I am having difficulty troubleshooting this error message:    I don't get any indication any details about the failed connection attempt.   How can I diagnose such timeouts and resolve the connection issue?  I am aware of and have tried methods like rest your airport, reset the computer, delete profiles, down to install new operating system and , I'd like to know how to pick apart the connection process to know where the problem lies.  When I successfully connect, system information has excellent details:    However, without changing anything, at a later time, I will time out again when joining. Can I see the details of the process for the connection and find what is making it fail? What would it take to create or access a log file of the wifi connection process?
I'm having issues with my macbook pro OS X 10.7.5.  It used to connect to the wifi router (D-Link N300, DIR=615) no problems.  But for the past several weeks, I haven't been able to at all.  What pops up when I select my wifi network from the list:   "Failed to join "network" A connection timeout occured".   What happens when I try to enter my password manually:   "Connection timeout"   What I've tried to do as solutions:   Google Restart router by pressing reset &amp; refresh button Delete System &amp; User (Login) Keychain access Network > Gear symbol by the + and - bottom left of the screen > Set Service Order > Drag Wifi to the top
How do I write a correct micro-benchmark in Java? How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related: How do you remove duplicates from a list whilst preserving order? What is the expected minimum euclidean distance between $N$ points uniformly and independently chosen on the shell(sphere) of 3-D ball of radius $R$?   Note that the expected minimum distance might be difficult to compute, so a good lower bound is also fine.   My approach  I take the approach similar to this   .   Suppose we put $N$ circles of radius $r$ uniformly on the surface of the ball. Therefore we could compute the expected minimum distance by the following expression \begin{align} E[D]=\int_0^\infty P(D&gt;t) dt. \end{align}  So, it remains to compute  $P(D&gt;t)$. Actually, since we are after a lower bound on  $E[D]$ it is enought to give a lower bound on $P(D&gt;t)$.  Let $S_i$ be the event that the pair of circles does not intersect which should be given by \begin{align} P(S_i) =  \frac{ Surf(R)-Surf(r)}{Surf(R)}= 1-\frac{  \pi r^2}{ 4\pi R^2}=1-\frac{ r^2}{ 4 R^2} \end{align}  Now the probability that euclidean minimum distance $D$ between $N$ balls is bigger than $t$ should be similar to  \begin{align} P[ D \ge t] \stackrel{?}{=}  P[ \cap S_i] \end{align} However, I think we somehow need to converte from the geodesic distance to euclidean distance but I am not very sure how to do that? Why is the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group realized as the vector space of Hermitian $2\times 2$ matrices? Recent feature changes to Stack Exchange This is an unofficial list/changelog of new features and various changes to Stack Overflow and the Stack Exchange network.  It is maintained by the community, while a Stack Exchange employee changes the accepted answer to ensure that the latest changes remain on top (given default user settings).  To see the list in reverse chronological order (latest entry on top), .  For those adding new features here: please post only feature changes that affect the whole network and have some global impact. i.e. bug fixes don't belong here, nor do mobile app updates. Posting a Solution of a problem that You faced to Help Newbies About an Hour ago, I faced a problem and tried different ways to solve it.  At last I was going to post my Question on Stack Overflow, but the last trick which came in my mind worked, and the problem got resolved.    Now, if I want to post that problem on Stack Overflow with the solution which worked for me, for the purpose to help other newbies to get their answer if they face the same problem, what is the proper way of posting such solution to a problem? Rotate touchscreen and disable the touchpad on Yoga 2 Pro in rotated mode On my Lenovo Yoga 2 pro I installed Ubuntu 14.04 32bit and kept the installed Windows 8 on another partition.  In Windows, When you turn it into tablet mode, the keyboard and touchpad turns off so you don't accidently click on it at the back of the "tablet".  In ubuntu 14.04 only the keyboard turns off, but the touchpad stays active. Not even the Fn+F6 combination doesn't turn it off.  So far I can only disable it with  synclient TouchpadOff=1   (and re-enable with 0)  I tried xev to get the keycode for Fn+F6 but pressing this combo generates no output. Turning the monitor to the back neither.  How can I disable the touchpad automatically when I rotate or turn the monitor on the back, and re-enable the Fn+F6 Hotkey?      UPDATE: After some weeks sudo apt-get upgrade Fn+F6 is working now, so there is only the question how to rotate the screen and how to disable the touchpad automatically when rotating the screen. What's the deal with a leading underscore in PHP class methods? While looking over various PHP libraries I've noticed that a lot of people choose to prefix some class methods with a single underscore, such as  public function _foo()   ...instead of...  public function foo()   I realize that ultimately this comes down to personal preference, but I was wondering if anyone had some insight into where this habit comes from.  My thought is that it's probably being carried over from PHP 4, before class methods could be marked as protected or private, as a way of implying "do not call this method from outside the class".  However, it also occurred to me that maybe it originates somewhere (a language) I'm not familiar with or that there may be good reasoning behind it that I would benefit from knowing.  Any thoughts, insights and/or opinions would be appreciated. How often do you have to roll a 6-sided die to obtain every number at least once? I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided die wins.  I won, eventually, and the others finished 1-2 turns later. Now I'm wondering: what is the expectation of the length of the game?  I know that the expectation of the number of rolls till you hit a specific number is  $\sum_{n=1}^\infty n\frac{1}{6}(\frac{5}{6})^{n-1}=6$.  However, I have two questions:   How many times to you have to roll a six-sided die until you get every number at least once?  Among four independent trials (i.e. with four players), what is the expectation of the maximum number of rolls needed? [note: it's maximum, not minimum, because at their age, it's more about finishing than about getting there first for my kids]   I can simulate the result, but I wonder how I would go about calculating it analytically.    Here's a Monte Carlo simulation in Matlab  mx=zeros(1000000,1); for i=1:1000000,    %# assume it's never going to take us &gt;100 rolls    r=randi(6,100,1);    %# since R2013a, unique returns the first occurrence    %# for earlier versions, take the minimum of x    %# and subtract it from the total array length    [~,x]=unique(r);     mx(i,1)=max(x); end  %# make sure we haven't violated an assumption assert(numel(x)==6)  %# find the expected value for the coupon collector problem expectationForOneRun = mean(mx)  %# find the expected number of rolls as a maximum of four independent players maxExpectationForFourRuns = mean( max( reshape( mx, 4, []), [], 1) )  expectationForOneRun =    14.7014 (SEM 0.006)  maxExpectationForFourRuns =    21.4815 (SEM 0.01) Can I downgrade to an earlier version of Android after installing an OTA update? I installed the KitKat upgrade on my Nexus 7, but I am unhappy with it. Is it possible to roll back to an earlier version of Android (Jelly Bean)? Did all Headmasters get a portrait in Hogwarts? Throughout the Harry Potter series, we see that deceased Headmasters of the school get a semi-sentient portrait of themselves in the Headmaster's Office, at the service of the current Headmaster. Do all Headmasters get a portrait? What are the conditions of getting one? For instance, there are a couple of times when Dumbledore is temporarily deposed as Headmaster: Dolores Umbridge takes over the job in Order of the Phoenix, and Minerva McGonagall takes the job in Chamber of Secrets and Half Blood Prince. Will Umbridge and McGonagall have portraits in the Headmaster's Office when they expire? Prove that  $ n &lt; 2^{n}  $ for all natural numbers $n$.  I tried this with induction: Inequality clearly holds when $n=1$. Supposing that when $n=k$, $k&lt;2^{k}$. Considering $k+1 &lt;2^{k}+1$, but where do I go from here?  Any other methods maybe? What do Pentax and Sigma DSLRs offer that differs from Canon and Nikon? We have a question and answers outlining the . I'm interested in the other DSLR makers, and how the cameras they make compare in terms of significant features, system design philosophy, and unique or interesting photographic capabilities enabled or made easier by these cameras. Likewise, what such things are not handled as well?  Take "the big two have more market share" and the associated advantages of availability, accessibility, and third-party support and documentation .  I'm not interested here in compact cameras, interchangeable-lens cameras with electronic viewfinders, or in rangefinders. (If you're interested in that, though, see )  P.S.: Differences in lens lineups are covered at How to show that the monomials are not a Schauder basis for $C[0,1]$ why the monomials are not a Schauder basis for $C[0,1]$?  $p_n(x)=x^n$ such that $(p_n)$ does not form a Schauder basis for $C[0,1]$  span$\lbrace p_n : n\ge 0\rbrace$ is dense in $C[0,1]$ by Weierstrass approxmation theorem, but I cannot figure out why they are not a Schauder basis.  Could you please explain Let $A$ be an $n\times n$ complex nilpotent matrix. Then we know that because all eigenvalues of $A$ must be $0$, it follows that $\text{tr}(A^n)=0$ for all positive integers $n$.  What I would like to show is the converse, that is,      if $\text{tr}(A^n)=0$ for all positive integers $n$, then $A$ is nilpotent.   I tried to show that $0$ must be an eigenvalue of $A$, then try to show that all other eigenvalues must be equal to 0. However, I am stuck at the point where I need to show that $\det(A)=0$.  May I know of the approach to show that $A$ is nilpotent? Prove that $n=\dfrac{5^{125}-1}{5^{25}-1}$ is a composite number   My attempt,  Let $x=5^{25}$, so that $5^{125}-1=x^5-1=(x-1)(x^4+x^3+x^2+x+1)$  $=(x^4+9x^2+1+6x^3+6x+2x^2-5x^3-10x^2-5x)(x-1)$  $=((x^2+3x+1)^2-5x(x+1)^2)(x-1)$  I'm stuck at this point and don't know how to continue anymore. Hope someone can provide a detailed solution. Thanks a lot. The simplistic undergrad explanation aside, I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?  Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I've learned from thermodynamics where it goes, but where does it come from?  I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can't grasp what it is. Maybe it is because I lack the mathematical understanding that I can't grasp the subtle things the universe is doing. Still, I want to understand what it is doing.  How do I get to the point of understanding what it's doing?  (Note: What prompted me to ask this was . I'm afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.) Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic. Is my proof below correct? What specific property of rationals did I exploit in my proof? It looks like the property I exploited is the following: Given any positive rational, I can always write it as sum of arbitrary number of positive rationals, whereas given any positive integer I cannot write it as a sum of arbitrary number of positive integers. Has it got to do with the fact that $\mathbb{Q}$ is a field?       Problem Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.   Solution Let there exist an isomorphism between $\mathbb{Z}$ and $\mathbb{Q}$. Now consider the element $1_{\mathbb{Q}}$. We then have $\phi(1_{\mathbb{Q}}) = z \in \mathbb{Z}$. Since $\phi$ has to be a bijection, $z$ cannot be zero, since $\phi(0) = 0$.  Now consider the element $\left(\dfrac1{z+1}\right)_{\mathbb{Q}}$. We now have $$z = \phi(1_{\mathbb{Q}}) = \phi\left(\underbrace{\left(\dfrac1{z+1}\right)_{\mathbb{Q}} + \left(\dfrac1{z+1}\right)_{\mathbb{Q}} + \cdots + \left(\dfrac1{z+1}\right)_{\mathbb{Q}}}_{z+1 \text{ times }} \right) = (z+1) \phi\left(\left(\dfrac1{z+1}\right)_{\mathbb{Q}}\right)$$ However, there is no element in $y \in \mathbb{Z}$ such that $(z+1)y = z$.    First update  Actually I realize that I complicated it unnecessarily. Instead, we can do like this. Since $\phi$ is an isomorphism, we have $\phi(q_{\mathbb{Q}}) = 1_{\mathbb{Z}}$ for some $q \in Q$. However, $$\phi(q) = \phi(q/2+q/2) = 2\phi(q/2)$$ And there is no $y \in Z$, such that $2y=1$. Hence, $\phi(q/2)$ remains unmapped.    Thanks At level 18,  get the  feature (PHB, p. 103):     Beginning at 18th level, when you roll damage for a spell and roll the highest number possible on any of the dice, choose one of those dice, roll it again and add that roll to the damage. You can use the feature only once per turn.   When you score a critical hit with an attack (even a spell attack), you double the amount of dice you roll.  Does the additional damage die from Spell Bombardment also get rolled twice on a critical hit? What determines who gets or becomes an MVP? This hasn't been asked yet, but what determines how or who gets an MVP award in CS:GO? After a match, there's always a little blurb that first states who got MVP first, and then a random fact (Player X got Y knife kills, Player X lasted Y rounds without dying, etc.).  Do these two factors both "factor" into getting an MVP award? Is it a set percentage of enemies you kill? Is there a priority list (ie, planting bomb, defusing, etc.)?