Java Swing : What is wrong with this method
What is a NullPointerException, and how do I fix it?
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$. Find all continuous functions $f$ satisfying   $$\int_0^xf=(f(x))^2+C$$ for some constant $C \neq 0$, assuming that $f$ has at most one $0$.  I have a question about the solution to this problem. It says that   Clearly $f^2$ is differentiable everywhere, its derivative at $x$ is $f(x)$ (I'm assuming that this is because the left hand side is differentiable, the right hand side must be differentiable as well). So $f$ is differentiable at $x$ whenever $f(x) \neq 0$, and  $$f(x)=2f(x)f'(x),$$ so $f'(x) = \frac{1}{2}$ at such points. Thus, $f= \frac{1}{2}x+b$ for some $b$ on any interval where it is non-zero; if $f$ has a zero, this gives two possible solutions, with two possible values of $b$, but since $f$ is assumed continuous, they must be the same. So we need $$\int_0^x(\frac{1}{2}t+b)dt=(\frac{1}{2}x+b)^2+C$$  so we must have $b=\sqrt{-C}$ or $-\sqrt{-C}$, leading to two solutions for $C \lt 0$.  I don't understand the bolded statements. First, how does the differentiability of $f^2$ guarantee that $f$ is differentiable, and why only at $x$ where $f(x) \neq 0$?  Next, why are there two possible solutions if $f$ has a zero, but since $f$ is continuous they must be the same?  Finally, does the last statement mean that if $C \gt 0$, then there is no solution, since we're restricted to real numbers here?  I would appreciate it if anyone answers my questions. Where can I travel for prolonged periods of time while legally working remotely for a company in my home country? I found several questions about inbound travelers to the US in this scenario, but little about other countries: I work for a company in my home country (USA) who are open to me working remotely while traveling.   Which countries allow me to legally work remotely for a company in my home country (USA) while traveling in their country? The work has absolutely no connection to the destination country, it would take place identically entirely within the USA if I weren't traveling. I used to have an icon on the Windows Vista taskbar showing the battery amount remaining (laptop). It has mysteriously vanished.  How can I get it back?  I followed the Windows  (see How can I hide the battery icon in the notification area? - hoping to reverse the instructions) but the Power checkbox on the Notification Area tab was greyed out and could not be checked or unchecked (it is currently unchecked). I've tried to set -g mouse on, and it works pretty well, but standard mouse behaviour (select, copy &amp; paste) is disabled. But, it enables if I press "Shift" button, and while I hold it, I can select, copy &amp; paste text from/to terminal. Can I inverse this behaviour? I want to use mouse inside tmux (for example to select panes or resize them) only with shift pressed. Permutation count of AABBC Given a string:  $AABBC=A^2B^2C^1$   I am trying to find the Total Permutations (this may be incorrect):  $\dfrac{5!}{2!\cdot2!}=30$  My question is how would I find the partial sums (perhaps the wrong choice in words) when added together would give an index such that:   $AABBC=1$ $ABABC=2$ $CBABA=29$ $CBBAA=30$   (30 might be the wrong number here but is suppose to be the last)   I have tried to draw out a tree structure to get an idea and thought with as the minimum:  $CAABB$  $4(\dfrac{4!}{2!\cdot2!})$ + 1  And:  $CABAB$  I would get something like:  $4(\dfrac{4!}{2!\cdot2!}) + 0 + 1(\dfrac{2!}{2!}) + 0 + 0$  But I am missing something here. How would I find the sums needed for $BACAB$ ?  More specifically I am trying to find the index of a word that is arbitrarily long in alphanumeric.  So the string may also be something like:  $AAAAABBBBDDEEFFFGGGGGHIIIIJJJJKLMOOOPZZZZZ$ Probability of two uniform random numbers being more than $\frac{1}{2}$ apart Two numbers are chosen randomly and independently from the unit interval $(0,1)$.  What is the probability that they differ by more than $\frac{1}{2}$? Hint: Think of the $2$ numbers chosen as coordinates in the Cartesian plane. Draw a square with vertices at $(0,0)$,$(1,0)$,$(1,1)$, and $(0,1)$. Allowable choices for the $2$ points lie below the line $y=x-\frac{1}{2}$ or the above $y=x+\frac{1}{2}$. Find the combined area of these regions.  I need help on this. I know what $y=x-\frac{1}{2}$ and $y=x+\frac{1}{2}$ looks like but I am not understanding the problem as a whole In iOS 7, when the phone is in Sleep mode and I receive a call, I don't see the "Decline" button. All I see is a green "Answer..." button that requires me to slide to the right to answer the call. Is there anyway we can change that? I know that there are buttons for "Remind Me Later, etc" but I want the "Decline" button.   It works fine when the phone is not in Sleep mode. restore table from .frm and .ibd file? I have previously saved a copy of /var/lib/mysql/ddms directory ("ddms" is the schema name). Now I installed a new MySQL on a freshly installed Ubuntu 10.04.3 LTS by running apt-get install mysql-server, I believe version 5.1 was installed. After I copy the ddms directory under /var/lib/mysql, some of its tables work fine, these are the tables with an associated set of three files: a .frm file, a .MYD file and a .MYI file.  However, there are two tables with a different set of files: a .frm file and a .ibd file. These two tables didn't show up in the table list in phpMyAdmin. When I look at the error log, it says:  [ERROR] Cannot find or open table ddms/dictionary_item from the internal data dictionary of InnoDB though the .frm file for the table exists. Maybe you have deleted and recreated InnoDB data files but have forgotten to delete the corresponding .frm files of InnoDB tables, or you have moved .frm files to another database? or, the table contains indexes that this version of the engine doesn't support.   Please help with restoring these two tables. Thanks. The camera in Far Cry 3 is useful for tagging enemies from a distance but also includes the ability to take pictures.  This does not seem to do anything useful when used on animals or enemies.  Is there a purpose? How can I "grep" patterns across multiple lines? It seems I am misusing grep/egrep.   I was trying to search for strings in multiple line and could not find a match while I know that what I'm looking for should match. Originally I thought that my regexes were wrong but I eventually read that these tools operate per line (also my regexes were so trivial it could not be the issue).  So which tool would one use to search patterns across multiple lines? How to set static IP address? Ping is a a program owned by root with the user id bit set.  $ ls -l `which ping` -rwsr-xr-x 1 root root 35752 Nov  4  2011 /bin/ping   As I understand it, if a user runs the ping process, then the effective user id will change from the real user id (i.e. the user id of the person who launched the process) to the user id root. However when I try this and look at the output of ps to see if the ping process is running as the root user, I still get the real user id showing.  ps -e -o user,ruser,euser,cmd,args | grep ping sashan   sashan   sashan   ping -i 10 -c 1000 www.goog ping -i 10 -c 1000 www.google.com Prove that to each $\epsilon >0$, there exists a $\delta >0$ so that the Lebesgue integral... Suppose $f$ is in $L^1$ space of $\mu$, where $\mu$ is the Lebesgue measure. Prove that to each $\epsilon &gt;0$, there exists a $\delta &gt;0$ so that the Lebesgue integral of the absolute value of $f$ is less than $\epsilon$ (over the set $E$) whenever the measure of $E$ is less than $\delta$.  I know that the integral of $f$ is finite. So for arbitrary $f$ we can find the integral of $f$ to be less than some $\epsilon$, but how would I connect that with the measure of $E$ less than $\delta$. Any help would be welcome. OS X lets me type special characters directly on the keyboard by holding the Option. For example: — is an em dash, “ and ” are curvy quotes, etc.  Is there a good cheat sheet listing all these keys somewhere? I tend to find myself holding option and running my hands up and down the keyboard looking for a specific character. As a grad student, I just find it tremendously frustrating when emails are ignored by faculty (both at my institution and at other places). Is this acceptable? I'd be content with a simple response with one line along the lines of "I have read this email and am busy right now, will respond in X days when I can write a more detailed email." I understand that, as a first year student in my field, I'm not really in a position to request anything of anyone, but it just seems like common decency.  Instead, I never hear back, as if my email has been jettisoned off into oblivion. How to use GROUP BY to concatenate strings in SQL Server? How do I get:  id       Name       Value 1          A          4 1          B          8 2          C          9   to  id          Column 1          A:4, B:8 2          C:9 Uniqueness in existence of a bilinear form Let $E$ be a finite dimensional vector space over field $\mathbb R$ with $E^*$ as the dual space of $E$.($\dim E=n$)   $\Omega^P(E):=\{ \alpha\colon \overbrace{E\times\cdots\times E}^{p- times}\rightarrow \mathbb R\  \ , \alpha \text{ is alternating multilinear map}\}$ $\Omega^P(E^*):=\{ u\colon \overbrace{E^*\times\cdots\times E^*}^{p- times}\rightarrow \mathbb R\  \ , u \text{ is alternating multilinear map}\}$  I wish to prove that there exist an $\textbf{unique}$ bilinear form $B\colon \Omega^p(E^*)\times\Omega^p(E)\rightarrow\mathbb R$   such that for all $ f_i\in E^* \ , u_j\in E^{**}\simeq E \qquad  i,j=1,\cdots,p$, it has the following rule:  $B(u_1\wedge\cdots\wedge u_p,f_1\wedge\cdots\wedge f_p)=\det[f_i(u_j)]$.  $\wedge$ is wedge product between alternating maps i.e. $\alpha\wedge\beta(v_1,\cdots,v_{p+p})=\dfrac{1}{p! p!}\displaystyle\sum_{\sigma\in S_{p+p}}sign(\sigma)\alpha(v_{\sigma(1)},\cdots,v_{\sigma(p)})\beta(v_{\sigma(p+1)},\cdots,v_{\sigma(p+p)})$  How can I do this? Step to reproduce  Answer a question; Answer gets accepted or upvoted; Receive notification in the app; Change the title of the question; Notification is duplicated with updated title.  Expected behavior When going into notifcations you should see only one entry for that reputation event. Actual behavior You get two notification entries. In the screen notice the two entries for the same question, the one related to EF. After answering I have changed the name to make it more searchable for future questions and i've noticed it.      App Version: 1.6.1.2 Device: iPhone 6s OS Version: Version 10.1.1 (Build 14B100) Why is the laboratory frame energy always greater than the center of mass frame energy? I have been looking for an answer to 'Why is the laboratory frame energy always greater than the center of mass frame energy during collisions?'.  A lot of resources provided mathematical explanations. I wanted to get some perspectives in terms of physics.  Could you explain this? At work we have a Domain Controller running Server 2008 R2. Our desktop support group has the ability to join computers to the domain using their network credentials. We are now running into a problem where if the name of the computer that is being joined is the same as an existing computer on the domain, the existing computer will get a "The trust relationship has failed..." error and will not authenticate at all unless someone logs in as a local admin, changes the computer name and rejoins it to the domain.  I want to make it so that Desktop Support can only join computers with unique names to the domain. If the name already exists on the domain the operation should fail. Looking through TechNet it looks like this functionality exists but I can't seem to find out how to enable it.  Any ideas?