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Maya is sister of dhara who is doctor. Maya is sister of dhara, who is doctor.   In both statements who is used for which person??? How do I solve the following second order partial differential equation?  $4u_{xx}+5u_{xy}+u_{yy}+u_x+u_y=2$  I have classified the equation to be hyperbolic and changed variables to obtain the canonical form as $u_{\epsilon\nu}={1\over{3u_\nu}}-{8\over9}$ which I believe is correct but I am struggling to find the general solution? A step by step solution would be appreciated. Ruby -- capitalize first letter of every sentence in a paragraph How do I find out the user name and password for an existing account? Wires do not connect in Circuitikz I've been trying to use relative coordinates to make my drawings more precise but it seems I don't know how the command \node works since I've been having this problem while connecting a circuit element to another:    I'm trying to eliminate the blank between the two wires.  This is the minimal code:  \documentclass{book} \usepackage[siunitx,RPvoltages]{circuitikz} %Circuit Schematics/Diagram \usetikzlibrary{arrows,shapes,calc,positioning} \begin{document}     \begin{circuitikz}             \path (0,0) coordinate (C);             % Comparatore             \path (C) + (0,-1) + (1,0) coordinate (com) node[above]{};             \path (com) + (1.5,-1) node[op amp] (comp) {};             % Collegamenti Comparatore             \node (G1) at ([shift=({-1.3cm,0cm})]comp.-) {};             \draw (G1) -- (comp.-);             \node (G2) at ([shift=({-1.3cm,0cm})]comp.+) {};             \draw (G2) -- (comp.+);             \draw (C) -- (G1); % Collegamento Rettificatore - Comparatore         \end{circuitikz} \end{document}   Thanks for any help! Hide and seek game $A$ and $B$ go to the Senate to play a game of Hide-and-Seek. There are $100$ rooms in the Senate, and $B$ picks one of them and hides there till the game ends.  $A$, at the beginning of every turn, picks one room and searches in it. Since he is human and thus fallible, he only has a $60\%$ chance of finding $B$ if she is in fact hiding in the room. If he fails to find her in the room, $B$'s score increases by one, and the next turn starts, whereupon $A$ must pick another room to check (he can also check the same room again). $B$ remains in the room she initially chose.  Given that $A$ and $B$ play with perfect strategies, what is the expected value of $B$'s score at the end of the game?  I tried with $1$ room. There is only one hiding place for $B$. So the expected score of $$B = \sum_{n=1}^{\infty}0.4^{n-1}0.6(n-1)=\frac{2}{3}.$$ I started thinking about the number of associative (binary) operations on a set with $n$ elements today.  Looking online I found  which indicates only $113$ of the possible $19,683$ operations on a three-element set satisfy association.  So, $50\%$ of binary operations on a two-element set satisfy association, and less than $0.6\%$ of all binary operations on a three element set satisfy association.  For an $n$-element set, where $n$ denotes a natural number, is the ratio $R_{n}=A_{n}/B_{n}$, of the number of associative binary operations $A_{n}$ to the number of all binary operations $B_{n}$, in general small?  I don't mean the following questions as equivalent, but since they seem more concretely answerable in principle, does   $$ \lim_{n \to +\infty} \frac{A_{n}}{B_{n}} = 0 ? $$       Also, is $F : n \to R_{n}$ a monotonically decreasing function?  Some Background of the Question: In his Linear Algebra Problem Book 1995 on p. 6 Paul Halmos writes "The commonly accepted attitudes toward the commutative law and the associative law are different.  Many real life operations fail to commute; the mathematical community has learned to live with that fact and even to enjoy it.  Violations of the associative law, on the other hand, are usually considered by specialists only."  For all I know, Halmos might only have written that to motivate the study of Linear Algebra and doesn't quite literally mean what he appears to say.  But, if he means what he appears to say, and if $F : n \to R_{n}$ is monotonically decreasing, or $R_{n}$ is generally small, I think there's something amiss with what Halmos says, since non-associative operations seem so common that one may as well enjoy them. What is the origin of non-conservative force? My understanding about  is a force that its work is independent of path such that we can construct another form of the work called potential to make our life easier.  For friction, if I start from microscopic point of view, it should be the macroscopic effect of the electric force or gravity which are both conservative force.  Why do we initially have description by conservative forces (electric/gravity force) but end up with a macroscopic description of nonconservative force(friction)? I wish to select areas of a mesh, but it would be much simpler to just select the ones I don't want selected (because they are easier to access), and then inverse the selection.  Is this possible? "who" vs. "whom" and when to omit the relative pronoun This is the boy who was asked by the teacher to stay back after school. This is the boy whom the teacher asked to stay back after school. This is the boy the teacher asked to stay back after school.   Are the sentences above correct ? Find the limit of $\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)$ I have to prove that      $$\Big[\log\Big(1+\frac 1{n^2}\Big)+ \log\Big(1+\frac 2{n^2}\Big)+...+ \log\Big(1+\frac n{n^2}\Big)\Big] \to \frac 12$$   I know that $$\log\Big(1+\frac 1{n^2}\Big)+ \log\Big(1+\frac 2{n^2}\Big)+...+ \log\Big(1+\frac n{n^2}\Big)= \\ =\log\Big(\frac {n^2+1}{n^2}\Big)+ \log\Big(\frac {n^2+2}{n^2}\Big)+...+ \log\Big(\frac {n^2+n}{n^2}\Big)=\\ =\log\Big(n^2+1\Big)+ \log\Big(n^2+2\Big)+...+ \log\Big(n^2+n\Big)-2n\log n$$  Doing some manipulation we get:           $$\lim_{n \to +\infty}\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)=\frac 12$$      How can I prove this limit? How can I move an object towards another along a straight line I'm trying to understand at a deeper level the ubiquity of log-likelihood (and perhaps more generally log-probability) in statistics and probability theory.  Log-probabilities show up all over the place: we usually work with the log-likelihood for analysis (e.g. for maximization), the Fisher information is defined in terms of the second derivative of the log-likelihood, entropy is an expected log-probability, Kullback-Liebler divergence involves log-probabilities, the expected diviance is an expected log-likelihood, etc.    Now I appreciate the many practical and convenient reasons.  Many common and useful pdfs are from exponential families, which leads to elegantly simplified terms when log-transformed.  Sums are easier to work with than products (esp for differentiating).  Log-probs have a great floating point advantage over straight probs.  Log-transforming a pdf often converts a non-concave function into a concave function.  But what is the theoretical reason/justification/motivation for log-probs?  As an example of my perplexity, consider the Fisher information (FI).  The usual explanation for intuiting the FI is that the second derivative of the log-likelihood tells us how "peaked" the log-likehood is:  a highly peaked log-likelihood means the MLE is well-specified and we are relatively sure of its value, while a nearly flat log-likehood (low curvature) means many different parameter values are nearly as good (in terms of the log-likelihood) as the MLE, so our MLE is more uncertain.   This is all well-and-good, but isn't it more natural to just find the curvature of the likelihood function itself (NOT log-transformed)?  At first glance the emphasis on the log-transform seems arbitrary and wrong.  Surely we are more interested in the curvature of the actual likelihood function.  What was Fisher's motivation for working with the score function and the Hessian of the log-likelihood instead?  Is the answer simply that, in the end, we have nice results from the log-likelihood asymptotically? E.g., Cramer-Rao and normality of the MLE/posterior.  Or is there a deeper reason? Why is the $S_{z} =0$ state forbidden for photons? Can you help me with my software dependency issue? This is a  about Compile Dependencies and Package Management.    I have a question regarding compiling ports/software or installing RPMs on my *nix server.  When I try to do this I receive lots of messages about missing dependencies.  Can the Server Fault community please help? What hash is concatenating with the data to be signed in TLS 1.3 CertificateVerify message? According to specification, to create data that will be signed with server private key for CertificateVerify message, we need to concatenate 64 space characters, the string &quot;TLS 1.3, server CertificateVerify&quot;, null and the hash of all handshake messages to this point. During the handshake process, we choosing the cipher suite and signature scheme... So, if the cipher suite is, for example, TLS_AES_256_GCM_SHA384 and the signature scheme is rsa_pss_rsae_sha256 (different hash algorithms), hash of which algorithm should be used as handshake hash in data to sign, SHA-384 or SHA-256? Getting a random object from NSArray without duplication The new top bar is out on meta. Consider it a beta EDIT Dec 4 -  We're doing it live! Please post bugs or concerns as questions tagged [top-bar]  We have rolled out our 95% completed top bar for feedback.  Note:   We are still adding a few final features, so if you have a request for a feature that is not there you might hold off on that for a day or two Yes, the bar is black1. Also give that a day or two to sink in.   I also want to specifically address the meta/main/chat links.  I'm very aware that many of you like having the links at the top of the page and that this new version is different.  The thought process behind moving these links is that the "site switcher" should be an automatic place to go when you are on a site and want to go to another one. If you haven't already developed the muscle memory for these links, getting between them required a bit of a cognitive load: You must first decide that you want to switch sites and then you have to decide which area to go to to switch.  Also, we find that less familiar users aren't entirely clear what a standalone link that says "main" or "meta" actually does... Not to mention that it hurts my UX sensibilities that we are dynamically changing links in an element that should be fixed.  It is true that we have added a click in the process, but we have also removed a lot of clicks for other common actions that are much more frequent than switching between main and meta.  All I ask is that you give it a few days and see if the new "switch sites at the top left" paradigm grows on you.  What do you think?  1.  points out that technically it's not quite black. How are you dealing with the  in your machine learning models? Let's say you used to predict the number of sales each month. The virus affected your results last year and it will affect for at least a couple of months. So your model, I guess, is missing a lot. What are some approaches we can use to fix our models? homemade chilli oil I am making chilli oil using light olive oil, crushed chilli, dried garlic, dried fennel seeds and parsley.  I have been making this for years. I am concerned about this Botulinum business. Should I be concerned? And what can i do to avoid this?  Currently, I heat the olive oil before putting it into the mixture, jar it, and normally keep it in the cupboard for months, with no problems with taste.  Another thing I am wondering is, how does one measure the expiry date on homemade chilli oil? Can someone help?