Notice:Undefined index error
"Notice: Undefined variable", "Notice: Undefined index", and "Notice: Undefined offset" using PHP
How to see what's going on during Windows shutdown/logging off process? Windows 7 msconfig lets users select the options No GUI boot and OS boot information to have a list of drivers being loaded during boot. Is it possible to have similar detailed messages during shutting down/restarting/logging off? Here's the screen I want disable or give me more details: Mobile web refresher, part 2 After a sizeable amount of work we are releasing a new version of the mobile web site, this time focusing on the question and answer page. We have also fixed or implemented a minimal large part of the issues and requests mentioned in the . Changes Question and answer page  SVG icons for upvote, downvote, favorite, comment upvote white background color for legibility general styling issues with notices (they actually exist now) bounty link is now in question menu (next to flag)   Ask question page  general styling and sizing of element use of placeholders where appropriate instead of page text styling of error messages   Pop-ups  Popups are now inlined in the page instead of being sometimes floating and draggable Many overdue styling issues Close button is SVG Flag indicators are readable Buttons   Misc pages  404 page did not exist. Now it does. Login, logout are formatted Pre-ask and pre-answer warnings are now formatted  Bugfixes  made search magnifying glass bigger fixed language in user timeline so it's consistent with the desktop site added login link on top bar made topbar icons ever so slightly smaller  Restating the obvious: send your &lt;3 to  and   for the most excellent design! Feedback , bugs and suggestions while we move to the next iteration? Please mark bugs with What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it. How to understand degrees of freedom? Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$ If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial Suppose $f$ is entire and that in every power series $f(z)=\sum_{n=0}^\infty c_n(z-a)^n$ at least one coefficient is $0$. Prove that $f$ is a polynomial. I think I have heard that the following is true before, but I don't know how to prove it:     Let $A$ be a matrix with real entries. Then the minimal polynomial of $A$ over $\mathbb{C}$ is the same as the minimal polynomial of $A$ over $\mathbb{R}$.   Is this true? Would anyone be willing to provide a proof?    Attempt at a proof:  Let $M(t)$ be the minimal polynomial over the reals, and $P(t)$ over the complex numbers. We can look at $M$ as a polynomial over $\Bbb C$, in which case it will fulfil $M(A)=0$, and therefore $P(t)$ divides it. In addition, we can look at $P(t)$ as the sum of two polynomials: $R(t)+iK(t)$. Plugging $A$ we get that $R(A)+iK(A)=P(A)=0$, but this forces both $R(A)=0$ and $K(A)=0$. Looking at both $K$ and $R$ as real polynomials, we get that $M(t)$ divides them both, and therefore divides $R+iK=P$.   Now $M$ and $P$ are monic polynomials, and they divide each other, therefore $M=P$.  Does this look to be correct?    More generally, one might prove the following     Let $A$ be any square matrix with entries in a field$~K$, and let $F$ be an extension field of$~K$. Then the minimal polynomial of$~A$ over$~F$ is the same as the minimal polynomial of $A$ over$~K$. How to determine whether the direction of rotating a 2D vector to another one is counter-clockwise or clockwise using the cross product? Vec2 a, b; // some random vector Vec2 cross = a.Cross(b); RelativeDirection(a,b,cross); // return true if the direction of                               // rotating a to b is counter-clockwise   How do I implement the function RelativeDirection()?  I got some suedo code from the textbook:  if a.Cross(b) &gt; 0 then ... else ...   but the cross product is a vector right? how do you compare it with an integer? Can Java's NullPointerException be changed to report on which variable was null? Number of equivalence relations on a set How can I use QGIS to create a metro style map Nexus 7 is stuck in reboot loop after full discharge I have a few day old Nexus 7 tablet, unrooted, bootloader still locked, and otherwise in factory condition. This morning, it ran its charge out. When I plugged in it, this happens:   Google Logo appears. Nexus Logo appears. Lock screen which shows charging: 0%. White screen, device powers off. Repeat.   What is happening? Thanks! This is a trivial problem, but it annoys me that I can't get to the bottom of it:  I'm running Windows 8, Powershell version 3.0. By right-clicking on the title bar I can go into the Properties and change the font, size, background colour etc without any problems.  After closing and restarting Powershell, all of the changes I've made stick except that if I've set the font to Lucida Console then on reopening I get the Raster font.  (Note that all of the above applies to when I run Powershell as Administrator.)  So:   If I set the font to Lucida, then it switches to Lucida for the remainder of the session. If I set the font to anything other than Lucida, then it stays as that after closing and reopening. If I alter the window sizes or text colours or anything else, the changes persist after reopening. The only thing that goes wrong is that if I set the font to Lucida, it switches to 'Raster fonts' when I reopen. But cmd and powershell ISE don't have this problem - only the powershell console.   Can anyone suggest what might be going wrong?  (One observation I've made is that upon re-opening Powershell after setting the font to Lucida, at first the width of the window is what it would be if the font were Lucida, but then after a second, it widens slightly to accommodate the raster font.) A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square?  For more general "rectangle" case, see . The proof found there is fairly complex, and I am looking for a simpler proof for this special case. I expect it could be significantly simpler.  See also . My Command is below and its print Free CPU and Used CPU below format.  I want to restrict awk output to 2 decimal place.  grep 'cpu ' /proc/stat | awk '{usage=($2+$4)*100/($2+$4+$5)} {free=($5)*100/($2+$3+$4+$5)} END {print "Used Cpu:",usage "%"} {print "Free Cpu:",free "%"}'   Output :   Free Cpu: 98.9588%  Used Cpu: 1.04125%   Desired output :  Free Cpu: 98.95%  Used Cpu: 1.04% Windows 10 on asus x44h touchpad scolling not working I have just updated Windows 7 to Windows 10.  My touchpad scolling (right-side) is not working anymore.    I have no idea how to fix this in Windows 10.  I have hit the start button and typed "synaptic", but have found nothing useful.  I used to have an icon on the taskbar that showed where I was touching the touchpad.  I used to be able to right-click that icon to change settings, but Windows 10 has not brought that icon over.  Also, the asus website has no synaptic touchpad drivers available for Windows 10.  I have tried the enaltech drivers, but upon the installation atempt I am told that my hardware is not correct. Why do I have to press Ctrl+D twice to close stdin? Qualitative variable coding in regression leads to "singularities" While drawing a simple 3D (fake 3D in fact) cube, I realized that the corners end up with unwanted extensions of the line. I understand this is related to the width of the lines themselves, but how can I remove them? An alternative solution of drawing the desired figure is also welcomed.  Example:  \documentclass{article} \usepackage{tikz}   \begin{document} \begin{tikzpicture}  \draw[draw=black,fill=gray!20] (0,0) --(4.8,0)-- (4.8,5)--(0, 5)--cycle; \draw[draw=black,fill=gray!20] (4.8,5) -- (4.9,4.8)--(4.9,-0.1)--(4.8,0)--cycle; \draw[draw=black,fill=gray!20] (0,0) -- (0.1,-0.1)--(4.9,-0.1)--(4.8,0)--cycle; \draw[dashed,draw=black] (4.8,5) -- (4.9,4.8)--(0.1,4.8)--(0.,5)--cycle; \draw[dashed,draw=black] (0.1,-0.1)--(0.1,4.8)--(0.,5)--(0,0)--cycle; \end{tikzpicture} \end{document} This is my first time posting on Math exchange. I have been self-teaching myself Mathematics and recently started learning some Algebra. I was posed the following questions, in which I would like to answer before I proceed, but having some trouble finding proper solutions. So the format will be question, and my answer.      What name do we give an element $a \in \mathbb{Z}_n$ that has a multiplicative inverse?   A modular multiplicative inverse of an integer $a$ is an integer $x$ such that $ax \cong 1 (\mod m)$. This means that the remainder after dividing $ax$ by integer $m$ is equal to $1$.      Give an example, for some $n \in \mathbb{N}$, of an element of $\mathbb{Z}_n$, that does not have a multiplicative inverse?   This question is throwing me off because - does the $n$ we speak of matter for both $n \in \mathbb{N}$ and $\mathbb{Z}_n$ ot solely $n$? My guess here would be $0$ because we cannot have an inverse of $0$.      Prove that multiplicative inverse are unique; an element $a \in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Suppose that an element $a\in\mathbb{Z}_n$ has an inverse $a'$. Next, suppose that $a^*$ is also an inverse of $a$. Then, $a'$ is a solution to $a \cdot_n x=1$, and similarly $a^*$ has a solution to $a \cdot_n x=1$.   Lemma: Suppose $a'$ is multiplicative inverse of $a$ in $\mathbb{Z}_n$, then for any $b \in \mathbb{Z}_n$ the equation $a \cdot_n x=b$ has a unique solution, such that $x = a' \cdot_n b$.   By Lemma, equation $a \cdot_n x = 1$ has a unique solution, namely $x=a'=a^*$. Therefore, an element $a\in \mathbb{Z}_n$ cannot have two multiplicative inverses.    Thank you for the help. I would love any constructive feedback for these. If you can help me elaborate on some ideas, that would be really helpful also.  Thank you very much!