Inexplicable behaviour: round brackets without parameters in C++ primitives/objects initialization
Default constructor with empty brackets
I have been using this command successfully, which changes a variable in a config file and then executes a Python script within a loop: for((i=114;i&lt;=255;i+=1)); do echo $i &gt; numbers.txt; python DoMyScript.py; done  As each DoMyScript.py instance takes about 30 seconds to run before terminating, I'd like to relegate them to the background while the next one can be spawned. I have tried what I am familiar with, by adding in an ampersand as below: for((i=114;i&lt;=255;i+=1)); do echo $i &gt; numbers.txt; python DoMyScript.py &amp;; done  However, this results in the below error: -bash: syntax error near unexpected token `;' What is $A^-$ in topology? Hartshorne Algebraic Geometry Proposition 1.5 (page5) In a notherian topological space $X$, every nomempty closed subset $Y$ can be expressed as a finite union $Y=Y_1 \cup \cdots \cup Y_r$ of irreducible closed subsets $Y_i$. If we require that $Y_i \nsupseteq Y_j$ for $i \neq j$, then the $Y_i$ are uniquely determined. They are called the irreducible components of $Y$.    I understood the existence of such a representation. But I can't understand a sentence in  the uniqueness part, which I highlighted: Let $Y=Y_1 \cup \cdots \cup Y_r$ and $Y=Y&#39;_1 \cup \cdots \cup Y&#39;_s$ be two such representation. Then we can deduce that $Y_1=Y&#39;_1$ (the details are in the textbook). Now let $Z=(Y-Y_1)^-$, then $Z=Y_2 \cup \cdots \cup Y_r$ and also $Z=Y&#39;_2 \cup \cdots \cup Y&#39;_s$.  What is the operator $^-$? I understood it as a closure, is it right? But then how can I deduce that $Z$ is represented as $Z=Y_2 \cup \cdots \cup Y_r=Y&#39;_2 \cup \cdots \cup Y&#39;_s$? Replace non-numeric with empty string Primary decomposition of a monomial ideal Can anyone give me an idea about the primary decomposition of the ideal $I=(x^3y,xy^4)$ of the ring $R=k[x,y]$?    I am trying to connect the primary decomposition with the set Ass(R/I) which i have find before.. Best way to create an system of equations environment? Anime about a boy and a girl who ride ostrich-like creatures through a valley I can not remember much but I have had this film in my head for years I searched everything I can remember on every website I can think of.  I don't remember the exact story but I'll list everything about it can   Apocalyptic future possibly Two main characters: a boy and a girl riding ostrich-like creatures through a valley An old blind lady that senses things Crashed spaceship looking like a submarine Giant creatures looks like yaks with blue eyes, whose eyes turn red when something is about to happen The old lady says "Some say they went to the stars" while looking at the spaceship The two main characters do something and their eyes turn blue in the distance and the village cheers   This film is at least ten years old and I would appreciate it so much if you knew anything about it, or could help me find the title. What does ` (backquote/backtick) mean in commands? I came across the following command:  sudo chown `id -u` /somedir   and I wonder: what is the meaning of the ` symbol. I noticed for instance that while the command above works well, the one below does not:  sudo chown 'id -u' /somedir 'bridges' on a PCB copper layer I've come across a design where each pad was connected using 4 'bridges' to the GND copper layar. What stands behind these 'bridges'? Why not make a full copper layer with only solder-mask defining the pads? How to handle a native OS (Ubuntu) file upload window in selenium webdriver with python? This is my first time here but I have already posted this question on SO. I keep getting solutions for Windows + Java and not for Linux or python for that matter.  I am using Selenium and Python to automate a file upload application for the past many hours but nothing helpful!   The HTML DOM structure for this file upload is an input tag with its type attribute value = 'file'. I know I can make use of the send_keys.   The problem is I am not supposed to use send_keys() (as per the question I am trying to solve). The assumption is there are other ways of doing it.  Can anyone suggest me alternative ways to upload the file? I do get solutions for windows but not for Linux(Ubuntu). I know there are applications/tools to automate GUI components like AutoIt but there is nothing for Linux close to AutoIt.  I can say I have done my homework to find a solution. Only after not finding anything useful, I am asking this question, please help! The question,  was closed at 04:50  And yet I was able to  at the time of 08:41 some four hours later.  The question was later reopened at 08:57 Let $P(z)=a_0+a_1z+\cdots+a_nz^n$ be a polynomial whose coefficients satisfy $$0&lt;a_0&lt;a_1&lt;\cdots&lt;a_n.$$  I want to show that the roots of $P$ live in unit disc. The obvious idea is to use Rouche's theorem, but that doesn't quite work here, at least with the choice $f(z)=a_nz^n, g(z)=$ (the rest).  Any ideas? Shannon confusion and diffusion concept I read the document(not the whole document) from Shannon where he speaks about the concepts of confusion and diffusion. I read in many places(not in the document but around the internet) that confusion is enforced using substitution. Diffusion is enforced using permutation/transposition. Ciphers must use both of them because either confusion or diffusion alone are not enough. I read that a substitution cipher can apply by itself confusion(only). Permutation/Transposition applies by itself diffusion(only). It's precisely the last case that bothers me: Can a permutation/transposition cipher by itself apply diffusion?  Shannon explains diffusion as a property that spreads statistic properties of text all over the text preventing statistic analysis. It's frequently translated to: an alteration to a plaintext symbol affects many cipher text symbols. Assuming permutation of bits or characters, how can diffusion be achieved by simple permutation? I mean, if you permute bits, there will be no other bits affected. But if you consider a symbol a character and you permute bits, a change in a character will affect many other characters. It's a question of what is a symbol.  I also read versions of this diffusion concept where the point was just changing bits order just to avoid pattern analysis of the text. But, where is the avalanche effect in simple permutation?  So, what is the correct definition and the implications of diffusion?  I hope you understand what is troubling me.  Thank you once more What is the difference between old style and new style classes in Python? What is the difference between old style and new style classes in Python?  When should I use one or the other? How do I get the source code for eglibc in a format that will allow stepping through the source with gdb?    I have tried using apt-get source libc6-dev and that works for getting the source code, but I think that since the pre-processor directives were not applied that the line numbers that gdb has does not match with the source I downloaded. This makes it less useful when trying to step through the source and look at how functions in libc are working. Why do clocks measure arc-length? Apologies in advance for the long question.  My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to $x^\mu(\lambda_b)$, then his clock will measure that an amount of time $t_{ba}$ given by the curve's arc length; $$   t_{ba} = \int_{\lambda_a}^{\lambda_b}d\lambda \sqrt{-g_{\mu\nu}(x(\lambda))\dot x^\mu(\lambda)\dot x^\nu(\lambda)} $$ will have elapsed where $g_{\mu\nu}$ is a metric on spacetime with signature $(-,+,+,+)$.    Why is this so?     Here is how I would attempt to justify this fact in special relativity with $g_{\mu\nu} = \eta_{\mu\nu}$.  Consider an inertial observer $O$ in $\mathbb R^{3,1}$, and suppose that this observer sees a clock, which I'll call observer $O'$ moving around on a curve $x^\mu(\lambda)$.  If $O'$ were also an inertial observer, then given any event with coordinates $x^\mu$ as measured by $O$, observer $O'$ would measure the coordinates of the event to be $x'^\mu = \Lambda^\mu_{\phantom\mu\nu} x^\nu + x_0^\mu$ for some Lorentz transformation $\Lambda$.  If $O'$ is not inertial, then this is no longer true, and there is some more complicated family of transformations, say $T_\lambda$ between events as seen by both observers.  I would argue, however, that if we were to partition the interval $[\lambda_a, \lambda_b]$ into a large number $N$ of intervals $I_1=[\lambda_a, \lambda_i], \dots, I_N=[\lambda_{N-1}, \lambda_b]$ with $\lambda_n = \lambda_a+n\epsilon_N$ and $\epsilon_N=(\lambda_b-\lambda_a)/N$, then on each interval $I_n$, $O'$ is approximately an inertial observer in the sense that $$   T_{\lambda_n} = P_n + \mathcal O(\epsilon_N), \qquad (\star) $$ for some Poincare transformation $P_n$.  Then we would note that since $O'$ is stationary in his own reference frame, he measures his worldline to have the property $\dot x'^\mu(\lambda) = (\dot t(\lambda), \mathbf 0)$ so that $$   I_{ba}=\int_{\lambda_a}^{\lambda_b}d\lambda \,\sqrt{-\eta_{\mu\nu}\dot x'^\mu\dot x'^\mu} = \int_{\lambda_a}^{\lambda_b} d\lambda \, \sqrt{\dot t^2} = t(\lambda_b) - t(\lambda_a) = t_{ba} $$ On the other hand the integral on the left can be written as a Riemann sum using the partition above, and we can invoke ($\star$) above to get \begin{align}   I_{ba}  &amp;= \lim_{N\to\infty}\left[\sum_{n=1}^N \epsilon_N\sqrt{-\eta_{\mu\nu}\dot x'^\mu(\lambda_n)\dot x'^\nu(\lambda_n)}\right] \notag\\ &amp;= \lim_{N\to\infty}\left[\sum_{n=1}^N \epsilon_N\sqrt{-\eta_{\mu\nu}\dot x^\mu(\lambda_n)\dot x^\nu(\lambda_n)} + \mathcal{O}(\epsilon_N^2)\right] \notag\\ &amp;= \int_{\lambda_a}^{\lambda_b}d\lambda \,\sqrt{-\eta_{\mu\nu}\dot x^\mu\dot x^\mu} \end{align} Combining these two computations gives the desired result.  How do others feel about this argument?  I'm not completely comfortable with it because of the assumption $(\star)$ I made on $T_\lambda$.  I imagine that in GR a similar argument could be made by invoking local flatness of the metric. Using induction, how can I show the following identity about the fibonacci numbers? I'm having trouble with simplification when doing the induction step.  Identity: $$f_n^2 + f_{n+1}^2 = f_{2n+1}$$  I get to:  $$f_{n+1}^2 + f_{n+2}^2$$  Should I replace $f_{n+2}$ using the recursion? When I do that, I end up with the product of terms, and that just doesn't seem right. Any guidance on how to get manipulate during the induction step?  Thanks! symmetric functions vs symmetric polynomials I am doing my thesis related with symmetric functions and representations.   It is for this reason that I am reading MacDonald's book Symmetric Functions and Hall Polynomials.  When reading chapter 1.2. The ring of symmetric functions, he also talks about symmetric polynomials. And he compares both notions and sometimes treats them as equivalent but sometimes not. Does anyone have a clearer explanation about what is the difference (if there are differences)?  So, what is the difference between symmetric functions and symmetric polynomials? Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$. Let $f$ be a real-valued function continuous on $[a,b]$ and differentiable on $(a,b)$. Suppose that $\lim_{x\rightarrow a}f'(x)$ exists. Then, prove that $f$ is differentiable at $a$ and $f'(a)=\lim_{x\rightarrow a}f'(x)$.    It seems like an easy example, but a little bit tricky. I'm not sure which theorems should be used in here.    ==============================================================  Using @David Mitra's advice and @Pete L. Clark's notes I tried to solve this proof. I want to know my proof is correct or not.  By MVT, for $h&gt;0$ and $c_h \in (a,a+h)$ $$\frac{f(a+h)-f(a)}{h}=f'(c_h)$$ and $\lim_{h \rightarrow 0^+}c_h=a$.    Then $$\lim_{h \rightarrow 0^+}\frac{f(a+h)-f(a)}{h}=\lim_{h \rightarrow 0^+}f'(c_h)=\lim_{h \rightarrow 0^+}f'(a)$$   But that's enough? I think I should show something more, but don't know what it is. I have seen some comments and speculations about the robot having an off switch or whatever. But I want to know if there is any source material or comment from the author on how they managed to pass the exam.  I have only seen the actual author's comment on Mineta:     But I was wondering if there are author notes for the other characters. How is floating point stored? When does it matter? In follow up to , it appears that some numbers cannot be represented by floating point at all, and instead are approximated.  How are floating point numbers stored?  Is there a common standard for the different sizes?  What kind of gotchas do I need to watch out for if I use floating point?  Are they cross-language compatible (ie, what conversions do I need to deal with to send a floating point number from a python program to a C program over TCP/IP)?