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Easy to bypass "Are You paying Attention" test by viewing question in detail I think many of us already aware, still I wanted to let you know that First Post and Late Answers review posts are generated on specific time interval. When time comes for post generation I follow some tricks   Click and till a Post appears for review Then right-click and select Open in new tab 5-8 time. Then in every page follow the below steps   Open the Question of post appeared in review in New tab If Page/Question not exists then simply downvote since post was deleted because of -ve response. Else if page exists then   Check the review post's Net Reputation If reputation is -ve then simply downvote the post came in review Else one may select No Action needed.    This way if in any case a post comes for "Are you paying attention" can be handled easily.  I think if a post comes in review should not allow to view post. Why don't we include $\rho g h$ in a hydraulic jack below? Consider a hydraulic jack with massless pistons as follows.    The famous equation for this system is   $$ \frac{F_1}{A_1}=\frac{F_2}{A_2} $$  My question is why isn't the equation as follows?  $$ \frac{F_1}{A_1}=\frac{F_2}{A_2} + \rho g h $$  It is based on  my understanding that any points in the same horizontal line have the same pressure.  Could you spot my misconception? Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$ I can follow the proofs in which the asymptotic normal-distribution of a maximum likelihood estimator $\tilde{\theta}_n$ is derived.   however, does this already imply that the maximum likelihood estimates are asymptotically unbiased, i.e. do we have $$E(\tilde{\theta}_n) \to \theta \text{ as } n \to \infty?$$  Since I am aware that in general it is not true that convergence in distribution implies convergence in moments, an explanation would be nice.  The result is often stated e.g.  as "...it means that the bias of the maximum likelihood estimator is equal to zero up to the order $n^{-1/2}$")  1.) Are  some kind of regularity conditions from the mle theory used to establish this result?  2.) Or is a $\sqrt{n}$-convergence of an estimator (to a normal distribution) in general already enough to establish convergence of its moments?  Note: the Wikipedia article mentions Cox, David R.; Snell, E. Joyce (1968).  , as a source where the order of the bias is derived (formula (12) or (20)).   However in this paper I can't follow the arguments 100%, since their Taylor approximation of $L'(\widehat{\beta})$ is lacking the remainder term. What is the argument used here to discard it completely? Please give me feedback on my answer to this question. Question: For all $ n\geq1:\binom{2n}{0}+\binom{2n}{2}+\binom{2n}{4}+\cdots+\binom{2n}{2k}+\cdots+\binom{2n}{2n} $   is equal to $ \binom{2n}{1}+\binom{2n}{3}+\binom{2n}{5}+\cdots+\binom{2n}{2k+1}+\cdots+\binom{2n}{2n-1} $. Answer: False, since;  Let $a=1,  b=-1$  and $n=1$  ,$k=0$   , using Binomial expression.  $$(a+b)^n=  \sum   \binom{n}{k}  a^{k}b^{n-k}$$  Then $(1+-1)^{2(1)}=\binom{2}{0}1^{0}(-1)^{2-0}+\binom{2}{1}1^{1}(-1)^{2-1}+\binom{2}{2}1^{2}(-1)^{2-2}=\binom{2}{0}-\binom{2}{1}+\binom{2}{2}$  Thus :For all $n\geq1:  \binom{2n}{0}+\binom{2n}{2}+\binom{2n}{4}+\cdots+\binom{2n}{2k}+\cdots+\binom{2n}{2n}   \ne \binom{2n}{1}+\binom{2n}{3}+\binom{2n}{5}+\cdots+\binom{2n}{2k+1}+\cdots+\binom{2n}{2n-1}$  . BJT in Reverse Active Mode of Operation What will happen if for a BJT transistor, it's emitter terminal is treated as collector and collector as emitter in a common emitter amplifier circuit? Triangle inequality for L2 norm I am posed with a problem as below.  Let $X$ be the collection of real valued functions that are measurable on $[0,1]$. For a given number $p\geq 1$ define the $L^p$ norm by $(\int_0^1|f(x)|^p)^\frac{1}{p}$.  I need to show for $p=1,2$ that this defines a semi norm on $X$. $p=1$ was simple as was all of $p=2$ except for the triangle inequality. I am having trouble proving the triangle inequality for this. Could anybody nudge me into the right direction or am I simply over thinking it? I think I can prove it for vectors but I'm not sure how to tackle it with integrals. Right now I can only use relatively basic results because this in for an introductory measure theory course.  Thanks! How long does it take for chat profiles to update? Following scenario:   user registers, has 1 point user visits chat, notes he cannot post because of only 1 point and needs 20 user goes back to SO, answers a question. gets enough points to chat user goes back to chat, but his profile still shows 1 point   Now my questions:   How long does it take for the profile on chat to update? Is there a way to force updating?   Update: Logging in and out did not help. How do I remove repeated elements from ArrayList? What does “{} \;” mean in find (in Linux)? Sometimes I see a command like  find . -name * -exec ls -a {} \;   I was asked to execute this.  What does {} \; mean here? Resampling GeoTIFF images to same resolution using QGIS I have two geotiff images that I would like to resample the same resolution. If I use ArcGIS Desktop this is easy to do but how do I do this using QGIS? The topological space $X=\omega_1\cup \{\omega_1\}$ is not first countable but $\omega_1$ is. Here $\omega_1$ denotes the set of all countable ordinals and $\{\omega_1\}$ is the first uncountable ordinal. Cardinality of $\omega_1$ is $\aleph_1.$And also $\omega_1$ is called the limit ordinal meaning it is the limit point of the set $\omega_1.$  Here I want to prove two things. $1)$ $\omega_1$ is first countable. and $2)$ $\{\omega_1\}$ is the limit point of $\omega_1$. But since no sequence converges to $\{\omega_1\}$, using this I could say that our space $X$ is not first countable.  $1)$ The proof of this I got from  with just one question: it says we need to prove that such an $S(y)$ exists,and I'm thinking $S(y)=\cap\{u\in \omega_1:u\gt y\}.$ This is correct$?$ But here is a chance that the countable base around $y$ may be finite and not countably infinite.  $2)$ If possible let us assume that $\omega_1$ is not a limit point of the set $\omega_1.$ $U$ be a nbd of $\omega_1$ that does not intersect $\omega_1.$ Then what are the elements of $U$ like? The ones coming before $\omega_1$  cannot be uncountable because $\omega_1$  is the first. Then they must be countable. This is absurd so no such $U$ exists. Thus $\{\omega_1\}$ is a limit point.  Are my proofs correct? Thank you. This is a  about Connection Refused    We see a lot of questions to the effect      When I try to connect to a system I get a message      Connection refused      Why is this ? What Is Exponentiation? What do I need to consider to choose between dSLR, mirrorless, or a compact as my first "serious" camera? I am thinking of buying a camera to learn photography. Most of the time I'll be shooting portraits and landscapes. But I am not sure where I should start. Most of my friends tell me that I should get an entry level DSLR, but I am not sure if I have the persistence and enthusiasm to carry it all day in a backpack. But the camera on my cellphone doesn't seem to be enough to begin with.  So what I want is some expert advice (preferably with professional experience). Can most compact fixed-lens or mirrorless cameras fit the situations I mentioned? Or do I really need to go to a DSLR to get a tool to learn photography? xUbuntu Default desktop Icons do not display? Even though I have the default icons set to display in Settings, they do not display. See the image below. Ideas???? Code: \documentclass[12pt]{article} \usepackage{pgfplots} \usepackage{float} \pgfplotsset{compat=1.17} \usepackage{tikz} \usetikzlibrary{shapes, arrows.meta, automata, positioning, matrix, calc} \usepackage[RPvoltages, american,siunitx]{circuitikz} \usepackage[margin=1in]{geometry}  \usepackage{steinmetz} \begin{document}         \begin{figure}[H]         \centering         \begin{circuitikz}             \draw(0,0) to[V = $\vec{V}_g$] ++(0, 3) to[R = 50 &lt;\ohm&gt;] ++(3, 0) to[C = 1&lt;\micro\farad&gt;, v = $\vec{V}_o$] ++(0, -3) to[short] ++(-3, 0);         \end{circuitikz}     \end{figure} \end{document}  Output:  As we can see, $\vec{V}_o$ is almost touching the capacitor. How to adjust the spacing for the voltage label? Actually, can  potentially solve the problem? Note that what I am trying to draw is based off of this: I'm trying to get my head around mutable vs immutable objects. Using mutable objects gets a lot of bad press (e.g. returning an array of strings from a method) but I'm having trouble understanding what the negative impacts are of this. What are the best practices around using mutable objects? Should you avoid them whenever possible? How do amortization schedules work and when are they used? Specifically, I notice that on a mortgage statement, my payment is "amortized" so that at the beginning of the loan, I am paying almost entirely interest and very little principal.  However, on a credit card balance, it seems interest is only charged on the balance.  Why do amortization schedules work the way they do, and are they typically used for most loans, and why? When I visit a site I haven't visited (while logged in) for a while, I see:  Welcome back! If you found this question useful, don't forget to vote both the question and the answers up.  That's often intended behavior. But today I visited  and was shown that banner even though the question and all its answers are locked. Voting arrows aren't even shown on any of the posts on that page. I believe that banner should be disabled on pages where there is no post that can be voted on by anyone.