilities are used. This is a hint to containers “Hey Containers, if you have an iterator capable of deference-then-read, then you can use me.” It turned out all containers except output stream has that capability. # ActionListener^Action Note that Action implementations tend to be more expensive in terms of storage than a typical ActionListener implementation class, which does not offer the benefits of centralized control of functionality and broadcast of property changes. For this reason, you should take care to only use Actions where their benefits are desired, and use simple ActionListeners elsewhere. I feel ActionListener objects are typically stateless. I feel they are pure functor objects. The word “Action” in “ActionListener” means very much like the generic “Event”. However, the word “Action” in Action.java seems to mean something else, such as the Control in Microsoft lingo. Anyway, i feel the word “Action” is ambiguous and overloaded. Let’s avoid it but do understand its various meanings. # remain relevant in a given technology(fundamentals Q: At age 55, will you still qualify as a swing developer, or SQL developer, or python developer, or Unix admin? 1) An important factor is the stability of the language and the changing demand on specific skillset in that Language (contrast java vs SQL), but let’s focus on another factor — fundamentals. 2) In every language, there’s a body of fundamental knowledge (“knowledge-pearls”) that are Empowering and Instrumental. They facilitate your learning of “superstructure”. Many hiring managers believe strong fundamentals are the most important skill with a given Language. I feel low-level knowledge will help you remain /relevant/ over 10 years. Some of the most tricky and frequently quizzed sub-topics are low-level — threading, memory-mgmt, collections, subclass memory layout, casting, RTTI, vptr, c++ big 3, … 3) I feel an appreciation of relative strengths/weaknesses of alternative technologies will help you remain relevant. Fundamental knowledge would help you appreciate them. 4) essential libraries of threading, collections, I/O, networking, … are not strictly part of the fundamentals, but part of mandatory skills anyway. # #1 usage of volatility surface I’d say end-of-day unrealized PnL is the most IMPORTANT usage. An integral part of it is mark-to-market. (However, For liquid option products with numerous “tight” market quotes, I don’t know if we really need the vol surface for PnL.) A more “fundamental” need for vol surface is the valuation of non-liquid volatility contracts, including structured, exotic, tailor-made contracts with optionality features. I prefer the words “contract” or “deal” rather than “instrument”, “product”, “security” or “asset”. Contract means there are at 2 counter-parties. If they really do the deal, at contract termination each will end up with a realized PnL, potentially humongous. The estimate, risk-management and analysis of that realized PnL is often the biggest job in a trading desk. In Equities and FX, vol surface is often the centerpiece (at least part thereof) of the valuation framework for such “contracts”. In a valuation framework, most other factors are simpler compared to the volatility factor. In a real London structured eq vol desk, such a valuation requires a Monte Carlo simulation which queries one or more vol surfaces repeatedly. However, i don’t think the valuation need to use the parameters (like skew, tail…). The surface is treated as a black box to query. The vol surface must be constructed by taking into consideration a variety of observed market data. Therefore a good surface is consistent with a diverse variety of market data, including but not limited to – dividend forecast, – tax schedule on dividends, – calendar convention, – holiday schedules…. But the most important market data is the premium on the liquid instruments, which typically cover the first few years only. Long-dated instruments are much less liquid. # fopen in various languages (file input/output –C++ ofstream outfile(“out.txt”); ifstream infile (“in.txt”); // class template –C FILE * pFile = fopen (“myfile.txt”,”w”); –php follows C <?php $handle = fopen(“a.txt”, “r”); ?> — python: outfile = open(“a.txt”, “w”) # semicolon is usually omitted –perl open (OUTFILE, “>>append.txt”) or die … ### No dollar sign. parentheses are optional but help readability –c# offers many convenient solutions — TextReader rd = new StreamReader(“in.txt”); TextWriter tw = new StreamWrioter(“out.txt”); Alternatively, File class offers variations of static string ReadAllText(string path) static void WriteAllText(string path, string contents) //creates or overwrites file –java I have written so many of them but paradoxically can’t recall which class we need to instantiate # java regex — replace with captured substring but modified Any time you have a string with lots of x.xx000001 or x.xx99999, it’s probably noise you want to get rid of. Here’s a java solution. Perl can do this in 1 line (at most 2). public static String cleanUp999or000(String orig) { final static Pattern PATTERN9999 = Pattern .compile(“(\\d\\.\\d)([0-8]9999+)(\\d\\s)”); Matcher m = PATTERN9999.matcher(orig); StringBuffer sb = new StringBuffer(); String without999 = orig; String without999_or_000 = orig; try { while (m.find()) { final long intEndingIn999 = Long.parseLong(m.group(2)); final long intEndingIn000 = intEndingIn999 + 1; System.out.println(intEndingIn000); m.appendReplacement(sb, m.group(1) + intEndingIn000 + m.group(3)); } m.appendTail(sb); without999 = sb.toString(); } catch (NumberFormatException e) { e.printStackTrace(); without999 = orig; } finally { without999_or_000 = without999.replaceAll( “(\\d\\.\\d+?)0000+\\d(\\s)”, “$1\$2”); } return without999_or_000; } Clients can trade by themselves through brokerage accounts, but for discretionary accounts, the traders are the investment professionals (IP) and portfolio managers (PM). PM are the bigger traders. A PM are product specialist, and manages a portfolio of several SMA (separately managed accounts) invested in a the product she specializes in. In terms of trading, PM are at the top of the food chain in wealth management.See also FX MA in [[Forex revolution]] PM actually uses specialized trading systems, custom made for them, with a dedicated IT team. They could, if they want to and equipped to, engage in high-frequency trading. As a buy-side trader in a sell-side bank, they enjoy preferential treatment in terms of transaction cost, provided they engage the parent firm’s sell-side trading desk. They can also by pass parent firm and execute on the street — i.e. through a competitor’s sell-side traders. This does happen and they get slapped on the wrist, hard. They have no relationship with clients. They don’t handle asset allocation — financial advisers do that. # swing OMS screen (PWM), briefly PWM screen, used till today (2012). Handles Eq, FX, FI, derivatives (esp. options), futures…. Real time OMS — “order state management”, including but not limited to order entry * manual order cancel/mod before fully executed Web GUI won’t provide the responsiveness and volume — At least 30,000 orders/day in US alone. 50-200 executions/order, executed in-house or on external liquidity venues. Typically 10 MOM messages per execution. – new order placed – acknowledged – partial fill – cancel/mod Each swing JVM has its own MOM subscriber(s). This codebase isn’t part of the IC build and has a frequent release cycle. # undefined behavior C++: #1 famous, unknown secrets (See below for smart ptr, template, non-RTTI) Deleting [1] a derived[3] object via a base[4] pointer is undefined behavior if base[6] class has non-virtual dtor, with or without vtable. This is well-known but it applies to a very specific situation. Many similar situations aren’t described by this rule — [1a] This rule requires pointer delete. In contrast, automatic destruction of a non-ref “auto” variable (on stack) is unrelated. [1b] This rule requires a heap object. Deleting a pointee on stack is a bug but it’s outside this rule. [1c] This rule is about delete-expression, not delete[] [3] if the object’s run-time type is base, then this rule is Inapplicable [4] if the pointer is declared as pointer-to-derived, then Inapplicable, as there is no ambiguity which dtor to run [3,4] if the object run time type is base, AND pointer is declared pointer-to-derived? Inapplicable — compiler or runtime would have failed much earlier before reaching this point. [6] what if derived class has non-virtual dtor? Well, that implies base non-virtual too. So Yes applicable. ) P62 [[effC++]] points out that even in the absence of virtual functions (i.e. in a world of non-RTTI objects), you can still hit this UB by deleting a subclass instance via a base pointer. ) The same example also shows a derived class-template is considered just like a derived class. Let me spell out the entire rule — deleting an instance of a derived-class-template via a pointer to base-class-template is UB if the base class-template has a non-virtual dtor. What if the pointee is deleted by a smart_ptr destructor? I think you can hit this UB. # xaml code behind Each xaml file describes the components, layout, data binding, event-handler and command binding associated with the visual components. The .xaml.cs file is the code behind file, implementing among others, the event-handlers mentioned in the xaml. The listeners don’t have to be part of an interface. It is probably mandatory to take 2 inputs — source and event. # table cell render – per column, per row, per data type Typically, you associate a table cell render (Instance, not class) on a column. (A column is a homogeneous data type.) You can also associate a render object to a class (such as Account or Student). It's less natural to associate a render to a row. You can, however, adapt the render behavior to a row, perhaps based on the row number, or any property of the actual “value” object # go short on tail-risk — my take Many sell-side [1] traders are described as being short tail-risk. In other words, they go short on tail-risk. [1] some hedge funds too * If you are long tail-risk (insurance buyers), you are LONGING for it to increase. You stand to profit if tail risk increases, such as underlier moving beyond 3sigma. Eg — buy deep OTM options, buy CDS insurance. * If you are short tail-risk (insurance sellers), you hope tail risk drops; you mentally downplay the extreme possibilities; you stand to Lose if tail risk actually escalates. Eg — sell OTM options, sell CDS insurance agressively (below the market). As a result, you would earn premiums quarter after quarter, but when an extreme tail risk does materialize, your loss might not be fully compensated by the premiums, because the insurance was (statistically) underpriced, because you underestimated the probability and magnitude of tail risk. Maybe you (the trader) is already paid the bonus, so the consequence is borne by the insurance seller firm. In this sense, the compensation system encourages traders to go short on tail risk. # convert a reference variable into a pointer variable You can’t declare a variable as a pointer to a reference, but we often take the address of a reference variable. I think it’s same as address of the referent. Q: If you need to pass a pointer to a 3rd party library, but you only received a reference variable — perhaps as an function input argument, how? A: Well, you can treat the variable as a non-ref and simply pass its address to the library. # ATM ^ ATF European calls, briefly Refer to my simplified BS formula in http://bigblog.tanbin.com/2011/06/my-simplified-form-of-bs.html. Q: for a ATF European call, where K == Sexp(rt) i.e. struck slightly Above current spot, how would the BS formulas be simplified d1 = -d2 = 0.5σt = $\frac{\sigma\sqrt{t}}{2}$ …………………. (in more visual form) C(S,t) = S [ N(d1) – N(-d1) ] = S * [2N(d1)-1] and depends only on sigma scaled Up for 2.5 years (our t) Q: how about an ATM European call, where S==K? A: the ATM call (slightly Lower strike than ATF) has more moneyness than the ATF call , because stock will drift past K long before expiry. The diffusion of the stock prices is “centered” around the drift. # ##common c++ run time errors In java, the undisputed #1 common run time error is NPE, so much so that half of all error checks are null-pointer-checks. In c++, divide-by-zero is similarly a must. But there are more… – divide by zero – pointer-move beyond bounds — remember all array sizes are compile-time constants, even with realloc() – read/write a heap object (heapy thingy) via a reference variable after de-allocation – return by reference an object allocated on the stack — bulldozed – dereference (unwrap) a dangling pointer – c-style cast failure – double-free – dereference (unwrap) a null pointer — undefined behavior, unlike java NPE. We should always check null before dereferencing. —-less common – delete a pointer to non-heap – free a pointer to non-heap – hold pointer/reference to a field of an object, not knowing it’s soon to be reclaimed/bulldozed. Object could be on heap or stack. More likely in multi-threaded programs. – misusing delete/delete[] on a pointer created with new/new[]. The variable always looks the same — plain pointers. ————- For any of the above, if it happens in a dtor, you are in double trouble, because the dtor could be executing due to another run time error. The authoritative [[essential c++]] says that for every exception, there must be a “throw” you can find. Divide-by-zero is something directly done on “hardware” so no chance to throw. I feel many error conditions in C are treated same as in C, without “throw”. In contrast, • I feel operator-new is a typical “managed” low level operation that can (therefore does) use exception. • dynamic_cast() is anther “managed” low level operation added over C, so it does throw in some cases Now, JVM “wraps” up all these runtime error Conditions into exceptions. Java creators generally prefer to push these error conditions to the compilation phase, to reduce the variety of Runtime errors. What remain are wrapped up as various RuntimeExceptions. It’s rather remarkable that JVM let’s you catch all(?) of these exceptions. No undefined behavior. # [12]case/group-by/self-join: #2 ] G9 (Simplest solution is at the end, which also returns #2 alone ….) I have seen many tricks in SELECT queries (Most using joins – Fine.), but now if I must name one keyword to be the most powerful yet unappreciated keyword, it has to be 1) CASE. 2) The combined power of case and group-by is even more impressive. 3) Yet more unthinkable is the combination of case/group/self-join. 4) correlated subquery (slow?) in SELECT, FROM, WHERE and HAVING. http://www.informit.com/articles/article.aspx?p=26856 explains “In addition to subqueries in the WHERE and HAVING clauses, the ANSI standard allows a subquery in the FROM clause, and some relational database management systems (RDBMSs) permit a subquery in the SELECT clause.” Key to understanding case_group_self-join is the intermediate work table. Mind you, intermediate table is the key to _every_ tricky self-join. P30 [[ transact-sql cookbook]] among many chapters, has a wonderful solution to find the top 5 values in a table without a 5-way self-join. Based on that, here’s a simplified but full example, showing several distinct solutions. These solutions can be adapted to find 5th largest value in a table, too. — setting up the data —- drop table public.students create table public.students( student varchar(44), score decimal(4,1), primary key (student) ) insert into students values( ‘Andrew’, 15.6) insert into students values( ‘Becky’, 13) insert into students values( ‘Chuck’, 12.2) insert into students values( ‘Dan’, 25.6) insert into students values( ‘Eric’, 15.6) insert into students values( ‘Fred’, 5.6) insert into students values( ‘Greg’, 5.6) select * from students Solution 1 —– top 3 scores — intermediate table select * from students h right join students L on h.score > L.score select L.student, ‘is lower than’, count(h.student), ‘competitors’ from students h right join students L on h.score > L.score group by L.student having count(L.student) < 3 —– lowest 4 scores — intermediate table select * from students h left join students L on h.score > L.score select h.student, ‘defeats’, count(L.student), ‘competitors’ from students h left join students L on h.score > L.score group by h.student having count(L.student) < 4 —- Solution 2, using case — intermediate table select , (case when h.score > L.score then 1 else 0 end) from students h left join — inner join ok since cartesian students L on 1=1 select h.student, ‘defeats’, sum(case when h.score > L.score then 1 else 0 end), ‘competitors’ from students h left join — inner join ok since cartesian students L on 1=1 group by h.student having sum(case when h.score > L.score then 1 else 0 end) < 4 –same solution tested on http://sqlzoo.net/howto/source/z.dir/tip915069/sqlserver select h.name, h.area, ‘is smaller than’, sum(case when h.area < L.area then 1 else 0 end), ‘countries’ from cia h, cia L group by h.name, h.area having sum(case when h.area < L.area then 1 else 0 end) < 4 —– (concise) Solution 3, using correlated sub-select, P295 [[sql hacks]] — without intermediate table select from students o where (select count(1) from students where score < o.score) < 4 –Same solution tested in http://sqlzoo.net/howto/source/z.dir/tip915069/sqlserver: select * from cia o where (select count(1) from cia where area > o.area) < 4 — shows top 4 …and (select count(1) from cia where area > o.area) > =3 — returns #4 alone …and (select count(1) from cia where area > o.area) > =2 — returns #4 #3 exactly –This technique shows its power when you want top 2 in each continent, without group-by select * from cia o where (select count(1) from cia where area > o.area and region=o.region) < 2 order by o.region, o.area I feel for a student/practitioner, it pays to think in terms of CASE. This strikingly simple solution can be rewritten using (messy) CASE. # swing automated test, briefly 3) http://www.codework-solutions.com/testing-tools/qfs-test/ says …event is constructed and inserted artificially into the system’s EventQueue. To the SUT it is indistinguishable whether an event was triggered by an actual user or by QF-Test. These artificial events are more reliable than “hard” events that could be generated with the help of the AWT-Robot, for example, which could be used to actually move the mouse cursor across the screen. Such “hard” events can be intercepted by the operating system or other applications. 2) http://jemmy.java.net/Jemmy3UserTutorial.html and http://wiki.netbeans.org/Jemmy_Tutorial explain some fundamentals about component searching. Jemmy can simulate user input by mouse and keyboard operations. 1) java.awt.Robot is probably the most low-level — Using the class to generate input events differs from posting events to the AWT event queue — the events are generated in the platform's native input queue. For example, Robot.mouseMove will actually move the mouse cursor instead of just generating mouse move events. # workhorse jcomponents ranked – 1) table — most business data are collections of Domain objects. Consider SQL. – 2) tree – (tree table) – grid (often implemented as table) – text components — displays or editors ** text pane, styled document – list –containers: panes tabs splitter # option valuations – a few more intuitions It’s quite useful to develop a feel for how much option valuation moves when underlier spot doubles or halves. Also, what if implied vol doubles or halves? What if TTL (time to expiration) halves? For OTM / ITM / any option, annualized i-vol multiplied by TTL is the real vol. For example, If you double vol and half TTL twice, valuation remains unchanged. If you compare a call vs a put with identical strike/expiry (E or A style), the ITM instrument and the OTM instrument have identical time value. Their valuations differ by exactly the intrinsic value of the ITM instrument. (See http://www.cboe.com/LearnCenter/OptionCalculator.aspx.) — Consistent with European option’s PCP, but to my surprise, American style also shows this exact relationship. I guess it’s because the put valuation is computed from a synthetic put (http://25yearsofprogramming.com/blog/20070412.htm). For ATM options, theoretical option valuation is proportional to both vol and TTL, i.e. time-to-live. http://www.cboe.com/LearnCenter/OptionCalculator.aspx and other calculators show that – when you change the vol number, valuation changes linearly – when you double TTL while holding vol constant, valuation grows quadratically. For OTM options? non-linear For ITM options, it’s approximately the OTM valuation + intrinsic value.	2020-09-26 22:32:05	{"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": 1, "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": 0.2573927342891693, "perplexity": 8546.06878753505}, "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/1600400245109.69/warc/CC-MAIN-20200926200523-20200926230523-00027.warc.gz"}
https://datascience.stackexchange.com/questions/10028/nlp-rules-for-chunking-verb-phrases	# NLP : Rules for chunking Verb Phrases I have read a lot of documentation surrounding NP chunking but what about Verb Phrases? Has there been a fixed set of rules for VP chunking?	2021-07-24 05:45:34	{"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": 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": 0.1710139513015747, "perplexity": 6435.936983426357}, "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/1627046150129.50/warc/CC-MAIN-20210724032221-20210724062221-00240.warc.gz"}