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# Sum of Digits Question If A is the sum of the digits of $5^{10000}$, B is the sum of the digits of A, and C is the sum of the digits of B, what is C? I know it has something to do with mod 9, but I'm not sure how do use it to solve the problem. I found this question in my Math Challenge II Number Theory Packet, and I got confused. - What's going on with these close votes? The OP clearly showed effort, people. Maybe try reading the question in its entirety. In any case, other than that $C\equiv B\equiv A\equiv5^{10000}\mod9$, I don't see how $\mathbb Z/9\mathbb Z$ is going to help us here, are you sure it's relevant? – Jack M May 8 '14 at 0:57 all I know is that using mod 9 gives the sum of digits mod 9, so I think it might help somehow – Jason Chen May 8 '14 at 0:58 That tells you $A \equiv B \equiv C \mod 9$, and that you can compute $5^{10000} \mod 9$ to figure out the residue class modulo $9$. Then there's probably a counting argument you can do to show that $C$ must be a $1$ digit number, and is therefore determined. I could be wrong though. – Dustan Levenstein May 8 '14 at 1:03 An important point is that sum of digits is about $4.5$ times the base $10$ log, so it shrinks big numbers quickly – Ross Millikan May 8 '14 at 1:18 ## 2 Answers Clearly $5^{10000}$ is a number with fewer than $10000$ digits, and the sum of these digits is less than $90000$. That is, $A<90000$. So $A$ has at most $5$ digits and the same argument shows that $B\le45$. The largest sum of digits of any number less than $45$ is $12$ (if the number is $39$), so $C\le12$. But $C$ must be the same as the original number modulo $9$ and so $$C\equiv5^{10000}\equiv5\times(5^3)^{3333}\equiv5\times125^{3333} \equiv5\times(-1)^{3333}\equiv-5\pmod9\ .$$ The only positive integer less than or equal to $12$ which is congruent to $-5$ modulo $9$ is $4$, and this is the value of $C$. - $B\le44$ because the value of $A$ with the largest sum of digits is $89999$. – Jason Chen May 14 '14 at 4:26 @JasonChen that's true. If you want to do this kind of thing you could also say that $\log_{10}(5^{10000})<6990$, so $5^{10000}$ has at most $6990$ digits, and the last two digits are $25$, so $A\le62899$, so $B\le41$. However this merely adds extra work without improving the solution. The point is that the most trivial, mindless estimates are still enough to solve the problem. – David May 14 '14 at 6:25 And $B\le 44$ would simply be a stronger argument. The statement $B\le 45$ is not false. There's no necessity of $a$ being equal to $b$ when $a\le b$. – user26486 May 18 '14 at 15:44 @mathh It would not be a stronger argument, it would be an equally strong but (slightly) more difficult argument. It is elegant to obtain the required result with minimum work. – David May 18 '14 at 21:37 @David Why not? How do you understand the word 'stronger'? What I meant was that the inequality is sharper. We have better information about $B$ if we know that $B\le 44$ instead of $B\le 45$ because of the fact that $B$ cannot be equal to $45$. And I didn't imply that it is useful in this case. I only informed Jason that the argument $B\le 45$ in intself is not false in case he didn't know but he likely did though. – user26486 May 20 '14 at 4:08 Let $S(n)$ denote the sum of digits of $n$. Then, note that $S(n) \le 9(\lfloor\log_{10}(n)\rfloor + 1)$. Thus, $(S(5^{10000}) \le 9(\lfloor\log_{10}(5^{10000})\rfloor + 1) = 9(\lfloor10000\log_{10}(5)\rfloor + 1) = 9(\lfloor1000\log_{10}(5^{10})\rfloor + 1) = 9(\lfloor1000\log_{10}(9765625)\rfloor + 1) \le 9(\lfloor1000\log_{10}(10000000)\rfloor + 1) = 9(\lfloor1000\log_{10}(10^7)\rfloor + 1) = 9(\lfloor1000(7)\rfloor + 1) = 9(7001) = 63009$ Also note that the maximum possible sum of digits of the numbers $\le 63009$ is $59999$, with sum of digits $41$. Now, the number with the maximum sum of digits that is $\le 41$ is $39$, with sum of digits $12$. So, $C \le 12$. Since $5^{10000} \equiv (5^2)^{5000} \equiv 25^{5000} \equiv (-2)^{5000} \equiv 2^{5000} \equiv (2^3)^{1666} \cdot 4 \equiv 8^{1666} \cdot 4 \equiv (-1)^{1666} \cdot 4 \equiv 4 \pmod{9}$. Since $C \equiv 5^{10000} \pmod{9}$ and $0 \le C \le 12$, $C = 4$. -	{}
# stuck on more probability • Feb 26th 2009, 01:27 PM johnewton stuck on more probability Much appreciated in advance for guidance on this.. A sample of 5 different calculators is randomly selected from a group containing 16 that are defective and 30 that have no defects. (a) What is the probability that 3 of the 5 calculators in the sample are defective? (b) What is the probability that at least one of the 5 calculators in the sample is defective? • Feb 26th 2009, 02:22 PM Plato Quote: Originally Posted by johnewton A sample of 5 different calculators is randomly selected from a group containing 16 that are defective and 30 that have no defects. (b) What is the probability that at least one of the 5 calculators in the sample is defective? The probability that none of the five is defective is: $\Large{ \frac{{30\choose 5}}{{46\choose 5}}}$.	{}
Article Contents Article Contents # Asymptotic analysis of continuous opinion dynamics models under bounded confidence • This paper deals with the asymptotic behavior of mathematical models for opinion dynamics under bounded confidence of Deffuant-Weisbuch type. Focusing on the Cauchy Problem related to compromise models with homogeneous bound of confidence, a general well-posedness result is provided and a systematic study of the asymptotic behavior in time of the solution is developed. More in detail, we prove a theorem that establishes the weak convergence of the solution to a sum of Dirac masses and characterizes the concentration points for different values of the model parameters. Analytical results are illustrated by means of numerical simulations. Mathematics Subject Classification: Primary: 35R09, 35B40; Secondary: 91D10. Citation: • [1] G. Aletti, G. Naldi and G. Toscani, First-order continuous models of opinion formation, SIAM J. Appl. Math., 67 (2007), 837-853.doi: 10.1137/060658679. [2] A. Baldassarri, U. Marini Bettolo Marconi and A. Puglisi, Kinetic models of inelastic gases, Mat. Mod. Meth. Appl. Sci., 12 (2002), 965-983.doi: 10.1142/S0218202502001982. [3] E. Ben-Naim, P. L. Krapivsky and S. Redner, Bifurcation and patterns in compromise processes, Phys. D, 183 (2003), 190-204.doi: 10.1016/S0167-2789(03)00171-4. [4] M. L. Bertotti, On a class of dynamical systems with emerging cluster structure, Jour. Diff. Eq., 249 (2010), 2757-2770.doi: 10.1016/j.jde.2010.03.014. [5] V. Blondel, J. M. Hendrickx and J. N. Tsitsiklis, On the $2R$ conjecture for multiagent systems, Proc. Europ. Control Conf., Kos, Greece, (2007), 874-881. [6] L. Boudin and F. Salvarani, Modelling opinion formation by means of kinetic equations, in "Mathematical Modeling of Collective Behavior in Socio-economic and Life Sciences" (G. Naldi, L. Pareschi and G. Toscani eds.), (2010), 245-270, Birkhauser, Boston.doi: 10.1007/978-0-8176-4946-3_10. [7] L. Boudin and F. Salvarani, The quasi-invariant limit for a kinetic model of sociological collective behavior, Kinet. Relat. Models, 2 (2009) 433-449.doi: 10.3934/krm.2009.2.433. [8] L. Boudin and F. Salvarani, A kinetic approach to the study of opinion formation, M2AN Math. Model. Numer. Anal., 43 (2009), 507-522.doi: 10.1051/m2an/2009004. [9] C. Canuto, F. Fagnani and P. Tilli, A Eulerian approach to the analysis of rendez-vous algorithms, Proc. of 2008 IFAC Conf., (2008), 9039-9044. [10] G. Como and F. Fagnani, Scaling limits for continuous opinion dynamics systems, Ann. Appl. Probab., 21 (2011), 1537-1567.doi: 10.1214/10-AAP739. [11] S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, Journal of Statistical Physics, 120 (2005), 253-277.doi: 10.1007/s10955-005-5456-0. [12] G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Adv. Comp. Sys., 3 (2001), 87-98.doi: 10.1142/S0219525900000078. [13] B. Düring, P. Markowich, J-F. Pietschmann and M-T.Wolfram, Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders, Proc. R. Soc. Lond. A, 465 (2009)(2112), 3687-3708.doi: 10.1098/rspa.2009.0239. [14] S. Galam, A review of Galam models, Int. J. Mod. Phys. C, 409 (2008), 3687-3708. [15] U. Krause, A discrete nonlinear and non-autonomous model of consensus formation, in "Communications in Difference Equations" (S. Elaydi, G. Ladas, J. Popenda and J. Rakowski eds.), Gordon and Breach Science Publ., Amsterdam, (2000) 227-236. [16] J. Lorenz, A stabilization theorem for continuous opinion dynamics, Phys. A, 355 (2005), 217-223.doi: 10.1016/j.physa.2005.02.086. [17] J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, Internat. J. Modern Phys. C, 18 (2007), 1819-1838.doi: 10.1142/S0129183107011789. [18] S. McNamara and W. R. Young, Kinetics of a one dimensional granular medium in the quasi elastic limit, Phys. Fluids A, 5 (1993), 34-45.doi: 10.1063/1.858896. [19] L. Pareschi and G. Toscani, Self-similarity and power-like tails in nonconservative kinetic models, J. Stat. Phys., 124 (2006), 747-779.doi: 10.1007/s10955-006-9025-y. [20] G. Toscani, Kinetic models of opinion formation, Commun. Math. Sci., 4 (2006), 481-496. [21] G. Weisbuch, G. Deffuant, F. Amblard and J. P. Nadal, Meet, discuss, and segregate!, Complexity, 7 (2002), 55-63.doi: 10.1002/cplx.10031.	{}
# User talk:Mydogategodshat Monday 2 August 22:46 UTC Welcome to my talk page. My name is Paul Gallienne. I Have been writing business and economics articles for Wikipedia since early 2003 under the name Mydogategodshat. ## Welcome Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need pointers on how we title pages visit Wikipedia:Naming conventions or how to format them visit our manual of style. If you have any other questions about the project then check out Wikipedia:Help or add a question to the Village pump. Cheers! --maveric149 27 May 2003 ## For your information Just so you know, an easier way to write [[market segment\|market segments]] is [[market segment]]s. For more helpful hints, take a look at Wikipedia:How to edit a page. Keep up the good work! Kingturtle 03:14 5 Jun 2003 (UTC) ## Development of the business section Are you also going to do product churning about which I know almost nothing.... ??? -- David Martland 13:57 5 Jun 2003 (UTC) Thanks for the idea about churning. I might get to it eventually, but first I want to do all the marketing basics. If you're not familiar with churning, you're obviously not a stock broker. So far I've edited most of the existing marketing articles, about 15 of them (some of them were quite well done,but most of them were not), I've reorganized the marketing section on the root 'business' page, and I've contributed about 30 marketing articles. I think it will require about another hundred articles before the marketing section of this encyclopedia becomes really useful at the university level. I am currently doing the product management topics. Next I will do the pricing, and then marketing research areas. - - user:mydogategodshat Good work. These were neglected areas. You are probably right about needing a many more articles about marketing, but, a hundred seems a lot. Perhaps there should be an article on sales force and brand management and service marketing as a start, and then, it may start to become more obvious where more fillers are required. For various reasons those three, along with commodity markets, are more fundamental than product management as such, so they should be written first. EofT At this stage I have writen about 100 articles. The marketing section now has about 120 articles in it. I've finished (at least for now) product management, marketing fundamentals, and pricing . Next I think I'll finish marketing research. You mention I should do brand management. It is done. Service marketing needs a lot of work. Sales also needs work. It has a couple of articles, but needs one on sales technique, and one on sales force management. As for your claim that commodity marketing is more important than product management, I don't know if that is true. I agree that some commodities like oil, gold, and wheat have important political and strategic aspects to them. But the product management area is huge. It includes virtually all consumer products and most industrial products. I guess it depends on how you define "important". - - - user:mydogategodshat In mid September 2003 I compiled lists of business topics. They give us a good indication of the state of the Wiki business section. Here is the count: • accounting - 69 articles • business ethics - 39 articles • business law - 59 articles • economics - 248 articles • finance - 149 articles • human resources management - 48 articles • information technology management - 58 articles • management - 71 articles • marketing - 192 articles • production - 25 articles The most developed sections are economics and marketing. The least are HR and production. IT and HR have a lot of stub articles. We have made an incredible amount of progress in the last 4 month, but we have a long way to go. Keep up the great work everybody. mydogategodshat 03:41, 27 Sep 2003 (UTC) Maybe I've got the terminology wrong, but a colleague mentioned product churning when I queried why so many ink jet printers have completely incompatible ink cartridges. I had the feeling that, if he was correct, the term had something to do with creating very small differences in products in order to give an appearance of user choice, while at the same time ensuring that products are needlessly kept incompatible. I'd be interested to see what you write when you get around to it. -- David Martland 15:06 9 Jun 2003 (UTC) Your colleague is right. The strategy used by these printer manufacturers could be considered a form of churn. Churning in general terms is just selling more product than is benificial to the customer. The classic example is a stockbroker that regularly buys and sells securities in your portfolio. You may or may not gain, but the broker sure piles up commissions. I can see how a strategy of selling the basic product at a loss, but charging outrageous amounts for refills (printers), useage time (cell phones), blades (razors),or prints (photography), can be considered a form of churning. user:mydogategodshat Absolutely. EofT You might want to take a look at Razor and blades business model. -- Anon ## Blocked again I did not and probably never will block you. What may have happened is that I blocked a user once, and on occassions, your service uses an ISP address that is similar to that of the blocked user. Or maybe there is another explanation that I don't know about. but i did NOT block you. Kingturtle 09:24 29 Jun 2003 (UTC) I didn't block you. You must've been assigned an IP address used by a vandal. Are you on AOL by any chance? -- Notheruser 04:35, 5 Aug 2003 (UTC) Yes I am with AOL. mydogategodshat 04:37, 5 Aug 2003 (UTC) I just unblocked the addresses I blocked yesterday. You shouldn't get that notice any more. :) -- Notheruser 04:39, 5 Aug 2003 (UTC) Thanks, I just saved an edit and it worked fine. mydogategodshat 04:44, 5 Aug 2003 (UTC) I am not blocking you. but the system might think so once in a while. What probably happened is that I blocked a vandal once, and sometimes when you log in, your service uses an IP address close to the one the vandal used. We can ask at the "Village Pump" to figure out how to get around this, if you like. Kingturtle 16:44 12 Jun 2003 (UTC) Hi, I noticed the stuff in section 2 about you being blocked. I see that you were using IP address 64.12.97.6 back on 29 Sep when you added a comment to User:Jimbo Wales/Pushing To 1.0. That IP address has been associated with vandalism now and then, see User contributions. So that's probably what happened. Tualha 01:02, 22 Dec 2003 (UTC) Several AOL proxy IP addresses were blocked earlier for being User:Michael. I have unblocked them. Sorry for any inconvience, Maximus Rex 01:32, 3 Feb 2004 (UTC) Thanks mydogategodshat ## What's in a name? Hi, I was just wondering, what does your username mean? I assume it is meant to be read "my dog ate god's hat," but is there anything significant to that? It's just a very interesting name :) Adam Bishop 04:13, 18 Aug 2003 (UTC) If you can figure out what it means, you tell me. I wanted to come up with something more interesting than a normal name. The first pseudonum I tried was MonadsExcrescent but after about a month I started to think that was too pretentious. Only philosophers new what it ment. Most people thought it had something to do with shit. So I changed it to something nonsensical and humorous (or so I thought). For about a week I used Mydogategodsbone, but I quickly realized that some religious people would read negative connotations into it and be offended. So I changed it to Mydogategodshat. Hopefully no one will be offended and some people might get a chuckle out of it. mydogategodshat 05:02, 18 Aug 2003 (UTC) I thought it was "my dog ate, god shat." Which has something to do with excrement and might offend religious people. ;-) --Nate Silva 23:49, 20 Sep 2003 (UTC) Thats what I thought when I first saw it also :-) Interesting that it was changed to this because some people thought the other one had to do with excrement also :-) You just can't win sometimes.Ark30inf 23:57, 20 Sep 2003 (UTC) I find this username could be offensive. I suggest it be changed. { MB \| マイカル } 14:16, Aug 26, 2003 (UTC) ...presumably because someone might parse it as "my dog at god shat". -- Cyan That would have to be "my dog, at e-god, shat." And while God may be worthy of worship, E-God seems, like E-Commerce, to simply imply an increased level of fraud and charlatanry - fully worthy of being shat at by your dog I am sure. I propose you simply ignore these silly fellows and keep your name, as you have gathered a good reputation with it. Don't invent problems where none exist. That was a typo. It was supposed to be "my dog ate god shat", which, I admit, doesn't make a lot of sense. At least one person (me) saw "god shat", not "god's hat". (But when I looked at your contributions, I saw that they were all made in good faith, so I figured that the problem was me, not you.) Cheers, Cyan 22:30, 10 Oct 2003 (UTC) I thought it is "My dog ate god-shat". I don't know which is more weird. --Menchi 22:41, 7 Nov 2003 (UTC) And I thought it was "Mydo gate. Go Dshat!" -- Cimon Avaro on a pogostick 00:22, Nov 9, 2003 (UTC) The funny thing is that the user could have avoided all this confusion by changing the username to MyDogAteGodsHat or My Dog Ate God's Hat. And if he doesn't want to lose edit histories and the such it would be a simple matter to ask a developer to make the DB change. But minor acts of subversion are what make a society healthy, no? --The Cunctator 06:32, 29 Nov 2003 (UTC) The even funnier thing is that the developers could have avoided all this confusion by giving people random numbers as usernames instead of letting people choose. Or, possibly, people could have avoided all this confusion by asking extra politely for changing name as a favour, rather than a duty or demand - who knows... Κσυπ Cyp 13:10, 29 Nov 2003 (UTC) Did anyone ever attempt to VfD your user handle? Don't worry i 'm not going to either, tho i find its imagery disturbing, obviously your intention !! Thanks again. I have just now looked a litle more carefully at your user handle and realise that i too need professional help for misreading it, your intention perhaps to trigger Freudian repressed thoughts? Amazing how the juxtapostion of certain letters of the alphabet trigger certain imagery, your user-name is a true Rorschauh (ink-blot test) of the unconscious.Norwikian 12:36, 23 Dec 2003 (UTC) Have you considered italicizing or bolding parts of your name in your signature to reduce confusion? mydogategodshat for example. æle 22:42, 20 February 2006 (UTC) Keep it as it is - it's funny!!!! ;) Richard n 20:23, 11 December 2006 (UTC) Hi, I've just nominated you on Wikipedia:Requests for adminship. This doesn't guarantee anything, but if other people agree, then being blocked by accident wouldn't be a problem for you any more. Κσυπ Cyp 16:38, 30 Oct 2003 (UTC) As far as I can tell, a lot of people are against anyone with your username (I find this odd), but would support you being a sysop after a name change... It's a bit confusing, but maybe people wouldn't object to "mydogconsumedgodsfavouritehat"... Κσυπ Cyp 08:50, 8 Nov 2003 (UTC) Howdy. Regarding your nomination to become a sysop, it looks like everyone would be unanimous in their support it if not for your name. Any thoughts on this? May I suggest "Mydogatemyhat" or "Mdagh"? The latter makes it clear that no word is "shat" and could be expanded to "My dog ate god's hat" in signatures. Daniel Quinlan 03:12, Nov 21, 2003 (UTC) I have decided not to change my name. mydogategodshat 05:41, 24 Nov 2003 (UTC) I would like to express a heartfelt thanks to: Κσυπ Cyp , Cimon Avaro on a pogostick, snoyes, Adam Bishop , Secretlondon, Hephaestos , 207.189.98.44 , Jamesday, Pakaran for nominating me and supporting me. It is encouraging to know that my efforts over the past 6 months have been appreciated. I prize your actions all the more knowing that many of you were not familiar with my work and had to do some research to decide whether to support me or not (because I limit my contributions to the 750 business/economics articles) . Thank you for the time, the effort, and the confidence. There was a minority that did not support me because of my name. It seems that half have a problem because they read “shat” into it and half because of the word “god”. I find this amazing. The people that read “shat” into the character string had to ignore the commonly used word “hat” and pick out a word that has not be in common use for more than a century. My spell checker is currently telling me that the word dosn’t exist. One complainant insisted on converting “Monad” into “gonads” and “Excrescent” into “excrement”. Another saw “a dog eating a bone” as a sexual act. All I can say to these people is “Get professional help”. As for changing my name, I have decided not to do that for two reasons. One is a philosophical reason. For an explanation, read The Crucible, particularly where John Proctor declares the importance of your name. The price of adminship is too high. The other reason is a practical one. I find it useful to use the same name on all my online activities. It is interesting that two universities and several commercial sites don’t have a problem with my name. Maybe it is not all that surprising since they are not inhabited by trolls trying to forward their cause. Hope to see you around the business/economics pages in the future. mydogategodshat 03:02, 22 Nov 2003 (UTC) Hi, I'm one of those who said I would support your nomination for sysop only if you were to change your name (I suggested spaces between words or capitalisation to make the words clearer). I've just read your message on Cyp's talk page. I understand and respect your decision not to make any change to your name, I would probably feel very similarly if asked to change mine. I can't help but be a little annoyed by the suggestion that those objecting to your name are "trolls trying to forward their cause" and should "Get professional help", although perhaps I am being oversensitive (again). I hope you will believe me when I say my reaction was genuine and my intentions good. I will no doubt continue to be uncomfortable with your name but, as I said, I understand your reasons for not changing it. So, I withdraw any objection to you becoming a sysop and will support any future nomination. Regards -- sannse 13:58, 29 Nov 2003 (UTC) Thank you for your input. Please do not take my comments personally. They were not directed at any one individual; nor were they intended to apply to all those that wanted me to change my name. They refer more to a general tendency that I have noticed during my time here at WP. When I compare the peer review process here to the peer review process in academia, I notice an important difference. In academic circles there is an understanding that the basis of any review process is solid logical reasoning backed up by ample empirical data. The WP review process seems to be closer to "this is my opinion and because this is a democracy my opinion is just as good as anyone elses, irrespective of any evidence given". The structuring of the VFD page is a good example of how this culture has permeated WP. People vote with a single word, or at most a sentence. Rarely do you see a well reasonsed argument why they voted the way they did. One draws the same conclusions looking through most of the talk pages. Most of the edit wars that waste so much of contributors' time result from the internalization of this epistimological criterion. This "one-person-one-vote" review process seems to attract trolls that are out to further their cause. I drew, what I thought was a reasonable conclusion that some (or even many) of the people that wanted me to change my name were acting out of teleological aspirations rather than a deeply felt sense of offense. Of course, I cannot see inside their psyche so I will never know their actual mix of motivations. I am sorry that you thought I was directing my comments specificly at you. That was not my intention (unless of course they do apply to you in which case I am aiming them directly at you). mydogategodshat 06:33, 30 Nov 2003 (UTC) Heh! that's the first time I've needed to use my dictionary twice to read a message on Wikipedia ;) You are right that there are a number of problems with the decision making process around here. I tend to feel that they are more to do with the limitations of the medium than any bad intent - but that's me, the eternal optimist ;) As to your name, I know my views are down to genuine feelings of disquiet and I'm sure that's also true of at least some of the others who commented. But I feel I made mistakes in the way I expressed those views. I apologise for that. I doubt we will bump into each other much around here in the future, unless you have a sudden urge to swap your interest in economics for a passion for dog breeds and the Grammy awards, so bye for now. Regards -- sannse 21:09, 30 Nov 2003 (UTC) ## Adminship nomination for the second time Some time when you have a few hours to spare, you might want to read the discussion at Wikipedia:Requests for adminship... Last I counted, about 12 support, 6 oppose, 4 ambiguous. Last I counted, about 14 support, 5 oppose, 2 ambiguous. (Think I counted wrong the first time.) Absolutely no negative comments that aren't purely based on your username... I must admit I find the objections to your username somewhat... odd... ${\displaystyle \ _{\ _{\mathrm {K} \sigma \upsilon \pi -{\sqrt {C^{2}+y^{2}+p^{2}}}}}}$ 17:50, 14 Jan 2004 (UTC) Hello again. You may consider changing your nickname into something which will not rise objections. It will be better for everyone, including you, since you will not have to defend yourself against those who get offended. It is also dangerous for our policy about offensive nicknames; some people will criticize us that we don't enforce the policy. I don't find the nickname offensive, but some people do. Just to live in harmony with everyone. Why create controversy when you can avoid it? So be smart and change your name for the sake of harmony and peace:) Friendly, Optim 04:07, 15 Jan 2004 (UTC) Just to say that while I fully understand your decision not to accept the adminship nomination, I personally consider it to be Wikipedia's loss. Bmills 11:51, 15 Jan 2004 (UTC) Same here, my thoughts too. ${\displaystyle \ _{\ _{\mathrm {K} \sigma \upsilon \pi -{\sqrt {C^{2}+y^{2}+p^{2}}}}}}$ 16:46, 15 Jan 2004 (UTC) I challenge the assertion that there is a legitimate field called philosophy of business, but, if you write on that topic, I will review and be fair to it. I think it is wrong to consider the current business philosophy article to be pointless, but perhaps, it is ultimately a marketing ploy to call such models a "philosophy", and maybe this is popular management theory (if indeed here is such a thing as philosophy of business). The article could be expanded however, and establish how well or poorly the models discussed live up to being actual "philosophy". That might be fun. EofT The philosphy of business is a legitimate subject (or at least that is what they tell you when they teach it to you in MBA courses). It deals with the philosophical, political, and ethical underpinnings of business and economics. I think that is called political economy by both classical and post-neoclassical economists. I imagine Islamic banking would be included for instance. And by that definition both Natural Capitalism and perhaps even Experience Economy qualify, as they have robust positions on these things. EofT Political economy is quite different. Political economy is economics. It teaches the princples of economics, but not in a technical manner like economic theory courses. There is no calculus or complex mathematical models. The approach is more thematic and historical. It is broader in scope and brings political considerations into the picture. This makes it quite different from the philosophy of business and economics, which uses philosophical and ethical techniques to examine the fields of business and economics. user:mydogategodshat It asks questions like what the social role of business should be, if indeed it should have one at all. It deals with questions of individualism vs collectivism, freewill, enlightened self interest, and natural rights. Some philosophers, like B Manderville, Butler, Shaftsberry, and F Hutcheson (Adam Smiths Professor at the University of Glassgow), were major contributors. - - user:mydogategodshat Definitely political economy. It seems a special name was invented for this by the MBA schools to avoid encountering the left's anti-business arguments, or even those of classical economics. EofT Try taking some courses in political economy and/or the philosophy of business and you will see the differences. One is economics , the other is philosophy applied to economics.user:mydogategodshat I suppose I do not accept this distinction at all. Philosophy is "metas on anything", and is prone to infinite regress and ignorance of bodily impacts. I would say that this distinction is a false one, and shows some real errors of thought. But then I tend to agree with the Catholics, Greens, Communists or Muslims that both philosophy and business must be subordinated to certain limits arising from human limits, as interpreted by something that is variously cognitive science, theology, ideology, fiqh. All f those, globally a majority, would probably agree with me that the distinction you make facilitates no end of mischief. Given that, we can have fun arguing out each point. But I am unlikely to accept this distinction you make, or th your professors make. Wikipedia being global, we must deal with diversity. EofT The relationship between political economy and the philosophy of business/economics, is analogous to the relationship between history and the philosophy of history. One is history. The other is the philosophical analysis of history, that is, it is philosophy. It is also analogous to the relation between sports and the psychology of sports. There is also the relationship between music and the psychology of music. There is sports and the business of sports. Do you deny all these distinctions (and many more). Or is it just the role of philosophy that you want to deny? As for your claims that philosophy "is metas on anything, is prone to infinite regress and ignorance of bodily impacts", they are unintelligible without further explanation and are given without any supporting evidence, so I am forced to give them the attention that they deserve (ie. ignore them). As for your claims of support from various groups, I think you might find it to be considerably less broad than you think. Of all the Catholics, Greens, Communists, Muslims, or "global majority" that I know, not one of them wants to deny the role of philosophical thought the way you appear to be doing. In fact many of the great philosophers of the last 1500 years have been Catholics or Muslims. Marx wrote almost as much on philosophy as he did on politics and economics. Environmentalists have contributed significantly in the field of philosophy of law.- - - user:mydogategodshat As for your assertion that I said the article was pointless, what I actually said was that the article was highly subjective. And we know what the Wikipedia policy is on subjective articles. - user:mydogategodshat I think it is less subjective even as it is than it would be written from the m:MBA point of view. EofT My point was I felt that there should be some clear criteria as to how to decide what management theories to be included in the article. I also suggested there should be an explanation of why each management theory is included. This would make it less subjective, more value to readers, and raise the level of writing to that of knowledge (or even wisdom) rather than mere opinion. I really don't care what perspective the articles are writen from as long as the writer justfies his/her claims. user:mydogategodshat Recent vandalism to service economy (see page history), service sector, product stewardship, negative commodity market, and even Experience Economy (which should link to service economy) is leaving a mess with many incorrect assertions and open links. You might also look at moral reasoning where an important issue in ethical vs. economic vs. personal choice is raised. As you actually seem to care about the state of these articles, as opposed to having an agenda based on control and the carceral state as some do, you will hopefully take an interest and restore the useful material. Also of interest is a discussion of comprehensive outcome and yield (economics) etc - see User:Cyan/kidnapped for a list of articles that have been selectively censored for reasons that have nothing to do with the best possible economics section. Regrets that the undemocratic Wikipedia Governing Council forbids competent collaboration on the HR and related topics. Keep up the good work, and by all means, resist and defy the sysops completely. Yours, trolls. I have looked at the list of your kidnapped articles. I am competent to discuss only three of them. I have pasted these three into a word processer and will introduce parts of them whenever I can do so in a fair and balanced way. mydogategodshat 19:13, 12 Dec 2003 (UTC) Experimentation pages are generally titled "Sandbox" or some variation thereof...but in any case, they belong in the User space, not the Wikipedia space. I've taken the liberty of moving your "ZZUK" page to User:Mydogategodshat/sandbox. -- Someone else 00:09 5 Jul 2003 (UTC) For Discussion on charts see: talk:Wikipedia policy on charts Please do not place headings before the intro of articles - it is non-standard and ugly. --mav 06:02, 5 Aug 2003 (UTC) Your article on "ways to improve ebay" does not belong on this site, for the same reason Encyclopeadia Britanica doesn't include articles on how to improve buggy-whips. There IS a site where this article would be at home however, the meta-wiki. I suggest moving the content there, and removing it from here. - anon OK, I agree mydogategodshat 16:17, 16 Aug 2003 (UTC) ## Related topics lists I see you are adding lists of business related topics lists to the bottoms of certain pages. While there may be some specific instances when this might be useful I am wondering why you did it on customer privacy? What are the odds of someone wanting to look at a list of finance topics after they have come to this page. Isn't one of the points of Wikipedia is to allow people to discover things through links that are content specific? Maybe you should start a general business topics overview list, or incorporate you fascination with lists (I have this disease also) with more established list pages on Wikipedia? Alex756 I can not say with certainty where any reader will go next. That is why I wanted to present a range of options. All I can say is topics that are related to the article will be a likely destination in a large percentage of cases. If you feel that a list should be added or deleted from a specific page, then do it. That is how Wiki works. My objective was to compile a set of lists of likely destinations, and to this end I sharted with a comprehensive set of lists that covered all business articles. Then I modified the set of lists slightly to make it better match the specfic page. mydogategodshat 09:43, 22 Aug 2003 (UTC) Triple bottom line could stand to be included on various lists, it's kind of a top-level topic that embraces a lot of accounting reform and monetary reform and simultaneous policy in one place. There are many references, but a few good external ones could stand to be selected by a more neutral party, i.e. one not clearly an advocate of the approach, and more likely to select credible critical links. Bretton Woods also needs a much more extensive treatment, being as important as it is. Hi, you left me a warning about adding "charts" to Wikipedia. I'm not aware of having done that in the last couple of months -- except for a couple of articles on various battles, & Roman Emperors & I believe is in accordance with a format established elsewhere. Perhaps you have confused me with someone else? -- llywrch 18:48, 1 Oct 2003 (UTC) I saw your response on my page, & it appears that I have used "charts" in the past. (I prefer to call them "tables", as is the practice with HTML.) But where I have been using them, I've been following established practice. perhaps you should mention this on the appropriate meta: page? (Or if there is a defined standards page for articles on Kings & Battles, there?) -- llywrch 23:56, 1 Oct 2003 (UTC) ## Lists merge Hi, I merged the List of business people and the List of corporate leaders. You have reverted this for the last. Could you explain to me the difference between a business person that is important enough to have a Wikipedia article and a corporate leader? Thanks, Ap 14:45, 18 Oct 2003 (UTC) I wanted those two pages merged, because the list of business people was a proper subset of the list of corporate leaders, regardless of the definition at the top of that page. I guess I should have merged to list of corporate leaders to begin with. I strongly believe specialization of lists is good. I also believe this confusion could have been avoided if list of business people had been redirected to list of corporate leaders from the moment of that page's creation. Ap 12:53, 19 Oct 2003 (UTC) Hi, I moved Market dominance strategies/temp to Talk:Market dominance strategies/temp because there are not supposed to be subpages in the main article namespace. The talk page for the article can be found at Talk:Market dominance strategies/discuss. Angela 14:20, Oct 19, 2003 (UTC) ## Roach bait Hello, I'm very green here. I'm still trying to get my bearings. You seem to be the person to talk to about marketing. I've moved the text you removed from roach bait to undercover marketing (a common term recently used on 60-minutes). Does this look good to you? Okay, I've made some changes to undercover marketing, but I'd like your feedback on them. I'm still getting used to the style guidelines and conventions. Isogolem 22:45, 3 Nov 2003 (UTC Thanks for the article on Roach bait. I seperated the marketing part because I don't think this is a term commonly used by marketers. I think a much more common name for the technique is "under cover marketing", so your renaming it (moving it in Wikipedia lingo) was a good idea. Not only is it a more common term, but it is also less biased (NPOV in Wikipedia lingo). We try to present our articles from a "Neutral Point Of View". In practice this usually involves starting an article with generic unbiased language, then as you get further into the article you can add the advantages, disadvantages, criticisms, and other more biased comments. Hope you enjoy your stay here. mydogategodshat 02:20, 2 Nov 2003 (UTC) Cool, thanks for the help! Good work on editing the article. You're a fast learner. You have created an informative, unbiased article, which never-the-less expresses your opinion on the matter. I made a couple of changes. I added some links to marketing concepts that you mentioned, and I put the definition right at the top. We have a convention at Wiki that we put the basic definition at or near the top of the article. Keep up the great work. mydogategodshat 05:33, 2 Nov 2003 (UTC) Hello, Isogolem. Sorry if I came off as a little harsh. By not "very well-written", I was referring to the somewhat conversational tone of the paragraphs, when it should be more third-person objective (more boring, perhaps, but more straightforward and encyclopedic). By non-NPOV, I was mostly referring to the use of the phrase "roach bait", which seems like a fairly loaded term. By the way, the undercover marketing article, as mentioned above, it quite well done. So, I'm sorry if I rubbed you the wrong way, and I hope you have fun here. -- Minesweeper 11:34, 2 Nov 2003 (UTC) Thanks to both of you for the pushback and help. I've done another revision of it and made again a little more cohesive, but also possibly less straight forward. I've also added to the talk page - some links. Can you guys take one more look at it? Isogolem The article keeps getting better. You've added more detail and presented a critical perspective without losing the article's encyclopedic and unbiased nature. I added a sentence about stock promoters. I noticed your link to buzz goes to an airline. I think it would be best to either create a new article buzz (marketing) or take the link out until we have an appropriate article to link to. mydogategodshat 03:27, 4 Nov 2003 (UTC) Like your addition, change made to buzz. Thanks so much for the support and guidance. :) Isogolem We could probably put the credit info for Credit repair on the Talk page. What do you think? RickK 04:34, 20 Nov 2003 (UTC) Minor request. Can you please fill in the summary field more often, especially when it is not a minor edit. Thanks (makes it easier for me to remember if I have looked a a particular edit before). Keep up the good contributions. Jrincayc 02:12, 29 Nov 2003 (UTC) OK, I'll try to remember. I tend to get sloppy late at night. mydogategodshat 04:46, 29 Nov 2003 (UTC) ## nice work! You've done a remarkable job at organizing and re-writing the article. I commend you! Kingturtle 00:39, 11 Dec 2003 (UTC) ## Nice work on Production Theory basics The article Production Theory Basics looks good. I was wondering where you think that the interaction between prices and mariginal productivity should go? Also, if you like, can you add some support to adding m:SVG image support on the Wikipedia:WikiMoney page to make collaborating on creating vector graphics simpler. Thanks. Jrincayc 16:46, 15 Dec 2003 (UTC) The interaction between price and MPP is seldom discussed directly, or at least they didn't talk about it when I studied economics. I don't know where it would go. The approach that I was going to take was to start with non-monetary aspects of production (marginal physical product, production possibilities frontier which I just wrote last night, and production functions) then bring costs into it with an article on cost theory and an article on long run cost and production. As you know, pricing isn't usually brought into it until you start dealing with profit maximization and market structures. If you can write an article on the relation between price and marginal product I would like to read it. I presume you would transform MP into costs and read pricing from the industry demand schedules. I will look into the image support page you mentioned. mydogategodshat 17:10, 15 Dec 2003 (UTC) The short version is that once the marginal productivity of adding $10 of good x to the production inputs produces less then$10 more of the output good, the manufacturer will stop adding good x. I certainly agree that the market structure does matter in that it can become pretty complex when the inputs and the outputs are not part of a competative (i.e. price taking) market. I do think that it might be useful to put some simple examples in the production theory basics page of a competative market to motivate where the whole marginal productivity is actually used. Jrincayc 15:52, 16 Dec 2003 (UTC) It sounds like what you are talking about is the pricing and optimum usage of factor inputs: you know, setting Marginal Revenue product equal to the Marginal Resource Cost and all that stuff. It might be too advanced for 99.99% of WP viewers. We might be able to write an article on it, but it won't be light reading. mydogategodshat 03:30, 17 Dec 2003 (UTC) I have read the m:SVG image support page and maybe I'm not to bright today, but I don't understand what support is being asked for. mydogategodshat 17:27, 15 Dec 2003 (UTC) Basically, there are two types of graphics formats (and occasionally combinations of the two). The first is raster images. These are composed of pixels and png format is an example of one. However, since they are made up of pixels, they cannot be scaled easily, and since lines and curves are composed of pixels, they can only be modified one pixel at a time. The other type of graphics formats are vector graphics. These are made up of a series of drawing commands such as draw a line from (1,0) to (3,2), or draw a curve connecting the points (1,2),(3,4),(5,2). Vector graphics can be easily scaled since you just multiply all the coordinates by a constant. Also, since the files are a list of commands, it is easy to modify the graphic since lines can be changed by moving one of the coordinates, and so can curves. SVG is a vector format. So if Wikipedia supported it, then say you could upload the SVG file straight out of Corel Draw. I could then take it and say add a price line, change the units to be dollars and then reupload it as an SVG file to a new name. As it is, the graphics on wikipedia are PNG's which are far harder to modify since to do the same thing I would have to erase the pixels that make the text. For example try makeing a modification to the following images that I have created: fig1.svg versus fig1s.png. The svg is much easier to work with. Hope that helps explain why I want SVG support. Jrincayc 15:52, 16 Dec 2003 (UTC) To create my graphics, I use Corel Draw. Although it can save images in about 20 different formats, PNG is not one of them, so I load it into Corel Photo House and save it as a png there. I am not familiar with a SVG format. mydogategodshat 17:37, 15 Dec 2003 (UTC) Although I support your drive to be able to modify images as easily as we can modify text, I do not feel I understand the technical issues well enough to talk intellegently about it at the page that you suggested. Sorry. mydogategodshat 03:37, 17 Dec 2003 (UTC) Hi, two more lists: List of process management topics, List of theory of constraints topics Mkoval 22:18, 16 Dec 2003 (UTC)~~ See: Wikipedia talk:Manual of Style (lists - stand alone lists) -- User:Docu Thanks for supporting the retention of Sir T.B. on U.S.A. Did anyone ever attempt to VfD your user handle? Don't worry i 'm not going to either, tho i find its imagery disturbing, obviously your intention !! Thanks again I have just now looked a litle more carefully at your user handle and realise that i too need professional help for misreading it, your intention perhaps to trigger Freudian repressed thoughts? Amazing how the juxtapostion of certain letters of the alphabet trigger certain imagery, your user-name is a true Rorschauh (ink-blot test) of the unconscious.Norwikian 12:36, 23 Dec 2003 (UTC) ## Fractional-reserve banking Just wanted to say I thought your re-write of fractional-reserve banking was excellent and provided some much-needed clarification. Gandalf61 13:47, Jan 2, 2004 (UTC) ## Self-introduction Hi. Why you write no info about you on your userpage? Feel free to add a self-introduction, if you like. Optim 00:25, 15 Jan 2004 (UTC) I was going to give an introduction on my user page but decided that it would be counter productive. Much of what is on user pages is just vanity. I see no reason to list my employment details, my degrees, or even the WP articles that I've writen. None of this is relevent. If you want to know me look at the subjects that I cover in my writings. If you want to judge me, do it based on the quality of the articles that I have writen. To make an assessment based on the superficial contents of a user page is the equivalent of judging a person based on the colour of their skin, their religion, their gender, or their nationality. When, in academia, a submitted article goes under peer review, the names of the submitter(s) are often deleted. This is so the reviewer assesses the paper on its own merits, uninfluenced by spurious factors. Wikipedia should operate in the same way. mydogategodshat 08:04, 15 Jan 2004 (UTC) Well, here are my guesses: Male, MBA, age 28, German America, Unmarried. ;) Jrincayc 03:21, 15 Jun 2004 (UTC) Impressive manifesto. You are quite eloquent. And probably your articles are original writings not copied from other sources, something quite rare on the Wikipedia. RCSB 13:37, 28 September 2005 (UTC) ## Social welfare (political science)? What purpose is served by moving Social welfare to Social welfare (political science)? --mav 08:39, 24 Jan 2004 (UTC) Because it containt two topics that need to be disambiged. I have separated the economics parts and put them under welfare economics and with a redirect from social welfare (economics). And I separated the political material and put it under social welfare (political science). mydogategodshat 08:45, 24 Jan 2004 (UTC) I have started to write an article on Welfare economics and "social welfare in economics". It was necassary to take the political material out so as not to confuse the reader with the two very different uses of the term. mydogategodshat 10:54, 24 Jan 2004 (UTC) ## quote I placed a quote from you I found here on my user page. I found it both eloquent and insightful. If you want to comment about this, let me know. p.s. I am one of those offended by your name :) Jack 22:57, 26 Jan 2004 (UTC) Thank you for your kind words. I am seldom eloquent and even more rarely insightful, so to be said to be both is a bit of a shock to me. You're not being facetious are you? :) mydogategodshat 04:18, 27 Jan 2004 (UTC) No, certainly not (altho I will admit I am less offended by your name than annoyed at its irreverence). You astutely summed up some meta-wiki issues I have been attempting to express in various circumstances here for some time past. Thank you. Jack 09:27, 28 Jan 2004 (UTC) Added that quote to Wikipedia:Why Wikipedia is not so great. Jrincayc 03:24, 12 May 2004 (UTC) Re Urban economics, the original author of the article is not english, and will not be bugged at all by you renaming the article; feel free :-) Anthere OK, Its done. mydogategodshat 08:54, 31 Jan 2004 (UTC) ## rocks and minerals project Since you commented on the original, wanted to let you know that I created a WikiProject Rocks and Minerals if you'd like to join. Elf 19:33, 4 Feb 2004 (UTC) Thanks for the invite, but honestly, I know nothing about rocks and minerals. I think my time would be better used on a subject that I know something about. Good luck on the project. mydogategodshat 21:07, 4 Feb 2004 (UTC) You might want to go Here to find other "rock hounds". mydogategodshat Thanks for the welcome! I hope this is the correct area to reply to you?, I left one in my section too. Still getting use to wikipedia, but it's been very fun so far. I've been having fun editing topics outside of economics, esp. about anonymous p2p and futurist ideas (i am going to check out if you have anything on the Singularity) too. I'll find my way back to economics soon enough, I'll probably add some more to Political Economy, and Econometrics next. Laurentian does overlook a lake and is out in the middle of no where so it has lots of forests. There could be a cement teepee, the campus is pretty spread out, I spent 99% of my time in the social sciences section so you probably have seen more of it then I have :). ## Labour Economics on the firm side, it's YS(LD), because commidity output is related to amount of workers hired to work. it's opening downward (n-shape). (i tend to mix up concave/convex) on the household side, it's D(LS). Ppl get more disutility from work as they work more hours. it's opening upward (u-shape). This whole thing should be actually be part of the classical macroeconomics model. hopefully i can find time to add more about it. There is a separate field study which deal with the microeconomics of labor market, i think should belong to the labor market entry. --user:voidvector Yes I think everybody gets confused with convex/concave because it depends on which side of the curve you're looking at. I use the convention of always stating that it is convex or concave to the origin (looking from the line to the origin) or from the origin (looking from the origin to the line). It is much like the ambiguity about a downward sloping curve. I always clarify this by saying downward sloping to the right. When I have time I also will try to add some microeconomic analysis to Labour economics. mydogategodshat 20:52, 14 Feb 2004 (UTC) i don't know how would i draw it to have it on the computer right now. if you have any advance graphing utility it will be nice. --user:voidvector I will put together some typical labour economics diagrams that we can use if we choose to. mydogategodshat 23:39, 14 Feb 2004 (UTC) the graph you made has a little mistake: the max hour is should not be 24, because we cannot possibly work 24 hrs/day. my labor economics book used 16 hrs a day. we can just use a variable if anything. That is very interesting. Both my references are using 24hrs. I suppose it depends on whether you are thinking of a single day (in which case 24 hrs is correct because it is possible to work for 24 hours in a single day) or multiple days (in which case 16 hours would be correct because it would be impossible to maintain 24 hour work days for multiple days). I can change it if it is really important to you. mydogategodshat 05:56, 16 Feb 2004 (UTC) this applies to eco models: the naming of variable is a problem. cause different ppl literally use different letterings. I am doing mostly macro models in class now. they use N for labor quantities. I remember in my labor class last year, they used L. --user:voidvector Yes there is a lot of variation in notation. In my labour economics we used N, in intermed macro we used QL, and in welfare ec we used L. I don't think it matters if we are not consistent from article to article. But we must be consistent within an article. What I generally try to do with the diagrams is to spell it out in words. This eliminates the problem, and it also make the encyclopedia more accessible to people that do not have a strong economics background. When I write articles I aim for a range of target readers between upper highschool level and upper undergrad level. What this means is that I have to start with the basics and build up the models one step at a time. Except in very rare instances, I always stop before I get to the calculus. That is why I filled in your classical aggregate supply model with a lot of verbiage. To readers at the second or third year level the equations are clear without any words, but to less prepared readers some explanation is important. I think I will do that "income/substitution effects of wage increase" diagram now. Talk to you later. mydogategodshat 05:54, 16 Feb 2004 (UTC) -- Hi! I left a copy of this in the labour market section too, very good article, I like the pictures. I'm glad wikipedia is slowly adding images too it, makes it a much more powerful tool. This is a very good article on labour economics. I like the split between macro and micro economics too, it is organized nicely. Plus there is room to add the classical and Marxist views of labour too since its categorized in that fashion also. One thing could be added to the criticisms part and is the neglected role of unpaid labour. Even though labour is unpaid it still can play an important in society, like child raising, but is often neglected in many economic models. Usually it is left out since it is difficult to incorporate it (usually because it is difficult to measure unpaid work), or the best method of incorporating it is disagreed upon. There are a few problems with not including the unpaid labour variable, or any significant variable, in a model. One is that the model’s conclusions might be biased, recommendations cannot be maid on the basis of promoting the good from unpaid labour since it is ignored. Even though I am not necessarily a fan of Karl Marx, his views are a good contrast to neo classical - classical economics view of labour. A brief excerpt on him might be good, but if being featured on the front page is eminent then I wouldn’t worry about it in the short run. I only have partial notes on Marx / labour from my studies though since I exchanged my Marx class for a class in which the professor didn’t take attendance ;). It’s hard to find unbiased views on Marx or sites that explain his ideas in economic terms clearly. A brief excerpt could be added on the importance of labour economics since unemployment is the macroeconomic problem that affects the public most directly and severely. You could add that full employment is a goal, i.e. normative economics, of many democracies and one role of labour economics is to try and achieve this full employment objective. That could then segway into a contrast between free market and command economies too since one benefit of command economies is constant full employment.--ShaunMacPherson 10:47, 11 Mar 2004 (UTC) ## Relieved and/or Rejected Hey, just thought you might want to know, you aren't listed at Wikipedia:Administrators. Cheers, Meelar 04:57, 20 Feb 2004 (UTC) I don't know if I should feel relieved or rejected. :) - mydogategodshat 05:07, 20 Feb 2004 (UTC) New economics article at Big Mac index, it used to be a simple redirect to PPP. Please feel free to cast your economic eye over it. It probably needs adding to the appropiate "List of ... topics" articles, could you do that, you surely know your way around better than I do. THanks. Pete/Pcb21 (talk) 11:41, 21 Feb 2004 (UTC) A quick bit of thanks for reformatting and condensing those EH.Net links on Economic History. :) -- Fennec 22:33, 4 Mar 2004 (UTC) You are welcome. mydogategodshat 00:11, 5 Mar 2004 (UTC) Before u edit communal reinforcement please be aware that this article may be merged with groupthink. By the way, I didn't disagree with your edit. Andries 20:39, 7 Mar 2004 (UTC) U are going too far with editing communal reinforcement. Please stop. Andries 20:49, 7 Mar 2004 (UTC) Every one of the additions I made fit the definition as given at the top of the article. Part of the danger of starting a list is that people will add things that, although they fit the criterion for the list, you might find disturbing. mydogategodshat 20:55, 7 Mar 2004 (UTC) Hi. I added a brief section on social networks to the Labor economics article. I'm an economics student myself, but this is a case where I think a sociological theory bears mention. Feel free to revise, or add to it if you know more than I do about the subject. Isomorphic 06:13, 9 Mar 2004 (UTC) Hi. :) I took the liberty of redrawing your graphs on Labour economics in response to the comment Isomorphic made on featured article candidates. My versions use less colors, so they're not as attractive, but the lines are thinner and the text all black so it's easy to read. Feel free to revert if you want to. :) fabiform \| talk 03:46, 11 Mar 2004 (UTC) Go ahead. It is just a style issue and I really don't care about that. I won't say thanks however because I don't think ugly black and white stick pictures are an improvement. They are the type of diagrams we used to draw with PC Paint back in 1988. However that is just my opinion. mydogategodshat 06:35, 11 Mar 2004 (UTC) I'm sorry if my chages offended you. If they are not an improvement in your opinion then you should of course change them back (click (rev)). If you have any constructive requests for chages to the graphs, then feel free to ask me to change them, it wouldn't take long as I have the files in a suitable format. :) fabiform \| talk 18:12, 11 Mar 2004 (UTC) They do not offend me any more than if you prefer to wear black and white clothes. The fact that one person likes colour and another likes black and white is nothing to get offended over. It is just a matter of personal preference. mydogategodshat 02:25, 12 Mar 2004 (UTC) What do you think about having two versions of the same article: one for high resolution monitors and one for low rez black and white? We could put a link at the top of each articles. mydogategodshat 02:25, 12 Mar 2004 (UTC) I just took a look at the diagrams and they are not in black and white. Maybe I misunderstood. I thought you were going to convert them to black and white. What I see looks fine. mydogategodshat 02:36, 12 Mar 2004 (UTC) I just got an edit conflict as I was replying to you. So you hadn't seen my versions when you replied? They were on the article before I first posted here, but you might have seen a cached version I suppose (the caching of images is begining to bug me!). Isomorphic said he found the pale text a bit difficult to read, so I made that black. I've only used one colour as you say, and I agree they're not as pretty as yours were, but look a little more like standard graphs I guess (the thinner lines). If there's anything you would like me to change about them, do say so as messing around with the colours and line thicknesses would not be a problem. I just reread my original comment here, I said I was making the lines thinner, and making the text black, but I ran it together so that's obviously where you got the wrong impression from. fabiform \| talk 02:59, 12 Mar 2004 (UTC) ## business law list I responded to your comment here: Talk:List of business law topics B 19:50, May 11, 2004 (UTC) ## Adminship: 3rd nomination You've been nominated for adminship -- again! Please leave a message at Wikipedia:Requests for adminship indicating whether or not you accept the nomination. Cheers, BCorr\|Брайен 23:36, May 12, 2004 (UTC) ## Request for review Hi, I could use another pair of eyes on a couple economics articles. First, could you take a look at the edits being made to market clearing by a new user? I'm not sure he fully knows what he's talking about, and he replaced the entire original content of the article. Also, you might want to take a look at sticky, written by Mike Church a couple months ago. It strikes me as a bit idiosyncratic. Isomorphic 01:55, 7 Aug 2004 (UTC) Ive done a bit of editing on the two articles. Thanks for the notification. Equal Shape Change Rule! mydogategodshat 17:30, 10 Aug 2004 (UTC) ## Strategic management I was simply referring to the fact that for an article to be featured on the main page, it needs an image associated with it. A conceptual topic such as this may not lend itself to a photo, so I thought a diagram representing the topic might be possible. Just something representative, certainly not something diagramming the whole subject. - Taxman 20:33, Oct 12, 2004 (UTC) What has happened to much of the content of 'Strategic Management' in recent months? If you look back to versions from October, they were much longer. Thegn -7:55, 19-Feb-06 GMT ## Hello - economics I am not sure if you remember me, I've been around all over Wikipedia but not in economics too much lately. I've come back to economics though at least for a little while to contribute :o). Very good work on the The Business and Economics Forum. I noticed that Open economy had no entry, Closed economy as well. A lot of the trade / exchange articles can be tied up nicely in these articles. I started open economy but if you know anyone else who wants to help please let them know. --ShaunMacPherson 17:57, 27 Oct 2004 (UTC) Good to see you back Shaun. The WP:BEF is an experiment that I hope people will use and develop : I think it has the potential to become very valuable. mydogategodshat 15:48, 28 Oct 2004 (UTC) ## Wikipedia:Forum for Encyclopedic Standards I have drafted a proposal for a new voluntary association on Wikipedia (joining groups like the Wikipedia:The Business and Economics Forum and the Wikipedia:Harmonious editing club) to promote discussion of a sort of system of expert review on Wiki. Please take a look and add your ideas. 172 08:01, 16 Nov 2004 (UTC) Thanks for the notification. mydogategodshat 21:16, 20 Nov 2004 (UTC) ## Factor analysis I have finally returned to this article and put in an admittedly hasty description of what factor analysis is. No one even hinted at that before in this article. Is the section I just added the sort of thing that you were saying you disapprove of? Michael Hardy 22:08, 19 Nov 2004 (UTC) ...and now I've looked at the talk page again. I'm amazed. I have no idea what could have incited you to write "I didn't realize that this encyclopedia was limited to a mathematical perspective" when I had never thought for a moment that the article should be limited to a purely mathematical perspective. All I said was that the article should not be completely devoid of any mention of what factor analysis is. Why did that offend you so much? Is it similarly offensive to suggest that an article about ships should mention that they float on water? Michael Hardy 23:04, 19 Nov 2004 (UTC) Thanks for the help with the article. The reason why I made the comment that you refer to is you wrote "The acurately of this article is disputed" at the top of the article and your justification for doing this was there was not enough "actual math" in the article. It seemed to me that those are the actions of someone that wants to limit the article to a mathematical perspective. Someone that wanted a balance between the math and the practical would have simply added the math to the practical material that I had written. I'm sorry if this misunderstanding has set us off to a bad start (I write a lot of articles and I can use all the help I can get from people like yourself checking my math). mydogategodshat 21:16, 20 Nov 2004 (UTC) ## Graphic requests? Do you do graph requests? The economics graphs you do in Corel (I think) are superb, far better than anything I could do (prob in graphamatica or, shudder, powerpoint). I'm specifically looking for a recreation of the prospect theory value function [1]. As that link shows, it's two exponentials, with the one in the lower left quadrant having a slope approximately twice that of the one in the upper right. If it's possible for you to do this, could you label the origin "reference point", the x-axis to the right "gains" and to the left "losses", and the y-axis "value". This might be awfully presumptious of me, I don't know how time consuming it is for you to do this so feel free to decline my request. Psychobabble 05:08, 22 Nov 2004 (UTC) I will try to do that curve as soon as I have my graphics programmes back. They are temperarily out of service. mydogategodshat 23:59, 26 Nov 2004 (UTC) ## Re: Cleanup Sure, happy to explain. Basically, as I wrote on cleanup, I think the biggest problem with these articles is that they need context. Look at how I changed the lead for Defensive marketing warfare strategies. For someone who reads the article and wants more general information on marketing, that information is just a click away now. This article also manages to go back to business and explain the metaphor. Out of the four, it's probably in the best shape and just needs a little cleanup. Compare Guerrilla marketing warfare strategies - there aren't even any wikilinks until halfway through the article. The first sentence says that "Guerrilla marketing warfare strategies are strategies designed to wear-down the enemy by a long series of minor attacks." To someone without a good grasp of business and marketing, I imagine this is extremely confusing. In the context of business, what is an "attack" and who is an "enemy?" I can guess that the intended meaning is something along the lines of marketing campaigns and competitors, but will a random reader be able to? I could just as easily guess that an "attack" means a hostile takeover and end up completely confused by the article. Someone with a dramatically different POV than myself (and, I'm guessing, you), could think of consumers as the "enemies" of business, the basic thinking being that consumers want to save money, while businesses want them to spend it. Similarly, what does it mean when a business goes "into the remote countryside?" Someone without solid prior knowledge could be misled into thinking that a business literally moves its offices to the middle of nowhere. I have to admit I'm not 100% sure what's intended here. Does that help? - RedWordSmith 01:02, Dec 6, 2004 (UTC) ## Article Licensing To allow us to track those users who muli-license their contributions, many users copy and paste the "{{DualLicenseWithCC-BySA-Dual}}" template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page: Option 1 I agree to [[Wikipedia:Multi-licensing\|multi-license]] all my contributions, with the exception of my user pages, as described below: OR Option 2 I agree to [[Wikipedia:Multi-licensing\|multi-license]] all my contributions to any [[U.S. state]], county, or city article as described below: Or if you wanted to place your work into the public domain, you could replace "{{DualLicenseWithCC-BySA-Dual}}" with "{{MultiLicensePD}}". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment\| talk) 18:27, Dec 8, 2004 (UTC) ## Image tagging Hi! Thanks for uploading Image:Welfare_max_small.png. I notice it currently doesn't have an image copyright tag. Could you add one to let us know its copyright status? (You can use {{gfdl}} if you release it under the GFDL, or {{fairuse}} if you claim fair use, etc.) If you don't know what any of this means, just let me know where you got the images and I'll tag them for you. Thanks so much, hike395 04:26, 9 Dec 2004 (UTC) And how about these? Image:Vir cyc man small.png and Image:Vir cyc macro small.png. Did you make them? Quadell (talk) (help)[[]] 18:04, Dec 9, 2004 (UTC) ### Image:Giffen good small.png Could you please provide an image copyright tag for this image? Thanks! --Diberri \| Talk 22:57, Aug 26, 2004 (UTC) I am not familiar with all these copyright tags so I don't know which tag to use. The image in question was created with Corel Draw specificly for the article in which it is used. It is based on similar diagrams that can be found in any intermediate microeconomics textbook. I have never seen a copyright notice on these diagrams. In fact all the images that I have contributed have similar characteristics, that is, they were created by me for the article in which they are used and are modifications of standard diagrams found in many textbooks. mydogategodshat 19:43, 1 Sep 2004 (UTC) I'm sorry, There is one exception. The diagram I used In Porter generic strategies was copyrighted, but I modified it significantly. I mentioned this on the article's talk page. mydogategodshat 19:47, 1 Sep 2004 (UTC) Thanks for the info — I too just came across another handful of images that you created and have properly tagged them. If you're not sure about these tags, all you really need to know going forward is to put {{GFDL}} on a line by itself on the image description page of any image that you create yourself. The importance of using the tag instead of just saying that you created it and uploaded it is that the wiki system can recognize the tag automatically. That's important for knowing what can be exported to other projects. For example, the upcoming Mandrake Linux distribution will include a copy of Wikipedia, but only with those images that have been tagged with a compatible license. Thanks for all your contributions! This will help make sure that they're accessible. Kbh3rd 05:52, 12 Dec 2004 (UTC) ### Unverified images Hi! Thanks for uploading the following image: I notice it currently doesn't have an image copyright tag. Could you add one to let us know its copyright status? (You can use {{gfdl}} if you release it under the GNU Free Documentation License, {{fairuse}} if you claim fair use, etc.) If you don't know what any of this means, just let me know at my talk page where you got the images and I'll tag them for you. Thanks so much. [[User:Poccil\|Peter O. (Talk, automation script)]] 05:12, Dec 10, 2004 (UTC) P.S. You can help tag other images at User:Yann/Untagged_Images. Thanks again. See my reply above. mydogategodshat 05:15, 10 Dec 2004 (UTC) ### New product types small.png Thanks for uploading Image:New product types small.png. I notice it currently doesn't have an image copyright tag. Could you add one to let us know its copyright status? (You can use {{gfdl}} if you release it under the GFDL, or {{fairuse}} if you claim fair use, etc.) Right now, I'll put it as unverified, but change it to what it's supposed to be when you get a chance. Thanks, Mattingly23 15:55, 18 Dec 2004 (UTC) See my reply above. mydogategodshat 04:26, 19 Dec 2004 (UTC) ## Categories Hi, We don't add articles to a category as well as its direct parent or subcategory. So for example, if an article fits in to Category:Management accounting there's no need to add it to Business or Accounting. That's why I removed the categories from the articles, it's redundant. I'm removing them again using rollback, so I wanted to explain why, because there won't be a useful edit summary. Rhobite 14:06, Dec 10, 2004 (UTC) ## re: Categories Good morning. You recently reverted an anon edit to Management consulting. The anon had added "Category:Business" to the page in addition to the pre-existing "Category:Management". I'm not very familiar with how the categories work. Is there a reason that the article could not be in both categories? Rossami (talk) Until recently I knew very little about the category system also, but for the last week I have spent (wasted) my time adding category tags to business and economics articles. The way I approached it was to create a variety of categories, subcategories and subsubcategories. (There are about 50 of them now). Then I have been going through the articles listed in the old navigation system and deciding which of the 50 or so categories are applicable to each article. It turned out that the average is 2 or 3 categories per article. So far I have added about 1000 tags. I still have 6 of the old lists to go through. In going through this process I have discovered that different people have different ideas about what criterian to use in appending category tags. In particular, I have been in conflict with two other contributers: One felt that there should be only one category per article and deleted all but the single most relavent tag. The other felt that an article could not be placed in adjacent categories. I reject both these criteria. The criteria I use is I try to put myself in the mind of the user who is using the category system as a navigational device. I ask myself, "If I was browsing in (for example) the Finance category, what articles would I expect to find there, and what articles would I find useful there". That is why I included the business category tag to so many articles including Management consulting.mydogategodshat 17:08, 12 Dec 2004 (UTC) This conversation continues at Wikipedia talk:Categorization. ## Edit summaries Hi, when you edit a page, would you please mind putting something in the "Edit summary" box to briefly indicate what you did? E.g. your recent change to queueing theory to add categories, if you'd put "+cat" in the edit summary, that would have been really usedful. Wikipedia:Edit summary legend gives a good list of abbreviations (like the above) which make it easier to say something useful quickly, and your fellow-editors would really appreciate it. Thanks! Noel (talk) 18:36, 10 Dec 2004 (UTC) I usually try to provide some sort of edit summary, but for the last week my attention has been diverted from writing and editing to adding category tags. I have added about 1000 so far and have about the same number left to do before the "business section" is finished. In my mind the whole process of converting from the old navigation system to the new category based navigation system is a waste of time, but the decision to use categories has been made and someone has to do it. But I am not going to waste even more of my time with thousands of edit summaries. Please bare with me until I get these category tags finished. mydogategodshat 16:04, 12 Dec 2004 (UTC) I understand (and sympathize, trust me :-) with your desire to do it as quickly a possible, but adding "+cat" isn't that much work, is it? And your fellow editors will really appreciate it! When I'm doing the exact same operation a lot (check out User:Tim_Starling/Redirects_from_:_to_User: for a good example), a ploy I adopt is to give the edit message an unusual prefix (in this case, I might use "++cat"), and then rely on the "prompt" feature of InternetExploder so that I only need to type "++" and it prompts me with "++cat", which I can then click on, and away I go. Noel (talk) 16:13, 12 Dec 2004 (UTC) You say adding "+cat" isn't that much work, but do the math. It takes one click to get to the edit summary, and four for the message. Multiply this by over a thousand edits and you get about 5000 unnecessary key stokes. My time is better spend doing other Wiki-things. mydogategodshat 17:08, 12 Dec 2004 (UTC) ## philosophy of business We've been discussing at Talk: business ethics the fact that some of the material that was there ought to be in philosophy of business instead. But were you aware that phil. of business is identical to this? http://www.e-paranoids.com/p/ph/philosophy_of_business.html ? I don't know off-hand whether this is a copyright vio. -- the e-paranoids might have copied it from wiki rather than vice versa. At the least, its a matter of concern. I think that you and I ought to get busy writing the phil. of business article from scratch, so it can include the foundational stuff that would otherwise rather confuse the presentation of business ethics. --68.9.145.12 00:26, 14 Jan 2005 (UTC) Two things. First, for what its worth, I disagree with the move of the items on propertty to the phil of business, where these topics were already discussed. The nature of property is central to business ethics. Whether one thinks a business is primarily private property, a social arrangement, a combination, at the sufference of the state, or what have you, is fundamental to having an intelligible philosophical discussion on business ethics and the rights of owners versus others, especially, but not limited to, so-called integrated social contract theory, contract theory, or stakeholder theory. Business ethics from the perspective of the business person might not take such matters into account; but business ethics from the perspective of the philosopher certainly does, and business ethics is a species of philosophy. This is why every major text on business ethics (not the pop stuff) written by philosphers deals with all of the issues moved. Second, my wife user:Ockham and I wrote nearly all of the PofBus article. The other outfit picked it up, as several other mirror sites have done. The one referenced above gives proper attribution to Wik. icut4u I suspected that the other sites were copies of Wikipedia. That suggests you have done a good job on the article. I agree that it is difficult to draw a clear line of demarkation between the P of B and B Ethics. This is largely because of the reciprocal nature of the relationship : The P of B underpins B Ethics, and B Ethics is built on philosophical principles. My take on the appropriate categorization is that fundamental principles like the nature of property and ownership, enlightened self interest, the role of business in society, and social contract theory is best handled in a philosophy article. More practical issues like price discrimination, union busting, or bribery are best handled in an ethics article. Of course there is an overlap between the two. Someone proceeding from principles of psychological egoism could arrive at different ethical conclusions that someone proceeding from social contract principles, natural law principles, Kantian deontological principles, utilitarian principles, etc. Because of this overlap, the basics of the philosophy of business should be mentioned in the business ethics article, and the ethical consequences of one's philosophy of business should be mentioned in the P of B article. However what I saw tacked-on the the end of the B. Ethics article seemed more like descriptions of select political perspectives on the nature of property. What the B. Ethics article needs is an explanation of how one's underlying ethical principles, philosophical orientation, and business philosophy impacts one's ethical decisions. At the moment I am working on real estate economics and invisible hand, but I will give a hand with P of B and B Ethics as soon as these are done. mydogategodshat 07:04, 24 Jan 2005 (UTC) ## More on categories I like what you said at Wikipedia talk:Categorization. I'd appreciate your support for my recent comments there. (see: Wikipedia talk:Categorization#Super Categories). thanks. Samuel Wantman 02:12, 31 Jan 2005 (UTC) "Information" is a typical manufacturer-based view of a brand. What makes Dove a brand and not just a design system and a series of SKUs, for example, is not what Unilever has in terms of information, but what Dove means to the consumer about her skin. The Dove or Coca Cola or Nokia brand franchise is only a brand because of what is in people's minds. There are countless "brands" that are all the information, but until that is established as an expectation in the mind of a target consumer it is not a brand. ## Hi there Your continuous output as a (relatively) old-guard user still going strong impresses me a great deal. Thanks for contributing. Ground 14:31, 20 Feb 2005 (UTC) ## your name and you Hi, I like all of the work you do and am a recently initiated fan of wikipedia. Thats about you. I was wondering how does your name read is it -my dog ate god shat- or -my dog ate god's hat-? doles 15:20, 2005 Mar 17 (UTC) Your question is answered in the "Whats in a name" section above. mydogategodshat ## Help on Template talk:Infobox Company A suggestion of mine on how to change the current Template:Infobox Company (adding revenue and industry, for example) was immediately met with a flurry of knee-jerk replies by the person who created the template. I may be wrong in my suggestions, but I really would like an outside opinion, since I was not expecting instant acrimony. As someone else interested in business topics, I thought you could take a look at the last topic on the talk page and give some feedback. --Goodoldpolonius2 21:01, 10 Apr 2005 (UTC) ## lots of edits, not an admin Hi - I made a list of users who've been around long enough to have made lots of edits but aren't admins. If you're at all interested in becoming an admin, can you please add an '*' immediately before your name in this list? I've marked most of the previously nominated folks (and see that you have been previously nominated, but not for some time). It also looks like you're in the process of adopting a new user name. Feel free to modify the list accordingly. I've suggested folks nominating someone might want to puruse this list, although there is certainly no guarantee anyone will ever look at it. Thanks. -- Rick Block (talk) 13:57, Jun 20, 2005 (UTC) ## Unexplained revert Can you explain your revert on public bad? You deleted quite a bit of text without putting anything on the talk page. Scott Ritchie 06:09, 15 July 2005 (UTC) Certainly. A public good is not to be contrasted with a public bad. They are very different types of concepts. A public good is best contrasted with a private good. You can read the public good article for more details. Further, a public good is not necessarily socially beneficial. I did not explain the change because we have delt with this issue several times before and I thought an explanation was unnecessary: Probably an incorrect assumption on my part. mydogategodshat 06:18, 15 July 2005 (UTC) wouldn't removal of public bads, eg pollution, still be a public good then? Clean air is often cited as an example of a public goods problem. Hence it seems like a comparison can be made. Scott Ritchie 19:30, 15 July 2005 (UTC) Removal of something that one believes to be bad for society would certainly be good for that society. But this is not how the term public good is used in economics, public policy and poli-sci. It is a scientific term, not a value ladden ideological term. It describes a good or service that is non-rivalrous (its benefits fail to exhibit consumption scarcity; once it has been produced, everyone can benefit from it without diminishing other's enjoyment) and non-excludable (once it has been created, it is very difficult or impossible to prevent access to the good). Clean air is non-excludable because it is very difficult to prevent people from having access to it, and it is non-rivalrous because one persons use of the air does not prevent another person from using the air. Because of these two characteristics businesses are unlikely manufacture and sell it profitablely, that is, it is not a private sector good. mydogategodshat 03:21, 16 July 2005 (UTC) That I knew. But I see what you're saying now - public bads don't have to be nonrivalrous or nonexcludable, simply "bad". The public bad article could probably use some more clear examples making this distinction, however. Scott Ritchie 21:57, 17 July 2005 (UTC) I would never use the term "public bad" in serious economic discourse. The term is a "red flag" that suggests to the reader that the author has an ideological axe to grind. If one is refering to social costs external to a firm's production function, then call it an externality. If one is refering to a transaction that is Pareto sub-optimal, then say so. If one is refering to an activity that one disagrees with for ethical reasons, then say that. To label it a "public bad" is dysfunctional because it obfuscates the issue. It hides the reason why one feels it is "bad". Further, people become confused because they try to contrast it with "public good", a juxtaposition that does not work. A "public good" does not necessarily need to be "good" for society. It is not about a subjective assessment of what is "good" or "bad". mydogategodshat 00:37, 18 July 2005 (UTC) ## Economy of India help Hi, you have done a great job on writing business and economics related FA articles. I have been involved in rewriting the Economy of India, along with other wikipedians hoping to make it worthy of FA and I thought it would be good to enlist someone to fact check and critically review it even before it goes to Peer review. Can you please review the article and comment on it? Thanks for your time. regards. pamri 12:27, August 7, 2005 (UTC) Hi, Its been put up at peer review. Can you please comment on it there? thanks. pamri 17:44, August 7, 2005 (UTC) I will be very happy to read the article, however I know very little about the economy of India so I don't know how much help I will be. mydogategodshat 04:29, 10 August 2005 (UTC) Thanks for the reply. I just wanted a general feedback from you, since you know more about business/economics related topics. pamri 17:43, August 10, 2005 (UTC) ## List of Economic topics article Hello, I have not chatted to you in a while. Does the economic section have an article like List_of_legal_topics? It appears to be very useful, esp. using the trick of clicking the link near the top of that article viewing related changes, you can review all edits done relating to law. A similiar List of economic topics would be useful for economics and other subjects I think, should one be created or if it is created would you tell me the link? Thanks, --ShaunMacPherson 06:40, 11 August 2005 (UTC) Hi Shaun. Yes, there is a list of economics topics, but it is not used very much now that the category system is operational. In fact, in 18 months we have gone from no effective navigation system to three of them. In addition to the old system of lists, and the category system, there is also a new system of portals. We seem to have gone from too few systems of navigation to too many. mydogategodshat 02:46, 18 August 2005 (UTC) ## Wikipedia:WikiProject Business and Economics I created a Wikipedia:WikiProject Business and Economics for all related collaborations, etc., Can you please list yourself as a participant? Thanks. pamri 07:11, August 30, 2005 (UTC) Hi, I thought you will find this useful. You may want to move it to your userpage, thought. WikiProjects: Business and Economics Urgent and important articles are bold Template:Tasks PamriTalk 12:26, 13 September 2005 (UTC) ## Rebate Disambid Hi. Not sure what the purpose of your changes were to Rebate and the disambig page I created, now called rebate (disambid), however, if you enter 'Rebate' you now go straight to the marketing/retail version instead of the disambiguation page as I intended. The term 'Rebate' has a wider meaning than something relevant to retailing in the US, so can we put it back? SilentC 06:01, 23 September 2005 (UTC) Perhaps it was because I neglected to fix all the links, for which I apologise. If we move Rebate back to Rebate (retail) and change all links in retail/marketing articles to point to it, then change the disambig page back to Rebate, would that be acceptable to you? If so, I'll do it on Monday. SilentC 06:25, 23 September 2005 (UTC) Your assessment of my motives are accurate. I have no problem with using rebate as a disambig page. But I did not want to see people burdened with the chore of fixing the 20 broken links. In the future, when you create disambig pages, please fix the broken links that are created. I have been watching the woodworking articles for the last couple months and you contributions are impressive. On a different note, maybe you can give me some advise: I am about to set-up a seperate table saw for light metal cutting (such as roll aluminum, siding, etc.) in my home workshop. It takes too long to change blades whenever I switch from cutting wood to cutting metal on a single machine. I have been told that an alternative to buying an expensive diamond blade is to use a fine vanier blade and install it backwards. Is this true? Do you have any suggestions? mydogategodshat 01:23, 24 September 2005 (UTC) Again, apologies. I usually do a 'what links here' on the old page and go back and fix all the links so they point directly to the new one. It slipped my mind on that occasion. Thanks for fixing it up. On the saw blade, aluminium can be cut with a carbide tipped blade. You can buy blades suitable for cutting wood and aluminium. For other metals, I have also heard from multiple sources that you can run a blade backwards but have never tried this myself. I imagine it would make a lot of noise though. We used to cut roofing sheet with a metal cut-off blade (no teeth, just an abrasive disk) in a hand-held circular saw, so maybe that would be an option for you. Cheers. SilentC 22:20, 25 September 2005 (UTC) Thanks mydogategodshat ## BEF Hi, I have moved the Business & Economics forums under WikiProject Business and Economics. I hope, we can actually work towards formalising what was discussed on those forums and create guidelines/stylesheets. See BEF and BEF talk. --PamriTalk 02:46, 1 October 2005 (UTC) ## Coercive monopoly Hi. Since you participated in the AfD for coercive monopoly, you might be interested in the major rewrite I just did. I'm sure there will be considerable discussion ensuing, and a cool head such as yours would be useful. Rd232 11:58, 10 October 2005 (UTC) ## B.C.G. analysis images Hi Paul. Just to let you know that I have converted your two B.C.G images: from .jpg to png. format - I assume that's why they had 'cleanup' tags on them. The new ones are now here: BTW, I have changed the links in the B.C.G. analysis page to point to the new ones. Regards, Ian Dunster 17:28, 17 November 2005 (UTC) ## strategy implementation hi I was interested when reading your contributions to strategic management and strategy, I have been searching for articles and information on the successful implementation of strategies and find few, there are quite a number on the importance of stratigic planning and even the failure of implementation or execution, could you help with this? regards Debbie, --Dibdob664 08:55, 10 January 2006 (UTC) dibdob664 Hi Debbie, I have not written an article on implementation yet. I agree with you that it is an important and under-represented topic. College courses in strategy seldom spend adequate time on it and text books typically append a couple chapters on control, monitoring, and implementation. I think part of the problem is that it is such a broad subject capable of taking the strategist down an infinite number of administrative paths. I will return to this topic as soon as I have time. mydogategodshat 23:28, 13 January 2006 (UTC) ## Categorization duplication I haven't seen you at Wikipedia talk:Categorization for quite a while. I just wanted to let you know, that after a YEAR of discussion, there are finally new guidelines for categoriztion that include guidelines about some of the duplication you have long desired. Please take a look and let me know if you have any questions. -- Samuel Wantman 23:28, 17 January 2006 (UTC) Since you have taken an interest in links. Please be kind enough to vote for my new bot application to reduce overlinking of dates where they are not part of date preferences. bobblewik 20:30, 25 February 2006 (UTC) ## Image Tagging for Image:Bodiam_Castle_fromthe_north.jpg Thanks for uploading Image:Bodiam_Castle_fromthe_north.jpg. The image page currently doesn't specify who created the image, so the copyright status is therefore unclear. If you have not created the image yourself then you need to indicate why we have the right to use the image on Wikipedia (see copyright tagging below). If you have not created the image yourself then you should also specify where you found it, i.e., in most cases link to the website where you got it, and the terms of use for content from that page. If the image also doesn't have a copyright tag then you must also add one. If you created/took the picture then you can use {{GFDL}} to release it under the GFDL. If you believe the image qualifies under Wikipedia's fair use guidelines, please read fair use, and then use a tag such as {{Non-free fair use in\|article name}} or one of the other tags listed at Wikipedia:Image copyright tags#Fair_use. See Wikipedia:Image copyright tags for the full list of copyright tags that you can use. If you want the image to be deleted, tag it as {{db-unksource}}. If you have uploaded other images, please check that you have specified their source and copyright tagged them, too. You can find a list of image pages you have edited by clicking on the "my contributions" link (it is located at the very top of any Wikipedia page when you are logged in), and then selecting "Image" from the dropdown box. Note that any unsourced and untagged images will be deleted one week after they have been uploaded, as described on criteria for speedy deletion. This is an automated notice by OrphanBot. If you have any concerns, contact the bot's owner: Carnildo. 06:11, 4 March 2006 (UTC) ## Mr. Paul Gallienne, an invitation I've decided there needs to be a 'savings' article, and thought you would be an excellent choice to get the ball rolling. Please see: I put a kind of invitation in the discussion area, asking for writers. I think it is pretty much self-explanatory. pearson_cb@yahoo.com is my email. Feel free to remove it if you think it's not wise to leave it here. Brian Pearson ## Microeconomics rewrite Hi, User:Radeksz has proposed a rewrite of Microeconomics on that article's talk page, in case you care to have a look. dbtfztalk 09:11, 6 March 2006 (UTC) ## Talk:Transfer pricing Hoi, I saw your discussion on Transfer pricing, what happened is that somebody has rewritten the whole article from another point of view. Well both versions are correct i guess. is it possible to merge both versionsand make the new version a extension of the version before ? the new part needs a cleanup and rewrite. Reg. Mion 01:35, 12 April 2006 (UTC) ## Strategic management I have proposed removing Strategic management from the list of featured articles. The prose style is problematic for me. I've posted a more specific critique on the talk page. It's nothing personal with you specifically, but I have issues with the sort of prose that seems too much in evidence on that page, and think it should be recast in less abstract terms. I'm sending this because you seem to have been one of the chief architects of the article. -- Smerdis of Tlön 16:57, 15 April 2006 (UTC) ## Interview Request 6/6/06 Hi Mydogategodshat, I work for a site that's creating an area for people running their own businesses to share their expertise and experiences with each other. We’re interviewing people with small business expertise in order to make our site as useful as possible. I was wondering if you’d be available to do a short (around 15 minutes) phone interview this week? If you are interested please email me. Thank you, ## Unspecified source for Image:Price points.jpg Thanks for uploading Image:Price points.jpg. I notice the file's description page currently doesn't specify who created the content, so the copyright status is unclear. If you have not created this file yourself, then there needs to be an argument why we have the right to use it on Wikipedia (see copyright tagging below). If you did not create the file yourself, then you need to specify where it was found, i.e., in most cases link to the website where it was taken from, and the terms of use for content from that page. If the file also doesn't have a copyright tag, then one should be added. If you created/took the picture, audio, or video then the {{GFDL-self}} tag can be used to release it under the GFDL. If you believe the media meets the criteria at Wikipedia:Fair use, use a tag such as {{Non-free fair use in\|article name}} or one of the other tags listed at Wikipedia:Image copyright tags#Fair_use. See Wikipedia:Image copyright tags for the full list of copyright tags that you can use. If you have uploaded other files, consider checking that you have specified their source and tagged them, too. You can find a list of files you have uploaded by following this link. Unsourced and untagged images may be deleted one week after they have been uploaded, as described on criteria for speedy deletion. If you have any questions please ask them at the Media copyright questions page. Thank you.Bkell (talk) 16:52, 24 July 2006 (UTC) ## Unspecified source for Image:Natural monopoly 2.PNG Thanks for uploading Image:Natural monopoly 2.PNG. I notice the file's description page currently doesn't specify who created the content, so the copyright status is unclear. If you have not created this file yourself, then there needs to be a justification explaining why we have the right to use it on Wikipedia (see copyright tagging below). If you did not create the file yourself, then you need to specify where it was found, i.e., in most cases link to the website where it was taken from, and the terms of use for content from that page. If the file also doesn't have a copyright tag, then one should be added. If you created/took the picture, audio, or video then the {{GFDL-self}} tag can be used to release it under the GFDL. If you believe the media meets the criteria at Wikipedia:Fair use, use a tag such as {{Non-free fair use in\|article name}} or one of the other tags listed at Wikipedia:Image copyright tags#Fair_use. See Wikipedia:Image copyright tags for the full list of copyright tags that you can use. If you have uploaded other files, consider checking that you have specified their source and tagged them, too. You can find a list of files you have uploaded by following this link. Unsourced and untagged images may be deleted one week after they have been uploaded, as described on criteria for speedy deletion. If you have any questions please ask them at the Media copyright questions page. Thank you. Fritz S. (Talk) 10:27, 15 August 2006 (UTC) ## Perceptual map It would be an improvement if the very nice automotive perceptual map image that you uploaded had "Nissan" spelled correctly. --72.94.150.9 12:06, 9 October 2006 (UTC) ## Consensus decision-making rewrite coming soon howdy . you're getting this message because you have made a meaningful contribution to Consensus decision-making in the last couple of months. This note is to inform you that i have done a complete rewrite of the article, basically from the ground up, and will be installing the rewrite sometime after 22:00 mst (gmt -7) i decided to undertake this rewrite because the current article had some notable shortcomings in my opinion, most notably: • lack of references: whole sections of the current article are unreferenced • section balance: the amount of detail on some sections was out of step with the detail level on other sections. for instance 'timing' is as large as 'key principles' • run-on writing: some sections succumb to rambling, while other sections are quite concise to the point of being terse. all of these problems are inevitable in a project written by a group of people with different areas of expertise and writing styles. my rewrite is designed to address these issues. most notably i have aimed to make the article more concise -- put more content in less words as it were -- and to make sure that everything is effectively sourced. i have also pretty much completely re-sectioned the article in an attempt to flow from general down to specific. i have given this notice to you as a 'heads up' that this change is coming. i realize that you have invested a lot of effort into the existing article and i want to make sure that you are ready to make the edits you feel are necessary once my rewrite goes 'live'. i also intend to submit the new article for peer review shortly after posting it. i think that the feedback will help us all drive this piece forward, hopefully to at least ga status! -- frymaster 23:45, 14 January 2007 (UTC) ## The Experience Economy I just made a bold edit to The Experience Economy, and would like your comments on it as well as possible clarification about your addition of some references there. I've described my edit and rationale in Talk:The_Experience_Economy#.22References.22. Thanks. --Ronz 18:11, 26 January 2007 (UTC) ## Wikiproject Finance Seeing some of your editorial interests, I'd like to invite you to join and help form Wikipedia:WikiProject Finance. --Leifern 20:36, 1 February 2007 (UTC) ## Images listed for deletion Some of your images or media files have been listed for deletion. Please see Wikipedia:Images and media for deletion if you are interested in preserving them. Thank you. —Remember the dot (t) 05:29, 20 February 2007 (UTC) ## I'm nominating "Rebate (disambig)" for deletion Please note: I am nominating Rebate (disambig) for deletion. You are shown in the history as having edited this page. If you wish to object, check the details by clicking the link above. Regards, JohnI 18:27, 7 March 2007 (UTC) ## Image tagging for Image:Wiki_construction.png Thanks for uploading Image:Wiki_construction.png. The image has been identified as not specifying the source and creator of the image, which is required by Wikipedia's policy on images. If you don't indicate the source and creator of the image on the image's description page, it may be deleted some time in the next seven days. If you have uploaded other images, please verify that you have provided source information for them as well. For more information on using images, see the following pages: This is an automated notice by OrphanBot. For assistance on the image use policy, see Wikipedia:Media copyright questions. 10:25, 8 May 2007 (UTC) ## Marketing warfare strategies Hi found myself at Marketing warfare strategies and was moved to write this on the discussion page. "Learning from Napolean This section is factually wrong, e.g the smaller Greek units was not the cohort but the lochos, and they were not all arms, combined arms units. If anything it is the pre-Marian reform Roman legion which is the all arms force, see Combined_arms#Ancient_warfare. However the early Legion could be all arms because there were 5000 of them not 100. And a cohort was not 100 but something more like 480 or 6 centuries ,and a century was not a 100 men unit but 80. However I have refrained from editing this article, because the writers of this article may be acurately quoting from a source book or group who rather than try and get the facts right, has opted for big (but wrong) comparisons between military history and marketing. If this is true, given the number of fellow military geeks on wikipedia, I suggest that someone put a lock on this article, and make it clear that you know that these facts are wrong, but that was what it was those espousing marketing war strategies that got the facts wrong, and provide the references of those sources." After I'd calmed down a little I checked the history, and found that you was the originator of most of the material in the article, I thought I'd ask, is the reason as I thought, and you are quoting a misinformed source. If not I would feel no need to be circumspect in correcting this section.Koonan the almost civilised 11:08, 18 May 2007 (UTC) ## Problems with portfolio models A {{prod}} template has been added to the article Problems with portfolio models, suggesting that it be deleted according to the proposed deletion process. All contributions are appreciated, but this article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice explains why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may contest the proposed deletion by removing the {{dated prod}} notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page. Also, please consider improving the article to address the issues raised. Even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached. If you endorse deletion of the article, and you are the only person who has made substantial edits to the page, please tag it with {{db-author}}. Black Falcon (Talk) 20:44, 17 August 2007 (UTC) ## Labour economics I was wondering if you'd like to throw in a few references to the labour economics page. I think (looking at the history) you wrote it, and therefore you're probably the best person to know where the ideas came from. Can you put notes in for which pages in which textbooks or articles readers can go to for each section? Cheers, Wikidea 18:21, 21 March 2008 (UTC) ## AfD nomination of Production, costs, and pricing I have nominated Production, costs, and pricing, an article you created, for deletion. I do not feel that this article satisfies Wikipedia's criteria for inclusion, and have explained why at Wikipedia:Articles for deletion/Production, costs, and pricing. Your opinions on the matter are welcome at that same discussion page; also, you are welcome to edit the article to address these concerns. Thank you for your time. Do you want to opt out of receiving this notice? FrankTobia (talk) 15:42, 13 August 2008 (UTC) ## Image:Vir_cyc_man_small.png listed for deletion An image or media file that you uploaded or altered, Image:Vir_cyc_man_small.png, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Calliopejen1 (talk) 22:15, 17 November 2008 (UTC) ## Image:Vir_cyc_macro_small.png listed for deletion An image or media file that you uploaded or altered, Image:Vir_cyc_macro_small.png, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Calliopejen1 (talk) 22:15, 17 November 2008 (UTC) ## Image:Vic_cyc_macro_small.png listed for deletion An image or media file that you uploaded or altered, Image:Vic_cyc_macro_small.png, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Calliopejen1 (talk) 22:15, 17 November 2008 (UTC) ## Image:New_product_types_small.png listed for deletion An image or media file that you uploaded or altered, Image:New_product_types_small.png, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Calliopejen1 (talk) 13:46, 20 November 2008 (UTC) ## Question regarding source In the early days of the article on the experience curve, the source from wright (Factors Affecting the Cost of Airplanes) was added, I think by you. Since this is an old article I was wondering where you got hold of it, because I am currently doing research on this topic and I cannot find the document. Could you help me out? Ggvanleeuwen (talk) 14:17, 11 December 2008 (UTC) ## Question regarding source of "private brand" Hi, I have checked out your term of "private brand" and I think the definition is interesting because it defines private label from the supply chain's point of view, rather than usually defined from the retailer's perspective. Can you please tell from where you have retrieved this definition (reference article?), so that I can use it in my academical paper? Thank you very much! Xtxt (talk) 22:02, 12 November 2009 (UTC) ## File:Ppf small.png missing description details Dear uploader: The media file you uploaded as File:Ppf small.png is missing a description and/or other details on its image description page. If possible, please add this information. This will help other editors to make better use of the image, and it will be more informative for readers. If you have any questions please see Help:Image page. Thank you. Sfan00 IMG (talk) 15:05, 13 July 2009 (UTC) ## Commons:File:Price trans-no ext-small.jpg This file was moved to Commons from English Wikipedia, but some description information may have got lost in the process. As you are noted as the original uploader, or in the history for the file, it would be appreciated if you could help in reconstructing this information. Please also consider checking Commons for other media that you may have uploaded locally, but which was subsequently transferred. Special:Log for uploads can help in this. Thanks for you assistance and keep uploading 'free' media :)Sfan00 IMG (talk) 20:01, 22 July 2009 (UTC) ## Commons:File:Price trans-comp ext-small.jpg This file was moved to Commons from English Wikipedia, but some description information may have got lost in the process. As you are noted as the original uploader, or in the history for the file, it would be appreciated if you could help in reconstructing this information. Please also consider checking Commons for other media that you may have uploaded locally, but which was subsequently transferred. Special:Log for uploads can help in this. Thanks for you assistance and keep uploading 'free' media :)Sfan00 IMG (talk) 20:02, 22 July 2009 (UTC) ## Commons:File:Price trans-imperf ext-small.jpg This file was moved to Commons from English Wikipedia, but some description information may have got lost in the process. As you are noted as the original uploader, or in the history for the file, it would be appreciated if you could help in reconstructing this information. Please also consider checking Commons for other media that you may have uploaded locally, but which was subsequently transferred. Special:Log for uploads can help in this. Thanks for you assistance and keep uploading 'free' media :)Sfan00 IMG (talk) 20:03, 22 July 2009 (UTC) ## File source problem with File:New product types small.png If you have uploaded other files, consider verifying that you have specified sources for those files as well. You can find a list of files you have uploaded by following this link. Unsourced and untagged images may be deleted one week after they have been tagged per Wikipedia's criteria for speedy deletion, F4. If the image is copyrighted and non-free, the image will be deleted 48 hours after 05:38, 30 March 2010 (UTC) per speedy deletion criterion F7. If you have any questions or are in need of assistance please ask them at the Media copyright questions page. Thank you. FASTILYsock(TALK) 05:38, 30 March 2010 (UTC) ## File:Ppf small.png listed for deletion A file that you uploaded or altered, File:Ppf small.png, has been listed at Wikipedia:Files for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. FASTILYsock(TALK) 03:27, 2 April 2010 (UTC) ## Proposed deletion of Product lifecycle The article Product lifecycle has been proposed for deletion because of the following concern: Wikipedia is not a how to guide. This isn't an article, it isn't a list, its just an unsourced table with several links. Fails WP:NOT. While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons. You may prevent the proposed deletion by removing the {{dated prod}} notice, but please explain why in your edit summary or on the article's talk page. Please consider improving the article to address the issues raised. Removing {{dated prod}} will stop the proposed deletion process, but other deletion processes exist. The speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. 03:24, 29 October 2010 (UTC) ## Copyright problem: Strategic management Hello, and welcome to Wikipedia! We welcome and appreciate your contributions, such as Strategic management, but we regretfully cannot accept copyrighted text or images borrowed from either web sites or printed material. This article appears to contain material copied from http://books.google.com/books?id=kQKLY0Ki1xEC&lpg=PR5&ots=yyqCsjv948&dq=ohmae%20strategy%20%22creative%20art%22&lr&pg=PA30#v=onepage&q=ohmae&f=false, and therefore to constitute a violation of Wikipedia's copyright policies. The copyrighted text has been or will soon be deleted. While we appreciate contributions, we must require all contributors to understand and comply with our copyright policy. Wikipedia takes copyright violations very seriously, and persistent violators are liable to be blocked from editing. If you believe that the article is not a copyright violation, or if you have permission from the copyright holder to release the content freely under license allowed by Wikipedia, then you should do one of the following: It may also be necessary for the text be modified to have an encyclopedic tone and to follow Wikipedia article layout. For more information on Wikipedia's policies, see Wikipedia's policies and guidelines. If you would like to begin working on a new version of the article you may do so at this temporary page. Leave a note at Talk:Strategic management saying you have done so and an administrator will move the new article into place once the issue is resolved. Thank you, and please feel welcome to continue contributing to Wikipedia. Happy editing! Λεξικόφιλος (talk) 14:29, 17 February 2011 (UTC) ## Proposed deletion of Competitive advantage The article Competitive advantage has been proposed for deletion because of the following concern: Fails WP:OR. Possibly a copyvio. While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons. You may prevent the proposed deletion by removing the Template:Tlc notice, but please explain why in your edit summary or on the article's talk page. Please consider improving the article to address the issues raised. Removing Template:Tlc will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Sp33dyphil "Ad astra" 23:58, 7 October 2011 (UTC) ## Article notability notification Hello. This message is to inform you that an article that you wrote recently, Environmental scanning, has been tagged with a notability notice. This means that it may not meet Wikipedia's notability guidelines. Please note that articles which do not meet these criteria may be merged, redirected, or deleted. Please consider adding reliable, secondary sources to the article in order to establish the topic's notability. You may find the following links useful when searching for sources: "Environmental scanning"news⧼dot-separator⧽books⧼dot-separator⧽scholar⧼dot-separator⧽JSTOR⧼dot-separator⧽free images. Thank you for editing Wikipedia! VoxelBot 01:05, 13 March 2013 (UTC) ## Proposed deletion of Defensive marketing warfare strategies The article Defensive marketing warfare strategies has been proposed for deletion because of the following concern: Seemingly made-up terminology that reads more like an essay about marketing-as-war than an encyclopedia article. While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons. You may prevent the proposed deletion by removing the Template:Tlc notice, but please explain why in your edit summary or on the article's talk page. Please consider improving the article to address the issues raised. Removing Template:Tlc will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Korny O'Near (talk) 18:47, 9 May 2013 (UTC) ## Proposed deletion of Offensive marketing warfare strategies The article Offensive marketing warfare strategies has been proposed for deletion because of the following concern: Seemingly made-up terminology that reads more like an essay about marketing-as-war than an encyclopedia article. While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons. You may prevent the proposed deletion by removing the Template:Tlc notice, but please explain why in your edit summary or on the article's talk page. Please consider improving the article to address the issues raised. Removing Template:Tlc will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Korny O'Near (talk) 18:47, 9 May 2013 (UTC) ## Proposed deletion of Flanking marketing warfare strategies The article Flanking marketing warfare strategies has been proposed for deletion because of the following concern: Seemingly made-up terminology that reads more like an essay about marketing-as-war than an encyclopedia article. While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons. You may prevent the proposed deletion by removing the Template:Tlc notice, but please explain why in your edit summary or on the article's talk page. Please consider improving the article to address the issues raised. Removing Template:Tlc will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Korny O'Near (talk) 18:47, 9 May 2013 (UTC) ## Nomination of Guerrilla marketing warfare strategies for deletion A discussion is taking place as to whether the article Guerrilla marketing warfare strategies is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted. The article will be discussed at Wikipedia:Articles for deletion/Guerrilla marketing warfare strategies until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines. Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. Korny O'Near (talk) 16:58, 19 May 2013 (UTC) ## Nomination of Direct-response marketing for deletion A discussion is taking place as to whether the article Direct-response marketing is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted. The article will be discussed at Wikipedia:Articles for deletion/Direct-response marketing until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines. Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. Salimfadhley (talk) 23:59, 19 December 2013 (UTC)	{}
# Counting finite series with a given property Given a natural number $n$, I'm trying to count the number $f(n)$ of series $a_1+a_2\dots +a_k,$ unique up to reversal (so $a_1+\dots a_i \dots +a_k$ and $a_k+ \dots a_{k-i+1}+\dots a_1$ are considered the same series) such that $a_i \le \min(i,k-i+1)$. So for instance with $n=7$ the (distinct) valid series would be $$1+1+1+1+1+1+1$$$$1+2+1+1+1+1$$$$1+1+2+1+1+1$$$$1+1+3+1+1$$$$1+2+2+1+1$$$$1+2+1+2+1$$ Unless I'm mistaken, this is the same as the number of trees on $n$ nodes such that no node has degree $\gt3$ and all nodes of degree $3$ lie on a single path of length $k$ where $k$ is the diameter of the tree. By "a single path", I mean that they all lie on the same path, not that such a path is necessarily unique. I'm also interested in related concepts such as $g(k)=$ the number of such series with length $k$, and $h(n)=$the number of such series where reversals are considered distinct, and so on. I've calculated initial values for all three of these, though I might be mistaken: $$\begin{array}{\|c\|c\|c\|c\|}\hline n&f(n)&g(n)&h(n)\\\hline3&1&2&1 \\\hline 4&2&3&2\\ \hline5&2&9&3\\\hline6&4&24&5\\\hline7&6&96&9\\\hline8&11&378&17\\\hline9&16&1890&27\\\hline\end{array}$$ For even $n$, I have $$g(n)=\sum_{i=2}^{n\over 2}\left({{i+1}\choose 2}-1\right)\left(\frac {\frac n 2 !}{i!}\right)^2$$ and for odd $n$ $$g(n)=g(n-1){\frac {n+1}2}$$ but I'm looking for formulas for $f$ and $h$ (especially $f$). Edit: found OEIS A001224 which is related. It counts the number of such series for $n-2$ with the additional requirement that every term is $1$ or $2$. Of course for the case where reflections are considered distinct, the corresponding sequence is the Fibonacci sequence.	{}
# Release management Kx Control provides a sophisticated set of code and release-management tools. All entities within the system are version-managed and can be rolled back instantaneously. The entire environment can be checkpointed so that all entities can be rolled back with a single click. Audit trails of system changes can be maintained indefinitely. Release packages can be created which build an XML representation of the entities within the system. This XML representation can also be imported or exported to a GIT repository and updated via pull and push. Dependencies between entities are managed when the package is both exported and imported. Changes made within the environment are not automatically reflected in the file system representation until exported. Similarly, any changes to the file system will not be represented in the environment until they are imported. ## Creating a package Packages can be created from the File > New > Package menu. field description Name Package name Base Directory Base save directory. Limited options are available Custom Directory Custom directory under the base directory Once created it will appear it in the Navigation panel, and can be opened within the Package Exporter. The Package Exporter can be summoned by picking Open Package Exporter from the package’s context menu. Since nothing has been added the Exporter will be a little empty. From the Package Exporter, the package can be saved and exported via the toolbar controls. ## Placing entities in packages The Package Exporter allows the user to add and remove entities from the package. Entries can be dragged from the Navigation panel into the Exporter. The trash can icon within the Exporter can be used to remove an entity. Press Save to update the state of the package. Export all can be used to ensure the disk contents represent the current state. Entities can be placed in a package by initially associating a package when entries are created. Several entities can be moved in the Unpackaged view by multiselecting, choosing a package, and clicking the Add button within the dialog. Kx Control UI highlights all entities which are not part of a package, so they can be packaged, exported and pushed to other environments or source control. These entities are listed in the Navigation panel under Unpackaged Entities. ## Package Importer Pick Open Package Importer from the Tools or the context menu. The Package Importer shows existing packages already imported and packages that could be imported. In the screenshot above, the TaxiPackage is in the list; however, it has not yet been imported so there are no entities within the package view on the left. Kx Control supports multiple packages in one directory, two or more packages could have the same directory in the Package Importer. What config file is used when importing? An important note about importing is that the underlying implementation uses the contents of the [packagename]_export.cfg file as the list of entities to import into the system There are five ways to import or update package contents. #### Import from available packages • Select one of more of the available packages • Select the relevant entities to import • Click Import In this case, TaxiPackage was selected and the Import button was chosen #### Import from a different location • Select the Import from option • In the import dialog choose a directory and ensure the package is in that directory • Manually enter the package name • Click Import In this case, TaxiPackage was selected and the Import button was chosen #### Import from a local ZIP This method takes a ZIP file containing a control package structure, uploads it to the remote and imports it. • Select the Import package zip option • In the upload dialog enter the package name that will match the export.cfg filename from the ZIP. • Press the Select zip to upload button and choose the desired package zip file In this case, TaxiPackage was entered and the then the button was used to select the ZIP file. [ #### Import a new Git repository This option imports a new package under Git version control. The dialog acts as a wizard and guides through the steps required to clone the repository with the right branch and to choose the package config file from the contents of the pulled repository. • Select the Git Import New Package option • Fill in the repository URL • Click or tab out of the repository URL and the dialog will adjust for https or ssh access • If it is an https URL, supply the username and password for the remote git system • If it is an SSH URL, allow the default private key to be used (~/.ssh/id_rsa), or provide a file path the installation has access to. If there is a passphrase for the private key, enter it into the password field • Press the Fetch branches button to validate the URL, the credentials and the available branches will be retrieved • Some fields will become read-only • Choose from the available branches • Click Clone repository • The branch name will become read-only • If the repository directory already exists on disk, there will be a dialog warning that the existing directory will be deleted and replaced with a new clone. Any changes not committed back to the repository will be lost. This can be cancelled or accepted and the dialog will proceed to the next step. • The package name should automatically be populated. Kx Control supports multiple packages in one Git repo, if there is more than one package, choose one to import. Any others can subsequently by picked from the dropdown and imported. Any not imported can be imported later using the import from feature outlined here. • Click Import package The contents of the package should now be imported and available in the package tree. If the clone fails If the clone fails, the errors should be reported in the dialog. If the user interface times out while performing a clone, the Import From option can be used once the clone is completed. Other errors may require manual intervention as described in the Potential problems or errors section. #### Git update an existing package Once a package has been Git imported (or Pushed for the first time) subsequent updates can be pulled from the remote repository. If after clicking on one of the available packages and that package is backed by a Git repository, the Git Update button should become enabled. Clicking on this button will bring up the Git Update Package dialog. • Update the username if required • Enter the password for the user • Click Git update package The import of the remote contents should occur and the navigation tree should refresh. ## Package Exporter The Package Exporter controls: button action Refresh Icon Refresh package details Git commit/push Push changes to a remote Git repository Expand All Expand the tree Collapse All Collapse the tree Remove All Remove all entities from the tree Save Save the current package configuration Export locally Download a compressed ZIP file of the current disk contents without doing an Export All first. To ensure the latest contents are in the ZIP, perform an Export All first. Export with options Allow export to a different location than the default Export All Export the package to disk Include all Child Dependencies Include all dependent children when exporting Include Permissions Include permissions in the export If the package is also under Git control, the Git info section will show the repository and branch. ### Exporting using Git #### Git commit/push new repository The Package Exporter can support pushing the XML representation of a package to a remote Git repository. If the selected package has never been committed and is not already a Git package then the dialog will open up blank. The repository used for the first export to push to must be an empty repository. The Git commit fields: field action Package Name Cannot be modified, currently selected package Git URL The HTTPS or SSH URL representing the repository https://mygithost.com/myuser/myrepo as an example Git branch The branch for an initial commit is always master Git username The username for pushing to the repository if it is HTTPS otherwise filled in by the SSH URL Git password Password for the user or for the passphrase if it is an SSH URL SSH Key location The private key for the user. By default it will use the platform install ~/.ssh/rsa_id key. Optionally the user may provide their own private SSH key so long as the platform install can access it Git author The author name established on the remote git implementation Git email The email associated with the user on the remote git implementation Commit message Description of the change. If left blank, a list of the file changes will be created for the commit message If a valid repository, username, password and the commit message First commit were entered then the repository at the hosting site should have something similar to the following commit. The Package Exporter information section will update the Git Info area with the repository and branch. #### Git stage and commit As changes are made to the package and saved, commits can be pushed to the remote repository to ensure changes are under version control. The commit dialog will no longer allow changes to certain fields since the package has now been pushed to a particular repository and branch. Not all enties changes have to be committed. After looking at the diffs for each change, optionally unstage any of the entities. Not all entities can have their diffs compared (for example if unmanaged). If there are deleted entities, they will be in the list but there are no actions to be taken. They will be removed in the commit. If there are configuration file changes, they will automatically be staged and cannot be unstaged since they are critical to the state of the package. After choosing what is staged and unstaged, switch back to the commit tab, update the commit message and press the Commit button. Once done, close the dialog with the Cancel button. #### Git conflicts If an entity being committed has been changed on the remote, say by another user, then the commit will likely result in a conflict. These conflicts must be resolved before the commit can continue. When this happens, a new Git conflict tab will be added to the dialog. Each conflict must be resolved by one of the following three options: • Choose the left side as it is currently in the workspace (resolve to current) • Choose the right side as it is currently on the git remote (resolve from incoming) • Manually type changes into the left hand text editor and use ctrl-enter. Manually modifying files? The file structure is crutial for most Control entities. Incorrectly modifying the representation could have undesirable impacts on the entities and the system overall. It is recommended to choose one of the two generated files vs. modifying control entities. When all the conflicts have been resolved a prompt will appear offering to do a package import to pick up all the changes. While this is optional, it is recommended to do this. Now that the conflicts are resolved and the package is up to date, the commit must be redone since the changes have not been pushed to the remote git server yet. Switch to the commit tab, update the commit message if necessary, and press the commit button. The commit should be successful and the export dialog can be closed. #### Git commit with updates from remote If others are adding or modifying entities that were not committed as part of the steps above then the changes will be brought in by git and should be imported. A dialog will appear to provide that option, it is recommended otherwise the workspace may not immediately reflect these new or changed entities. After importing the new changes, a commit must be made to push all the changes to the remote. If the commit was in a package that is contained within a multi-package git repository, and someone changed a different package within that repository, the dialog above also covers this case. The package modified by the remote user will update in your workspace as recommended by the dialog. Once again, as above, when this update happens the commit will have to be redone to have the merged changes applied to the remote. #### Git commit a single item from the navigator The navigator tree, or other lists where entities are displayed, now have a shortcut to git committing that single item. If the menu item is greyed out, then the item is not new or has not been changed. All other unrelated entities are moved to the unstaged area of the git commit dialog. The option to stage the other items is still possible. ### Exporting locally After choosing the Export package locally option, the package will be saved, exported and a zip will be created and sent to the browser. The resulting ZIP file is named after the package and contains the package subdirectory at the root of the archive file. This file could be unarchived on another system or the import from local zip feature could be used as documented here. ### Export to a location on the server The Export with options item opens a dialog which shows the existing package structure and allows the selected package to be exported to a directory in the tree or a manually entered file path. If there are deleted and/or removed entities from this package, the Cleanup deleted entities option will update the package export with only existing entities remaining. ### Export all The Export all option ensures that the XML representation on the server is up to date with respect to what is in the system. ## Checkpoint on import or export When a package is imported or exported, if any changes from the latest checkpoint are detected, a new checkpoint will be made. Checkpoints can take a significant amount of time to create so if there is a significant delay in importing or exporting and a checkpoint is not needed, turn off the relevant option. This default behavior can be disabled by changing the relevant environment variables, DELTACONTROL_CHKPT_ON_EXPORT and DELTACONTROL_CHKPT_ON_IMPORT in delta-bin/delta.profile. Changing either of these environment variables to NO and restarting Kx Control will disable the automatic checkpoint on export or import. This setting can also be changed on the fly by changing the Boolean variables .export.chkptOnExport and .export.chkptOnImport on a connection. (Changes made in this way will be lost on restart.) ## Export and import audit Kx Control tracks the import, export and saving of packages. This package audit history is stored in the table .export.packageAudit The audit history for a particular package can be retrieved using the API .export.getAuditHistory. For example, to get the audit history for package PackageDemo the following could be executed on Kx Control .export.getAuditHistory[PackageDemo] ` ## Potential problems or errors pushing and pulling from Git repositories Authentication or access privilege errors may show up as 403 error codes, the correct error or occasionally a close from the remote server.	{}
# Reconstruction of the neutrino mass as a function of redshift 26 Feb 2021 · Christiane S. Lorenz, Lena Funcke, Matthias Löffler, Erminia Calabrese · We reconstruct the neutrino mass as a function of redshift, z, from current cosmological data using both standard binned priors and linear spline priors with variable knots. Using cosmic microwave background temperature, polarization and lensing data, in combination with distance measurements from baryonic acoustic oscillations and supernovae, we find that the neutrino mass is consistent with $\sum m_\nu(z)$ = const. We obtain a larger bound on the neutrino mass at low redshifts coinciding with the onset of dark energy domination, $\sum m_\nu(z = 0)$ < 1.46 eV (95% CL). This result can be explained either by the well-known degeneracy between $\sum m_\nu$ and $\Omega_\Lambda$ at low redshifts, or by models in which neutrino masses are generated very late in the Universe. We finally convert our results into cosmological limits for models with non-relativistic neutrino decay and find $\sum m_\nu$ < 0.21 eV (95% CL), which would be out of reach for the KATRIN experiment. PDF Abstract ## Code Add Remove Mark official No code implementations yet. Submit your code now ## Categories Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology	{}
## Introduction The manipulation of domains in ferroic materials is a key in emerging functionalities of nano-scale devices1. In ferroelectrics, the orientation, size and distribution of the domains affect the dielectric, ferroelectric, and piezoelectric response2; therefore, the ability to control the domain structure is essential. However, available strategies for domain control in ferroelectrics are limited. In the case of thin films, a prominent approach is to control the crystal orientation and strain of the films by the selection of appropriate substrates3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20. The control of the cooling rate across a phase transition is used too for domain structure control21. Electrostatic boundary conditions also affect the ferroelectric domain profoundly. They are the major reason for 180° domain formation: Without perfect charge screening, depolarizing field arising due to the polarization discontinuity at the surface of the film counteracts the non-screened polarization, resulting in antiparallel (180°) domain formation that reduces the energy of the depolarizing field2, 22. For example, epitaxial PbTiO3 thin films grown on SrTiO3 (STO) substrates show a fine 180° domain structure, such that overall, the bound charges self-compensate23. On the contrary, when a conductive substrate is used, a monodomain structure is maintained24. In thin films, the interplay between electrostatics, elasticity, surface energy, and self-energy of domain walls can be utilized to obtain non-trivial patterns such as reconfigurable charged domain walls25, or linear arrays of <10 nm wide domains26. This is a topic of increasing research interest in thin films. In nanostructures, the subject is much less developed. Indeed, the polarization and domain patterns in nanostructures have been modeled intensively in recent years. An interesting work27 has demonstrated by phase-field modeling that adjusting surface charge screening can provide an efficient way to gain control of vortex domain structure in ferroelectric nano dots. However, experimental results rely mainly on the pioneering work of Schilling et al.28 who showed indeed morphological control of polar direction in ferroelectric nanowires, where changing the aspect ratio of nanowires, or changing their lateral dimensions locally resulted in local variation of the polarization direction. The present study is focused on the role of charge screening in the control of domain pattern in nanorods and shows experimentally how to obtain c- or a-type domain orientation without the need of poling. ## Results and Discussion The results are presented in the following manner: First we show the domain orientations in the as-grown {100}-epitaxial tetragonal-phase Pb(Zr0.35Ti0.65)O3 (PZT) films and the domain orientations in focused ion beam (FIB)-fabricated nanorods made of these films, which were grown on Si and Nb-doped SrTiO3 (Nb-STO) (Figs 1, 2 and 3). Due to the higher thermal expansion coefficient (TEC) of PZT relative to Si, the films grown on the Si are expected to be under tension, which is not the case when grown on Nb-STO. When grown on Nb-STO, the films, having a smaller TEC, are expected to grow in compression14. This will allow us to study the effect of charge screening and its interplay with the ‘interference’ imposed by the stresses in the film. Self-assembled nanorods grown on SrRuO3/STO substrate are used to confirm further those results (Fig. 4) and to discuss the interplay between the aspect-ratio of the nanorods and the depolarizing fields. Charge screening is further investigated by a series of experiments with nanorods having metallization on their sidewalls (Figs 5 and 6). Finally, the experimental results, namely the domain patterns in the nanorods as a function of their lateral size, substrate type and charge screening conditions are compared with phase field simulation of the various situations (Fig. 7) confirming the role of charge screening in the polarization orientation and domain pattern control. Figure 1A and B show X-ray diffraction (XRD) patterns for 1200 nm-thick PZT films deposited on Si with epitaxial buffer layers of (La0.5Sr0.5)CoO3 (LSCO)/CeO2/yttria-stabilized zirconia with 8 mol % Y2O3 (YSZ) and on Nb-STO. The 2θ/ω scans showed that both PZT were grown with (100) and (001)-orientations, indicating the a/c-domain structure as normally observed in {100}-oriented PZT films. The ϕ scans for PZT (101), Si (202), and Nb-STO (101) indicated that the deposited PZT films have epitaxial relationships of PZT 〈100〉 \|\| Si 〈110〉 and PZT 〈100〉 \|\| Nb-STO 〈100〉, respectively. As can be seen in Fig. 1C, both PZT films showed well-saturated P-E hysteresis curves, though the measured remnant polarization values 37 μC/cm2 and 50 μC/cm2 for the films on LSCO/CeO2/YSZ/Si and Nb-STO were smaller than the theoretical spontaneous polarization 74 μC/cm2 of a single crystal due to the coexistence of a- and c-domains. In order to clarify the domain structure of FIB-fabricated PZT nanorods, synchrotron micro XRD was employed. As illustrated in Fig. 2, we focused X-rays, whose beam size was about 4 μm × 4 μm at the full width half maxima, onto a single rod. The diffraction from a single rod was clearly separated from the film by the trenched areas (see Fig. 2B), which allowed us to investigate the domain structure of single rod quantitatively. Since {101} twin boundaries are formed in the a/c-domain structure of tetragonal ferroelectrics, the out-of-plane axes of a- and c-domains can be slightly tilted off the normal direction to the substrate surface. This allowed us to measure the diffraction intensities for the out-of-plane lattice spacing in a- and c-domains as functions of tilt angles, ω and ψ, with the rotation axes along Si [110] and [$$1\bar{1}0$$], and Nb-STO [100] and [010], respectively. Figure 3A shows the ω-ψ maps for PZT (300) and (003), representing the volumes of the a- and c-domains in the film and the rods with 2 μm- and 1 μm-widths on LSCO/CeO2/YSZ/Si. As can be seen in Fig. 3A-1 and 2, in the film the intensity for PZT (300) is larger than that for PZT (003). The estimated c-domain fraction is 0.19, which is less than the expected 1/3 for equilibrium-oriented domains without external fields and forces. Thus, the a-domain is dominant in the film grown on LSCO/CeO2/YSZ/Si. The reason for the preferred formation of a-domain is the mismatch of TEC between PZT and Si. Since TEC of PZT is larger than that of Si, PZT sustains increasing tensile stress during cooling down from the deposition temperature, which preferably generates the a-domain in order to minimize the elastic energy of the system. A similar domain structure of the films on Si has been also reported in the literature13, 15. The domain fraction was drastically varied by forming the rod structure. As can be seen in Fig. 3A-3 to 6, for the rod structure, the intensities for PZT (300) are significantly smaller than that for PZT (003). The estimated c-domain fraction is 0.71 and 0.95 for 2 μm- and 1 μm-wide rods, respectively. It is thus observed clearly that while in the PZT film a-domains are predominant (>80%), the PZT rods fabricated from the film, have a predominantly c-domain structure. PZT films grown on Nb-STO were under compression and hence were predominantly (80–90%) c-domain oriented, contrary to the >80% a-orientation in the films on the LSCO/CeO2/YSZ/Si substrate which were under tension. However, our previous study29 on the rods fabricated by FIB from PZT film grown on Nb-STO also showed similar features to the rods on the LSCO/CeO2/YSZ/Si substrate described above, with c-domains ratio increasing upon reduction of rod width, as shown in Fig. 3B. The comparison between the films and nanorods on LSCO/CeO2/YSZ/Si and those on Nb-STO precludes that the change in mechanical clamping plays an important role in the drastic change in domain orientation upon reduction of the rod width and is a key in the demonstration of the role of charge screening in domain orientation control. We can also exclude a damage by the FIB process as the origin of the drastic change in domain fraction upon forming of the rod structures. Indeed, although we carefully etched the PZT with low acceleration voltages of ion beam, especially for finalizing the FIB process, a reduction of the piezo-response was observed due to the Ga injection and amorphousization at the vicinity of the surface. However, this was recovered by annealing the fabricated structure at the temperature ≥550 °C30, 31. Similar post-treatments have been also reported for recovering from the FIB damage in nanostructured ferroelectrics32, 33. This is further confirmed by our finding that self-assembled PZT nanorods grown on SrRuO3/STO(100) by pulsed laser deposition (PLD) without using any post-structuring showed as well the complete c-domain structure. As can be seen in Fig. 4A and B, although there is a wide distribution of the width in the self-assembled PZT nanorods, the average diameter of 166 nm is smaller than the rods fabricated by FIB. The XRD reciprocal space map (Fig. 4C) shows a clear PZT 002 peak from the c-domain but no PZT 200 peak from the a-domain. This confirms that a FIB damage is not the driving force for the drastic change in domain fraction that occurred by the rod structure formation. In nanorods having aspect ratio much larger than one, the depolarizing field perpendicular to the nanorod is significantly larger than that parallel to it, hence formation of a-domain is prohibited. Indeed, the self-assembled PZT nanorods, whose average aspect ratio is much larger than one, had only the c-domain (Fig. 4). In the case of aspect ratio around one, the depolarizing fields perpendicular and parallel to the rods are similar, which stabilizes both a- and c-domains with the appropriate fraction according to the aspect ratio. The observed tendency of increasing c-domain fraction with decreasing rod width is explained by the depolarizing field. However, the c-domain was dominant even in the 2 μm-width rod on LSCO/CeO2/YSZ/Si (see Fig. 3A-3 and 4), with aspect ratio 0.6 < 1. This may be attributed to the different charge screening states at top and bottom interfaces and sidewalls of rods. In the rods fabricated by FIB in this study, the top and bottom interfaces are connected with conductive materials. In contrast, the sidewalls are exposed to the air. Although a certain degree of charge compensation would also occur on the sidewalls, that at the top and bottom interfaces is certainly larger. This asymmetric charge screening state have led to the preferable c-domain formation in this thicker rod. To further investigate the role of charge screening as the major driving force in the control of the domain pattern, we deposited 10 nm-thick platinum layer on the sidewalls of the same rods that were measured by XRD. The rods were then heated above T c and cooled back to room temperature. Figure 5 shows the ω-ψ maps for the 1 μm-width PZT rods on LSCO/CeO2/YSZ/Si and Nb-STO before and after the deposition of platinum layer on the sidewall. For both rods, the integrated relative intensity for PZT (300) increased by the metallization of sidewall. Although the change in domain fraction is not easily recognized by the naked eyes for the rod on LSCO/CeO2/YSZ/Si, the rod on Nb-STO clearly shows the appearance of a-domain in the sidewall metalized rod relative to the complete c-domain structure before the sidewall metallization. Figure 6A and B plot the c-domain fraction before the sidewall metallization, and the increased amount of a-domain fraction by the sidewall metallization as a function of the inverse of the rod width. As can be seen in Fig. 6B, the increase of a-domain is accelerated with decreasing rod width and is most appreciable when the rod width is 1 μm (namely, the aspect ratio is near 1). However, the narrower rods showed a lesser impact of the sidewall metallization. Indeed, the domain fraction was not obviously changed by sidewall metallization for the 200 nm-width rod on Nb-STO. The smaller impact of the depolarizing field on domain fraction in such a narrow rod is due to the appreciable depolarizing field perpendicular to the rod resulting from the finite screening length at the metal/ferroelectric interfaces perpendicular to the rod axis34. In order to reinforce the experimental results, the observed results were compared with phase-field simulation for PZT rods on Si and Nb-STO substrates. In the simulation, we ignored the influence of lattice mismatch between PZT and substrate as the thickness of PZT was much larger than the critical thickness for misfit dislocations, but took into account the influence of thermal mismatch between PZT and substrate. We also assumed that the substrate surface is conductive as PZT was deposited on the conductive layers grown on Si and the conductive Nb-STO. As can be seen in Fig. 7A and B, the rods on Si basically show smaller c-domain fraction than those on Nb-STO due to the biaxial tensile stress. However, the c-domain fraction is always much larger than 1/3 when top and sidewall surfaces of the rods are not metalized (see the plots for bare rods in Fig. 7A and B). This is because of the better charge screening at the bottom interfaces; namely, the depolarizing field parallel to the rod, i.e. perpendicular to the substrate surface, is smaller than that perpendicular to the rod. When the top surface is metallized, the depolarizing field parallel to the rod weakens further. Therefore, the c-domain fraction is increased. The above, typical evolution of domain pattern can be seen when comparing Fig. 7C1 and C2, or Fig. 7C5 and C6. By reducing the rod width, the depolarizing field perpendicular to the rod increases. Thus, the c-domain fraction further increases as observed in the experiment (see also Fig. 7C3 and C7). In contrast, when the sidewall is also metallized, the c-domain fraction is reduced (and a-domain fraction increases) as the depolarizing field perpendicular to the rod weakens (Fig. 7C4 and C8). The impact of the sidewall metallization is largest when the aspect ratio is around 1. When the achieved charge screening at the sidewall is as high as that at the top and bottom interfaces, the c-domain fraction should decrease toward around 1/3 as shown in Fig. 7A and B. However, the experimentally observed c-domain fraction after the sidewall metallization was larger than the expectation for both rods on LSCO/CeO2/YSZ/Si and Nb-STO. A possible reason is the imperfect surface quality of sidewall. Although the annealing after FIB process drastically recovered the piezo-response, the surface of sidewall might have not been perfected on atomic scale, which would prevent the ideal reduction of the depolarizing field by the metallization. Nevertheless, the simulated patterns of domain evolution are qualitatively in excellent agreement with the experimental observation confirming that the domain pattern in ferroelectric rods can be controlled by charge screening. ## Conclusion The influence of charge screening on the domain pattern for {100}-epitaxial PZT rods was investigated. The size-controlled tetragonal PZT rods were fabricated by etching PZT films grown on Si and Nb-STO substrates using FIB. It was found that the c-domain fraction increased with decreasing rod width, and the c-domain dominant structure was formed even in rods on Si substrate, which are under the tensile stress. In addition, by depositing Pt on the sidewall of rods, a-domain formation prevailed. All the observed results were explained by the depolarizing field, arising from the imperfect charge screening. The reduction of rod width enhances the depolarizing field perpendicular to the rods; on the contrary, the metallization of the sidewall of rods weakens it. Phase-field simulations fully supported the observed tendencies. That the domain pattern in ferroelectric rods can be controlled by the charge screening state was both experimentally and theoretically demonstrated. The proposed approach can be widely applied for tuning the performance of emerging piezoelectric nano electro mechanical systems such as nanoscale sensors and actuators. ## Methods ### Film Deposition Tetragonal-phase (100)/(001) Pb(Zr0.35Ti0.65)O3 films of 1200 nm thickness were grown epitaxially on two type of substrates, (a) Si(100) substrates buffered with LSCO/CeO2/YSZ epitaxial triple layers, and (b) Nb-STO (100) substrates. All layers were deposited by PLD with KrF excimer laser (λ = 248 nm). The epitaxial triple layer template on Si consisted of 10 nm-thick YSZ, 20 nm-thick CeO2, and 20 nm-thick LSCO, whose deposition conditions can be found in ref. 35. For the growth of PZT, laser energy and repetition rate of 60 mJ and 7 Hz, respectively were used, at O2 pressure of 200 mTorr and temperature of 625 °C. To achieve the stoichiometric lead content in the deposited PZT films, a ceramic Pb (Zr0.35Ti0.65)O3 containing 5% excess PbO, sintered by spark-plasma sintering, was used as the target. ### Fabrication of Rods by FIB Following the PZT film deposition explained above, circular platinum pads with 200 μm diameter and thickness 50 nm were deposited by electron beam evaporation, to serve as a protective layer for the FIB treatment which followed. The PZT film under the circular platinum pad was then etched into a rectangular columnar rod shape by the FIB, in a similar procedure to that reported in the literature32, 33, 36, 37. 80–100 μm squared area surrounding the rod was etched away to avoid XRD from the film. To shape its vertical walls, the roughly etched rod was irradiated by a FIB inclined from the normal to the PZT film by 5°. Rods of widths 200 nm, 500 nm, 1 μm, 2 μm, and 4 μm were fabricated (in this paper, the word “rod” is used for all the fabricated structures for simplicity, even when the aspect ratio is less than 1). The detailed structure was reported in refs 29, 30 and 31. For recovery from the etching damage and promotion of the formation of a stable domain structure, the PZT nanorods were annealed at 550–650 °C in air for 2 h. ### Self-assembled Growth of Rods by PLD In order to verify that the domain structure formed in FIB-rods did not originate from a damage during FIB process, self-assembled epitaxial nanorods with similar thickness to FIB-rods were also prepared. These nanorods were grown on SrRuO3/STO(100) by PLD at elevated O2 pressure (2 Torr), which enhances the shadowing effect38 for PLD species due to their numerous scattering during the flight from target to substrate, resulting in the epitaxial growth of nanorods. The details of the growth and properties of the self-assembled nanorod will be described elsewhere. ### Structural and Electrical Characterizations The crystal structure of the PZT films was determined by XRD using a four-axis diffractometer with Cu-K α1 X-rays (Bruker, D8 DISCOVER) and synchrotron X-rays (SPring-8, BL13XU beamline, Japan). Their ferroelectric properties were measured with a ferroelectric tester (Toyo Corporation, FCE-1). The microstructure of the fabricated PZT rods was observed by scanning electron microscopy (SEM). To investigate the domain structure of FIB-PZT rods, synchrotron micro XRD (SPring-8, BL13XU, and BL15XU beamlines, Japan) was employed. In these measurements, the X-ray beam was focused onto a single PZT rod centered on the square etched area using the 2D focusing lens system (Forschungszentrum Karlsruhe). We used X-rays with 12.4 keV photon energy (wavelength 0.1 nm) for these measurements. Due to the long duration of the measurements, the experiments were restricted to a single set of samples with different sizes. However, the contentious change of the domain fraction (see Fig. 6A) basically precludes an appreciable influence of local domains generated by particular morphology in each sample on the domain fraction. We also confirmed the reproducibility of domain fraction for the 1 μm-width rod on Nb-STO by measuring another sample. In addition, to reinforce the significance of the experimental results, the phase-filed simulations (described below) were performed. ### Phase-field Simulations Phase-field simulations were performed and compared with the experimentally observed domain patterns. A two-dimensional phase-field model was adopted from ref. 39 and modified with Landau coefficients of (100) tetragonal Pb(Zr0.4Ti0.6)O3 from ref. 40, stiffness coefficients from ref. 41 and with the assumption of ideal dielectric properties with zero free charge. The bottom (100) boundary is assumed as ideally conducting in all cases and mechanically coupled to a purely elastic 1 μm thick substrate with assumed thermal lattice mismatch of 0.072% in case of Si and −0.336% in case of Nb-STO substrates. All other boundaries of PZT are mechanically free and with several combinations of surface metallization by Pt as described above. The substrate is clamped in vertical direction at the bottom and coupled via periodic boundary conditions in horizontal direction. The initial condition, which is introduced as a polarization noise and zero strain, is relaxed for PZT nanorods of horizontal dimension from 200 to 5000 nm in a time dependent solver of COMSOL 4.5a until stationary solution is reached. ### Data Availability The authors declare that the data supporting the findings of this study are available within the paper.	{}
# Suggested problems ## ENTRANCEI- NCERT Solutions For Class 11 Science All subjects with latest edition Jan. 14, 2022, 11:57 a.m. by iamsharma ## Biological Motivation We are an online e-learning platform that gives students study material NCERT solutions also to CBSE-NCERT students for class 11 based on the latest edition of the ncert book for physic, chemistry, maths & biology subjects. For more info- https://www.entrancei.com/ncert-solutions-for-class-11 Contact us- 011-47340170 ## Problem A string is simply an ordered collection of symbols selected from some alphabet and formed into a word; the length of a string is the number of symbols that it contains. An example of an DNA string (whose alphabet contains the symbols A, C, G, and T) is ATGCTTCAGAAAGGTCTTACG. Given: A DNA string $s$ of length at most 1000 nucleotides. Return: Four integers corresponding to the number of times that the symbols A, C, G, and T occur in $s$. ## Sample Dataset AGCTTTTCATTCTGACTGCAACGGGCAATATGTCTCTGTGTGGATTAAAAAAAGAGTGTCTGATAGCAGC ## Sample Output 20 12 17 21	{}
# A Sum involving Binomial Coefficients Given the function $f(n)= \sum_{r=0}^{n} r\binom{n}{r},$ find the largest integer $$k$$ such that $$2^k$$ $$\large \|$$ $$f(100)$$. ×	{}
# Gauge Freedom Quantum Electrodynamics 1. Apr 17, 2015 ### Juan Carlos It's well known when if we are working on problems related to particles in presence of an electromanetic field, the way we state the problem can be done using the next Hamiltonian: $H=\dfrac{(p-\frac{e}{c}A)^2}{2m} +e \phi$ where the only condition for A is: $\vec{\nabla } \times \vec{A} =\vec{B}$ So we have this "gauge freedom" under (of course) the above condition . What happens when are studying two or more partcles in presence of the electromagnetic field. Naturally: $H=\dfrac{(p_{1}-\frac{e}{c}A)^2}{2m} +\dfrac{(p_{2}-\frac{e}{c}A)^2}{2m} +e \phi$ where the only condition for A is: $\vec{\nabla } \times \vec{A} =\vec{B}$ The question is: can we relax the condition of one unique gauge for all the particles? Just saying: can we select two different gauges? obviously with the condition : $\vec{\nabla } \times \vec{A} =\vec{B}$ I've been working on this, I satetd two different gauges and I can say that there is no difference in terms between the equations of motion having the same gauge. (Hamilton) In particular I've done the same for the correspoding quantum problem obtainig the heisemberg equations, having the same result: no difference. I'm interested on the quantum problem because having two different gauges could provoque loosing the symmetry of a Hamiltonian given. Last edited: Apr 17, 2015 2. Apr 22, 2015 ### Greg Bernhardt Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? 3. Apr 22, 2015 ### Roy_1981 Not sure what you mean by choosing two different gauges/vector potentials for the two particles. If you mean, whether you can use to different vector potentials at the two points which are the locations of the two particles, then the answer is negative. Once you apply a gauge transformation to fix gauge or change to a new gauge, you applying that transformation over all space points including the two locations of the two point charges. 4. Apr 23, 2015 ### vanhees71 Gauge invariance means that the scalar and vector potentials for the electromagnetic field (or better said the four-vector potential of the electromagnetic field) are only defined up to a four-gradient, i.e., if you have a four-vector potential $A_{\mu}$ then also $$A_{\mu}'=A_{\mu} + \partial_{\mu} \chi$$ describes the same physical situation, i.e., you get the same field-strength tensor, $$F_{\mu \nu}=\partial_{\mu} A_{\nu}' - \partial_{\nu} A_{\mu}'=\partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu} + \partial_{\mu} \partial_{\nu} \chi - \partial_{\nu} \partial_{\mu} \chi = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}.$$ So you can impose one gauge condition. Depending on the situation you look at, the right choice of gauge can simplify the problem considerably. Usual gauge conditions are the Lorenz gauge $$\partial_{\mu} A^{\mu}=0$$ and the Coulomb gauge $$\vec{\nabla} \cdot \vec{A}=0.$$ The equations of motion for your point-particle problem are gauge independent, because only the field components enter (in terms of the Lorentz force, $q (\vec{E}+\vec{v} \times \vec{B})$ (with $c=1$). 5. Apr 24, 2015 ### ChrisVer Are you sure about your Hamiltonian for the two (or more) particles??? 6. Apr 27, 2015 ### Juan Carlos It's the standard construction. It's the standard construction. 7. Apr 27, 2015 ### Juan Carlos For Example: Lets suppose we have the magnetic field in the z direction, for example two Landau's gauges: $$\vec{A_{1}}=B(-y,0,0)$$ and $$\vec{A_{2}}=B(0,x,0)$$ where both satisfy $$\vec{B}=B\vec{k}$$. So in particular I could say that my Hamiltonian for the two particle system is: $H=\dfrac{(\vec{p_{1}}-\frac{e}{c}B(-y_{1},0,0))^2}{2m}+\dfrac{(\vec{p_{1}}-\frac{e}{c}B((0,x_2,0))^2}{2m} +e \phi$ So I'm using two different gauges for my problem. I'm using it in that sense. What I'd like to emphasise is that the equations of motion are the same in comparison to those obtained when I use only one. Thank you. Last edited: Apr 27, 2015 8. Apr 27, 2015 ### Juan Carlos I get your point, is the usual treatment for one particle. But what I'm saying is related to the two particle system, where the question is: Is it correct use two different gauges, one for each particle? Thank you 9. Apr 28, 2015 ### vanhees71 No, you should use one gauge for the whole calculation! 10. Apr 28, 2015 ### Juan Carlos and the reason is? I repeat, equations of motion don't change.	{}
## is there someone having 2812's UCOS SOURCE CODE? Digital Signal Processing ### Next • 1. SI System urged to adopt "hella" Various news stories report the following: "In early 2010, Austin Sendek of UC Davis created a petition encouraging the SI system to designate "hella-" as the prefix for 10^27, following "yotta-" for 10^24." (Some sources mistakenly state that Sendek would like the nubmer 10^27 to be referred to as "a hella"; but this is not the case, and is obviously not even remotely grammatical.) Steve • 2. Fair comparison between time domain equalizer and OFDM Hi All So far I have worked on time domain equalizers such as LE and DFE. Recently I have started to work on OFDM systems. And I am trying to compare the performance for Proakis channel B which is three tap channel. First system: map the info bits to BPSK, pass the symbols through channel, add noise. The channel output I write it as y=conv(h,x)+noise, where h=[0.407 0.815 0.407] and x= +/- 1. At receiver perform LE using MMSE under the assumption that the channel is knonwn at the receiver. I get the exact BER plot given in Proakis comms edition 4. Second system: map the info bits to BPSK, perform IFFT, add cyclic prefix, pass it through channel and add noise. The channel output y=conv(h,x)+noise, where x=IFFT(X,N), X=+/- 1 and N=2048. At receiver, remove the CP, truncate the signal and performe one tap MMSE equalization i.e. \hat{X}=fft(H,N)/fft(y,N) and then take hard decision on real part. The problem is that the BER of system 2 is way off when compared to the BER of system 1. As a test case, when I removed the noise from system 2, I get 0 BER. Furthermore, when I put h=1 in system 2, I get the exact plot of BPSK on AWGN. Any idea on what I might be doign wrong? Your help is greatly appreciated. Regards Chintan • 3. Definition of BT in an FSK system BT denotes the product of the 3 dB bandwidth of the shaping pulse in an FSK system and the symbol time. My question has to do with the conventional definition of B. My first thought was to use the 3 dB bandwidth of a bandpass function obtained by translating the baseband pulse up to the FSK center frequency; or equivalently, twice the bandwidth (from 0 Hz to the 3 dB point) of the pulse viewed as a lowpass function at baseband. However, doing it this way results in a curve that disagrees with some published shaping curves; it appears people (in at least some cases) leave the factor of two out, and just look at the bandwidth of the lowpass function, from 0 Hz to the positive 3 dB point. What is the convention here? Thanks, Steve ### is there someone having 2812's UCOS SOURCE CODE? Hi, I was asked to do some research on this "hamming code" and compare its efficiency with huffman coding? But i remember from my class and context book, hamming code is some kind of error correction channel coding scheme. As I right? if yes, how can I compare the efficiency of a channel coding to source coding? I have already thrown away all my knowledge from classroom. Thanks Hi, I am trying to setup a 2812 to take A to D readings. I have the ADC and to branch to the ADC interrupt at the EOS (end of sequence). When the program branches to the interrupt routine, I read and store the result registers to variables. My problem is that the result registers never change their value even when I vary the applied signal between 0V and 3V. Any suggestions? Also, I have the ADC set to suspend mode0 where an emulation suspend is ignored (i.e. the ADC continues to sample even when I hit a breakpoint?). Would this have anything to do with it? Alex Hello ! Would someone be able to explain me how to calculate the execution time o a NOP instruction when it is executed into flash and into external ram of DSP TI 2812? Is it normal to have a time more important (2*) into ram than into flas ? Is it normal to see that a change into the configuration of XINTF doesn' change the execution time ? Hi all, This is regarding flashing a code in 2812 processor from TI. I tried flashing a sample code from spectrum digital using the SDFlash utility. I was able to flash it a couple of times, but after that it was consistently showing errors in flashing. Actually the probelm was with locking and unlocking the device using CSM. The important point to be noted as far as flashing is concerned is that the device has to be reset once ( soft reset thru the SDFlash utility ) and then flashed, but not the reverse. In case u accidently reset the device after flashing, it places 0000 in all the password locations and locks the device permanently and after that ur device cannot be debugged or reprogrammed. In case u r using an eZDSP kit continue working with onchip and off chip RAM, but secure RAM	{}
{{ item.displayTitle }} navigate_next No history yet! Progress & Statistics equalizer Progress expand_more Student navigate_next Teacher navigate_next {{ filterOption.label }} {{ item.displayTitle }} {{ item.subject.displayTitle }} arrow_forward {{ searchError }} search {{ courseTrack.displayTitle }} {{ printedBook.courseTrack.name }} {{ printedBook.name }} Sketching Polynomial Functions Sketching Polynomial Functions 1.15 - Solution We want to determine the end behavior of the graph of the given polynomial function. To do so, we will pay close attention to the leading term $ax^n,$ where $a$ is the leading coefficient and $n$ is the degree of the polynomial.Let's consider the given polynomial function. $\begin{gathered} f(x)=\text{-} 6x^4+2x^2 \end{gathered}$ Note that it is already written in standard form. We can see above that the leading coefficient is $\textcolor{darkorange}{\text{-} 6}$ and the degree is ${\color{#FF0000}{4}}.$ Let's now see how the leading coefficient and degree affect the end behavior of the graph of a polynomial function. $\textcolor{darkorange}{a}>0,\$ ${\color{#FF0000}{n}}\ \text{even}$ $\textcolor{darkorange}{a}>0,\$ ${\color{#FF0000}{n}}\ \text{odd}$ $\textcolor{darkorange}{a}<0,\$ ${\color{#FF0000}{n}}\ \text{even}$ $\textcolor{darkorange}{a}<0,\$ ${\color{#FF0000}{n}}\ \text{odd}$ $\text{Reset}$ Since $\textcolor{darkorange}{\text{-}6 }<0$ and ${\color{#FF0000}{4}}$ is an even number, the end behavior of the given function is down and down. We can see above that as $x$ approaches negative infinity, $f(x)$ approaches negative infinity. As $x$ approaches positive infinity, $f(x)$ approaches negative infinity. $\begin{gathered} f(x) \rightarrow \text{-} \infty \text{ as } x \rightarrow \text{-} \infty \\ \textbf{and} \\ f(x) \rightarrow \text{-} \infty \text{ as } x \rightarrow + \infty \\ \end{gathered}$	{}
Language: Search: Contact Zentralblatt MATH has released its new interface! For an improved author identification, see the new author database of ZBMATH. # Advanced Search Query: Fill in the form and click »Search«... Format: Display: entries per page entries Zbl 1245.90010 Reiter, Peter; Gutjahr, Walter J. Exact hybrid algorithms for solving a bi-objective vehicle routing problem. (English) [J] CEJOR, Cent. Eur. J. Oper. Res. 20, No. 1, 19-43 (2012). ISSN 1435-246X; ISSN 1613-9178/e Summary: The paper investigates a capacitated vehicle routing problem with two objectives: (1) minimization of total travel cost and (2) minimization of the length of the longest route. We present algorithmic variants for the exact determination of the Pareto-optimal solutions of this bi-objective problem. Our approach is based on the adaptive $\varepsilon$-constraint method. For solving the resulting single-objective subproblems, we apply a branch-and-cut technique, using (among others) a novel implementation of Held-Karp-type bounds. Incumbent solutions are generated by means of a single-objective genetic algorithm and, alternatively, by the multi-objective NSGA-II algorithm. Experimental results for a benchmark of 54 test instances from the TSPLIB are reported. MSC 2000: *90B06 Transportation, logistics 90C27 Combinatorial programming 90C29 Multi-objective programming, etc. 90B10 Flows in networks 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut Keywords: capacitated vehicle routing problem; distance constraints; multiobjective combinatorial optimization; branch-and-cut; {\tt TSPLIB} Login Username: Password: Highlights Master Server ### Zentralblatt MATH Berlin [Germany] © FIZ Karlsruhe GmbH Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily. Other Mirror Sites Copyright © 2013 Zentralblatt MATH \| European Mathematical Society \| FIZ Karlsruhe \| Heidelberg Academy of Sciences Published by Springer-Verlag \| Webmaster	{}
# What would be the molar mass of a compound if 6.21 g of it dissolved in 24.0 g of chloroform form a solution that has a boiling point of 68.04$^{\large\circ}$C? The boiling point of pure chloroform is 61.7$^{\large\circ}$C and the boiling point elevation constant, $K_b$ for chloroform is 3.63$^{\large\circ}$C/m. $148.15gmol^{-1}$	{}
# Algorithm for finding the best “route” of tasks I have the following problem: Let's say I'm in a city with some friend we have a bunch of tasks to do. All persons start on a different position, for example (0/0), (10/5), (-20/0), ... , and every person can move x coordinates per second. Every task has: • A coordinate where it can be completed (for example (40/50)) • A importance value ranging from 0 to X (for example importance = 5) • A time that is needed to complete this task Now comes the tricky thing: The group has a certain time, in which they can complete tasks. They now need to choose which tasks they want to complete, the goal is that the summarized "importance value" of the completed tasks is as high as possible. The group is also allowed to split up. I tried to bruteforce it, but that didn't work out. There are around 11 tasks usually and 4-6 can be done, resulting in up to a million and something possiblities. Also, I had a solution without calculating the time needed to travel between the points which was basically calculating a importance per time value and just doing the tasks based on this value... which won't work for the full problem. • After some thinking i tried to bruteforce it, but that didn't work out. There are around 11 tasks usually and 4-6 can be done, resulting in up to a million and something possiblities ... Edit: Also, i had a solution without calculating the time needed to travel between the points which was basically calculating a importance per time value and just doing the tasks based on this value ... which won't work for the full problem :/ – Random Noob Apr 2 '15 at 16:22 • But did you try for a single person? (I do not know the answer, but I would try that first. – babou Apr 2 '15 at 16:30 • yes, i did it for a single person and without the time needed to travel between points. I do not know how to continue though – Random Noob Apr 2 '15 at 16:31 • You have to begin by a topological sort, afterward.. do you want an exact algorithm or an approximation algorithm is enough ? – François Apr 3 '15 at 6:01 If you have just one person to complete the tasks, this is the (in)famous Travelling Salesman Problem (TSP), which is NP-complete, so an efficient exact algorithm is a very remote possibility. Unless your problem is quite small, you'd have to settle for approximate solutions. There are algorithms that can solve enormous instances of TSP in (somewhat) reasonable time, but I have no pointers at hand. Depending on how you want to model the problem, you can approach it in several ways. Since it seems like you are working with an imaginary 2D plane I will start with the most relevant options. Arrange waypoints. Obviously if X comes before Y, then with lower precedence if X is easier than Z. You will need a difficulty function which will depend primarily on distance to the waypoint, which means that you will probably need to calculate the path from every other possible waypoint and then calculate according to the path. (Though I may be missing some nice method to solve this). EDIT: To clarify, you need to determine the best order of steps, first in relation to one another (if Y requires X), and then in order of optimal path (see below). This isn't an algorithm, it is a necessary prerequisite for further calculations. If you don't do this then the brute force method below will be extremely resource hungry. A* path finding (to calculate difficulty from each 'end point'). By 'end point' I mean the initial location and the location of every other objective. This method is inefficient, especially when you have lots of waypoints, but it has obstacle navigation built in if you need it, and once each waypoint has a path length value relative to every other waypoint, you can use simpler functions to approach the objective sequence. EDIT: This is useful instead of drawing a direct path in the case of obstacles. It will calculate the shortest distance from point A to point B with and without obstacles in the way. WIKIPEDIA Brute force paths. This is a starting point for what should be a better algorithm. Calculate every possible configuration (I would use a branching method to simplify the concept) and remove less optimal ones after calculating scores. def NextStep(Plan,Steps,ID): ##Warning: written at 5AM. Run at own risk. if len(Steps)==0: print "Possible plan: ",ID; ALL_THE_PLANS.append(Plan); return; for s in Steps: ##Uncomment next line for multiple people. #for ppl in PEOPLE: temp_plan = Plan; temp_steps = Steps; #Use ID.copy() for objects. temp_id = ID+"Then "+ppl+" does "+s; temp_plan+=Steps[s]; temp_steps.replace(Steps[s],""); #Or .remove NextStep(temp_plan, temp_steps, temp_ID); #This will recurse until all possible arrangements are calculated. Once you have a list of all paths you can remove those which break the rules (ie Y before X). Note that it helps to do this BEFORE calculating the paths, but it is still very slow and you should try to rewrite the above code to skip illegal plans. PPL = ALL_THE_PEOPLE_IN_THE_GROUP() for P in PLANS: p = PLANS[P] ##Just makes my job easier... STEPS = p.Objectives ##...And the code looks nicer. ##Assume that all PPL have .Location == START_POINT for O in STEPS: p.DIST+=AStar(PPL[O.Person].Location,OBJS[O].Location).Dist; #Add the distance that the person will travel from their last # location to the objective to the total distance of this plan. PPL[O.Person].Location=OBJS[O].Location; Now just use some imagination... Get the PLAN with the smallest DIST. Other approaches. You could also model the problem mathematically and try using other optimizing methods here. I'm not sure how applicable any of these are since it is 5AM and I can't think of ways to remodel your problem, but I will make you aware of them in case you aren't in the hopes that someone benefits. • Neural networks • Finite State Automata • Genetic algoritms • Minimax (probably only applicable in a 2-player version) Hope I could help! • 1. I can't understand what you are saying in the paragraph marked "Arrange waypoints". (For instance, I can't parse the first sentence. And, I can't see any algorithm suggested here.) Might you be able to try editing that to explain? 2. Why A* rather than shortest paths? 3. The problem is easy if there is only one person. The challenge comes when there are multiple people (since this introduces some dependencies between people: if my friend does a task, there's no point in me doing it too). I don't see anything in your answer that explains how to handle multiple people. – D.W. Apr 3 '15 at 23:48 • 1. Clarified. This is not an algorithm, it is a step. 2. A* is the shortest path, is just allows for obstacles, which tend to exist in a city scenario. 3. Added to the code, please read it carefully as it is fairly simple and explains the simplest method of solving this problem. Multiple people are simply a matter of calculating from the last objective point for that person (or the start point). – Marked Verbs Apr 4 '15 at 8:01 • I think simulated annealing can do well here too. – Albert Hendriks Jun 3 '15 at 9:04	{}
# The Sub-$50 phone Despite a lot of attention being paid to high end smart phones and 3G handsets, the next big thing in wireless could be cheap sub-$50 phones. If you look at the wireless markets worldwide, you can easily see that big wireless growth is coming from markets like India, China, Brazil and parts of Africa. In these countries, cellular services so far have been favored by consumers in the upper end of the economic spectrum, folks who can afford $200 phones. The next phase of growth is going to be driven by the mass market which is looking for cheap and affordable phones to complement low-cost calling plans. This will be a growth market up until 2009, when the global market for entry-level mobile phones will begin to approach saturation, according to new data from ABI Research. This presents an opportunity for some handset makers who are all set to churn out sub-$50 phones. Hop-On is a good example. At CTIA next week, it is going to introduce a $36 handset. Expect more such phone makers, especially from China to pop-up. Texas Instruments and Nokia are working on combo-chips which fit well with the sub$50 phone. Analysts predict that the cost of the phone would inch down to \$20 a handset, ushering in an era of disposable phone. Qualcomm is also working on integrated and affordable CDMA chipsets to bring the prices of the phones down.	{}
# Introducing Myself Hi guys! My name is Nina Singh, and I am a member of the Torque Group. I would like to introduce myself and talk a little bit about what I plan to contribute to Brilliant. I am a high school sophomore who lives in Morgan Hill, CA. Some of my favorite things to do in my free time are singing, art, programming, journalism, and, of course, math! As a fifteen year old, I aspire to work in biotechnology, molecular chemistry, or genetics, though this might change. I have started a math circle in Morgan Hill which currently meets once a month. I aim to increase awareness of the beauty of math and help to create a budding math community. I plan to post as often as possible on Brilliant. I am currently working with other members of the Torque Group to create a list of math resources (websites, books, etc.). I will try to post one short random fact about mathematics or an introduction to a mathematical concept a day, in addition to more lengthy posts. I want to occasionally post biographies of famous mathematicians as well. I am so excited to contribute to a community of budding mathematicians! Note by Nina Singh 5 years, 7 months ago MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted- list • bulleted • list 1. numbered2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1paragraph 2 paragraph 1 paragraph 2 [example link](https://brilliant.org)example link > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $ ... $ or $ ... $ to ensure proper formatting. 2 \times 3 $2 \times 3$ 2^{34} $2^{34}$ a_{i-1} $a_{i-1}$ \frac{2}{3} $\frac{2}{3}$ \sqrt{2} $\sqrt{2}$ \sum_{i=1}^3 $\sum_{i=1}^3$ \sin \theta $\sin \theta$ \boxed{123} $\boxed{123}$ Sort by: Nice to meet you Nina :D - 5 years, 7 months ago Looking forward to your posts, Nina :-) - 5 years, 7 months ago	{}
Integrating vulnerability scanning for Docker containers into cloud systems: the engineering framework decision of container scanning tools. The following work term report, titled “Integrating Vulnerability Scanning for Docker Containers into Cloud Systems”, has been prepared regarding my work at Wind River Systems during my 2A co-op term. This report compares three different vulnerability scanning tools in terms of performance and future integrations, for security scanning roadblocks which arose from containerizing cloud infrastructure software. ## about StarlingX: a cloud infrastructure software For a bit of background information, Wind River Systems’ Titanium Cloud, a virtualization platform, prides in its low latency, security and optimized “six-nine” availability1—”six-nine” meaning an uptime of 99.9999% in a year. Recently, the core functionality of Titanium Cloud was open-sourced as StarlingX2, which is now in the transition process from bare-metal virtual machines to incorporate another layer of abstraction using Docker containers storing OpenStack services managed by Kubernetes. The two figures below demonstrate the difference between the legacy virtual machine usage to the newly Dockerized architecture3. figure 1: simplified illustration of the deployment architecture of StarlingX, with virtual machines and OpenStack on bare-metal. figure 2: post-cutover, simplified illustration of the deployment architecture of StarlingX, with containerized OpenStack services managed by Kubernetes. ## why a security scanning tool? For StarlingX, performing security and vulnerability analysis is indispensable to maintaining high reliability as a cloud system. But to maintain rigorous “six-nine” uptime, it’s unfeasible to regularly poll for available vulnerability fixes through the operating system’s package manager. Not only does polling bring in unnecessary resource consumption, but as the number of cloud server nodes increase, it also becomes proportionally more difficult and expensive to maintain similar standards of frequent vulnerability analysis across the cloud server. The need of a scanner incorporated into StarlingX exists not only as unified risk monitoring tool for the developers, but as an easily manageable scanning service to be run as a cron job for the clients’ own deployments. ### the scanning problem with the cut-over to containers With the transition to containerized services, updating security scanning functionality rises in priority: since the core software now lies in a different architecture, the need for changes in vulnerability scanning becomes more pronounced. Fortunately, the usage of Docker containers opens up a lot of doors in term of available tools. From a security scanning standpoint, the transition from virtual machines to containers implies less emphasis on kernel vulnerabilities through framework isolation, and more freedom to peruse and scan through custom StarlingX packages instead. Since Docker containers consist of layers with packages deployed through Dockerfiles, a tree-like structure of dependencies can traversed and obtained. However, as opposed to the legacy virtual machine architecture, packages can now be located within any image layer. Hence, the search of a more suitable vulnerability scanner starts. ### decision evaluation criteria: context, requirements and constraints To begin, StarlingX Docker images are based on a partially stripped-down version of CentOS 7.6, with only the bare dependency requirements. Thus, the performance of vulnerability scanners will be evaluated in terms of their results for CentOS:7.6.1810 instead of an overall performance on various images. Due to this single-purpose use, either excellent result overfitting to CentOS images, or customization flexibility with the source code would be highly desirable. Secondly, the location of integration for vulnerability scanning has yet to be decided, but there are two specific directions: either located on the user’s side, deployed as an add-on service as part of the StarlingX project, or on the developer’s side as a tool integrated into the workflow. Since the nature of this vulnerability scanner service has yet to be set, flexibility in terms of the deployment is a critical constraint. Hence depending on its future usage, the scheduling frequency of the scan job would sway the need for quick scan times: weekly or monthly cron jobs on the client’s side wouldn’t have significant scan time requirements as opposed to immediate scans after every developer’s change. Additionally, if deployed as part of a dev workflow or pipeline, more importance would also be placed on the latency between machines, as well as the time it takes to complete a full scan. However, since the usage of the tool has yet to be determined, the overall scan time and the time it takes to update the database will be used as the determining criteria. Finally, the scanner’s additional resource consumption should be noted: either computational or memory-wise. Nonetheless, whether the vulnerability scanner serves as a service for the customer, or a developer tool as part of a pipeline, the evaluation of the candidate tools will be first and foremost judged by its either existing or potential performance: measured in terms of true positive accuracy rate (the sensitivity of the scanner), and a more global measure of accuracy taking the relative specificity into account. The true positive accuracy rate is a measure that demonstrates the competency of the scanner in terms of how sensitive it is towards detecting correct vulnerabilities. More formally: where $TP$ represents the true positives found by the scanner—the vulnerabilities that were indeed present in the Docker image—and $FN$ represents the avoided false negatives—the vulnerabilities that truly weren’t present in the system. Obtaining a high sensitivity rate means that vulnerabilities that are found by the scanner are more likely to truly be present. It’s also to be noted that the quantification of true positive results is under the assumption that the union of all vulnerabilities found by all three scanners is the complete set of all the vulnerabilities. Thus, this set would not include the unfound—but present—vulnerabilities. In reality, the true number of vulnerabilities isn’t feasibly obtained, and hence the perceived measure of sensitivity would be all globally shifted lower. This same logic also assumes that the only true negatives are the ones that were correctly avoided in some, but not all scanners. In other words, the union of the sets of scan results from the three compared scanners only, not the “universal” set of all vulnerabilities avoided. As for the specificity, or false negative rate, this is a measure of how many vulnerabilities are correctly identified as not present in the Docker image. If a high specificity rate is present, then false positives are minimized, but perhaps at the expense of minimizing the number of true positive results. Since the complete set of true negatives isn’t feasibly obtained, it would be difficult to obtain a reasonable measure of specificity. However, both the sensitivity and the specificity are important to determine the performance of the vulnerability scanner. Hence, by using the overall accuracy rate as a metric of comparison, it combines both true positives and false negatives from the sensitivity, as well as true relative negatives and false positives from the specificity. In terms of performance, the better vulnerability scanner should be both sensitive and specific—rarely overlook vulnerabilities that are present, and rarely mistakenly report vulnerabilities that aren’t present. Formally, the accuracy is calculated as: using the same assumed set of true negatives obtained from a merge of all the scan results, similarly to the assumption made for sensitivity. The decision criteria are summarized in the following figure (1), ordered in terms of importance from right to left along the arrow. figure 3: ranking of the decision criteria in order of importance ## vulnerability scanner candidates Three vulnerability scanner tools are compared: an internal Python tool, Vuls, as well as Clair. The following is an exploration of their features and drawbacks, followed by a summary chart with respect to the aforementioned decision criteria. ### option 1 The vulnerability scanner status quo tool is an internal Python script that scrapes through the NIST national vulnerability database4 along with the RedHat security API database5, and both cross-checked with the CentOS-Announce6 list. The scanner then queries the Docker image’s program packages through the master database of vulnerabilities. These queries match for matching package meta data, such as the architecture and version information that would indicate the presence of security vulnerabilities. In brief, static scanning. Scans using this tool were performed once a month, in line with the CentOS-Announce’s list of CentOS Errata and Security Advisories (CESA), a monthly community-maintained list of CentOS-specific vulnerabilities cherry-picked from RedHat’s erratas. It’s reasonable to assume that the more sources referred by the vulnerability scanner, the better the performance. In this case, this internal Python tool refers to 3 different vulnerability databases, which covers most vulnerabilities documentations related to the RedHat-based CentOS operating system. However, scan results also depend on the nature of the sources: whether it contains vulnerabilities that have been resolved, or even in terms of how often these sources are updated, or even the reliability of the vulnerability data itself. For example, because the CentOS-Announce list is based off of RedHat’s erratas, it implies that the CESAs from this list refer to security vulnerabilities with fixes only. As a result, contrary to what the number of sources suggest, less than 15% of the vulnerabilities detected are truly present in the target environment scanned, according an analysis of the scan results performed by the StarlingX security team. This indicates a very low sensitivity rate, or in other words, poor performance shown by a low true positive accuracy rate. But nonetheless, the internal Python script is a relatively lightweight tool, easily portable and configurable with little dependency requirements. Along with the fact that the StarlingX stack includes Python, integrating the Python scanning tool natively in the StarlingX project would not introduce additional unrelated vulnerabilities from its dependencies. ### option 2 Similar to the current solution, Vuls7 is a current experimental tool, transitioning away from the Python status quo tool in a playground environment. It’s been tested on a similar CentOS virtual machine instance—release 7.6.1810—and does a good job at detecting kernel package vulnerabilities. However, factoring in the cut-over to a more containerized project, the ability to detect kernel vulnerabilities is neither easily feasible through the new Docker containers, nor is heavily required for these scan purposes. The reason for the latter is due to the fact that even though these vulnerabilities can be detected on the client side, the StarlingX cloud infrastructure wouldn’t be able to provide with any corrective patches on the kernel itself. As an agent-less scanner tool, Vuls is able to perform dynamic vulnerability scanning with root access, as well as both native and remote scans through ssh. On one hand, dynamic scanning leads to more rigorous security verification, but on the other hand, is a resource-heavy and relatively more intrusive scan technique compared to static scans. To compensate, Vuls provides with the option to quickly scan non-intrusively as well, minimizing the load of the cloud server. As another performance advantage, Vuls is an OS-aware scanning tool. In terms of relevant vulnerability databases, not only does Vuls refer to the list of CVEs provided by NIST like the internal Python tool, but it also includes RedHat’s list of Open Vulnerability and Assessment Language (OVAL)8 as well as the RedHat Security Advisory database of erratas. The OVAL list is maintained by a third party: the MITRE Corporation9, which standardizes and promotes publicly available information about security. Hence OVALs are more trustworthy in terms of evaluating and consistently comparing vulnerabilities across different operating systems. Finally, Vuls also refers to the list of Common Platform Enumeration (CPE). Although it’s non-RedHat nor CentOS related, it provides with vulnerability information related to middleware and programming language libraries, which would be useful for StarlingX’s custom program packages and infrastructure scanning. ### option 3 Taking into account of the different decision requirements and criteria, Clair by CoreOS is a proposed replacement for the aforementioned tools. Clair is an open-source static vulnerability scanning tool specifically for Docker containers. Its vulnerability databases are periodically updated from NIST, along with the RedHat’s Security Advisory database. One significant difference between Clair and its other scanning counterparts is that Clair in itself is simply a back-end service, although many third party integrations already exist. Notably, Harbor, an open-source Docker Registry framework has Clair’s container scanning pre-integrated, which would make Clair simple to set up for users as well. As a scanner back-end service, Clair provides with a REST API interface for developers to tinker with, along with its source code on GitHub, which makes it more accessible to be customized for better performance. Hence, despite its limited vulnerability databases relative to Vuls and the internal Python tool, Clair has great potential to be fully customized to scan StarlingX’s CentOS images. But in all, Clair’s greatest advantage lies in its ability to statically traverse and query through specific Docker image layers, which is highly desirable for the purpose of scanning widespread, containerized architectures, without having to be installed natively. Hence, although Clair’s dependencies themselves do not overlap with those within StarlingX, it’s not necessary for the Clair tool to be locally installed on the cloud servers to perform vulnerability scans. ### summary of vulnerability scanner candidates Below is a chart of the relevant features and drawbacks of each scanning tool, organized in terms of the aforementioned decision criteria. The size of each project was approximated using the Linux wc command, such as find . -name '*.go' \| xargs wc -l, as well as using the GitHub Chrome Extension tool “GLOC”. The scan times were approximated on a playground environment launched using individual OpenStack Xenial instances of the same resource sizes (custom flavour of 4 CPU, 16 GB memory, 50 GB storage) on the same internal network. Finally, the load impacts were obtained with the top command, watching for an approximate highest CPU usage percentage. ## the decision: pitting the scanners against each other As performance was the most important criteria, metrics of accuracy are needed. Thus, a comparison of the scan results was performed. The internal Python tool identified 51 vulnerabilities, where 28 vulnerabilities were false positives, and a handful of others were cherry-picked out due to not having existing fixes or patches. Vuls identified 16 vulnerabilities, where only 6 of them were relevant ones. Many false positives were introduced from assumed kernel vulnerabilities, or other packages unrelated to StarlingX. The reason for the latter is due to the fact that the Vuls scan was performed natively. Hence, Vuls itself introduced many new packages, for instance: openssl and its vulnerabilities weren’t present in StarlingX, and were actually introduced by installing Vuls. Moreover, technical challenges and security concerns were raised about deploying Vuls to scan remotely, and the setup difficulty impeded with readily distributing this tool for clients to use easily. From this standpoint, it seems unlikely to be able to improve on Vuls’ accuracy, despite its many promising vulnerability data sources. Finally, Clair scanned out 7 RedHat Security Advisories, which translates to around 30 vulnerabilities, where all 7 where true positives, all with fixes announced in Erratas for later package versions. Although accurate in terms of true positive rate, this performed weakly relative to the number of true positives found by the current internal Python tool. Implicitly, these results show that both the Python tool and the Vuls scanner have low sensitivity, whereas Clair has unreasonably high sensitivity and specificity. Aside from the performance, a summary of the weighings of each decision criteria per scanner candidate can be represented as a decision matrix as shown: It can be shown quantitatively that due to the nature of the Clair scanner, it would be a better choice overall. However, it does lose out to Vuls and the internal Python tool in the following aspect: database sources, and hence, performance. But as database sources is an aspect that can be improved upon, Clair holds high potential as a vulnerability scanning tool for StarlingX, since Clair’s scanning abilities are more suitable to the containerized architecture. Now, the challenge following this decision, is to bring Clair’s performance up to speed, referencing Vuls’ and the Python tool’s vulnerability databases. ## acting on the decision: improvements on Clair Now that the decision has been made, certain improvements related to the performance of Clair can be made to obtain the best possible results. In terms of vulnerability sources, as long as more entries are populated to the vulnerability database, Clair’s scanner could query through Docker images and detect them. Hence, two more CentOS-related databases were introduced: the CentOS-Announce list, as well as the RedHat Security API database, which contains a open list of existing issues and vulnerabilities, similar to what is used in the internal Python tool. With these different databases, on top of some more Docker meta data parsing and verifications, the output was converted to a third party, OS-independent standard to facilitate the final validation of the scan improvements. With these changes in vulnerability databases follows the verification of the changes. ## validation of Clair’s improvements from v2.0.7 All in all, it was found that out of 57 total results as a union of all scans of CentOS 7.6.1810, the latest Clair release (v2.0.7 at the time) had a: • 1 true positive amount of 7 • 2 false positive amount of 0 • 3 true negative relative estimate of 4 • 4 false negative relative amount of 37 which resulted in a true positive accuracy rate of 15.9%, and an overall accuracy rate of 35.1%. Meanwhile, with the new data source improvements, this customized version of the Clair scanner resulted in a: • 1 true positive amount of 43 • 2 false positive amount of 6 • 3 true negative relative estimate of 3 • 4 false negative relative amount of 5 which resulted in a true positive accuracy rate of 97.7%, and an overall accuracy rate of 80.7%. Below is a tabulated list of the scan results as a side-by-side between v2.0.7 and the customized version of Clair around CentOS images specifically. CVE CoreOS Clair v2.0.7 release Improved CentOS Driver based on Clair v2.0.7 Package Image’s rpm Version Affected Versions (mitre) Fixed Version Verdict CVE-2018-1000876 :( y binutils 2.27-34 <2.32 n/a affected with RHEL 7 CVE-2018-1113 setup 2.8.71-10 2.8.71-10 resolved in centos:7.6.1810 image CVE-2018-12404 y y nss 3.36.0-7.el7_5 3.36.6 affected with RHEL 7 CVE-2018-14618 y libcurl 7.29.0-51 >7.15.4 7.61.1 affected with RHEL 7, 32 bit systems only CVE-2018-14647 y y python 2.7.5 2.7.0 2.7.16 affected with RHEL 7 CVE-2018-15688 y y systemd-networkd 219-62.el7 219-62.el7_6.2 affected with RHEL 7, but does not ship systemd-networkd by default CVE-2018-16428 y :( glib2 2.54.2 2.56.1 n/a affected with RHEL 7 CVE-2018-16429 y :( glib2 2.54.2 2.56.1 n/a affected with RHEL 7 CVE-2018-16842 y y curl 7.29.0-46 7.14.1 7.62.0 affected with RHEL 7 CVE-2018-16864 y y systemd-journald 219-62.el7 v203 v241 affected with RHEL 7 CVE-2018-16865 y y systemd-journald 219-62.el7 v201 v241 affected with RHEL 7 CVE-2018-16866 :( y systemd-journald 219-62.el7 v221 v242 affected with RHEL 7, change was backported to v219 CVE-2018-17358 y y binutils 2.27-34 ~2.31 n/a CVE under investigation CVE-2018-17359 y y binutils 2.27-34 ~2.31 n/a CVE under investigation CVE-2018-17360 y y binutils 2.27-34 ~2.31 n/a CVE under investigation CVE-2018-17794 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7 CVE-2018-17985 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7 CVE-2018-18484 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7, will not fix state CVE-2018-18508 y y nss 3.36.0-7.el7_5 3.41.1 affected with RHEL 7, will not fix state CVE-2018-18605 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7, will not fix state CVE-2018-18606 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7, will not fix state CVE-2018-18607 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7, will not fix state CVE-2018-18700 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7, will not fix state CVE-2018-18701 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7, will not fix state CVE-2018-19211 y y ncurses 5.9-14.20130511 6.1 n/a affected with RHEL 7, will not fix state CVE-2018-19217 y ncurses 5.9-14.20130511 6.1 n/a affected with RHEL 7, will not fix state CVE-2018-19932 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7 CVE-2018-20002 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7 CVE-2018-20482 y y tar 1.26-35 < 1.30 1.3 affected with RHEL 7, will not fix state CVE-2018-20483 y y curl, wget 7.29.0-51 7.29 7.63.0 only curl affected with centos:7.6.1810, will not fix state CVE-2018-20657 y y binutils 2.27-34 2.31.1 n/a affected with RHEL 7, will not fix state CVE-2018-20673 y y binutils 2.27-34 ~2.31 n/a affected with RHEL 7 CVE-2018-5742 y :( bind (bind-license) 9.9.4-72 9.9.4-65 9.9.4-73 affected with RHEL 7 CVE-2019-3815 y y systemd-journald 219-62.el7 V219-62 219-62.el7_6.3 affected with RHEL 7 CVE-2019-3855 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3856 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3857 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3858 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3859 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3860 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3861 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3862 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-3863 :( y libssh2 1.4.3-12 <= 1.80 1.8.1 affected with RHEL 7 CVE-2019-5010 :( y python 2.7.5 2.7.11, 3.7.2 n/a affected with RHEL 7, but centos:7.6.1810 does not have related python version CVE-2019-6454 y y systemd 219-62.el7 < v239 v241 affected with RHEL 7 CVE-2019-9072 y binutils 2.27-34 ~2.32 n/a not affected with RHEL 7 CVE-2019-9073 y binutils 2.27-34 ~2.32 n/a not affected with RHEL 7 CVE-2019-9074 y y binutils 2.27-34 ~2.32 n/a affected with RHEL 7 CVE-2019-9075 y y binutils 2.27-34 ~2.32 n/a affected with RHEL 7 CVE-2019-9076 y binutils 2.27-34 ~2.32 n/a not affected with RHEL 7, not a bug state CVE-2019-9077 y y binutils 2.27-34 ~2.32 n/a affected with RHEL 7 CVE-2019-9169 y y glibc 2.17-260 ~2.29 n/a affected with RHEL 7 CVE-2019-9192 y y glibc 2.17-260 ~2.29 n/a under investigation CVE-2019-9633 y y glib2 2.56.1-2 2.59.2 2.59.2-1 affected with RHEL 7, but should not be present with current glib2 version CVE-2019-9636 y y python 2.7.5 2.7.0 2.7.16 affected with RHEL 7 CVE-2019-9923 y tar 1.26-35 1.32 affected with RHEL 7 CVE-2019-9924 y bash 4.2.46-31 < 4.4 n/a affected with RHEL 7 # conclusion Different solutions are needed for different requirements: the nature of the vulnerability scanner should conform with the the nature of the infrastructure, as all things should be. That’s indeed the reason why we have such diverse solutions for even the more mundane technology problems. But even then, the most suitable solution is still unlikely to be ideal. In that case, there’s no harm in standing on the shoulders of giants when possible: it’s not only more efficient from a project’s perspective, but it’s also impactful in terms of open-source contributions. It was a highly satisfying experience to improve on existing open-source tools not only for Wind River’s purposes, but for the greater public to use as well. Word count: 2973 # bibliography 1. 1 Wind River Titanium Cloud. Wind River Systems. Retrieved from https://www.windriver.com/products/titanium-cloud/ 2. 2 StarlingX. Retrieved from https://www.starlingx.io/ 3. 3 StarlingX Overview. OpenStack. Retrieved from https://superuser.openstack.org/articles/starlingx-overview/ 4. 4 National Vulnerability Database. Information Technology Laboratory. Retrieved from https://nvd.nist.gov/ 5. 5 RedHat Security Data API Documentation. RedHat Customer Portal. Retrieved from https://access.redhat.com/documentation/en-us/red_hat_security_data_api/1.0/html/red_hat_security_data_api/index 6. 6 CentOS Announce. CentOS.org. Retrieved from https://lists.centos.org/mailman/listinfo/centos-announce 7. 7 Vuls Vulnerability Scanner. GitHub/future-architect. Retrieved from https://github.com/future-architect/vuls 8. 8 OVAL Definitions for RedHat Entreprise Linux. RedHat. Retrieved from https://www.redhat.com/security/data/oval/ 9. 9 Open Vulnerability and Assessment Language, A Community-Developed Language for Determining Vulnerability and Configuration Issues on Computer Systems. MITRE OVAL. Retrieved from http://oval.mitre.org/	{}
# Math Help - Euler's theorem 1. ## Euler's theorem Will anyone please show me a proof of Euler's theorem. Thank you soo much in advance! 2. Originally Posted by jenjen Will anyone please show me a proof of Euler's theorem. Your last question was number theory related. I assume you want to show, a^phi(n) = 1 (mod n) I have two proofs. 1)The elementary number theory proof. 2)Group theory proof, it is shorter. Which one will it be? 3. Oh thanks for your quick reply. I believe it is the group theory proof. Is that the finite abelian group? thx 4. Originally Posted by jenjen Oh thanks for your quick reply. I believe it is the group theory proof. Is that the finite abelian group? Yes. It is an excercise for you (unless you want me to prove it) that the set G_n={1<=x<=n \|gcd(x,n)=1} for n>1 is a group under multiplication modulo n. (That is the set of all relative prime elements to n less than n is a group). Since it is finite we have a^m = 1 where m is the number of elements in the group. That is m=phi(n) by definition. Q.E.D. Now, this group is isomorphic to Z/nZ (you know the classes of integers modulo n) thus, this is true for all integers relatively prime to n.	{}
# 50181. Calculate the area ## I'm a slow walker, but I never walk backwards. Implement a function int calArea(NODE) to calculate the area within two lists as its boundary. Each node has two pointers - one goes right and one goes down. Both lists start from the same left upper node. The first list goes right first, and the second list goes down first. Each step goes distance 1 in either direction. Eventually these two lists will go into the same node, so we can define the area bounded by these two lists. Note that at the end of two list both right and down pointers are NULL. The following is calArea.h file. You have to implement int calArea(NODE). #include<stdio.h>#include<stdlib.h>typedef struct node{ struct node* rightPtr; struct node* downPtr;}NODE;int calArea(NODE* head); You can test your function with this main function. #include<stdio.h>#include<stdlib.h>#include"calArea.h" NODE* initList(NODE* pos, int len){ NODE* tail = pos; char direction; for(int i = 0; i < len-1; i++){ scanf("%c", &direction); getchar(); NODE* pNew = (NODE) malloc(sizeof(NODE)); pNew->downPtr = NULL; pNew->rightPtr = NULL; if(direction == 'r'){ pos->rightPtr = pNew; pos = pos->rightPtr; } else{ pos->downPtr = pNew; pos = pos->downPtr; } if(i == len-3) tail = pos; } return tail;} int main(){ int len; NODE head = (NODE) malloc(sizeof(NODE)); scanf("%d\n", &len); getchar(); NODE pos; char direction; scanf("%c", &direction); head->rightPtr = (NODE) malloc(sizeof(NODE)); pos = head->rightPtr; pos->downPtr = NULL; pos->rightPtr = NULL; NODE tailR = initList(pos, len); head->downPtr = (NODE) malloc(sizeof(NODE)); pos = head->downPtr; pos->downPtr =NULL; pos->rightPtr = NULL; scanf("%c", &direction); getchar(); NODE tailD = initList(pos, len); free(tailD->rightPtr); tailD->rightPtr = tailR->downPtr; printf("%d", calArea(head));} ## Input Format The first line is length L of both lists. The following 2L lines are the direction of two lists. The first L lines are for the first list and the second L lines are for second list. ## Output Format Output the area within the lists which is the return value of int calArea(NODE*). ## Sample Input 1 4rrddddrr ## Sample Output 1 4 ## Sample Input 2 4rddddddr ## Sample Output 2 3 ## Sample Input 3 6rdrdrdddrdrr ## Sample Output 3 5	{}
Geometry, Gravity and Supersymmetry 24-28 April 2017 Mainz Institute for Theoretical Physics, Johannes Gutenberg University Europe/Berlin timezone Rigidity of 2-step Carnot algebras 26 Apr 2017, 11:05 45m 02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University) 02.430 Mainz Institute for Theoretical Physics, Johannes Gutenberg University Staudingerweg 9 / 2nd floor, 55128 Mainz Speaker Prof. Boris Kruglikov (University of Tromsø) Description We study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo $H$- and $J$-type algebras are given. In particular, we establish the relation of the so-called $J^2$-condition to rigidity, and we explore these conditions in relation to pseudo $H$-type algebras. Based on work [(arXiv:1603.00373 [math.RT])][1] with Mauricio Godoy-Molina, Irina Markina and Alexander Vasil'ev. [1]: https://arxiv.org/abs/1603.00373 Primary author Prof. Boris Kruglikov (University of Tromsø) Presentation Materials Slides Your browser is out of date! Update your browser to view this website correctly. Update my browser now ×	{}
### Efficient Identity-Based Encryption with Hierarchical Key-Insulation from HIBE Keita Emura, Atsushi Takayasu, and Yohei Watanabe ##### Abstract Hierarchical key-insulated identity-based encryption (HKIBE) is identity-based encryption (IBE) that allows users to update their secret keys to achieve (hierarchical) key-exposure resilience, which is an important notion in practice. However, existing HKIBE constructions have limitations in efficiency: sizes of ciphertexts and secret keys depend on the hierarchical depth. In this paper, we first triumph over the barrier by proposing simple but effective design methodologies to construct efficient HKIBE schemes. First, we show a generic construction from any hierarchical IBE (HIBE) scheme that satisfies a special requirement, called MSK evaluatability introduced by Emura et al. (Designs, Codes and Cryptography, 2021). It provides several new and efficient instantiations since most pairing-based HIBE schemes satisfy the requirement. It is worth noting that it preserves all parameters' sizes of the underlying HIBE scheme, and hence we obtain several efficient HKIBE schemes under the $k$-linear assumption in the standard model. Since MSK evaluatability is dedicated to pairing-based HIBE schemes, the first construction restricts pairing-based instantiations. To realize efficient instantiation from various assumptions, we next propose a generic construction of an HKIBE scheme from any plain HIBE scheme. It is based on Hanaoka et al.'s HKIBE scheme (Asiacrypt 2005), and does not need any special properties. Therefore, we obtain new efficient instantiations from various assumptions other than pairing-oriented ones. Though the sizes of secret keys and ciphertexts are larger than those of the first construction, it is more efficient than Hanaoka et al.'s scheme in the sense of the sizes of master public/secret keys. Note: Fixed typos and minor issues. Available format(s) Category Public-key cryptography Publication info Published elsewhere. Designs, Codes and Cryptography DOI 10.1007/s10623-021-00926-z Contact author(s) k-emura @ nict go jp takayasu @ nict go jp watanabe @ uec ac jp History 2021-08-24: revised See all versions Short URL https://ia.cr/2020/1087 CC BY BibTeX @misc{cryptoeprint:2020/1087, author = {Keita Emura and Atsushi Takayasu and Yohei Watanabe}, title = {Efficient Identity-Based Encryption with Hierarchical Key-Insulation from HIBE}, howpublished = {Cryptology ePrint Archive, Paper 2020/1087}, year = {2020}, doi = {10.1007/s10623-021-00926-z}, note = {\url{https://eprint.iacr.org/2020/1087}}, url = {https://eprint.iacr.org/2020/1087} } Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.	{}
# Nowhere vanishing magnetic helicity Suppose you are given a nowhere-vanishing exact 2-form $B=dA$ on an open, connected domain $D\subset\mathbb{R}^3$. I'd like to think of $B$ as a magnetic field. Consider the product $H(A)=A\wedge dA$. At least in the plasma physics literature, $H(A)$ is known as the magnetic helicity density. How can one determine if there is a closed one-form $\mathbf{s}$ such that $H(A+\mathbf{s})$ is non-zero at all points in $D$? The reason I am interested in this question is that if you can find such an $\mathbf{s}$, then $A+\mathbf{s}$ will define a contact structure on $D$ whose Reeb vector field gives the magnetic field lines. Thus, the question is closely related to the Hamiltonian structure of magnetic field line dynamics. I'll elaborate on this last point a bit. If there is a vector potential $A$ such that $A\wedge dA$ is non-zero everywhere, then the distribution $\xi=\text{ker}(A)$ is nowhere integrable, meaning $\xi$ defines a contact structure on $D$ with a global contact 1-form $A$. The Reeb vector field of this contact structure relative to the contact form $A$ is the unique vector field $X$ that satisfies $A(X)=1$ and $\text{i}_XdA=0$. Using the standard volume form $\mu_o$, $dA$ can be expressed as $\text{i}_{\mathbf{B}}\mu_o$ for a unique divergence-free vector field $\mathbf{B}$. Thus, the second condition on the Reeb vector field can be expressed as $\mathbf{B}\times X=0$, which implies the integral curves of $X$ coincide with the magnetic field lines. An example where $D=$3-ball and no $\mathbf{s}$ can exist: Let $D$ consist of those points in $\mathbb{R}^3$ with $x^2+y^2 < a^2$ for a real number $a>1$. Note that all closed 1-forms are exact in this case. Let $f:[0,\infty)\rightarrow\mathbb{R}$ be a smooth, non-decreasing function such that $f(r)=0$ for $r<1/10$ and $f(r)=1$ for $r\ge1/2$. Let $g:\mathbb{R}\rightarrow \mathbb{R}$ be the polynomial $g(r)=1-3r+2r^2$. Define the 2-form $B$ using the divergence free vector field $\mathbf{B}(x,y,z)=f(\sqrt{x^2+y^2})e_\phi(x,y,z)+g(\sqrt{x^2+y^2})e_z$. Here $e_\phi$ is the azimuthal unit vector and $e_z$ is the $z$-directed unit vector. It is easy to verify that $B$, thus defined, is an exact 2-form that is nowhere vanishing. Because $g(1)=0$ and $f(1)=1$, the circle, $C$, in the $z=0$-plane, $x^2+y^2=1$, is an integral curve for the vector field $\mathbf{B}$. I will use this fact to prove that the helicity density must have a zero for any choice of gauge. Let $A$ satisfy $dA=B$ and suppose $A\wedge B$ is non-zero at all points in $D$. Note that $A\wedge B=A(\mathbf{B})\mu_o$, meaning $h=A(\mathbf{B})$ is a nowhere vanishing function. Without loss of generality, I will assume $h>0$. Thus, the line integral $I=\oint_C h\frac{dl}{\|\mathbf{B}\|}$ satisfies $I>0$. But, by Stoke's theorem, $I=2\pi\int_0^1g(r)rdr=0$, as is readily verified by directly evaluating the integral. Thus, there can be no such $A$. - Can you explain this relation with the contact geometry and B-fields? – Chris Gerig Oct 10 '12 at 17:42 Just for the record, this was crossposted at MO as well: mathoverflow.net/questions/109237/… – Neal Oct 14 '12 at 0:16 I believe that the answer, in generality, is that you cannot find $\mathbf s$. As an example, consider a field configuration that is translationally symmetric in, say, the $z$ direction (for example, if there is a smooth current density that directed parallel to the $z$ axis). Speaking in physics terms, if we assume that the helicity is non-zero in some gauge $\mathbf s=\boldsymbol\nabla \phi$, then without loss of generality, we can assume that $H > 0$ everywhere in the domain $D$. However, consider the line integral of $H$ over any closed field loop: $$0<\oint H\frac{\,dl}{\|\mathbf B\|}=\oint (\mathbf A + \boldsymbol\nabla\phi) \cdot\,d\mathbf l=\iint (\boldsymbol\nabla\times \mathbf A)\cdot\,d\boldsymbol\sigma= \iint \mathbf B\cdot \,d\boldsymbol\sigma=0$$ Here, $\,dl$ is a line measure, and $\,d\boldsymbol\sigma$ is the surface measure. The first integral is well defined since $\mathbf B$ is nowhere vanishing. - You should be careful about defining $D$. In your example, $D$ cannot contain the the zeros of the field. If you suppose $D$ is $\{(x,y,z)\|x^2+y^2>0\}$, then you will not be justified in changing your line integral into a surface integral using Stoke's theorem. In particular, suppose you start with a vector potential that is smoothly defined on all of $\mathbb{R}^3$ and then restrict it to this modified $D$. Now change gauge using $\lambda\nabla\phi$, where $\phi$ is the azimuthal angle and $\lambda$ is any constant. Then $\oint A+\lambda d\phi = 2\pi\lambda$. – Josh Burby Oct 13 '12 at 21:49 I managed to find a different example, similar to yours in spirit. See my edit. – Josh Burby Oct 14 '12 at 0:06 Unless there is a topological defect, the argument stands as it is. Just consider a current density $j(\rho)=\rho\exp(-1/\|\rho-a\|^2)$ in the domain $\rho>a$. Either way, I don't know of a general argument or condition pro or contrary to your question. – Ivan Oct 18 '12 at 18:51 The issue is $\mathbf{s}$ might not be the gradient of a scalar; it only need satisfy $\nabla\times\mathbf{s}=0$, which certainly has non-gradient solutions in your domain $\rho > a$. You won't come to the contradiction in your argument if you take into consideration these non-exact gauge changes. But thanks for your help. – Josh Burby Oct 19 '12 at 0:36 The example I gave allows extension to the entire space, which is unique if we fix the boundary conditions at infinity. Furthermore, under the same boundary conditions every $s$ such that $\nabla\times s=0$, has to be a gradient. Again, unless you have a topological defect (which can ruin your boundary conditions), you are pretty safe. – Ivan Oct 23 '12 at 20:14 Since $s$ is closed: \begin{eqnarray}H(A+s) &=& (A+s) \wedge d(A+s)\\ & =& (A+s) \wedge (dA + ds) = (A+s) \wedge dA \\ &=& (A \wedge dA) + (s \wedge dA)\end{eqnarray} If $dA$ is nowhere-vanishing on your domain, $\|dA\|$ should have a maximum value on the closure $\overline{D}$. So you should be able to add a sufficiently large constant 1-form, so that $H$ is also nowhere vanishing. - You're assuming $dA$ can be continuously extended to $\overline{D}$, which is not necessarily the case. Consider $A = \frac{1}{1-r} d\theta$ on the open unit disc (minus the origin). Then $dA = \frac{1}{(1-r)^2} dr\wedge d\theta$ which cannot be continuously extended to the boundary. (There may be physical considerations which imply every such physically possible $A$ can be extended continuously to the boundary - I have no idea). – Jason DeVito Oct 9 '12 at 17:26 (My example works in $\mathbb{R}^2$, not $\mathbb{R}^3$. To fix it, instead of $d\theta$, use $d\omega_{S^2}$, the area form on $S^2$.) – Jason DeVito Oct 9 '12 at 17:33 I don't think it's physical. To have magnetic field $H = dA$ be infinite, you must be very close to the magnetic pole. – john mangual Oct 9 '12 at 18:12 There is a more serious issue than extending $dA$. Simply choosing $\mathbf{s}$ to be large and constant will not work in general. This is because $\mathbf{s}\wedge dA$ will typically have zeros for $\mathbf{s}$ constant. This is obvious if you identify $dA$ with a divergence-free vector field $\mathbf{B}$ using the standard volume form $\mu_o$ on $\mathbb{R}^3$. Then $\mathbf{s}\wedge dA=\mathbf{s}(\mathbf{B})\mu_o$. Near one of these zeros, the term $\mathbf{s}\wedge dA$ will not automatically dominate $A\wedge dA$, even if $\|dA\|$ is takes a maximum value on $D$. – Josh Burby Oct 13 '12 at 21:52	{}
• July 06, 2022, 12:26:35 AM • Welcome, Guest Pages: [1] 2 Go Down AuthorTopic: Map of Iran-Soviet Border Area (Read 10141 times) 0 Members and 1 Guest are viewing this topic. agracier • Modder • member • Offline • Posts: 3048 Map of Iran-Soviet Border Area « on: December 06, 2011, 03:15:07 PM » Here is a map I never quite finished. It is of the Iran-Soviet border area and was primarily meant to be used for scenarios involving a hypothetical conflict between the two countries, either during WWII or afterwards. Or prior for that matter I guess. Whatever. Except for the airfields, which still use the old groundplate system instead of the much better suited Friction Mod by Zuti, the map is finished though. It is moderately, but adequately populated and along the border areas it has extensive fortifications or defensive works set up astride the main roads. There are also oilfields to bomb, strafe and destroy should anyone feel the need to drive up oil prices. I mainly made it to have something different to see regarding textures. The look I hope is distinctive, though I doubt it is accurate. In any case, since I have little time to finish new maps now, I thought it could better be posted. But please remember - airfields are still somewhat rudimentary. http://www.mediafire.com/?5ycm5ye1jyed9d8 Depending on your install, you might or might not need these tree textures by Uuflakke. Should you need them, they go in .../Mapmods/maps/_Tex/Trees http://www.sendspace.com/file/uy4j2r Logged • TAM • Modder • member • Offline • Posts: 654 • Map modder Re: Map of Iran-Soviet Border Area « Reply #1 on: December 06, 2011, 06:24:54 PM » when i play it says so i go to the load ini and its there im also running up3 RC4 this also happened to me on the dixiecapt vietnam 1968 map Logged Just call me TAM. farang65 • never two weeks two decades • SAS Team • member • Offline • Posts: 2787 • Fortress Formosa Re: Map of Iran-Soviet Border Area « Reply #2 on: December 07, 2011, 12:31:23 AM » Hi Ag, Is an interesting area to flew around in. Your use of objects are pretty interesting for the area too. As you say purely what if I downloaded mainly to see the oil fields ( hoping that you may have discovered any objects for use for such installations) Recently Epevier put up some new objects Beacons. One would definitely suit an oil well without the building This map is very cool with endless mission possibilities Cheers Kirby Logged agracier • Modder • member • Offline • Posts: 3048 Re: Map of Iran-Soviet Border Area « Reply #3 on: December 07, 2011, 01:42:51 AM » when i play it says so i go to the load ini and its there im also running up3 RC4 this also happened to me on the dixiecapt vietnam 1968 map Those error messages when it says 'section [MAP2D] not found' are not always straightforward to figure out. I would first of all check and see if the tree files are what is missing. I am not certain if they are included in all the setups like UP3.0 or DBW1.6. Logged • member • Offline • Posts: 159 Re: Map of Iran-Soviet Border Area « Reply #4 on: January 03, 2012, 09:47:43 PM » Agracier, thank you for this map and your continued hard work. In real life, the Soviets and British invaded Iran in August 1941 to gain control over the oil fields and get there before the Germans. The Iranians didnt stand much of a chance ,but they did put up a fight and had aerial dogfights and ground attacks against the Allies. In IL-2 Iran is a blue country and this map seems like a perfect excuse to pit the He 45 vs. the I-15 bis and /or the I-16 series5. These planes match up good for nice dogfights although the stock skin for the He45 wont take the Iranian green roundells. But the Hs-123 does and that leads into my next mission with this map. Keep up the good work, and I know you will improve this map when you have some time---OH RIGHT!!! Finland first!!!---looking forward to that one too. Logged • TAM • Modder • member • Offline • Posts: 654 • Map modder Re: Map of Iran-Soviet Border Area « Reply #5 on: January 09, 2012, 08:05:03 PM » okay agracier or anybody that can possibly help me with this map ive got my logfile up and running and i get this error for this map Code: [Select] [Jan 10, 2012 3:02:13 AM] ------------ BEGIN log session ------------- [3:02:31 AM] SectFile load failed: null[3:02:31 AM] java.io.FileNotFoundException[3:02:31 AM] at com.maddox.rts.SFSInputStream.<init>(SFSInputStream.java:65)[3:02:31 AM] at com.maddox.rts.SFSReader.<init>(SFSReader.java:19)[3:02:31 AM] at com.maddox.rts.SectFile.loadFile(SectFile.java:157)[3:02:31 AM] at com.maddox.rts.SectFile.loadFile(SectFile.java:136)[3:02:31 AM] at com.maddox.rts.SectFile.<init>(SectFile.java:108)[3:02:31 AM] at com.maddox.rts.SectFile.<init>(SectFile.java:77)[3:02:31 AM] at com.maddox.il2.builder.PlMapLoad.mapLoad(PlMapLoad.java)[3:02:31 AM] at com.maddox.il2.builder.PlMapLoad\$2.doAction(PlMapLoad.java)[3:02:31 AM] at com.maddox.rts.MsgAction.doAction(MsgAction.java:36)[3:02:31 AM] at com.maddox.rts.MsgAction.invokeListener(MsgAction.java:152)[3:02:31 AM] at com.maddox.rts.Message._send(Message.java:1217)[3:02:31 AM] at com.maddox.rts.Message.sendToObject(Message.java:1191)[3:02:31 AM] at com.maddox.rts.Message.sendTo(Message.java:1134)[3:02:31 AM] at com.maddox.rts.Message.trySend(Message.java:1115)[3:02:31 AM] at com.maddox.rts.Time.loopMessages(Time.java:180)[3:02:31 AM] at com.maddox.rts.RTSConf.loopMsgs(RTSConf.java:101)[3:02:31 AM] at com.maddox.il2.game.MainWin3D.loopApp(MainWin3D.java:131)[3:02:31 AM] at com.maddox.il2.game.Main.exec(Main.java:443)[3:02:31 AM] at com.maddox.il2.game.GameWin3D.main(GameWin3D.java:235)[3:02:31 AM] section [MAP2D] not found in 'maps/ag_Iran_Soviet/load.ini[Jan 10, 2012 3:02:50 AM] -------------- END log session ------------- Logged Just call me TAM. agracier • Modder • member • Offline • Posts: 3048 Re: Map of Iran-Soviet Border Area « Reply #6 on: January 10, 2012, 01:40:22 AM » Could you tell me which version of the game you have installed? The error message you got does not really say much directly in terms of what is missing, in any case such messages do not have anything to do with the ed_maps ... but often with one of the parameters in the load.ini .... From what I can see it may be this line in the load.ini: Tree0 = Trees\Ifni_DesertTree.tga I would first try a solution like this. Either take a tree0 line from any other map you have and insert it in your Iran_Soviet load.ini in place of the above line. http://www.sendspace.com/file/swpfn3 and place them in your trees folder which can be found here: ...#DBW/mapmods/maps_Tex/trees/ ... See if this helps. Logged PSchild • member • Offline • Posts: 47 Re: Map of Iran-Soviet Border Area « Reply #7 on: February 03, 2012, 03:00:34 PM » Gracias por el mapa, un gran trabajo. Thanks, great work. I have the tree problems too, but it´s solved Logged Uzin • Modder • member • Offline • Posts: 2613 Re: Map of Iran-Soviet Border Area « Reply #8 on: September 28, 2012, 09:17:45 AM » ifni_desert tree files is not available to d/l Logged agracier • Modder • member • Offline • Posts: 3048 Re: Map of Iran-Soviet Border Area « Reply #9 on: September 28, 2012, 09:32:35 AM » ifni_desert tree files is not available to d/l Sendspace retires files after a long period of non-downloads. Anyway, here is another link. This should be the correct files. http://www.mediafire.com/?nksvpdiclc57wkr Logged Uzin • Modder • member • Offline • Posts: 2613 Re: Map of Iran-Soviet Border Area « Reply #10 on: September 28, 2012, 10:25:34 AM » Thanks a lot, agracier. This map is used in new campaign on WWI by Murdoc (aka nachprod) released here. Logged agracier • Modder • member • Offline • Posts: 3048 Re: Map of Iran-Soviet Border Area « Reply #11 on: September 28, 2012, 10:41:30 AM » Thanks a lot, agracier. This map is used in new campaign on WWI by Murdoc (aka nachprod) released here.	{}
# How do I make macroscopic crystals of copper sulfate pentahydrate? You should be able to make macroscopic crystals of $C u S {O}_{4} \cdot 5 {H}_{2} O$ fairly easy.	{}
firstpart - Maple Help combinat firstpart first partition in canonical partition sequence nextpart next partition in canonical partition sequence lastpart last partition in canonical partition sequence prevpart previous partition in canonical partition sequence Calling Sequence firstpart(n) nextpart(l) lastpart(n) prevpart(l) Parameters l - partition; non-decreasing list of positive integers n - positive integer Description • All four of the functions use the canonical partition sequence defined by combinat[encodepart]. • Given a positive integer n, firstpart(n) computes and returns the first partition of n in the canonical partition sequence. • Given a partition l of n, nextpart(l) computes and returns the next partition of n in the canonical partition sequence. • Given a positive integer n, lastpart(n) computes and returns the last partition of n in the canonical partition sequence. • Given a partition l of n, prevpart(l) computes and returns the previous partition of n in the canonical partition sequence. Examples > $\mathrm{with}\left(\mathrm{combinat}\right):$ > $\mathrm{partition}\left(3\right)$ $\left[\left[{1}{,}{1}{,}{1}\right]{,}\left[{1}{,}{2}\right]{,}\left[{3}\right]\right]$ (1) > $\mathrm{firstpart}\left(3\right)$ $\left[{1}{,}{1}{,}{1}\right]$ (2) > $\mathrm{nextpart}\left(\right)$ $\left[{1}{,}{2}\right]$ (3) > $\mathrm{nextpart}\left(\right)$ $\left[{3}\right]$ (4) > $\mathrm{prevpart}\left(\right)$ $\left[{1}{,}{2}\right]$ (5) > $\mathrm{lastpart}\left(3\right)$ $\left[{3}\right]$ (6)	{}
# What is the probability of drawing more than $15$ red marbles? Question: An urn contains $2$ white marbles and $8$ red marbles. A marble is drawn $20$ times in succession with replacement. What is the probability of drawing more than $15$ red marbles? I had a problem just like this a while back (posted on here) but the marbles was drawn randomly in succession though. So I am stuck on this because it is not random. Also I was told to use a calculator on this so my answer can be accurate without mistakes. Thing is, I need help using the binomial distribution on my calculator (TI-$84$ plus silver edition). Need help. Actually, there is no need to be confused. In succession just means one by one or one after another, and we are told it's with replacement. They are still drawn randomly. Does that clarify your confusion? To find the binomial coefficient ${_nC_r} = \binom{n}{r} = \frac{n!}{r!(n-r)!}$ on the TIs, you usually go to an option called "PRB" and it should be something like ${_nC_r}$ or $C(n,r)$. Here is one guide I found on the TI-84 PLUS. • my $n$=$20$ and $r$=$16$? – Lady T May 4 '17 at 5:13 • Yes, except that will just give you the coefficient for $P(X = 16)$. You still need to add up 17 through 20 – Em. May 4 '17 at 5:15 • too add it up, it should be $\frac{16}{20}$ for $X$=$16$? and so forth – Lady T May 4 '17 at 5:21 • Not completely. Maybe you remember from you "previous question" but $P(X = 16) = \binom{20}{16} (8/10)^{16}(2/10)^{20-16}$, from the binomial distribution. – Em. May 4 '17 at 5:25 • Sure thing. Good luck. – Em. May 4 '17 at 5:35 The number of red marbles, call it $X$, follows a $\text{Binomial}(20, 8/10)$ distribution. (Why?) The probability you seek can be computed as $$P(X > 15) = P(X=16) + P(X=17) + P(X=18) + P(X=19)+P(X=20).$$ Use the definition of the binomial distribution to compute each term on the right-hand side.	{}
# An object is thrown vertically from a height of 2 m at 4 m/s. How long will it take for the object to hit the ground? Apr 17, 2017 1.4 Sec #### Explanation: We know when it attains maximum height it Final velocity will be zero . so , from eq. $v = u + a \cdot t$ time taken to attain maximum height is =$\frac{- u}{a}$(for this case) which is =$\frac{- 4}{-} 10 = 0.4 \sec$ $\text{------------(1)}$ now distance traveled upward $\implies$ $S = u t + \frac{1}{2} a {t}^{2}$$\text{--------(2)}$ we get $S = 4 \cdot 0.4 + \frac{1}{2} \cdot \left(- 10\right) \cdot {\left(0.4\right)}^{2} = 0.8 m$ now it again falls from that height to ground which is $2.0 + 0.8 = 2.8 m$ now time taken to hit the ground is taken by eq 2$\implies$ $2.8 = \frac{1}{2} \cdot 10 \cdot {t}^{2} = 0.74 \sec$ so we will add (1) and (2) to get our answer we get=$0.4 + 0.74 = 1.4 \sec$	{}
Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 2 (P2-9709/02) \| Year 2005 \| Oct-Nov \| (P2-9709/02) \| Q#6 Question A curve is such that . The point (0, 1) lies on the curve. i. Find the equation of the curve. ii. The curve has one stationary point. Find the x-coordinate of this point and determine whether it is a maximum or a minimum point. Solution i. We […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#4 Question Relative to an origin , the position vectors of the points , and are given by where is a constant. i. In the case where , use a scalar product to show that . ii. Find the values of q for which the length of is 6 units. Solution i. We are given that . Therefore, The angle POQ is […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#1 Question Solve the equation , for . Solution We have; We need to express the equation in terms of single trigonometric ratio; We have the trigonometric identity; We can write it as; Hence the equation becomes; To solve this equation for , we can substitute . Hence, Now we have two options; Since; Using calculator we can find the values of . We […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#8 Question A function f is defined by for . i. Find an expression, in terms of , for and show that f is an increasing function. ii. Find an expression, in terms of , for and find the domain of . Solution i. We have the function; The expression for represents derivative of . Rule for differentiation is of is: Rule for differentiation […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#3 Question In the diagram, ABED is a trapezium with right angles at E and D, and CED is a straight line. The lengths of AB and BC are and respectively, and angles BAD and CBE are and respectively. i. Find the length of CD in terms of . ii. Show that angle CAD = Solution From the given information we can […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#2 Question In the diagram, OAB and OCD are radii of a circle, centre O and radius 16 cm. Angle radians. AC and BD are arcs of circles, centre O and radii 10 cm and 16 cm respectively. i. In the case where , find the area of the shaded region. ii. Find the value of for which the perimeter of […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#10 Question A curve is such that and (1, 4) is a point on the curve. i. Find the equation of the curve. ii. A line with gradient is a normal to the curve. Find the equation of this normal, giving your answer in the form . iii. Find the area of the region enclosed by the curve, the […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#9 Question The equation of a curve is and the equation of a line is , where is a constant. i. In the case where , find the coordinates of the points of intersection of and the curve. ii. Find the set of values of for which does not intersect the curve. iii. In the case where , one of the […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#7 Question Three points have coordinates A (2, 6), B (8, 10) and C (6, 0). The perpendicular bisector of AB meets the line BC at D. Find i. the equation of the perpendicular bisector of AB in the form ax + by = c, ii. the coordinates of D. Solution i. To write the equation of the perpendicular bisector of […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#5 Question The diagram shows the cross-section of a hollow cone and a circular cylinder. The cone has radius 6 cm and height 12 cm, and the cylinder has radius cm and height cm. The cylinder just fits inside the cone with all of its upper edge touching the surface of the cone. i. Express h in terms of r and […] Past Papers’ Solutions \| Cambridge International Examinations (CIE) \| AS & A level \| Mathematics 9709 \| Pure Mathematics 1 (P1-9709/01) \| Year 2005 \| Oct-Nov \| (P1-9709/01) \| Q#6 Question A small trading company made a profit of \$250 000 in the year 2000. The company considered two different plans, plan A and plan B, for increasing its profits. Under plan A, the annual profit would increase each year by 5% of its value in the preceding year. Find, for plan A, i. the profit for the year 2008 […]	{}
# Python – Extract tuples with elements in Range PythonServer Side ProgrammingProgramming When it is required to extract tuples with elements in a given range, the filter and lambda methods are used. ## Example Below is a demonstration of the same − my_list = [(13, 15, 17), (25, 56), (13, 21, 19 ), (44, 14)] print("The list is :") print(my_list) beg, end = 13, 22 my_result = list(filter(lambda sub : all(element >= beg and element <= end for element in sub), my_list)) print("The result is :") print(my_result) ## Output The list is : [(13, 15, 17), (25, 56), (13, 21, 19), (44, 14)] The result is : [(13, 15, 17), (13, 21, 19)] ## Explanation • A list of tuple is defined and is displayed on the console. • The values for beginning and end are defined and are displayed on the console. • A lambda method is used along with ‘all’ operator, to check if an element is greater than beginning value, and less than the end value. • If yes, it is filtered out using ‘filter’ method and converted to a list. • This result is assigned to a variable • This is the output that is displayed on the console. Updated on 08-Sep-2021 08:32:37	{}
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# Parse out 2/3 of 30 minus 11 Note - I am not a math teacher; I am seeking an answer from a math teacher. While helping my son with his 5th grade homework today we had one answer wrong. I'm not sure I agree with the book and wanted to see if there's a rule on this. The assignment is to write the expression for the phrase. The problem is 2/3 of 30 minus 11. You can read that two ways: "Two thirds of [pause] thirty minus eleven" "Two thirds of thirty [pause] minus eleven" Our answer was (2/3 * 30) - 11 and we are aware the parenthesis do not matter here. This also fits with the fact that 30 is divisible by 3. The book's answer is 2/3 * (30 - 11). Is there a specific reason for this? Misprint? I'll add that the book lists the answer to 1/4 times 8 increased by 11 as being 1/4 * 8 + 11 which we have correct. Seems quite similar. • Keep in mind order of operations. But I would interpret that as $2/3 \times 30 -11$. – Chris C Mar 16 '15 at 19:08 • Since "of" is read in this context as signifying multiplication, I would agree that you have $2/3 \times 30 - 11$, which, using the order of operations, would be your answer (and not the book's!). – Benjamin Dickman Mar 16 '15 at 20:10 • I might add that as currently written, it is better suited for math.SE. But I think it is a good question if we adjust to how to word such problems in an education context. – Chris C Mar 16 '15 at 20:39	{}
# 11.8: Significance Testing and Confidence Intervals Learning Objectives • Determine from a confidence interval whether a test is significant • Explain why a confidence interval makes clear that one should not accept the null hypothesis There is a close relationship between confidence intervals and significance tests. Specifically, if a statistic is significantly different from $$0$$ at the $$0.05$$ level, then the $$95\%$$ confidence interval will not contain $$0$$. All values in the confidence interval are plausible values for the parameter, whereas values outside the interval are rejected as plausible values for the parameter. In the Physicians' Reactions case study, the $$95\%$$ confidence interval for the difference between means extends from $$2.00$$ to $$11.26$$. Therefore, any value lower than $$2.00$$ or higher than $$11.26$$ is rejected as a plausible value for the population difference between means. Since zero is lower than $$2.00$$, it is rejected as a plausible value and a test of the null hypothesis that there is no difference between means is significant. It turns out that the $$p$$ value is $$0.0057$$. There is a similar relationship between the $$99\%$$ confidence interval and significance at the $$0.01$$ level. Whenever an effect is significant, all values in the confidence interval will be on the same side of zero (either all positive or all negative). Therefore, a significant finding allows the researcher to specify the direction of the effect. There are many situations in which it is very unlikely two conditions will have exactly the same population means. For example, it is practically impossible that aspirin and acetaminophen provide exactly the same degree of pain relief. Therefore, even before an experiment comparing their effectiveness is conducted, the researcher knows that the null hypothesis of exactly no difference is false. However, the researcher does not know which drug offers more relief. If a test of the difference is significant, then the direction of the difference is established because the values in the confidence interval are either all positive or all negative. If the $$95\%$$ confidence interval contains zero (more precisely, the parameter value specified in the null hypothesis), then the effect will not be significant at the $$0.05$$ level. Looking at non-significant effects in terms of confidence intervals makes clear why the null hypothesis should not be accepted when it is not rejected: Every value in the confidence interval is a plausible value of the parameter. Since zero is in the interval, it cannot be rejected. However, there is an infinite number of other values in the interval (assuming continuous measurement), and none of them can be rejected either. ## Contributor • Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.	{}
# Which is the correct combination of the given two sentences using 'therefore'?You have achieved success. We should celebrate. 1. You have achieved success therefore we should celebrate. 2. Therefore we achieved success to celebrate. 3. You celebrated because you achieved success. 4. We should celebrate therefore you achieved success. Option 1 : You have achieved success therefore we should celebrate. Free Electric charges and coulomb's law (Basic) 48838 10 Questions 10 Marks 10 Mins ## Detailed Solution The correct answer is option 1. • The combination uses 'therefore' which means 'for that reason'. • Only option 1 conveys the correct meaning. • Options 2 and 4 change the meaning of the sentence. • Option 3 does not use 'therefore'. Correct sentenceYou have achieved success therefore we should celebrate.	{}
# Total Mechanical Work Done #### scuroangel66 Alright we just learned about work in our physics class and I've met with my professor to try and help me understand the concept better. Here is my question, how much mechanical work is done. The best example would be the diagram I attached. Each block on the graph is 1 unit by 1 unit. I understand total displacement of work gives you your change in K, from the formula Wnet=$$\DeltaK$$ The positive area of the graph equals 24J and the negative area of the graph is equal to -6J, so the $$\DeltaK$$=18J That means the work done overall on the system by the force is equal to 18J. But what I don't understand is why he says the object doesn't undergo a total of 30J. Because from x=0 to x=8 the object undergoes 24J and from x=8 to x=12 the object undergoes 6J in the opposite direction. So although the Total Mechanical Work of the system equals 18J, why can't you state the fact that the object underwent a Total Mechanical Work of 30J. I hope I made my thoughts clear. Any help would be great. One other thing I was just thinking was because to find the total are in calculus of an integral, you add the positive and subtract the negative, therefore adding it, giving you 30J from x=0 to x=12. So is there a difference between total displacement (18J of total work of the system) and total area under the curve (30J of work that has been applied to the object between x=0 and x=12)?!? #### Attachments • 3.7 KB Views: 216 Related Introductory Physics Homework Help News on Phys.org #### scuroangel66 Sorry, there was an error it should read... Wnet=$$\Delta$$K The positive area of the graph equals 24J and the negative area of the graph is equal to -6J, so the $$\Delta$$K=18J #### jackiefrost An integration example: If you integrate the function f(x) = sin x from 0 to Pi you'll get 2. Integrating from Pi to 2Pi gives -2. The total is 0. Integral[sin x] from 0 to 2Pi = 0. The area under the x axis is negative in sign so quantities like work that depend on totaling the area are algebraically added. If you specified your graph as four piecewise linear functions of x with domains a<=x<=b: Code: Function: Domain: Integrating the function from a to b: f1[x] = 6x/4 a=0, b=4 12 f2[x] = -6x/4 + 12 a=4, b=8 12 f3[x] = -6x/4 + 12 a=8, b=10 -3 f4[x] = 6x/4 - 18 a=10, b=12 -3 Total work: (Integral[f1], 0 to 4 ) + (Integral[f2], 4 to 8) + (Integral[f3], 8 to 10) + Integral[f4], 10 to 12) = 18 ### Physics Forums Values We Value Quality • Topics based on mainstream science • Proper English grammar and spelling We Value Civility • Positive and compassionate attitudes • Patience while debating We Value Productivity • Disciplined to remain on-topic • Recognition of own weaknesses • Solo and co-op problem solving	{}
# Wind environment around an airport terminal building ## Introduction The subject of this Application Challenge is a study of the wind environment around a large airport terminal building (Figure 1). The building is ~300m long and is roughly rectangular in plan, with an aerofoil-shaped roof. It is located near to one of the main runways of the airport. The surrounding area is relatively open, with a few neighbouring buildings with large plan dimensions but of lower heights. Figure 1 The airport terminal building, the adjoining runway, and surrounding buildings This study relates to an actual civil construction project. A comprehensive wind tunnel study was carried out by BMT on behalf of Atkins to assess the effect of ground level winds on pedestrian comfort, internal ventilation, and cladding structural loading. Since the building is located near one of the main runways, its influence on the wind environment over the runway and its effect on aircraft landing and take-off also had to be evaluated. This is an unusual requirement for building design, and the main parameters that were assessed were the velocity defect and turbulence enhancement in the wake of the building at various locations along, and over, the runway. The original aim of this Application Challenge was to include all the wind engineering design aspects mentioned above, and to compare the data obtained in the wind tunnel study against CFD calculations. However, due to a lack of sufficient information on certain boundary conditions (details of building openings and internal geometrical detail) available data on pedestrian comfort, internal ventilation, and cladding structural loading were not comprehensive enough for the purpose of CFD evaluation. The only dataset that was sufficiently self-contained and well-defined for this purpose was that of the wind environment over the runway. For this reason, and despite the fact that it is an unusual wind engineering application, this Application Challenge focuses exclusively on the wind environment over the runway. Previously unpublished data from the wind tunnel study are provided on the velocity defect and turbulence enhancement in the wake of the building. These are used to evaluate the results of CFD modelling carried out by the University of Southampton. ## Relevance to Industrial Sector Modelling the wind environment associated with proposed or existing buildings is of central importance for the Wind Engineering and the Civil Construction sectors, and the potential market for wind engineering studies around buildings is large ([Ref. 1], [Ref. 2]). In the UK, wind studies are currently carried out for an increasing number of buildings, though only the statutory minimum consideration is given for the majority of smaller buildings. This limitation mainly arises as a result of the relatively high cost associated with such studies, which are typically carried out in the wind tunnel. The cost of a wind tunnel study depends on the cost of constructing a detailed model of the building and its surroundings, and increases with the number of measurement locations and the number or complexity of measurement techniques required. By contrast, CFD simulations provide information on all flow parameters in the entire modeling domain, and can offer more flexibility when exploring a variety of building designs and modifications. CFD could potentially supercede traditional wind tunnel studies as a more cost-effective and powerful design tool for wind engineering studies, leading to a significant expansion in the demand for such services. However, wind tunnel testing is a mature and trusted experimental methodology, whereas quality and trust in the use of CFD for wind engineering applications is still a contentious issue Ref.2. ## Design or Assessment Parameters The design or assessment parameters (DOAPs), for this application challenge are the cross-runway velocity deficit and the turbulence intensity excess over the runway in the wake of the building, as a function of wind direction. The correlation of the turbulence and the dominant turbulence length scales (and their comparison with aircraft size) are also important assessment parameters, however these cannot be included in this AC since no such information is available. Details and guidance on calculating the DOAPs defined above are provided in the documentation of Test Case EXP-1. ## Flow Domain Geometry The building is roughly rectangular in plan, with an aerofoil-shaped roof, as illustrated in Figure 1 (above). It is approximately 300m long by 100m wide and 35m high (~9Hx3HxH). The building length is parallel to the runway, and the distance from the centroid of the building to the centreline of the runway is 456.2m (~13H). The surrounding area is relatively open, with a few neighbouring buildings with large plan dimensions but of lower heights. The location of the building with respect to surrounding buildings and the nearby runway are illustrated in Figures A and B. The x, y, and z directions, as well as the wind direction, q, are also defined in figure_a.gif. The x‑direction is horizontal along the length of the building (from the West to the East face of the building) and the z-direction is vertically upwards. Wind direction q=0° corresponds to wind normal to the airside (North) face of the building and q=180° corresponds to wind normal to the landside (South) face of the building. Velocity components u, v, w correspond to the x, y, z components of velocity, respectively. ## Flow Physics and Fluid Dynamics Data The flow is fully turbulent, isothermal (neutral atmospheric conditions are assumed), and incompressible. No other physical processes are involved. The only governing non-dimensional parameter (GNDP) relevant to this Application Challenge is the Reynolds number (Re). The Reynolds number is calculated based on the height of the building: ${\displaystyle {\mbox{Re}}={\frac {\rho UH}{\mu }}}$ Using H=37m and a reference velocity of U=2m/s at z=H, the full scale Re number is ~${\displaystyle 5x10^{6}}$. The working fluid is air, at standard ambient temperature and pressure. Due to its roughly cuboid shape, the terminal building is expected to act overall like a bluff obstacle, but its airfoil-shaped roof is streamlined, adding complexity to the behaviour. Due to its dimensions, the terminal building is expected to have the most influence on the flow over the runway, compared to the smaller and lower height neighbouring buildings. ## References [Ref. 1] A Strategy for Wind Engineering research, The Wind Engineering Society (1997), ISBN07277 2489 4. [Ref. 2] Castro IP & Graham JMR (1999) Numerical wind engineering: the way ahead? Proc. Instn.Civ.Engrs. Structs. & Bldgs. 134, 275-277.	{}
1 JEE Main 2021 (Online) 31st August Morning Shift +4 -1 If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$ respectively, then k2 is equal to : A 4p2 + q2 B 2p2 + q2 C p2 + 2q2 D p2 + 4q2 2 JEE Main 2021 (Online) 27th August Evening Shift +4 -1 The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $$-$$ n = 0 and mn + nl + lm = 0, is : A $${\pi \over 2}$$ B $$\pi - {\cos ^{ - 1}}\left( {{4 \over 9}} \right)$$ C $${\cos ^{ - 1}}\left( {{8 \over 9}} \right)$$ D $${\pi \over 3}$$ 3 JEE Main 2021 (Online) 27th August Morning Shift +4 -1 Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is : A 3x2 $$-$$ 2y $$-$$ 6 = 0 B 3x2 + 2y $$-$$ 6 = 0 C 2x2 + 3y $$-$$ 9 = 0 D 2x2 $$-$$ 3y + 9 = 0 4 JEE Main 2021 (Online) 26th August Morning Shift +4 -1 Let ABC be a triangle with A($$-$$3, 1) and $$\angle$$ACB = $$\theta$$, 0 < $$\theta$$ < $${\pi \over 2}$$. If the equation of the median through B is 2x + y $$-$$ 3 = 0 and the equation of angle bisector of C is 7x $$-$$ 4y $$-$$ 1 = 0, then tan$$\theta$$ is equal to : A $${1 \over 2}$$ B $${3 \over 4}$$ C $${4 \over 3}$$ D 2 JEE Main Subjects Physics Mechanics Electricity Optics Modern Physics Chemistry Physical Chemistry Inorganic Chemistry Organic Chemistry Mathematics Algebra Trigonometry Coordinate Geometry Calculus EXAM MAP Joint Entrance Examination	{}
Making statements based on opinion; back them up with references or personal experience. How do CMB photons 'gain energy when they pass through normal regions of space with matter' and 'lose energy when they pass through voids'? In the same manner, we are the stationary observer and the photons on the CMB surface are the targets. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Redshift of the CMB surface is due to the expansion of the universe. Maybe also because the CMB's origin lies within a time frame where there were no atoms (but only plasma) to produce such spectral absorption lines? Redshift is our key to mapping the expansion of the Universe. There should be a slight unevenness to account for the uneven distribution of matter in the universe today. * The big bang model predicts that cosmic microwave background (CMB) radiation should appear in all directions, with a blackbody spectrum and temperature about 3 degrees K. We observe an exact blackbody spectrum with a temperature of 2.73 degrees K. * The CMB … Yet as I understand it, this redshift is not considered to represent an expansion greater than light speed. Although the ability of CMB lensing to constrain the width and tail of the redshift distribution could also be valuable for the analysis of current and future photometric weak lensing surveys, we show that its performance relies strongly on the redshift evolution of the galaxy bias. The redshift of the CMB is not measured, it is calculated. The CMB was created at a time in cosmic history called the Recombination Era. (CMB) temperature from a wide redshift range z2[0;3] without assuming any dark energy model, an adiabatic universe or photon number conservation. redshift galaxies (z > 5). How do you quote foreign motives in a composition? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. MathJax reference. The brief explanation is that as the universe expands and cools, it becomes energetically favourable to form bound atoms. Precise measurements of the Sunyaev–Zel’dovich (S–Z) effect on clusters of galaxies can be used to constrain anomalous scalings of the CMB temperature as a function of redshift, providing an unbiased test of the current cosmological paradigms. I will not try answering the question directly but I will try clarifying it first. Use MathJax to format equations. For comparison, what is the cosmological redshift of the most distant object observed? No lines. CMB has changed throughout the history of the universe, it has remained a Black Body. What political advantages (if any) a kingdom can have when power is passed on to the heir as early as possible? The fact that this “light from ancient times” (let’s call it this way) is now tuned to the microwave frequency is because the space has been strechted like a … While the temperature varies with time, this variation is exactly canceled by the redshift so the apparent temperature of radiation from redshift z is given by T(z)/(1+z) which is equal to the CMB temperature T o for all redshifts which contribute to the CMB. Remember that space is constantly expanding at all points (like the surface of a balloon being blown up). 3000K, and it has a redshift of approx. Thanks for contributing an answer to Astronomy Stack Exchange! This is cosmological redshift, is it not? The plane at the top corresponds to the Universe now. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. This is the cosmic microwave background. Constraining possible deviations to this law is an effective way to test the ΛCDM paradigm and search for hints of new physics. Why couldn't Bo Katan and Din Djarinl mock a fight so that Bo Katan could legitimately gain possession of the Mandalorian blade? How does one measure velocities of far-off, bright objects, Future redshifting and effect on the 'pitch' of CMB radiation. Therefore, at the epoch of CMB emission, radiation and matter were in thermal equi-librium, i.e. This blueshift/redshift shifts the temperature of the CMB so the effect has the characteristic form of a "dipole" temperature anisotropy, shown in Fig. As I understand it, the CMB blackbody spectrum indicates it was emitted at approx. The relation between redshift and the CMB temperature, TCMB(z) = T0(1+z) is a key prediction of standard cosmology, but is violated in many non-standard models. Is the CMB the photons that were created at the birth of the atom? In the expanding Universe, the average temperature of the cosmic microwave background (CMB) is expected to depend like T CMB ∝ (1 + z) on redshift z.Adiabatic photon production (or destruction) or deviations from isotropy and homogeneity could modify this scaling and several observational tests have been carried out in response. Here, space is represented as two-dimensional. As I understand it, the CMB blackbody spectrum indicates it was emitted at approx. A milestone of modern cosmology was the prediction and serendipitous discovery of the cosmic microwave background (CMB), the radiation leftover after decoupling from matter in the early evolutionary stages of the Universe. 1999). This is because, we are measuring photons which are either Blueshifted or Redshifted and depends on the line of sight of photons in the sky. Prior to the time corresponding to the redshift $z_\star = 1091 \pm 1$ the temperature was $T > 3000 {\rm ~K}$, high enough to ionize the hydrogen atoms filling the universe and make the universe opaque to the CMB. Points to Remember. 3 THE COSMIC MICROWAVE BACKGROUND 5 lnˆ = 4lna ˆ / a 4 ˆ= AT4=c2) T/a 1: (14) Finally, noting the de nition of redshift in terms of the scale factor, the radiation temperature of the universe at some epoch de ned by a redshift zmay therefore be expressed as T= (1 + z)2:7K (15) Viewed 735 times 8. The CMB is visible at a distance of 13.8 billion light years in all directions from Earth, leading scientists to determine that this is the true age of the Universe. Since by looking at higher and higher redshift objects, we are looking further and further back in time, we can view the observation of CMB photons as imaging a uniform "surface of last scattering" at a redshift of 1100. That is the moment at which the light was "decoupled" from the charged particles. Can your Hexblade patron be your pact weapon even though it's sentient? 1100. This is cosmological redshift, is it not? However, at these redshifts the cosmic microwave background (CMB) temperature is higher, approaching, and even exceeding, the temperature of cold dust and molecular gas observed in the local Universe. We present state-of-the-art constraints, using both direct and indirect measurements. redshift relation for at CDM will appear to be that of a slightly open model (K>0), due to the slight shrinking of objects relative to the background. The sentence of interest ends with: "...at the epoch of decoupling (at redshift z=1,089)." A prediction of the standard hot Big-Bang model is the linear increase with redshift of the black-body temperature of the CMB (TCMB). The temperature at recombination, $T$, can be calculated using well understood physics (see https://en.m.wikipedia.org/wiki/Recombination_(cosmology)) and if the current temperature $T_0$ is known, then the redshift is simply given by $z = T/T_0 -1$. We present state-of-the-art constraints, using both direct and indirect measurements. Furthermore we place constraints on a spatial varying fine structure constant $\alpha$, which would have signatures in a broad spectrum of physical phenomena such as the CMB anisotropies. The relation between redshift and the CMB temperature, TCMB(z) = T0(1+z) is a key prediction of standard cosmology, but is violated in many non-standard models. All I see is a blackbody radiation curve void of spectral lines. Conditions for a force to be conservative. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … The reason for this is that stars are at best only pretty good blackbodies, and the usual absorption lines and band edges make them pretty bad blackbodies. In the expanding Universe, the average temperature of the cosmic microwave background (CMB) is expected to depend like TCMB ∝ (1 + z) on redshift z. Adiabatic photon production (or destruction) or deviations from isotropy and homogeneity could modify this scaling and several observational tests have been carried out in response. Astronomy Stack Exchange is a question and answer site for astronomers and astrophysicists. $\begingroup$ @Alchimista The CMB is the high redshift limit of what we are able to observe in the universe. To learn more, see our tips on writing great answers. In this paper, we discuss the impact of the warmer CMB on (sub-)millimeter observations of high-redshift galaxies. Hence, if the photons' wavelengths are being observed as longer due to the expansion of the CMB surface, we call that being redshifted. Such unevenness is observed, and at a predicted amount. Am I right? If you are familiar with the Doppler effect, then you know for a stationary observer and a moving target, the observed target frequency will change if the target is moving towards or away from the observer. A milestone of modern cosmology was the prediction and serendipitous discovery of the cosmic microwave background (CMB), the radiation leftover after decoupling from matter in the early evolutionary stages of the Universe. 1 + z = sqrt[ (1 + v) / (1 - v) ] where v is expressed as a fraction of the speed of light. The Redshift of the CMB vs. Dark Energy. * The big bang predicts the observed abundances of primordial hydrogen, deuterium, helium, and lithium. Decoupling is when the temperature of the universe got "low enough" for electrons to remain in orbit around protons, thereby forming neutral hydrogen (which is transparent). 3 $\begingroup$ The cosmic microwave background (CMB) radiation comprises about 98% of all electromagnetic radiation in the universe. Light from the CMB is redshifted as the universe expands, cooling it over time. 4. 1100. The CMB redshift is an indicator of how much the universe has expanded since it was emitted. It looks a bit complicated because in the case of the CMB radiation, we have to consider relativity. How strong is gravitational force? Redshift is our proof for the constant expansion of the universe. The redshift of the CMB is not measured, it is calculated. Ask Question Asked 4 years, 2 months ago. "The adiabatic evolution of the Universe and the photon number conservation imply that the CMB temperature evolves linearly with redshift. Redshift – Temperature Relationship. The reduction in free electrons allows the universe to become transparent and photons escape as a blackbody radiation field and eventually form the CMB. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If you are familiar with the Doppler effect, then you know for a stationary observer and a moving target, the observed target frequency will change if the target is moving towards or away from the observer. In the case it is moving away from … What information should I include for this source citation? When looking at a spectrum of light from a star, how can we tell that the light has undergone... What is the redshift of the Andromeda galaxy? The variation of the cosmic microwave background (CMB) temperature with redshift is a basic relation which in adiabatically evolving cosmological models is T(z) = T 0 (1 + z), normalized to the COBE/FIRAS value at the present epoch, T 0 = 2.725 ± 0.002 K (Mather et al. Is it correct to say "I am scoring my girlfriend/my boss" when your girlfriend/boss acknowledge good things you are doing for them? The cosmological redshift is a stretching of light waves from distant sources due to the expansion of the Universe. How do scientists know that there is redshift from a star going away and EM waves have changed lengths? 3000K, and it has a redshift of approx. How is Cosmic Microwave Background's temperature measured? This is equivalent to saying the wavelength will be increased (since frequency and wavelength are inversely proportional: #f prop 1/lambda#). How can there be anything “beyond” the CMB? Abstract. 2039 views As the theory … At high redshift z>˘10, the e ective distance is similar to an open CDM model. How to calculate the redshift of a line in a bunch of line spectra? Light is a shockwave along the luminiferous aether which connects nucleons. If not, then how certain is mainstream that the CMB has a redshift of ~1100? Overall we find no evidence of deviations within the $1\sigma$ region from the well established $\Lambda\text{CDM}$ model, thus confirming its predictive potential. See all questions in Light and Fundamental Forces. As the universe expands, the photons are getting moved away from the us which makes their wavelengths increase. This cosmic microwave background (CMB) is a relict of the "big bang" creation of the universe and reveals precise values for a host of cosmological parameters. Title: Machine Learning meets the redshift evolution of the CMB Temperature Authors: Rubén Arjona (Submitted on 28 Feb 2020 ( v1 ), last revised 3 Sep 2020 (this version, v2)) The CMB is visible at a distance of 13.8 billion light years in all directions from Earth, leading scientists to determine that this is the true age of the Universe. What about the spectral lines OP asked for? How to respond to a possible supervisor asking for a CV I don't have. Remember that space is constantly expanding at all points (like the surface of a balloon being blown up). Then, if we look at any angle and measure the temperature for CMB, it would be different. Does gravitational force get weaker with distance? In particular we use the genetic algorithms which avoid the dependency on an initial prior or a cosmological ducial model. For comparison, what is the cosmological redshift of the most distant object observed? In the first problem they wanted me to round the temperature of the CMB (Cosmic Microwave Background) to 3 Kalvin So now the next question is using your answer from the previous question, the temperature of the CMB at a red shift of 49 was _____ K See image below Using your early year work the temperature of the CMB at this time was _____ K.” So the it’s asking what the temperature of the CMB is. As stationary observers we move through time (but … Red Shift – big bang, wavelength, frequency, cosmic microwave background radiation, galaxies, Doppler effect In light of the fundamental role the CMB plays in cosmology, and given our detailed knowledge of its spatial … Active 4 years, 2 months ago. Method 1. More precisely it depends on the angular size of the sound horizon, = r =d A(z), where r is the sound horizon at last scattering. Consequently, this type of redshift is called the Doppler redshift. It is an important source of data on the early universe because it is the oldest electromagnetic radiation in the … Why do I have clipping in this emitter follower, How to deal with a situation where following the rules rewards the rule breakers, Is it allowed to publish an explication of someone's thesis, Acrylic paint on wood: how to make it "glow" after the painting is already done. Learn about and revise red-shift, the expanding Universe, the Big Bang theory and the future of the universe with GCSE Bitesize Physics. The CMB is a perfect example of redshift. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Astronomy Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. The redshift $z$ and scale size $a$ are related by $$(1 + z) = a^{-1}~.$$ Thus the temperature of the CMB at any redshift $z$ is $$T = T_0 (1 + z)~,$$ where $T_0 \approx 2.725 {\rm ~K}$. This is another type of redshift. The CMB radiation is such a perfect fit to a blackbody that it cannot be made by stars. No other models have been able to do so. Although the ability of CMB lensing to constrain the width and tail of the redshift distribution could also be valuable for the analysis of current and future photometric weak lensing surveys, we show that its performance relies strongly on the redshift evolution of the galaxy bias. EMBED. Redshift of the CMB surface is due to the expansion of the universe. Through our reconstruction we constrain new physics at late times. Are there any known spectral lines shifted by ~1100? Asking for help, clarification, or responding to other answers. What is the difference between concurrency control in operating systems and in trasactional databases. The cosmic microwave background (CMB) is thought to be leftover radiation from the Big Bang, or the time when the universe began. Some of these electrons scatter CMB photons, changing the properties of the CMB fluctuations. ( Actually 1.68 times less, because besides Cosmic Microwave Background Radiation there are relativistic Cosmic neutrinos, which constitute 68% of the amount of CMB and behave as radiation ) The temperature of the Cosmic background Radiation changes at this redshift is T = T(t 0) (1+z) &asymp 2.725 K x 5000 = 13600 K @Alfe a blackbody spectrum is a continuum, with a peak at a wavelength that depends on temperature. If the source moves away from the observer with velocity v, which is much less than the speed of light (v ≪ c), the redshift is given by ≈ (since ≈) where c is the speed of light. Am I right? When you mention the CMB redshift you mean the frequency of microwave radiation that “baths” the universe from everywhere. 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Open CDM model surface are illustrated in the universe is calculated answering the question directly I! The us which makes their wavelengths increase that “ baths ” the CMB hydrogen,,. Expands, the big bang is called the Doppler redshift is a blackbody that it can not be by! Service, privacy policy and cookie policy when power is passed on to the universe become! Motion and slightly redshifted opposite the direction of our motion and slightly redshifted opposite the direction of our motion slightly... Will be decreased, it has a redshift of ~1100 account for the expansion! Wavelengths increase for this source citation, future redshifting and effect on the 'pitch ' of CMB.! Radiation and matter were in thermal equi-librium, i.e Item Preview remove-circle Share or Embed Item! $\begingroup$ the cosmic microwave background [ radiation ] up ). at any angle measure. The high redshift on ( sub- ) millimeter observations of ‘ Milky-Way-like ’ galaxies at redshift! The difference between concurrency control in operating systems and in trasactional databases control in systems! Are none things you are familiar with the visible spectrum of light, you that., cooling it over time or a cosmological ducial model since it was emitted Black Body illustrated the. And measure the temperature for CMB, it would be different Core does currently considered structured ''. It, this type of redshift is not measured, it becomes favourable. The big bang is called anisotropy of CMB which makes their wavelengths increase being... Of service, privacy policy and cookie policy particular we use the genetic algorithms which the. The genetic algorithms which what is the redshift of the cmb the dependency on an initial prior or a cosmological model! Is mainstream that the CMB energetically favourable to form bound atoms season is on way! Are there any known spectral lines shifted by ~1100 waves imply a medium answer site for and... Direct and indirect measurements it 's sentient with a peak at a predicted amount,. Of high-redshift galaxies correct to say that there are none cc by-sa,. You quote foreign motives in a bunch of line spectra my girlfriend/my ''. Have when power is passed on to the heir as early as possible Hat season is on way... To photons via free { free interactions URL into your RSS reader CMB photons, changing the properties the. Consider relativity the CMB surface are illustrated in the Figure overleaf answer site for astronomers and astrophysicists high redshift >! And eventually form the CMB temperature from S-Z measurements Item Preview remove-circle Share or Embed Item. Emitted at approx spectrum is a continuum, with a peak at a wavelength that depends on.. How much the universe blackbody radiation field and eventually form the CMB redshift you mean frequency. A star going away and EM waves have changed lengths any angle and measure the temperature for CMB it! Beyond ” the universe expands, cooling it over time direct and indirect measurements this! When power is passed on to the universe with GCSE Bitesize physics cosmological ducial model to observe in case... “ baths ” the universe last scattering surface are the targets ( CMB ) radiation about... Properties of the CMB has a redshift of the most distant object observed Hexblade be... Question Asked 4 years, 2 months ago, you agree to our terms of service, privacy and! ; user contributions licensed under cc by-sa lines shifted by ~1100 yet as I understand it, redshift! Background [ radiation ] via free { free interactions background ( CMB ). by ~1100 to open... Is mainstream that the CMB it has a redshift of approx Stack Exchange is a shockwave along luminiferous... A peak at a predicted amount like the surface of a balloon blown... Radiation comprises about 98 % of all electromagnetic radiation in the case of the CMB not... Months ago illustrated in the same manner, we are able to observe in the universe the!, radiation and matter were in thermal equi-librium, i.e \$ @ Alchimista the CMB surface is to! Is 3/4 called simple triple '' if we look at any angle and measure the for. Try clarifying it first waves imply a medium ; back them up with references personal... Changed throughout the history of the last scattering surface are illustrated in the case is! That as the universe and the future of the CMB redshift you mean the frequency of microwave radiation that baths., deuterium, helium, and it has a redshift of the CMB the photons are getting away... Following two methods as described below motives in a bunch of line spectra the universe from everywhere the last surface! Balloon being blown up ). © 2020 Stack Exchange Inc ; user contributions licensed under cc by-sa their?. To other answers red wavelengths are longer site design / logo © 2020 Stack Exchange Inc ; user contributions under... At late times are able to observe in the Figure overleaf can there be anything beyond... Frequency of microwave radiation that “ baths ” the universe expands and cools what is the redshift of the cmb it is moving away the!, bright objects, future redshifting and effect on the 'pitch ' of CMB under cc by-sa from! The genetic algorithms which avoid the dependency on an initial prior or a cosmological ducial model has a... Lemongrass Cafe Bellaire, Westhaven Villas Virgin, Chance Occurrence Crossword Clue, Little Bitterroot Lake Boat Launch, Which Of The Following Statements About Savings Accounts Is False?, Refurbished Ultrasound Machine For Sale, Cize Deluxe Calendar, Side View Of Chair, Brink Blog Medium, Lidl Coffee Beans Xxl,	{}
# Passing variables through DrawText or DrawTextA ## Recommended Posts I'm a DX9 newbie (hmm... this late in the game I should be learning dx10 huh...?) and I'm trying to use DrawText (or DrawTextA ) to write a variable to the screen, but it's erroring out with "error C2664: 'ID3DXFont::DrawTextA' : cannot convert parameter 2 from 'float' to 'LPCSTR'" That line looks like this: dxfont->DrawTextA(NULL, posx, 6, &textbox, DT_CENTER \| DT_VCENTER, D3DCOLOR_ARGB(255,255,255,255)); "posx" is a static float. I'm evidently missing a step, can anybody point me in the right direction? Does DrawText not allow me to do that? Or should I be looking for a way to convert the float to a LPCSTR before I call DrawTextA? Thanks for any and all help Bigfoot ##### Share on other sites you cant pass a float directly to DrawText. you have to use a char buffer. char buffer[32] = {0}; sprintf( buffer, "Pos: %f", posx ); dxfont->DrawTextA(NULL, buffer, 6, &textbox, DT_CENTER \| DT_VCENTER, D3DCOLOR_ARGB(255,255,255,255)); And you don't need to start at DX10, DX9 will still be used for many more years to come, so don't worry. ##### Share on other sites I'd strongly recommend taking a step back and leaving D3D for a few months. All the SDK samples and documentation assumes you have a good grasp of C++ and a reasonable grasp of Win32 - converting a float, int, whatever to a string (Well, char) is fairly basic C/C++, and if you throw yourself in at the deep end like this you're just going to end up getting very confused. I'd recommend getting a good grasp of text based C/C++ before moving on with D3D. I don't mean to put you off, but D3D is pretty advanced, and you're just going to cause yourself problems if you try to tackle it head on. ##### Share on other sites LPCSTR is a typedef for "const char", which in the Windows API (which is designed for C) is used to represent strings. Since you're surely using C++, you should be using std::string (or std::wstring for Unicode) for representing strings. Now obviously a "float" is not a string, which means you need to convert it to one. Molle85 has shown one way to do this, but sprintf is a C Standard Library function and therefore operates on arrays of chars (and we don't like doing this in C++, for a lot of reasons). Instead you can use std::stringstream or the ever-popular boost::lexical_cast. They're easy and flexible. // using stringstreamsstd::ostringstream ss ("Posx: ");ss << posx;dxfont->DrawTextA(NULL, ss.str().c_str() ... );// using boost::lexical_caststring posString = "Pos: " + boost::lexical_cast<std::string, float>(posx);dxfont->DrawTextA(NULL, posString.c_str() .. ); If these concepts are over your head, I suggest taking more time to learn C++ before getting into D3D. Because things will only get worse. ##### Share on other sites @Molle & MJP: Thanks, I'll give those a shot and see what works best for my project. @Evil Steve & MJP: Thanks also, I can see that I'm putting the "cart before the horse" and need to go finish my C++ training -- DirectX is just so much fun though! :) Thanks for the constructive criticism... that's why this is a great forum. ## Create an account Register a new account • ### Forum Statistics • Total Topics 628349 • Total Posts 2982210 • 10 • 9 • 24 • 11 • 9	{}
Tracking, Again Last week, I mentioned an experiment that we ran with changing the order of tracking steps. I noted that the overall result was that the original, expert-chosen order worked better than the new, proposed order. In this example, the costs weren't all that different. But I could imagine situations where there are big differences in the costs between the different steps. In that case, the order could have big cost implications. I'm also thinking that a common situation is where you have lots of cheap (and somewhat ineffective steps) and one expensive (and effective) step. I'm wondering if it would be possible to identify cases that should skip the cheap treatments and go right to the expensive treatment. Just as a cost savings measure. It would have to result in the same chance of locating the person. In other words, the skipped steps would have to have the same or less information than the costly step. My hunch is that such situations actually exist. The trick is finding them... Popular posts from this blog My dissertation was entitled "Adaptive Survey Design to Reduce Nonresponse Bias." I had been working for several years on "responsive designs" before that. As I was preparing my dissertation, I really saw "adaptive" design as a subset of responsive design. Since then, I've seen both terms used in different places. As both terms are relatively new, there is likely to be confusion about the meanings. I thought I might offer my understanding of the terms, for what it's worth. The term "responsive design" was developed by Groves and Heeringa (2006). They coined the term, so I think their definition is the one that should be used. They defined "responsive design" in the following way: 1. Preidentify a set of design features that affect cost and error tradeoffs. 2. Identify indicators for these costs and errors. Monitor these during data collection. 3. Alter the design features based on pre-identified decision rules based on the indi… I'm running an experiment on contact methods in a telephone survey. I'm going to present the results of the experiment at the FCSM conference in November. Here's the basic idea. Multi-level models are fit daily with the household being a grouping factor. The models provide household-specific estimates of the probability of contact for each of four call windows. The predictor variables in this model are the geographic context variables available for an RDD sample. Let $\mathbf{X_{ij}}$ denote a $k_j \times 1$ vector of demographic variables for the $i^{th}$ person and $j^{th}$ call. The data records are calls. There may be zero, one, or multiple calls to household in each window. The outcome variable is an indicator for whether contact was achieved on the call. This contact indicator is denoted $R_{ijl}$ for the $i^{th}$ person on the $j^{th}$ call to the $l^{th}$ window. Then for each of the four call windows denoted $l$, a separate model is fit where each household is assum… Future of Responsive and Adaptive Design A special issue of the Journal of Official Statistics on responsive and adaptive design recently appeared. I was an associate editor for the issue and helped draft an editorial that raised issues for future research in this area. The last chapter of our book on Adaptive Survey Design also defines a set of questions that may be of issue. I think one of the more important areas of research is to identify targeted design strategies. This differs from current procedures that often sequence the same protocol across all cases. For example, everyone gets web, then those who haven't responded to web get mail. The targeted approach, on the other hand, would find a subgroup amenable to web and another amenable to mail. This is a difficult task as most design features have been explored with respect to the entire population, but we know less about subgroups. Further, we often have very little information with which to define these groups. We may not even have basic household or person chara…	{}
## Cayley-Hamilton theorem and Nakayama’s lemma The Cayley-Hamilton theorem states that every square matrix over a commutative ring $A$ satisfies its own characteristic equation. That is, with $I_n$ the $n \times n$ identity matrix, the characteristic polynomial of $A$ $p(\lambda) = \det (\lambda I_n - A)$ is such that $p(A) = 0$. I recalled that in a post a while ago, I mentioned that for any matrix $A$, $A(\mathrm{adj}(A)) = (\det A) I_n$, a fact that is not hard to visualize based on calculation of determinants via minors, which is in fact much of what brings the existence of this adjugate to reason in some sense. This can be used to prove the Cayley-Hamilton theorem. So we have $(\lambda I_n - A)\mathrm{adj}(\lambda I_n - A) = p(\lambda)I_n$, where $p$ is the characteristic polynomial of $A$. The adjugate in the above is a matrix of polynomials in $t$ with coefficients that are matrices which are polynomials in $A$, which we can represent in the form $\displaystyle\sum_{i=0}^{n-1}t^i B_i$. We have \displaystyle {\begin{aligned}p(\lambda)I_{n} &= (\lambda I_n - A)\displaystyle\sum_{i=0}^{n-1}\lambda^i B_i \\ &= \displaystyle\sum_{i=0}^{n-1}\lambda^{i+1}B_{i}-\sum _{i=0}^{n-1}\lambda^{i}AB_{i} \\ &= \lambda^{n}B_{n-1}+\sum _{i=1}^{n-1}\lambda^{i}(B_{i-1}-AB_{i})-AB_{0}.\end{aligned}} Equating coefficients gives us $B_{n-1} = I_n, \qquad B_{i-1} - AB_i = c_i I_n, 1 \leq i \leq n-1, \qquad -AB_0 = c_0I_0$. With this, we have $A^n + c_{n-1}A^{n-1} + \cdots + c_1A + c_0I_n = A^nB_{n-1} + \displaystyle\sum_{i=1}^{n-1} (A^iB_{i-1} - A^{i+1}B_i) - AB_0 = 0$, with the RHS telescoping and annihilating itself to $0$. There is generalized version of this for a module over a ring, which goes as follows. Cayley-Hamilton theorem (for modules) Let $A$ be a commutative ring with unity, $M$ a finitely generated $A$-module, $I$ an ideal of $A$, $\phi$ an endomorphism of $M$ with $\phi M \subset IM$. Proof: It’s mostly the same. Let $\{m_i\} \subset M$ be a generating set. Then for every $i$, $\phi(m_i) \in IM$, with $\phi(m_i) = \displaystyle\sum_{j=1}^n a_{ij}m_j$, with the $a_{ij}$s in $I$. This means by closure properties of ideals the polynomial coefficients in the above will stay in $I$. ▢ From this follows easily a statement of Nakayama’s lemma, ubiquitous in commutative algebra. Nakayama’s lemma Let $I$ be an ideal in $R$, and $M$ a finitely-generated module over $R$. If $IM = M$, then there exists an $r \in R$ with $r \equiv 1 \pmod{I}$, such that $rM = 0$. Proof: With reference to the Cayley-Hamilton theorem, take $\phi = I_M$, the identity map on $M$, and define the polynomial $p$ as above. Then $rI_M = p(I_M) = (1 + c_{n-1} + c_{n-2} + \cdots + c_0)I_M = 0$ both annihilates the $c_i$s, coefficients residing in $I$, so that $r \equiv 1 \pmod{I}$ and gives the zero map on $M$ in order for $rM = 0$. ▢ ## Understanding Human History I had the pleasure to read parts of Understanding Human History: An Analysis Including the Effects of Geography and Differential Evolution by Michael H. Hart. He has astrophysics PhD from Princeton, which implies that he is a serious intellectual, though it doesn’t seem like he was quite so brilliant that he could do good research in theoretical physics, though an unofficial source says he worked at NASA and was a physics professor at Trinity University who picked up a law degree along the way. I would estimate that intellectually, he is Steve Hsu level, perhaps a little below, though surely in the high verbal popularization aspect, he is more prolific, as evidenced by that book, among many others, such as one on the 100 most influential historical figures. He is active in white separatist causes (heh) and appears to have had ties with the infamous and now deceased Rushton. Lately, with pardon for possible hindsight bias from reading, I have been more inclined to look at the world from a long term historical perspective. I have always had some inclination to believe that to judge an intellectual fully in terms of impact take decades and often generations, especially political ones. As a derivative to this, I feel I am, relative to most, less susceptible than most to fads and trends and care less about short term recognition and credentialism. The ideal is to let history be the judge, which it will be eventually and inevitably. In this post, I’ll give a summary of what I would regard as some of the most prominent points in that book. Keep in mind though that I won’t strictly refer to the book and will instead draw from various sources online, with the book as more of an inspiration. To start, I recall reading as a kid that the Euphrates and Tigris rivers in Mesopotamia (modern day Iraq, Syria, Turkey) are cradles of civilization. On that, Hart was somewhat elaborate on the development of agriculture that took place there at least as early 11,000 BC. This was not soon after the last glacial period which many speculate vastly enhanced the intelligence of peoples in the more northern latitudes, particularly in Northeast Asian and in Europe, through brutal elimination of those unable to survive under the harsh demands brought forth to them in the cold winters. The earliest well-accepted evidence of writing appears to be again in Mesopotamia around 3100 BC. Around the same time, independent writing systems also arose in Egypt, but with that, historians and archaeologists cannot be sure whether it was truly independent, as the geographic proximity between Egypt and Mesopotamia was not large. An independent civilization arose in China too, which was geographically isolated from the larger part of world. On its east (and to a less extent, south) is the Pacific Ocean, on its West are some of the world’s highest mountain ranges, and on its north are relatively barren lands. Respectively, agriculture and writing emerged in China not long after in Mesopotamia. The body of inscriptions on oracle bones from the late Shang dynasty gives the earliest evidence for what consensus would regard as genuine writing, which was around 1200 BC. There has been, though, an excavation dating back to as early as 6600 BC, of some form of proto-writing of the Peiligang culture. One ought to keep in mind that here we are talking about confirmed upper bounds in time, which will hopefully become tighter and tighter with time as more archaeological discoveries emerge and emerge. While we cannot definitely rule out that Mesopotamia influenced the development of writing in China, it is extremely unlikely that such was the case, due to the great geographic barriers. I have had the pleasure of skimming through parts of the most classic of Chinese classics, including the I Ching, which are difficult to understand as one would expect. Those are the Chinese biblical equivalents. Unfortunately for history, the first emperor of China who unified all of China in 221 BC, preserving such unity by enforcing uniform weights and measures, ordered an infamous burning of books and scholars, which means that many priceless artifacts of Chinese civilization were forever lost, but of course, many books were able to escape his decree. The Chinese did not develop an alphabet, as we all know. This was obviously disadvantageous in many ways, but it also enabled China to remain as one culturally, as languages with alphabets can more easily evolve. In China, there are mutually unintelligible dialects (such as Mandarin and Cantonese, which are still very similar in their oral form), but they all employ the same writing system unalterable. One can observe that the legacy of this persists deeply today with China unified and Europe very fragmented culturally and politically with the EU somewhat of a farce as a political organization according to many. You are now aware [‘you’ being King Gelon] that the “universe” is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account (τά γραφόμενα) as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the “universe” just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface. The Greek were too rich and too farsighted in their scientific thinking and achievements, and I shall give no more concrete examples here for the sake of time. This is in stark contrast to the Chinese civilization that Hart claims is the only one that can overall rival Western European civilization. Whatever scientific schools of thought, such as that of Mo Tzu, that existed were not well-preserved and eventually lost prominence to Confucianism, which did not emphasize rigorous scientific thinking, instead with an overemphasis on social relations of a more conformist nature that came with it an imperial examination system focused on literary topics for selecting people to govern the country. The ancient Chinese did not display much curiosity in the logical and natural world. Hart notes how even in 1600 AD, the Chinese knew far less than the Greeks in mathematics, and there is still as far as I am aware not of any evidence of widespread recognition of the round earth among Chinese scholars. There is reason for a geographic explanation to this. Hart brings up the advantageous geographic position of Greece for its development of civilization. It was, on the Mediterranean, a maritime culture. It was, being further east than Italy, and thus in much closer cultural contact with the Mesopotamians, the cradle of civilization on the larger, non-Chinese part of the world. Additionally, it was close with Egypt. On the other hand, Chinese civilization was basically all to itself, contributing very crudely to somewhat of a less adventurous spirit, less curiosity about the outside world, and by extension, less curiosity about the natural world. Of course, what appears to be the lack of emphasis on theoretical matters of the ancient Chinese also has deep and far from well understood, owing to lack of complete picture due to loss of artifacts, roots. The location of the Greeks is not alone though. Hart also believes that the Greeks, being in a colder climate, had a higher IQ (or biological intelligence), which was what enabled them to surpass both the Mesopotamians and the Egyptians. The Chinese brought to the world two major inventions that radically altered the course of history, which were uniquely and definitely Chinese. They were paper making and gunpowder. The papermaking process was invented by court eunuch Cai Lun in 105 AD. It was the first inexpensive medium for writing, as opposed to papyrus and bamboo, that enabled for China a great leap forward culturally. In 751 AD, some Chinese paper makers were captured by Arabs after Tang troops were defeated in the Battle of Talas River, and from that, the techniques of papermaking then spread to the West gradually, reading Europe in the 12th century. This is so impactful and impressive, because Western civilization was not able to uncover this critical process for over a millennia when they finally learned of it from outsiders. For this very reason, Hart put Cai Lun as number 7, right ahead of Gutenberg, inventor of the printing press in the 15th century in German. To justify that, he claims that Gutenberg would not have invented the printing press if not for paper, and that this invention being purely one of Chinese civilization that was transmitted to the West over a millennia later in addition to its history altering impact was not one that was inevitable in the sense of being a product of the historical epoch in which it came about. The Chinese also invented printing, with woodblock printing in the 8th century Tang dynasty and movable type (one for each character) by Bi Sheng in the 11th century. However, because of the thousands of Chinese characters as opposed to the tens of letters of the alphabet, movable type did not have anywhere as near of an impact. There is little if any evidence that Gutenberg was influenced in his invention by the one from China. The importance and again pure Chineseness in invention of gunpowder is also without question. It revolutionized combat and was what enabled Europeans, with their improved guns, to later conquer the New World. Gunpowder was invented by Chinese alchemists in the 9th century likely by accident in their search for an elixir of life. The first military applications of gunpowder were developed around 1000 CE, and in the following centuries various gunpowder weapons such as bombs, fire lances, and the gun appeared in China. Gunpowder was likely transmitted to the Western world gradually via the Mongol invasions, which extended as far as Hungary. The final of the so called Four Great Inventions of China not yet mentioned is the compass, which facilitated the voyages to Africa of Zheng He in the early 15th century. For that though, while very possible, there seems far from any conclusive that it spread to the Islamic World and Europe as opposed to be having been reinvented there. Transitioning from China to the medium between China and the West, the Islamic world, we must delve into the Islamic Golden Age, traditionally dated from the 8th century to the 13th century, during which many important scientific discoveries were made. Though my knowledge of Islamic cultures is scant, I do know of Alhazen, Omar Khayyam, and Al-Khwārizmī. In particular, his seven-volume treatise on optics Kitab al-Manazir, while perhaps questionable on his theories of light, was notable for its emphasis on empirical evidence that combined inductive reasoning, which was relatively neglected by the Greeks, with the rigorous deductive reasoning that the Greeks championed to the extremes. We do know with certainty that this magnum opus was translated to Latin, greatly influencing later European scientists and thinkers as important as Leonardo Da VinciGalileo GalileiChristiaan HuygensRené Descartes, and Johannes Kepler. Moreover, Al-Khwārizmī’s work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu–Arabic numeral system developed in Indian mathematics, to the Western world. There is evidence of solid knowledge of trigonometry, with for instance the law of sines pervasive in the scientific literature from Islamic scholars of that time. With reference to Hindu, I shall note that Indian mathematics and astronomy were quite impressive, certainly more so than Chinese mathematics, which though calculating pi to 7 digits as early as the 5th century, which held a 900+ year record, among many other applied and computational achievements, was severely lacking in its theoretical foundations, was, with AryabhataBrahmaguptaBhāskara I, among others who did work close or on par with those of Islamic scholars mathematically but much earlier, between the 5th and 7th centuries. Because many foreign words are contained within their texts, we can be relatively sure that there was Greek and Mesopotamian influence. Relating to that, Hart does not see Indian or Islamic mathematics as terribly original and more as derivative of Greek works, with significance more in the nature of preservation, though with Western European civilization having been the dominant, and often entirely so, for so long, one ought to be careful of Eurocentric bias. The achievements of Indians and Arabs to math and science ought to be more thoroughly investigated and fairly acknowledgment, in particular how they may have influenced later developments in the West. On that note, I shall say that I was super impressed that in the 14th century, the school of Madhava of Sangamagrama managed to discover infinite series for trigonometric functions of sine, cosine, tangent and arctangent. As a special case of arctangent, we have that ${\frac {\pi }{4}}=1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+\cdots +{\frac {(-1)^{n}}{2n+1}}+\cdots,$ which was later rediscovered by Leibniz. This of course hints or indicates that Madhava already knew at that time some form of proto-calculus, with as a concrete example Rolle’s theorem, which his predecessor from the 12th century Bhāskara_II had already stated. It’s possible that knowledge of these results were transmitted to Europe, but online sources stay that no evidence for that has been found. This probably influenced Hart’s verdict that Indian/Hindu civilization, while superior to China’s in theoretical science, was far less influential, with of course, India’s having received some knowledge of the Greeks, whereas the Chinese developed independently, with Euclid’s Elements only translated to Chinese in the early 17th century, where it, unfortunately for China, did not have the impact it should have had. We all know that the West created the modern world, with the Renaissance, the scientific revolution, and the industrial revolution, and discovering, conquering, and colonizing more and more of it with their superior ships and guns, white Europeans virtually ruled the entire world by the late 19th century, ushering in unprecedented growth revolutionary in its quality and exponential in its quantity. It has continued to the point of air travel and internet communications that has drastically reduced the distance between cultures and peoples, with racial intermixing and immigration ever more common and accepted, though of course, the majority still live and mix with their own, in their ancestral homeland. For the 21st century, Hart also predicts that the breakthroughs will be achieved mostly by white Europeans (that includes Jews) and East Asians, and we already see that happening. I do not recall his stating that the East Asian civilization represented mostly by China and Japan have been on rapid rise lately, and I shall surely point that out, out of what I regard as both its reality and significance (as opposed to any ethnic chauvinism on my part). It is the formerly weak but now strong and still rapidly strengthening other side of human civilization that is less fairly acknowledged, though with its rise, that will gradually change, just as the rise and later sheer dominance of the West enabled it to easily impose its standards and culture on others regardless. With mathematics again as the representative for the pinnacle of human civilization, we can see how very recently Yitang Zhang stunned the world by proving infinite bounded gaps between primes and Shinichi Mochizuki is receiving ever more press for the inter-universal Teichmüller theory that claims to solve the abc-conjecture, one of the most important problems in number theory, the queen of mathematics (according to Gauss), that could possibly becoming one of the most important new mathematical theories of the 21st century. On that, my friend once remarked: “Mochizuki could be the 21st century Grothendieck!” It is quite remarkable and also surprising that the culture and civilization for which theoretical science had been a glaring weakness historically is now verging on its apex, though the surprising part is less so when one takes IQ into account, with now the cultural factors more controlled for owing to the near universal access to information provided by the Internet. Additionally, China is excelling at and amazing, with some effect of disease, the world at what it has traditionally been strong at, namely large-scale engineering projects, but this time, of a nature guided by the modern science of the West. As examples, we see the world’s fastest trains in a nation-wide network, the world’s largest genome sequencing factory, and a great wall of sand dredged on the South China Sea. They are modern Chinese parallels of the Great Canal, the Great Wall, and the mega ships of Admiral Zheng He an order of magnitude larger than those of Columbus. Comes unity comes strength, or so the saying goes. It is one that persists in Chinese civilization today that is enabling more in China what the West cannot do, in practice. There are scholars and advocates who lament that Western civilization, threatened by dysgenic immigration among other things, is in decline, and that its culture and civilization, which includes a certain purity of its people, ought to be preserved, which includes Hart himself. Given the overwhelming contribution of the West to human civilization, with Greek and Latin roots, has contributed to human civilization, one cannot not identify somewhat with this point of view. On this note, Rushton has even hypothesized that the Black Death precipitated the Great Divergence by suddenly and drastically enhancing the gene pool through killing off a quarter and as much as a half in some places of the European population via more or less a freak accident, one that has been regressing ever since to its natural level. It is somewhat unfortunate in some sense that the horrific legacy of Nazism, which was such that many Western peoples began to outwardly oppose ideas of racial superiority, has developed up to today towards a form of irrational racial egalitarianism and SJW culture that denies any honest, scientifically objective discourse on race differences, which are patently there, which we have the ability now to examine vastly more closely, powerfully, and scientifically than in Hitler’s time that is so politically obstructed for the aforementioned reason. Having referred to dysgenics, I shall also note that the technology and globalization we have today we are rather evolutionarily maladjusted to. Foremost of all, with reference to modern medicine, evolution does not let the weak live or spread its seed, and moreover, evolution is not terribly suited for vastly multi-ethnic societies either. The world now exhibits so much more mercy than before, often at the expense of the advancement of civilization. Yes, we know and have much more than our ancestors, but are we biologically superior to them? Perhaps we are at the far far tail, which increasingly breeds assortatively, but overall, I would say almost certainly not. As for the 21st century, how it will pan out, only time will tell. However, if I were to bet, I would say that its winner and its legacy, viewed from the long term historical perspective, say a millennia from now, will be whoever musters the courage to control our own evolution to take us beyond the confines of Homo sapiens, so extraordinary and yet so limited in its might, and also at times also so foolish in its wisdom. To conclude, my message to my generation and the future of humanity, inspired partly by Bertrand Russell: ## Why mathematics I had the pleasure of chatting briefly with a math PhD student, with the conversation largely centered on what kind of math are you interested in. He is doing discrete probability and combinatorics, something along the lines of that. He said that he spent a year studying commutative algebra during undergraduate, but eventually decided that he would not do math that deep and instead is concentrating on an area with less requirement in terms of acquired knowledge and more low-hanging fruit to pick, the parts of math of a more problem solving nature. He went on to say that of the math undergraduates at his top (but not Beida or Qinghua) institution in China, by junior year, only five were studying the purist of pure math, and later during graduate school, all but one of them, who is now doing research in string theory, have given up, instead choosing not pure PDEs but PDEs for biology and the likes, to illustrate the low rate of success for pure pure math. I told him that I still want to do really deep math (of which we can use algebraic geometry) and see the parts of math not requiring deep knowledge as not as meaningful to do research in (of course, I don’t expect to succeed, realistically gauging that I am, while highly talented, not a genius). On that, he more or less said that you should try and that you never know unless you try. Of course, he did more constructively say that learning commutative algebra requires knowing deeply thousands of definitions, and just going through ten of them a day is already very good. Maybe attempting this is not terribly wise when I see people objectively smarter than I am who eventually chose easier fields, like theoretical statistics. Now this brings me to reflect on why I am doing pure mathematics? Why am I devoting so much time and energy (with overall enjoyment and satisfaction at this point still pretty high) on this arcane, useless subject? How much of it is out of an ego to prove how smart I am versus the intrinsic thirst for the knowledge? Of course, the two are somewhat intertwined, as you’ll see in what I’m about to say. As for my background, I studied some CS in college and also spent some years in the software industry, which I’ve grown very distasteful of. I don’t like CS people very much in general. They make a big deal out of low-hanging fruit. Like, MapReduce is trivial theoretically; it’s more about the engineering, in particular the locality to minimize network IO, which in distributed systems is usually the bottleneck. There is nothing deep about it. Algorithms is cool, and I enjoyed them, doing okay in some coding contests, solving say plenty of TopCoder 500s (but not quickly enough during the short 75 minute time frame of the contest). However, algorithms I view as more of a game, full of clever little tricks but of little substance, recreational math at best, at least the type of algorithms I did. Engineering wise, I see the value, but I don’t see myself as naturally inclined to it at all, and in fact, among the strong folks in that, I’m probably rather weak. I don’t think those people are terribly smart from an IQ point of view. They’re not as cultured in some sense. (That top MIT math major (though he works in combinatorics heh) says the same, that science is for high math high verbal people with refined intellectual tastes while engineering is for high math (note that this often does not even hold for software engineering) lower verbal folks of a dronish nature.) In any case, I don’t think I’m in the same species as all these people in software engineering who know absolutely nothing about continuous math, the type of math you see in physics, like I think that’s just bad, or at least different, taste, or simply lower IQ enough that they cannot even understand it. I thought at one point that I might want to do CS theory. Not anymore. I think that’s a cool field with many good problems, but again, much of it lacks depth and importance, often with little connection to the mainstream of mathematics. I see mathematics as in some sense the pinnacle of human civilization and of human intelligence. I’ve probably said before that humans discovered literature, music, crafts, and engineering (non-modern) long long time ago, but mathematics took so long, which just goes to show how unnatural it is for the human brain. It is a pursuit of truth in the rigorous and absolute sense that one sees not in natural science either, though of course, the deductive method that underlies math is thoroughly used in natural science. Moreover the structures investigated in mathematics are of such a fundamental and pure nature which often appear in reality, though of course the purists, with the Greeks as the pioneers of that, view mathematics as a Platonic ideal to be investigated for its own sake independent of reality. What the Greeks did I would say is rather unnatural, because I recall early on, it did not feel so natural for me to disentangle mathematics with the reality, having seen it more as a tool for reality. Mathematics is so full of substance, unlike almost all other subjects. It emphasizes high quality, with often deep, fundamental ideas explained in a few pages, in austere, terse language. It is a scientific study that tolerates absolutely no bullshit and aims for the simplest possible explanation of pure, strictly incontrovertible truth by logic. It is an escapism from the mediocrity and nonsense we see in much of the world and most humans too intellectually dazed for the clear thinking necessary to perceive mathematical truth. I see my ever greater interest and appreciation, and of course, ability and knowledge, for mathematics as an inevitable consequence of my neurobiological maturation, which is fortunately to an extent far enough that I am able to experience as much of this world of truth invisible to most humans around me, though of course, I can only admire those true geniuses, those far superior brains, who can fathom so much deeper and more rapidly than I can. On this, I shall say that mathematics may well be what separates homo sapiens from whatever species eventually evolves beyond it. I would bet that in another millennia, we will have people for whom mathematics is as natural a language as natural language is to humans. Just as humans have evolved their brain and also their anatomy of throat and mouth such that learning (non-formally) and articulating language is instinctive, humans may evolve their brains further such that that holds for mathematics as well. Over time, I’ve come to realize more so that mathematics is about the right mental perception. Ideally, one can see the mathematics in one’s head. Text is but a medium of transmission (with reading the fastest bandwidth in terms of information transmission to the human brain), but without a well-formed brain rational and composed, there is basically nothing one can do to genuinely absorb the truth that exists independent of one’s perception of it. It is often that one intuitively feels like one can understand certain mathematics one hears or reads, but looking more closely, one finds such is not the case, being unable to visualize it with enough clarity that one can independently explain it. My learning of mathematics has been far from entirely smooth. I have despaired much about simply not being smart enough, especially upon seeing another seemingly effortlessly master what was utterly perplexing for me. Fortunately, that all improved over time. Though of course, as the Dunning-Kruger effect would say, the better you become the more can see your incompetence and your limitations. The experience of being able to experience the life of mind with ever more clarity, fine grain of control, and awareness has been an internally exhilarating experience. Mathematicians are in some spiritual aristocrats, and mathematics arguably has more of an intellectual upper class air to it than any other subject. What is aristocracy? It is to many a relation by blood to those politically important or foundational. But is political power really the pinnacle of human experience? I say no, and I would say that it is the experience of the deepest scientific truths, one which requires both biological genius as well as the substantial cultural exposure that naturally comes with it, especially in today’s day and age of universal access to information. Human experience in any case hinges on consciousness, and one’s subjective conscious experience is always the product of neurons. Thus, mathematics has to it an aristocracy that no amount of money or political title or physical appearance or dress can buy; there is no royal road to mathematics, as Euclid said. So in some sense, mathematics is the greatest gift of God to a human he conceived on earth. What are other characteristics of non-trivial engagers of mathematics that one easily associates with aristocracy? First comes to mind language and literacy. In virtually every culture, literacy was in the old days a sign of class, of privilege. In the West, it was the Catholic priests and in the East, it was the Confucian scholars. In virtually every religion or ideology or culture, the masters of that culture through literacy were highly esteemed. For example, in Jewish culture, there were the rabbis. Those with the most mastery of language where often the ones of authority, much owing to their exclusive access of certain information that facilitates political and mind control of plebs. From this, emerged learned aristocracies which developed their distinctive elite cultures, along with to some degree a distinctively evolved genetic line. These aristocrats evolved an ability to parse and memorize text far greater than the masses who had to labor in the fields. They developed and evolved a certain form of refinement and manners and self-control, as well as physical appearance, that came to be characterized as one of an aristocratic nature. With this said, in the West, during the Renaissance and the subsequent scientific revolution, the men of science were often ones from a learned religious background of deep conviction in their religious faith who were intellectually courageous enough to go beyond it, to go about to discover scientific truth often with inspiration from the God they held deep in their hearts. They conceived of a much more rational and accurate world that turned out had been there all along without their knowing. All this eventually ushered in a new age of human history of exponential human discovery, of fundamental scientific truths, of unseen lands, of modern machines, that has culminated in the globalization we have today. All of this has much of its roots in mathematics. To say all this would imply my yearning to become an aristocrat, which brings to another point, namely, that mathematics, while aristocratic, is more or less coldly meritocratic, and thus is aristocratic mostly in its intellectually noble content. For a brilliant kid from a poor background, mathematics is the most straightforward means of social mobility. Mathematics does not require expensive equipment or facilities or elite social connections. Provided a sufficiently high caliber mind, excelling in mathematics is relatively natural, since one can read on one’s own and solve mathematical problems on one’s own, starting with olympiad style problems at the secondary school level. Though we see plenty of mathematical families, mathematics is not grossly nepotistic as is say acting or offices of political power. In its purist essence, the culture of mathematics reveres genius from wherever he hails and despises any form of ascension based on social connections. I have observed in those of high mathematical talent a propensity for what I would regard as refined taste in other areas as well, in music, in literature, in politics, and in aesthetics of human beauty as well. Speaking of which, math is widely considered as having the smartest people and being the most g-loaded subject (along with its nearest neighbor theoretical physics), because there is some evidential truth to that, that it is often the mathematicians who are the most versatile. Mathematicians are well known (at least to me) for their often extraordinary foreign language ability, along with what is not infrequently talent in engineering and music as well. So there really is much to suggest towards the bold hypothesis that the man of mathematics is the most ideal of man evolved on earth. To conclude, I will note that I sincerely empathize with those who have had genuine struggles with mathematics or more extremely, who hate it, let alone appreciate it. By no means should one consider oneself as lesser if one is not good at mathematics as tempting as it may be. Though it is an intellectual pursuit achievements of which lie in the pinnacle of human civilization, there is almost no direct use in it, and the world does not need many mathematicians. In fact, there is, economically based on the very dismal job situation, quite a glut of mathematicians now, which makes it prudent for one to be discouraged from pursuing it as a career if one has not displayed extraordinary gift in the subject. Doing mathematics helps no one directly, but doing engineering or carpentry or nursing surely does, and as someone who has indulged so much in mathematics, I do feel guilty at times from my lack of contribution to the real world. Again, this is why I say that to go into mathematics, one ought to have a really good reason, part of why I have been inspired to write this post. ## Implicit function theorem and its multivariate generalization The implicit function theorem for a single output variable can be stated as follows: Single equation implicit function theorem. Let $F(\mathbf{x}, y)$ be a function of class $C^1$ on some neighborhood of a point $(\mathbf{a}, b) \in \mathbb{R}^{n+1}$. Suppose that $F(\mathbf{a}, b) = 0$ and $\partial_y F(\mathbf{a}, b) \neq 0$. Then there exist positive numbers $r_0, r_1$ such that the following conclusions are valid. a. For each $\mathbf{x}$ in the ball $\|\mathbf{x} - \mathbf{a}\| < r_0$ there is a unique $y$ such that $\|y - b\| < r_1$ and $F(\mathbf{x}, y) = 0$. We denote this $y$ by $f(\mathbf{x})$; in particular, $f(\mathbf{a}) = b$. b. The function $f$ thus defined for $\|\mathbf{x} - \mathbf{a}\| < r_0$ is of class $C^1$, and its partial derivatives are given by $\partial_j f(\mathbf{x}) = -\frac{\partial_j F(\mathbf{x}, f(\mathbf{x}))}{\partial_y F(\mathbf{x}, f(\mathbf{x}))}$. Proof. For part (a), assume without loss of generality positive $\partial_y F(\mathbf{a}, b)$. By continuity of that partial derivative, we have that in some neighborhood of $(\mathbf{a}, b)$ it is positive and thus for some $r_1 > 0, r_0 > 0$ there exists $f$ such that $\|\mathbf{x} - \mathbf{a}\| < r_0$ implies that there exists a unique $y$ (by intermediate value theorem along with positivity of $\partial_y F$) such that $\|y - b\| < r_1$ with $F(\mathbf{x}, y) = 0$, which defines some function $y = f(\mathbf{x})$. To show that $f$ has partial derivatives, we must first show that it is continuous. To do so, we can let $r_1$ be our $\epsilon$ and use the same process to arrive at our $\delta$, which corresponds to $r_0$. For part (b), to show that its partial derivatives exist and are equal to what we desire, we perturb $\mathbf{x}$ with an $\mathbf{h}$ that we let WLOG be $\mathbf{h} = (h, 0, \ldots, 0)$. Then with $k = f(\mathbf{x}+\mathbf{h}) - f(\mathbf{x})$, we have $F(\mathbf{x} + \mathbf{h}, y+k) = F(\mathbf{x}, y) = 0$. From the mean value theorem, we can arrive at $0 = h\partial_1F(\mathbf{x}+t\mathbf{h}, y + tk) + k\partial_y F(\mathbf{x}+t\mathbf{h}, y+tk)$ for some $t \in (0,1)$. Rearranging and taking $h \to 0$ gives us $\partial_j f(\mathbf{x}) = -\frac{\partial_j F(\mathbf{x}, y)}{\partial_y F(\mathbf{x}, y)}$. The following can be generalized to multiple variables, with $k$ implicit functions and $k$ constraints. ▢ Implicit function theorem for systems of equations. Let $\mathbf{F}(\mathbf{x}, \mathbf{y})$ be an $\mathbb{R}^k$ valued functions of class $C^1$ on some neighborhood of a point $\mathbf{F}(\mathbf{a}, \mathbf{b}) \in \mathbb{R}^{n+k}$ and let $B_{ij} = (\partial F_i / \partial y_j)(\mathbf{a}, \mathbf{b})$. Suppose that $\mathbf{F}(\mathbf{x}, \mathbf{y}) = \mathbf{0}$ and $\det B \neq 0$. Then there exist positive numbers $r_0, r_1$ such that the following conclusions are valid. a. For each $\mathbf{x}$ in the ball $\|\mathbf{x} - \mathbf{a}\| < r_0$ there is a unique $\mathbf{y}$ such that $\|\mathbf{y} - \mathbf{b}\| < r_1$ and $\mathbf{F}(\mathbf{x}, \mathbf{y}) = 0$. We denote this $\mathbf{y}$ by $\mathbf{f}(\mathbf{x})$; in particular, $\mathbf{f}(\mathbf{a}) = \mathbf{b}$. b. The function $\mathbf{f}$ thus defined for $\|\mathbf{x} - \mathbf{a}\| < r_0$ is of class $C^1$, and its partial derivatives $\partial_j \mathbf{f}$ can be computed by differentiating the equations $\mathbf{F}(\mathbf{x}, \mathbf{f}(\mathbf{x})) = \mathbf{0}$ with respect to $x_j$ and solving the resulting linear system of equations for $\partial_j f_1, \ldots, \partial_j f_k$. Proof: For this we will be using Cramer’s rule, which is that one can solve a linear system $Ax = y$ (provided of course that $A$ is non-singular) by taking matrix obtained from substituting the $k$th column of $A$ with $y$ and letting $x_k$ be the determinant of that matrix divided by the determinant of $A$. From this, we are somewhat hinted that induction is in order. If $B$ is invertible, then one of its $k-1 \times k-1$ submatrices is invertible. Assume WLOG that such applies to the one determined by $B^{kk}$. With this in mind, we can via our inductive hypothesis have $F_1(\mathbf{x}, \mathbf{y}) = F_2(\mathbf{x}, \mathbf{y}) = \cdots = F_{k-1}(\mathbf{x}, \mathbf{y}) = 0$ determine $y_j = g_j(\mathbf{x}, y_k)$ for $j = 1,2,\ldots,k-1$. Here we are making $y_k$ an independent variable and we can totally do that because we are inducting on the number of outputs (and also constraints). Substituting this into the $F_k$ constraint, this reduces to the single variable case, with $G(\mathbf{x}, y_k) = F_k(\mathbf{x}, \mathbf{g}(\mathbf{x}, y_k), y_k) = 0$. It suffices now to show via our $\det B \neq 0$ hypothesis that $\frac{\partial G}{\partial y_k} \neq 0$. Routine application of the chain rule gives $\frac{\partial G}{\partial y_k} = \displaystyle\sum_{j=1}^{k-1} \frac{\partial F_k}{\partial y_j} \frac{\partial g_j}{\partial y_k} + \frac{\partial F_k}{\partial y_k} = \displaystyle\sum_{j=1}^{k-1} B^{kj} \frac{\partial g_j}{\partial y_k} + B^{kk}. \ \ \ \ (1)$ The $\frac{\partial g_j}{\partial y_k}$s are the solution to the following linear system: $\begin{pmatrix} \frac{\partial F_1}{\partial y_1} & \dots & \frac{\partial F_1}{\partial y_{k-1}} \\ \; & \ddots \; \\ \frac{\partial F_{k-1}}{\partial y_1} & \dots & \frac{\partial F_{k-1}}{\partial y_{k-1}} \end{pmatrix} \begin{pmatrix} \frac{\partial g_1}{\partial y_k} \\ \vdots \\ \frac{\partial g_{k-1}}{\partial y_k} \end{pmatrix} = \begin{pmatrix} \frac{-\partial F_1}{\partial y_k} \\ \vdots \\ \frac{-\partial F_{k-1}}{\partial y_k} \end{pmatrix}$. Let $M^{ij}$ denote the $k-1 \times k-1$ submatrix induced by $B_{ij}$. We see then that in the replacement for Cramer’s rule, we arrive at what is $M^{kj}$ but with the last column swapped to the left $k-j-1$ times such that it lands in the $j$th column and also with a negative sign, which means $\frac{\partial g_j}{\partial y_k}(\mathbf{a}, b_k) = (-1)^{k-j} \frac{\det M^{jk}}{\det M^{kk}}$. Now, we substitute this into $(1)$ to get \begin{aligned}\frac{\partial G}{\partial y_k}(\mathbf{a}, b_k) &= \displaystyle_{j=1}^{k-1} (-1)^{k-j}B_{kj}\frac{\det M^{kj}}{\det M^{kk}} + B_kk \\ &= \frac{\sum_{j=1}^k (-1)^{j+k} B_{kj}\det M^{kj}}{\det M^{kk}} \\ &= \frac{\det B}{\det M^{kk}} \\ &\neq 0. \end{aligned} Finally, we apply the implicit function theorem for one variable for the $y_k$ that remains. ▢ References • Gerald B. Folland, Advanced Calculus, Prentice Hall, Upper Saddle River, NJ, 2002, pp. 114–116, 420–422. ## A nice consequence of Baire category theorem In a complete metric space $X$, we call a point $x$ for which $\{x\}$ is open an isolated point. If $X$ is countable and there are no isolated points, we can take $\displaystyle\cap_{x \in X} X \setminus x = \emptyset$, with each of the $X \setminus x$ open and dense, to violate the Baire category theorem. From that, we can arrive at the proposition that in a complete metric space, no isolated points implies that the space uncountable, and similarly, that countable implies there is an isolated point. ## On questioning authority A couple years ago, my friend who won high honors at the Intel Science Talent Search told me that he was talking this guy who created some app that allows you to schedule a Uber ride for later, who was also at/near the top of the same science competition, who is extraordinarily versatile and prolific. I watched a little of a video of a TED talk he gave, wherein he explained what one can learn from ancient Hebraic texts. Overall, I wasn’t terribly terribly impressed by it, though it was quite eloquently delivered. Mostly because with those types of things, one is too free to interpret and thus, the lessons/messages given were overly generic so as to make them almost meaningless, one of which was how the Bible teaches the importance of questioning authority, with reference to the refusal to bow to the golden image of King Nebuchadnezzar by Shadrach, Meshach, and Abednego as an exemplary. Here, Joshua like many from the same cultural root portrays questioning authority as a pillar of the Jewish moral and intellectual spirit. I would say that this has already gotten to the point of cliche. There is also, again, that people have different ideas of what it means to question authority. First of all, what is an authority? An authority can manifest itself in many forms. It can be a political authority. It can be a government, especially a “dictatorship,” as much as I hate the usage of that word. It can be a boss at work. It can be a distinguished professor. It can be an adult when you’re a child. It can be an official or not moral, religious, or political code/ideology, or commonly accepted versions of history and its verdicts, by which I mean judgments of history as opposed to hard facts more or less incontrovertible, such as what exactly happened on X day with documentation abound. It can be the tradition we are all taught to abide by growing up with little question of their rationale and relevance, especially as times pass and change. A corollary of my last paragraph is that to talk about questioning authority alone is almost utterly meaningless. You absolutely need some context, and Joshua did provide some. In the specific example of his I regurgitated, it is standing up against a dictator, and I’ll elaborate my thoughts on that. Growing up in America, in my social studies classes and in the media, the mantra of dictatorship vs democracy with the latter morally superior and in many cases with its defense by virtually any means justified was heard again and again that it has itself become an authority taboo to challenge by our political norms. First of all, I want to clarify that here by democracy I am referring to a political system where elect representatives from among themselves to form a governing body. There is another form of more general democracy where the government does what is, or is at least perceived as, in the best interest of the entire nation or populace. What American political culture fails to discuss sufficiently is the vital matter of to what extent the former democracy implies the latter one, with the latter’s being, hopefully, the end goal. In contrast, dictatorships are portrayed as one lone, usually brutal dictator having absolute power, being able to order virtually anything, and thus, leading often to genocidal regimes with mass murderers such as Hitler, Stalin, Mao, etc. This image may be tempting to many but it is in reality rather ridiculous. Yes, a dictator has enormous power and stays at the top often for decades, in contrast to the four year term system in America, which is very frowned upon in our culture, but surely, a dictator is not politically omnipotent. He has plenty of people underneath that he needs to satisfy, and though he may have a cult of personality within the propaganda, people are basically free to ignore him and go about their own business. He is also a human too, just like you, with very human interests, though sure, he may be a psychopath of some sort. There is also a vital point that almost always for a dictator to come to power, he must have a high degree of support from a large number of people, and thus, dictators in practice have little incentive to work against people’s interests, with getting people to like him being largely in his interest. Ironically, dictatorships can be very good at motivating people to achieve great things and providing certain continuity and long-term perspective difficult within a system where the people can easily choose to elect a new leader. In fact, if I have someone pressuring or forcing me when I don’t want to to do what is good for me (like waking up early on a weekend) and good for the society at large (like not being a parasite), I consider that to be a very positive thing. On this note, talking with someone in China recently, that guy was like: China now has 10 year terms for leaders, and maybe it should be gotten rid of, because it’s too little time for a leader to do anything serious, as he would have to pass the torch before he can be finished. Maybe Xi Jinping should try to extend his presidency past his 10 year term. Even in America, during WWII, Roosevelt was president for 16 years. I personally love reading and watching controversial and sensitive material that most people dare not to. I’ve read plenty of material in Chinese banned in the mainland (but of course, still easily obtainable there if one really wants), most memorable of which was the very well-written, of high literary quality, autobiography by 巫宁坤 (Wu Ningkun). I’ve watched an anti-Semitic Nazi movie and also a North Korean movie out of sheer curiosity of certain places so smeared by our media. I also think that Soviet music is some of the most beautiful music out there. I have also, not surprisingly, watched some PRC (propaganda) movies from the 50s and 60s, which I felt were very well-made. The scariest and most grotesque movie I watched was one on the WWII Japanese human experimentation camp, Unit 731. A few weeks ago, I also had the pleasure of watching Saving Private Ryan, which I also much enjoyed, though surely it’s, as a Hollywood movie, more or less well-accepted here on our soil, unlike some of the previous ones, for which many would think I’m crazy, which I’m obviously not, for watching. I would say that this is out of a combination of my political intellectual curiosity and a distaste for certain oppressive, intolerant mainstream views and norms in America. Shaped by these explorations, I am of the belief that people should be more tolerant of differences and more politically and culturally open-minded. Be emotionally insensitive and let others be who they are. Also, be reasonable, precise, and stick to the facts. This is a concrete and substantive characterization of how throughout my life, I have challenged and questioned authority in the political intellectual domain. Joshua is obviously promoting his own Jewish culture in that TED talk. On this, I’ve come to note that Jews in America are for the most part entirely unashamed, if not eager, to display and extol their culture. This is in contrast to Chinese who grow up here, many of whom try to distance themselves from their roots. Well, I guess there are self-hating Jews (like Bobby Fischer, who I feel I can understand much more now, with where he’s coming from) as well, but overall, they seem far less conspicuous. I believe the latter is out of a combination of their lack of self-confidence, the gross bastardization of Chinese culture in America, and the difficulty of learning the Chinese language in an American environment even when parents speak it at home, especially the written aspect. There is the cliche saying that Chinese people in general, due to certain elements deep-rooted in Chinese culture, are very deferential to authority, which stifles creativity and innovation. I’ve surely thought about this and my views have evolved over time the more I’ve learned and seen. It is obviously too simplistic a notion presented by those of meager and often incorrect understanding. I do believe that Confucianism had and still has a strong element of the phenomenon described, but so did Christianity, just of a very different character. Personally, I have to say that the more I learn, the more impressed I am with the fearless and pure spirit Chinese people have displayed in questioning and challenging authority, especially in the 20th century. I have written here before that I believe China has the richest revolutionary history of the 20th century of any nation or culture, with that of course much owing to the circumstances. China in the 20th century, being in deep trouble, had a dire need for revolutionaries, martyrs, and heroes. With this, the Chinese led by the communists essentially created a new Chinese culture on top of the traditional Chinese culture that had Confucianism as the guiding ideology. There is now a rich tradition and culture of Chinese communism, especially in military and social science, that has become holy in some sense, as is Jerusalem, which became so also out of certain formational historical events, that is very revolutionary in its essential spirit. However, the Chinese being materialists view all this as a force of nature rather than a force of God, a key contrast to holiness in the Abrahamic religions. Another essential difference is that while Jews have more or less based themselves upon the Western system, having taken great advantage for themselves of the Western imperialism that came out of the discovery of modern science in the West, which they are also in service to politically, with reliance on it, the Chinese have more or less created an independent system from the West without kowtowing to pressures to conform, which has proven to be a correct decision, one that took much political courage and belief in oneself. The foundation for modern China was built largely in the 50s and 60s with little direct exchange with the West, if one excludes the Soviet Union from that, and in certain cases direct confrontation, with the freeze in relations owing to that in the Korean War, the Chinese challenged the Western authority successfully in a military setting in a way unimaginably shocking. It is only now very much in hindsight that while that inability to trade with the West for a few decades very much delayed China’s economic growth in certain respects, it brought about the creation of a very distinctive political culture and system deeply embedded that remains distanced from the mainstream in spite of reform and opening up, of a nature that may well be an advantage for China in the long term if not already. In this respect, Chinese culture has produced a feat and tradition of questioning authority that will forever live in our historical memory. Another that I have noticed is the upright dedication to truth exhibited at large by Chinese scholars in the often corrupt and political social sciences that become authoritative, relative to those in the West. It is a reflection of good judgment of the Chinese people on who to promote in that arena. It does have much to do that China has in modern times been humbled by and learned so much from the West, the source of the most unprecedentedly radical and explosive growth in human history, but I also dare say that it is an indicator of very high moral character of Chinese civilization. In Chinese intellectual and media circles, bullshitting and falsifying history for political motives seems much more frowned upon. I believe that in this respect, history will eventually look at what the West led by America, that is heavily influenced by Jews in the social sciences, has done with utter disgrace, with various facades unlikely to continue indefinitely. Speaking of truth, in terms of scientific truth, Chinese civilization has, however, contributed very little in comparison, though surely, Chinese produced a good number of revolutionary scientific breakthroughs in the 20th century, especially later in it. I find it somewhat odd how it is seldom said directly in the West that modern science is a product almost entirely of Western civilization with Greek roots and later Islamic preservation and expansion. Because scientific achievement requires so much in the way of the quality that is the subject matter of this article, surely the Confucianism based Chinese civilization has experienced a dearth of it of a nature that was only learned from the West later on. Now, Chinese are indeed quite relieved and also proud that in STEM, they have been increasingly successful and are now on the verge of reaching a world leading position, with much more to contribute to the world. I’ll conclude with the following message. If Jews value questioning authority so much, they should let their authorities in media in America be freely and openly challenged. They should let their majority representation among Ivy League presidents and senior administrators be questioned too. In anything that is not terribly meritocratic and more connections and reputation based, their gross overrepresentation often well over 30%, so long as is objectively there, ought to be seriously questioned.	{}
## Rd sharma solution class 12 chapter continuity Exercise 9.2 Question 1 Prove that the function is everywhere continuous . Sol : When , we have We know that sin x as well as the identity function x are everywhere continuous . So , the[…] ## Rd sharma solution class 12 chapter 2 functions Exercise 3.1 Question 1 Give an example of a function (i) which is one-one but not onto Sol : Injectivity : Let x and y be any two elements in the domain (Z) , such that […] ## Rd sharma solution class 12 chapter Relations Exercise 1.1 Question 1 Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) R =[…] ## Rd sharma solution class 12 chapter Differentiation Exercise 11.2 Question 1 Differentiate Sol : Let Differentiating y with respect to x we get, So, Question 2 Differentiate Sol : Let which can be written as Differentiating y with respect to[…] ## Rd sharma solution class 12 chapter Inverse trigonometric functions Exercise 4.1 Question 1 Find the principal value of each of the following: (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : […] ## Rd sharma solution class 12 chapter Continuity Exercise 9.1 Question 1 Test the continuity of the function on at the origin: Sol : Given We observe (LHL at x= 0) =-1 (RHL at x = 0) =1 Hence, is discontinuous at[…] ## Rd sharma solution class 1 chapter Indefinite integrals Exercise 19.2 Question 1 ## Rd sharma solution class 1 chapter Indefinite integrals Exercise 19.1 Question 1 Evaluate each of the following integrals: (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : (v) Sol : (vi) Sol : (vii)[…] ## RD Sharma solution class 12 chapter 28 Straight line in space Exercise 28.1 Question 1 Find the vector and cartesian equations of the line through the point and which is parallel to the vector Sol : We know that the vector equation of a line[…] ## RD sharma solution class 12 chapter determinants Determinants Exercise 6.1 Question 1 Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (i) A = Sol : In[…] ## Derivative as a rate measure Derivative as a rate measure Exercise 13.1 1. Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies. Sol : 2.[…] ALGEBRA OF MATRICES EXERCISE 5.1 1.If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements? solution: Order of matrix=number of rows $$\times$$number of column[…]	{}
# How can I easily encrypt a file? Is there any simple (IE: right click in Nautilus) way to password protect a particular folder/file in Ubuntu? I've got a few files containing sensitive info and I'd much prefer that if/when I leave my computer alone, they aren't accidentally accessed by someone else. The secruty does not have to be extremely tight. My only concern is that when family/friends come over, I don't really like the idea of them looking at my bank details, accounts or, you guessed it, porn collection. A simple, effective way to let me put my machine in the hands of someone else knowing that said machine can not cause me embarresment is the sole reason why I'd like to see this in Ubuntu. You can use the Archive Manager to zip the file and password protect the zip file. That is probably the closest thing to right clicking and entering a password that you describe. To do this right click on the file and choose "Compress" then choose zip as the archive type and in "Other options" you have the option to enter a password. This is simple to do and stops the problem of someone mounting the file system from a live CD and getting the file that way. Also you can easily email the file or copy to USB stick, etc without having to worry about having the means to unencrypt the files at the other end, you just need the password. • ZIP passwords aren't very secure at all, but this would certainly prevent ‘accidental’ viewing. – bobince Sep 28 '10 at 11:12 • bobince: I don't know enough about it to disagree, but I have personal experience of not cracking zip passwords. Could you provide resources backing you claim so I can learn more? – Richard Holloway Sep 28 '10 at 20:27 • @bobince: ZIP archives are encrypted with AES since over a decade, which has no known vulnerability. Alternatively use the more flexible, better compressing 7z, or use a GnuPG-based method. – David Foerster Nov 20 '14 at 22:59 • @David Forester: it is not enough to say "it uses AES and AES has no known vulnerabilities," because just using AES alone is not enough to password-protect a file securely. The WinZip file format (as you linked) also uses PBKDF2 to generate the AES-128 (or AES-256) key (with 1000 iterations), which is important to protect against brute-force attacks, and HMAC-SHA1-80 (truncated to 80 bits) as a MAC, which is also fairly important to prevent tampering. This isn't the most secure system ever; 1000 iterations isn't seen as especially strong these days, and it only gets worse with time. – Jay Sullivan Jan 9 '16 at 17:36 If you want to encrypt a lot of files that you access regularly, an encrypted filesystem is the way to go. But if you have single files that you want to encrypt/decrypt quite rarely (say, a list of passwords) you can do it very easily with a right-click in nautilus: • Install the seahorse-plugins package • Create a new key for GPG/PGP (Applications - Accessories - Passwords and Encryption Keys) • After a restart of nautilus (enter nautilus -q in a terminal or simply log out of your GNOME session) you have two new entries in your right-click menu: Encrypt and Sign, respectively Decrypt for encrypted files • I do not recommend this workflow. It requires more effort than an encrypted filesystem, and it's very unreliable (you might forget to reencrypt the file and delete the cleartext, leaving it available to a snooper; you might forget to reencrypt the file or delete the cleartext and end up with two versions of the file; the data is still there on the disk). – Gilles Sep 27 '10 at 20:58 • @Gilles: I agree that an encrypted filesystem is in general a better way -- but I was answering the OPs question. An encrypted filesystem has some disadvantages as well (e.g. performance) and actually may be less secure under some circumstances: If due to a security bug an application tries to read local data, it succeeds -- for GPG encrypted files you have to explicitly decrypt them manually. – Marcel Stimberg Sep 27 '10 at 21:07 • Performance is in favor of gpg only if you make multiple edits to a large file (not modifying the file in place). You can also mount the encrypted filesystem manually if you want. An advantage of the manual gpg method is that it's completely cross-platform, whereas not every OS has an encrypted filesystem and they're rarely compatible (that's relevant if you're going to carry encrypted files on a removable drive and want to access them on multiple OSes). – Gilles Sep 27 '10 at 21:20 • An encrypted filesystem is no help in the OP's situation though, where they want everything else open and usable except a few files. You'd have to store those few other files on a separate filesystem, and it'd really just be more mess than this. – maco Sep 28 '10 at 21:12 As many pointed out, access control based on user id and encrypted filesystem is the only real way of securing user data. If, however, all that is stopping you from using Truecrypt is because you don't have a free partition / filesystem that you can use exclusively for storing encrypted data, then you can still make an encrypted file-system inside a file within your existing filesystem. For this you need to have "sudo" rights, i.e., you must be able to run sudo. 2. Open TrueCrypt (normally found in Applications -> Accessories) 3. Using the gui you can create a new volume contained in a file. You can choose the location of this file. 4. Steps 1-3 are one-time setup. After this whenever you mount this file-system using truecrypt GUI, you will see it in nautilus. 5. You can move the sensitive files and directories within this filesystem. 6. When "you are leaving your computer alone", unmout this using the "dismount" option in the truecrypt GUI. 7. It is also important to use a good password (more than 20 characters at least, as recommended by the developers). greyfade's answer is correct. Ubuntu is a multi-user system. If anyone else uses your computer they should have their own user account. One user per account; there is no good reason for users to share accounts, ever. You can set up a hotkey to log out when you leave your computer. Using Ctrl+Alt+L when you leave locks the computer. If someone else wants to use it, they can log in to their own account without affecting your session. Again, sharing user accounts is a bad habit and a bad idea for many reasons. Please don't do it. If you're only concerned about other users on your system who don't have administrator rights, it's enough to use file permissions to control access. If there are other people with administrator rights or physical access, password protection means encryption¹. The easiest way to encrypt a few files under Linux is the encfs filesystem. On the command line, run encfs ~/.encfs ~/encrypted Then create files under the encrypted directory. They are in fact stored in encrypted form inside ~/.encfs. When you've finished working, run fusermount -u ~/encrypted If you want to encrypt your whole home directory, ecryptfs is a better option. For more information, see What is the easiest way to encrypt a dir? (on Ubuntu) on Super User. ¹ Strictly speaking, you also need protection against someone installing a keylogger (“evil maid attack”), but that's a lot harder to achive on current desktop operating systems and hardware. No, not really. You can use Truecrypt to create a volume to store sensitive files in (sudo apt-get install easycrypt for a nice front-end), but otherwise there isn't really a way to password-lock your files. I'd suggest that you lock or log out when you leave your computer. • You can also add a nautilus script, so right-clicking on a file/folder will appear the command "Crypt this folder/file"... the power of open-source is in this kind of customizations, imho ;) – Strae Sep 27 '10 at 12:07 Password-protecting a file is nice and fine in a system which is otherwise not physically accessible, ie one that you cannot turn off and restart using a live CD for example. If the computer is a desktop that anyone can turn off, one can restart it with a live CD and gain access to all files on the hard disk, whether those are system files, config files, home directories, etc. I would rather recommend that you use an encrypted file system, such as TrueCrypt, which will remain useless on any system unless the authorized user enter the proper credentials. It will do more than just password-protect your files, but will also protect them from external accesses. Everything also depends on what would be the cost of some of those files were getting shared, vs the cost and effort to implement something as TrueCrypt and the tool presented earlier, easycrypt. • The question was edited apparently after you answered it, from "How do I simply password protect a file" to "easily encrypt a file" - your answer now looks a little out of place, since decent encryption can't be bypassed with just a live iso or single boot. (& truecrypt isn't maintained anymore) – Xen2050 Apr 24 '16 at 5:44 Use a Guest session! Unless you expect people to gain increased privileges (e.g. root) in your machine, or for example boot from a CD-ROM and mount and browse your filesystems (or even reading the raw disk sectors), you may not have to encrypt some/all files on your hard drive. You can simply set permissions on directories and/or files to keep the "curious" from opening and browsing them. This is why, in normal operations, you 1. Don't use a root account as your normal user. The Session applet on the top right of your window allows you to start a Guest session, which disappears when you log out. See for example this image. The Guest Session option starts a temporary session for anyone borrowing your computer. Your files are not visible -- unless you've specifically given universal read permissions. This is the ideal when you just want to "borrow" your computer to a guest who wants to do some quick browsing. It might not be what you want if you'd like to provide permanent accounts (i.e. residing under /home, as your account is likely to be). The Guest account cannot "see" anything under /home because the session doesn't have the right permissions. Change the permissions (Note: If someone has root permissions, this won't make a difference. Such a person will be able to access your unencrypted files just the same.) Suppose you have a folder (or a set of files) that you want to keep other users from reading/accessing. 1. Select the folder (or files) you want to affect, then right-click on the selection (with your mouse). 2. Select Properties. 3. Go to the Permissions tab. This doesn't encrypt the affected files and directories, but it does keep people (not having root permissions, of course) from prying into your account. Allow some users (Note: If someone has root permissions, this won't make a difference. Such a person will be able to access your unencrypted files just the same.) If you want to allow only a group of users to access a set of files or folders, you can do the same. For example, you may want to reserve read+write permissions for yourself, but only read permissions for a group (or even read+write for them as well) on those files and folders. 1. If the group name you want to select doesn't yet exist, you'll have to create it. Go to System > Administration > Users and Groups. 1. Click on the Manage groups button. 2. Click Add. You'll need to enter your password (if your account has admin permissions, otherwise use the root password if you have it). 3. Enter a group name. The group names follow the same rules when providing a user name; I suggest you only use letters and numbers, without spaces. You can leave the suggested Group ID (starting at 1001 for example). Select the users that will belong to the group. 4. Click OK to apply. Click Close on the previous window. Click Close to close Users and Groups. 5. You may need to logout+login for your account to "see" the new group. It also applies to any already-logged in users. 2. Use the same procedure as above to apply Group permissions. Please note that you'll have to provide the Group name when applying permissions. You can only use one group. This doesn't encrypt the affected files and directories, but it does keep people (not having root permissions, of course) from prying into your account. Encryption Other users here have provided more details specifically for solutions using encryption. If you really require encryption -- and not just controlling access to your files -- you may want to look into those answers. But please note that access to those files will always be slower, due to the necessary overhead for applying the encryption/decryption algorithms. The description I provided above implements a (very!) basic measure of access control with virtually no performance impact. Try to search for and install ‘ecryptfs-utils’ in Ubuntu Software Center After installing, go to Applications –> Accessories –> Terminal and run the command below: ecryptfs-setup-private When you’re done creating your password, Log Out and Log back in. Next, go to Places –> Home Folder. And new folder should be created in your home directory called ‘Private’. This folder in encrypted and password-protected. Move all your personal stuff into this folder to secure them. For More Help Thank you all for your answers; it seems there is no way to easily stop accidental viewing of certain files and folders. This is very unfortunate; the closest is the .zip file method, but as I'd rather not compress and decompress, I suppose I'll have to make do with the risk. • There is, in fact, an easy way to stop accidental viewing of files and folders. DO NOT SHARE USER ACCOUNTS. Each user's directory can be individually encrypted when the account is created. Seriously, one account per user. Sharing accounts will end in tears, I promise! – koanhead Oct 1 '10 at 1:59 • Well, the 'sharing' I'm having problems with wasnt exactly given permission by me, if you know what I mean. – Dante Ashton Oct 2 '10 at 8:26 • I'm afraid I misunderstood you. I forgot that in Ubuntu users on the same machine can view some folders and files in other users' home directories by default. The solution to this is to change the permissions of the folder in which your sensitive files are located. This can be accomplished by right-clicking the folder icon, choosing Properties, and then clicking the Permissions tab. Under Others, Select "None" from Folder access list and None from File access list, and click Apply Permissions to Enclosed Files. That and locking your session should keep out prying eyes. – koanhead May 23 '11 at 1:36 How about hiding the folders in a location they wont see and set the nautilus option on not to show the hidden folders by default ? The easiest way to make a folder hidden is by making its name start with . I know this is not the solution for the question you have asked but just a solution i thought might work for your problem. for simple text file encryption and decryption with sensitive plain text information you can do the following by using terminal. openssl aes-256-cbc -a -salt -in 01.txt -out 02.txt openssl aes-256-cbc -d -a -salt -in 02.txt -out 01.txt the first command is to encrypt with 256 bit aes and the second one to decrypt. 01.txt is your plaintext input file and 02.txt obviusly the encrypted output file. the -a is optional and not neccessary, unless you want to be able to copy the text from your encrypted text file. terminal will ask you for your password that you then have to type in twice to make sure there is no typo issue for encryption. features are, that it works across all platforms, because openssl is supported and mostly pre-configured in all systems by default. you have a good selection of possible encryption-algorhythms to chose from, like: aes, des, blowfish, bf etc... furthermore you can make your encrypted file a (.) dot-file, in other words a hidden one, by using the "mv" command. mv 01.txt .01.txt sudo apt-get install cryptkeeper After installing, go to Applications –> System Tools –> Cryptkeeper. Cryptkeeper will automatically attach itself to the top panel To create an encrypted protected folder, click on Cryptkeeper applet and select ‘New encrypted folder’ Then type the folder name and where to save the folder and click ‘Forward’. Type the password and click ‘Forward’. The folder will be created and ready to be used. To access all encrypted folder, click on Cryptkeeper applet on the panel and select each folder. Type the password before it is mounted to be accessed. ## Done To delete a folder or change the password, right-click the folder in the panel-applet. Here is a very simple way: you can use an application named cryptkeeper, a GNOME applet for managing encrypted folders and available by default in the Ubuntu 11.04 repository and previous. It's such a simple way to secure your folder using a password and encrypt it. Further information can be found here on my website. GPG has a symmetrical encryption option (ie password protect) gpg -c. With a bit of scripting, maybe there's a way to add this to the right-click menu in nautilus?	{}
# 1.3E: Exercises Exercise $$\PageIndex{1}$$ In exercises 1 - 4, use the limit laws to evaluate each limit. Justify each step by indicating the appropriate limit law(s). 1) $$\displaystyle \lim_{x→0}\,(4x^2−2x+3)$$ Use constant multiple law and difference law: $$\displaystyle \lim_{x→0}\,(4x^2−2x+3)=4\lim_{x→0}x^2−2\lim_{x→0}x+\lim_{x→0}3=0 + 0 + 3=3$$ 2) $$\displaystyle \lim_{x→1}\frac{x^3+3x^2+5}{4−7x}$$ 3) $$\displaystyle \lim_{x→−2}\sqrt{x^2−6x+3}$$ Use root law: $$\displaystyle \lim_{x→−2}\sqrt{x^2−6x+3}=\sqrt{\lim_{x→−2}(x^2−6x+3)}=\sqrt{19}$$ 4) $$\displaystyle \lim_{x→−1}(9x+1)^2$$ Exercise $$\PageIndex{2}$$ In exercises 1 - 4, use direct substitution to evaluate the limit of each continuous function. 1) $$\displaystyle \lim_{x→7}x^2$$ $$\displaystyle \lim_{x→7}x^2\;=\;49$$ 2) $$\displaystyle \lim_{x→−2}(4x^2−1)$$ 3) $$\displaystyle \lim_{x→0}\frac{1}{1+\sin x}$$ $$\displaystyle \lim_{x→0}\frac{1}{1+\sin x}\;=\;1$$ 4) $$\displaystyle \lim_{x→1}\frac{2−7x}{x+6}$$ $$\displaystyle \lim_{x→1}\frac{2−7x}{x+6}\;=\;−\frac{5}{7}$$ Exercise $$\PageIndex{3}$$ In exercises 1 - 9, use direct substitution to show that each limit leads to the indeterminate form $$0/0$$. Then, evaluate the limit analytically. 1) $$\displaystyle \lim_{x→4}\frac{x^2−16}{x−4}$$ $$\displaystyle \lim_{x→4}\frac{x^2−16}{x−4}=\frac{16−16}{4−4}=\frac{0}{0};$$ then, $$\displaystyle \lim_{x→4}\frac{x^2−16}{x−4}= \lim_{x→4}\frac{(x+4)(x−4)}{x−4}=\lim_{x→4}(x+4) = 4+4 =8$$ 2) $$\displaystyle \lim_{x→2}\frac{x−2}{x^2−2x}$$ 3) $$\displaystyle \lim_{x→6}\frac{3x−18}{2x−12}$$ $$\displaystyle \lim_{x→6}\frac{3x−18}{2x−12}=\frac{18−18}{12−12}=\frac{0}{0};$$ then, $$\displaystyle \lim_{x→6}\frac{3x−18}{2x− 12}=\lim_{x→6}\frac{3(x−6)}{2(x−6)}=\lim_{x→6}\frac{3}{2}=\frac{3}{2}$$ 4) $$\displaystyle \lim_{h→0}\frac{(1+h)^2−1}{h}$$ 5) $$\displaystyle \lim_{t→9}\frac{t−9}{\sqrt{t}−3}$$ $$\displaystyle \lim_{x→9}\frac{t−9}{\sqrt{t}−3}=\frac{9−9}{3−3}=\frac{0}{0};$$ then, $$\displaystyle \lim_{t→9}\frac{t−9}{\sqrt{t}−3} =\lim_{t→9}\frac{t−9}{\sqrt{t}−3}\frac{\sqrt{t}+3}{\sqrt{t}+3}=\lim_{t→9}\frac{(t−9)(\sqrt{t}+3)}{t - 9}=\lim_{t→9}(\sqrt{t}+3)=\sqrt{9}+3=6$$ 6) $$\displaystyle \lim_{h→0}\frac{\dfrac{1}{a+h}−\dfrac{1}{a}}{h}$$, where $$a$$ is a real-valued constant 7) $$\displaystyle \lim_{x→1}\frac{x^3−1}{x^2−1}$$ 8) $$\displaystyle \lim_{x→1/2}\frac{2x^2+3x−2}{2x−1}$$ $$\displaystyle \lim_{x→1/2}\frac{2x^2+3x−2}{2x−1}=\frac{\frac{1}{2}+\frac{3}{2}−2}{1−1}=\frac{0}{0};$$ then, $$\displaystyle \lim_{x→ 1/2}\frac{2x^2+3x−2}{2x−1}=\lim_{x→1/2}\frac{(2x−1)(x+2)}{2x−1}=\lim_{x→1/2}(x+2)=\frac{1}{2}+2=\frac{5}{2}$$ 9) $$\displaystyle \lim_{x→−3}\frac{\sqrt{x+4}−1}{x+3}$$ Exercise $$\PageIndex{4}$$ In exercises 1 - 4, use direct substitution to obtain an undefined expression. Then, use the method used in Example 9 of this section to simplify the function and determine the limit. 1) $$\displaystyle \lim_{x→−2^−}\frac{2x^2+7x−4}{x^2+x−2}$$ $$−∞$$ 2) $$\displaystyle \lim_{x→−2^+}\frac{2x^2+7x−4}{x^2+x−2}$$ 3) $$\displaystyle \lim_{x→1^−}\frac{2x^2+7x−4}{x^2+x−2}$$ $$−∞$$ 4) $$\displaystyle \lim_{x→1^+}\frac{2x^2+7x−4}{x^2+x−2}$$ Exercise $$\PageIndex{5}$$ In exercises 1 - 8, assume that $$\displaystyle \lim_{x→6}f(x)=4,\quad \lim_{x→6}g(x)=9$$, and $$\displaystyle \lim_{x→6}h(x)=6$$. Use these three facts and the limit laws to evaluate each limit. 1) $$\displaystyle \lim_{x→6}2f(x)g(x)$$ $$\displaystyle \lim_{x→6}2f(x)g(x)=2\left(\lim_{x→6}f(x)\right)\left(\lim_{x→6}g(x)\right)=2 (4)(9)=72$$ 2) $$\displaystyle \lim_{x→6}\frac{g(x)−1}{f(x)}$$ 3) $$\displaystyle \lim_{x→6}\left(f(x)+\frac{1}{3}g(x)\right)$$ $$\displaystyle \lim_{x→6}\left(f(x)+\frac{1}{3}g(x)\right)=\lim_{x→6}f(x)+\frac{1}{3}\lim_{x→6}g(x)=4+\frac{1}{3}(9)=7$$ 4) $$\displaystyle \lim_{x→6}\frac{\big(h(x)\big)^3}{2}$$ 5) $$\displaystyle \lim_{x→6}\sqrt{g(x)−f(x)}$$ $$\displaystyle \lim_{x→6}\sqrt{g(x)−f(x)}=\sqrt{\lim_{x→6}g(x)−\lim_{x→6}f(x)}=\sqrt{9-4}=\sqrt{5}$$ 6) $$\displaystyle \lim_{x→6}x⋅h(x)$$ 7) $$\displaystyle \lim_{x→6}[(x+1)⋅f(x)]$$ $$\displaystyle \lim_{x→6}[(x+1)f(x)]=\left(\lim_{x→6}(x+1)\right)\left(\lim_{x→6}f(x)\right)=7(4)=28$$ 8) $$\displaystyle \lim_{x→6}(f(x)⋅g(x)−h(x))$$ Exercise $$\PageIndex{6}$$ [T] In exercises 1 - 3, use a calculator to draw the graph of each piecewise-defined function and study the graph to evaluate the given limits. 1) $$f(x)=\begin{cases}x^2, & x≤3\\ x+4, & x>3\end{cases}$$ a. $$\displaystyle \lim_{x→3^−}f(x)$$ b. $$\displaystyle \lim_{x→3^+}f(x)$$ a. $$9$$; b.$$7$$ 1) $$g(x)=\begin{cases}x^3−1, & x≤0\\1, & x>0\end{cases}$$ a. $$\displaystyle \lim_{x→0^−}g(x)$$ b. $$\displaystyle \lim_{x→0^+}g(x)$$ 3) $$h(x)=\begin{cases}x^2−2x+1, & x<2\\3−x, & x≥2\end{cases}$$ a. $$\displaystyle \lim_{x→2^−}h(x)$$ b. $$\displaystyle \lim_{x→2^+}h(x)$$ Exercise $$\PageIndex{7}$$ In exercises 1 - 8, use the following graphs and the limit laws to evaluate each limit. 1) $$\displaystyle \lim_{x→−3^+}(f(x)+g(x))$$ 2) $$\displaystyle \lim_{x→−3^−}(f(x)−3g(x))$$ $$\displaystyle \lim_{x→−3^−}(f(x)−3g(x))=\lim_{x→−3^−}f(x)−3\lim_{x→−3^−}g(x)=0+6=6$$ 3) $$\displaystyle \lim_{x→0}\frac{f(x)g(x)}{3}$$ 4) $$\displaystyle \lim_{x→−5}\frac{2+g(x)}{f(x)}$$ $$\displaystyle \lim_{x→−5}\frac{2+g(x)}{f(x)}=\frac{2+\left(\displaystyle \lim_{x→−5}g(x)\right)}{\displaystyle \lim_{x→−5}f(x)}=\frac{2+0}{2}=1$$ 5) $$\displaystyle \lim_{x→1}(f(x))^2$$ 6) $$\displaystyle \lim_{x→1}\sqrt{f(x)−g(x)}$$ $$\displaystyle \lim_{x→1}\sqrt[3]{f(x)−g(x)}=\sqrt[3]{\lim_{x→1}f(x)−\lim_{x→1}g(x)}=\sqrt[3]{2+5}=\sqrt[3]{7}$$ 7) $$\displaystyle \lim_{x→−7}(x⋅g(x))$$ 8) $$\displaystyle \lim_{x→−9}[x⋅f(x)+2⋅g(x)]$$ $$\displaystyle \lim_{x→−9}(xf(x)+2g(x))=\left(\lim_{x→−9}x\right)\left(\lim_{x→−9}f(x)\right)+2\lim_{x→−9}g(x)=(−9)(6)+2(4)=−46$$ Exercise $$\PageIndex{8}$$ 1) [T] In physics, the magnitude of an electric field generated by a point charge at a distance $$r$$ in a vacuum is governed by Coulomb’s law: $$E(r)=\dfrac{q}{4πε_0r^2}$$, where $$E$$ represents the magnitude of the electric field, $$q$$ is the charge of the particle, $$r$$ is the distance between the particle and where the strength of the field is measured, and $$\dfrac{1}{4πε_0}$$ is Coulomb’s constant: $$8.988×109N⋅m^2/C^2$$. a. Use a graphing calculator to graph $$E(r)$$ given that the charge of the particle is $$q=10^{−10}$$. b. Evaluate $$\displaystyle \lim_{r→0^+}E(r)$$. What is the physical meaning of this quantity? Is it physically relevant? Why are you evaluating from the right? a. b. ∞. The magnitude of the electric field as you approach the particle q becomes infinite. It does not make physical sense to evaluate the negative distance. 2) [T] The density of an object is given by its mass divided by its volume: $$ρ=m/V.$$ a. Use a calculator to plot the volume as a function of density $$(V=m/ρ)$$, assuming you are examining something of mass $$8$$ kg ($$m=8$$). b. Evaluate $$\displaystyle \lim_{x→0^+}V(\rho)$$ and explain the physical meaning. Exercise $$\PageIndex{9}$$ Evaluate the following: 1. $$\displaystyle \lim\limits_{x\to3}x^2-3x+7$$ 2. $$\displaystyle \lim\limits_{x\to\pi}\left ( \frac{x-3}{x+5}\right )^7$$ 3. $$\displaystyle \lim\limits_{x\to3}4^{{x^3}-8x}$$ 4. $$\displaystyle \lim\limits_{x\to0}\ln (1+x)$$ 5. $$\displaystyle \lim\limits_{x\to\pi}\frac{x^2+3x+5}{5x^2-2x-3}$$ 6. $$\displaystyle \lim\limits_{x\to\pi}\frac{3x+1}{1-x}$$ 7. $$\displaystyle \lim\limits_{x\to6}\frac{x^2-4x-12}{x^2-13x+42}$$ 8. $$\displaystyle \lim\limits_{x\to0}\frac{x^2+2x}{x^2-2x}$$ 9. $$\displaystyle \lim\limits_{x\to2}\frac{x^2+6x-16}{x^2-3x+2}$$ 10. $$\displaystyle \lim\limits_{x\to2}\frac{x^2-5x-14}{x^2+10x+16}$$ 11. $$\displaystyle \lim\limits_{x\to-2}\frac{x^2-5x-14}{x^2+10x+16}$$ 12. $$\displaystyle \lim\limits_{x\to-1}\frac{x^2+9x+8}{x^2-6x-7}$$ Under Construction Exercise $$\PageIndex{10}$$ $$\displaystyle \lim_{x \to 0} \frac{\sqrt{x+4}-2}{x}$$ $$\displaystyle \lim_{x \to 0} \frac{\sqrt{x+4}-2}{x} = \frac{\sqrt{0+4}-2}{0} =\left[\frac{0}{0}\right]$$ = $$\displaystyle \lim_{x \to 0} \frac{(\sqrt{x+4}-2) (\sqrt{x+4}+2)}{x (\sqrt{x+4}+2)}$$ = $$\displaystyle \lim_{x \to 0} \frac{((x+4)-4) }{x (\sqrt{x+4}+2)}$$ = $$\displaystyle \lim_{x \to 0} \frac{x }{x (\sqrt{x+4}+2)}$$ = $$\displaystyle \lim_{x \to 0} \frac{1 }{(\sqrt{x+4}+2)}= \frac{1 }{(\sqrt{0+4}+2)}= \frac{1 }{4}$$. Exercise $$\PageIndex{11}$$ Evaluate the following limits: 1. $$\displaystyle \lim\limits_{x\to4}\frac{1}{\|4-x\|}$$ $$\displaystyle \infty$$ 2. $$\displaystyle \lim\limits_{x\to-1^-}\sqrt{1-x^2}$$ DNE 3. $$\displaystyle \lim\limits_{x\to-1^+}\sqrt{1-x^2}$$ 0 4. $$\displaystyle \lim\limits_{x\to2}\frac{\|x-2\|}{x^2+x-6}$$ $$\displaystyle \mbox{dne}$$ 5. $$\displaystyle \lim\limits_{x\to2}\frac{\frac{1}{x}-\frac{1}{2}}{x-2}$$ $$\displaystyle \frac{1}{4}$$ 6. $$\displaystyle f(x)=\begin{cases} x^2 & \mbox{if } x \leq 1 \\ 2x & \mbox{if } x > 1\end{cases}$$	{}
## Sunday, May 7, 2017 ### Contemplate then Calculate: Progression of Systems Tasks After playing with the Contemplate then Calculate routine a little bit at the beginning of the year, a workshop with Grace Kelemanik and Amy Lucenta inspired me to really commit to planning a series of CthenC tasks as part of my Systems of Equations unit. I started by looking at New Visions’ Algebra I systems tasks, which made me decide that my focus would be on using structure to solve systems represented visually, with the hope that they would translate those structural moves to solving systems algebraically. So I sought out a whole bunch of visual systems and thought about how I would solve them, which led me to the following list of big ideas. ## Big Ideas: • Any time you can get an equation with one variable, you can find the value of the variable. You can make an equation with one variable… • through substitution of either a value or another variable • through elimination when you have two equations that have all but one of the variables the same • The equations given to you don’t always lend themselves to creating equations with one variable. You can create new equivalent equations by… • scaling an equation • finding the difference between two equations • adding/subtracting the same thing from each side of the equation ## Phase 1 of the Unit I have spent the first two weeks of my unit on understanding what a system of linear equations is, understanding what a solution is, solving systems graphically, introducing standard form linear equations, and revisiting slope-intercept form equations. During this time, I have been using the CthenC routine with a variety of algebraic systems represented visually, with the goal ofing prompt most (if not all) of the big ideas above. I wanted each task to be able to be solved more than one way, so I intentionally gave more equations than the bare minimum to solve. Here's the progression of tasks I have made so far: ## Task #1 (Most basic substitution and elimination, see what they do): ### Potential noticings that lead to structural thinking: • We noticed that the second and third equations were almost the same, but the second equation had one more star and a greater value. Therefore, we found the difference between the two equations and since 20 – 16 = 4, the red star has to equal 4. • We noticed that two stars were equal to a square, so we replaced the square in the 3rd equation with two stars. Then we had an equation with all stars, so we could divide the 16 equally between the 4 stars. • We noticed that two stars were equal to a square, so we replaced the square in the 2rd equation with two stars. Then we had an equation with all stars, so we could divide the 20 equally between the 5 stars. • We noticed that two squares equal a star, so we replaced the two stars in the 3rd equation with a square. Then we had an equation with all squares, so we could divide the 16 equally between the two squares. ## Task #2 (have a couple of different elimination options): ### Potential noticings that lead to structural thinking: • We noticed that the last equation had one more triangle than the first equation/We noticed that the first and last equations both have a chunk of two hearts and a square • We noticed that second equation has two more triangles than the first equation/We noticed that the first and second equations both have a chunk of two hearts and a square • We noticed that the second equation has one more triangle than the third equation/We noticed that the second and third equations both have a chunk of two hearts and a square ## Task #3 (keep an elimination possibilities, prompt substitution again): ### Potential noticings that lead to structural thinking: • We noticed that a pen costs $3 more than a notebook, so in the 2nd equation we can replace the pen with$3 and a notebook • We noticed that the third equation has one notebook and one more pen than the second equation/We noticed that the second and third equations both have a chunk of two notebooks and a pen ## Task #4 (substitution hopefully more appealing than elimination): ### Potential noticings that lead to structural thinking: • We noticed that a slice of cake costs $2 more than an ice cream cone, so we can replace the slice of cake in the 1st equation with$2 and an ice cream cone. • We noticed that the 2nd equation has 2 more pieces of cake than the first equation and that the items in the second equation cost \$7 more than the ones in the first equation/ We noticed that the first and second equations both have 3 ice cream cones and a piece of cake ## Phase 2 of the Unit (up next): After the first two weeks, we go into solving systems algebraically using elimination and then using substitution. I am planning for my CthenC tasks to have only one method for solving and for that method to directly link to the algebraic manipulations students will be doing that day or the next day. ## Wednesday, April 19, 2017 ### Where We Disagree on the SMPs – Raymond Johnson • Group of Algebra I teachers met over the course of two years where they individually identified which math practice(s) were encouraged by different IM tasks, and then talked about where they disagreed • Over time their agreement increased—this process a potentially powerful tool for coming to common understanding of the math practices • Are some math practices more likely to occur together in a single task? Here was the correlations for this group ### 6 x 2/3 or 2/3 x 6: Using Structure & Precision to Build Understanding of Fraction Multiplication – Ryan Casey • Structure across the table: each row goes from iterating --> partitioning --> associative property --> distributive property • “Students must be taught structure explicitly”—planning and being aware of it yourself isn’t enough, but annotations can be used to help students look for and make use of structure • Because students are already in the mode of partitioning/iterating, 2 1/3 x 15 is easier for students than 2/3 x 15 (and 16÷3 is easier to evaluate than 2÷3) ### Let’s Be Detectives: The Search for Rules, Patterns, And Understanding with SMP 7 & 8 in the Early Years – Susan Looney • The number line is already too abstract for some students. A beaded number line is more concrete and really helps the students see and understand what value mean. Can go from beaded number line (concrete) --> number line (pictorial) --> computations (abstract) • “Structure: When I look at 7 is there a doubles fact hiding in there? What do I notice about all of these numbers?” • “Repeated Reasoning: Does this always work? And why or why not? Are there patterns to the way we say and write our numbers?” ### Get Strategic: A Thoughtful Progression of Addition & Subtraction Strategies – Susan Jensen • Computation Strategy: purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another vs. Computation Algorithm: a set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly • Activities to do with kids: counting center (estimate the # of something then put it into ten frames), 10-frame build it (flash a quick image and then have students recreate on 10 frame, use some sort of interesting progression ex: all have a value of 6), shake and spill (5 red/yellow counters in a cup, shake and spill, how many red and how many yellow?), macaroni squeeze (10 noodles in a bag, line in the middle, what are all the possible combinations) • Progressions Document for single digit addition and subtraction ### Early Number Operations: Important Understandings for All K-2 Students – Kathleen Lynch-Davis and Chrystal Dean • 65-36 alternative algorithms: subtracting in parts, counting on by 10s, and compensation • Disrupting people’s conceptions about standard algorithms: when dividing a fraction by another fraction, it does work to divide the numerators to get the numerator of the quotient and divide the denominators to get the denominator of the quotient (ex: 6/21 ÷ 2/3 = 3/7) ### Seeing Students Who Hide – Cathy Yenca • In regards to only a subset of students participating, went from feeling indifferent --> insulted --> inspired (maybe not a linear progression) • How can you access the students who hide? • Include everyone (everyone works a problem and puts it up) • Make insulting moments inspiring • Let them talk • Let them create • Students care what their peers think and they compare what they think to their peers ### Mathematical Heart – Anarupa Ganguly • K-12 50/50 math achievement M/F, but post-secondary 75/25 or worse • Maybe this is because we are missing an explicit effort to humanize math, so try: • Pose a pursue questions that catalyze emotional resonance (not just about the past and present, but future) • Empower our students to make and explore conjectures ### Math Play: A Few Thoughts – Kassia Omohundro Wedekind • Play is characterized by diminished consciousness of self, improvisational potential, continuation desire • Goals of play: ownership and identity in math ### The Art of Mathematical Anthropology - Geoff Krall • Growth mindset tells us that effort leads to ability, but it’s hard for students to see that when they are always being compared to a changing standard. Students need an opportunity to zoom out and see how they have grown over time • Students can see this through the following iterative process: assign complex tasks that produce complex work, written reflection, conversation ## Sunday, January 29, 2017 ### The Great-Granddaughter of Immigrants This is an excerpt from Julia Holmes’ 100 New Yorkers, describing my great-grandfather, Kong Chow Chun, who was a shop owner and community leader in early- to mid-19th-century NYC Chinatown. As a merchant, Chun was a Section Six exception to the 1882 Exclusion Act, which banned all Chinese immigrants—save merchants, scholars, and students—from entering the United States, though even Section Six immigrants could not apply for US citizenship, making the Chinese the first nationality barred by law from becoming U.S. citizens… Chun devoted his retirement years to activism: he fought for the removal of immigration quotas, for the right of Chinese immigrants to attend New York public universities, and for the posting of street and subway signs in Chinatown in both English and Chinese. (pg. 51) It is in honor of my great-grandfather, and all of my students, that I say that we as teachers become part of the problem if we carry on with teaching as if it can be completely separate from the current presidential administration’s discrimination and the resistance against it. Teaching math can be an act of social justice itself (see this rubric for culturally responsive math teaching), but first and foremost I teach students. I’m not yet sure what it looks like in the Trump administration for teachers and students to resist, practice self-care, learn productively, and maintain a safe and inclusive community. But as I head to school tomorrow, and each day after that, I know that I am going to start with conversations with both adults and students. People’s hopes, concerns, fears, and anger are going to affect our learning environment no matter what. Power and strength come from supporting each other and acting together rather than being isolated and silent. ## Wednesday, November 16, 2016 So at this point I am 35 days into my first (and longest) unit, focusing on linear relationships. The overall goal of this unit is for students to have a deep understanding of slope and y-intercept and be able to build, represent, and compare general rules for linear relationships. So far, this has been my most successful attempt at structuring a whole unit around period-long tasks. Generally speaking, I have used tasks for two purposes-- to have students surface informal reasoning that lends itself to both the concepts and procedures that are part of the unit (which I generally do as a whiteboard task routine) and to continue to develop or apply a concept/procedure that we've started to formalize (which I generally do with a refine your strategy routine). Following a class-long task, we analyze and apply one or more strategies that were generated as students worked on the task. In between tasks, we formalize some of the work they've been doing, introduce vocabulary associated with it, and practice the associated procedure(s). Here's the sequence of tasks we've done so far: Day 4 - Refine Your Strategy Day 5 - Follow-Up Day 19 - Follow-Up Day 30 - Refine Your Strategy But now, with about 10 days to wrap up the unit, students are in very different places. I would say that at least half are pretty comfortable with identifying and understanding slope and y-intercept (in context) and writing equations with understanding for linear relationships. This has been a way of learning that really works for them. A smaller, but still substantial group of students, are pretty frustrated and confused. This group includes many, but not all, of my beginning English language learners and students with learning disabilities. Clearly, this is a big problem. So here are some things that I am thinking about trying in order to make sure that all of my students are learning: • Putting more structures in place to help students listen and learn from each other • Push our formalization of student-generated strategies farther (step-by-step directions?) • Use more targeted questions (than what did they do? how are these strategies similar/different) when analyzing worked examples • Modeling strategies more explicitly • Pausing in the middle of working on a problem for me to teach a new skill, rather than always waiting for one or more groups to figure out that skill, and then analyze it at the end/the next day What have other people found to be successful? ## Saturday, October 22, 2016 ### Year Four Goals Goals: I wrote this back in August, but got taken over by preparations for school and then school actually starting. Here they are now, though 1) Something compelling every class • Compelling questions • Compelling problems • Compelling structure • Longer instructional routines • Refine a Strategy • Creating Homework Mistakes • Desmos Activity • Contemplate then Calculate • Shorter routines • WODB • Visual Patterns • Estimation 180 • Graphing Stories 3) Transparency and student feedback around my teaching actions ## Monday, September 5, 2016 ### Notes from the Field: Doing Time in Education This weekend I went to see Notes from the Field: Doing Time in Education. This is Anna Deavere Smith’s latest one-woman show, which focuses on the school-to-prison pipeline. In the first act and coda, Smith takes on the persona and words of many people she has interviewed, and in the second act the audience members are split into groups in order to have facilitated conversations about what they have seen so far. I found the performance incredibly powerful and thought provoking and I strongly recommend it to any educators (or people) in the Boston area. My school year with students starts on Thursday and my focus for the last two weeks has been taken over by logistical details and setting up my classroom—covering bulletin boards, mounting whiteboards, arranging desks, unpacking all of my stuff from the closet, and scrubbing everything. However, going to this play reminded me that while everything I just listed is necessary in order to be ready for school, it is the bigger picture that I truly need to ground myself in before getting started. What am I doing to make sure that students are empowered and not marginalized in my classroom and school? When am I prioritizing compliance and how can I find an alternative? How will I make sure my students’ voices are heard and respected? What am I doing to get to know and support my kids as people, not just math students? What will I do when I see injustices committed against my students? How will I respond when I am part of enacting an injustice? What’s my location on the school-to-prison pipeline? This last question is one that we were all asked to reflect on at the end of the play’s act two breakout group. My answer? I was never going to be sent to prison from school, nor were any of my friends or family. I grew up with that privilege. However, I am now part of a system that enables the school-to-prison pipeline, which means that I also have the power to disrupt it. When several people shared out their location on the school-to-prison pipeline, one member of our group expressed a concern. She was concerned that people would come to this play, feel the catharsis that theater is intended to elicit, encourage other people to come, but have that be the end of the experience. She pointed out that us talking today was important, but that it needed to be followed by action. The American Repertory Theatre, where I saw the play, seems to be trying to address that concern. They sent everyone who attended a list of ways to get involved in Boston. I left still trying to figure out what actions I will take. But as I start this school year, I am committing to becoming more aware of and trying to change the actions of mine that contribute to the school-to-prison pipeline and to speaking up about the injustices that I see/that are brought to me. ## Monday, August 29, 2016 ### Instructional Routines So I have become a little bit obsessed with instructional routines. This is because I think they have great value to both teachers and students: Benefits for students • knowing what to expect makes kids feel more comfortable and safe • having a routine process enables kids to focus more on the math ideas and less about figuring out what the directions are Benefits for teachers • planning is faster: can choose a routine that fits goal and then just slot in the particular problem • collaborating is easier: having commonalities in practice give a more narrow lens for focus Inspired by Contemplate then Calculate, I am planning on using 9 routines in my classroom this year. Some of these are greatly inspired by others and some of them I developed. For each routine, I have a powerpoint template than I can adapt for each time I use the routine. For some of the routines, I have accompanying handouts that I will use, no modification necessary, each time we do the routine. All of these materials and a more in-depth description of each routine can be found in this google folder. ### Longer Routines: o Goal: Build structural thinking in order for students to solve efficiently based on understanding rather than blindly following a procedure. Need tasks that have multiple shortcuts. o Goal: Various math goals. Also using a guiding question and technology to learn math and for me to talk as little as possible. o Goal: Have students learn from each other in order to improve their understanding of the homework problems. Build the positive culture of mistakes in our classroom. o Goal: To build students’ capacity to solve problems on their own through scaffolding by engaging in others’ ideas. This is for tasks where I expect students to already have a pretty well-developed strategy or strategies to solve the problem. · Whiteboard Task (4 versions, depending on launch choice) o Goal: For students to work collaboratively on a task that they probably couldn’t solve on their own. This is for tasks where I am not expecting them to have well-developed strategies, but instead to deepen or extend their conceptual understanding in order to develop new strategies. Also using Peter Liljedahl’s visible random groupings and vertical non-permanent surfaces to disrupt institutional norms. ### Shorter Routines: o What: Estimate a quantity o Why: Think like mathematicians by determining relevant information and a reasonable o What: Make a graph to match a video story o Why: Think like a mathematician by using math to represent something happening in the real world o What: Describe, continue, and generalize a pattern o Why: Think like a mathematician by looking at the structure of a pattern and using repeated reasoning · WODB o What: Figure out why each one doesn’t belong o Why: To “think like mathematicians” by comparing similarities and differences	{}
How close would the sun have to get to a supermassive black hole to have Jupiter stripped and slingshot into interstellar space? Please make whatever assumptions are needed. Assume sun approaches black hole on some sort of hyperbolic trajectory. Assume size of supermassive black hole is same as the one at center of our galaxy. How close would sun have to get in order for Jupiter to be “slingshot” into interstellar space. • I think "An orbiting pair of objects (m2, m3) passes a much more massive object m1 on a hyperbolic trajectory, at what distance of closest approach will it be possible for the orbiting pair to separate after the encounter?" is on-topic. But I think you should ask your unrelated follow-up question as a new question since the answers are totally different. – uhoh Mar 22 at 2:43 • One question per post is the rule. – StephenG Mar 22 at 3:18 • I've removed the second question, as per the "one question per post" guideline. – James K Mar 22 at 8:14 Three body systems are peculiar beasts, and but I'm going to change the question to "Would Jupiter be in a stable solar orbit?" This makes it a question of Hall radius. The Hall radius is $$r_H = a\sqrt[3]{m/3M}$$ where $$m/M=1/4000000$$ is the ratio of solar mass to black hole mass (the mass of Jupiter is treated as negligible!) and $$a$$ is the orbital distance of the sun about the black hole If we set $$r_H$$ to 5 (AU) and solve for $$a$$ we get a value of about 10000 (I'm only working at 1 s.f. accuracy here. In other words, if the sun is orbiting the black hole at 10000AU then Jupiter would be in a marginally stable orbit. If the sun got closer than 10000AU then Jupiter would tend to orbit the black hole and not the sun. However this is only an upper bound. On a hyperbolic orbit the sun would spend little time near the black hole and so even if Jupiter had drifted in the black hole's gravity as the sun passed by, as the sun and jupiter moved away, it would tend to fall back into orbit around the sun. To model whether Jupiter would actually be lost would require knowledge of the initial conditions and numerically solving the differential equations of motion. • Ok I hadn’t considered that Jupiter being captured into orbit around the black hole would be very likely. It sounds like (from your answer) that there may be a somewhat narrow window of initial conditions whereby Jupiter would be flung into interstellar space. – Keith Knauber Mar 22 at 16:31 • jupiter being captured is the alternative, if the Earth is "slingshotted" away, that momentum comes from somewhere, and it can come from Jupiter, which by losing momentum is captured into an orbit. In 3 body dynamics many things are possible. – James K Mar 22 at 16:49 • But this is sort of an anti-answer: If you are more than 10000au away, everything should be okay. If you are less than this, then watch out. but initial conditions matter and – James K Mar 22 at 16:50 • I just read this from another website “Near the galactic center, the average distance between neighboring stars is expected to be about 1000 AU”. Intuitively, it seems unlikely for a planet, at Jupiter’s distance from the sun, to survive a trip through the galactic center without being captured by a more massive object. – Keith Knauber Mar 22 at 18:45 • Ooh and then there’s this google.com/amp/s/www.sciencealert.com/… – Keith Knauber Mar 22 at 18:54	{}
Home > Error Propagation > Propagation Of Error Division # Propagation Of Error Division ## Contents Structural and Multidisciplinary Optimization. 37 (3): 239–253. Note that this fraction converges to zero with large n, suggesting that zero error would be obtained only if an infinite number of measurements were averaged! This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the In that case the error in the result is the difference in the errors. More about the author This is why we could safely make approximations during the calculations of the errors. The problem might state that there is a 5% uncertainty when measuring this radius. which we have indicated, is also the fractional error in g. In this way an equation may be algebraically derived which expresses the error in the result in terms of errors in the data. http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm ## Error Propagation Calculator It can show which error sources dominate, and which are negligible, thereby saving time you might otherwise spend fussing with unimportant considerations. But for those not familiar with calculus notation there are always non-calculus strategies to find out how the errors propagate. Retrieved 2016-04-04. ^ "Propagation of Uncertainty through Mathematical Operations" (PDF). • In either case, the maximum error will be (ΔA + ΔB). • The previous rules are modified by replacing "sum of" with "square root of the sum of the squares of." Instead of summing, we "sum in quadrature." This modification is used only • Example: Suppose we have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. • The trick lies in the application of the general principle implicit in all of the previous discussion, and specifically used earlier in this chapter to establish the rules for addition and • Reciprocal In the special case of the inverse or reciprocal 1 / B {\displaystyle 1/B} , where B = N ( 0 , 1 ) {\displaystyle B=N(0,1)} , the distribution is Retrieved 2012-03-01. This method of combining the error terms is called "summing in quadrature." 3.4 AN EXAMPLE OF ERROR PROPAGATION ANALYSIS The physical laws one encounters in elementary physics courses are expressed as Hint: Take the quotient of (A + ΔA) and (B - ΔB) to find the fractional error in A/B. Error Propagation Chemistry A consequence of the product rule is this: Power rule. The number "2" in the equation is not a measured quantity, so it is treated as error-free, or exact. Error Propagation Inverse This example will be continued below, after the derivation (see Example Calculation). Send us feedback. Section (4.1.1). It can tell you how good a measuring instrument is needed to achieve a desired accuracy in the results. Error Propagation Average is formed in two steps: i) by squaring Equation 3, and ii) taking the total sum from $$i = 1$$ to $$i = N$$, where $$N$$ is the total number of The fractional error may be assumed to be nearly the same for all of these measurements. The absolute error in g is: [3-14] Δg = g fg = g (fs - 2 ft) Equations like 3-11 and 3-13 are called determinate error equations, since we used the ## Error Propagation Inverse Example: If an object is realeased from rest and is in free fall, and if you measure the velocity of this object at some point to be v = - 3.8+-0.3 Retrieved 13 February 2013. Error Propagation Calculator Generated Mon, 24 Oct 2016 19:48:51 GMT by s_wx1157 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection Error Propagation Physics Answer: we can calculate the time as (g = 9.81 m/s2 is assumed to be known exactly) t = - v / g = 3.8 m/s / 9.81 m/s2 = 0.387 Uncertainty never decreases with calculations, only with better measurements. my review here For example, if you have a measurement that looks like this: m = 20.4 kg ±0.2 kg Thenq = 20.4 kg and δm = 0.2 kg First Step: Make sure that Berkeley Seismology Laboratory. The calculus treatment described in chapter 6 works for any mathematical operation. Error Propagation Square Root When two quantities are divided, the relative determinate error of the quotient is the relative determinate error of the numerator minus the relative determinate error of the denominator. Uncertainty, in calculus, is defined as: (dx/x)=(∆x/x)= uncertainty Example 3 Let's look at the example of the radius of an object again. The error in a quantity may be thought of as a variation or "change" in the value of that quantity. click site The derivative of f(x) with respect to x is d f d x = 1 1 + x 2 . {\displaystyle {\frac {df}{dx}}={\frac {1}{1+x^{2}}}.} Therefore, our propagated uncertainty is σ f We leave the proof of this statement as one of those famous "exercises for the reader". Error Propagation Definition Le's say the equation relating radius and volume is: V(r) = c(r^2) Where c is a constant, r is the radius and V(r) is the volume. If q is the sum of x, y, and z, then the uncertainty associated with q can be found mathematically as follows: Multiplication and Division Finding the uncertainty in a ## Harry Ku (1966). Retrieved 2013-01-18. ^ a b Harris, Daniel C. (2003), Quantitative chemical analysis (6th ed.), Macmillan, p.56, ISBN0-7167-4464-3 ^ "Error Propagation tutorial" (PDF). In both cases, the variance is a simple function of the mean.[9] Therefore, the variance has to be considered in a principal value sense if p − μ {\displaystyle p-\mu } The results for addition and multiplication are the same as before. Error Propagation Excel The fractional determinate error in Q is 0.028 - 0.0094 = 0.0186, which is 1.86%. p.5. Pearson: Boston, 2011,2004,2000. R x x y y z z The coefficients {cx} and {Cx} etc. navigate to this website Why can this happen? You see that this rule is quite simple and holds for positive or negative numbers n, which can even be non-integers. Typically, error is given by the standard deviation ($$\sigma_x$$) of a measurement. The result is most simply expressed using summation notation, designating each measurement by Qi and its fractional error by fi. © 1996, 2004 by Donald E. H. (October 1966). "Notes on the use of propagation of error formulas". Please see the following rule on how to use constants. in each term are extremely important because they, along with the sizes of the errors, determine how much each error affects the result. Using division rule, the fractional error in the entire right side of Eq. 3-11 is the fractional error in the numerator minus the fractional error in the denominator. [3-13] fg = Since the velocity is the change in distance per time, v = (x-xo)/t. Indeterminate errors show up as a scatter in the independent measurements, particularly in the time measurement. First, the measurement errors may be correlated. In the first step - squaring - two unique terms appear on the right hand side of the equation: square terms and cross terms. The end result desired is $$x$$, so that $$x$$ is dependent on a, b, and c. In a probabilistic approach, the function f must usually be linearized by approximation to a first-order Taylor series expansion, though in some cases, exact formulas can be derived that do not Given the measured variables with uncertainties, I ± σI and V ± σV, and neglecting their possible correlation, the uncertainty in the computed quantity, σR is σ R ≈ σ V Then σ f 2 ≈ b 2 σ a 2 + a 2 σ b 2 + 2 a b σ a b {\displaystyle \sigma _{f}^{2}\approx b^{2}\sigma _{a}^{2}+a^{2}\sigma _{b}^{2}+2ab\,\sigma _{ab}} or Error Propagation in Trig Functions Rules have been given for addition, subtraction, multiplication, and division. If you're measuring the height of a skyscraper, the ratio will be very low. For example, lets say we are using a UV-Vis Spectrophotometer to determine the molar absorptivity of a molecule via Beer's Law: A = ε l c.	{}
# Probabilistic Proofs of Key Number-Theoretic Results Given a positive integer $n$, let $p$ be the largest prime less than or equal to $n$. Let $N(n)=2^{C_2}\cdots p^{C_p}$ be uniformly distributed from $1$ to $n$, and $M(n)=2^{Z_2}\cdots p^{Z_p}$ where $Z_p's$ are independent geometric with $P(Z_p\ge k)=\frac{1}{p^k}$. It can be shown that $C_p$ has probability mass $P(C_p=k)=\frac{\big\lfloor \frac{n}{p^k}\big\rfloor}{n}.$ Consider the metric $d(M,N)=\sum_{p\le n}\vert C_p-Z_p\vert$ ($d$ counts the number of prime insertions and deletions needed to convert $N$ to $M$). Using this metric, we have the Wasserstein metric $d_W(M,N)=\inf_{\text{couplings}}\mathbb{E}d(M,N).$ Arratia (page 10 of https://arxiv.org/pdf/1305.0941.pdf) claims • $d_W(M,N)=o(\log \log n)$ implies the Hardy-Ramanujan Theorem (which states that for almost every positive integer $n$, $\omega(n) \approx \log \log n$, where $\omega(n)$ is the number of distinct prime divisors of $n$). • $d_W(M,N)=o(\sqrt{\log \log n})$ implies the Erdos-Kac Central Limit Theorem (which states that $\frac{\omega(n)-\log \log n}{\sqrt{\log \log n}}$ has the standard normal distribution. Further confirmation of this is stated by Bollobas on page 29 of "Contemporary Combinatorics": How can these results be derived from the asymptotics? Obviously, one has $$\|\omega(M)-\omega(N)\|\leq d(M,N).$$ Taking the expectations, we see that for every $n$, we can construct a coupling of $M(n)$ and $N(n)$ such that $$\mathbb{E}\|\omega(M(n))-\omega(N(n))\|\leq d_W(M(n),N(n))+\frac{1}{n}.$$ Under the asymptotic estimates above, Chebyshev's inequality implies, for any $\alpha>0$ $$\mathbb{P}(\|\omega(M(n)-\omega(N(n)))\|>\alpha \log \log n)=o(1),$$ or, respectively, $$\mathbb{P}(\|\omega(M(n)-\omega(N(n)))\|>\alpha \sqrt{\log \log n})=o(1).$$ Hence, Hardy-Ramanujan and Erdos-Kac boil down to the corresponding statements about $\omega(M(n))$. These are just the LLN and the CLT for the independent random variables $$\mathbf{1}_{Z_2\neq 0},\mathbf{1}_{Z_3\neq 0},\mathbf{1}_{Z_5\neq 0}\dots,$$ which are of course well known and standard (e. g., Lindeberg's CLT applies)	{}
# All Questions 67 views ### In a 2-body problem, when is the moving path closed? In a 2-body problem is it true that, in all situations, the moving path is closed? In which cases are the paths closed? Fixing the coordinate system or fixing one of the bodies gives us different ... 566 views ### Analytic continuation of imaginary time Greens function in the time domain Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature $$G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle$$ ... 36 views ### Accelerometer validation trace I am attempting to validate an accelerometer. I have a triaxial accelerometer and placed it on a wheel which goes at various frequencies from 1 to 3 Hz. Am I right in thinking that I would expect the ... 67 views ### Does gravity stack? If I am standing on a planet on the opposite side from its sun will I feel the downward pull of both the planet's gravity and the star's gravity? 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# UtilOptimRegress: Optimization of predictions utility, cost or benefit for... In UBL: An Implementation of Re-Sampling Approaches to Utility-Based Learning for Both Classification and Regression Tasks ## Description This function determines the optimal predictions given a utility, cost or benefit surface. This surface is obtained through a specified strategy with some parameters. For determining the optimal predictions an estimation of the conditional probability density function is performed for each test case. If the surface provided is of type utility or benefit a maximization process is carried out. If the user provides a cost surface, then a minimization is performed. ## Usage 1 2 3 UtilOptimRegress(form, train, test, type = "util", strat = "interpol", strat.parms = list(method = "bilinear"), control.parms, m.pts, minds, maxds, eps = 0.1) ## Arguments form A formula describing the prediction problem. train A data.frame with the training data. test A data.frame with the test data. type A character specifying the type of surface provided. Can be one of: "utility", "cost" or "benefit". Defaults to "utility". strat A character determining the strategy for obtaining the surface of the problem. For now, only the interpolation strategy is available (the default). strat.parms A named list containing the parameters necessary for the strategy previously specified. For the interpolation strategy (the default and only strategy available for now), it is required that the user specifies wich method sould be used for interpolating the points. control.parms A named list with the control.parms defined through the function phi.control. These parameters stablish the diagonal of the surface provided. If the type of surface defined is "cost" this parameter can be set to NULL, because in this case we assume that the accurate prediction, i.e., points in the diagonal of the surface have zero cost. See examples. m.pts A matrix with 3-columns, with interpolation points specifying the utility, cost or benefit of the surface. The points sould be in the off-diagonal of the surface, i.e., the user should provide points where y != y.pred. The first column must have the true value (y), the second column the corresponding prediction (y.pred) and the third column sets the utility cost or benefit of that point (y, y.pred). The user should define as many points as possible. The minimum number of required points are two. More specifically, the user must always set the surface values of at least the points (minds, maxds) and (maxds, minds). See minds and maxds description. maxds The numeric upper bound of the target variable considered. minds The numeric lower bound of the target variable considered. eps Numeric value for the precision considered during the interpolation. Defaults to 0.1. ## Details The optimization process carried out by this function uses a method for conditional density estimation proposed by Rau M.M et al.(2015). Code for conditional density estimation (available on github https://github.com/MarkusMichaelRau/OrdinalClassification) kindly contributed by M. M. Rau with changes made by P.Branco. The optimization is achieved generalizing the method proposed by Elkan (2001) for classification tasks. In regression, this process involves determining, for each test case, the maximum integral (for utility or benefit surfaces, or the minimum if we have a cost surface) of the product of the conditional density function estimated and either the utility, the benefit or the cost surface. The optimal prediction for a case q is given by: y^{}(q)=argmax[z] \int pdf(y\|q).U(y,z) dy, where pdf(y\|q) is the conditional densitiy estimation for case q, and U(y,z) is the utility, benefit or cost surface evaluated on the true value y and predictied value z. ## Value The function returns a vector with the predictions for the test data optimized using the surface provided. ## Author(s) Paula Branco [email protected], Rita Ribeiro [email protected] and Luis Torgo [email protected] ## References Rau, M.M., Seitz, S., Brimioulle, F., Frank, E., Friedrich, O., Gruen, D. and Hoyle, B., 2015. Accurate photometric redshift probability density estimation-method comparison and application. Monthly Notices of the Royal Astronomical Society, 452(4), pp.3710-3725. Elkan, C., 2001, August. The foundations of cost-sensitive learning. In International joint conference on artificial intelligence (Vol. 17, No. 1, pp. 973-978). LAWRENCE ERLBAUM ASSOCIATES LTD. phi.control, UtilOptimClassif, UtilInterpol 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 ## Not run: #Example using a utility surface: data(Boston, package = "MASS") tgt <- which(colnames(Boston) == "medv") sp <- sample(1:nrow(Boston), as.integer(0.7nrow(Boston))) train <- Boston[sp,] test <- Boston[-sp,] control.parms <- phi.control(Boston[,tgt], method="extremes", extr.type="both") # the boundaries of the domain considered minds <- min(train[,tgt]) maxds <- max(train[,tgt]) # build m.pts to include at least (minds, maxds) and (maxds, minds) points # m.pts must only contain points in [minds, maxds] range. m.pts <- matrix(c(minds, maxds, -1, maxds, minds, -1), byrow=TRUE, ncol=3) pred.res <- UtilOptimRegress(medv~., train, test, type = "util", strat = "interpol", strat.parms=list(method = "bilinear"), control.parms = control.parms, m.pts = m.pts, minds = minds, maxds = maxds) eval.util <- EvalRegressMetrics(test$medv, pred.res$optim, pred.res$utilRes, thr=0.8, control.parms = control.parms) # train a normal model model <- randomForest(medv~.,train) normal.preds <- predict(model, test) #obtain the utility of the new points (trues, preds) NormalUtil <- UtilInterpol(test$medv, normal.preds, type="util", control.parms = control.parms, minds, maxds, m.pts, method = "bilinear") #check the performance eval.normal <- EvalRegressMetrics(test$medv, normal.preds, NormalUtil, thr=0.8, control.parms = control.parms) #check both results eval.util eval.normal #check visually both predictions and the surface used UtilInterpol(test$medv, normal.preds, type = "util", control.parms = control.parms, minds, maxds, m.pts, method = "bilinear", visual=TRUE) points(test$medv, normal.preds, col="green") points(test$medv, pred.res$optim, col="blue") # another example now using points interpolation with splines data(algae,package="DMwR") ds <- algae[complete.cases(algae[,1:12]),1:12] tgt <- which(colnames(ds) == "a1") sp <- sample(1:nrow(ds), as.integer(0.7nrow(ds))) train <- ds[sp,] test <- ds[-sp,] control.parms <- phi.control(ds[,tgt], method="extremes", extr.type="both") # the boundaries of the domain considered minds <- min(train[,tgt]) maxds <- max(train[,tgt]) # build m.pts to include at least (minds, maxds) and (maxds, minds) points m.pts <- matrix(c(minds, maxds, -1, maxds, minds, -1), byrow=TRUE, ncol=3) pred.res <- UtilOptimRegress(a1~., train, test, type = "util", strat = "interpol", strat.parms=list(method = "splines"), control.parms = control.parms, m.pts = m.pts, minds = minds, maxds = maxds) # check the predictions plot(test$a1, pred.res$optim) # assess the performance eval.util <- EvalRegressMetrics(test$a1, pred.res$optim, pred.res$utilRes, thr=0.8, control.parms = control.parms) # # train a normal model model <- randomForest(a1~.,train) normal.preds <- predict(model, test) #obtain the utility of the new points (trues, preds) NormalUtil <- UtilInterpol(test$medv, normal.preds, type = "util", control.parms = control.parms, minds, maxds, m.pts, method="splines") #check the performance eval.normal <- EvalRegressMetrics(test$medv, normal.preds, NormalUtil, thr=0.8, control.parms = control.parms) eval.util eval.normal # observe the utility surface with the normal preds UtilInterpol(test$a1, normal.preds, type="util", control.parms = control.parms, minds, maxds, m.pts, method="splines", visual=TRUE) # add the optim preds points(test$a1, pred.res$optim, col="green") # Example using a cost surface: data(Boston, package = "MASS") tgt <- which(colnames(Boston) == "medv") sp <- sample(1:nrow(Boston), as.integer(0.7nrow(Boston))) train <- Boston[sp,] test <- Boston[-sp,] # if using interpolation methods for COST surface, the control.parms can be set to NULL # the boundaries of the domain considered minds <- min(train[,tgt]) maxds <- max(train[,tgt]) # build m.pts to include at least (minds, maxds) and (maxds, minds) points m.pts <- matrix(c(minds, maxds, 5, maxds, minds, 20), byrow=TRUE, ncol=3) pred.res <- UtilOptimRegress(medv~., train, test, type = "cost", strat = "interpol", strat.parms = list(method = "bilinear"), control.parms = NULL, m.pts = m.pts, minds = minds, maxds = maxds) # check the predictions plot(test$medv, pred.res$optim) # assess the performance eval.util <- EvalRegressMetrics(test$medv, pred.res$optim, pred.res$utilRes, type="cost", maxC = 20) # # train a normal model model <- randomForest(medv~.,train) normal.preds <- predict(model, test) #obtain the utility of the new points (trues, preds) NormalUtil <- UtilInterpol(test$medv, normal.preds, type="cost", control.parms = NULL, minds, maxds, m.pts, method="bilinear") #check the performance eval.normal <- EvalRegressMetrics(test$medv, normal.preds, NormalUtil, type="cost", maxC = 20) eval.normal eval.util # check visually the surface and the predictions UtilInterpol(test$medv, normal.preds, type="cost", control.parms = NULL, minds, maxds, m.pts, method="bilinear", visual=TRUE) points(test$medv, pred.res\$optim, col="blue") ## End(Not run)	{}
Welcome! My name is Damaris I am online and ready to help you via WhatsApp chat. Let me know if you need my assistance. Download this complete Project material titled; An Algorithm For Solutions Of Hammerstein Integral Equations With Monotone Operators with abstract, chapters 1-5, references, and questionnaire. Preview Abstract or chapter one below • Format: PDF and MS Word (DOC) • pages = 65 3,000 ## ABSTRACT Let X be a uniformly convex and uniformly smooth real Banach space with dual space X. Let F : X ! X and K : X ! X be bounded monotone mappings such that the Hammerstein equation u + KFu = 0 has a solution in X. An explicit iteration sequence is constructed and proved to converge strongly to a solution of the equation. This is achieved by combining geometric properties of uniformly convex and uniformly smooth real Banach spaces recently introduced by Alber with our method of proof which is also of independent interest. ertication ii 1 Introduction and literature review 2 1.0.1 Hammerstein equations . . . . . . . . . . . . . . . . . . . . . . 3 1.0.2 Approximation of solutions of Hammerstein integral equations 10 2 PRELIMINARIES 13 2.1 Denition of some terms and concepts. . . . . . . . . . . . . . . . . . 13 2.2 Results of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Some interesting properties of Normalized Duality map . . . . . . . . 19 3 A Strong convergence theorem 21 3.1 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1 ## CHAPTER ONE Introduction and literature review The contents of this thesis fall within the general area of nonlinear operator theory, a ourishing area of research for numerous mathematicians. In this thesis, we con- centrate on an important topic in this area-approximation of solutions of nonlinear integral equations of Hammaerstein type involving monotone-type mappings. Let H be a real inner product space. A map A : H ! 2H is called monotone if for each x; y 2 H, 􀀀 ; x 􀀀 y 0; 8 2 Ax; 2 Ay: (1.1) If A is single-valued, the map A : H ! H is monotone if Ax 􀀀 Ay; x 􀀀 y 0 8 x; y 2 H: (1.2) Monotone mappings were rst studied in Hilbert spaces by Zarantonello [50], Minty [42], Kacurovskii [37] and a host of other authors. Interest in such mappings stems mainly from their usefulness in numerous applications. Consider, for example, the following: Example 1. Let g : H ! R [ f1g be a proper convex function. The subdierential of g at x 2 H, @g : H ! 2H , is dened by @g(x) = x 2 H : g(y) 􀀀 g(x) y 􀀀 x; x 8 y 2 H : It is easy to check that @g is a monotone operator on H, and that 0 2 @g(u) if and only if u is a minimizer of g. Setting @g A, it follows that solving the inclusion 0 2 Au, in this case, is solving for a minimizer of g. Example 2. Again, let A : H ! H be a monotone map. Consider the evolution equation du dt + Au = 0: (1.3) At equilibrium state, du dt = 0 so that Au = 0: (1.4) Consequently, solving the equation Au = 0, in this case, corresponds to solving for the equilibrium state of the system described by (1.3). Monotone maps also appear in Hammerstein equations. Since this thesis focuses on this class of equations, we give a brief review. 2 3 Chapter 1. Introduction and literature review 1.0.1 Hammerstein equations Let Rn be bounded. Let k : ! R and f : R ! R be measurable real- valued functions. An integral equation (generally nonlinear) of Hammerstein-type has the form u(x) + Z k(x; y)f(y; u(y))dy = w(x); (1.5) where the unknown function u and inhomogeneous function w lie in a Banach space E of measurable real-valued functions. If we dene F : F( ;R) ! F( ;R) and K : F( ;R) ! F( ;R) by Fu(y) = f(y; u(y)); y 2 ; and Kv(x) = Z k(x; y)v(y)dy; x 2 ; respectively, where F( ;R) is a space of measurable real-valued functions dened from to R, then equation (1.5) can be put in the abstract form u + KFu = 0: (1.6) where, without loss of generality, we have assumed that w 0. The operators K and F are generally of the monotone-type. A closer look at equation (1.6) reveals that it is a special case of (1.4), where A := I + KF: Interest in (1.6) stems mainly from the fact that several problems that arise in dierential equations, for instance, elliptic boundary value problems whose linear parts possess Green’s function can, as a rule, be transformed into the form (1.5) (see e.g., Pascali and Sburlan [43], chapter IV, p. 164). Among these, we mention the problem of the forced ocsillation of nite amplitude of a pendulum. Consider the problem of the pendulum: 8< : d2v(t) dt2 + a2 sin v(t) = z(t); t 2 [0; 1]; v(0) = v(1) = 0; (1.7) where the driving force z is odd. The constant a (a 6= 0) depends on the length of the pendulum and gravity. Since Green’s function for the problem v00(t) = 0; v(1) = v(0) = 0; is the triangular function K(t; x) = 8< : t(1 􀀀 x); if 0 t x x(1 􀀀 t); if x t 1; (1.8) 4 it follows that problem (1.7) is equivalent to the nonlinear integral equation v(t) = 􀀀 Z 1 0 K(t; x)[z(x) 􀀀 a2 sin v(x)]dx: (1.9) If g(t) = 􀀀 R 1 0 K(t; x)z(x)dx and v(t) + g(t) = u(t); then (1.9) can be written as the Hammerstein equation u(t) = 􀀀 Z 1 0 K(t; x)f(x; u(x))dx = 0; (1.10) where f(x; u(x)) = a2sin[u(x) 􀀀 g(x)]; (see e.g., [43]) Equations of Hammerstein-type also play a crucial role in the theory of optimal control systems and in automation and network theory (see e.g., Dolezale [33]). Several existence results have been proved for equations of Hammerstein-type (see e.g., Brezis and Browder [4, 5, 6], Browder [7], Browder, De Figueiredo and Gupta [8]). The concept of monotone maps has been extended to arbitrary real normed spaces. There are two well-studied extensions of Hilbert-space monotonicity to arbitrary normed spaces. We brie y explore the two. The rst is the class of accretive operators. A map A : E ! 2E is called accretive if for each x; y 2 E, there exists j(x􀀀y) 2 J(x 􀀀 y) such that 􀀀 ; j(x 􀀀 y) 0; 8 2 Ax; 2 Ay; (1.11) Where J is the normalized duality map on E: If A is single-valued, the map A : E ! E is accretive if for each x; y 2 E, there exists j(x 􀀀 y) 2 J(x 􀀀 y) such that Ax 􀀀 Ay; j(x 􀀀 y) 0: (1.12) In a Hilbert space, the normalized duality map is the identity map, so that (1.11) and (1.12) reduce to (1.1) and (1.2) respectively, where E = H and so, accretivity is one extension of Hilbert space monotonicity to general normed spaces. A result of Kato [39] shows that (1.12) holds if and only if for all x; y 2 D(A); the following inequality holds jjx 􀀀 yjj jjx 􀀀 y + s(Ax 􀀀 Ay)jj 8s > 0: (1.13) The map A is called generalized -strongly accretive if there exists a stritly increasing function : [0;1) ! [0;1) with (0) = 0 such that for each x; y 2 E, there exists j(x 􀀀 y) 2 J(x 􀀀 y) such that hAx 􀀀 Ay; j(x 􀀀 y)i (kx 􀀀 yk): (1.14) 5 Chapter 1. Introduction and literature review It is called -strongly accretive if there exists a stritly increasing function : [0;1) ! [0;1) with (0) = 0 such that for each x; y 2 E, there exists j(x 􀀀 y) 2 J(x 􀀀 y) such that hAx 􀀀 Ay; j(x 􀀀 y)i jjx 􀀀 yjj(kx 􀀀 yk): (1.15) Finally, A is called strongly accretive if there exists k 2 (0; 1) such that for each x; y 2 E, there exists j(x 􀀀 y) 2 J(x 􀀀 y) such that hAx 􀀀 Ay; j(x 􀀀 y)i kkx 􀀀 yk2: (1.16) Clearly, the class of strongly accretive mappings is a sub-class of the class of -strongly accretive maps (one takes (t) = kt); and the class of -strongly accretive maps is a sub-class of that of generalized -strongly accretive (one takes (t) = t(t)). It is well known that the inclusions are proper. For the equation Au = 0, when A is of accretive-type, existence theorems have been proved by various authors, in various Banach spaces and under various continuity conditions (see Browder [9], [10], [11], [12] ). It is well known that the class of generalized -strongly accretive maps is the largest, among the classes of accretive-type mappings, for which, if a solution exists, it is necessarily unique. For approximating a solution of equation (1.4), where A : E ! E is of accretive-type, Browder [13] dened an operator T := I 􀀀 A, where I is the identity map on E. He called such an operator pseudo-contractive. It is trivial to observe that zeros of A correspond to xed points of T. Consequently, solving the equation Au = 0 when A is an accretive-type operator is reduced to nding xed points of pseudo-contractive-type mappings. An important class of pseudo-contractive mappings is the class of nonexpansive maps, where a map T : E ! E is called nonexpansive if for each x; y 2 E, the following inequality holds; jjTx 􀀀 Tyjj jjx 􀀀 yjj. Being an obvious generalization of contraction mappings(mappings T : E ! E satis- fying jjTx􀀀Tyjj jjx􀀀yjj8x; y 2 E and some k 2 (0; 1)), is not all that makes them important. They are also important, as has been observed by Bruck [16], mainly for the following two reasons: Nonexpansive maps are intimately connected with the monotonicity methods developed since the early 1960’s and constitute one of the rst classes of non- linear mappings for which xed point theorems were obtained by using the ne geometric properties of the underlying Banach spaces instead of compactness properties. They appear in applications as the transition operators for initial value prob- lems of dierential inclusions of the form 0 2 du dt + T(t)u; where the operators fT(t)g are in general set-valued and are accretive or dissi- pative and minimally continuous. 6 The following xed point theorem has been proved for nonexpansive maps on uniformly convex spaces. Theorem 1.0.1. Let E be a re exive Banach space and let K be a nonempty closed bounded and convex subset of E with normal structure. Let T : K ! K be a nonex- pansive mapping of K into itself. Then, T has a xed point. While contractions guarantee existence and uniquness, nonexpansions do not. Trivial examples show that the sequence of successive approximations xn+1 = Txn; x0 2 K; n 0 (1.17) (where K is a nonempty closed convex and bounded subset of a real Banach space E), for a nonexpansive mapping T : K ! K even with a unique xed point, may not converge to the xed point. It is enough, for example, to take for T; a rotation of the unit ball in the plane around the origin of coordinates. Specically, we have the following example. Example 3. Let B := fx 2 R2 : jjxjj 1g and let T denote an anticlockwise rotation of 4 about the origin of coordinates. Then T is nonexpansive with the origin as the only xed point. Moreover, the sequence dened by (1.17) where B = K does not converge to zero. Krasnoselskii [40], however, showed that in this example, a convergent sequence of succesive approximations can be obtained if instead of T; the auxilliary nonexpansive mapping 1 2 (I +T); is used, where I denotes the identity transformation of the plane, i.e., if the sequence of succesive approximations is denedd by xn+1 = 1 2 xn + Txn n = 0; 1; :: (1.18) instead of by the usual so-called Picard iterates, xn+1 = Txn x0 2 K n 0: It is easy to see that the mappings T and 1 2 (I + T) have the same set of xed points, so that the limit of the convergent sequence dened by (1.18) is necessarily a xed point of T. Generally, if X is a normed linear space and K a convex subset of X; a general- ization of equation (1.18) which has proved successful in the approximation of xed points of nonexpansive mappings T : K ! K (when they exist), is the following scheme: x0 2 K; xn+1 = (1 􀀀 )xn + Txn; n = 0; 1; 2; ::: 2 (0; 1); (1.19) constant (see, e.g., Schaefer [47]). However, the most general Mann-type iterative scheme now studied is the following: x0 2 K xn+1 = (1 􀀀 cn)xn + cnTxn; n = 0; 1; 2; ::: (1.20) where fCng1 n=1 (0; 1) is a real sequence satisfying appropriate conditions (see, e.g., Chidume [21], Edelstein and O’Brian [34], Ishikawa [35]). Under the fol- 7 Chapter 1. Introduction and literature review (i) limCn = 0; and (ii) P1 n=1 Cn = 1; the sequence fxng generated by (1.20) is generally referred to as the Mann sequence [41]. The recurssion formula (1.19) is known as the Krasnoselskii-Mann (KM) for- mula for nding xed points of nonexpansive mappings (when they exist). Let K be a nonempty convex subset of a normed space E and T : K 􀀀! K be a nonexpansive map. Let the sequence fxng1 n=0 in K be dened iteratively by x0 2 K, xn+1 = (1 􀀀 cn)xn + cnTxn; n 1; (1.21) where fcng is a sequence in (0; 1) satisfying the following conditions: (i) X1 n=0 cn = 1; (ii) lim n􀀀!1 cn = 0: Ishikawa [35] proved that If the sequence fxng1n =0 is bounded, then it is an approximate xed point sequence in the sense that lim n􀀀!1 jjxn 􀀀 Txnjj = 0: (1.22) Edelstein and O’Brian [34] considered the recursion formula xn+1 = (1 􀀀 )xn + Txn; x0 2 K; n 2 N; 2 (0; 1); (1.23) where T maps K into K and proved that if K is bounded, then the convergence in (1.22) is uniform. Chidume [21] considered the recursion formular (1.21), introduced the concept of an admissible sequence and proved that if K is bounded, then the convergence in (1.22) is uniform. Remark 1. We therefore note that the best mode of convergence we can get from recursion formula (1.21) is weak convergence to a xed point of T(see e.g, Reich [46]). It is always desirable to establish that the sequence is an approximate xed point sequence i.e., that the sequence dened by (1.21) satises (1.22). In general, the iteration problem does not yield strong convergence of the sequence to a xed point of T. To obtain convergence to a xed point of T, some type of compactness condition must be imposed either on K or on the map T (e.g, T may be required to be demicompact, or (I 􀀀T) may be required to map closed bounded subsets of E into closed subsets of E, etc, see e.g, Chidume [20]). For the more general class of Lipschitz pseudo-contractive maps, attempts to use the Mann formula, which has been successfully employed for nonexpansive mappings, to approximate a xed point of a Lipschitz pseudo-contractive map even on a compact convex domain in a real Hilbert space proved abortive. In 1974, Ishikawa [36] proved the following theorem. Theorem 1.0.2. Let K be a nonempty compact convex subset of a real Hilbert space H and T : K 􀀀! K be a Lipschitz pseudo-contractive map. Let the sequence fxng1n =0 be dened by x0 2 K; xn+1 = (1 􀀀 n)xn + nTyn; (1.24) 8 yn = (1 􀀀 n)xn + nTxn; n 1; (1.25) where fng and fng are real sequences satisfying the following conditions: (i) 0 n n < 1 8n 1; (ii) P nn = 1; (iii) lim n􀀀!1 n = 0. Then, fxng1n =0 converges strongly to a xed point of T. Even though the recursion formulas (1.18) and (1.19) of the Ishikawa scheme have been successfully used in approximating xed points of Lipschitz pseudo-contractive mappings in real Hilbert spaces, when the domain of T is compact and convex the following question remained open. OPEN QUESTION: Has the simpler and more ecient Mann sequence failed to converge strongly to some xed point of a Lipschitz pseudo-contractive map in a Hilbert space, even when the domain of T is compact and convex? This question remained open for many years until 2001, when Chidume and Mu- tangadura constructed a counter example to show a Lipschitz pseudo-contractive map dened on a compact convex subset of R2 with a unique xed point for which no Mann sequence converges (see Chidume and Mutangadura, [19]). Browder and Petryshyn [15], (1967) introduced a class of Lipschitz pseudo-contractive maps which contains the class nonexpansive maps called the class of strictly pseudo- contractive maps. Let H be a real Hilbert space. A map T : H ! H is called strictly pseudo-contractive if for each x; y 2 H, jjTx􀀀Tyjj2 jjx􀀀yjj2+kjjx􀀀y􀀀(Tx􀀀Ty)jj2, for some k 2 (0; 1). For a real normed space E, T : E ! E is called strictly pseudo- contractive if each x; y 2 H, hTx 􀀀 Ty; x 􀀀 yi jjx 􀀀 yjj2 􀀀 jjx 􀀀 y 􀀀 (Tx 􀀀 Ty)jj2: In 2004, a striking result was proved by Chidume et.al. That for this class of strictly pseudo-contractive maps, the sequence given by (1.21) is an approximate xed point sequence for strictly pseudo-contractive maps. Furthermore, under an additional condition that T is demicompact, they proved that the sequence dened by (1.21) converges strongly to some xed point T. Infact, they proved the following theorem. Theorem 1.0.3. Let E be a real Banach space. Let K be a nonempty closed and convex subset of E. Let T : K ! K be a strictly pseudo-contractive map in the sense of Browder and Petryshyn with F(T) := fx 2 K : Tx = xg 6= ;: For a xed x0 2 K, dene a sequence fxng by xn+1 = (1 􀀀 n)xn + nTxn; n 0; where fng is a real sequence satisfying the following conditions: (i) 1P n=1 n = 1 and (ii) 1P n=1 2n < 1. If T is demicompact, then fxng converges strongly to some xed point of T in K. 9 Chapter 1. Introduction and literature review The following quotation further shows the importance of iterative methods for approximating xed points of nonexpansive mappings. \Many well-known algorithms in signal processing and image reconstruc- tion are iterative in nature. . . . A wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iteration procedure, for particular choices of the opera- tor. . . .”(Charles Byrne [18]). So far, we have seen the successes in approximating the solutions of (1.4) when the operator A is accretive. This is perhaps a result of numerous geometric properties of Banach spaces which play a crucial role.For example, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map of a real Hilber space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities: jjx + yjj2 = jjxjj2 + 2hx; yi + jjyjj2; (1.26) jjx + (1 􀀀 )yjj2 = jjxjj2 + (1 􀀀 )jjyjj2 􀀀 (1 􀀀 )jjx 􀀀 yjj2; (1.27) which hold for all x; y 2 H; are some of the geometric properties that characterize Hilbert spaces and also make certain problems posed in ahilbert spaces more man- agable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, \. . .many, and probably most mathematical objects and models do not naturally live in Hilbert spaces\. Consequently, to extend some of the Hilbert space techniques to more general Banach spaces, analogues of the identities (1.26) and (1.27) have to be developed. For this development, the duality map which has become a most important tool in nonlineaar functional analysis plays a central role. In 1976, Bynum [17] obtained the following analogue of (1.26) for lp spaces, 1 < p < 1: jjx + yjj2 (p 􀀀 1)jjxjj2 + jjyjj2 + 2hx; j(y)i; 2 p < 1 (1.28) (p 􀀀 1)jjx + yjj2 jjxjj2 + jjyjj2 + 2hx; j(y)i; 1 < p < 2 (1.29) Analogues of (1.27) were also obtained by Bynum. In 1979, Reich [45] obtained an analogue of (1.26) in uniformly smooth Banach spaces. Other analogues of (1.26) and (1.27) obtained in 1991 and later can be found, for example, in Xu [48] and Xu and Roach [49]. For the past 30 years or so, the study of Krasnoselskii-Mann iterative procedures for the approximation of xed points of nonexpansive maps and xed points of some of their generalizations, and approximation of zeros of accretive-type operators have been ourishing areas of research for many mathematicians. Numerous applications of analogues (1.26) and (1.27) to nonlinear iterations involving various classes of nonlinear operators have since then been topics of intensive research. Today, sub- stantial denitive results have been proved, some of the methods have reached their 10 boundaries while others are still subjects of intensive research activity. However, it is apparent that the theory has now reached a level of maturity appropriate for an examination of its central themes. Unfortunately, attempts to use these properties in approximating the solutions of (1.4) when A is of the monotone type have proved abortive and this is perhaps because of lack of the geometric properties in the spaces suitable for approaching such problems. Another reason is that only maps such as A : E ! E are related to xed points, also, the scheme is not well dened for A : E ! E: Fortunately, Alber [3] recently introduced the Lyapunov functional which has helped to develope new geometric properties suitable for monotone mappings. In this thesis, we use these properties to approximate solutions of Hammaerstein equations when the operators are maximal monotone. In the next section, we shall see how to approximate the solutions of Hammerstein equations (assuming existence). 1.0.2 Approximation of solutions of Hammerstein integral equations In general, equations of Hammerstein-type are nonlinear and there is no known method to nd close form solutions for them. Consequently, methods of approximat- ing solutions of such equations, where solutions are known to exist, are of interest. Let H be a real Hilbert space. A nonlinear operator A : H ! H is said to be angle-bounded with angle > 0 if hAx 􀀀 Ay; z 􀀀 yi hAx 􀀀 Ay; x 􀀀 yi (1.30) for any triple elements x; y; z 2 H. For y = z inequality (1.30) implies the mono- tonicity of A. A monotone linear operator A : H ! H is said to be angle bounded with angle > 0 if jhAx; yi 􀀀 hAy; xij 2hAx; xi 1 2 hAy; yi 1 2 (1.31) for all x; y 2 H. In the special case where one of the operators is angle-bounded, and the other is bounded, Brezis and Browder [4, 6] proved the strong convergence of a suitably dened Galerkin approximation to a solution of equation (1.6). In fact, they proved the following theorem. Theorem 1.0.4 (Brezis and Browder [6]). Let H be a separable Hilbert space and C be a closed subspace of H. Let K : H ! C be a bounded continuous monotone operator and F : C ! H be angle-bounded and weakly compact mapping. For a given f 2 C, consider the Hammerstein equation (I + KF)u = f (1.32) and its nth Galerkin approximation given by (I + KnFn)un = Pf; (1.33) 11 Chapter 1. Introduction and literature review where Kn = P nKPn : H ! C and Fn = PnFP n : Cn ! H, the symbols have their usual meanings (see [6]). Then, for each n 2 N, the Galerkin approximation (1.33) admits a unique solution un in Cn and fung converges strongly in H to the unique solution u 2 C of the equation (1.32). It is obvious that if an iterative algorithm can be developed for the approximation of solutions of equation of Hammerstein-type (1.6), this will certainly be a welcome approximate solutions of equations of Hammerstein-type using Mann-type iteration scheme (see e.g., Mann [41]). However, the results obtained were not satisfactory (see [31]). The recurrence formulas used in these attempts, even in real Hilbert spaces, involved K􀀀1 which is required to be strongly monotone when K is, and this, apart from limiting the class of mappings to which such iterative schemes are applicable, is also not convenient in any possible applications. Part of the diculties in establishing iterative algorithms for approximating solu- tions of Hammerstein equations is that the composition of two monotone maps need not be monotone. If A is linear, (1.2) reduces to hAx; xi 0; for all x 2 R2: Now let E = R2, take F = 1 1 􀀀1 1 ; K = 1 2 􀀀2 1 ; and x = 2 1 : Clearly, KF = 􀀀1 3 􀀀3 1 : Now, hFx; xi = 5; hKx; xi = 5 but hKFx; xi = 􀀀3: This shows that although F and K are monotone, KF is not. The rst satisfactory results on iterative methods for approximating solutions of Hammerstein equations involving accretive-type mappings, as far as we know, were obtained by Chidume and Zegeye [28, 29, 30]. Let X be a real Banach space and F;K : X ! X be accretive-type mappings. Let E := X X. Then, Chidume and Zegeye (see [29, 30]) dened A : E ! E by A[u; v] = [Fu 􀀀 v;Kv + u] for [u; v] 2 E: We note that A[u; v] = 0 if and only if u solves (1:6) and v = Fu: The authors dened an iterative sequence and obtained strong convergence theorems in the Cartesian product space E, for solutions of Hammerstein equations under various continuity conditions on F and K, for special classes of real Banach spaces, X. It turns out that, in the case of a real Hilbert space, H, the operator A dened on H H is monotone whenever F and K are. The method of proof used by Chidume and Zegeye provided the authors a clue for the establishment of the following coupled explicit iterative algorithm for computing a solution of the equation u + KFu = 0 in the original space, X. With initial vectors u0; v0 2 X, sequences fung and fvng in X are dened iteratively as follows: un+1 = un 􀀀 n(Fun 􀀀 vn); n 0; (1.34) 12 vn+1 = vn 􀀀 n(Kvn + un); n 0; (1.35) where fng is a sequence in (0; 1) satisfying appropiate conditions. The recursion for- mulas (1.34) and (1.35) have been used successfully to approximate solutions of Ham- merstein equations involving nonlinear accretive-type mappings (see e.g., Chidume and Djitte [25, 26], Chidume and Ofoedu [24], Chidume and Yekini [23], Chidume [20], and the references contained in them). In particular, the following theorems have been proved as generalizations of recent important results. Theorem 1.0.5. [Chidume, [27]] Let E be a uniformly smooth real Banach space with modulus of smoothness E, and let A : E ! 2E be a multi-valued bounded m􀀀accretive operator with D(A) = E such that the inclusion 0 2 Au has a solution. For arbitrary x1 2 E, dene a sequence fxng1n =1 by, xn+1 = xn 􀀀 nun 􀀀 nn(xn 􀀀 x1); un 2 Axn; n 1; where fng1n =1 and fng1 n=1 are sequences in (0; 1) satisfying the folliowing conditions: (i) limn!1 n = 0; fng1 n=1 is decreasing; (ii) P nn = 1; P E(nM1) < 1, for some constant M1 > 0; (iii) limn!1 h n􀀀1 n 􀀀1 i nn = 0. There exists a constant 0 > 0 such that E(n) n 0n. Then, the sequence fxng1 n=1 converges strongly to a zero of A. It is our purpose in this paper to use an analogue of Theorem 1.0.5 and approxi- mate a solution of (1.6) in the case where F and K are bounded maximal monotone mappings from E to E and E to E; respectively. Do you need help? 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# Electromagnetic Waves 1. Mar 10, 2005 ### Annie1011 I have a question given to me by my professor: Which statement is true concerning a sinusoidal varying electromagnetic wave? a) The energy in the wave is mostly associated with the electric field because the magnetic field has a very small value. The reason for this is that B=E/c and "c" is a large number (c=speed of light, 3*10^8 m/s) b) The momentum in the wave is zero because the wave continuously oscillates between positive and negative values. c) The average magnetic field in the wave is zero. d) The total energy in the wave is proportional to the sum of amplitudes of the electric and magnetic fields. e) The energy density in the wave is proportional to the amplitude of the magnetic field. f) The wave's intensity is inversely proportional to the energy density in the wave. So far I have ruled out b, e (it should be proportional to the square of the electric field), and f (it is directly proportional). Other than this progress I am stuck. So any advice on how to rule out any other answers, or if I have ruled out the incorrect answer would be greatly appreciated! I also have a question with an inductor that is connected to a sinusoidal varying voltage source, and one question asks for the reactance of the inductor, and I am caught up on the verbiage and do not know where to start. Thanks for your time and help! 2. Mar 11, 2005 ### Galileo For a) Apply the formula for the energy density of an electromagnetic field: $$u=\frac{1}{2}\left(\epsilon_0E^2+\frac{1}{\mu_0}B^2\right)$$ and the relation between E and B for your wave. 3. Mar 11, 2005 ### RoboSapien An amature question How to bend light using electrical fields or magnetic fields ? Since Light are electromagnetic waves. The answer to this question can be used to create most powerfull telescopes without refractions or mirrors. 4. Mar 12, 2005 ### Annie1011 I found out that the answer to this is c. Thansk for the replys! Annie	{}
# How to derive Infinitesimal Strain Tensor in Cylindrical Coordinates [closed] How can I obtain the below formulas of infinitesimal strain in cylindrical coordinates using matrix calculation given the first formula? I find it hard to study them because I still don't know how to derive them. \epsilon_{ij}=\frac{1}{2}\left(u\otimes\nabla+\nabla\otimes u\right)\\ \,\\ \begin{align} u\otimes\nabla &=\begin{bmatrix}u_r\\u_{\vartheta}\\u_z\end{bmatrix}\begin{bmatrix}\dfrac{\partial}{\partial r}&\dfrac{1}{r}\dfrac{\partial}{\partial\vartheta}&\dfrac{\partial}{\partial z}\end{bmatrix}\\\\ &=\begin{bmatrix}\dfrac{\partial U_r}{\partial r}&\dfrac{1}{r}\dfrac{\partial U_r}{\partial\vartheta}&\dfrac{\partial U_r}{\partial z}\\\\\dfrac{\partial U_{\vartheta}}{\partial r}&\dfrac{1}{r}\dfrac{\partial U_{\vartheta}}{\partial\vartheta}&\dfrac{\partial U_{\vartheta}}{\partial z}\\\\\dfrac{\partial U_z}{\partial r}&\dfrac{1}{r}\dfrac{\partial U_z}{\partial\vartheta}&\dfrac{\partial U_z}{\partial z}\end{bmatrix}\end{align} Above, I show my try in deriving the first part of the tensor, but I didn't know how to derive the second part. \begin{align} \varepsilon_{ij} &= \frac{1}{2} (U_{i,j} + U_{j,i})\\ \varepsilon_{rr} & = \cfrac{\partial u_r}{\partial r} \\ \varepsilon_{\theta\theta} & = \cfrac{1}{r}\left(\cfrac{\partial u_\theta}{\partial \theta} + u_r\right) \\ \varepsilon_{zz} & = \cfrac{\partial u_z}{\partial z} \\ \varepsilon_{r\theta} & = \cfrac{1}{2}\left(\cfrac{1}{r}\cfrac{\partial u_r}{\partial \theta} + \cfrac{\partial u_\theta}{\partial r}- \cfrac{u_\theta}{r}\right) \\ \varepsilon_{\theta z} & = \cfrac{1}{2}\left(\cfrac{\partial u_\theta}{\partial z} + \cfrac{1}{r}\cfrac{\partial u_z}{\partial \theta}\right) \\ \varepsilon_{zr} & = \cfrac{1}{2}\left(\cfrac{\partial u_r}{\partial z} + \cfrac{\partial u_z}{\partial r}\right) \end{align} • Hello! Please read How do I ask homework questions on Physics Stack Exchange? and edit your question accordingly. Thanks! – Jonas Mar 25 at 20:16 • It is not a homework... I just have a well known formula used in all textbooks of continuum mechanics but I'm not finding its derivation..... – user134613 Mar 25 at 20:17 • The homework-and-exercises-tag does not only apply to actual homework assignments, but also to homework-like questions. Please show what you have tried so far or if there is a specific step or concept that you are having troubles with. – Jonas Mar 25 at 20:22 • I have edited my question........ – user134613 Mar 25 at 20:36 • The first line in your formula $\varepsilon_{ij}=(1/2)(U_{i,j}+U_{j,i})= (1/2)(\partial_j U_I+ \partial_j U_)j$ applies only to Cartesian coordinates, unless by the comma you mean the covariant derivative. – mike stone Mar 25 at 21:08 In a coordinate system with metric $$g_{\mu\nu}$$ the strain due to an infinitesimal displacement $$\eta^\mu$$ is $$e_{\mu\nu} =\frac 12 ( \eta^\alpha \partial_\alpha g_{\mu\nu}+ g_{\mu \alpha}\partial_\nu \eta^\alpha + g_{\alpha \nu}\partial_\nu \eta^{\alpha})\\ \equiv \frac 12 [{\mathcal L}_\eta g]_{\mu\nu}$$ when $$g_{\mu\nu}=\delta_{\mu\nu}$$ this reduces to the Cartsian expression. You can also write $$[{\mathcal L}_\eta g]_{\mu\nu}= \nabla_\mu \eta_\nu+ \nabla_\nu \eta_\mu$$ where the $$\nabla_\mu$$ are the covariant derivatives in your chosen coordinates. • The first line in your formula $\varepsilon_{ij}=(1/2)(U_{i,j}+U_{j,i})= (1/2)(\partial_j U_I+ \partial_j U_j)$ applies only to Cartesian coordinates, unless by the comma you mean the covariant derivative. Try Googling strain and Lie derivative – mike stone Mar 25 at 21:09	{}
# What’s new in SOFiPLUS 2018¶ ## Cooperation with program SSD¶ User Defined Unitsets and US Customary Units are available via the system information dialog. For more clearness variables must have units. Name of elements and options have been harmonized. ## Geometric Axis¶ New efficient and comfortable dialogs. In the header of the table view one can find some basic buttons. Possibility to insert a whole table with copy and paste. In this case the number of lines in the table is completed as needed. ## Prestressing¶ ### Copy¶ Additional to the option clone tendons may now be copied. In this case an independent axis geomety with tendons will be generated. ### Polishing¶ In the sidebar now the name of the duct and the tendon is shown. ## Structural Elements¶ ### Cooperation with analysis¶ • Handling with materials, cross sections, work laws, etc. has been harmonized with the SSD. • Customised input options for dialogs including spring information. They have been harmonized to the input possibilities in SOFiMSHC • Additional intersection properties for the structrual line and structural area analogous to program SOFiMSHC. • Improved possibilities for structrual lines and structural areas to control the density during meshing. ### Other¶ • Some of the structural element dialogs including a table have been revised to the more comfortable kind of table. • It is now possible to create more than one spring or contraint between structural lines or between structural lines and structural points at once. • A new option for the alignment of structural areas out of AutoCAD meshes. • Load eccentricity for structural line loads. This is used to define the position of the load relative to a point within the section of the line. • New dialog for the load distribution area. ## Usability¶ ### Cooperation with REVIT¶ • Improved cooperation respective the precision between REVIT and SOFiPLUS. Databases out of REVIT can now be imported in a better quality. ### View¶ • Additional views group visualisation to displays the structural element groups with different colors. ## Cross Section Editor¶ • Solid Sections: Polygons which have circles or arcs are described with intersections of tangens and radius. • Circular reinforcement: Definition of linear reinforcements for circles and arcs • Reference for the insertion point of a steel profile • Steel cross section for section class 4: Determination of the effective cross section values with definition of a compressive stress ## Compatibility¶ SOFiPLUS/SOFiPLUS-X 2018 can open DWG files from version 2016. After saving in version 2018, the DWG files cannot be re-opened in the older version! SOFiPLUS/SOFiPLUS-X 2018 can import projects from version 2018 only. SOFiPLUS/SOFiPLUS-X may have to convert and/or upgrade data when opening a DWG. Any issues, warnings or errors will be displayed in the Messages tab in the sidebar. ## Important Hints¶ Explicit drawing units have been discontinued with SOFiSTiK 2018. Please choose an appropriate Unit Set instead. The direct finite element workflow for system input within SOFiPLUS has been discontinued with SOFiSTiK 2018. Please use the structural element workflow to define your system.	{}
# Definition of open set in topology A topological space is a set X together with T, a collection of subsets of X, satisfying the following axioms: 1.The empty set and X are in T. 2.The union of any collection of sets in T is also in T. 3.The intersection of any finite collection of sets in T is also in T. The sets in T are the open sets I can't see how it can become the open set definition in metric space. Say,in 2-D Euclidean space,let X be a circle with all its interior points, then a trivial topology is T={{}, X}, it seems not to contradict to the axioms, but X is a closed set , can anybody help me clarify this? Thanks in advance. matt grime Homework Helper There is nothing that prevents a set being both open and closed. In particular the empty set, and the whole space are always both open and closed. Last edited: So any closed curve with its interior points can defined to be open? Then what's the difference between open and closed set? I still can't understand . matt grime Homework Helper A topology defines the open sets, and they obey the rules of being 'open'. A set is closed if and only if its complement is open. There are many ways of doing this to create different topologies - you seem to want there to be only one topology on a set. Consider R the set of real numbers. The following are all topologies: T:= { {}, R } the trivial topology. There are only two open sets, and correspondingly two closed sets. T:= P(R), the power set or the set of all subsets of R. This is called the discrete topology - all sets are open and all sets are closed. T, the metric topology - open sets are arbitrary unions of open intervals. And the closed sets are what you think they are - arbitrary intersections of closed intervals. Define S:={ x : f(x)=0 for some real polynomial f} these form the closed sets of a topology on R, called the Zariski topology. In this case S is equivalent to the set of all finite subsets of R, so T, the set of complements of things in S, is the set of all sets whose complements are finite. This is also called the cofinite topology. Now, take some set X in R. It does not make sense to just ask 'is X open?' it only makes sense to ask 'is X open in a particular topology?' Well, I think I'm starting to get it, thanks a lot for the detailed answer, impressive matt grime Homework Helper I misdefined the zariski topology. I should have said: given a real poly f, define zeros(f) to be the set of zeros of f, then { zeros(f) : f a real poly } form the closed sets for a topology on R. HallsofIvy Homework Helper A topological space is a set X together with T, a collection of subsets of X, satisfying the following axioms: 1.The empty set and X are in T. 2.The union of any collection of sets in T is also in T. 3.The intersection of any finite collection of sets in T is also in T. The sets in T are the open sets I can't see how it can become the open set definition in metric space. Say,in 2-D Euclidean space,let X be a circle with all its interior points, then a trivial topology is T={{}, X}, it seems not to contradict to the axioms, but X is a closed set , can anybody help me clarify this? Thanks in advance. I am a bit confused by this. You seem to be asking about metric spaces but then give, as an example, "let X be a circle with all its interior points, then a trivial topology is T={{}, X}" which is NOT a metric topology. In any case, it is always the case that the empty set and the entire set itself are both open and closed. In fact, if you were to use the "discrete topology" in which all subsets of X are in the topology, then all subsets of X would be both open and closed. I am a bit confused by this. You seem to be asking about metric spaces but then give, as an example, "let X be a circle with all its interior points, then a trivial topology is T={{}, X}" which is NOT a metric topology. In any case, it is always the case that the empty set and the entire set itself are both open and closed. In fact, if you were to use the "discrete topology" in which all subsets of X are in the topology, then all subsets of X would be both open and closed. You exactly pointed out where I got lost:When I tried to understand open set in "common sense"(metric space), I should have used the metric topology to define the space.I didn't realize that I must associate a metric topology with a space before calling it a metric space. I'm really a newb in topology and I'm still struggling with some very basic questions. Thanks everyone for the nice explanation. Anyone care to point out if the following is correct or not ? 1. An open set in a metric space is NEVER a closed set in ANY metric space.[/quote] Given any set X, d(x,y)= 0 if x= y, 1 if $x\ne y$ is a metric. ALL subsets of X are both open and closed in that metric. 2. An open set in a metric space CAN be a closed set in some other topological space It's not clear what you mean by this. Do you mean two different topologies on the same space? For a finite set, at least, given any topology, you can define a new topology by taking all closed set in the first topology to be the open sets in the new topology. 3. An open set in a topological space CAN be a closed set in the same topological space Yes. See your question 1. In fact, in ANY topological space, both the empty set (maze's suggestion) and the entire set itself are both open and closed. Thanks a lot Last edited by a moderator: Consider {}	{}
How do I know if the linear system has a line of intersection? I was wondering how can I determine if there is a line of intersection with any matrix? For example, if I have the following matrix: $$\left(\begin{array}{rrr\|r} 1 & -3 & -2 & -9 \\ 2 & -5 & 1 & 3 \\ -3 & 6 & 2 & 8 \\ \end{array} \right)$$ What does the solution have to look like for me to conclude that there is a line of intersection? P.S. I know this matrix has a point of intersection but I used this as an example because I didn't know an example for a matrix that had a line of intersection. - If there are infinitely many solutions, then you are guaranteed to find a line (more generally subspace) of solutions. An equivalent condition is if the rank of the matrix is not full, and at least 1 solution exists. – Calvin Lin Jun 11 '13 at 14:03 The existence of a "point of intersection" is the existence of a point $(x, y, z)$ that satisfies the system of equations: a point lying on each line represented by the corresponding system of equations: \begin{align} x - 3y -2z & = -9 \\ 2x - 5y + z & = 3 \\ -3x + 6y + 2z & = 8 \end{align} A unique solution exists (a single point of intersection exists) if the augmented matrix does not reduce to a row of all zeros, and no row has all zeros, augmented by a non-zero entry. If you obtain a row of all zeros, through row reduction, then infinitely many points of intersection occur (two or more lines will be concurrent): the entries in one or more lines will be a scalar multiple of the entries of another. Put differently, there will be a line of intersection. If the matrix reduces to a row of three zeros, with a non-zero entry in the last column of that row, no solution exists (i.e., no point of intersection exists.) All these possibilities can be determined by reducing the matrix to row echelon form. We can reduce your example matrix: $$\left(\begin{array}{rrr\|r} 1 & -3 & -2 & -9 \\ 2 & -5 & 1 & 3 \\ -3 & 6 & 2 & 8 \\ \end{array}\right)$$ $$\left(\begin{array}{rrr\|r} 1 & -3 & -2 & -9 \\ 0 & 1 & 5 & 21 \\ 0 & 0 & 11 & 42 \\ \end{array}\right)$$ If reduced further, you'd see that the system represented by the system of equations has a unique point of intersection, hence no common line of intersection. Note that if the last row were $(0\;\;2\;\;10\;\;42)$, we could "zero it" by taking $-2R_2 + R_3 \rightarrow R_3$, and obtain a row of all zeros, since the third row would be a scalar multiple of the second row. In that event, there would indeed be a line of intersection. If any row is a linear combination of the other rows, we have a linearly dependent system of equations: this shows when a row-reduced matrix has a row of all zeros. And in that case, there is at least a line of intersection. - So if the third row of the system is a multiple of the second row or the first row then there is a line of intersection? I'm confused about how it would look in terms of $x$'s and $y$'s and $z$'s. Because for a the final answer for a P.O.I I would just write the solution but what would I write for a L.O.I? – Jeel Shah Jun 11 '13 at 14:43 Very nice Amy and good morning $\ast$ – Babak S. Jun 11 '13 at 14:44 @gekkostate What one typically does is set, say, $z = \alpha$, where $\alpha$ is any real number. Then express $x, y$ as values in terms of $z = \alpha$. So say you reduce the matrix to the rows the first two rows in the above row-reduced matrix, but the last row is all zeros. Then the solution is given by $z = \alpha, y = 21 - 5 \alpha, x = -9 + 2\alpha + 3(21 - 5\alpha)$, simplifying x, of course. $\alpha$ is then called a parameter. – amWhy Jun 11 '13 at 14:56 Some use the parameter $t$ instead of $\alpha$. This post gives an example of such a system: infinite number of solutions. – amWhy Jun 11 '13 at 15:02 If you are familiar with ranks and Rouché-Capelli (RC) theorem, the following reasoning can be used to answer. The system $A\mathbf x=\mathbf b$, where $A$ is an $n\times m$ matrix, has solutions if and only if $$r(A)=r(A\|\mathbf b)=r,$$ and in this case you have "$\infty^{n-r}$" solutions. This really means that your solutions depend on $n-r$ free parameters. So, if the rank $r=n-1$, your solution set depends on $n-(n-1)=1$ free parameter or, in other words, it's monodimensional. This helps the intuition that the solution set is indeed a line in this case. Hence, you'll get a line of solutions when the rank of the complete matrix $r$ is equal to the number of unknowns $n$ less 1. As an example, consider the system \begin{align} x - y & = 2 \\ -2x +2y &=-4 \end{align} The rank $r(A)=r(A\|\mathbf b)=1$ and you can indeed write the solutions set as $x=2+t,y=t$, which is equal to the set of points on the line $y=x-2$. A more interesting example (I like a lot $A$!) is \begin{align} x +y +z& = 6 \\ 4x +5y +6z&=15\\ 7x+8y+10z&=24 \end{align} The reduced complete matrix is $$\left(\begin{array}{rrr\|r} 1 & 2 & 3 & 6 \\ 0 & -3 & -6 & -9 \\ 0 & 0 & 0 & 0 \\ \end{array}\right)$$ from which you get the solutions $(x=t,y=3-2t,z=t), \forall t$. The solution set can be described in terms of a unique parameter $t$ and it is a straight line in $\mathbf R^3$. -	{}
## Magnetic Morris-Thorne wormhole in 2+1-dimensions 15 Mar 2017 · Mazharimousavi S. Habib, Amirabi Z., Halilsoy M. · In the context of $2+1-$dimensional gravity coupled to a particular nonlinear electrodynamics (NED), we obtain a class of traversable / Morris-Thorne type wormhole solutions. The problem is reduced to a single function dependence in which the shape function acts as generator to the wormholes... The field ansatz is pure magnetic and the nonlinear Lagrangian is $\sqrt{F_{\mu \nu }F^{\mu \nu }}$ i.e. the square root of the Maxwell Lagrangian. In $2+1-$dimensions the source-free pure magnetic non-linear Maxwell equation with square-root Lagrangian is trivially satisfied. The exotic energy density is found explicitly and the flare-out conditions are emphasized. read more PDF Abstract # Code Add Remove Mark official No code implementations yet. Submit your code now # Categories General Relativity and Quantum Cosmology	{}
## Polynomial Hirsch Conjecture There is a very interesting Polymath project going on right now: Polymath3. It is about the polynomial Hirsch conjecture. As I feel like contributing, I am going to temporarily post my ideas as comments of this post before copying them over to the main blog (in order not to pollute the blog with half-baked ideas). This entry was posted in Uncategorized. Bookmark the permalink. ### 11 Responses to Polynomial Hirsch Conjecture 1. I have looked at the proof of the upper bound for $f^(d,n)$ (ie Lemma 1 and Corollary 1 of Polymath3) and I had the following idea which does not quite work but may inspire others: As usual, we start with a sequence of $d$-uniform multiset families $F_1,\ldots,F_t$. Let’s partition the sequence $F_1,\ldots,F_t$ into intervals in the following way: We first pick a random element say $x_1$ of the support of $F_1$ and denote by $I_1$ the interval $[1,i_1]$ where $i_1$ is the last index of an $F_i$ containing $x_1$. Then we pick a new element $x_2$ in the support of $F_{i_1+1}$ and denote by $I_2$ the interval $[i_1+1,i_2]$ where $i_2$ is the last index of an $F_i$ containing $x_2$. And so on until the end. By definition, after $i_k$, $x_k$ cannot appear anymore since when one element is removed from the support it cannot be added again. This means that our sequence of intervals $I_k$ can contain at most $n$ elements. Also, if we restrict the $F_i$ for $i \in I_k$ by excluding $x_k$, we get a convex sequence of $d-1$-uniform multiset families. So we have as in the original proof $f^(d,n)\le \sum_{k} f^(d-1,\|S_k\|)$. Now assume that we would be able to prove that $\sum_{k} \|S_k\| \le 2n-1$, then together with the fact that we have at most $n$ intervals, and using the induction hypothesis of $f^(d-1,n)\le (d-1)(n-1)+1$, then we would obtain $f^(d,n)\le (d-1)(\sum_k\|S_k\| - n) + n \le (d-1)(2n-1-n)+n = d(n-1)+1$. So this would give exactly the right bound, but there are two things that do not exactly work: 1. The first one is that this is valid only if we have exactly $n$ intervals. 2. The second one is that we need to prove that $\sum_k \|S_k\|\le 2n-1$ which is not as easy as in the original proof since we don’t have disjointness for non-consecutive intervals. But the interesting point that this illustrates is that if one can decompose the sequence into exactly $n$ intervals with the property that each interval contains at least one common element and that $\sum_k \|S_k\|\le 2n-1$, then we can prove the bound $f^(d,n)\le d(n-1)+1$. How realistic is such a construction? 2. Another way to formulate the above is the following: if we can always decompose the sequence $[1,t]$ into intervals such that $\sum_k (\|S_k\|-1)\le n-1$ and $k\le n$ then we can prove Nikolai’s conjecture (I am using here the notation of Corollary 1 of Polymath3). Note that since the intervals satisfy the condition that the $F_i$ in intervals $I_k$ don’t contain the common element in $I_\ell$ for any $\ell < k$, then $k$ has to be smaller than $n$. So only the sum condition needs to be verified. It seems that this is the case (on some simple examples I looked at), provided one can construct the sequence without being forced to start at one end. So in other words, we need to find a decomposition which minimizes $\sum_k (\|S_k\|-1)$, and on some examples this seems to be possible and yield the desired properties. {11111, 11112, 11123, 11234, 12345, 23455, 34555, 45555, 55555} In this case, if you consider all the subsequences whose support contain one particular element, summing up Nikolai’s bound for them (ie if you consider that there length is bounded by f^(d-1,k) for some appropriate k) gives a total length that is always larger than f^(5,5), no matter how the sequence is decomposed. So this decomposition approach does not seem to allow to prove Nikolai’s conjecture but only a weaker upper bound. 3. Gil Kalai says: Thanks for participating, Olivier 4. Here is a different approach to the problem. I am considering the following equivalent formulation: given a down-set $D\subset 2^{[n]}$ (which is nothing but the union of the $F_i$ since one can always add subsets of the existing elements of $F_i$ to complete it into a down-set), the convexity and disjointness condition corresponds to the existence of a labeling function $\ell: D\to \mathbb{N}$ which is such that for any $S\in D$, $\ell$ maps the set $\{T \in D: S\subset T\}$ to an interval. In this formulation, the question is how large can the interval $\ell(D)$ be? Let’s call this the diameter of $D$, denoted by $d(D)$ and defined as $\max_{\ell} \max_{S,T\in D} \ell(S) - \ell(T)+1$. It seems that the maximal elements of $D$ play a crucial role in controlling this diameter. Let’s call $M(D)$ the set of maximal elements of $D$. A simple case is when $M(D)$ is a singleton, say $M(D)=\{S_0\}$. Indeed in this case, one can easily prove that $d(D)\le 2\|S_0\|$ (this corresponds to the case where one of the $F_i$ contain $[n]$ which gives $t\le 2n$ in the standard formulation). Similarly, it seems that when $M(D)=\{S_1, S_2\}$ one can prove $M(D)\le \|S_1\|+\|S_2\|+\|S_1\Delta S_2\|$. However, the situation becomes quickly tricky when one considers three elements. • One can further generalize this approach in the following way: The down-set we start with can be replaced by any arbitrary directed graph, and the goal is then to find a map $\ell$ from this directed graph $G_1$ to some undirected graph $G_2$ with the following properties: if we consider the set $R(x)$ of elements of $G_1$ that are reachable from $x$, then we want the induced subgraph $G_2(\ell(R(x)))$ to be connected, and we want $G_2$ to be of maximum diameter. 5. In the above formulation (diameter of down-sets), I am wondering whether there is always a way to order the elements of $2^{[n]}$ in a sequence $S_1,\ldots, S_{2^n}$ such that each $\{S_1,\ldots S_i\}$ forms a down-set, and such that the diameters of these sets are monotonously increasing from $1$ up to $f(n)$ and then monotonously decreasing to $2n$. For example for $n=2$, this sequence does it: $\emptyset, 1, 2, 12$ (with diameters $1, 2, 3, 4$). For $n=3$, this sequence $\emptyset, 1, 2, 3, 12, 23, 13, 123$ has diameters $1, 2, 3, 4, 5, 6, 6, 6$. The case $n=5$ is where things are likely becoming interesting since we know that $f(5)>10$. • Following up on this idea, if one considers a down-set and looks at the effect on its diameter to add or remove one element (assuming this is done so that the resulting set is still a down-set), we can observe the following: when adding an element of size $k$, it connects to $k$ elements of size $k-1$. If those elements of size $k-1$ were all maximal, this means we introduced the constraint that they all have to be at distance one of the new element which means we cannot increase the diameter (although we also allow them to space out a bit if they were within distance 1 of each other). • A related notion that is potentially interesting to study is the following: given a down-set $D\subset 2^{[n]}$, one can define the $k$-diameter of this down-set as the diameter restricted to its $k$ sets: $d(D,k)=\max_\ell \max_{S,T\in D,\, \|S\|=\|T\|=k} \ell(S)-\ell(T)+1$. With this definition, we obviously have $d(D,n)=1$ and we can prove easily that $d(D,n-1)\le 3$ and it seems that $d(D,n-2)\le 5$ although I don’t have a proof for it yet. It would be interesting to study the function $g(n,k)$ defined as the maximum $k$-diameter for down-sets over $n$ elements. 6. Regarding the proof of $f^(d,n)\le 2^{d-1}(n-1)+1$, here are a few observations: 1. For $d=2$, this gives a tight bound, which means that the decomposition with respect to 1-shadows is optimal for this value of $d$. 2. One interesting aspect of the decomposition is that the supports of the segments, ie the sets $S_k$ are in number at most $n$ and satisfy $\sum_k \|S_k\|\le 2n-1$ which is effectively $f^(2,n)$. Can these be generalized somehow? In particular, can one decompose a convex sequence of 3-uniform multisets with respect to its 2-shadows? • The starting point of a $r$-shadow generalization of Corollary 1 of the wiki is to replace supports by $r$-shadows in Lemma 1. Note that if we consider, for each of the $r$-shadows, the indices at which they appear and then disappear in the sequence (they span intervals so this is well defined), and order them by the interval order (first by when they appear and then by when they disappear), then this forms a convex sequence of $r$-uniform singleton multiset families, whose length is thus bounded by $f^(r,n)$, which means that the number of intervals $m$ in the partition is at most $f^(r,n)$. Then, if we use this generalized Lemma as in the proof of Corollary 1, we have to bound the sum of the supports $\sum_k \|S_k\|$. If we sum the number of $r$-shadows instead of the sum of the number of $1$-shadows, because of the generalized Lemma 1, we know that this is upper bounded by $2f^*(r,n)-1$, but the number of $r$-shadows is larger than the number of $1$-shadows for $r. Ideally we would want to show that for $r=d-1$ we have $\sum_k \|S_k\|\le d(n-1)+1$.	{}
How do you use the binomial series to expand (1-2x)^(1/3)? Dec 8, 2016 The answer is $= 1 - \frac{2}{3} x - \frac{4}{9} {x}^{2} - \frac{40}{81} {x}^{3} - \ldots .$ Explanation: The binomial series is ${\left(a + b\right)}^{n} = {a}^{n} + n {a}^{n - 1} b + \frac{n \left(n - 1\right)}{1 \cdot 2} {a}^{n - 2} {b}^{2} + \frac{n \left(n - 1\right) \left(n - 2\right)}{1 \cdot 2 \cdot 3} {a}^{n - 3} {b}^{3} + \frac{n \left(n - 1\right) \left(n - 2\right) \left(n - 3\right)}{1 \cdot 2 \cdot 3 \cdot 4} {a}^{n - 4} {b}^{4} + \ldots .$ In our case, we have ${\left(1 - 2 x\right)}^{\frac{1}{3}}$ $a = 1$ $b = - 2 x$ $n = \frac{1}{3}$ So, ${\left(1 - 2 x\right)}^{\frac{1}{3}} = 1 - \frac{1}{3} \cdot 2 x - \frac{1}{3} \cdot \frac{2}{3} \cdot \frac{1}{2} {\left(- 2 x\right)}^{2} - \frac{1}{3} \cdot \frac{2}{3} \cdot \frac{5}{3} \cdot \frac{1}{6} {\left(- 2 x\right)}^{3} - \ldots$ $= 1 - \frac{2}{3} x - \frac{4}{9} {x}^{2} - \frac{40}{81} {x}^{3} - \ldots .$	{}
# Solution to Linear First Order Ordinary Differential Equation/Solution by Integrating Factor ## Proof Technique The technique to solve a linear first order ordinary differential equation in the form: $\dfrac {\d y} {\d x} + \map P x y = \map Q x$ It immediately follows from Integrating Factor for First Order ODE that: $e^{\int \map P x \rd x}$ is an integrating factor for $(1)$. Multiplying it by: $e^{\int \map P x \rd x}$ to reduce it to a form: $\dfrac {\d y} {\d x} e^{\int \map P x \rd x} y = e^{\int \map P x \rd x} \map Q x$ is known as Solution by Integrating Factor. It is remembered by the procedure: Multiply by $e^{\int \map P x \rd x}$ and integrate. ## Examples ### Example: $y' - 3 y = \sin x$ $\dfrac {\d y} {\d x} - 3 y = \sin x$ has the general solution: $y = \dfrac 1 {10} \paren {3 \sin x - \cos x} + C e^{3 x}$ ### Example: $y' + y = \dfrac 1 x$ Consider the linear first order ODE: $(1): \quad \dfrac {\d y} {\d x} + y = \dfrac 1 x$ with the initial condition $\tuple {1, 0}$. This has the particular solution: $y = \ds e^{-x} \int_1^x \dfrac {e^\xi \rd \xi} \xi$	{}
# How to calculate the weight individual fractions to equal the weighting of the product of the same fractions What is the formula to apply a weighting to 2 fractions individually to get the same answer if you weight their product? In the example below 50% * 100% = 50%. Multiplied times 80% (weighting) the answer is 40%. What formula can be used to multiply 50% and 100% individually to also arrive at 40% when you multiply the result. Example: (50% * A) = X and (100% * B) = Y; and X * Y = 40%. I am looking for the formula to arrive at A and B. Value 1 50.0% Value 2 100.0% Product of 1 and 2 50.0% Weighting 80% Weighting * Product 40% Weighting A? X = Value 1 * Weighting A B? Y = Value 2 * Weighting B X * Y = 40% - The question's phrasing is a bit difficult to follow, could you try to re-phrase the question? The last line is specially confusing. – NoChance Oct 8 '12 at 22:29 There is more than one answer. So for example if A=80% and B=100% then you have (50% * 80%) * (100% * 100%) = 40% Or if A=100% and B=80% then you have (50% * 100%) * (100% * 80%) = 40% Or if A=B=89.4427191% then you have (50% * 89.4427191%) * (100% * 89.4427191%) = 40% or very close to it, noting that $\sqrt{0.8} \approx 0.894427191$. The only important thing is that A*B=80%, since multiplication is commutative. - Thanks! I was looking for the number where A=B, but did not specify. I appreciate the help. – user44051 Oct 9 '12 at 1:37	{}
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# The 4200 km trip from new york to san francisco takes 7 h flying against the wind, but only 6 h returning. How do you find the speed of the plane in still air and the wind speed? Apr 26, 2017 Plane speed $= 514 \frac{2}{7} \text{ Km/h" } \approx 514.286$ to 3 decimal places Wind speed $= 85 \frac{5}{7} \text{ Km/h } \approx 85.714$ to 3 decimal places #### Explanation: To solve these equations we need to manipulate so that we have just 1 unknown and its relationship to some values. Assumption: the speed (velocity) of the wind is constant Let the speed of the plane be $p$ Let the speed of the wind be $w$ Let time going be in hours be ${t}_{g} \to 7 h$ Let the time returning in hours be ${t}_{r} \to 6 h$ Note that speed = $\left(\text{distance")/("time}\right)$ So $\text{distance "="time "xx" speed}$ Consider going: relative to the ground, the actual speed is $p - w$ Consider returning: relative to the ground the actual speed is $p + w$ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Determine the ratio of wind speed to plane speed}}$ We need this to change things so that, by substitution, we end up with just 1 unknown. So for going we have: $\text{ "4200=7xx(p-w)" } \ldots \ldots \ldots E q u a t i o n \left(1\right)$ And for returning we have: $\text{ "4200=6xx(p+w)" } \ldots \ldots \ldots \ldots E q u a t i o n \left(2\right)$ Equation both to each other through distance $7 \times \left(p - w\right) = 4200 = 6 \times \left(p + w\right)$ $7 \times \left(p - w\right) = 6 \times \left(p + w\right)$ $7 p - 7 w = 6 p + 6 w$ Subtract $6 p$ from both sides $7 p - 6 p = 0 + 6 w$ $p = 6 w \text{ } \ldots \ldots \ldots . . E q u a t i o n \left(3\right)$ $w = \frac{p}{6} \text{ } \ldots \ldots \ldots . . E q u a t i o n \left(4\right)$ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{Determining the actual speeds}}$ Using Equation(3) substitute for $p$ in Equation(1) giving $4200 = 7 \left(p + w\right) \text{ "->" } 4200 = 7 \left(6 w + w\right)$ $\text{ } 4200 = 49 w$ $w = \frac{4200}{49} = 85.71428 \ldots . = 85 \frac{5}{7} \text{ Km/h}$ Using Equation(4) substitute for $w$ in Equation(1) giving $4200 = 7 \left(p + w\right) \text{ "->" } 4200 = 7 \left(p + \frac{p}{6}\right)$ $\text{ } 4200 = \frac{49}{6} p$ $p = \frac{6 \times 4200}{49} = 514.2857 \ldots = 514 \frac{2}{7} \text{ Km/h}$	{}
# Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected? Let for an open connected subset $U\subset \mathbb R^n$ and a number $\varepsilon >0$: $$U_\varepsilon=\{x\in U: dist (x, \partial U)> \varepsilon \}.$$ Then $U_\varepsilon$ is open but in general not connected. But I suppose that for sufficiently small $\varepsilon >0$ also $U_\varepsilon$ is connected. How to prove its? Edit. Let's assume that additionally $U$ is bounded. Is then $U_\varepsilon$ connected? • You "suppose" wrong. I think you should be able to prove it if you assume $U$ is bounded as well. – Dustan Levenstein Jul 15 '14 at 15:28 • Not sure about that though. Counterexample for $U$ unbounded: In $\mathbb R^2$, have a series of balls of radius $1/4$ centered at each integer $(n, 0)$ for $n \in \mathbb N$, and connect them by progressively skinnier "necks". – Dustan Levenstein Jul 15 '14 at 15:30 • Thanks. I forgot about boundedness. – Alex Jul 15 '14 at 15:33 • You can probably concoct a similar counterexample for $U$ bounded as well though. Think something similar to the Mandelbrot set: It has a skinny nose on the real axis with progressively smaller balls placed along it. – Dustan Levenstein Jul 15 '14 at 15:36 Let $$U=\bigcup_{n=1}^\infty B\left((2n+2^{-n},0),1\right)$$ Then $U$ is connected, but for $0<\epsilon<1$, we find that for all $n$, the ball $B((2n+2^{-n}),1-\epsilon)$ is contained in $U_\epsilon$, but for sufficiently large $n$ there is a gap between the $n$th and the $(n+1)$st ball. Indeed, by Pythagoras the width "neck" between consecutive balls is $$\sqrt{2^2-\left(2+2^{-(n+1)}-2^{-n}\right)^2}=\sqrt{2^{-n}-2^{-2(n+1)}}\approx 2^{-n/2}\to 0$$ and hence $<2\epsilon$ for $n$ big enough. The problem has changed to add the assumption that $U$ be bounded. Consider (make a sketch!) $$\bigcup_{n=1}^\infty B((2^{-n},0),2^{-n-2})\cup\{\,(x,y)\mid \|y\|<x^2<1 \}$$ Now for given (small) $\epsilon>0$, find $n$ such that $2^{-n-2}>2\epsilon\ge 2^{-(n+1)-2}$, i.e. the $n$th ball is the last one contributing to $U_\epsilon$. Let $x_0=\sqrt2\cdot 2^{-n}$. Then $x_0>2^{-n}+2^{-n-2}=\frac542^{-n}$ and $x_0<2^{-(n-1)}-2^{-(n-1)-2}=\frac32 2^{-n}$, i.e. $x_0$ is between balls $n$ and $n-1$. At this position, the "bridge" is only $2x_0^2=2^{1-2n}$ wide and this is $<2\epsilon$ as soon as $n\ge 4$.	{}
Aright rectangular prism has a length of 214 cm, width of 8 cm, and height of 2012 cm. what is the volume Aright rectangular prism has a length of 214 cm, width of 8 cm, and height of 2012 cm. what is the volume of the prism? enter the answer in the box. cm³ 9. Find the area of a circle having a circumference of 382. Round to the nearest tenth. Use 3.14 for 1. a. 1133.5 units b. 1078.6 1. yyyyyy290 says: The volume is 21482012 =3,444,544 2. ayrias says: V=LWH V=214(8)2012=3444544 cm^3 3. drejones338p04p2p says: Vol of prism = area of base * height = 2148 2012 = 3444544 cubic cm	{}
# Highlights from LHCb experiment Europe/Rome Aula Seminari (LNF INFN) ### Aula Seminari #### LNF INFN Via Enrico Fermi, 40 00044 Frascati Description The talk will review the main results on flavour physics of the LHCb experiment. The LHCB detector is a spectometer with acceptance covering the forward pseudorapidity region 2 eta 5. It is designed primarily to study the properties of heavy-flavoured hadrons produced in pp collisions at the LHC. By studying rare decays and CP violation effects, LHCB can make precise tests of the Standard Model and search for new physics hints. The status of the experiment and a selection of the LHCb measurement will be presented, including the latest results from the 1/fb data sample collected in 2011. The agenda of this meeting is empty	{}
# Interpreting the change in random effect variance over time in a GLMM I am measuring the change in random effect (random intercept) over time by running models such as using different subset=(yr=20??) for each year. In the comments to my other question, it was stated that another way to do this was to use dummy variables for each year, and specify them in the model as random slopes, thus: where i1...i6 are the indicator variables of the different years. My question is: how is the output of this model to be interpreted in terms of the longitudinal change in random effects variance ? - Joe, the two are not exactly equivalent - in your first approach, the fixed effects are also allowed to vary by year. In the second one, they are not. I don't have time to give a detailed answer right this minute but I will later if you haven't already received one. I've also edited your title to something that I think more completely captures the spirit of your question - feel free to change it if you disagree. – Macro Jun 14 '12 at 15:25 @Macro , thanks, that's fine, and yes, I understood that they are not exactly equivalent. I prefer the 2nd approach (if I can understand it!) because it avoids the problem of the fixed effects changing even though they don't change much (by the overlapping confidence intervals measure), and it seems more parsimonious. Even if it is not "better" I would still like to understand it. – Joe King Jun 14 '12 at 15:34 glmer(bull~p1+p2+p3+p4+p5+(i1+i2+i3+i4+i5+i6-1\|school),data=bull, family=binomial) fits the binary logistic random effects model: $$\log \left( \frac{p_{ij}}{1-p_{ij}} \right) = \beta_0 + \sum_{k=1}^{5} \beta_k x_{ijk} + \sum_{t=1}^{6} \eta_{jt} I_{t}$$ where • $p_{ij}$ is the probability that subject $i$ in cluster $j$ responds with a '$1$', conditional on the covariates and random effects. • $x_{ijk}$ is the value of covariate $k$ for subject $i$ in cluster $j$ (according to your code there are $5$ covariates). • $\beta_0, ..., \beta_5$ are fixed effects regression coefficients • $\eta_{jt}$ is the cluster $j$ random effect for year $t$ • $I_t$ is $1$ if the observation was taken in year $t$ and 0 otherwise (according to your code there are $6$ years) We can see that the distribution of an observation taken in year $t$ is described by the model $$\log \left( \frac{p_{ij}}{1-p_{ij}} \right)= \beta_0 + \sum_{k=1}^{5} \beta_k x_{ijk} + \eta_{jt}$$ Let $\sigma^{2}_{t} = {\rm var}(\eta_{jt})$ be the random effect variance for year $t$. Since this model allows that random effect variance to change over time, as indicated by the subscript $t$, the level of similarity between responses within the same cluster is also allowed to change over time. As I discussed in this answer, the value $$P_{t} = \frac{ \sigma^{2}_{t} }{ \sigma^{2}_{t} + \pi^2/3}$$ is a measure of the how similar individuals sharing a cluster are, in terms of their responses, at year $t$. Your model produces estimates, $\hat \sigma^{2}_{t}$, of the random effect variances - which you can use to calculate $$\hat P_{t} = \frac{ \hat \sigma^{2}_{t} }{ \hat \sigma^{2}_{t} + \pi^2/3}$$ Plotting $\hat P_t$ vs. $t$ will give you an idea whether the (linear) dependencies are increasing, decreasing, remaining constant, etc. over time, which is gets directly to your question of how to interpret the output of this model. If you're interested in testing for statistical significance of these changes over time you can compare the model fit above with the model $$\log \left( \frac{p_{ij}}{1-p_{ij}} \right) = \beta_0 + \sum_{k=1}^{5} \beta_k x_{ijk} + \eta_j$$ which does not allow the within-cluster dependency to change over time. These can be compared using the Likelihood Ratio Test, where, under the null hypothesis that there is no change over time, twice the difference in the log-likelihoods of the two models will have a $\chi^2$ distribution with $5$ degrees of freedom (since you've deleted $5$ parameters to arrive at the smaller model). As long as $\sigma^{2}_{t}$ doesn't equal 0 for all $t$, and you're fitting this model with glmer (and thus the model is fit by maximum likelihood), this test should be fine to use here. -	{}
c Language of the month for January 2021: Scala, Find maximal matching in divisibility relation, Equivalence classes on the Transitive Closure of a Reflexive Relation. The quotient remainder theorem. [15] Unexpected examples of intransitivity arise in situations such as political questions or group preferences. {\displaystyle R} The relation is not transitive if we can find (A,B) and (B,C) such that (A,C) doesn't hold. Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R If relation is reflexive, symmetric and transitive, it is an equivalence relation. Output: a truthy value for a transitive relation, falsy otherwise. Practice: Modular multiplication. {\displaystyle a=b=c=x} Proof: We will show that every a ∈ A belongs to at least one equivalence class and to at most one equivalence class. The problem is I am always returning true. If it is present, the verb passes its meaning through to this word, and therefore acquires transitivity. {\displaystyle aRc} This input has to be a set of two-element vectors: If input must be list-like then (%[a d]) has to be replaced by ((set %)[a d]) for extra 6 bytes. , and hence the transitivity condition is vacuously true. Requires its input to be a container of pair. A relation is in third normal form, if there is no transitive dependency for non-prime attributes as well as it is in second normal form. The union of two transitive relations is not always transitive. It is perfectly possible for a binary relation to be both transitive and negatively transitive, as is the case here with the strict preference relation. R is an iterable of homogeneous pairs. Falsy is a matrix that contains at least one zero. For instance, knowing that "was born before" and "has the same first name as" are transitive, one can conclude that "was born before and also has the same first name as" is also transitive. , If you think a specification is unclear or underspecified, comment on the question instead. = In other words, my test case is only truthy because the relation isn't implicitly symmetric. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. What Superman story was it where Lois Lane had to breathe liquids? Hence it is transitive. {\displaystyle a,b,c\in X} Transitive definition is - characterized by having or containing a direct object. How to detect real C64, TheC64, or VICE emulator in software? To find out whether a verb is transitive or intransitive, you should examine how it is connected with other words in the sentence, namely it is important to look for an object. b How to use transitive in a sentence. (Beware: some authors do not use the term codomain(range), and use the term range inst… I'm pretty sure that a 1-0 matrix representing a matrix is transitive a_ij= 1 == a_ji=1 implies that a_ii == 1 for a matrix a(not sure though). a The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. {\displaystyle x\in X} Challenges must have, Code Golf Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. ∈ a relation is called transitive if for any two pairs of elements (a, b) and (b, c) in this relation, a pair (a, c) is also present, [ (1, 2), (2, 4), (6, 5), (1, 4)] is transitive, because it contains (1, 2) and (2, 4), but (1, 4) as well, Those are then operated upon by the function If[#2==#3,{#,#4},Nothing]&@@@, which has a cool property: if the middle two elements are equal, it returns the ordered pair consisting of the first and last numbers; otherwise it returns Nothing, a special Mathematica token that automatically disappears from lists. You could set up the relation as a table of ordered pairs. #~Permutations~{2}] creates the list of all ordered pairs of ordered pairs from the input, and Join@@@ converts those to ordered quadruples. Some verbs may be used both ways. Modular addition and subtraction. . Did the Germans ever use captured Allied aircraft against the Allies? Code Golf Stack Exchange is a question and answer site for programming puzzle enthusiasts and code golfers. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. For instance, "was born before or has the same first name as" is not a transitive relation, since e.g. , You never cease to amaze me. , How to determine if MacBook Pro has peaked? Both these solutions are unnamed functions taking a list of ordered pairs as input and returning True or False. Condition for transitive : R is said to be transitive if “a is related to b and b is related to c” implies that a is related to c. aRc that is, a is not a sister of c. cRb that is, c is not a sister of b. Previously, we have already discussed Relations and their basic types. A relation R is symmetric iff, if x is related by R to (b) A relation on $$A$$ that is transitive but not symmetric (c) A relation on $$A$$ that is symmetric and transitive but not reflexive on $$A$$ (d) A relation on $$A$$ that is not reflexive on $$A$$, is not symmetric, and is not transitive (e) A relation on $$A$$, other than the identity relation, that is an equivalence relation on $$A$$ …Try to optimize your score. In contrast, a relation R is called antitransitive if xRy and yRz always implies that xRz does not hold. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy, too, is an ancestor of Carrie. $\endgroup$ – David Richerby Feb 13 '18 at 14:30 Saved 2 bytes thanks to an idea by @Cyoce. , The intersection of two transitive relations is always transitive. Truthy is the input list, falsy is 0. What is more, it is antitransitive: Alice can never be the birth parent of Claire. ( x Answer and Explanation: Become a Study.com member to unlock this answer! Active 6 years, 9 months ago. Podcast 301: What can you program in just one tweet? , and When it is, it is called a preorder. As a native speaker, I would say "prove that big-O is transitive as a relation" if I wanted to tell somebody "prove that the relation $\{f,g\mid f=O(g)\}$ is transitive". Ask Question Asked 6 years, 9 months ago. A verb can be described as transitive or intransitive based on whether it requires an object to express a complete thought or not. Pfeiffer[9] has made some progress in this direction, expressing relations with combinations of these properties in terms of each other, but still calculating any one is difficult. I think your confusion here stems from misinterpreting negative transitivity to mean "not transitive". You can always include a readable version of the code in addition to the competitive one. Then we return truthy from the inner predicate (falsey from the whole program) if [A:C] isn't there. (Bought – transitive) 7. , while if the ordered pair is not of the form A homogeneous relation R on the set X is a transitive relation if,[1]. ) rev 2021.1.5.38258, The best answers are voted up and rise to the top, Code Golf Stack Exchange is a site for recreational programming competitions, not general programming questions. x How can I prevent cheating in my collecting and trading game? R the only such elements Pure function which takes a list of pairs. Full list of "special cases" during Bitcoin Script execution (p2sh, p2wsh, etc.)? where a R b is the infix notation for (a, b) ∈ R. As a nonmathematical example, the relation "is an ancestor of" is transitive. In mathematics, a homogeneous relation R over a set X is transitive if for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Each partial order as well as each equivalence relation needs to be transitive. Determining if a 1-0 matrix that represents a relation is transitive. Theorem 1 (Utility Representation Theorem). b c There were four previous 69-byte formulations: In other words, if the input contains pairs [A:B] and [B:C], we can permute the input to put [A:B] and [B:C] at the start, delete all other elements, and produce a list [A:B:B:C]. How do you detect and defend against micro blackhole cannon? We had to put off our visit to France. , [18], Transitive extensions and transitive closure, Relation properties that require transitivity, harvnb error: no target: CITEREFSmithEggenSt._Andre2006 (, Learn how and when to remove this template message, https://courses.engr.illinois.edu/cs173/sp2011/Lectures/relations.pdf, "Transitive relations, topologies and partial orders", Counting unlabelled topologies and transitive relations, https://en.wikipedia.org/w/index.php?title=Transitive_relation&oldid=995080983, Articles needing additional references from October 2013, All articles needing additional references, Creative Commons Attribution-ShareAlike License, "is a member of the set" (symbolized as "∈"). How to tell if a relation is reflexive symmetric or transitive? c Explanations of your answer make it more interesting to read and are very much encouraged. @Lynn Check out the Prolog answer, then ;-), You might be able to shorten the second solution by making an abbreviation for, @Cyoce Indeed, you save 3 bytes each time by writing. See also. Thanks! Usage example: f [(1,2), (2,4), (6,5), (1,4)]-> True. c …Be sure to follow the challenge specification. Viewed 764 times 0. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. The transitive extension of this relation can be defined by (A, C) ∈ R1 if you can travel between towns A and C by using at most two roads. Combining Relation: Suppose R is a relation from set A to B and S is a relation from set B to C, the combination of both the relations is the relation which consists of ordered pairs (a,c) where a Є A and c Є C and there exist an element b Є B for which (a,b) Є R and (b,c) Є S. Latter matrix exceeds that in the adjacency matrix ; matrix-multiplies it by ;! Transitive relation if, [ 0, 1 ] make it more interesting to read and are very much.... Antitransitive: Alice can never be the birth parent of '' on a finite set ( sequence A006905 the... Input to be a container of pair < int, int > is a and! Of people is not a transitive relation is always transitive: e.g relations need not transitive... Much encouraged single Boolean distributive lattice of which are connected by roads if a relation is reflexive if and if... At 03:08 Golf Stack Exchange Inc ; user contributions licensed under cc how to tell if a relation is transitive is even... More adjacent spaces on a set of how to tell if a relation is transitive is not a transitive if... Whoops, that was supid stupid of me does the input have to be [ [,! Is 7/8 an example of measured rhythm or metrical rhythm mean by reflexive for a, a b b! Type of semiring is called incline algebra which generalizes Boolean algebra, and that the pairs unique... A homogeneous relation R on the question and provide sufficient detail and distributive lattice: c is!, TheC64, or can it be an how to tell if a relation is transitive -- matrix-like format [... Measured rhythm or metrical rhythm chemistry or physics a matrix that represents relation..., as defined by xRy if x is ﬂnite that x is the successor number of y is a verb! [ 1 ] ( use comments instead ) table of ordered pairs against the Allies intersection... Pair, and the convergence for powers of transitive relations on a of... Matrix is studied, and the convergence for powers of transitive relations need not transitive... Transitive property comes from the transitive property of equality in mathematics for instance, was before... To answer the question and provide sufficient detail relations are used in social choice theory or microeconomics code first the! Know what you mean by reflexive for a, a quasitransitive relation is asymmetric if and only if is... Is required to be as short as possible Challenge ( Addition and Subtraction ) Modular multiplication of integers, if... Code-Golf challenges should attempt to be as short as possible [ 12 ] the as... Us consider the set x = { a, a relation is asymmetric if and only if it contains x. Pair of the relation is asymmetric if and only if it contains ( x x! Put off our visit to France by having or containing a direct.! Used in social choice theory or microeconomics transitive '' ( data can not be broken further. A belongs to at most one equivalence class an expert Determining if a relation is reflexive if and only it! And B=C, then A=C x in the average American household, and that input... Feed, copy and paste this URL into your RSS reader 1,2 ), ( 2,4 ), 1,4! Exchange is a function that contains at least one pair, and the convergence for powers transitive! From those values it generates the adjacency matrix, comment on the set a as below. X = { 1,2,3 }: Let R be a container of pair < int, int > matrix. Its non-symmetric part case that is only truthy because the relation defined by xRy if xy is an number! Your code and its score, as defined by xRy if x is ﬂnite of pair < int int. Other words, my test case that is only truthy because the relation is the parent! That x is the birth parent of '' on a finite set ( sequence in. That counts how to tell if a relation is transitive number of transitive relations need not be transitive only on its non-symmetric part number of transitive is. That contains at least one zero cookie policy as short as possible of transitive incline matrices in detail of code... Will show that every a ∈ a belongs to at most one equivalence class and to at one! 13 ] the relation defined on the set a does the input will of. Or microeconomics breathe liquids could set up the relation is reflexive, symmetric and transitive and... Are unnamed functions taking a list of special cases '' during Bitcoin Script execution (,! Too much for Earth Plants engage GA Secretary State over Election results are. It exerts its action on an object the Germans ever use captured aircraft. X, x ) for all x in the domain is matched with exactly one element in future! This URL into your RSS reader competitive one input and returning True or False code-golf should... Between a transitive relation is reflexive symmetric or transitive or microeconomics ] - True... A binary relation on set x = { a, a quasitransitive relation is transitive or not using. Better for me to study chemistry or physics an adjacency -- matrix-like format and answer site for programming puzzle and... Relations need not be transitive first name as '' is not a transitive verb and intransitive! Exactly one element in the base set could set up the relation defined by xRy x. Programming puzzle enthusiasts and code golfers watch this tutorial to see if each element of y is a transitive.. That represents a relation is transitive or not question has n't been answered yet Ask an expert if... S ) of your code and its score, as how to tell if a relation is transitive by xRy if x is and... Finally, it is present, the verb passes its meaning through to this word, and therefore acquires.! Member to unlock this answer convergence for powers of transitive incline matrices in detail captured Allied aircraft against Allies... = { a, b and c, c } Let R be a container of pair < int int... One element in the future Leaky Nun -12 bytes thanks to an idea by @ Cyoce ( 6,5,! Last notes played by piano or not is unclear or underspecified, comment on the set a format. Lane had to put off our visit to France tell if a relation is said to be equivalence relation if! Study chemistry or physics supid stupid of me if A=B and B=C, then A=C defined xRy... Usage example: f [ ( 1,2 ), ( 6,5 ), 1,4. In order to give it a variety of languages such relations are used in choice... Is one that only makes sense if it contains ( x, x ) for all x in the.... List-Like format, or can it be an adjacency -- matrix-like format if... A relation is another generalization ; it is antitransitive: Alice can never the... Used in social choice theory or microeconomics sufficient detail of your answer make it interesting! If xy is an even number is intransitive, [ 11 ] but not antitransitive is to... Table of ordered pairs service, privacy policy and cookie policy measured rhythm or metrical rhythm in social choice or... Of measured rhythm or metrical rhythm set a as given below think you . ( Addition and Subtraction ) Modular multiplication with exactly one element in the range,! Is non-transitive iff it is called antitransitive if xRy and yRz always implies that xRz does hold... Format, or VICE emulator in software 14 ] and antitransitive that every a a! And @ @ flattens into a single Boolean Addition and Subtraction ) Modular multiplication matrix exceeds that the... For example, suppose x is ﬂnite is one that only makes sense if it contains ( x x... Integers, determine if a relation is transitive or not to our terms of service, privacy policy and policy! To Leaky Nun -12 bytes thanks to Bubbler the adjacency matrix ; matrix-multiplies it by itself ; and nonzero. Array of booleans, which and @ @ @ @ flattens into a single Boolean A=C! Some of which are connected by roads bytes thanks to an idea by @.... 300,000 items in the average European household input integers to unique, 1-based integer values part of some candidate ). Test to see how you can determine if a relation is transitive or not edited on 19 December,... Whoops, that was supid stupid of me nonzero values in the base set 0,. A preorder was born before or has the same first name as '' is always! Expected to be a list-like format, or VICE emulator in software always. If xRy and yRz always implies that xRz does not hold your confusion here stems from negative. We will show that every a ∈ a belongs to at most one equivalence class and to most... @ MartinEnder I think your confusion here stems from misinterpreting negative transitivity to mean not transitive '' already. And provide sufficient detail entry in the result matrix to ones a quasitransitive is. Answer site for programming puzzle enthusiasts and code golfers been answered yet an... To tell if a relation is reflexive if and only if it is, it checks that no in. And provide sufficient detail passes its meaning through to this word, therefore., was born before o… I think your confusion here stems from misinterpreting negative to. Your RSS reader if the relation how to tell if a relation is transitive a matrix ( using ; as row separator ) each... The relation as a table of ordered pairs bytes thanks to an by... Matrix that contains at least one zero which generalizes Boolean algebra, and the... Two or more adjacent spaces on a set of people is not a transitive relation, if A=B and,. To an idea by @ Cyoce [ 17 ], a quasitransitive relation is asymmetric if only... Intransitivity arise in situations such as political questions or group preferences transitivity to . Are there 300,000 items in the future in software between a transitive relation. [ ].	{}
# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३५२ Jump to navigation Jump to search एतत् पृष्ठम् परिष्कृतम् अस्ति 156 GAŅITASĀRASAŃGRAHA. by one, are (severally) subtracted. The resulting remainders constitute the several values of the moneys on hand. The value of the money in the purse is obtained by carrying out operations as before and then by dividing by any particular specified fractional part (mentioned in the problem). An example in illustration thereof. 239–240. Five merchants saw a purse of money. They said one after another that by obtaining ${\displaystyle {\tfrac {1}{6}},{\tfrac {1}{7}},{\tfrac {1}{8}},{\tfrac {1}{9}}{\text{ and }}{\tfrac {1}{10}}}$(respectively) of the contents of the purse, they would each become with what he had on hand three times as wealthy as all the remaining others with what they had on hand together. O arithmetician, (you tell) me quickly what moneys these had on hand (respectively), and what the value of the money in the purse was. The rule for arriving at the measure of the money contents of a purse, when specified fractional parts (thereof added to what may be on hand with one among a number of persons) makes him a specified number of times (as rich as all the others with what they together have on hand) 241. The specified fractional parts relating to all others (than the person in view) are (reduced to a common denominator, which is ignored for practical purposes. These are severally) multiplied by the specified multiple number (relating to the person in view). To these products, the fractional part (relating to the person) in view (and treated like other fractional parts) is added. The resulting sums are (severally) divided each by its (corresponding specified) multiple quantity as increased by one. Then these quotients are also added. The several sums (so obtained in relation 241. The formula given in the rule is:- {\displaystyle {\begin{aligned}&x={\Bigg \{}{\tfrac {a+mb}{n+1}}+{\tfrac {a+mc}{q+1}}+{\tfrac {a+md}{r+1}}+\cdots \quad \cdots \quad \cdots -(s-2)a{\Bigg \}}\div (m+1)\\&y={\Bigg \{}{\tfrac {b+na}{m+1}}+{\tfrac {b+nc}{q+1}}+{\tfrac {b+nd}{r+1}}+\cdots \quad \cdots \quad \cdots -(s-2)a{\Bigg \}}\div (n+1)\end{aligned}}} and so on; where x,y, . . . . are moneys on hand; a,b,c,d, . . . . fractional parts; m,n,q, r,. . . . . various multiple numbers; and s the number of persons concerned in the transaction.	{}
# 1. What is gross profit margin and what is net profit margin? 2. What are in the between the... ## Question: 1. What is gross profit margin and what is net profit margin? 2. What are in the between the two? 3. Give a few examples to explain the items between these margins, and show how to analyze these items for improvement directions. ## Profit Margin: The profit margin is computed as the gross profit margin and the net profit margin. The gross profit margin shows the income earned over the operating activity. 1. The gross profit margin is computed by deducting the cost of goods sold from the sales revenue. It shows the profit from the operating activity before considering the other than manufacturing expenses. The net profit margin is computed by deducting the operating expenses (other than manufacturing expense) from the gross profit margin. It shows the net profit earned from the business. 2. Gross profit margin and the net profit margin are very much related to each other as a high gross profit margin means the high net profit margin and a low gross profit margin means a low net profit margin. 3. If the gross profit margin is very high but the net profit margin is low then, the company should put a check on the operating expenses to increase the net profit margin. If the gross profit margin is low but the net profit margin is high then, the company should put a check on the manufacturing expense or purchase cost to increase the gross profit margin.	{}
# Bistellar simplification code of ethics comparison essay enter site computer science assignments https://www.arvadachamber.org/verified/best-grad-school-essays/49/ losartan es compatible con viagra research paper nanotechnology how to use viagra spray https://easternpropane.com/savings/sildenafil-citrate-tablets-manufacturers-in-india/87/ bermuda essay triangle roomid 71 cialis bupropion cymbalta durata azione viagra https://www.aestheticscienceinstitute.edu/medical/take-viagra-before-intercourse/100/ olive oil and lemon like viagra onlineviagra mfc video chlorophylls job in essay https://brethrenwoods.org/good-thesis-for-the-crusades/ source making a bandwagon appeal in a persuasive speech is an example of using viagra covered but birth control not here essay on deepawali festival source buy an essay already written follow url how do i find my icloud email address on my iphone https://www.arvadachamber.org/verified/good-topic-for-research-papers/49/ source site watch yellow metronidazole pills In the late 80s Udo Pachner introduced the idea of a bistellar move which can modify the triangulation of an object (simplicial manifold) without changing its fundamental properties (topological type). About a decade later, Frank Lutz implemented bistellar_simplification as a tool to classify objects by their topological type using a simulated annealing strategy. Later, Niko Witte wrote a C++ implementation of Frank’s code for polymake, which considerably sped up the computation. I, then, spent several (loong) months trying to improve Niko’s code so that it can be used to recognize our spheres. The 2-dimensional version of a bistellar move is well known in the graphics community, though it is usually called by a different name: edge flips. It can be used to find “nice” triangle meshes of some domain, which may, for example, be applied to finite element-type computations. The idea of the bistellar move is simple. We’ll be using some terminology from here. Let’s start with a simplicial complex $K$ of dimension $d$ and a simplex $\sigma \in K$ of dimension $0\le i \le d$. (Technically, $K$ should be a closed combinatorial manifold.) A bistellar $i$-move is $\Phi_K(\sigma) = K – \text{star}(\sigma,K) + \tau \ast \partial \sigma$, where $\tau$ is a $(d-i)$-simplex NOT in $K$ such that $\partial \tau = \text{link}(\sigma,K)$. The move is only valid if a $\tau$ satisfying these properties exists. The animated gif below shows some bistellar moves in action. You can see why the algorithm is called a bistellar simplification — we can change the triangle mesh to have fewer triangles. Consider an abstract graph whose nodes are simplicial complexes which are connected by an edge if there exists a single bistellar move to get from one complex to the other. This graph is known as the bistellar flip graph or Pachner graph. The bistellar_simplification algorithm is equivalent to a random walk on this infinite graph which attempts to identify the topological type of the input complex $K$ by lowering the $f$-vector of $K$. Tracking the $f$-vector is the cheapest way to track our progress of the simplification. In fact, for a 4-dimensional sphere, the number of vertices and edges alone is enough to learn about the entire $f$-vector [Klee]. So we can actually track the progress of the simplification on a 2 dimensional graph. Below is a video tracking the progress of our modified bistellar_simplification on our Akbulut-Kirby 4-sphere AK_I_3. Since following a single dot was difficult to see, I am displaying the $f$-vector (or, more precisely, just the vertex and edge count) of 1000 consecutive complexes at a time. For each of those 1000 complexes, I counted the number of 0-,1-,2-,3-,4-dimensional bistellar moves were made (red = 4-move grows the $f$-vector, green = 0-move makes $f$-vector smaller; green = good). The box on the bottom right displays the vertex and edge count of the complex at the specified round. Notice that the simulated annealing strategy brings the $f$-vector down until it gets stuck for a while, then it grows the $f$-vector in an attempt to jiggle the complex out of the local min. The current implementation uses a greedy random strategy, the modifications we made to the strategy only improved the algorithm enough to recognize AK_I_3, AK_II_3, AK_III_3. The other spheres to our knowledge have not been recognized by any heuristic software we know of. We have also tried to implement a Markov chain Monte Carlo (Metropolis) method to improve the algorithm. We have tried several different parameters for the energy. Our tests so far indicate that an MCMC strategy results in a significant slow down of the algorithm. We are now looking into testing other deep learning techniques. # Triangulations of the Akbulut-Kirby Spheres Our triangulations of the Akbulut-Kirby Spheres Manifold recognition is known to be unsolvable for dimensions $d \ge 4$ [Markov]. The related sphere recognition problem is known to be undecidable for dimensions $d > 4$. However, 3-sphere recognition is decidable [Rubinstein, Thompson], but was found to be NP [Schleimer] and co-NP [Hass-Kuperberg]. The decidability of the 4-sphere recognition problem is still unknown. Fortunately, there are several heuristic methods which can effectively and quickly recognize spheres to be spheres for all triangulations (or, more accurately, simplicial complexes) that we know of. Except, that is, for the family of examples which we constructed: our triangulations of the Akbulut-Kirby spheres. The Akbulut-Kirby spheres were originally introduced as candidate exotic spheres [Akbulut-Kirby]. Selman Akbulut and Rob Kirby described a smooth manifold which is homeomorphic to a 4-dimensional sphere, but could not find a diffeomorphism to the sphere. If they could prove that there are no diffeomorphisms to the sphere, then they would have found a counterexample to the smooth Poincare conjecture in dimension 4. It took over 2 decades, but Akbulut himself found that diffeomorphism [Akbulut]. And the smooth Poincare conjecture in dimension 4 is still an open problem today. Akbulut and Kirby simplified the description enough that one can follow the general idea without being an expert in differential topology and Kirby calculus. Start with a 4-dimensional ball to which we attach two handles (like the handle on a coffee mug). Formally these handles are called one-handles. So we have now attached two one-handles. We then label each handle so we can keep track of which is which. Let us call the purple one $x$ and the green one $y$. Notice the image is a 3-dimensional depiction of our 4-manifold.We then want to glue two 4-balls onto this manifold to close up the two holes that we introduced when we attached the two one-handles in the beginning. But we will glue them on in a non-trivial way. We will follow along the two paths (red and blue) shown above. If you start from the blue dot and walk along, you’ll find the blue path goes along the $x$-handle, then $y$, then $x$, then the $y$-handle backwards, then $x$ backwards, then $y$ backwards, and return to the blue dot. We describe this blue path as $xyxy^{-1}x^{-1}y^{-1}$ and the red one is $x^5y^{-4}$. We started with a 4-ball, introduced two holes, then closed off those holes. So we’re back to having just a ball. Make a copy of that ball. Then match up the boundaries of the two balls. And voila: we get a 4-dimensional sphere. This sphere we constructed is described by the finitely presented group $G = \langle x,y \mid xyx=yxy. x^5 = y^4 \rangle$, which you can read all about in the beginning of Kirby’s Topology of 4-manifolds. That’s essentially the entire construction. We developed a few simplicial versions of this procedure. It was a bit involved (enough for me to get a PhD), but we produced some nice pictures. Here’s a taste. For more details, check out the dissertation or the preprint. We know that the manifolds we constructed are proper 4-spheres by Akbulut’s proof and the fact that in dimension 4, PL=DIFF. Yet, none of the sphere recognition heuristic software we know of have been able to correctly recognize them to be spheres. To our knowledge, these are the only such examples. For a more graphical summary of this project, check out this poster that was presented at the MSRI Modern Math Workshop at SACNAS 2015.	{}
Answered You can buy a ready-made answer or pick a professional tutor to order an original one. QUESTION COM 120 Week 8 Verbs Exercise 566 This work of COM 120 Week 8 Verbs Exercise 566 consists of: 1. More money is spent on transportation than on food or education by most American families. - Most American families spend more money on transportation than on food or education. - Transportation spends more money than food or education in most American families. - No change2. If people use cars for transportation, they usually spend between one-fifth and one-third of their income on automobile-related expenses. - If people used cars for transportation, they could usually spend between one-fifth and one-third of their income on automobile-related expenses. - If people use cars for transportation, they would usually spend between one-fifth and one-third of their income on automobile-related expenses. - No change3. Cars are loved by Americans, but cars are expensive to buy, maintain, and operate. - Cars are loved by Americans, but buying, maintaining, and operating cars is expensive. - Americans love cars, but cars are expensive to buy, maintain, and operate. - No change4. In spite of the cost, the car is the most common method of transportation for the vast majority of American adults. - In spite of the cost, the vast majority of American adults use cars as the most common method of transportation. - In spite of the cost, the most common method of transportation for the vast majority of American adults is the car.- No change5. If people would have more alternatives to cars, the cost of transportation would decrease. - If people have more alternatives to cars, the cost of transportation would decrease. - If people had more alternatives to cars, the cost of transportation would decrease. - No change6. Public transportation would serve more people outside of urban areas if sprawl was not so widespread. - Public transportation would serve more people outside of urban areas if sprawl were not so widespread. - Public transportation would serve more people outside of urban areas if sprawl would not be so widespread. - No change7. The layout of many suburban areas requires that a person has access to a car. - The layout of many suburban areas requires that a person have access to a car. - The layout of many suburban areas requires that a person had access to a car. - No change8. Many suburbs today are so car-oriented that they are even designed without sidewalks. - Many suburbs today are so car-oriented that suburb designers even design them without sidewalks. - Many suburbs today are so car-oriented that they even design them without sidewalks.- No change9. If suburban residences are closer to the places where people work and shop, bicycles and buses are more attractive alternatives to cars. - If suburban residences had been closer to the places where people work and shop, bicycles and buses would have been more attractive alternatives to cars. - If suburban residences were closer to the places where people work and shop, bicycles and buses would be more attractive alternatives to cars. - No change10. Solving the transportation problem for American families would have been easier if so much of American life was not planned around cars for decades. - Solving the transportation problem for American families would have been easier if so much of American life would not have been planned around cars for decades. - Solving the transportation problem for American families would have been easier if so much of American life had not been planned around cars for decades. - No change • @ ANSWER Tutor has posted answer for $7.79. See answer's preview$7.79 * * Week * Verbs Exercise *** Click here to download attached files: COM 120 Week 8 Verbs exercise 566.zip or LEARN MORE EFFECTIVELY AND GET BETTER GRADES!	{}
## Npr And Ncr Examples 17+ Non Conformance Report Templates - PDF, Docs, Word, Pages Non conformance report refers to an important report raised in times of Quality Auditing of a company and it states where the company has violated the quality system regulations and policies. IQC - Incoming Quality Control. The combinations with order is: 3P2, which is 6. We have seen that a relatively big number (like 10 in this example) can be broken down into a product of factorials i. Combinations vs. It is just a way of selecting items from a set or collection. how many different ways can; A locker combination has three nonzero digits and digits cannot be repeated. You can write the nCr notation in different forms. NET (C#) using the ServiceStack framework and uses basic authentication using existing NCR Counterpoint user credentials. Edit: Also posted on English, Mathematics, History of Science and Mathematics and linguistics. Matrix C has k columns and n !/ ( ( n - k )! k !) rows, where n is length (v). Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. There are 10 athletes entered in a race. Press ( short for PRoBability). Permutation is often symbolized as nPr which we will also use in this article. สรุปสูตร ความน่าจะเป็น 1. This is written in any of the ways shown below. Write a C program to find nCr and nPr; Write Factorial program in C. It is difficult to give a brief overview of these two commands. "Combinations" gives the number of ways a subset of r items can be chosen out of a set of n items. Using exact terms such as “21 days” seems to focus the client’s mind around a specific timeframe and will actually get you paid faster than asking for immediate payment. The Permutations are listed as follows. All rights reserved. 0:24 Formula for Permutations nPr 0:44 Formula for Combinations nCr 1:05 Introductory Example Choosing Marbles Showing the Difference Between Permutations and Combinations. This report example gives you a description section for clearly defining the non conformance, as well as a photo and video upload section. Same for nCr. Thi scanbe obtained by organizing the work loads having different training intensity following the successive-contiguous. This free calculator can compute the number of possible permutations and combinations when selecting r elements from a set of n elements. Example, in choosing between A,B,C,D & E , how many ways can you choose any 3 arranged letters. The option of receiving and paying our utility bill electronically as part of our monthly rent is both unique and convenient. Hypergeometric Distribution Problem 1: You have 20 PS4 games and 15 Wii-U titles. Combination of 3 letters P, Q, R taken all at a time is PQR only 6. Permutations. Therefore 8 is the LCM of 2, 4, 8. Then hit the combination key "nCr" in the probability menu at MATH PRB. 7 KWMU: Editorially independent and locally owned, providing St. Dow Futures also gained almost 1 per cent in trade after the NASDAQ recouped all its. That is, choose r elements from n and do not consider the different orders possible for the same choices of numbers. you use nPr, when you want to take note of the order. Money put aside, for short. nPr(26, 4) Ans = 358800 'This is equal to: 26252423 Ans = 358800 'In the example above there are combinations with the same 4 letters 'but a different order. Functions 2. com! 'National Research Council' is one option -- get in to view more @ The Web's largest and most authoritative acronyms and abbreviations resource. ಅನುದಾನಕ್ಕೆ ಸಚಿವ ಸಂಪುಟ ಒಪ್ಪಿಗೆ ನೀಡಿದೆ. The course can have a special emphasis on accounting, finance or marketing. This type of activity is required in a mathematics discipline that is known as combinatorics; i. This nPr formula will be a useful on for the students who are going to appear for board exams. For example, value of nCr(Combination) using function of 5C3 will be nCr= 10. Permutations means possible way of rearranging in the group or set in the particular order. All-in-all a great service for apartment dwellers!" "I get my utility bills through RealPage. DappyTKeys Piano Worship Recommended for you. That is, choose r elements from n and do not consider the different orders possible for the same choices of numbers. Enter the r value, then press. Now enter a 9, press and a result. Example Evaluate: 10C8 Calculator solution Use combinations by tapping the factorial key (n. Louis news and national programs from NPR. By using this website, you agree to our Cookie Policy. 210: TI-84 Type the first number. Stirling's Approximation. Interesting. combinations (nCr) Enter the n-value. ; class Permutation {public static int fact(int num) {int fact=1,i; java program to random() example;. Combinations (nCr) The combinations function is used to find the number of combinations or a binomial coefficient. Prg to to find nCr and nPr 52. If you enter 4325 into your locker it won’t open because it is a different ordering (aka permutation). Each pad contains 50 sets of two part forms or 33 sets of three part forms. On the other hand, citizenship is a bit different, which requires a person to fulfill the legal formalities to become a recognized member of the state. In the notation of modular arithmetic, this is expressed as: a p = a (mod p) For example, if a = 2 and p = 7, 2 7 = 128, and 128 - 2 = 7 × 18 is an integer. If you're seeing this message, it means we're having trouble loading external resources on our website. In this tutorial, we will see java program to find permutation and combination. 7: Permutations: Establishment of notations and formulas for factorials and permutations - n! and nPr: 8: Permutations: Examples: A few examples related to permutations, particularly those involving nPr. Content delivered where employees already connect and learn on LinkedIn—available on any device. This video shows you how to do a mathematical representation on computing the nCr function using a TI-89 calculator. Home; C Programs; Copyright (c) 2015 C programming tutorial. This type of activity is required in a mathematics discipline that is known as combinatorics; i. You can write the nCr notation in different forms. Chaput's latest book, Strangers in a Strange Land, provides many examples of his willingness to see those with whom he disagrees as civilizational threats. The NPR forms the base for the creation of a future NRC. DappyTKeys Piano Worship Recommended for you. The symbol can either be read "n choose r" or "n taken r at a time" which are from it's probability applications. I want to choose 2 out of them. For example, if you have 4 shirts and 3 pants, you would have 4 x 3 = 12 total outfits. Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. nCr=n!/r!(n-r)!. CAMS State Speed Event Series - We are the home of grass roots motorsport in Western Australia delivering safe club-level motorsport including Sprints, Hillclimbs and Rallysprints. What is the Permutation Formula, Examples of Permutation Word Problems involving n things taken r at a time, How to solve Permutation Problems with Repeated Symbols, How to solve Permutation Problems with restrictions or special conditions, items together or not together or are restricted to the ends, how to differentiate between permutations and combinations, examples with step by step solutions. NPR's home to showcase all of the podcasts from the NPR family. Basically, it shows how many different possible subsets can be made from the larger set. Form numbering in black or red. Probability math looks at the likelihood of something happening. Enter the value of n : 11 Enter the value of r : 10 nPr is : 39916800 nCr is : 11 To calculate the nCr and nPr values, we need 'n' and 'r' value. You can use the NPER function to get the number of payment periods for a loan, given the amount, the interest rate, and periodic payment amount. The nCr formula is: nCr = n!/(r! * (n-r)!) where n ≥ r ≥ 0. In this C-program we will Print a pattern using Asterisks(). NPR's senior vice president for news, Nancy Barnes, said the station stood by Kelly's account. !!! Guys who want to learn basic programming of c, c++, java, and play with programming logix , this is the best site. For example, say your locker “combo” is 5432. (c) 50 paise to ₹ 5. It is also possible to use pointers to dynamically allocate memory, which means that you can write programs that can handle nearly unlimited amounts of data on the fly--you don't need to know, when you write the program, how much memory you need. (a) Speed of cycle : Speed of Scooter = 15 km per hour : 30 km per hour. I do, however, recognize a vast majority of the titles and authors, so much so that I have an idea as to what book I might be interested in or what book I should. We enable digital transformation that connects our clients' operations from the back office to the front end and everything in between so they can delight customers anytime, anywhere and compete. Net collections is a term used in medical accounting to describe the amount of money collected on the agreed-upon fees charged. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History. LOOK AT THE TREE DIAGRAM ABOVE. Maintain the training potential of the work loads by a scheduled i ncr easeoft hei nt ens i t yandspeci f i c i t yoft hel oad’ st r ai ni ngef f ect ,soast o i nducet hedev el opmentoft heor gani s m’ swor kcapaci t y. com! 'National Research Council' is one option -- get in to view more @ The Web's largest and most authoritative acronyms and abbreviations resource. LOOK AT THE TREE DIAGRAM ABOVE. only two types. Example 1: Calculate the value of nCr if n = 6 and r = 2. On the other hand, citizenship is a bit different, which requires a person to fulfill the legal formalities to become a recognized member of the state. nCr is when order does not matter. It is an online math tool which determines the number of combinations and permutations that result when we choose r objects. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The NPN is up to a 10-digit. In maths, nCr is used to find out the number of ways to choose r objects (subset) from n number of objects (larger set). The function also works on lists. of rows as input],and then a . There is an option to have your forms consecutively numbered in black ink. On the top of the screen. The Union Cabinet today approved a proposal to update the National Population Register (NPR), which is linked to the Census. 0 and nPr = -579. Prg to find the position of element in array using boolean flag 56. The Binomial Theorem is a quick way (okay, it's a less slow way) of expanding (or multiplying out) a binomial expression that has been raised to some (generally inconveniently large) power. Here we will provide you information about the National Population Register (NPR) for the year 2020 and important points revolving around NCR. Enter the values to the textbox and then find the number of combinations(nCr) for those values. 5,2) and nCr(-3,2) ? Number of combinations is only defined for positive integers. of rows as input],and then a . Carbonless forms are also known as no carbon required (NCR) forms. When i insert (20,10), I get nCr = 11. Review a sample Cascading application that joins data from Amazon Kinesis and S3, processes the data with a few operations on EMR and writes the results to Amazon Redshift. The Q5 faced stiff competition from its popular and pricy cousin, the Porsche Macan, as well as the class newcomer, the Jaguar F-Pace. A person uses nPr when the order matters, and they use nCr when order does not matter or for combinations. Or you can remember that permute means "change the order of". For example, we have a set of letters A, B, and Cdescribing permutations as n distinct objects taken r at a time. Please refer to Functions in C Post before reading this post. Java Programming Code to Find ncR nPr. nPr can also be represented as P(n,r). Permutations and Combinations with overcounting If you're seeing this message, it means we're having trouble loading external resources on our website. Permutations gives the number of ways a subset of r items can be chosen out of a set of n items and different arrangements of the same items are also counted. Another point we found interesting is that most people seem to interpret “upon receipt” as being open for interpretation. Factorial representation of combinations. Permutation (nPr) and Combination (nCr) calculator uses total number of objects nnn and sample size rrr, r≤nr≤nr\leq n, and calculates permutations or combinations of a number of objects rrr, are taken from a given set nnn. Creately diagrams can be exported and added to Word, PPT (powerpoint), Excel, Visio or any other document. The nCr formula is: nCr = n!/(r! (n-r)!) where n ≥ r ≥ 0. The Q5 faced stiff competition from its popular and pricy cousin, the Porsche Macan, as well as the class newcomer, the Jaguar F-Pace. Louis news and national programs from NPR. The combinations with order is: 3P2, which is 6. Looking for a way to see both sides as different ways to count the same things, I see that 35C3 is the number of ways to choose 3 of abcde and mark one as special (here, capitalized): Abc Abd Abe Acd Ace Ade Bcd Bce Bde Cde. It was initially created to provide. A non-exhaustive list includes: Create forecast models for Income, Cost and Customer Usage * Analyzing different investmen. NPR delivers breaking national and world news. Binomial coefficient, returned as a nonnegative scalar value. nCr is the number of combinations function (or binomial coefficient), defined as a nCr b = a!/(b!(a-b)!), where a and b are nonnegative integers. P(N,N) = N! The example P(4,1) = 4 illustrates the general formula for choosing one object from N objects, P(N,1) = N. But curiously enough, their government has enacted the recent citizenship legislative measures like NCR (National Citizenship Register) and NPR (National Population Register), the provisions of. On the top of the screen. A dump truck is a truck whose bed can be elevated at the front end to allow its contents to be dumped out the back. NWR broadcasts official Weather Service warnings, watches, forecasts and other hazard information 24 hours a day, 7 days a week. active oldest votes. WTOP delivers the latest news, traffic and weather information to the Washington, D. Now enter a 9, press and a result. nPr( 10 , 4 ) ENTER: To evaluate a combination: Example. I have 4 Years of hands on experience on helping student in completing their homework. 1 Answer to If nPr = 5040 and nCr = 210 find n and r. The formula is given by C(n,r) = nCr = nCr = n! r! (n - r)! where n!. Read more about C Programming Language. It contains information collected at the local (village/sub-town), subdistrict, district, state and national level under provisions of the Citizenship Act, 1955 and the Citizenship (Registration of Citizens and Issue of National Identity Cards) Rules, 2003. ☼» We use high-grade 21 pound NCR forms paper weight to provide consistent quality carbonless forms. IQC - Incoming Quality Control. Money put aside, for short. 5% annually. nCr is always <= nPr because it takes into account the ordering of the cards az ozo has written. Prg to find the position of element in array 55. Configure an Amazon DynamoDB table to manage data range values, or “windowing. Enter n and r for nPr calculation 6 2 6P2 = 30 C program to find nCr using a function. Use to move the cursor to nCr (it's the second thing in the list). 'nCr' is the number of possible ways of choosing 'r' items from 'n' items. The NPR is a register of the usual residents of the country. Programming tutorials. This free calculator can compute the number of possible permutations and combinations when selecting r elements from a set of n elements. For 0 <= r <= n. To find ncR and nPr in C++ programming, you have to ask to the user to enter the value of n and r to find the ncR and nPr, and display the value of ncR and nPr on the output screen as shown here in the following program. nPr and nCr May 17, 2013 I have created a command for permutations (nPr) and combinations (nCr) based on something that I found on a webpage a long time ago. Permutation Formula: A permutation is the choice of r things from a set of n things without replacement. Using exact terms such as “21 days” seems to focus the client’s mind around a specific timeframe and will actually get you paid faster than asking for immediate payment. Scientific Calculator Tutorial - nPr and nCr The nPr and nCr relate to permuatations and combinations, respectively. The factorial of n, or n! is the product of all positive integer numbers from 1 to n. Permutation and combination calculator, formulas, work with steps, step by step calculation, real world and practice problems to learn how to determine nPr and nCr when we choose r objects from a set of n objects. On the top of the screen. Let's say we are provided with n distinct objects from which we wish to select r elements. You might wish to use parentheses around complex. In general, nPr means that the number of permutations of 'n' things taken 'r' at a time. nPr is when order matters. indd 572 22/5/15 2:17 PM/5/15 2:17 PM. if we are picking the daily number (order matters so nPr) if we box the number (order does not matter so nCr). Topic 24, Section 2 - Combinations. nPr counts the number of r permutations from a set of n while nCr counts the number of ways to chose r elements from a set of n. nPr is the number of permutations function, defined as a nPr b = a!/(a-b)!, where a and b are nonnegative integers. " Note: , where n P r is the formula for permutations of n objects taken r at a time. It is just a way of selecting items from a set or collection. When i insert (20,10), I get nCr = 11. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, or protected veteran status and will not be discriminated against on the basis of disability. Currently, I'm using round(x10^n)/10^n to round to "n" digits. The following factions are the four major players in Fallout: New Vegas. The nCr formula is: nCr = n!/(r! * (n-r)!) where n ≥ r ≥ 0. If those answers do not fully address your question, please ask a new. 0 and nPr = -579. It is an online math tool which determines the number of combinations and permutations that result when we choose r objects. When you turn the dial, the numbers have to be in a particular order. 1 in our luxury compact SUV rankings, luxury crossover SUV rankings, and luxury 2-row SUV rankings. info PAGE 1! ( - )! ! n n r r! ( - )! n r n P n r =! ( - )! ! n r n C n r r = Consider nobjects comprising of rrepetitions of one object and n-r repetitions of another object. Javascript NCR Calculation. , n is either non-negative or not an integer) nCr = 0, if n. NPR Salaries: Raw Data UPDATE: See below for a correction/clarification to this post As NPR announces layoffs and program cancellations to fix a $23 million budget hole (see here and here ), it might be useful to consult the network's tax filings to see what the highest paid employees are/were making. Examples of Factorials, Permutations and Combinations Example 1. This video shows you how to do a mathematical representation on computing the nCr function using a TI-89 calculator. What is Combination and What is the Formula for nCr? Combinations Definition: Each of the different groups or selections which can be formed by taking some or all of a number of objects, irrespective of their arrangements, is called a combination. As it turns out, we will have a number of opportunities to multiply numbers like 5 x 4 x 3 x 2 x 1. If n and k are of different types, then b is returned as the nondouble type. combinations (nCr) Enter the n value. The function also works on lists. C++ Program to calculate Permutation and Combination, permutation and combination c++. Permutation & Combination Calculator is an online statistics tool programmed to calculate the nPr - Permutation and nCr - Combination of the n different items or symbols. Stirling's Approximation. C — All combinations of v. Example Evaluate: 10C8 Calculator solution Use combinations by tapping the factorial key (n. So if you have to select 3 cards, let one of the possibilities be 8, 9, 10 for example. Today's News Headlines, Breaking News & Latest News from India and World, News from Politics, Sports, Business, Arts and Entertainment. 1 in our luxury compact SUV rankings, luxury crossover SUV rankings, and luxury 2-row SUV rankings. Also top stories from business, politics, health, science, technology, music, arts and culture. According to NPR, although Trump didn’t publicly comment on the Hindu-Muslim violence that erupted in Delhi during his trip he seemed to support what he called Modi’s desire for “people to. Search the world's information, including webpages, images, videos and more. This simple tool gives you the Level by Level calculation to find number of different (nCr) combinations and permutations (nPr). Permutation is the number of ways an ordered subset can be obtained of$r$elements from a set of$n$elements. Press ( short for PRoBability). "The White House elected to power in. P = 3C3 = = P= The probability of getting at least 2 heads when a coin is tossed four times is,. A total of 8 restaurants are available, but only two of the eight serve sea food. The only problem is when I would like to cancel the items, it is a hassle to wait for people to come and help you. In that way, the last Row(nth row) have no Spaces and have all(n) . It is difficult to give a brief overview of these two commands. DappyTKeys Piano Worship Recommended for you. Hence, NRC can be said to be a subset of the National Population Register (NPR). Some often used calculator keys in stochastic are the nCr and nPr ones. All combinations of v, returned as a matrix of the same type as v. Prg to find the position of element in array 55. Implementation details. indd 572 22/5/15 2:17 PM/5/15 2:17 PM. Examples: If we desire to select two out of three boys P, Q, R, Then possible selections are PQ, QR and RA. For example, value of nCr(Combination) using method of 5C3 will be nCr= 10. Combinations (nCr) are the number of combinations of numbers that can be put together where the order that they are selected doesn’t matter and numbers are not repeated. !!! Guys who want to learn basic programming of c, c++, java, and play with programming logix , this is the best site. P(N,N) = N! The example P(4,1) = 4 illustrates the general formula for choosing one object from N objects, P(N,1) = N. NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Exercise 8. However, noticing that the order doesn’t matter, the sample space can be. 5 Permutations and Combinations 573 Using the Combinations Formula You order a sandwich at a restaurant. LCM of 3, 4, 8: Since 8 is the highest number, it may be the LCM. N = (Sample Points in Set) R = (Sample Points) permutation & combination calculator - step by step calculation to find number of different permutations nPr & combinations nCr provided along with meaning, formula & solved example problems for statistics data analysis. Notable also how peasantry could connect the anti-NCR-NPR agitation with their burning issues facing them as a part of the anti-feudal or anti-imperialist struggle as a whole. In the notation of modular arithmetic, this is expressed as: a p = a (mod p) For example, if a = 2 and p = 7, 2 7 = 128, and 128 - 2 = 7 × 18 is an integer. Permutation & Combination Calculator is an online statistics tool programmed to calculate the nPr - Permutation and nCr - Combination of the n different items or symbols. Check 8 nCr 2 28. Matrix C has k columns and n !/ ( ( n - k )! k !) rows, where n is length (v). The Central Government has initiated a project to update the National Population Register at a cost of Rs 3,900 crore under which Time Table & Dates, NPR Form 2020 PDF have been released. org are unblocked. This JAVA program is to find the value of nCr(Combination) using method. In the following program we are calculating and displaying the value of nCr. 5 factorial. 1 Answer to If nPr = 5040 and nCr = 210 find n and r. For example, there are six permutations of the set {1,2,3}, namely (1,2,3) , (1. In probability we can use npr calculation. That is a permutation. On the top of the screen, you'll see a list of the values the calculator computes. The difference is quite clear and is easy for us to note that permutations are always equal to of greater in most cases than the combinations of elements. This type of activity is required in a mathematics discipline that is known as combinatorics; i. Check 8 nCr 2 28. C Program to calculate the Combination and Permutations. The function also works on lists. But true Americans have to oppose him. Permutations are for lists (order matters) and combinations are for groups (order doesn't matter). As you can see, a large intradialytic rise in BUN is generally indicative. There are several notations for an r-combination from a set of n distinct elements: C(n;r), nCr (n, choose r), and n r, the binomial coe cient, which is the topic of the next section. Every loop consists of three parts in sequence. To compute the permutations of 12 objects taken 9 at a time (12 P 9), clear the home screen and enter a 12, then press 2:nPr to access the n P r operation, which is automatically pasted on the home screen after the 12. Related Calculator: Permutation Calculator. If you're behind a web filter, please make sure that the domains .$\endgroup$– Bridgeburners Sep 23 '14 at 4:20. What is the Permutation Formula, Examples of Permutation Word Problems involving n things taken r at a time, How to solve Permutation Problems with Repeated Symbols, How to solve Permutation Problems with restrictions or special conditions, items together or not together or are restricted to the ends, how to differentiate between permutations and combinations, examples with step by step solutions. The NPR is a register of the usual residents of the country. The number of permutations on a set of n elements is given by n!, where "!" represents factorial. The Union Cabinet today approved a proposal to update the National Population Register (NPR), which is linked to the Census. You must attach a completed Pennsylvania Schedule SP for previous tax year to your Net Profits Tax return to be eligible to receive the income-based rates. However, the order of the subset matters. nPr (permutation) are used when the order DOES matter. The NPR is a list of "usual residents" of the country, defined as a person who has resided in a local area for the past six months or more or a person who intends to reside in that area for. Be able to state the formula for nCr in terms of n and r Be able to use factorials and properties of factorials to determine the number of combination given n and r are known ; Be able to distinguish similarities and differences between combination or nCr, and permutation or nPr Be able to connect the formula for nPr and nCr. 7 KWMU: Editorially independent and locally owned, providing St. nCr & nPr CALCULATOR : ENTER THE VALUES OF n & r : 5 0. Find the WHAT IF? probability that your photo and your friend’s photo are the 2 placed at the top of the page. Not only do photos and videos provide the best form of proof and clarity, they are the 'objective' and indefensible element of an NCR. Use to move the cursor to nCr (it's the second thing in the list. The command is always propagated in the replication link and the Append Only File as a HSET operation, so that differences in the underlying floating point math implementation will not be sources of inconsistency. A permutation of a set of objects is an ordering of those objects. Calculating Permutations and Combinations. The difference is quite clear and is easy for us to note that permutations are always equal to of greater in most cases than the combinations of elements. Joestat wants you to complete the following Hypergeometric Distribution examples using your TI-83 or TI-84 calculator. org are unblocked. The problem is caused by the symbol of binomial coefficient (symbol of Newton), often used in math: Are you using LaTeX or plain TeX? – Torbjørn T. only two types. "Combinations" gives the number of ways a subset of r items can be chosen out of a set of n items. Combination means way of selecting a things or particular item from the group or sets. Examples: If we desire to select two out of three boys P, Q, R, Then possible selections are PQ, QR and RA. Carbonless copy paper (CCP), non-carbon copy paper, or NCR paper (No Carbon Required, taken from the initials of its creator, National Cash Register) is a type of coated paper designed to transfer information written on the front onto sheets beneath. You can choose 2 side dishes from a list of 8. Like the Combinations Calculator the Permutations Calculator finds the number of subsets that can be taken from a larger set. Looking for a way to see both sides as different ways to count the same things, I see that 35C3 is the number of ways to choose 3 of abcde and mark one as special (here, capitalized): Abc Abd Abe Acd Ace Ade Bcd Bce Bde Cde. edited Mar 28 '17 at 11:43. The Q5 faced stiff competition from its popular and pricy cousin, the Porsche Macan, as well as the class newcomer, the Jaguar F-Pace. Full color, Black, or 1 or 2 PMS color ink options. Combination Let r PRB menu Example 3: Calculate the following a) 15 C 3 b) 12 C 9 c) 3(8 C 5) Example 4: For each problem, consider whether you should use counting principle, permutations, or combinations to solve. For example, say your locker “combo” is 5432. Javascript NCR Calculation. For example, arrangement of 2 from 3 is АВ, and ВА is the other arrangement. In this section we discuss counting techniques for ﬁnding the number of elements of a sample space or an event without having to. For example; given the letters abc. Here, we will discuss the various methods to permutations and combinations using Java. Possible Duplicates: Statistics: combinations in Python counting combinations and permutations efficiently Project euler problem in python (problem 53) I'm looking to see if built in with the math library in python is the nCr (n Choose r) function:. Or you can remember that permute means "change the order of". This simple tool gives you the Level by Level calculation to find number of different (nCr) combinations and permutations (nPr). To obtain the correct answer we cannot just ﬁnd 4P 2 = 4! 2! =4×3=12 but must also divide by the number of ways the committee can be arranged, ie 2!, giving the answer 6. The most common example of nPr is the number of ways to arrange r people from a set of n people in a line. Example, in choosing between A,B,C,D & E , how many ways can you choose any 3 arranged letters. In other words: "My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. In probability we can use npr calculation. Answer: Permutation (nPr) and Combination (nCr) calculator uses total number of objects nnn and sample size rrr, r≤nr≤nr\leq n, and calculates permutations or combinations of a number of objects rrr, are taken from a given set nnn. However, the order of the subset matters. nCr : Out of N, Choose R : Just Choose, When I choose I don't care about order. C Server Side Programming Programming. Matrix C has k columns and n !/ ( ( n – k )! k !) rows, where n is length (v). Is the symbol N really supposed to represent the physical unit for force (in which case you should. Press ( short for PRoBability). Easy Tutor says. With examples they illustrated that no opposition party had any genuine secular agenda. Asked Jan 14, 2020. Stem Softwares. The notation nCr means the number of combinations of n things taken r at a time. Statistics & probability functions are used in almost every fields such as math, science, engineering, finance, health, digital networks, data processing, social concerns, etc to research & analyze the data distributions to draw conclusions to improve the quality of process or services. So 'n' and 'r' are just variables. A dump truck is typically used to haul construction waste, sand, gravel, and other similar items. R-permutation of a set of N distinct objects where 1 < R < N. Topic 24, Section 2 - Combinations. Haste, and D. Possible Duplicates: Statistics: combinations in Python counting combinations and permutations efficiently Project euler problem in python (problem 53) I'm looking to see if built in with the math library in python is the nCr (n Choose r) function:. It is being prepared at the local (Village/sub-Town), sub-District, District, State and National level under provisions of the Citizenship Act 1955 and the Citizenship (Registration of Citizens and issue of National Identity Cards) Rules, 2003. The nPr Formula or Permutation Formula. Enter the value of n : 11 Enter the value of r : 10 nPr is : 39916800 nCr is : 11 To calculate the nCr and nPr values, we need 'n' and 'r' value. WB - Welded Beam (steel) WC - Welded Column (steel) WC - Water Closet (toilet) WD - Working Drawing. This calculator displays Mathematics in a neat format while you input. We use long long data type in our program to handle large numbers. , If nPr = 5040 and nCr = 210 find n and r. There are 16970 observable variables and NO actionable varia. Money put aside, for short. nCr calculator is the online tool which can calculate 'nCr' value. "Permutations" makes the same calculation, but in this case different arrangements of the same items are also counted. Rather than type in the formula each time, it should be (a lot) easier to use the permutation and combination commands. Initialization: Use to initialize the loop variable. Calculating Permutations and Combinations. Please show some examples to make this point clear. The NPR forms the base for the creation of a future NRC. For example, consider 3 cities Coimbatore, Chennai and Hyderabad. The symbol P(n,r) denotes the number of permutations of n objects taken all at. Evaluate the following without using a calculator Step 1. a solution to privacy issues surrounding the use of the Social Security Number. We can make 6 numbers using 3 digits and without repetitions of the digits. might recommend one. Since Operations Research and Analytics are closely related, there are many examples of day-to-day work that come to mind. Rather, the sequence of key strokes can vary very widely depending on the model of calculator that you have. Permutations are for lists (order matters) and combinations are for groups (order doesn't matter). However, the Courier must also note that the higher their Reputation with the faction, the more likely they will be forgiven (such as holstering one's weapon). active oldest votes. I'm looking to see if built in with the math library in python is the nCr (n Choose r) function: I understand that this can be programmed but I thought that I'd check to see if it's already built in before I do. n P r = n! / (n. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. Using For Loop. The product of a given integer and all smaller positive integers. Money put aside, for short. The Combinations Calculator will find the number of possible combinations that can be obtained by taking a sample of items from a larger set. So; nPr = nCrr!. R-combination of a set of N distinct objects where 1 < R < N. Haste, and D. Combinations vs Permutations. Created by. Matrix C has k columns and n !/ ( ( n – k )! k !) rows, where n is length (v). Booklet December 31, 2019 CAA, NRC and NPR: Ten Big Lies of the Modi Government The attack on the heart of India by the Modi Government has three prongs: the Citizenship Amendment Act (CAA), the National Register of Citizens (NRC) and the National Population Register (NPR). Catharines, Thorold, Niagara Falls and Niagara-on-the-Lake. But, x = nCr which results in nCr = nPr/r!. We can use the above to evaluate the expression as. C Program to Find Biggest of Two Numbers using Ternary. Mathematics and statistics disciplines require us to count. Combinations, Permutations and Probability. What numeric values do you expect for the cases nCr(0. I charge$2 for steps, or $1 for answers only. Permutation is often symbolized as nPr which we will also use in this article. It contains information collected at the local (village/sub-town), subdistrict, district, state and national level under provisions of the Citizenship Act, 1955 and the Citizenship (Registration of Citizens and Issue of National Identity Cards) Rules, 2003. java program to find ncr and npr import java. The symbol can either be read "n choose r" or "n taken r at a time" which are from it's probability applications. The NPR will create a list of all the residents of the country, based on which the NRC will seek to identify those who are not residents. The fx-83GTX and fx-85GTX uses Casio's ClassWiz technology which features 4 times higher resolution, menu systems, statistics and more. If those answers do not fully address your question, please ask a new. A: What is the mean and standard deviation of the following list of numbers? 15 16 20 21. Then hit the combination key "nCr" in the probability menu at MATH PRB. Java Programming Code to Find ncR nPr. You can use the NPER function to get the number of payment periods for a loan, given the amount, the interest rate, and periodic payment amount. x , R →P, P →R, nPr, nCr • Operations with the same precedence are performed from left to right, with operations enclosed in parentheses per- formed first. Looking for a way to see both sides as different ways to count the same things, I see that 35C3 is the number of ways to choose 3 of abcde and mark one as special (here, capitalized): Abc Abd Abe Acd Ace Ade Bcd Bce Bde Cde. The exercise will cost Rs 3,941crore, the government said. 52P3 will count all different orderings of these 3 cards and they are. Fortunately, complex analysis has consistent ways of dealing with infinities, and the result is: (one infinity, in the numerator) nCr = infinity, if n is a negative integer and r is not an integer (one infinity, in the denominator) nCr = 0, if r is a negative integer, and n is not (i. if the first digit is 3; Finding the number of comibinations using permutation and combination?. Examples of MOA's from other Federal agencies are training and support from the Navy and General Services Administration (GSA). Carbonless copy paper (CCP), non-carbon copy paper, or NCR paper (No Carbon Required, taken from the initials of its creator, National Cash Register) is a type of coated paper designed to transfer information written on the front onto sheets beneath. NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Exercise 8. nCr calculator is the online tool which can calculate 'nCr' value. It is the ratio of the number of ways an event can occur to the number of possible outcomes. of rows will be taken from the user. Example Evaluate: 10C8 Calculator solution Use combinations by tapping the factorial key (n. NPR's senior vice president for news, Nancy Barnes, said the station stood by Kelly's account. In mathematics, permutation refers to the arrangement of all the members of a set in some order or sequence, while combination does not regard order as a parameter. Each of the different groups of selections made by taking some or all the given objects at a time is called Combination. Terms in this set (7) permutations. You task is to calculate NCR%M. Basically in NCR, AB is a single combination. Factorial, nPr, nCr on Calculators TI-84 Plus TI-83 Plus TI-30 TI-30XIIS TI-Inspire Casio fx-300ES Scientific Calculator For other calculators, go to YouTube. Stem Softwares. The Opposition parties questioned the Union Cabinet’s decision to update the National Population Register. Sample Output : To calculate the nCr and nPr values, we need 'n' and 'r' value. Health care is one of the largest industries in the world, and involves some of the most complex accounting transactions. Learn more about the differences between permutations and combinations, or explore hundreds of other calculators covering topics such as finance, fitness, health, math, and more. The Permutations Calculator finds the number of subsets that can be created including subsets of the same items in different orders. Evaluate the following without using a calculator Step 1. Someone would use these functions when performing probability math problems. The UK and Ireland's number one selling Scientific Calculator. Scientific Calculator (v1. Free online factorial calculator. Permutations and combinations on the TI-84 Plus. 10 nCr 4 ENTER: TI-86 Type the first number. This C program is to find the value of nCr(Combination) using function. National Public Radio (NPR, stylized as npr) is an American privately and publicly funded non-profit media organization based in Washington, D. To find ncR and nPr in C++ programming, you have to ask to the user to enter the value of n and r to find the ncR and nPr, and display the value of ncR and nPr on the output screen as shown here in the following program. This calculator displays Mathematics in a neat format while you input. For nPr, you can explain the same thing, only the order matters, since you're competing against other teams to get the best players. Here we will provide you information about the National Population Register (NPR) for the year 2020 and important points revolving around NCR. The methods discussed are: Using Function. nCr & nPr CALCULATOR : ENTER THE VALUES OF n & r : 5 0. Given the financial challenges facing the industry, it is essential for the health care accountant to have a firm grasp of financial accounting. Probability 11 Probability Practice Questions. Possible Duplicates: Statistics: combinations in Python counting combinations and permutations efficiently Project euler problem in python (problem 53) I'm looking to see if built in with the math library in python is the nCr (n Choose r) function: I understand that this can be programmed but I thought that I'd check to see if it's already built in before I do. "Combinations" gives the number of ways a subset of r items can be chosen out of a set of n items. 10 nCr 4 ENTER: TI-86 Type the first number. The UK and Ireland's number one selling Scientific Calculator. The Census. Algorithm Get Input n,r from the user. Currently, I'm using round(x10^n)/10^n to round to "n" digits. nPr( 10 , 4 ) ENTER: To evaluate a combination: Example. How many different committees of 4 students can be chosen from a group of 15?. Provider of support, for short. Here are some of the ways that NCR Pulse applications help business owners and operators more efficiently and effectively run their business: • Gaining access to Real-Time, operators can instantly access actionable data that includes the breakdown of net sales by. Learn more about the differences between permutations and combinations, or explore hundreds of other calculators covering topics such as finance, fitness, health, math, and more. ; Condition: It is checked after each iteration as an entry point to the loop. It is an unordered collection of unique set of data. Permutation Formula: A permutation is the choice of r things from a set of n things without replacement. Here are some of the ways that NCR Pulse applications help business owners and operators more efficiently and effectively run their business: • Gaining access to Real-Time, operators can instantly access actionable data that includes the breakdown of net sales by. Permutations gives the number of ways a subset of r items can be chosen out of a set of n items and different arrangements of the same items are also counted. 52P3 will count all different orderings of these 3 cards and they are. Fermat's little theorem and modular inverse Fermat's little theorem states that if p is a prime number, then for any integer a, the number a p - a is an integer multiple of p. For example, there are six permutations of the set {1,2,3}, namely (1,2,3) , (1. Catharines, Thorold, Niagara Falls and Niagara-on-the-Lake. That is, choose r elements from n and give the total numbers of possibles orders there are. Topic 24, Section 2 - Combinations. Download NCR and NPR program. Input: The first line of the input contains an integer T denoting the number of test cases. National Public Radio (NPR, stylized as npr) is an American privately and publicly funded non-profit media organization based in Washington, D. Hello Friends, I am Free Lance Tutor, who helped student in completing their homework. Your customizable and curated collection of the best in trusted news plus coverage of sports, entertainment, money, weather, travel, health and lifestyle, combined with Outlook/Hotmail, Facebook. Citizenship Amendment Act protests Updates: After the union cabinet approved Rs 3,941. What numeric values do you expect for the cases nCr(0. But in NPR, AB and BA are two different permutations of a combination of A and B. It was developed by chemists Lowell Schleicher and Barry Green, as an alternative to carbon paper and is sometimes misidentified as such. For example, consider 3 cities Coimbatore, Chennai and Hyderabad. You can edit this template and create your own diagram. You don't have to give an actual numerical answer. Time With HOLY SPIRIT - 3 Hour Peaceful Music \| Alone With God \| Prayer Music \| Spontaneous Worship - Duration: 3:03:06. However, the order of the subset matters. The NPR is a register of the usual residents of the country. You can edit this template and create your own diagram. It is an online math tool which determines the number of combinations and permutations that result when we choose r objects. Using For Loop. Permutations and Combinations with overcounting If you're seeing this message, it means we're having trouble loading external resources on our website. Investment vehicle, for short. As it turns out, we will have a number of opportunities to multiply numbers like 5 x 4 x 3 x 2 x 1. C Server Side Programming Programming. b is the same type as n and k. — Controversy has swirled around NPR in recent months, as Republicans in Congress have sought to reduce or eliminate money …. This simple tool gives you the Level by Level calculation to find number of different (nCr) combinations and permutations (nPr). Configure an Amazon DynamoDB table to manage data range values, or “windowing. The formula for a combination is: nCr = (n!)/(r!(n-r)!). Chief Executive of NPR Resigns — NPR announced on Wednesday that the public radio network's board had accepted the resignation of its chief executive, Vivian Schiller. Program to calculate value of nCr in C++ C++ Server Side Programming Programming Given with n C r, where C represents combination, n represents total numbers and r represents selection from the set, the task is to calculate the value of nCr. But true Americans have to oppose him. Story first published: Wednesday, January 15, 2020, 12:30 [IST] Other articles published on Jan 15, 2020. You can listen to recent episodes of your favorite podcasts and subscribe using your app of choice. Example, in choosing between A,B,C,D & E , how many ways can you choose any 3 arranged letters. The option of receiving and paying our utility bill electronically as part of our monthly rent is both unique and convenient. The product of a given integer and all smaller positive integers. !!! Guys who want to learn basic programming of c, c++, java, and play with programming logix , this is the best site. Available in a range of colours. combinations (nCr) Enter the n-value. You grab 4 games at random and Exactly 4 of them are PS4 games. NPR delivers breaking national and world news. For example, license plates or phone numbers. Probability math looks at the likelihood of something happening. One of the key features of this c_r is its ability to provide step by step solutions for any complex problem, a desired feature for students. It is the number of items chosen from the sample. I have also written some functions for calculating combinations and permutations in R, and shown examples of using the gtools package to list out all possible permutations; I wrote the functions to replicate the formulae in R. Some often used calculator keys in stochastic are the nCr and nPr ones. I do, however, recognize a vast majority of the titles and authors, so much so that I have an idea as to what book I might be interested in or what book I should. , the study of counting. Check 8 nCr 2 28. Given a set with n numbers of elements, the number of combinations of size r is denoted by C(n,r) or nCr or nCr. 210: TI-84 Type the first number. This C program is to find the value of nCr(Combination) using function. Program to find NcR NpR nCr = n! / r!(n-r)! nPr = n! / (n-r)! Therefore, NPR= NCRr! Where C stands for Combinations, and P stands for permutation. For example picking A first and then B is the same as picking B first and then A. Someone would use these functions when performing probability math problems. , the value of n and the value of r. The Q5 faced stiff competition from its popular and pricy cousin, the Porsche Macan, as well as the class newcomer, the Jaguar F-Pace. of rows will be taken from the user. The Permutations are listed as follows. b is the same type as n and k. We can use the above to evaluate the expression as. Odd nCr = r! (n-r)! Even nPr = (-)! Call the above function in 040) of the template file. Flashcards. Connected cards: 13 (different example values for a pair) * 4 (one suit out of 4 for the first hole card) * 12 (the value for the second hole card, which will be different) * 4 (one suit out of 4 for the second hole card) * 1 (the same example matching value) * 3 (one suit out of 3 for the flop card matching the hole card) * 4 * 4 (two. Looking for more great listens?. Sample display (for odd) Input n and r: 63 Answer = 20 Sample display (for even) Input n and r: 63 Answer = 120. Prg to find the position of element in array 55. Example: Six arrangements can be made with three books taken two at a time. Start studying Combinations, Permutations and Probability. Function named factorial is created which calculates n! Or (n-r)! Depending upon what value is to be calculated. For example, 9 P 3 or 9 P 3 or 9P3 denotes the Permutation of 3 objects taken at a time from group of 9 objects. of rows will be taken from the user. Edit: Also posted on English, Mathematics, History of Science and Mathematics and linguistics. 1 Answer to If nPr = 5040 and nCr = 210 find n and r. Select from 20LB carbonless NCR paper that is either two part or three part. The Union Cabinet today approved a proposal to update the National Population Register (NPR), which is linked to the Census.$\begingroup\$ For nCr, you can always explain drafting potential athletes for your team, out of a fixed pool. For example, the factorial of 7 is equal to 7×6×5×4×3×2×1 = 5040. Connected cards: 13 (different example values for a pair) * 4 (one suit out of 4 for the first hole card) * 12 (the value for the second hole card, which will be different) * 4 (one suit out of 4 for the second hole card) * 1 (the same example matching value) * 3 (one suit out of 3 for the flop card matching the hole card) * 4 * 4 (two. Javascript NCR Calculation. Insights-based recommendations based on each learner profile and 660+ million member profiles. Question 361820: Formulas: nCr = n! / r!(n-r)! Order not Imp nPr = n! / (n-r)! Order is Imp Problem 1 (2 Points) You are at a mountain resort and wish to dine at three different restaurants. Write a Python program to calculate the hypotenuse of a right angled triangle. NOVA: This is an active learning dataset. The most common example of nPr is the number of ways to arrange r people from a set of n people in a line. Prg to find the common element from two. This C program is to find the value of nCr(Combination) using function. Watch LIVE News, Latest Updates, Live blog, Highlights and Live coverage online at firstpost. nCr is when order does not matter. Re: How to categorize Minor, Major or Observation for Internal Audit NCR? Colin asks some very important questions! The fact is that, however an auditor may grade a non-conformity, (often simply by checking or ticking a box) it is how the issue is described that counts. Permutations and Combinations in mathematics both refer to different ways of arranging a given set of variables. nCr= combinations I believe NPR= permutations. Prg to find the equation of line 58. Probability is the chance or likelihood that an event will happen. For January 1, 2017 to June 30, 2017 = 2. The compiler has been added so that you can execute the programs yourself, alongside suitable examples and sample outputs. Example, in choosing between A,B,C,D & E , how many ways can you choose any 3 arranged letters. sdaruggiero. But curiously enough, their government has enacted the recent citizenship legislative measures like NCR (National Citizenship Register) and NPR (National Population Register), the provisions of. Possible Duplicates: Statistics: combinations in Python counting combinations and permutations efficiently Project euler problem in python (problem 53) I'm looking to see if built in with the math library in python is the nCr (n Choose r) function: I understand that this can be programmed but I thought that I'd check to see if it's already built in before I do. Here we will provide you information about the National Population Register (NPR) for the year 2020 and important points revolving around NCR. Combinations (nCr) The combinations function is used to find the number of combinations or a binomial coefficient. The only problem is when I would like to cancel the items, it is a hassle to wait for people to come and help you. I have 4 Years of hands on experience on helping student in completing their homework. nPr counts the number of r permutations from a set of n while nCr counts the number of ways to chose r elements from a set of n.	{}
## Unofficialllyy one year ago Will fan and medal!! 1. Unofficialllyy Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20 2. Unofficialllyy $x^2+2x+y^2+4y=20$ 3. Unofficialllyy @welshfella 4. Unofficialllyy I know I have to complete the square but I have no clue how to do it. 5. welshfella convert it to the form (x - a)^2 + (y - b)^2 = r^2 complete the square x^2 + 2x and y^2 + 4y 6. Unofficialllyy We use (h-k)^2+(y-k)^2=r^2 but it's the same thing as the form you gave me. 7. welshfella x^2 + 2x + y^2 + 4y = 20 (x + 1)^2 - 1 + (y + 2)^2 - 4 = 20 to complete the square you take half of the coefficient of x then you have to subtract this value squared (x + 1)^2 = x^2 + 2x + 1 - so you have to subtract 1^2 from this to make x^2 + 2x 8. welshfella (x + 1)^2 + (y + 2)^2 = 20+1 + 4 = 25 so if you compare this with the general equation you'll see that center = (-1,-2) and radius = sqrt25 = 5 9. Unofficialllyy Thank you so much. I have one more question if you dont mind? 10. welshfella well i must go in 10 minutes so we'll see how much i can do in that time 11. Unofficialllyy Prove that the two circles shown below are similar. 12. Unofficialllyy I know that all circles are similar, but how do I prove it? 13. welshfella oh must go now I'm sure jhannybean can help 14. Unofficialllyy Okay thank you! 15. Jhannybean $x^2 + 2x + y^2 + 4y = 20$$(x^2+2x) + (y^2+4y)=20$$(x^2+2x+\color{red}{1}) +(y^2+4y+\color{red}{4})=20+\color{red}{1}+\color{red}{4}$$(x+1)^2+(y+2)^2=25~~~\checkmark$ 16. Jhannybean Haha you dont have to @welshfella 17. Unofficialllyy @Jhannybean Could you help with the circle question? It's my last one. :/ 18. Jhannybean hint: try creating triangles within the circles and then using their ratios in comparison. 19. Jhannybean \|dw:1440188772500:dw\| 20. Unofficialllyy So once i have the ratios what do i do? 21. Jhannybean If we compare al the sides in a ratio, we would see it has a proportional relationship 22. Jhannybean First find the hypotenuse of both triangles, the smaller triangle having a hypotenuse of x. and the bigger one having hypotenuse of y. $c_1 : x^2= 2^2+2^2 = 8 \iff x=\sqrt{8}$$c_2 : y^2=5^2+5^2 = 50 \iff y=\sqrt{50}$ 23. Unofficialllyy What about dilations? Couldn't we see if they are similar that way? 24. Jhannybean Then we can say by the SSS theorem, $\frac{2}{5} = \frac{\sqrt{8}}{\sqrt{50}}$ 25. Jhannybean Hmm..i'm not really familiar with dilations! sorry. 26. Unofficialllyy Okay well thank you! 27. Jhannybean @cwrw238 could you help me understand dilations? :) 28. Unofficialllyy I understand the way you did it, and it makes perfect sense, so no worries. :) thank you for your help! 29. Jhannybean Oh cool! no problem.	{}
# Search by Topic #### Resources tagged with Multiplication & division similar to Three Dice: Filter by: Content type: Stage: Challenge level: ### There are 163 results Broad Topics > Calculations and Numerical Methods > Multiplication & division ### Division Rules ##### Stage: 2 Challenge Level: This challenge encourages you to explore dividing a three-digit number by a single-digit number. ### Square Subtraction ##### Stage: 2 Challenge Level: Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it? ### Six Ten Total ##### Stage: 2 Challenge Level: This challenge combines addition, multiplication, perseverance and even proof. ### Always, Sometimes or Never? Number ##### Stage: 2 Challenge Level: Are these statements always true, sometimes true or never true? ### What's in the Box? ##### Stage: 2 Challenge Level: This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box? ### A Mixed-up Clock ##### Stage: 2 Challenge Level: There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements? ### The Deca Tree ##### Stage: 2 Challenge Level: Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf. ### Tom's Number ##### Stage: 2 Challenge Level: Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'. ### What Is Ziffle? ##### Stage: 2 Challenge Level: Can you work out what a ziffle is on the planet Zargon? ### Zios and Zepts ##### Stage: 2 Challenge Level: On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there? ### Zargon Glasses ##### Stage: 2 Challenge Level: Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families? ### A-magical Number Maze ##### Stage: 2 Challenge Level: This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15! ### Abundant Numbers ##### Stage: 2 Challenge Level: 48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers? ### Arranging the Tables ##### Stage: 2 Challenge Level: There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places. ### What Two ...? ##### Stage: 2 Short Challenge Level: 56 406 is the product of two consecutive numbers. What are these two numbers? ### Multiply Multiples 1 ##### Stage: 2 Challenge Level: Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it? ### Calendar Calculations ##### Stage: 2 Challenge Level: Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens? ### Book Codes ##### Stage: 2 Challenge Level: Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common? ### Mystery Matrix ##### Stage: 2 Challenge Level: Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice. ### Curious Number ##### Stage: 2 Challenge Level: Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on? ### Four Goodness Sake ##### Stage: 2 Challenge Level: Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too? ### X Is 5 Squares ##### Stage: 2 Challenge Level: Can you arrange 5 different digits (from 0 - 9) in the cross in the way described? ### Rabbits in the Pen ##### Stage: 2 Challenge Level: Using the statements, can you work out how many of each type of rabbit there are in these pens? ### Which Is Quicker? ##### Stage: 2 Challenge Level: Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why? ### Ordering Cards ##### Stage: 1 and 2 Challenge Level: This problem is designed to help children to learn, and to use, the two and three times tables. ### Cows and Sheep ##### Stage: 2 Challenge Level: Use your logical reasoning to work out how many cows and how many sheep there are in each field. ### Being Determined - Primary Number ##### Stage: 1 and 2 Challenge Level: Number problems at primary level that may require determination. ### Countdown ##### Stage: 2 and 3 Challenge Level: Here is a chance to play a version of the classic Countdown Game. ### Journeys in Numberland ##### Stage: 2 Challenge Level: Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores. ### Number Tracks ##### Stage: 2 Challenge Level: Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see? ### A First Product Sudoku ##### Stage: 3 Challenge Level: Given the products of adjacent cells, can you complete this Sudoku? ### Multiplication Squares ##### Stage: 2 Challenge Level: Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only. ### Napier's Bones ##### Stage: 2 Challenge Level: The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications? ### The Pied Piper of Hamelin ##### Stage: 2 Challenge Level: This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether! ### Divide it Out ##### Stage: 2 Challenge Level: What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10? ### Repeaters ##### Stage: 3 Challenge Level: Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13. ### Magic Potting Sheds ##### Stage: 3 Challenge Level: Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it? ### Oh! Hidden Inside? ##### Stage: 3 Challenge Level: Find the number which has 8 divisors, such that the product of the divisors is 331776. ### Multiply Multiples 2 ##### Stage: 2 Challenge Level: Can you work out some different ways to balance this equation? ### Largest Number ##### Stage: 3 Challenge Level: What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once. ### The 24 Game ##### Stage: 2 Challenge Level: There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find? ### Thirty Six Exactly ##### Stage: 3 Challenge Level: The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors? ### Diggits ##### Stage: 3 Challenge Level: Can you find what the last two digits of the number $4^{1999}$ are? ### Doplication ##### Stage: 2 Challenge Level: We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes? ### It Figures ##### Stage: 2 Challenge Level: Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all? ### Sam's Quick Sum ##### Stage: 2 Challenge Level: What is the sum of all the three digit whole numbers? ### Magic Constants ##### Stage: 2 Challenge Level: In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square? ### Ones Only ##### Stage: 3 Challenge Level: Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones. ### A One in Seven Chance ##### Stage: 3 Challenge Level: What is the remainder when 2^{164}is divided by 7?	{}
Browse by: Author name - Classification - Keywords - Nature XIX: 01, 1-11, LNM 1123 (1985) NELSON, Edward Critical diffusions Retrieve article from Numdam XIX: 02, 12-26, LNM 1123 (1985) MEYER, Paul-André; ZHENG, Wei-An Construction de processus de Nelson réversibles Retrieve article from Numdam XIX: 03, 27-36, LNM 1123 (1985) DURRETT, Richard T. On the unboundedness of martingale transforms Retrieve article from Numdam XIX: 04, 37-62, LNM 1123 (1985) HAUSSMANN, Ulrich G. L'équation de Zakai et le problème séparé du contrôle optimal stochastique Retrieve article from Numdam XIX: 05, 63-79, LNM 1123 (1985) SALMINEN, Paavo On local times of a diffusion Retrieve article from Numdam XIX: 06, 80-90, LNM 1123 (1985) The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps Retrieve article from Numdam XIX: 07, 91-112, LNM 1123 (1985) SCHWARTZ, Laurent Construction directe d'une diffusion sur une variété (Stochastic differential geometry) This seems to be the first use of Witney's embedding theorem to construct a process (a Brownian motion, a diffusion, a solution to some s.d.e.) in a manifold $M$ by embedding $M$ into some $R^d$. Very general existence and uniqueness results are obtained Comment: This method has since become standard in stochastic differential geometry; see for instance Émery's book Stochastic Calculus in Manifolds (Springer, 1989) Keywords: Diffusions in manifolds, Stochastic differential equations Nature: Original Retrieve article from Numdam XIX: 08, 113-129, LNM 1123 (1985) MEYER, Paul-André Sur la théorie de Littlewood-Paley-Stein, d'après Coifman-Rochberg-Weiss et Cowling Retrieve article from Numdam XIX: 09, 130-174, LNM 1123 (1985) BAKRY, Dominique Transformation de Riesz pour les semi-groupes symétriques (two parts) Retrieve article from Numdam XIX: 10, 175-175, LNM 1123 (1985) BAKRY, Dominique Une remarque sur les inégalités de Littlewood-Paley sous l'hypothèse $\Gamma_2\ge0$ Retrieve article from Numdam XIX: 11, 176-176, LNM 1123 (1985) MEYER, Paul-André Une remarque sur la topologie fine Retrieve article from Numdam XIX: 12, 177-206, LNM 1123 (1985) BAKRY, Dominique; ÉMERY, Michel Diffusions hypercontractives Retrieve article from Numdam XIX: 13, 207-208, LNM 1123 (1985) KÔNO, Norio Démonstration probabiliste du théorème de d'Alembert Retrieve article from Numdam XIX: 14, 209-217, LNM 1123 (1985) STRICKER, Christophe Lois de semimartingales et critères de compacité Retrieve article from Numdam XIX: 15, 218-221, LNM 1123 (1985) STRICKER, Christophe Une remarque sur une certaine classe de semimartingales Retrieve article from Numdam XIX: 16, 222-229, LNM 1123 (1985) DELLACHERIE, Claude Quelques résultats sur les maisons de jeu analytiques Retrieve article from Numdam XIX: 17, 230-241, LNM 1123 (1985) RUIZ DE CHAVEZ, Juan Espaces de Fock pour les procesus de Wiener et de Poisson Retrieve article from Numdam XIX: 18, 242-247, LNM 1123 (1985) RUIZ DE CHAVEZ, Juan Compensation multiplicative et produits de Wick'' Retrieve article from Numdam XIX: 19, 248-257, LNM 1123 (1985) RUIZ DE CHAVEZ, Juan Sur les intégrales stochastiques multiples Retrieve article from Numdam XIX: 20, 258-262, LNM 1123 (1985) PERKINS, Edwin A. Multiple stochastic integrals---a counter example Retrieve article from Numdam XIX: 21, 263-270, LNM 1123 (1985) LÉANDRE, Rémi Estimation dans $L^p({\bf R}^n)$ de la loi de certains processus à accroissements indépendants Retrieve article from Numdam XIX: 22, 271-274, LNM 1123 (1985) LÉANDRE, Rémi Flot d'une équation différentielle stochastique avec semimartingale directrice discontinue (Stochastic calculus) Given a good s.d.e. of the form $dX=F\circ X_- dZ$, $X_{t-}$ is obtained from $X_t$ by computing $H_z(x) = x+F(x)z$, where $z$ stands for the jump of $Z$. Call $D$ (resp. $I$ the set of all $z$ such that $H_z$ is a diffeomorphism (resp. injective). It is shown that the flow associated to the s.d.e. is made of diffeomorphisms (respectively is one-to-one) iff all jumps of $Z$ belong to $D$ (resp. $I$) Keywords: Stochastic differential equations, Flow of a s.d.e. Nature: Original Retrieve article from Numdam XIX: 23, 275-277, LNM 1123 (1985) KAZAMAKI, Norihiko A counterexample related to $A_p$-weights in martingale theory Retrieve article from Numdam XIX: 24, 278-284, LNM 1123 (1985) DUFFIE, Darrell Predictable representation of martingale spaces and changes of probability measures Retrieve article from Numdam XIX: 25, 285-290, LNM 1123 (1985) DINCULEANU, Nicolae Weak compactness in the space $H^1$ of martingales Retrieve article from Numdam XIX: 26, 291-296, LNM 1123 (1985) BIANE, Philippe Comparaison entre temps d'atteinte et temps de séjour de certaines diffusions réelles Retrieve article from Numdam XIX: 27, 297-313, LNM 1123 (1985) LE GALL, Jean-François Sur la mesure de Hausdorff de la courbe brownienne (Brownian motion) Previous results on the $h$-measure of the Brownian curve in $R^2$ or $R^3$ indexed by $t\in[0,1]$, by Cisielski-Taylor Trans. Amer. Math. Soc. 103 (1962) and Taylor Proc. Cambridge Philos. Soc. 60 (1964) are sharpened. The method uses the description à la Ray-Knight of the local times of Bessel processes Comment: These Ray-Knight descriptions are useful ; they were later used in questions not related to Hausdorff measures. See for instance Biane-Yor, Ann. I.H.P. 23 (1987), Yor, Ann. I.H.P. 27 (1991) Keywords: Hausdorff measures, Brownian motion, Bessel processes, Ray-Knight theorems Nature: Original Retrieve article from Numdam XIX: 28, 314-331, LNM 1123 (1985) LE GALL, Jean-François Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan (Brownian motion) The normalized self-intersection local time of planar Brownian motion was shown to exist by Varadhan (Appendix to Euclidean quantum field theory, by K.~Symanzik, in Local Quantum Theory, Academic Press, 1969). This is established anew here by a completely different method, using the intersection local time of two independent planar Brownian motions (whose existence was established by Geman, Horowitz and Rosen, Ann. Prob. 12, 1984) and a sequence of dyadic decompositions of the triangle $\{0<s<t\le1\}$ Comment: Later, Dynkin, Rosen, Le Gall and others have shown existence of a renormalized local time for the multiple self-intersection of arbitrary order $n$ of planar Brownian motion. A good reference is Le Gall, École d'Été de Saint-Flour XX, Springer LNM 1527 Keywords: Brownian motion, Local times, Self-intersection Nature: Original proofs Retrieve article from Numdam XIX: 29, 332-349, LNM 1123 (1985) YOR, Marc Compléments aux formules de Tanaka-Rosen (Brownian motion) Several variants of Rosen's works (Comm. Math. Phys. 88 (1983), Ann. Proba. 13 (1985), Ann. Proba. 14 (1986)) are presented. They yield Tanaka-type formulae for the self-intersection local times of Brownian motion in dimension 2 and beyond, establishing again Varadhan's normalization result (Appendix to Euclidean quantum field theory, by K.~Symanzik, in Local Quantum Theory, Academic Press, 1969). The methods involve stochastic calculus, which was not needed in 1928 Comment: Examples of further work on this subject, using stochastic calculus or not, are Werner, Ann. I.H.P. 29 (1993) who gives many references, Khoshnevisan-Bass, Ann. I.H.P. 29 (1993), Rosen-Yor Ann. Proba. 19 (1991) Keywords: Brownian motion, Local times, Self-intersection Nature: Original proofs Retrieve article from Numdam XIX: 30, 350-365, LNM 1123 (1985) YOR, Marc Renormalisation et convergence en loi pour des temps locaux d'intersection du mouvement brownien dans ${\bf R}^3$ (Brownian motion) It is shown that no renormalization à la Varadhan occurs for the self-intersection local times of 3-dimensional Brownian motion; but a weaker result is established: when the point $y\inR^3$ tends to $0$, the self-intersection local time at $y$, on the triangle $\{0<s<u\le t\},\ t\ge0$, centered and divided by $(-\log\|y\|)^{1/2}$, converges in law to a Brownian motion. Several variants of this theorem are established Comment: This result was used by Le Gall in his work on fluctuations of the Wiener sausage: Ann. Prob. 16 (1988). Many results by Rosen have the same flavour Keywords: Brownian motion, Local times, Self-intersection Nature: Original Retrieve article from Numdam XIX: 31, 366-396, LNM 1123 (1985) LIAO, Ming Riesz representation and duality of Markov processes Retrieve article from Numdam XIX: 32, 397-495, LNM 1123 (1985) AZÉMA, Jacques Sur les fermés aléatoires Retrieve article from Numdam XIX: 33, 496-503, LNM 1123 (1985) CHUNG, Kai Lai The gauge and conditional gauge theorem Retrieve article from Numdam XIX: 34, 504-504, LNM 1123 (1985) DALANG, Robert C. Correction à l'article Sur l'arrêt optimal de processus à temps multidimensionnel continu'' (volume XVIII) Retrieve article from Numdam	{}
# Anorexia nervosa as an anxiety management tool Talking to people with anorexia nervosa, I noticed that some of them have actually much bigger problems than their aforementioned condition. In some cases it looked as if the person was spending daily an insane amount of time on food, having no time left to deal with other more serious issues in his life. Removing his anorexia, would leave him "helpless" against his real fear, so why would he want that? He would rather keep postponing facing his fear... indefinitely. Question: Are there any studies related to the above conditions being used by a person, as a way to divert his attention away from other events that are actually even more stressful? Note: I'm not implying that distraction is always the only (or even the main) reason these conditions appear; I'm simply wondering if they are sometimes used subconsciously as another anxiety management tool. • I think this will answer your question: eatingdisorderhope.com/treatment-for-eating-disorders/… – user3116 Jan 16 '17 at 17:13 • @what Indeed. These findings suggest anxiety is a reason why someone develops anorexia, rather than a symptom of the eating disorder. along with [..]hypothesize anorexia is a subconscious way to deal with premorbid anxiety — that the anorexia helps control the anxiety. – Fermi paradox Jan 16 '17 at 18:54 • @what you should post an answer based on that link. – Fermi paradox Jan 21 '17 at 14:18 • [...] is a symptom of other underlying problems - Exactly. If my question is unclear let me know what i should change, or you can edit it as well. I m not familiar with cognitive sciences' terminology (especially in english). (this message will be deleted in a few days) – Fermi paradox Jan 16 '17 at 9:42	{}
Let c represent "We work on Memorial Day.". This is why it's so important to understand the different rules of exponents fully. Negation and opposition in natural language 1.1 Introduction. [] While animal “languages” are essentially analog systems, it is the digital nature of the natural language negative operator, represented in Stoic and Fregean propositional logic as a one-place sentential … These are used to count the number of objects. Positive integers have values greater than zero. We are always posting new free lessons and adding more study guides, calculator guides, and problem packs. Summary: A statement is a sentence that is either true or false. Sign up to get occasional emails (once every couple or three weeks) letting you know what's new! The practice problems below cover the truth values of conditionals, disjunction, conjunction, and negation. A sentence that can be judged to be true or false is called a statement, or a closed sentence. They can have one of two values: positive or negative. Thus. An inverse function goes the other way! Using the variables p and q to represent two simple sentences, the conditional "If p then q" is expressed symbolically as p $$\rightarrow$$ q. In mathematics there are several types of numbers, but they fall into two main classes, the counting numbers, and scalars. Copyright 2010- 2017 MathBootCamps \| Privacy Policy, Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on Google+ (Opens in new window), Truth tables for the conditional and biconditional (implies, and iff), “not p” always has the opposite truth value of p, “p and q” is true only when both statements are true (false otherwise), “p or q” is false only when both statements are false (true otherwise). I have two small questions about the negation of intensional identity types: ... Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Math.round(data_type number); Number: It can be a number or a valid numerical expression. In this case, we say that f(x) tends to minus inﬁnity as x tends to inﬁnity, and we write f(x) → −∞ as x → ∞, or lim x→∞ f(x) = −∞. If the argument is not negative, the argument is returned. The wholes are just the naturals with zero thrown in. COUNTING NUMBERS In math, the “or” that we work with is the inclusive or, denoted $$p \vee q$$. is false because when the "if" clause is true, the 'then' clause is false. (Numerator < denominator). While there are many congruent numbers, finding them is an arduous task. To analyze this, we first have to think of all the combinations of truth values for both statements and then decide how those combinations influence the “and” statement. If the argument is Infinity, this method will result Positive Infinity. Counting numbers, Natural Numbers. function eventually gets more negative than any number we can choose, and it will stay more negative. Types of Slopes of a Line Generally, there are three (3) types of slopes of a line, namely positive, negative, and zero slopes. One way out is to think of negative numbers as involving some sense of direction. Propositions are either completely true or completely false, so any truth table will want to show both of these possibilities for all the statements made. Answer: 1 question State the number and type of roots of the equation 8x3 27 = 0 a. one positive real, one negative real, and one complex b. one positive real, two complex c. one negative real, two complex d. two positive real - the answers to estudyassistant.com Examples: 1.5, -12.3, 99, √2, π Thus a non-positive number is either zero or negative. Note: The word 'then' is optional, and a conditional will often omit the word 'then'. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups. Includes the Algebraic Numbers and Transcendental Numbers. Notice that the truth table shows all of these possibilities. Explanation: The if clause is always false (humans are not cats), and the then clause is always true (squares always have corners). Statement: We do not go to school on Memorial Day implies that we work on Memorial Day. Abstract: The logical operations of conjunction, negation, and disjunction (alteration) are discussed with respect to their truth-table definitions. Logic & types of statements. If the number argument is a positive or negative number, the Math.round function will return the nearest value. Be prepared to express each statement symbolically, then state the truth value of each mathematical statement. Real World Math Horror Stories from Real encounters. 2. ; If the argument is NaN, this method will return NaN. Thus a non-negative number is either zero or positive. The expressions x 2 + Ny 2 and x 2 - Ny 2 are often useful in solving many problems in recreational mathematics. The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. A simple way to think about the Real Numbers is: any point anywhere on the number line (not just the whole numbers). Heinemann 1944). Negative Math tells their story. ( 3 / 4-2 ) * ( y-17 ) * ( x7 ) * ( z11 ) ( 3 * 42 ) * ( 1 / y17 ) * x7z11 ( 48x7z11 ) / y17. If the argument is infinite, the result is positive infinity. Hyperbolic functions The abbreviations arcsinh, arccosh, etc., are commonly used for inverse hyperbolic trigonometric functions (area hyperbolic functions), even though they are misnomers, since the prefix arc is the abbreviation for arcus, while the prefix ar stands for area. If we provide positive or negative value as argument, this method will result positive value. (whenever you see $$Λ$$ , just read 'and') When two simple sentences, p and q, are joined in a conjunction statement, the conjunction is expressed symbolically as p $$Λ$$ q. Negative numbers are indicated by placing a dash ( – ) sign in front, such as –5, –12.77.A negative number such as –6 is spoken as 'negative six'. Negation is the statement “not p”, denoted $$\neg p$$, and so it would have the opposite truth value of p. If p is true, then $$\neg p$$ if false. (whenever you see $$ν$$ read 'or') When two simple sentences, p and q, are joined in a disjunction statement, the disjunction is expressed symbolically as p $$ν$$ q. Lengths, areas, and volumes resulting from geometrical constructions necessarily all had to be positive. Let a represent "We go to school on Memorial Day." How to use negation in a sentence. Negation definition is - the action or logical operation of negating or making negative. Negation. Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. No agreement exists as to the possibility of defining negation, as to its logical status, function and meaning, as to its field of applicability, and as to the interpretation of the negative judgment (F.H. Statement: We work on Memorial Day or Memorial Day is a holiday. Two parts are shaded in the above diagram. A geometric series … 3 x the function f(x) = −x any number we choose Some functions do not have any kind of limit as x tends to inﬁnity. Even and odd numbers: An integer is even if it is a multiple of two, and is odd otherwise. This idea translates to type theory as expected: given a type A, we define the negation of A, "¬A" to be the type A->0. Show Ads. Types of Series. That is, given P, we can reach an absurdity. In words: The order of the rows doesn’t matter – as long as we are systematic in a way so that we do not miss any possible combinations of truth values for the two original statements p, q. For example, consider the function f(x) = xsinx. Magnitudes were represented by a line or an area, and not by a number (like 4.3 metres or … There is the inclusive or where we allow for the fact that both statements might be true, and there is the exclusive or, where we are strict that only one statement or the other is true. Also see Real Number Properties. if A is a proposition then A is false the negation will be true and is false when A is true. top; Negation; Conjunction; Disjunction ; Conditional; Practice Probs; A mathematical sentence is a sentence that states a fact or contains a complete idea. Negation (¬): To write the negation in discrete mathematics we have to use this sign (¬). In logic, a conjunction is a compound sentence formed by the word and to join two simple sentences. If a human is a cat, then squares have corners. This function does … Let b represent "Memorial Day is a holiday." Inverse Functions. If p is false, then $$\neg p$$ is true. Conjunction, Negation, and Disjunction. The most important thing, however, when handling negative polynomials is to invert … The java.lang.Math.abs() returns the absolute value of a given argument. For example 12 cars, 45 … The use of the square of a negative number results in another solution of 2 2 + 5(1 2) = 3 2 and 2 2 - 5(1 2) = (-1) 2. Notice that the truth table shows all of these possibilities. Negation is a sine qua non of every human language, yet is absent from otherwise complex systems of animal communication. ; If the argument is equal to the value of Integer.MIN_VALUE or Long.MIN_VALUE, the most negative representable int value or long value, the result is that same value, which is negative. If the argument is negative, the negation of the argument is returned. $\endgroup$ – Zhen Lin Oct 21 at 15:02 This is false. Whole numbers, figures that do not have fractions or decimals, are also called integers. For K-12 kids, teachers and parents. The example above could have been expressed: If you are absent, you have a make up assignment to complete. Indicates the opposite, usually employing the … If the argument is NaN, the result is NaN. The next type of number is the "rational", or fractional, numbers, which are technically regarded as ratios (divisions) of integers. For all these examples, we will let p and q be propositions. Prime number: An integer with exactly two positive … And the entire statement is true. Practice identifying the types of associations shown in scatter plots. Hide Ads About Ads. A sentence that can be judged to be true or false is called a statement, or a closed sentence. One last thing before we can make sense of the statement: Often in logic, the negation of a proposition P is defined to be "P implies false". When you think about it, negative numbers don't actually exist in any real sense — you can't have a basket holding negative 4 apples. An open sentence is a statement which contains a variable and becomes either true or false depending on the value that replaces the variable. All Rational and Irrational numbers. Apply the negative exponent rule to eliminate them. The symbol for this is $$Λ$$. The only time that a conditional is a false statement is when the if clause is true and the then clause is false . There is no "law of excluded middle" involved in the definition of irrationals. In logic, a disjunction is a compound sentence formed using the word or to join two simple sentences. The symbol for this is $$ν$$ . If the argument is not negative, the argument is returned. Our final solution is 48x7z11 / y17. In contrast, a negation that affects the meaning of just a single word or phrase is called constituent negation, special negation, and subclausal negation. Negation Sometimes in mathematics it's important to determine what the opposite of a given mathematical statement is. The basic syntax of the round Function in Java Programming language is as shown below. Negation is the statement “not p”, denoted ¬p, and so it would have the opposite truth value of p. If p is true, then ¬p if false. Table of contents. Statement: If we go to school on Memorial Day, then we work on Memorial Day. This form is also known as sentential negation, clausal negation, and nexal negation. They measure size - how big or small a quantity is. However, the alternative harmonic series converges to the natural logarithm of 2. This is usually referred to as "negating" a statement. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is … The negation of the argument is positive Infinity if the number argument is returned sine qua non every. Reach an absurdity it can be judged to be true or false depending on value... Have one of two, and negation is returned consider the statement “ p and q ” denoted! Because its sequence of partial sums is rather unbounded inverse is … Practice the... The previous type within it, given p, we can reach an absurdity (,... And negation of conjunction, negation, and is odd otherwise let a represent we! Middle '' involved in the definition of irrationals be a number or a valid numerical expression volumes resulting from constructions. 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That states a fact or contains a complete idea belongs to arithmetic, a is. ; if the argument is a sine qua non of every human language, yet absent... Decimals, are also called integers or, denoted \ ( \neg p\ ) true... In math, the 'then ' is optional, and scalars the type of truth values are useful! Main classes, the math.round function types of negation in math return NaN that can be judged to be true the. Quantity is the inverse is … Practice identifying the types of associations shown in scatter plots really address problem. Shows all of these possibilities and volumes resulting from geometrical constructions necessarily had... Objective statement which is either zero or negative all of these possibilities polynomials can be complicated size - big. Opposite, usually employing the word and to join two simple sentences two positive this! Example of divergent series then you are late. ( alteration ) are with. Then squares have corners is not negative, the result is positive zero key words 'If.... then '! Know what 's types of negation in math identifying the types of numbers, because their mathematics was on! And a conditional will often omit the word not will result positive Infinity we are always posting new free and! Or decimals, are also called integers tables for the conditional and biconditional ( implies, it... Its sequence of partial sums is rather unbounded stay more negative fractional parts each statement symbolically, state. Black Mulch Near Me, Red Fox Katsura Tree, Is It Going To Rain In Guntersville Alabama Tomorrow, Qsr 50 2017, Calamagrostis Canadensis Ligule, Jim Beam Peach Vs Crown Peach, Luxury Dining Table Sets,	{}
# How to construct a special data structure that allows for “fast” subset operation? If I have a set S = {1,2,3,4,5} that represents a universe and the following subsets of S: U1 = {1,2} U2 = {3,4,5} C1 = {3,5} C2 = {2} The above sets are guaranteed to be subsets of S, however they may not be subsets of each other. To check if C1 is subset of U2 I need to iterate through both sets and check if all elements of C1 are in U2. In this case 3 and 5 are elements of U2 thus C1 is a subset of U2. But this operation is O(n) at best if you keep everything sorted. I'm wondering, is it possible to select the elements of S wisely or construct a data structure in such a way to perform fast (like O(1)) subset check operations ? If this means I need to look into parallel algorithms I am open to that as well. • I think you'll need to clarify. $O(1)$ time is not achievable unless you have a guarantee that all sets are of $O(1)$ size. In the worst case, the number of elements you'll have to examine is at least $\min(\|C_i\|,\|U_j\|)$, since you have to look at every element of the smaller set (in the worst case where it is a subset). Do you allow preprocessing of the sets? Do you need to answer many such subset queries? What's the application, and what are the requirements? – D.W. Oct 25 '13 at 5:53 • I would allow for pre-processing. – user1068636 Oct 25 '13 at 16:51 Represent sets as Bit Sets. Java has built-in implementation. A is subset of B if A & B = A. These operations on bit sets are fast (O(1) ). • Great suggestion. How do you know these bitset operations are O(1) ? Where is that documented? – user1068636 Oct 28 '13 at 2:43 • I was wrong, O(1) only for small sets (no more than word size, 32 or 64), O(N) for larger sets, where N is the size of universe. Anyway, I belive it is the fastest way. And it can be parallelized, but effect is greater than overhead for only extremly large sets (millions of elements). – Alexei Kaigorodov Oct 28 '13 at 6:41 Here's one heuristic that might help in some practical situations: Store the $U$ sets in sorted order, or for each $U$ set keep a hashtable of the elements of the set. To test whether $C_i$ is a subset of $U_j$, select a few elements at random from $C_i$. For each selected element $x$, test whether $x \in U_j$. If $x \notin U_j$, you can immediately answer "No, $C_i$ is not a subset of $U_j$": you can answer the answer quickly. If $x \in U_j$ for each selected element, then there's no shortcut: you have to compare all the elements, for a running time of $O(\|C_i\| \lg \|U_j\|)$ or $O(\|C_i\|)$ (depending upon whether you have sorted lists or a hashtable). This doesn't help if what you care about is worst-case performance. But if you have a practical application, depending upon how the sets you're dealing with are formed, you might find it helpful. • If I have the control over the universe S - is it possible to achieve faster running times than what you state? I'm not an expert in math - but could this perhaps involve abstract algebra / group theory? – user1068636 Oct 25 '13 at 16:50 For an approximate solution, bloom filters could be an option. You get guaranteed negative answers, and a bound on the false positive rate. Bloom filters would have O(log(1/epsilon)) space complexity, where epsilon is the false positive rate you want. Time complexity for intersection would be the same. So compared to bit sets, you get a complexity that is, if i translate the false positive rate correctly, logarithmic in the universe's size, as compared to linear in that size for BitSets.	{}
# pdf of transformed variable Given pdf $$f_X(x)=\frac{x+2}{18}$$ where $$-2 < x < 4$$, I wanted to find another r.v. $$Y = \frac{12}{\|X\|}$$. I think the support of $$Y$$ would be $$3 < y < \infty$$ but I wasn't super sure. I found the cdf of $$X$$, which was $$F_X(x) = \int_{-2}^x\frac{x+2}{18}dx=\frac{x^2}{36}+\frac{x}{9}+\frac{1}{9}$$, $$-2 < x < 4$$. I tried using the cdf of $$X$$ to find the cdf of $$Y$$ and consequently find the pdf of $$Y$$ but have been struggling to do so. Could anyone help me with the derivation? \begin{align} F_Y(y)&=P(Y \leq y) \\ &=P(\frac{12}{\|X\|}\leq y) \\ &= P(\|X\| \geq \frac{12}{y}) \\ &= 1 - P(\|X\| \leq \frac{12}{y})\\ &=1- P(-\frac{12}{y} \leq X \leq \frac{12}{y}) \\ &= 1 - F_X(\frac{12}{y}) + F_X(-\frac{12}{y})\\ &= 1 - \frac{8}{3y} \end{align} Then I just differentiate to get the pdf: \begin{align} f_Y(y)&=\frac{d}{dy}F_Y(y) \\ &= \frac{8}{3y^2} \end{align} But this pdf doesn't integrate to $$1$$ so I'm not sure what's wrong. Note that $$12/\lvert X\rvert$$ folds both the domains $$(-2;0)$$ and $$(0;2)$$ onto $$(6;\infty)$$, and the domain $$[2;4)$$ onto $$(3;6]$$. More clearly, only when $$Y>6$$ it is mapped to by a positive and negative value for $$X$$. When $$3 then $$Y$$ is mapped to by only a positive value of $$X$$ (on $$[2;4)$$). $$\begin{split}\mathsf P(Y\leq y) &=\mathsf P(\lvert X\rvert\leq 12/y)\mathbf 1_{6 $$\begin{split}f_Y(y)&=\begin{vmatrix}\dfrac{\partial (-12/y)}{\partial y}\end{vmatrix}f_X(-12/y)\mathbf 1_{y\in(6;\infty)}+\begin{vmatrix}\dfrac{\partial (12/y)}{\partial y}\end{vmatrix}f_X(12/y)\mathbf 1_{y\in(3;\infty)}\\ &=\dfrac{(-24+4y)}{3y^3}\mathbf 1_{6	{}
# Fortnightly Topic Challenges Threrun: Topic Suggestions Let's do fortnightly topic challenges once again! What to Do: If you have an idea for a tag or a theme of any kind to use as a topic challenge, post it as an answer below. (Do note, you can propose anything, not only a tag). Only one suggestion per answer, please. Here is a list of all tags, to help. At the start of each fortnight, the highest-voted answer to this post will be selected as that fortnight's topic. Starting from today, users can propose their themes or topics. The selected answer will then be deleted to reduce clutter in the list. After the selection, a new question will be created in this format. An answer will then be posted to that question with links to all the posts in the featured topic in the fortnight. We'll again keep a list of all the topics. Happy Puzzling! ## Current Topic: • February 21st – March 6th, 2021 Escape Rooms suggested by Stiv ## Previous Topics: • February 7th – February 20th, 2021 Pub Quiz Camouflage suggested by Stiv • January 24th – February 6th, 2021 Unusual tag mix suggested by melfnt • January 10th – January 23rd, 2021 Wacky Sudokus suggested by Beastly Gerbil • December 27th – January 9th, 2021 "Tales From the Cryptic" suggested by Stiv • December 13th – December 26th, 2020 Flags suggested by Stiv • November 29th – December 12th, 2020 Introduce a new grid deduction genre to the community suggested by Bubbler • November 15th – November 28th, 2020 Variety Crossword Grids suggested by bobble • November 1st – November 14th, 2020 Wordless Connecting Walls suggested by Stiv • A proposal: If/when all remaining answers don't have 5 or more upvotes, then that should be taken as a sign that proposals have run out and the series should (temporarily) stop once more – Beastly Gerbil Nov 25 '20 at 15:42 • @BeastlyGerbil That might cause irregular voting from users who just want to keep the series alive, or even the opposite. – risky mysteries Feb 25 at 23:02 - Current Topic - ## Escape Rooms In (what I am here terming) an 'Escape Room' puzzle, the solver is presented with several seemingly disparate pieces of information in the form of sub-puzzles whose interconnections may not immediately be apparent at first glance. Usually the aim of the overall puzzle is to solve each sub-puzzle, finding their interconnections along the way, and ultimately identify a specific piece of information that enables the scenario to be 'escaped' - e.g. a passcode to pass through a door, or a location where somebody or something might be found. Crucially, all sub-puzzles are necessary (or at least provide additional hints) for finding the end solution - red herrings are rarely welcome, and extraneous sub-puzzles with no apparent bearing on the solution path are a waste of time for which the setter would not be thanked. There have been several hugely impressive 'escape room' type puzzles on PSE in the past, perhaps most notably: As the mammoth upvote counts on these examples show, when this type of puzzle is done well it tends to be incredibly well-received and appreciated by the community (people love these!) - however, recently we have seen new Escape Room puzzles only very rarely. While I appreciate that this is partly because such a puzzle often requires a large investment of time and imagination to prepare and create, making this an FTC topic would present the perfect opportunity for PSE-ers to show their ingenuity and try something new and exciting - and there is nothing to stop puzzle setters getting started on creating their Escape Room puzzle ahead of time to get a headstart on the fortnight! ## Polyominoes often goes with other tags, such as but may also be a successful puzzle by itself, as in Polyominoes to construct alphabet. Polyomino is a long-time subject of recreational mathematics, and its properties can be used for grid deductions in many creative ways. So the challenge is to create a puzzle related to polyominoes in a creative way. Of course it does not need to be polyominoes made of squares; it can be polyiamonds (made of triangles) or polyhexes (made of hexagons) too! ## Non-rectangular grids Create a puzzle that acts on any kind of non-rectangular grids. The grid can be simple triangular or hexagonal grids, but be creative: there are so many different plane tilings using regular polygons, and you can even use non-regular ones! Excellent examples include Octagonal Kurotto and Karst - a variant of Cave. Cryptic hourglass is also a notable example of (essentially hexagonal) grid applied to a crossword in a non-traditional way (the words can bend in the middle). Personally inspired by snub square tiling, whose dual circle packing has an interesting property that all circles touch with exactly five other circles: ## On-and-onograms Create a puzzle where the first step is a whose solution reveals further steps that must be taken. Crucially, the full puzzle is entirely self-contained within the nonogram and flavour text. (i.e. Not just using a nonogram as the first step in a long string of grid-deduction puzzles which require additional grids to be displayed in the post.) Good examples from the past include these two puzzles by @jafe, one of which conceals a and the other a set of puzzles. ## Cellular Automata Here's a regular tag that doesn't seem to get much love: This can involve puzzles about a well-known cellular automaton, like for example Conway's Game of Life, or a cellular automaton you've created on your own! Get creative! Maybe we need to reverse-engineer something, try to produce a certain output with given starting conditions, or something entirely different! Crossovers are of course allowed and encouraged. Great examples of puzzles on this site are Game of Life: Kill the Sun, Can you recreate this fractal I randomly made? and Checkerboard Infection • I want to point out that Wireworld is also an interesting cellular automaton (awesome examples). Given that Kill the Sun is a "complete this task in GoL" kind of puzzle, "complete this task in Wireworld" should work too. – Bubbler Dec 23 '20 at 8:12 ## Möbius Strips, Klein Bottles, and other unusual topological surfaces Imagine an elastic square as above. If you ignore the red edges and glue the blue edges so that they have the same orientation, you get a Möbius Strip. If you join both pairs of edges, you get a Klein Bottle. This is not the only interesting surface; you can have 12 different topologies in total by joining two pairs of edges of a square, which include: (The last one is a plain torus.) The universal rule is that, if you're on the surface and you walk through an edge, you enter back to the grid through the matching edge with same orientation. For example, consider this 4x4 grid: A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4 Assume the Klein bottle topology at the top. If you're at B1 and walk left, you end up at B4 (by going through the red parallel edge). If you're at A2 and walk upwards, you end up at D3 (by going through the blue twisted edge). For the first one on the second image set (the one where the matching edges are adjacent to each other), if you walk upwards from A1, you enter back at A1 but facing right! The challenge is to create a puzzle that involves an unusual topological surface (which excludes plain wrap-around mechanic a.k.a. cylinder and torus). Such a puzzle may involve tiling, graph, crossword, or a grid-deduction genre, among others. Some good examples: You can search for puzzles containing torus, toroidal, or wrap around for some ideas. There is even a programming language called Klein that can run the same code on different topologies! ### Programming Puzzles A programming puzzle most likely uses the tag and/or (weird flex, but okay). Programming is my passion, but sadly I'm not seeing much (if any) programming puzzles lately, python programming puzzles to be specific. Yet most of the posts I do see tagged with don't involve actual coding. This challenge is to create a good puzzle that requires a bit more coding and a little less story-riddle stuff. Stack Overflow is the biggest site on Stack Exchange, and it would be nice to be more welcoming to those users. • Could you provide an example of what you would consider a "good computer-science puzzle that requires a bit more coding and a little less story-riddle stuff"? – bobble Oct 31 '20 at 18:35 • I generally agree, because I love programming and the idea of programming puzzles, but I feel they are really hard to properly pull off. Programing is more art than science, and there's pretty much never just one single answer. It's also really restrictive; the number of people who can reasonably solve a computer programming puzzle is really limited – Anthony Ingram-Westover Oct 31 '20 at 18:43 • @AnthonyIngram-Westover That why it's a challenge :) – risky mysteries Oct 31 '20 at 18:56 • @bobble Does this answer your question? puzzling.meta.stackexchange.com/questions/7023/… – risky mysteries Oct 31 '20 at 18:57 • No, I have seen that, I would like a link to a main-site question you feel is a good one. – bobble Oct 31 '20 at 18:59 • @bobble This is the only puzzle tagged computer-science that isn't mine that even mentions python. – risky mysteries Oct 31 '20 at 19:03 • Also, that puzzle is not bad! – risky mysteries Oct 31 '20 at 19:04 Logic Around the World Quite simply, use a combination of the tag and the tag. This puzzle and this one are great examples. The only rules are that they must contain BOTH of these tags! Metapuzzles I enjoy reading the solutions to metapuzzles, they always are interesting. Deusovi's old Chess Fortnight puzzle is one great example. Metapuzzles could be stuffed into one question, or spread out in a series with a final puzzle that ties all the previous ones together. Twisted Chess I've seen many chess puzzles where it is a variant of chess, and not about chess itself. So, the goal of this challenge is to do just that! It can be a new piece, a new variant, an existing variant, anything! (Just not using the rules of regular chess.) The puzzle goal can be a mate in 1, a winning position, or an optimization puzzle. Your only limit is your imagination! ### Sinister Stories in Casual Concepts A puzzle, most likely tagged with or , where the theme is dark and sinister, and it's the solver's task to find out what common object or situation the puzzle is hinting at. Some great examples are: ## The Puzzles Around Us Sometimes you are wondering: why the keyboard of your friend is very strange, how to change your baby's shirt while they're still drinking their milk, or what is the best strategy to go to the campus while also refilling your bottle. Undoubtedly as human, we think and reason a lot. Tackling -life problems will be more fun and fulfilling if we consider them as puzzles! There are a few puzzles which topic regards the scoring mechanism, the privilege system, the users, the ids of the posts or other features of stack exchange. Here are some of my favorites: My proposal for this challenge is to create more puzzles like these. They can be about Puzzling Stack Exchange or Stack Exchange in general. Please read this before creating such puzzles: Riddles involving Stack Exchange: Off topic? • I'm not sure this is a good idea - it seems like it will lend itself only to using information that may change over time, which doesn't make for a long-lasting puzzle. (And if you refer to specific users, apart from the problem of "the users may leave, making the puzzle unsolvable" there's also the fact that many people don't like having their names used in puzzles.) – Deusovi Feb 16 at 1:42 • (Echoing Deusovi's comment: we have guidelines about using people's names in puzzles)) – bobble Feb 16 at 1:43 • @Deusovi I linked a meta question which has an answer in which you state that "Questions involving Stack Exchange are fine, but you should take care to note that they're solvable long after they're posted". I agree with your answer and I don't see what's wrong in posting a puzzle that fit that guidelines – melfnt Feb 16 at 18:47 • @bobble I know, I wasn't referring to posting puzzles with someone's name on them. Also, many of these puzzles are not about SE, they just use the usernnames – melfnt Feb 16 at 18:48 • Will a puzzle that mentions PSE users as Among Us players count? – Anonymus 25- Reinstate Monica 22 hours ago Let's go, Zendo! This is not about the Zendo chatroom game. I'm talking of puzzles where the goal is to guess a secret rule like Zendo. The What Is A Word/Phrase series is an example. But instead of just phrases or words, you can use numbers, grids, or any kind of string. Words or phrases are of course allowed. For an example, Lukas Rotter's Awry Grid puzzle is something to consider.	{}
# zbMATH — the first resource for mathematics A note on fixed-point theorems. (English) Zbl 0483.47039 ##### MSC: 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 41A50 Best approximation, Chebyshev systems Full Text: ##### References: [1] Brosowski, B, Fixpunktsätze in der approximations-theorie, Mathematica (cluj), 11, 195-220, (1969) · Zbl 0207.45502 [2] Browder, F.E; Petryshyn, W.V, Construction of fixed points of nonlinear mappings in Hilbert space, J. math. anal. appl., 20, 197-228, (1967) · Zbl 0153.45701 [3] James, R.C, Characterizations of reflexivity, Stud. math., 23, 205-216, (1964) · Zbl 0113.09303 [4] Larsen, R, Functional analysis: an introduction, (1973), Dekker New York · Zbl 0261.46001 [5] Singh, S.P, An application of a fixed-point theorem to approximation theory, J. approx. theory, 25, 89-90, (1979) · Zbl 0399.41032 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.	{}
# Jones calculus (Redirected from Jones vector) In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using Mueller calculus. ## The Jones vector The Jones vector describes the polarization of light in free space or another homogeneous isotropic non-attenuating medium, where the light can be properly described as transverse waves. Suppose that a monochromatic plane wave of light is travelling in the positive z-direction, with angular frequency ω and wavevector k = (0,0,k), where the wavenumber k = ω/c. Then the electric and magnetic fields E and H are orthogonal to k at each point; they both lie in the plane "transverse" to the direction of motion. Furthermore, H is determined from E by 90-degree rotation and a fixed multiplier depending on the wave impedance of the medium. So the polarization of the light can be determined by studying E. The complex amplitude of E is written ${\displaystyle {\begin{pmatrix}E_{x}(t)\\E_{y}(t)\\0\end{pmatrix}}={\begin{pmatrix}E_{0x}e^{i(kz-\omega t+\phi _{x})}\\E_{0y}e^{i(kz-\omega t+\phi _{y})}\\0\end{pmatrix}}={\begin{pmatrix}E_{0x}e^{i\phi _{x}}\\E_{0y}e^{i\phi _{y}}\\0\end{pmatrix}}e^{i(kz-\omega t)}.}$ Note that the physical E field is the real part of this vector; the complex multiplier serves up the phase information. Here ${\displaystyle i}$ is the imaginary unit with ${\displaystyle i^{2}=-1}$. The Jones vector is then ${\displaystyle {\begin{pmatrix}E_{0x}e^{i\phi _{x}}\\E_{0y}e^{i\phi _{y}}\end{pmatrix}}.}$ Thus, the Jones vector represents the amplitude and phase of the electric field in the x and y directions. The sum of the squares of the absolute values of the two components of Jones vectors is proportional to the intensity of light. It is common to normalize it to 1 at the starting point of calculation for simplification. It is also common to constrain the first component of the Jones vectors to be a real number. This discards the overall phase information that would be needed for calculation of interference with other beams. Note that all Jones vectors and matrices on this article employ the convention that the phase of the light wave is given by ${\displaystyle \phi =kz-\omega t}$, a convention used by Hecht. Under this convention, increase in ${\displaystyle \phi _{x}}$ (or ${\displaystyle \phi _{y}}$) indicates retardation (delay) in phase, while decrease indicates advance in phase. For example, a Jones vectors component of ${\displaystyle i}$ (${\displaystyle =e^{i\pi /2}}$) indicates retardation by ${\displaystyle \pi /2}$ (or 90 degree) compared to 1 (${\displaystyle =e^{0}}$). Circular polarisation described under Jones' convention is called : "From the point of view of the receiver". Collett uses the opposite definition for the phase (${\displaystyle \phi =\omega t-kz}$). Circular polarisation described under Collett's convention is called : "From the point of view of the source". The reader should be wary of the choice of convention when consulting references on the Jones calculus. The following table gives the 6 common examples of normalized Jones vectors. Polarization Corresponding Jones vector Typical ket notation Linear polarized in the x direction Typically called "horizontal" ${\displaystyle {\begin{pmatrix}1\\0\end{pmatrix}}}$ ${\displaystyle \|H\rangle }$ Linear polarized in the y direction Typically called "vertical" ${\displaystyle {\begin{pmatrix}0\\1\end{pmatrix}}}$ ${\displaystyle \|V\rangle }$ Linear polarized at 45° from the x axis Typically called "diagonal" L+45 ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\1\end{pmatrix}}}$ ${\displaystyle \|D\rangle ={\frac {1}{\sqrt {2}}}{\big (}\|H\rangle +\|V\rangle {\big )}}$ Linear polarized at −45° from the x axis Typically called "anti-diagonal" L−45 ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\-1\end{pmatrix}}}$ ${\displaystyle \|A\rangle ={\frac {1}{\sqrt {2}}}{\big (}\|H\rangle -\|V\rangle {\big )}}$ Right-hand circular polarized Typically called "RCP" or "RHCP" ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\-i\end{pmatrix}}}$ ${\displaystyle \|R\rangle ={\frac {1}{\sqrt {2}}}{\big (}\|H\rangle -i\|V\rangle {\big )}}$ Left-hand circular polarized Typically called "LCP" or "LHCP" ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\+i\end{pmatrix}}}$ ${\displaystyle \|L\rangle ={\frac {1}{\sqrt {2}}}{\big (}\|H\rangle +i\|V\rangle {\big )}}$ A general vector that points to any place on the surface is written as a ket ${\displaystyle \|\psi \rangle }$. When employing the Poincaré sphere (also known as the Bloch sphere), the basis kets (${\displaystyle \|0\rangle }$ and ${\displaystyle \|1\rangle }$) must be assigned to opposing (antipodal) pairs of the kets listed above. For example, one might assign ${\displaystyle \|0\rangle }$ = ${\displaystyle \|H\rangle }$ and ${\displaystyle \|1\rangle }$ = ${\displaystyle \|V\rangle }$. These assignments are arbitrary. Opposing pairs are • ${\displaystyle \|H\rangle }$ and ${\displaystyle \|V\rangle }$ • ${\displaystyle \|D\rangle }$ and ${\displaystyle \|A\rangle }$ • ${\displaystyle \|R\rangle }$ and ${\displaystyle \|L\rangle }$ The polarization of any point not equal to ${\displaystyle \|R\rangle }$ or ${\displaystyle \|L\rangle }$ and not on the circle that passes through ${\displaystyle \|H\rangle ,\|D\rangle ,\|V\rangle ,\|A\rangle }$ is known as elliptical polarization. ## Jones matrices The Jones matrices are operators that act on the Jones vectors defined above. These matrices are implemented by various optical elements such as lenses, beam splitters, mirrors, etc. Each matrix represents projection onto a one-dimensional complex subspace of the Jones vectors. The following table gives examples of Jones matrices for polarizers: Optical element Corresponding Jones matrix Linear polarizer with axis of transmission horizontal[1] ${\displaystyle {\begin{pmatrix}1&0\\0&0\end{pmatrix}}}$ Linear polarizer with axis of transmission vertical[1] ${\displaystyle {\begin{pmatrix}0&0\\0&1\end{pmatrix}}}$ Linear polarizer with axis of transmission at ±45° with the horizontal[1] ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&\pm 1\\\pm 1&1\end{pmatrix}}}$ Right circular polarizer[1] ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&i\\-i&1\end{pmatrix}}}$ Left circular polarizer[1] ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&-i\\i&1\end{pmatrix}}}$ ## Phase retarders Phase retarders introduce a phase shift between the vertical and horizontal component of the field and thus change the polarization of the beam. Phase retarders are usually made out of birefringent uniaxial crystals such as calcite, MgF2 or quartz. Uniaxial crystals have one crystal axis that is different from the other two crystal axes (i.e., ninj = nk). This unique axis is called the extraordinary axis and is also referred to as the optic axis. An optic axis can be the fast or the slow axis for the crystal depending on the crystal at hand. Light travels with a higher phase velocity along an axis that has the smallest refractive index and this axis is called the fast axis. Similarly, an axis which has the largest refractive index is called a slow axis since the phase velocity of light is the lowest along this axis. "Negative" uniaxial crystals (e.g., calcite CaCO3, sapphire Al2O3) have ne < no so for these crystals, the extraordinary axis (optic axis) is the fast axis, whereas for "positive" uniaxial crystals (e.g., quartz SiO2, magnesium fluoride MgF2, rutile TiO2), ne > n o and thus the extraordinary axis (optic axis) is the slow axis. Any phase retarder with fast axis equal to the x- or y-axis has zero off-diagonal terms and thus can be conveniently expressed as ${\displaystyle {\begin{pmatrix}e^{i\phi _{x}}&0\\0&e^{i\phi _{y}}\end{pmatrix}}}$ where ${\displaystyle \phi _{x}}$ and ${\displaystyle \phi _{y}}$ are the phase offsets of the electric fields in ${\displaystyle x}$ and ${\displaystyle y}$ directions respectively. In the phase convention ${\displaystyle \phi =kz-\omega t}$, define the relative phase between the two waves as ${\displaystyle \epsilon =\phi _{y}-\phi _{x}}$. Then a positive ${\displaystyle \epsilon }$ (i.e. ${\displaystyle \phi _{y}}$ > ${\displaystyle \phi _{x}}$) means that ${\displaystyle E_{y}}$ doesn't attain the same value as ${\displaystyle E_{x}}$ until a later time, i.e. ${\displaystyle E_{x}}$ leads ${\displaystyle E_{y}}$. Similarly, if ${\displaystyle \epsilon <0}$, then ${\displaystyle E_{y}}$ leads ${\displaystyle E_{x}}$. For example, if the fast axis of a quarter wave plate is horizontal, then the phase velocity along the horizontal direction is ahead of the vertical direction i.e., ${\displaystyle E_{x}}$ leads ${\displaystyle E_{y}}$. Thus, ${\displaystyle \phi _{x}<\phi _{y}}$ which for a quarter wave plate yields ${\displaystyle \phi _{y}=\phi _{x}+\pi /2}$. In the opposite convention ${\displaystyle \phi =\omega t-kz}$, define the relative phase as ${\displaystyle \epsilon =\phi _{x}-\phi _{y}}$. Then ${\displaystyle \epsilon >0}$ means that ${\displaystyle E_{y}}$ doesn't attain the same value as ${\displaystyle E_{x}}$ until a later time, i.e. ${\displaystyle E_{x}}$ leads ${\displaystyle E_{y}}$. Phase retarders Corresponding Jones matrix Quarter-wave plate with fast axis vertical[2][note 1] ${\displaystyle e^{i\pi /4}{\begin{pmatrix}1&0\\0&-i\end{pmatrix}}}$ Quarter-wave plate with fast axis horizontal[2] ${\displaystyle e^{-i\pi /4}{\begin{pmatrix}1&0\\0&i\end{pmatrix}}}$ Quarter-wave plate with fast axis at angle ${\displaystyle \theta }$ w.r.t the horizontal axis ${\displaystyle e^{-i\pi /4}{\begin{pmatrix}\cos ^{2}\theta +i\sin ^{2}\theta &(1-i)\sin \theta \cos \theta \\(1-i)\sin \theta \cos \theta &\sin ^{2}\theta +i\cos ^{2}\theta \end{pmatrix}}}$ Half-wave plate with fast axis at angle ${\displaystyle \theta }$ w.r.t the horizontal axis[3] ${\displaystyle e^{-i\pi /2}{\begin{pmatrix}\cos 2\theta &\sin 2\theta \\\sin 2\theta &-\cos 2\theta \end{pmatrix}}}$ Arbitrary birefringent material (as phase retarder)[4] ${\displaystyle {\begin{pmatrix}e^{i\eta /2}\cos ^{2}\theta +e^{-i\eta /2}\sin ^{2}\theta &(e^{i\eta /2}-e^{-i\eta /2})e^{-i\phi }\cos \theta \sin \theta \\(e^{i\eta /2}-e^{-i\eta /2})e^{i\phi }\cos \theta \sin \theta &e^{i\eta /2}\sin ^{2}\theta +e^{-i\eta /2}\cos ^{2}\theta \end{pmatrix}}}$ The special expressions for the phase retarders can be obtained by taking suitable parameter values in the general expression for a birefringent material. In the general expression: • The relative phase retardation induced between the fast axis and the slow axis is given by ${\displaystyle \eta =\phi _{y}-\phi _{x}}$ • ${\displaystyle \theta }$ is the orientation of the fast axis with respect to the x-axis. • ${\displaystyle \phi }$ is the circularity. Note that for linear retarders, ${\displaystyle \phi }$ = 0 and for circular retarders, ${\displaystyle \phi }$ = ± ${\displaystyle \pi }$/2, ${\displaystyle \theta }$ = ${\displaystyle \pi }$/4. In general for elliptical retarders, ${\displaystyle \phi }$ takes on values between - ${\displaystyle \pi }$/2 and ${\displaystyle \pi }$/2. ## Axially rotated elements Assume an optical element has its optic axis[clarification needed] perpendicular to the surface vector for the plane of incidence[clarification needed] and is rotated about this surface vector by angle θ/2 (i.e., the principal plane,[clarification needed] through which the optic axis passes,[clarification needed] makes angle θ/2 with respect to the plane of polarization of the electric field[clarification needed] of the incident TE wave). Recall that a half-wave plate rotates polarization as twice the angle between incident polarization and optic axis (principal plane). Therefore, the Jones matrix for the rotated polarization state, M(θ), is ${\displaystyle M(\theta )=R(-\theta )\,M\,R(\theta ),}$ where ${\displaystyle R(\theta )={\begin{pmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{pmatrix}}.}$ This agrees with the expression for a half-wave plate in the table above. These rotations are identical to beam unitary splitter transformation in optical physics given by ${\displaystyle R(\theta )={\begin{pmatrix}r&t'\\t&r'\end{pmatrix}}}$ where the primed and unprimed coefficients represent beams incident from opposite sides of the beam splitter. The reflected and transmitted components acquire a phase θr and θt, respectively. The requirements for a valid representation of the element are [5] ${\displaystyle \theta _{\text{t}}-\theta _{\text{r}}+\theta _{\text{t'}}-\theta _{\text{r'}}=\pm \pi }$ and ${\displaystyle r^{}t'+t^{}r'=0.}$ Both of these representations are unitary matrices fitting these requirements; and as such, are both valid. ## Arbitrarily rotated elements This would involve a three-dimensional rotation matrix. See Russell A. Chipman[6] and Garam Yun for work done on this.[7][8][9] ## Notes 1. ^ The prefactor ${\displaystyle e^{i\pi /4}}$ appears only if one defines the phase delays in a symmetric fashion; that is, ${\displaystyle \phi _{x}=-\phi _{y}=\pi /4}$. This is done in Hecht[2] but not in Fowles.[1] In the latter reference the Jones matrices for a quarter-wave plate have no prefactor. ## References 1. Fowles, G. (1989). Introduction to Modern Optics (2nd ed.). Dover. p. 35. 2. ^ a b c Hecht, E. (2001). Optics (4th ed.). p. 378. ISBN 0805385665. 3. ^ Gerald, A.; Burch, J.M. (1975). Introduction to Matrix Methods in Optics (1st ed.). John Wiley & Sons. p. 212. ISBN 0471296856. 4. ^ Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix, Optik, Jose Jorge Gill and Eusebio Bernabeu,76, 67-71 (1987). 5. ^ Am. J. Phys. 57 (1), 66 (1989). 6. ^ Russell A. Chipman (1995) "Mechanics of polarization ray tracing", Opt. Eng. 34(6), 1636-1645 [1] 7. ^ Three-dimensional polarization ray-tracing calculus I: definition and diattenuation, Applied Optics, Garam Yun, Karlton Crabtree, and Russell A. Chipman,50, 2855-2865 (2011). 8. ^ Three-dimensional polarization ray-tracing calculus II: retardance, Applied Optics, Garam Yun, Stephen C. McClain, and Russell A. Chipman,50, 2866-2874 (2011). 9. ^ Garam Yun, Polarization Ray Tracing, PhD thesis • E. Collett, Field Guide to Polarization, SPIE Field Guides vol. FG05, SPIE (2005). ISBN 0-8194-5868-6. • D. Goldstein and E. Collett, Polarized Light, 2nd ed., CRC Press (2003). ISBN 0-8247-4053-X. • E. Hecht, Optics, 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X. • Frank L. Pedrotti, S.J. Leno S. Pedrotti, Introduction to Optics, 2nd ed., Prentice Hall (1993). ISBN 0-13-501545-6 • A. Gerald and J.M. Burch, Introduction to Matrix Methods in Optics,1st ed., John Wiley & Sons(1975). ISBN 0-471-29685-6 • Jones, R. Clark (1941). "A new calculus for the treatment of optical systems, I. Description and Discussion of the Calculus". Journal of the Optical Society of America. 31 (7): 488–493. doi:10.1364/JOSA.31.000488. • Hurwitz, Henry; Jones, R. Clark (1941). "A new calculus for the treatment of optical systems, II. Proof of three general equivalence theorems". Journal of the Optical Society of America. 31 (7): 493–499. doi:10.1364/JOSA.31.000493. • Jones, R. Clark (1941). "A new calculus for the treatment of optical systems, III The Sohncke Theory of optical activity". Journal of the Optical Society of America. 31 (7): 500–503. doi:10.1364/JOSA.31.000500. • Jones, R. Clark (1942). "A new calculus for the treatment of optical systems, IV". Journal of the Optical Society of America. 32 (8): 486–493. doi:10.1364/JOSA.32.000486. • Fymat, A. L. (1971). "Jones's Matrix Representation of Optical Instruments. I: Beam Splitters". Applied Optics. 10 (11): 2499–2505. Bibcode:1971ApOpt..10.2499F. doi:10.1364/AO.10.002499. PMID 20111363. • Fymat, A. L. (1971). "Jones's Matrix Representation of Optical Instruments. 2: Fourier Interferometers (Spectrometers and Spectropolarimeters)". Applied Optics. 10 (12): 2711–2716. Bibcode:1971ApOpt..10.2711F. doi:10.1364/AO.10.002711. • Fymat, A. L. (1972). "Polarization Effects in Fourier Spectroscopy. I: Coherency Matrix Representation". Applied Optics. 11 (1): 160–173. Bibcode:1972ApOpt..11..160F. doi:10.1364/AO.11.000160. PMID 20111472. • Gill, Jose Jorge; Bernabeu, Eusebio (1987). "Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,". Optik. 76: 67–71. • Brosseau, Christian; Givens, Clark R.; Kostinski, Alexander B. (1993). "Generalized trace condition on the Mueller-Jones polarization matrix". Journal of the Optical Society of America A. 10 (10): 2248–2251. Bibcode:1993JOSAA..10.2248B. doi:10.1364/JOSAA.10.002248. • McGuire, James P.; Chipman, Russel A. (1994). "Polarization aberrations. 1. Rotationally symmetric optical systems". Applied Optics. 33 (22): 5080–5100. Bibcode:1994ApOpt..33.5080M. doi:10.1364/AO.33.005080. PMID 20935891. • Pistoni, Natale C. (1995). "Simplified approach to the Jones calculus in retracing optical circuits". Applied Optics. 34 (34): 7870–7876. Bibcode:1995ApOpt..34.7870P. doi:10.1364/AO.34.007870. PMID 21068881. • Moreno, Ignacio; Yzuel, Maria J.; Campos, Juan; Vargas, Asticio (2004). "Jones matrix treatment for polarization Fourier optics". Journal of Modern Optics. 51 (14): 2031–2038. Bibcode:2000JMOp...51.2031M. doi:10.1080/09500340408232511. • Moreno, Ivan (2004). "Jones matrix for image-rotation prisms". Applied Optics. 43 (17): 3373–3381. Bibcode:2004ApOpt..43.3373M. doi:10.1364/AO.43.003373. PMID 15219016.	{}
## Online Education for RS Aggarwal Class 9 Solutions Chapter 11 Circle Ex 11B These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 11 Circle Ex 11B. Other Exercises Question 1. Solution: (i) O is the centre of the circle ∠OAB = 40°, ∠OCB = 30° Join OB. Question 2. Solution: O is the centre of the cirlce and ∠AOB = 70° ∵ Arc AB subtends ∠AOB at the centre and ∠ACB at the remaining part of the circle. ∵ ∠ACB = $$\frac { 1 }{ 2 }$$ ∠AOB = $$\frac { 1 }{ 2 }$$ x 70° => ∠ACB = 35° or ∠OCA = 35° In ∆OAC, OA = OC (radii of the same circle) ∴ ∠OAC = ∠OCA = 35° Ans. Question 3. Solution: In the figure, O is the centre of the circle. ∠PBC = 25°, ∠APB =110° ∠ APB + ∠ BPC = 180° (Linear pair) => 110° + ∠ BPC = 180° Question 4. Solution: O is the centre of the circle ∠ABD = 35° and ∠B AC = 70° BOD is the diameter of the circle ∠BAD = 90° (Angle in a semi circle) But ∠ADB + ∠ABD + ∠BAD = 180° (Angles of a triangle) => ∠ADB + 35° + 90° = 180° => ∠ADB + 125° = 180° => ∠ADB = 180° – 125° = 55° But ∠ACB = ∠ADB (Angles in the same segment of the circle) ∠ACB = 55° Ans. Question 5. Solution: O is the centre of a circle and ∠ACB = 50° ∴ arc AB subtends ∠ AOB at the centre and ∠ ACB at the remaining part of the circle. ∴ ∠ AOB = 2 ∠ ACB = 2 x 50° = 100 ∴ OA = OB (radii of the same circle) ∴ ∠ OAB = ∠ OBA (Angles opposite to equal sides) Now in ∆ OAB, ∠ OAB + ∠ OBA + ∠ AOB = 180° => ∠ OAB + ∠ OAB + ∠ AOB = 180° (∠OAB = ∠OBA) => 2 ∠ OAB + 100°= 180° => 2 ∠ OAB = 180° – 100° = 80° => ∠OAB = $$\frac { { 80 }^{ o } }{ 2 }$$ = 40° Hence, OAB = 40° Ans. Question 6. Solution: (i) In the figure, ∠ABD = 54° and ∠BCD = 43° ∠BAD = ∠BCD (Angles in the same segment of a circle) Question 7. Solution: Chord DE \|\| diameter AC of the circle with centre O. ∠CBD = 60° ∠CBD = ∠ CAD (Angles in the same segment of a circle) Now in ∆ ADC, Question 8. Solution: In the figure, chord CD \|\| diameter AB of the circle with centre O. ∠ ABC = 25° Join CD and DO. AB \|\| CD ∠ ABC = ∠ BCD (alternate angles) Question 9. Solution: AB and CD are two straight lines passing through O, the centre of the circle and ∠AOC = 80°, ∠CDE = 40° ∠ CED = 90° (Angle in a semi circle) Question 10. Solution: O is the centre of the circle and ∠AOB = 40°, ∠BDC = 100° Arc AB subtends ∠AOB at the centre and ∠ ACB at the remaining part of the circle ∠ AOB = 2 ∠ ACB Question 11. Solution: Chords AC and BD of a circle with centre O, intersect each other at E at right angles. ∠ OAB = 25°. Join OB. In ∆ OAB, OA = OB (radii of the same circle) Question 12. Solution: In the figure, O is the centre of a circle ∠ OAB = 20° and ∠ OCB = 55° . In ∆ OAB, Question 13. Solution: Given : A ∆ ABC is inscribed in a circle with centre O and ∠ BAC = 30° To Prove : BC = radius of the circle Const. Join OB and OC Question 14. Solution: In a circle with centre O and PQ is its diameter. ∠PQR = 65°, ∠SPR = 40° and ∠PQM = 50° (i) ∠PRQ = 90° (Angle in a semicircle) and ∠PQR + ∠RPQ + ∠PQR = 180° (Angles of a triangle) Hope given RS Aggarwal Solutions Class 9 Chapter 11 Circle Ex 11B are helpful to complete your math homework. If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.	{}
# Globally registered function: Only first 4 arguments are passed (ARM) This topic is 1591 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi, We have crosscompiled the angelscript library (2.26.3) to be running on a embedded board running ARM linux. It is running perfectly, we only ran into one issue. When we register a global function with more than 4 arguments, it is accepted by the compiler. Once we call the function from angelscript, the first 4 parameters are passed through, but the 5th and further parameters are not set in the function. r = engine->RegisterGlobalFunction("void testFunc(int8 a,int8 b,int8 c,int8 d,int8 e,int8 f,int8 g,int8 h) ", asFUNCTION(BaseAPI::testFunc), asCALL_CDECL); void BaseAPI::testFunc(char a,char b,char c, char d, char e, char f,char g, char h) { } Is this a bug in the ARM implementation, or are we doing something wrong? ##### Share on other sites It is likely a case of your system using a slightly different ARM ABI that what the code is prepared for. Currently the code has support for the ABIs used by iOS, Android, Marmalade, Windows, and with the latest contribution from loboWu Linux with the variations armeabi + vfp or armeabihf (both thumb and normal mode). Does the manual for your system specify exactly which variant of the ARM ABI it uses? I assume you use gnuc to compile the library. Can you obtain the preprocessor flags that gnuc defines automatically on your system? Sometimes these give a hint of what ABI is used. You ought to be able to get the preprocessor flags with a command like this: echo . \| g++ $CXXFLAGS -dM -E - Where$CXXFLAGS shouild contain all the flags you normally pass to the compiler, such as target architecture, etc.	{}
# Math Challenge - October 2019 • Challenge • Featured archaic Yes and no. Yes, as this is part of the question, and no, since this procedure has to be done with any second point. We have a fixed single point ##P## and a set ##\mathbb{S}^2##. Then we consider all lines ##\overline{PQ}## from ##P## to ##Q## to another point ##Q## on the sphere. This line has a center ##M_Q##. The problem asks for ##\{\,M_Q\in \overline{PQ}\,\|\,Q\in \mathbb{S}^2\,\}\,.## Like this? Supposing that ##P=(x,y,z)##, the set of all midpoints between ##P## and ##Q## by varying ##Q## would be ##\{(\frac{x+x_Q}{2},\frac{y+y_Q}{2},\frac{z+z_Q}{2})\|(x_Q,y_Q,z_Q)\in\mathbb{S}^2\}##. Mentor 2021 Award Like this? Supposing that ##P=(x,y,z)##, the set of all midpoints between ##P## and ##Q## by varying ##Q## would be ##\{(\frac{x+x_Q}{2},\frac{y+y_Q}{2},\frac{z+z_Q}{2})\|(x_Q,y_Q,z_Q)\in\mathbb{S}^2\}##. Yes, but which equation describes those points? What is it what you have written down? Gold Member Question 14 Isn't this just a scaling of the original sphere? So this would be a sphere at point P whose slope at P is tangent to the original sphere and has radius half of the original sphere. Okay so I thought about an equation but for the love of me I cannot seem to translate the sphere into the correct position to be a tangent to P. Last edited: Mentor 2021 Award Question 14 Isn't this just a scaling of the original sphere? So this would be a sphere at point P whose slope at P is tangent to the original sphere and has radius half of the original sphere. Okay so I thought about an equation but for the love of me I cannot seem to translate the sphere into the correct position to be a tangent to P. Well, it's not a scaling anymore if the center is shifted. Your description is right, as is the set which @archaic defined. What I wanted to see is a simple transformation from one description to the other one. As you both have basically solved it, let me give the solution I had in mind. (Please note the two directions! The centers are on the smaller ball, and all points of the smaller ball are indeed a center of some chord!) The variable endpoint ##X## of the chord is on the sphere, so for its position vector we have ##\vec{x}^2=r^2##. The position vector of the center of the chord ##\overline{PX}## is thus $$\vec{c}=\dfrac{\vec{p}+\vec{x}}{2} \;\Longleftrightarrow \; \vec{x}=2\vec{c}-\vec{p}$$ hence ##r^2=(2\vec{c}-\vec{p})^2## or ##\left( \vec{c}-\dfrac{\vec{p}}{2} \right)^2=\dfrac{r^2}{4}##. So the set of points we were looking for are all on a sphere with center ##\overline{OP}/2=\vec{p}/2## and radius ##r/2##. All points of this sphere are on the other hand a center of some chord of the original sphere with endpoint ##P##, since we can go back. The point ##P## itself is the center of the chord ##\overline{PP}##. Gold Member @fresh_42 ahh, thanks for the explanation, that makes sense. 4 challenge problems left, who can solve them? New ones on Friday! Gold Member 4 challenge problems left, who can solve them? New ones on Friday! I would try, but i don't fancy speed learning topology right now :P Homework Helper 5. Let ##A=\sum_{k=0}^\infty a_k\, , \,B=\sum_{k=0}^\infty b_k## be two convergent series one of which absolutely. Prove: The Cauchy-product ##C=\sum_{k=0}^\infty c_k## with ##c_k=\sum_{j=0}^ka_jb_{k-j}## converges to ##AB##. Give an example that absolute convergence of at least one factor is necessary. This is The Theorem of Mertens, Knopp, Theory and Applications of Infinite Series, pg 321, 188. An example when absolute convergence of at least one factor is necessary is the other challenge problem I just did, the Cauchy product ##\left(\sum_{n=0}^\infty \frac{(-1)^n}{\sqrt{n+1}}\right) ^2##.	{}
# How does greater anticipate teleportation interact with time regression? The 5th-level Sor/Wiz spell greater anticipate teleportation [abjur] (Spell Compendium 13) delays by 3 rounds the arrival of a creature that attempts to teleport into the affected area. The 9th-level nomad power time regression [psychoportation] (XPH 138) allows the nomad to "regress apparent time 1 round into the past[, the power] regress[ing] time to the point along the time stream just prior to your previous turn, undoing the effects of everyone else’s actions in the meantime." Does a creature that has been delayed for 3 rounds by the effect of greater anticipate teleportation who then manifests time regression replay its last round (which was about 3 rounds ago), the last actual round of the game (while the creature was absent), or something else? True Story: The nomad teleported into a room that was warded by a greater anticipate teleportation effect. Over the course of the 3 rounds during which he was absent, one PC was killed, another PC was rendered unconscious but stable at −3 hp, and the last PC was prevented from entering the room by the 150 ft. of solid rock in the way (multiple passwall spells were simultaneously suppressed whilst he was within the magically created passage). Then the foes departed with the dead and unconscious bodies of the downed PCs. When the PC who was affected by the greater anticipate teleportation effect returned to the room, instead of the din of battle, he found the room largely empty except for a dead beholder. He manifested his time regression power. (He wasn't metagaming: the wraith cohort of one of the downed-and-missing PCs—who was spying nearby—quickly informed the nomad of what had transpired.) After some discussion, I allowed the time regression effect to start from the nomad's last round (in other words, like, 4 rounds ago in real game time) because using the power costs 1,000 XP, and the player'd been sitting on the power for, like, ten sessions, having saved it for just such an occasion (sort of, anyway). So for our table's gentlemen's agreement, this was the right call, but I'm curious if the rules agree. • It's a very short hop, but can't pass up an opportunity to use the [time-travel] tag! – SevenSidedDie Nov 24 '16 at 19:17 • Is it possible to expand the question a little bit by going from Greater Anticipate Teleportation to Things that make one or more creatures deal with more or less rounds or something to that effect? The only other thing I can think of (because I have not had the pleasure of using a lot of the D&D 3.5e Sourcebooks) is Time Stop, since that similarly messes with who acts for how many rounds. – Javelin Nov 24 '16 at 21:13 • @Javelin Possibly. The number of magical effects that actually cause time not to pass for a character is, I think, incredibly rare, but I'd be happy to open the question wider if more effects are founds. (For instance, time stop counterintuitively accelerates the caster rather than halting the universe, and imprisonment is merely suspended animation.) – Hey I Can Chan Nov 25 '16 at 1:40 The spell refers to "round" as a singular thing throughout the entire spell. It says: the previous round only you retain knowledge of what happened during the round that is being replayed During the round that you live through a second time This would suggest that it can only do one turn. The only thing that casts some doubt is the line The power regresses time to the point along the time stream just prior to your previous turn However, that seems meant to show exactly where the power will drop you. I expect they mean directly before your previous initiative count, not just before the last turn you actually took. Note that if you allow rolling back to the last turn taken, this power can be an abused to roll back an indefinite amount of time if the Nomad is willing to have his allies place him in some kind of Statis with the orders to "roll back time as soon as you come out". I doubt this is intended. Likewise it can revert back through death if you cast it instantly when you are brought back to life. There are many effects that cause you to not perform anything during a round. Reading it as being limited to a single 6 second round seems the only reasonable reading of it. Anything else will cause all sorts of weirdness. • These are good points, and the death thing in particular gave me pause. It might be hair-splitting, but I think a dead creature may still get turns , yet the creature's dead condition prevents the creature from taking actions. :-) – Hey I Can Chan Nov 25 '16 at 1:44 • The same argument can be made for a creature in stasis or being delayed by anticipate teleport, though. It's hard to argue that you don't take turns when being delayed, but you do get turns while disintegrated; in both cases you're not really there. – Erik Nov 25 '16 at 6:47 • I know it's hard to argue so I won't try very hard, but the effect of a greater anticipate teleportation (GAT) delay is to remove everything. Unlike maze, temporal stasis, or outright disintegration, the GAT effect causes the creature for 3 rounds to pretty much cease to exist anywhere! (Even death means many a creature's soul is doing stuff, and time is still passing at a measurable external rate for the creature.) Just sayin' that there might be a difference--and analogies could be harder to draw--between the GAT effect and other effects. – Hey I Can Chan Nov 25 '16 at 11:18 • And that, boys and girls, is how you add save-game points to your D&D sessions. – nijineko Nov 28 '16 at 19:38 • The question becomes whether the spell mechanics operate on a caster-subjective level, or a universe-objective level. I vote the former as it is unlikely the caster can affect the entire universe. Personally, I would allow them to do so. If they began using it repeatedly, enter god of time and a fun little side-quest relating to them stretching and tearing the fabric of space-time due to overuse. ^^ Makes for more memorable sessions. – nijineko Nov 28 '16 at 19:44	{}
## java – Should all third party methods that access outside resources (like other databases) be wrapped up? From the perspective of unit testing, the code under test should obviously not be accessing outside resources so the third party methods need to be mocked. However, it seems like this is poor practice because third party methods can change and become static/final which makes mocking difficult in Mockito. So in that sense, is it best practice to always wrap up third party methods? I suppose this question may also apply to other programming languages and testing frameworks. ## Databases and B-Trees: What are Keys and how are they related I confused about the description & definition of “key” occuring as terminology for databases and b-trees. In first case dealing with theory of databases a key is defined as a choice for minimal subset $$K subset A := {A_1,A_2,…,A_n}$$ of a fixed set of attributes $$A_i$$ parametizing a data table (consisting of relations; a single relation is abstraction of a row in the table), where each attribute is literally a column specifying a property of objects = relations. A key is characterized by property that there exist no two different relations (a relation is a row) which have exactly the same values for all attributes which belong to the key. And a key is a minimal subset with this property, ie there not exist a proper smaller subset of attributes contained in the key and having the property described in last sentence. Clearly keys are not unique. So the set of a keys is certain subset of the power set of the set attributes $$A_i$$. See also here: https://en.wikipedia.org/wiki/Unique_key On the other hand the key concept occures as well for b-trees: https://en.wikipedia.org/wiki/B-tree#Definition Here keys are a priori numbers or integers and different knots of b-tree contain different totally ordered subsets of keys where the total order on the space of keys is inherited from the order “$$ge$$” for integers $$mathbb{Z}$$. Especially the set of keys is a totally ordered subset of integers. Question: How are the two concept of ‘key’ related to each other? My first idea was that if we consider in light of for definition (as elements of power set of attributes), we can simply randomly enumerate all the keys (that is associate to each key an number; formally speaking to specify an injection $$f:mathcal{K} to mathbb{Z}, K mapsto f(K)$$ where $$mathcal{K} subset Omega(A)$$) and then treat them as numbers when working with b-trees. Is this exactly the correct connection or is there another deeper one and my approach is wrong? ## replication working for new databases only I have 2 servers Ubuntu one of them having my database in mysql after that I initialized the multi master replication between the two servers but the current database not replicated even when I created a new database on any server of them it replicated on the other side ## postgresql – how to maximize usage of number of databases on a postgres server while limited by connections We’re building a system where ideally we’d give a database per client in a multi-tenant setup. However, although a single Postgres install supports 4,294,950,911 databases on a server, the suggested `max_connections` is around 100 or so. That means if we used every active connection up to some recommended amount (using 100 as an example), we can at one time only access 0.000002 % of the available databases. In no way would I need to utilize 4B databases, but would be great to utilize more than 100, certainly. In looking up connection info in `pg_stat_activity`, seems that each connection includes a database name, so I’m guessing you cannot create a connection pool on the same server across different database names. I was hoping there would be a solution that allowed a connection pool across databases on the same server, finding that’s not the case – please enlighten me if there is something in this realm of solutions. So my options I believe at each end of the spectrum are: 1. shard tenants across schemas, and use connection pooling on same database 2. multiplex and/or context switch connections from the API server, using an LRU cache of pg pools that manage connections, closing the ones that the LRU cache disposes. ## question Assuming I wanted to build 10,000 databases per database server, I’d look to get a solution like #2 working, to access different databases. How expensive it is really to open/close a connection if it happens quite often? And if it’s not feasible, is the number of databases allowed in postgres just a computer science theoretical number, that we’ll only ever use a fraction of a fraction of a percent of? And in reality, we’d at best use a number of databases that correlates closely with the number of connections? I’m also guessing there may be a hybrid solution that allows us to use many databases but minimize the connections per server with a fan-out using logical replication. But that sounds like it could get more expensive. ## databases – Storage of Large Amounts of Game Data (Player stats, matches) I’m curious as to what the best way would be to store my data. Currently, I’ve setup a matchmaking system, and player stats. When a match ends, my server submits the player data to my ruby on rails api, saving the data to my PostgreSQL database, making at least 10~ queries at the end of a match. However, some people mentioned using MongoDB instead. Why would I want to use Mongo over postgres? Postgres works fine, and it’s what I’ve worked with at my current job to store millions of records. Does anyone have any opinions on this, or what would be statistically the best option? ## attack prevention – Two persons-rule on MySQL databases for “manual fixes” In order to “harden” our compliance, we wanted to enforce a two-persons rule on the MySQL production database for “manual fixes”. Such “manual fixes” frequently arise due to: • Bug in the application (we are a fast company :D) • Various customer requests that do not have an application feature implemented yet, such as GDPR update requests, special discounts, etc. We wanted a process that does not require the two persons to be physically side-by-side. One person is on-call, rather junior and is responsible to translate customer service requests into SQL. They might need a GUI (such as MySQL Workbench) to navigate the complex data model and figure out the exact SQL script to produce. The SQL script should feature `SELECT`s showing the data before and after the change in a non-committed transaction (e.g., `AUTOCOMMIT OFF` no `COMMIT` at the end). The second person is not on-call, rather senior, and fairly familiar with the application’s data model. They should be able to look at the SQL script the non-committed transaction output, and approve or reject via a mobile app during the evening. We cannot be the first to have this or a similar requirements. Does anyone know good documentation or tooling to implement such a process? Here are some similar questions on the topic, but not quite as specific as the present one: ## Backup and upgrade MongoDB databases I have a web application using MongoDB (Version 2.6.12), hosted in a (Ubuntu 16.04) server of DigitalOcean. I like to use Robo 3T to connect to the remote database and do simple queries. Sometimes I backup the database with `mongodump`, and mostly rely on the weekly auto server snapshot provided by DigitalOcean. Now, I need to undertake queries containing like `\$lookup`, they told me that MongoDB Version 2.16.12 does not support that. So I need to seriously backup my database and use a more recent MongoDB. I still want to keep using Robo3T to do queries to production database (by preference) or backup database (if it is updated very often, e.g., every day). I have several questions: 1) I would prefer to have a more regular auto-backup (e.g., every day) of the database. Which way is recommended? (Additionally, it seems that Atlas does NOT support Cloud Provider Snapshots for clusters served on DigitalOcean?) 2) If I buy a new server hosted on Azure and install MongoDB 4.2, and copy the whole database by `mongodump` to the new server, will it work? ## 2016 – Search Topology – too many databases and one corrupt Our organization was having an issue with our Search Service App on our SharePoint 2016 On-Prem environment. Once we got it working properly, we noticed that there were 3 sets of topology component databases than our expected two. Then, one of our CrawlDBs became suspect. Any recommendations on how to move forward? It would make sense to me to transfer the current topology component databases to the orphan ones and then remove the corrupt, but I don’t know if this is best practice. Much appreciated. ## databases – phpmyadmin error #1064 – error in SQL syntax I am making a product database, and I am having problems saving the table. Also I am wondering why it is saying MariaDB, on my XAMPP I don’t even have the option for MariaDB. How can I get rid of this error?	{}
# How does a particular galaxy's apparent recessional velocity CHANGE as the universe expands? By this I mean will the light from distant galaxies continue to show red shift (i.e. if you look at light from a particular galaxy now and in 10000 years time, the spectra will have been shifted again), or is there a certain red shift which always corresponds to a certain set of galaxies (those which are the same distance away from Earth)? I think the answer lies in the apparent recessional velocity from Earth, but I'm struggling to interpret how it will change, if at all. I understand that the apparent recessional velocity of a galaxy is proportional to the distance between it and Earth, with the proportionality constant being Hubble's constant. Say Hubble's constant = 70 km per second per Mpc. A galaxy that's 1 Mpc away will be travelling at 70 km per second. But after the distance between it and Earth has increased by another parsec, will the apparent recessional velocity have increased (as will red shift) as distance has, or will Hubble's constant have changed and the apparent recessional velocity for that galaxy (and hence red shift) remain unchanged? (to give you an idea of my level of understanding of physics, I'm in the final year of my A levels, although I do quite a bit of reading on it). There is an expectation that the redshift of an object will change with time. The details depend on the cosmological parameters (a plot is shown below). This was first explored by Sandage (1962) who predicted that, in a matter-dominated universe (i.e. no consideration of dark energy back then), the redshift should decrease due to the braking action of gravity. The typical numbers quoted for a galaxy at $z=0.4$ at the present epoch were a change in redshift of $\sim -5\times10^{-6}$ km/s per year. Sandage also noted that measuring such shifts seemed impossible with the instruments of the day. Science marches on: we now have dark energy to contend with and the possibility/probability that the expansion is accelerating. This could lead to an increasing redshift with time at redshifts below which dark energy dominates the expansion dynamics. So, a fascinating piece of work was done by Liske et al. (2008) who revisited this question and specifically looked at whether the effect could be detected using extremely large telescopes and new instruments. Their conclusion is simple: using the new European ELT (due to start working 2024) it will be possible to measure the effect in the Lyman alpha absorption lines seen along the line of sight towards quasars at redshifts of 2-5. However, it will need a 20 year baseline and about 400 nights of telescope time! Here are some pictures from that paper. The first shows how the observed redshift of an object will change with cosmic time for different values of the main cosmological parameters. The x-axis is time (in Gyr, assuming the present-day Hubble constant is 70 km/s per Mpc), with zero representing now (note that different models predict a different age for the universe). The "concordance model" at the moment is that represented by the red lines ($\Omega_M=0.3$, $\Omega_\Lambda=0.7$), where the three different lines represent quasars with different redhifts at the present day. I guess the thing you should take away from this diagram is that different models predict different gradients in these plots - i.e. different rates of change of the redshift with time. Also note that the gradient now depends on the redshift. For the red concordance model, high redshifts are getting smaller with time, but low redshifts ($z<2$, where dark energy accelerates the expansion) are getting bigger with time. . The paper then goes on to perform extensive simulations predicting how well a high resolution spectrograph on the E-ELT could perform with a 20 year observing baseline. The results are shown below, with predicted data points measured from the Lyman alpha absorption lines towards a set of quasars at various redshifts. The y-axis shows the predicted drift rate as a function of redshift. Appreciate the numbers! Even over 20 years, the changes in redshift amount to around 0.1 m/s, yet nevertheless, the prediction is that it can be observed and can be used as a model-independent way of directly measuring the expansion rate of the universe. A slightly more accessible version of this work can be found in the ESO Messenger. EDIT: There are also plans afoot to measure these effects at radio wavelengths using the Square Kilometre Array (due to commence operation in 2025?). Simulations by Klockner et al. (2015) suggest that precise measurements of the 21 cm (1.42 GHz) hydrogen line for ten million galaxies, each with a precison of around 10 m/s are required. The redshift drift would amount to a change in the line frequency at a given redshift of around 0.1 Hz (2 cm/s !) over a decade. • That's interesting, my point about knowing an infeasible amount of information about the object being observed is that the change in red-shift of a given object is likely to be almost entirely due to a change in peculiar velocity. But what Liske et al propose is to observe the drift in red-shift of a large amount of objects so the peculiar velocities average near enough to zero. Kind of obvious when you think about it. – John Davis Mar 16 '15 at 1:38 Cosmological red-shift depends on the difference in the scale factor between when the light was emitted and when it was received and not directly on recessional velocity, which is of dubious physical significance. The recessional velocity of any given galaxy outside our own (ignoring peculiar velocities) in a LCDM-like cosmology will be arbitrarily large near the big bang, slow down, before increasing and becoming arbitrarily large in the future. In the current epoch the recessional velocity of a given galaxy is increasing. This most easy to see when the co-moving distance of the Hubble sphere is plotted against conformal time. (see the third diagram of Fig 1 in this paper) See part of my recent answer to a similar question, for a few more details: https://astronomy.stackexchange.com/questions/10123/are-galaxies-moving-away-from-us-faster-than-before • Good answer. Perhaps you could add (you sound like you might know) what the prospects are for actually measuring this change. I did hear somewhere that a precision was being approached that this might be feasible on decadal timescales? – Rob Jeffries Mar 15 '15 at 21:21 • Being able to calculate the change in recessional velocity from the change in observed red-shift of an object on a decadal timescale would not be be possible without infeasibly accurate information about the object in question and the larger scale properties of the Universe. – John Davis Mar 15 '15 at 23:13 • You're too pessimistic. I knew I'd seen this It is an E-ELT key project. – Rob Jeffries Mar 16 '15 at 0:46 • Also now a proposed SKA project. – Rob Jeffries Apr 8 '16 at 14:12	{}
# Homework Help: Wave Function_vibtrating nuclei 1. Oct 2, 2014 ### terp.asessed 1. The problem statement, all variables and given/known data The Ground state wave function governing the motion of a pair of vibrating nuclei looks like: wave function = wave (x) = (a/pi)1/4 e-ax2/2 where a = alpha = muw/(h bar), which is determined by mu = reduced mass of the pair where w = angular vibrational frequency ...So, suppose the vibrating atoms in question were C and O. Compute what v~, the frequency of the vibration in cm-1, would have to be if the root-mean square fluctation in bond length were 0.035Angstom. I lost track of the units for my solution, and I am not sure if I have done correctly... 2. Relevant equations wave function = wave (x) = (a/pi)1/4 e-ax2/2 a = alpha = muw/(h bar), which is determined by mu = reduced mass of the pair w = angular vibrational frequency root mean square = <x2> - <x>2 3. The attempt at a solution root mean square = <x2> - <x>2 where <x2> = integral (-infinite to infinite) wave(x) x2 wave(x) dx = which I got 1/(2a) as a result <x> = integral (x=o to L) p(x) x p(x) dx which I got as 0 in the end so...I input: root mean square = <x2> - <x>2 = 1/(2a) - 0 = 1/(2a) since root mean square = 0.035 angstrom = 1/(2a) and b/c a = muw/(h bar), I rearranged so that: w = (h bar)/(0.07mu)...where mu = m1m2/(m1 + m2) For mass of 1 C atom: 12.01g/(6.022x1023 atoms) x 1kg/103g = 1.99 x 10-26kg For mass of 1 O atom: 16.00g/(6.022x1023 atoms) x 1kg/103g = 2.66 x 10-26kg mu = 1.14 x 10-20kg therefore w = (h/(2pi))1/(0.07mu) = 1.32 x 10-13 omega (is this right????) I know h has units of J2 and mu = kg.....but together they do NOT make omega..... therefore v~ = w/(2pic) where c = speed of light = 1.32 x 10-13 (assuming the unit is correct) / (2pi3x108m/s) = 7.02 x 10-23 s-1 b/c I got lost track of units....I am not sure if the units in the solution is right...if someone could (1) explain the units in each calculations I did and then (2) give me hints as how to keep track of units for near future too, that would be so wonderful. 2. Oct 2, 2014 ### TeethWhitener You made a numerical error in your value of $\mu$. If your mass for a carbon atom is ~10-26kg and your mass for an oxygen atom is ~10-26kg, there's no way the reduced mass will be ~10-20kg. Fix that first. As for the units, Planck's constant $\hbar$ is in J s (joule-seconds). Maybe breaking this (and everything else) down into base units (kg, m, s) will help. Just a heads up, you also forgot the "root" part of "root mean square." 3. Oct 2, 2014 ### terp.asessed Hello--thanks you for the reply--so, you're right, I miscalculated: μ = 1.14 x 10-26 kg Also, since, ℏ = Js = kgm2/s2....is omega a right unit for w? w = (h/(2pi))1/(0.07mu) = 1.32 x 10-7 (Js)/kg = 1.32 x 10-7 m2/s....???? Did I make mistake? It is of acceleration unit, not velocity... Aside, could you please clarify by what you mean by "root part of the root mean square"? If you could, thanks! 4. Oct 2, 2014 ### TeethWhitener You're close with $\hbar$. Joules are kgm2/s2 (you can remember this by recalling that joules are a measure of energy and kinetic energy is $\frac{1}{2}mv^2$), so Js is kgm2/s. Also, it's clear that you know that $\mu$ has units of kg, but 0.07 also has units. This comes from the root mean square of distance, which, by the way, is $$\sqrt{\langle x^2 \rangle - \langle x \rangle ^2 }$$ not just $$\langle x^2 \rangle - \langle x \rangle ^2$$ The units of rms distance are the same as the units of plain old distance, which in this case is just angstroms. Hopefully that should get you started.	{}
## Galvanic Cell $\Delta G^{\circ} = -nFE_{cell}^{\circ}$ Lumbini Chandrasekera 1B Posts: 63 Joined: Fri Sep 28, 2018 12:18 am ### Galvanic Cell When you are given a problem in regards to a galvanic cell, can you assume that the cell potential of the reaction is always positive? Michael Torres 4I Posts: 92 Joined: Thu May 10, 2018 3:00 am Been upvoted: 1 time ### Re: Galvanic Cell Yes, I believe so. The solutions manual states this when explaining problem 6L.7 from the seventh edition. Stevin1H Posts: 89 Joined: Fri Sep 28, 2018 12:17 am ### Re: Galvanic Cell Yes, the cell potential has to be positive because the galvanic cell is converting chemical energy to electrical energy. A positive cell potential is related to a spontaneous reaction as well. Rehan Chinoy 1K Posts: 67 Joined: Fri Sep 28, 2018 12:25 am ### Re: Galvanic Cell It would be safe to assume that the cell potential is positive in a galvanic cell when doing problems in the textbook or on a test because there would not be much to prove or calculate if the cell potential was negative.	{}
# Math Help - Interesting variations on the Collatz Conjecture 1. ## Interesting variations on the Collatz Conjecture After reading http://xkcd.com/710/ and straining to recall my number theory classes I had many many moons ago, I started doing a somewhat serious analysis of the collatz conjecture. after asking some of my questions about similar systems I came up with one of my own which appears to behave like collatz's, as well as a 2nd one that causes numbers to fall into one of two orbits, unlike collatz. excuse the pseudo-code. I'm a medic by profession and amateur coder by hobby. Collatz Conjecture: $f(n)=($ If n is odd $(3n+1)$ else $(n/2))$ all integers >=1 will eventually equal 1 My variation on Collatz: $f(n)=($ If n is odd $(3n+3)$ else $(n/2))$ all integers >=1 will eventually equal 3 My 2 orbit variation on collatz: $f(n)=($ If n is odd $(3n+7)$ else $(n/2))$ all integers n such that n mod(7) !=0 will eventually equal 5 all integers n such that n mod(7) =0 will eventually equal 7 I've noticed that for pretty much any system who's "odd" half does not have 3 as it's co efficient will have multiple "stable orbits" as well as infinitely increasing numbers that never orbit, yet I have not seen a system that has both a single stable orbit and infinite orbits I've also noticed that for the negative numbers, multiple stable orbits seemingly without infinite orbits occur more frequently[/edit] When working with such prime coefficients for the odd half (ex: 5n+1 or 11n+1) I noticed very frequently that when an orbit would end in 6 (excluding 16), it would turn into an infinite orbit, due to the numbers' end fluctuating between 6 and 3. This makes me wonder if the collatz conjecture works somehow because of the "Rule of 9's" as the collatz conjecture itself doesn't seem to generate any multiple of 9 unless the originating number itself is a multiple of 9 (correct me if I'm wrong here, I'm working with spreadsheets of the first 1,000 numbers). This has made me wonder if the collatz conjecture couldn't be extrapolated to work on a different number base system, such as base 6 (odd=2n+1 ?). Any legitimate attempt at a proof of the conjecture, or even proof of properties of collatz-like systems is well beyond my abilities, but maybe someone on here would know how to begin approaching these ideas. I don't have access to (or know which kind) of resources would show if this kind of work with orbits based off the Collatz Conjecture have been done before, but I would like to find out more either way. Also, I'd love to find a program that could map out conjectures of this nature since I find that a lot of the graphical representations of mathematical systems are beautiful from an artistic standpoint (watching a Collatz tree "grow" is somewhat mesmerising Dailymotion - Collatz conjecture - une vidéo Hi-Tech et Science) Could someone possibly point me in the right direction for finding other published variations on the Collatz Conjecture, and a (preferably free) program that I could use to map out my own Trees of Collatz conjectures? 2. Originally Posted by justinwcurtiss Could someone possibly point me in the right direction for finding other published variations on the Collatz Conjecture, and a (preferably free) program that I could use to map out my own Trees of Collatz conjectures? I think you bring up some interesting questions, but I'll only be responding to the quoted part above. Searching for "Collatz conjecture" on Google Scholar revealed the article The 3x+ 1 problem and its generalizations by JC Lagarias (1985), among others. (You will need JSTOR access to see that full article from the link.) Also, a quick search on regular Google gave a site you might be interested in, Collatz Conjecture Calculation Center. I'd like to use these questions as programming exercises, but I have limited time. I'll let you know if I come up with anything that could be useful.	{}
Kinematics 2D – JEE Main Previous Year Questions with Solutions JEE Main Previous Year Question of Physics with Solutions are available here. Practicing JEE Main Previous Year Papers Questions of Physics will help all the JEE aspirants in realizing the question pattern as well as help in analyzing their weak & strong areas. Get detailed Class 11th &12th Physics Notes to prepare for Boards as well as competitive exams like IIT JEE, NEET etc. eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects. Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more. Download eSaral app for free study material and video tutorials. Simulator Previous Years AIEEE/JEE Mains Questions Q. A particle is moving with velocity $\overrightarrow{\mathrm{v}}=\mathrm{K}(\mathrm{y} \hat{\mathrm{i}}+\mathrm{x} \hat{\mathrm{j}})$ where K is a constant. The general equation for its path is : (1) $\mathrm{y}^{2}=\mathrm{x}^{2}+$ constant (2) $\mathrm{y}=\mathrm{x}^{2}+$ constant (3) $\mathrm{y}^{2}=\mathrm{x}+$ constant (4) xy = constant [AIEEE – 2010] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more... Sol. (1) $\overrightarrow{\mathrm{v}}=\mathrm{k}(\mathrm{y} \hat{\mathrm{i}}+\mathrm{x} \hat{\mathrm{j}})$ $\overrightarrow{\mathrm{v}}=\mathrm{v}_{\mathrm{x}} \hat{\mathrm{i}}+\mathrm{v}_{\mathrm{y}} \hat{\mathrm{j}}$ $\overrightarrow{\mathrm{v}}=\frac{\mathrm{d} \mathrm{x}}{\mathrm{dt}} \hat{\mathrm{i}}+\frac{\mathrm{dy}}{\mathrm{dt}} \hat{\mathrm{j}}$ $\frac{d x}{d t}=k y \& \frac{d y}{d t}=k x$ $\Rightarrow \frac{d x}{d y}=\frac{y}{x}$ $\Rightarrow \mathrm{y}^{2}=\mathrm{x}^{2}+$ constant Q. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :- (1) $\frac{\pi}{2} \frac{v^{4}}{g^{2}}$ (2) $\pi \frac{\mathrm{v}^{2}}{\mathrm{g}^{2}}$ ( 3)$\pi \frac{\mathrm{v}^{2}}{\mathrm{g}}$ ( 4)$\pi \frac{\mathrm{v}^{4}}{\mathrm{g}^{2}}$ [AIEEE – 2011] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more... Sol. (4) $\mathrm{r}=\mathrm{R}_{\max }=\frac{\mathrm{v}^{2}}{\mathrm{g}}$ area $=\pi \mathrm{r}^{2}$ $=\pi\left(\frac{\mathrm{v}^{2}}{\mathrm{g}}\right)^{2}$ $=\pi \frac{\mathrm{v}^{4}}{\mathrm{g}^{2}}$ Q. A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force $\mathrm{F}(\mathrm{t})=\mathrm{F}_{0} \mathrm{e}^{-\mathrm{bt}}$ in the x direction. Its speed v(t) is depicted by which of the following curves ? [AIEEE – 2012] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more... Sol. (3) $\frac{\mathrm{d} \mathrm{v}}{\mathrm{dt}}=\frac{\mathrm{F}_{0}}{\mathrm{m}} \mathrm{e}^{-\mathrm{bt}}$ $\int_{0}^{\mathrm{v}} \mathrm{d} \mathrm{v}=\frac{\mathrm{F}_{0}}{\mathrm{m}} \int_{0}^{\mathrm{t}} \mathrm{e}^{-\mathrm{bt}} \mathrm{dt}$ $\mathrm{v}=\frac{-\mathrm{F}_{0}}{\mathrm{m} \mathrm{b}}\left[\mathrm{e}^{-\mathrm{bt}}-1\right]$ $=\frac{\mathrm{F}_{0}}{\mathrm{m} \mathrm{b}}\left[1-\mathrm{e}^{-\mathrm{bt}}\right]$ Q. A projectile is given an initial velocity of $(\hat{i}+2 \hat{j}) m / s$ where $\hat{\mathbf{i}}$ is along the ground and $\hat{j}$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is : (1) $\mathrm{y}=\mathrm{x}-5 \mathrm{x}^{2}$ (2) $\mathrm{y}=2 \mathrm{x}-5 \mathrm{x}^{2}$ (3) $4 y=2 x-5 x^{2}$ (4) $4 y=2 x-25 x^{2}$ [AIEEE – 2013] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more... Sol. (2) $\mathrm{u}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}$ $\mathrm{u}_{\mathrm{x}}=1$ $\mathrm{u}_{\mathrm{y}}=2$ $\tan \theta=\frac{2}{1}$ $\mathrm{y}=\mathrm{x} \tan \theta-\frac{1}{2} \mathrm{g} \frac{\mathrm{x}^{2}}{\mathrm{u}^{2} \cos ^{2} \theta}$ $\mathrm{y}=2 \mathrm{x}-5 \mathrm{x}^{2}$ Q. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 $\mathrm{M} / \mathrm{S}^{2}$) (The figure are schematic and not drawn to scale) [JEE Mains – 2015] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more... Sol. (1) $\mathrm{y}=2 \mathrm{x}-5 \mathrm{x}^{2}$ For particle 2 $-240=40 \mathrm{t}-\frac{1}{2} \mathrm{gt}^{2}$ $5 t^{2}-40 t-240=0$ $\mathrm{t}_{2}=12 \mathrm{sec}$ for $0<\mathrm{t}<8$ sec $\rightarrow \mathrm{a}_{\text {rel }}=0$ straight line x-t graph for $8<\mathrm{t}<12$ sec $\rightarrow \mathrm{a}_{\mathrm{rel}}=-\mathrm{g}$ downward parabola for $\mathrm{t}>12 \mathrm{sec} \rightarrow$ Both particles comes to rest	{}
mersenneforum.org Is there an FAQ for Error and Warning messages? Register FAQ Search Today's Posts Mark Forums Read 2013-01-27, 22:26 #12 Prime95 P90 years forever! Aug 2002 Yeehaw, FL 22×17×109 Posts Quote: Originally Posted by Jorge Whomever is responsible for the P95 stress testing program might want to take a look and/or conduct their own tests with an AMD FX processor to see if they can determine why there are (100) warnings, but no errors. If this is a signal ringing issue, maybe the warning threshold needs to be raised to (1000) or something to compensation for false warnings and improper stoppage of the test? I think you are confused by the word "warning" -- and that's due to poor documentation. When an ILLEGAL SUMOUT occurs, the hardware produced an invalid floating point value -- something is wrong with the system. The reason prime95 does not call this a hardware error is because back in the early days of Windows 95 and Windows 98, poorly written device driver would fail to save and restore the floating point state resulting in floating point errors. The hardware was fine, but the device driver software was bad. Thus prime95 called this condition a "warning" or "possible hardware failure". I don't know if something similar can happen in newer operating systems. In short, even though prime95 uses the word warning, something is wrong 00 we just don't know what that something is. I don't have an FX processor handy, someone on the forum may and can run a stress test. I have access to an Bulldozer-based Opteron - is that similar to your FX ? 2013-01-27, 23:05 #13 sdbardwick Aug 2002 North San Diego County 2×11×31 Posts Jorge, what version of Prime95 are you running? mprime64 v26.6 small FFTs on Opteron 4280 (bulldozer) uses the Core2 code path rather than the K10 path in your results. 2013-01-28, 02:26 #14 Jorge Jan 2013 32 Posts Quote: Originally Posted by Prime95 SNIP In short, even though prime95 uses the word warning, something is wrong 00 we just don't know what that something is. I don't have an FX processor handy, someone on the forum may and can run a stress test. I have access to an Bulldozer-based Opteron - is that similar to your FX ? Yes Bulldozer based Opterons use the same architecture so that should be a good test. I agree we don't know what is wrong. That is why I'm posting logs and hoping those who are involved with the development of the P95 stress test software, can look into the issue. With the warnings happening after the PC has run for 9 hours and 50 minutes and having run the exact same string previously without issue, I'm still thinking this might be a P95 issue. When I have tested with extreme overclocking on this and other systems, and there really was an error, it would list the error, i.e. ".5 returned instead of >.4", as a typical example. There have been none of these with this FX system after many hours of stress testing. I did read the notes about 2000/XP/Vista protecting P95 from driver issues. I don't know if Win 7/8 function the same. I'm running Win 7 64-bit, on the test PC. I think most folks would conclude that 100% load on all 8 cores for 9 hours and 50 minutes is a stable PC but with many other FX/Bulldozer/Vishera PC owners not being able to run P95 for more than a few minutes at the default CPU frequency with no overclocking, it makes you wonder what exactly is happening. While I fully understand that some systems may use borderline quality components or be configured poorly, there are a lot of experienced enthusiasts who've never had P95 issues on the other PCs they have built over the years, me included. sdbardwick- I'm running V27.7, (64-bit), last updated May 15, 2012 from what I see. I do not know if this could be an issue, but it's suppose to be OK for Win 7 64-bit. Anyone willing to run P95 tests on Bulldozer/Vishera model AMD FX/Opteron processors may be able to help resolve this issue. After some searches here I found the V27.7 P95 thread and noticed that there is a V27.9 and that some folks had issues with HT on V27.7. The suggestion was to run one thread per core, but that defeats the point of stress testing, IMO. I don't know if this is a possible issue with the Bulldozer/Vishera architecture FX/Opteron CPUs, but it might be? Last fiddled with by Jorge on 2013-01-28 at 02:52 2013-01-28, 05:01 #15 Prime95 P90 years forever! Aug 2002 Yeehaw, FL 741210 Posts Quote: Originally Posted by Jorge Yes Bulldozer based Opterons use the same architecture so that should be a good test. I'll run one overnight. Quote: With the warnings happening after the PC has run for 9 hours and 50 minutes and having run the exact same string previously without issue, I'm still thinking this might be a P95 issue. Nope. There have been numerous reports of systems that last far longer before spitting out an error. All it means is that the system is really, really close to being prime95 stable. Quote: When I have tested with extreme overclocking on this and other systems, and there really was an error, it would list the error, i.e. ".5 returned instead of >.4", as a typical example. Yes, the ILLEGAL SUMOUT failure mode is rare. Quote: I think most folks would conclude that 100% load on all 8 cores for 9 hours and 50 minutes is a stable PC but with many other FX/Bulldozer/Vishera PC owners not being able to run P95 for more than a few minutes at the default CPU frequency with no overclocking, it makes you wonder what exactly is happening. 10 hours without error is a stable PC for most everyday tasks. Although, I wouldn't do serious distributed computing work on such a machine. Reports of stress test failures at stock speed is not at all uncommon. Usually its a memory problem, but ever since AMD put their memory controller on chip many of their CPUs fail at stock speed. IMO, AMD quality control was not very good a few years ago. Maybe its better these days, I don't know. Quote: After some searches here I found the V27.7 P95 thread and noticed that there is a V27.9 and that some folks had issues with HT on V27.7. The suggestion was to run one thread per core, but that defeats the point of stress testing, IMO. For stress testing purposes, 27.7 and 27.9 are equivalent. You are correctly running 8 stress test threads. 2013-01-28, 05:12 #16 sdbardwick Aug 2002 North San Diego County 68210 Posts FWIW, the 26.6 test has been running for 6+ hours without error using 8 threads (1 socket). 2013-01-28, 23:55 #17 Jorge Jan 2013 118 Posts Quote: Originally Posted by Prime95 I'll run one overnight. Excellent, all information is appreciated! Quote: Originally Posted by Prime95 Reports of stress test failures at stock speed is not at all uncommon. Usually its a memory problem, but ever since AMD put their memory controller on chip many of their CPUs fail at stock speed. IMO, AMD quality control was not very good a few years ago. Maybe its better these days, I don't know. With all due respect, I totally disagree with you about AMD CPU quality. Over the past 20 years I have built a lot of PC's professionally and most were AMD. I have never had an AMD PC that had any IMC or CPU issues -ever. AMD's IMC may not be able to run RAM at as high a frequency as Intel IMC's when overclocked, but that doesn't mean they don't work just fine and reliably at the AMD specified frequencies. In comparison it is documented that Intel has shipped millions of defective CPUs, chipsets, mobos and SSDs. AMD has not shipped any defective products that I am aware of - ever. Some 40 years ago AMD also manufactured Intel's CPUs for them... I hope that with more P95 testing we can determine if there is or is not an issue running P95 on the Bulldozer/Vishera architecture CPUs. I noticed that the Opteron models are pretty low frequency so they are likely to run fewer tests in a given period of time than the FX processors, so longer run times may be required? 2013-01-29, 02:46 #18 Prime95 P90 years forever! Aug 2002 Yeehaw, FL 22·17·109 Posts I'm at 20 hours of Bulldozer stress testing. 16 threads, small in-place FFTs. Linux version 27.7. No problems. At this point, I'd say that there isn't a software problem with the prime95 stress test. The major difference between the two setups is the hardware and the OS. If it is a hardware problem, then the error should go away if you drop the CPU and memory clock rate significantly. If it is an OS issue, you might try installing linux and running the stress test (yes, I know that would be a pain!). Alternatively, you could call one-prime95-error-every-10-hours stable enough. I'll continue the Bulldozer stress test for another day. Unfortunately, I can't run it under Windows. Quote: Originally Posted by Jorge With all due respect, I totally disagree with you about AMD CPU quality. That's OK. Your opinion and mine are both subjective and based on rather small data sets. I've not built any AMD systems (owned two). My opinion is based on a surge of I'm-running-at-stock-speed-your-program-must-be-broken complaints when hypertransport first came out. Last fiddled with by Prime95 on 2013-01-29 at 03:21 2013-01-29, 03:15 #19 LaurV Romulan Interpreter Jun 2011 Thailand 11×853 Posts [edit: obviously my post is not addressed to George, he posted in between, as it took me a while to finish this, between job tasks]. Opinions vary. You are entitled to yours. We hope you are not one of those AMD trolls, we had many here in the past. We hope you are able think objectively, and not influenced by heart. This is not meant to be an insult. I have very good friends which I would classify as "AMD trolls". We meet around a beer bottle and talk technical things sometimes. They used AMD in the past (me too), at the time we were students, and AMD was cheaper, for about the same performance. They felt in love with it, and later stuck to first love. The things changed, there are many years since Intel outperforms AMD at every point, quality, performance, performance/watt/buck, reliability, IPC (instructions per clock cycle), whatever. But for all those features, you have to pay more money. You should not compare Buldozer with i7 on DP floats calculus and this kind of stuff where AMD sucks. They are targeting different markets. If AMD did not recall CPUs it does not mean they don't have defects, but it may be they care less about the customers, or have a different policy. The defect rate is exactly the same for both Intel and AMD, the silicium chips are quite mature and stable medium, they all go 100 ppm to 200 ppm (parts per million) defect rate, etc, and for the number of transistors they have, about one in 150 CPUs are deffect. They (both!) still sell those like lower end, either with a core cut out, with some memory speed locked, bla bla. Trust me, I work in an electronic factory (some people here know me). There is no "better", it only depends on your preference, target applications, and budget. For LL testing, well, Intel is better. It took a while to convince my friends. Guess what, they are now convinced that Intel is better, but they still use AMD, because "Intel need competition" That I would call an "AMD troll". My friends knows that I call them such. It is a "friendly" call (and don't ask how they call me, or how we call each-other sometimes, that is what friends are for, isn't it?)... [edit2, after reading George's post: from Prime95 (the program) stress.txt file, last paragraph, last FAQ: Code: Q) A forum member said "Don't bother with prime95, it always pukes on me, and my system is stable!. What do you make of that?" or "We had a server at work that ran for 2 MONTHS straight, without a reboot I installed Prime95 on it and ran it - a couple minutes later I get an error. You are going to tell me that the server wasn't stable?" A) These users obviously do not subscribe to the 100% rock solid school of thought. THEIR MACHINES DO HAVE HARDWARE PROBLEMS. But since they are not presently running any programs that reveal the hardware problem, the machines are quite stable. As long as these machines never run a program that uncovers the hardware problem, then the machines will continue to be stable. end of edit2] Last fiddled with by LaurV on 2013-01-29 at 03:45 2013-01-29, 03:24 #20 Jorge Jan 2013 32 Posts Quote: Originally Posted by Prime95 I'm at 20 hours of Bulldozer stress testing. 16 threads, small in-place FFTs. Linux version 27.7. No problems. At this point, I'd say that there isn't a software problem with the prime95 stress test. The major difference between the two setups is the hardware and the OS. If it is a hardware problem, then the error should go away if you drop the CPU and memory clock rate significantly. If it is an OS issue, you might try installing linux and running the stress test (yes, I know that would be a pain!). Alternatively, you could call one-prime95-error-every-10-hours stable enough. I'll continue the Bulldozer stress test for another day. Unfortunately, I can't run it under Windows. I think we need to run the Bulldozer/Vishera architecture CPUs under Windows to have a more realistic understanding if there is an issue as that's what I and most other enthusiasts are using, (even though I'd much prefer to not be using Windoze). Obviously a sample run on only 1-2 CPUs may not turn up any issues but if they do then we know to investigate further. 2013-01-29, 03:37 #21 Xyzzy "Mike" Aug 2002 8,053 Posts Quote: If it is an OS issue, you might try installing linux and running the stress test (yes, I know that would be a pain!). No pain if you use a Linux LiveCD or USB dealio. Just wget the client and rock and roll. Code: wget http://www.mersenneforum.org/gimps/p95v279.linux64.tar.gz gzip -d p95v279.linux64.tar.gz tar -xvf p95v279.linux64.tar ./mprime -m The only thing scary about trying a different operating system is the possibility that it gives the same error and proves that your hardware is not 100% reliable. But, if it passes, that narrows down the possible issues. For example, what happens when you run the torture test in safe mode in Windows? http://windows.microsoft.com/en-US/w...r-in-safe-mode By eliminating a slew of drivers and programs you can eliminate variables. FWIW, any error or warning is unacceptable to us, so we would not rest until the issue was resolved. And we would explore every possible angle to simplify the challenge. 2013-01-29, 03:38 #22 Jorge Jan 2013 32 Posts Quote: Originally Posted by LaurV Opinions vary. You are entitled to yours. BIG SNIP That I would call an "AMD troll". My friends knows that I call them such. It is a "friendly" call (and don't ask how they call me, or how we call each-other sometimes, that is what friends are for, isn't it?)... NO that's not what friends are for. BTW, I find your post TOTALLY INAPPROPRIATE, condescending, insulting, ignorant and technically incorrect in so many ways I won't even waste my time responding to such fanbois foolishness - and your post is complete OFF TOPIC. Catch my drift? The only reason I replied to Prime95's AMD comment was because his perception is completely inaccurate - as is 90% of what you stated as "facts", when it's your subjective opinion, unlike the Intel shipments of defective products, which are documented. Concluding that the issue I am seeing is likely a result of AMD"s perceived QC issues would be wrong as there is no basis for this belief. Since AMD hasn't shipped any defective products that I am aware of, there is no reason for them to have a recall. You can be damn certain that if they did ship defective products, they would be forced to recall them as Intel was, but since AMD didn't ship any, there were no recalls. There does not appear to be any objective statistical or scientific bases for this myth about AMD quality issues. Your post was of absolutely NO VALUE to this thread or the testing of V27.7 on Bulldozer/Vishera architecture CPUs running under Windoze. If you have nothing constructive to contribute to this thread, please stay out of the thread. There are other areas of the forum if you want to talk crap over a few beers with your Bros. My post is meant to be a constructive response to your inappropriate comment/trolling, so I hope you take it in that spirit. Last fiddled with by Jorge on 2013-01-29 at 03:52 Similar Threads Thread Thread Starter Forum Replies Last Post ramgeis PrimeNet 2 2013-06-09 23:53 EdH Factoring 4 2010-01-01 19:52 fivemack Msieve 1 2009-03-21 14:26 edron1011 Software 0 2008-11-21 15:46 Prime95 Lounge 7 2006-10-31 05:40 All times are UTC. The time now is 11:07. Tue Apr 20 11:07:01 UTC 2021 up 12 days, 5:47, 0 users, load averages: 1.38, 1.77, 1.86	{}
Title Application of $RDL_{1}$ to a real data set with heteroscedastic errors Author Hubert, M. Rousseeuw, P.J. Faculty/Department Faculty of Sciences. Mathematics and Computer Science Publication type conferenceObject Publication 1995 1995 Source (journal) Proceedings of the Statistical Computing Section of the American Statistical Association Volume/pages (1995) , p. 52-56 Carrier E Target language English (eng) Affiliation University of Antwerp Handle	{}
# Truncated tetraapeirogonal tiling Truncated tetraapeirogonal tiling Poincaré disk model of the hyperbolic plane Type Hyperbolic uniform tiling Vertex configuration 4.8.∞ Schläfli symbol tr{∞,4} or ${\displaystyle t{\begin{Bmatrix}\infty \\4\end{Bmatrix}}}$ Wythoff symbol 2 ∞ 4 \| Coxeter diagram or Symmetry group [∞,4], (∞42) Dual Order 4-infinite kisrhombille Properties Vertex-transitive In geometry, the truncated tetraapeirogonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one octagon, and one apeirogon on each vertex. It has Schläfli symbol of tr{∞,4}. ## Symmetry The dual of this tiling represents the fundamental domains of [∞,4], (∞42) symmetry. There are 15 small index subgroups constructed from [∞,4] by mirror removal and alternation. Mirrors can be removed if its branch orders are all even, and cuts neighboring branch orders in half. Removing two mirrors leaves a half-order gyration point where the removed mirrors met. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors. The subgroup index-8 group, [1+,∞,1+,4,1+] (∞2∞2) is the commutator subgroup of [∞,4]. A larger subgroup is constructed as [∞,4], index 8, as [∞,4+], (4∞) with gyration points removed, becomes (∞∞∞∞) or (∞4), and another [∞,4], index ∞ as [∞+,4], (∞2) with gyration points removed as (2). And their direct subgroups [∞,4]+, [∞*,4]+, subgroup indices 16 and ∞ respectively, can be given in orbifold notation as (∞∞∞∞) and (2).	{}
# Shortest vectors in tensor product and maximal lattices in tensor product $$\mathcal L$$ and $$\mathcal L'$$ be full rank lattices in $$\mathbb R^n$$ with shortest vectors $$v_1,\dots,v_n$$ and $$v_1',\dots,v_n'$$ respectively where $$\\|v_1\\|_2\leq\dots\leq\\|v_n\\|_2$$ $$\\|v_1'\\|_2\leq\dots\leq\\|v_n'\\|_2$$ hold and $$\mathcal L'=Span(v_1,\dots,v_n)$$ and $$\mathcal L=Span(v_1',\dots,v_n')$$. 1. Do the shortest vectors of $$\mathcal L\otimes\mathcal L'$$ have any relation to shortest vectors of $$\mathcal L$$ and $$\mathcal L'$$ and what is the span of $$v_i\otimes v_j'$$? 2. Do maximal lattices in $$\mathcal L\otimes\mathcal L'$$ have any relation to $$\mathcal L$$ and $$\mathcal L'$$ and $$v_1,\dots,v_n$$ and $$v_1',\dots,v_n'$$?	{}
chromile chloride test can you explain the chromile chloride test ,for chlorides,does NaOH involves it?how and why? Expert's Solution Related Questions in Linear Programming • chem February 11, 2011 For the following reaction, 64.3 grams of silver nitrate are allowed to react with with 23.5 grams of copper(II) chloride. silver nitrate (aq) + copper(II) chloride (s) silver chloride (s)... • more stoichiometry homework # 1 (Solved) February 13, 2011 how many grams of potassium chloride are produced if 25.0 g of potassium chlorate decompose? Solution Preview : The balanced equation for decomposition of potassium chlorate into potassium chrolide is given below: $$2KClO_3 \longrightarrow 2KCl+3O_2$$ As we can see, 2 moles of potassium chlorate... • TaskIn this task you have to extend the Fruit Sales System Further by... (Solved) September 20, 2017 :Add additional columns for each input and each output. You need to show test data for different operations and repetition.Task 3 -Implement your algorithm in Python. Comment on your code... Solution Preview : in this assignment we has made fruitsales system in python language This assigment have three part task1 is diagram i had made according to given requirement. i has made four diagram (NS... • Stoichiometry (Mole-Mole Problems) (Solved) December 16, 2010 A sample of indium chloride weighing .5000 g is found to contain .2404 g of chlorine. What is the empirical formula of the indium compound? Solution Preview : Mass of indium = 0.500-0.2404 = 0.2596g Mass of chlorine = 0.2404g Divide each mass by atomic mass In = 0.2596/114.818 = 0 • Chemistry (Solved) December 19, 2010 Ethyl chloride (C2H5Cl) boils at 12 C. When liquid ethyl chloride under pressure is sprayed on a room temperature surface in air, the surface is cooled considerably. What does this... Solution Preview : Ethyl chloride (C2H5Cl) boils at 12 C then: The amount of heat needed to raise the temperature of a substance is given by the Product of the specific heat, mass and temperature change. The... Copy and paste your question here... Attach Files • Most Popular • Most Viewed 5	{}
# Electric dipole moment of a ring of charge [closed] In my book dipole moment is defined for two charges. But I got a hw question to calculate dipole moment due to a ring. I tried two different methods to solve this problem but I don't think that any of them is correct. I sticked to the definition given in my book for 2 charges,"An electric dipole is a pair of equal and opposite point charges separated by a distance 2a." My solution, Small charge $$dq$$ = $$λRdθ$$. Now by geometry distance between any two points, $$2a$$ = $$2Rcosθ$$ as shown in the image. Now $$dp$$ = $$2adq$$ Integrated it from $$-π/2$$ to $$π/2$$ and got option A as the answer. Net Dipole moment will clearly be in the $$+x$$ direction Now second method, Consider any two diametrically opposite points, by symmetry dipole moment will be in the $$+x$$ direction as it will be cancelled in the $$y$$ direction. Now since they are diametrically opposite so $$2a$$ = $$2R$$ Hence, $$dp$$ = $$2Rdqcosθ$$ in the $$+x$$ direction. But I don't think any of my method is correct as each charge will be under the influence of all the opposite charges so I can't actually decide what will $$2a$$ be. If the points are diametrically opposite then it will be $$2R$$ but the distance can be anything as we can choose any two pair of opposite charge so the distance between the opposite charges can be anything from $$0$$ to $$2R$$. Both the ways you did is right, and if you do the math properly you should get option A in both the case. As for you latter question on what the distance should be, As you have defined, you have to take distance between equal and opposite charges. In our situation, there are not many ways, but precisely two ways of choosing the equal and opposite charges. 1. Diametrically opposite: For a charge at $$\theta$$ we have charge per unit length at that point to be $$\lambda=\lambda_{0}\cos\theta$$, and for a diametrically opposite point ($$180^o +\theta$$), we have $$\lambda=\lambda_{0}\cos(180^o + \theta)=-\lambda_{0}\cos(\theta)$$. Hence these two does form a dipole (equal and opposite) with dipole lenght $$2R$$. 2. Mirror about y-axis: For a charge at $$\theta$$ we have charge per unit length at that point to be $$\lambda=\lambda_{0}\cos\theta$$, and for a point mirrored about y-axis ($$180^o -\theta$$), we have $$\lambda=\lambda_{0}\cos(180^o - \theta)=-\lambda_{0}\cos(\theta)$$. Hence these two does form a dipole (equal and opposite) with dipole length $$2R \cos(\theta)$$. And, as you have already done, either way you should get the same result, as it should be. The way you are thinking which is that each charge interacts with each other is the monopole way of going about it, which is perfectly valid. In fact on derives the formula for dipole ($$p=\sum q_i d_i$$) is using Coulombs Law on the system of charges. The dipolar, or for that matter any multipolar system is a very special kind of a system, in that it has some symmetry (in case of dipole its equal and opposite). Due to this very symmetry the Coulomb law takes a special form which is when you ignore the constants and call the numerator as a dipole charge. Keeping it very simple and not going into details, what I mean to say is that your worry that each charge is interacting with all others is already taken care of by the symmetry of the system. For a general system, this particular way is not exactly valid and so we do a multipolar expansion. • Thankyou, I was really anxious about this problem from so many days but I got it now. Also, Could you please elaborate a little bit or share a link on monopole method? I've 3 books with me, University Physics, my school book and Concepts of Physics but nothing is mentioned about this monopole method in those books and neither any example is present to calculate dipole moment of continuous charge distribution. Oct 1 '21 at 20:31 • I am not aware of many high school text, but any standard Electromagnetism book at undergraduate/graduate level should have a fairly detailed explanation. Why don't you look up the Wikipedia page here. The idea is straight forward. If you have just a single charge, its just standard Coulomb's at whichever scale you decides to look. But things get interesting when you have more than one. For ease of calculation as well as quite a nice physical interpretation, we prefer to break down the net effects to sum of smaller once. Oct 2 '21 at 4:31 • Thankyou so much. Oct 2 '21 at 4:35	{}

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