Bus error when printing to output file
Where is the itoa function in Linux?
I can't seem to figure out how to get past this step. Any suggestions? Proposition      Let $\mathcal{P_e}$ be the set of functions $p_e(x) = a_o + a_2x^2 +  \cdots + a_{2n}x^{2n}$, $p_e : \mathbb{R} \to \mathbb{R}$      Show that all $f:[0,1]\to\mathbb{R}$ can be uniformly approximated by   elements in $\mathcal{P_e}$   Attempt:    Since we are talking about polynomials let's try play with Weierstrass Theorem  By definition $\mathcal{P_e}$ is dense in  $C^0([0,1], \mathbb{R})$ , if for every funciton $f \in C^0([0,1], \mathbb{R})$, $\exists p_e \in \mathcal{P_e}$ such that $\forall \epsilon &gt; 0, \forall x \in [0,1], ||p_e-f||&lt; \epsilon$  So we want to show $\|p_e - f\| &lt; \epsilon$  Try something like...since every continuous function is approximated by polynomials i.e. $\forall \epsilon &gt; 0,\ \|f - p\| &lt; \epsilon$, therefore let $p$ be a polynomial, $p = a_0 + a_1x + a_2x^2 + a_3x^3 + \cdots$  $$\|p_e - f\| \leq \|f - p\| + \|p - p_e\|$$  $$\Rightarrow \|p_e - f\| &lt; \epsilon + \|p_o\|,$$ where $p_o$ is an odd polynomial  $$\Rightarrow \|p_e - f\| &lt; \epsilon + \sup_x|a_1+a_3+\cdots+a_{2_n+1}|$$  Stuck.   In any case, $p$ and $p_o$ is poorly defined. What would be the standard approach to prove the proposition? Differences between derivatives and strong derivatives Definition: Let $f$ be a real valued function. We say $f$ is $\mathbf{strongly}$ $\mathbf{differentiable}$ at $x = a$ if the following limits exists and is finite:  $$ \lim_{x \to a, y \to a, x \neq y} \frac{ f(x)-f(y)}{x-y} = f^*(a) $$  and we can $f^*(a)$ the strong derivative of $f$ at $a$. Why is this definition of derivative different than the usual one? What is the main crucial point to understand here that makes it different? The system of equations Let $a,b,c\in \mathbb{R}$ that $a^{2}+b^{2}+c^{2}=1$. We want to find $x,y,z,w$ in the following equations:  $$\begin{align} x^{2}+y^{2}+z^{2}+w^{2}&amp;=1 \tag{1}\\ x^{2}+y^{2}-z^{2}-w^{2}&amp;=a \tag{2}\\ xw+yz&amp;=2b \tag{3}\\ yw-xz&amp;=2c.\tag{4} \end{align}$$ In C# why can't a conditional operator implicitly cast to a nullable type What is the best collation to use for MySQL with PHP? How to select a Master's thesis topic if your advisor won't suggest one? If a master's degree candidate needs to select a thesis topic, but their advisor is unwilling to offer suggestions on the matter, how should one go about selecting a thesis?   How might one select an area to study? How can one evaluate if if is a suitable topic? Does the thesis need to focus on an area which is relatively unexplored by prior research? When I run sudo, what exactly happens to my environment?  When I run sudo command, it doesn't seem to see my or root's environment. For example, my path for both includes /usr/local/bin, but if I try to run one of the program's without the full path, it fails.  I thought sudo ran as root, and hence got root`s environment. Is there a different way that bash executes under sudo than under root or my normal user?  EDIT:  I have been using sudo -i lately, but recently it has been causing problems because my current working directory gets set to /root. This is as expected (sorta), but I still don't understand why sudo isn't recognizing my executables in /usr/local/bin.  EDIT:  I am running Fedora 15. Checking for null before event dispatching... thread safe? I just came across this idiom in some open-source Python, and I choked on my drink.  Rather than:  if isUp:     return "Up" else:     return "Down"   or even:  return "Up" if isUp else "Down"   the code read:  return isUp and "Up" or "Down"   I can see this is the same result, but is this a typical idiom in Python? If so, is it some performance hack that runs fast? Or is it just a once-off that needs a code review? Is it possible to reconstruct the Hamiltonian from knowledge of its ground state wave function? Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the Hamiltonian contains more information (the full spectrum) than a single state vector. But are there any special cases where it's possible to obtain the Hamiltonian? Some examples would be really helpful. What is an "Emergency Call," and can I  set number for it? When searching for the desired SE site, the down arrow key (down) should work in order to choose the site one is looking for and hit enter to visit it, instead of using the mouse point to choose it. Would be pretty convenient. Is there a way to set initial state with rigid bodies? Let's say I set up a Rigid Body simulation in Blender (not in GE), and then run the simulation for a number of frames. Is there a way to tell Blender to use the current state and position as the initial state? So that when I go back to frame 1, the rigid bodies stay in the same place they did in frame X.  For instance, if I want a pile of bricks, I first place the bricks in the air and then let them drop down on the ground, coming to rest. When they have come to rest, I want to use that position as the starting position. Time travel film: character with male and female reproductive organs is taken back in time by a barman who turns out to be themselves I have had a friend give me a rough description of a film and I'm curious to find out what it actually is. I don't know very much. I understand this will be difficult, especially since every time my friend explains the tale it's different so this description is likely to contain some inaccuracies.  The film's plot begins with a recounting given by the main character, who had both male and female reproductive organs but had one set removed (not sure which, think male ones were removed). The main character is narrating this tale to the barman in a bar. The barman then takes the main character back in time, where they make love to themselves and produce a child.  The child, once born, is abandoned by the mother in the past - but the barman takes the child to the orphanage and leaves them there, ensuring their survival. Eventually it is revealed that the child was the main character themselves, and so was the barman.  In other words every major character introduced up to that point was the same person who had severely messed with their own timeline. Xubuntu Dropbox icon fail Let $f(z)=\sum\limits_{n=0}^{\infty}a_n z^n$ be an analytic function in $|z|\leq R$ such that $|f(z)|\leq M$. Prove an inequality about $f$'s zero What is taking up so much space on my disk, beside the filesystem? How to fix "Notification access is not available" on Android Go? Access to journals for individuals outside of an institution? For all that is said about the wealth of information that is freely available on the internet, the fact is that most of it is incomplete, dumbed down, lacking in context or downright wrong.   Individuals spend the best part of 20 years completely oblivious to the existence of journals and the process of peer review and even then we'd be lucky if 10% of those with access to journals (usually through an institution) actually bother to invest in them.   Granted that some journals will be totally inaccessible to those without a solid background in some particular field but by and large exposure is a good thing and there are many areas of research where individuals will benefit directly from having read these.  Where does this come from?  I decided I wanted to read Popular Politics in the Late Medieval City: York and Bruge in The English Historical Review today, mainly because it looks interesting and I'm hoping to invest more time into learning about British and European History. Incidentally I also wouldn't mind tucking into Super Stable Clocks, Nature 500, 505 (29 August 2013) and a number of data analysis and big data journals in order to advance my career.   Now, not being affiliated with an institution that subscribes to these journals means that I would typically have to pay between £5 ($10) and £15 ($25) per article that I read... I could probably spend £100 just to pass an hour by.  Question   What's being done to address the lockdown on 'higher' education material? I've noticed that the Directory of Open Access Journals publishes open articles and other firms are doing similar, mainly with journals in new fields? How could I, as an individual outside of an institution, gain journal access without it costing so much money?