getting wrong output in java String, and == sign What i have,  suppose I am creating two object like below,  String s1 = "abc"; String s2 = s1;  System.out.println("== comparison "+ s1==s2);   i am expecting the output is      == comparison true   but i get     false   What is the problem?  I am not getting output as my expectation.  Question why it is not matching the expected output.  please reply and explain why it is coming like this.  Thanks in advance tofek khan
How do I compare strings in Java? I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?
Title restated: Show that $A\in\mathbb{C}_n$ is normal $\iff$ $tr(A^*A) = \sum_{i = 1}^n|\lambda_i|^2$, where $\lambda_1,...,\lambda_n$ are the eigenvalues of $A$.  This question comes from "Matrices and Linear Transformations" by Charles Cullen. I'm studying for an exam and am trying to do some problems but I'm having trouble with this one. Any help would be appreciated.  Thank you. Industry standard file format deliverables for logos? Problem putting matrix operations in an equation Possible Duplicate:          I'm trying to use official equation container for the first time, and it's giving me some trouble.  I have this equation of a simple matrix operation, and LaTeX isn't liking it.  What's wrong with this statement?  \begin{equation}      y = \begin{bmatrix}         T &amp; I      \end{bmatrix}     \begin{bmatrix}         a \\         e     \end{bmatrix}  \end{equation} I remember seeing an upper bound for the binomial $\binom{n}{k}$ with an exponential function, something like $\binom{n}{k}\leq \left(ne/k\right)^k$. What exactly is it, and are there other similar good upper bounds for $\binom{n}{k}$?  Edit: As the link in Macavity's comment shows, the bound is indeed $\binom{n}{k}\leq \left(ne/k\right)^k$. How can we prove this? Let $A\neq I$ be a $5\times5$ matrix with real entries such that the sum of the entries in each row of $A$ is $1$. Then the sum of all the entries in $A^3$ is  1)$\space 3$ $\qquad $2)$\space 15$ $\qquad$ 3)$\space 5$ $\qquad$ 4)$\space 125$  Solution:  The answer is $5$ if $A = I$, but for $A \neq I$,  I found that vectors $\begin{pmatrix} 1\\ 1\\ 1\\ 1\\ 1\\ \end{pmatrix}$ and  $\begin{pmatrix} -1\\ -1\\ -1\\ -1\\ -1\\ \end{pmatrix}$  are eigen vectors for the matrix $A$ corresponding to eigen value $1$. From here, I dont know how to proceed, please help me solve the question..and if there are mistakes in my argument, please tell me.. "exec: gnome-session: not found" when logging in using lightdm On login the password is accepted but I'm returned to the login screen. Tried multiple times even after reboot... same behavior.  I left my laptop (Lenovo Ideapad z510) in suspend mode (lid down) last night, but it did not resume this morning, as it usually does. It had shutdown or crashed, and on booting with Ubuntu the login failure mentioned above started.  cat ~/.xsession-errors /usr/sbin/lightdm-session: 1: /usr/sbin/lightdm-session: ls: not found /usr/sbin/lightdm-session: 104: exec: gnome-session: not found   Okay. I've tried a bunch of suggestions from    Changed id to /usr/sbin/id in /etc/profile removed .Xauthority removed /tmp removed,  purged and re-installed lightdm checked .profile for syntax errors (source .profile worked fine, so I guess no syntax errors)   Nothing worked. My guest login is working fine, so another user should also work. I'm now going to create another user and continue working, but a solution to this problem is still warranted... it's likely going to repeat in future.  Installing and reconfiguring gdm also did not work.  sudo apt-get install gdm $100$-th derivative of the function $f(x)=e^{x}\cos(x)$ I've got this task I'm not able to solve. So i need to find the 100-th derivative of $$f(x)=e^{x}\cos(x)$$ where $x=\pi$.  I've tried using Leibniz's formula but it got me nowhere, induction doesn't seem to help either, so if you could just give me a hint, I'd be very grateful.  Many thanks! In the new header could we please move the chat link back to where it was? (One click away)  As a daily frequent to the JavaScript room that's the one link I'd love to have visible 100% of the time.  Aside from that, I actually love the new header. (Maybe take it a step further an add a customizable header with (X) link spots for your most used links?)  Just my thoughts The sum of powers of two and two's complement – is there a deeper meaning behind this? How can I cite a range of papers, the output is a range of numbers, instead of a list of numbers? In other words, when I type  ... some dummy text here is due to me \cite{me1, me2, me3, me4} ...   I want the output to be     ... some dummy text here is due to me [3-6] ...   instead of     ... some dummy text here is due to me [3.4.5.6] ...   (I use LaTeX, and am currently using the amsart class and whatever it includes. But I am open to other suggestions.) I'm aware there are been several similar questions, and some great answers with hints on how to prove this, for example  and .  But I've never really seen a detailed proof of the absolute convergence of the Riemann zeta function in the half-plane $\Re(s)&gt; 1$.  I hope there's interest on a detailed proof of this for reference. Here is my attempt. Please, fill in any detail that might be missing, or point out any mistake!  On $\Re(s)=\sigma&gt; 1$, we have  $$\sum_{n=1}^{\infty}\bigg|\frac{1}{n^s}\bigg|=\sum_{n=1}^{\infty}\frac{1}{n^\sigma}$$  and  $$\frac{1}{n^\sigma}\leq\frac{1}{n^{1+\epsilon}}$$  for any $\epsilon &gt;0$, so by the direct comparison test, if   $$\sum_{n=1}^{\infty}\frac{1}{n^{1+\epsilon}}$$  converges absolutely, then so do $\sum_{n=1}^{\infty}|1/n^s|$ and $\zeta(s)$.  By the integral test, the convergence of $\sum_{n=1}^{\infty}1/n^{1+\epsilon}$ is equivalente to the finitude of the integral  $$\int_1^\infty \frac{1}{n^{1+\epsilon}}=\bigg[-\frac{1}{\epsilon x^\epsilon}\bigg]=\frac{1}{\epsilon}$$  which holds for any $\epsilon &lt; \infty$.  Any correction or improvement is welcomed! Thanks in advance. Select 1px aliased border When I choose Select > Modify > Border and select a 1px border - the border I get is anti-aliased, hence if I fill my selection a 3px border is affected.  Is there a way to select a 1px aliased border? Find whether the integral converges or diverges. $$\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$$  I simplified it to $$\int_{0}^{1}\frac{\log(x)}{(1-x)(1+x)}dx$$  Here I have $2$ "bad" bounds (both $0$ and $1$).  I think, to prove such integral converges, I should find something that is equivalent to or less than $\log(x)$ so I can exchange them, maybe $\sqrt{x}$, so it may cancel out the fraction, and I can compare it to $$\int_{0}^{1}\frac{dx}{x^p}$$  Also I had an idea to substitute $x$ with $u+1$ so I can use $\log(1+u) \sim  u$ when $u \rightarrow 0$. I'm allowed(not familiar with anything else) to use direct comparision test, limit comparision test, Cauchy test and Abel-Dirichlet's test.   Any hints are much appreciated, I just want to get the big picture.   Thank you. Meaning of different Orders of Derivative I have been trying to analyse the meaning of higher order derivatives and their geometrical significance.  Given a function $f(x)$ what are the unique geometric interpretation of its higher orders?   $f'(x)$ - slope (rate of change of x w.r.t y) $f''(x)$ - convexity / concavity of $f(x)$ based on $sign(f''(x))$ $f'''(x)$ - increasing / decreasing slope of $f'(x)$ $f''''(x)$ - ?? ... $f^n(x)$ - ??   I apologize if this question is rudimentary. If your application requires a database and it comes with built in data, what is the best way to ship that application? Should I:   Precreate the SQLite database and include it in the .apk? Include the SQL commands with the application and have it create the database and insert the data on first use?   The drawbacks I see are:   Possible SQLite version mismatches might cause problems and I currently don't know where the database should go and how to access it. It may take a really long time to create and populate the database on the device.   Any suggestions? Pointers to the documentation regarding any issues would be greatly appreciated. Do you capitalize both parts of a hyphenated word in a title? Do you capitalize both parts of a hyphenated word in a title?  "My Ex-Wife Hates Me"  or  "My Ex-wife Hates Me" For a project I'm working on, I need to represent network flows over 1,000 zones with directionality.    Any suggestions on displaying the information in a nice and non overwhelming way?  Any examples on displaying network flows in heavy urban areas? Color suggestions and thickness schemes? any "not to dos" when representing network flows? I've searched the net for such information and found different command lines, like these ones:  sudo apt-get remove application sudo apt-get remove application*  sudo apt-get remove --purge application sudo apt-get remove --purge application*  sudo apt-get purge application sudo apt-get purge application*   So, what is the correct way? Is it necessary to use that "*"?  After that, I also found these commands:  sudo updatedb sudo locate application sudo rm -rf (file/folder name) Headers and font in KOMA-script I am setting up the layout for my bachelor thesis using scrbook as basis for a self-made documentclass with twosided print. I want a header containing the current part number and name on the outer side (left on even pages, right on odd pages), the current chapter number and name on the center of the head and the same for section on the inner side. I found this example in the KOMA-Script documentation:  \usepackage{scrlayer-scrpage} \pagestyle{scrheadings} \automark[chapter]{chapter} \automark*[section]{}   It puts the chapter on the outer side on even pages and the section on the outer side on odd pages. Sadly, I was not able to modify this to fit my needs because I do not really understand the way KOMA-Script works here. If a part starts but there is still no chapter in it, the place for the chapter shall remain empty (same for chapter and section). Can anyone help?  Furthermore, I would like to change all fonts that KOMA-Script changes (e.g. toc, section, chapter...) back to the default computer modern as I do not like the font KOMA-Script uses here. Is there a better way than changing all the fonts manually like this:  \addtokomafont{section}{\fontfamily{cmr}\selectfont} I tried to reproduce the results from the  unfortunately the video link is broken. And I might have overlooked some related settings.  The spot light is barley visible on the ground.    Increasing the Density of the Volume Scatter Node darkens the sky texture but leads to some light cone from the car's headlight. (only 10 samples in preview).    Which settings do I need to change or should I try a different approach?  Integrator settings are default and spotlight settings were copied from the example found in the docs.  Related:    (pre 2.7)  (BI only)