Using the crop package, we can easily add printer marks. I am look for .     I am wondering if there is a package for this?
A standard proof for press needs crop marks and color bars as below    With the package crop, the crop marks can be easily added.  But how about the color bar ?  Is there a way or a package to make it ?  An example is   \documentclass[b5paper,10pt]{article} \usepackage[utf8]{inputenc} \usepackage[cross,a4,center,info,axes]{crop}  \title{Test} \author{User} \begin{document} \maketitle \section{Fox} The quick brown fox jumps over a lazy dog. \end{document}
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$) Let $A$ and $B$ be sets. Let $A\cup B\subseteq A\cap B.$ Prove that $A\subseteq  B.$   My understanding of this question is that all the elements of set $A$ that intersects with set $B$ exists in the union of sets $A$ and $B$ and because in order for the elements to intersect, the elements must exist in both sets $A$ and $B$. Therefore set $A$ is a subset of $B$.  My question is how do I write the proof down so that it is an acceptable answer? Also does this mean set $B$ is a subset of $A$? JAXB Java generating XML, Why lowercase? How do I view 'git diff' output with my preferred diff tool/ viewer? When I type git diff, I want to view the output with my visual diff tool of choice (SourceGear "diffmerge" on Windows). How do I configure git to do this? I found "A sledgehammer to crack a nut" as one example. What are some others? For what values of $\theta$ does $\sum_{1}^{\infty} \frac{e^{i n\theta}}{n}$ Converge? I just came across the problem of what happens in the boundary cases of .  More concisely, for what $\theta$ will the following sum converge? $$\sum_{n=1}^{\infty} \frac{e^{ni\theta}}{n}$$ It is well known that this sum will diverge for $\theta=0$ and will converge for $\theta=\pi$. In fact, for any odd multiple of an even root of unity, since we have symmetry, for each line through the origin of the complex plane, we can use the alternating series theorem to show that they converge.  Another idea I had was to split  the sum into imaginary and real parts, and if we can prove each of these converges, then we are all set. So now we must prove that both of the following converge $$\sum_{n=1}^{\infty}\frac{\cos(n\theta)}{n}\space, \space \sum_{n=1}^{\infty}\frac{\sin(n\theta)}{n}$$ Now these can be shown to converge easily by Dirichlet's test for any rational multiple of pi, but what about irrational multiples of pi? I know it has been shown to converge with $\theta=1$, but I don't see how to generalize this. Integral of sinc function multiplied by Gaussian I am wondering whether the following integral $$\int_{-\infty}^{\infty}  \frac{\exp( - a x^2 ) \sin( bx )}{x} \,\mathrm{d}x$$ exists in closed form. I would like to use it for numerical calculation and find an efficient way to evaluate it. If analytical form does not exist, I really appreciate any alternative means for evaluating the integral. One method would be numerical quadrature including Gaussian quadrature, but it may be inefficient when the parameters $a$ and $b$ are very different in scale.  EDIT : In view of  discussion, we have decided to add OP's self-answer to the end of the question, for it does not qualify as an answer yet contains vital details. The copying is unabridged. Thanks very much for your comments, and the following result was obtained including the case for $x_0 \ne 0$: $$ \int_{-\infty}^{\infty} dx \exp[-a(x-x_0)^2] \frac{ \sin(bx) }{ x } = \pi \exp(-a x_0^2) \mathrm{Re}\left(\mathrm{erf}\left[\frac{b+2iax_0}{2\sqrt{a}}\right] - \mathrm{erf}\left[\frac{2iax_0}{2\sqrt{a}}\right]\right) $$ where $a\gt0, b, x_0$ are assumed to be all real. (note: coefficients etc may be still wrong...) This integral appears in a type of electronic structure calculation based on a grid representation (sinc-function basis). I believe the above result should be definitely useful. Thanks much!! --jaian What theorems can I use to prove this? Poisson distribution (solution check) How do I reset a lost password (using recovery mode requires me to type the password)? What are the technical obstacles that doesn't allow OSX to be installed in a PC? Are hand motions required to use the Force? In almost every canon (that is, visual) source, Force users typically wave a hand to invoke the Force to move or manipulate objects, people and thoughts. I get out-of-universe this is a visual cue that the Force is being used, but in-universe is it strictly necessary?  (The only exception I can think of is when Luke is training on Dagobah and is balancing rocks while standing on one hand with Yoda on his foot. He doesn't appear to be waving his hand to move the rocks.)  Is this addressed anywhere in-universe, even in Legends? Let $\mathcal{C}$ be a finite binary code such that for any two sequences $\{a_n\},\{b_n\}\in \mathcal{C}$ if $a_j\not=b_j$ for some $j$ then the concatenation binary sequence $a_1a_2\cdots a_n\not=b_1b_2\cdots b_n$, the Kraft-Mcmillan Inequality says that $$\sum_{i}\frac{N_i}{2^{i}}\le 1,$$where $N_i$ is the number of codes in $\mathcal{C}$ with length of $i$.  If we assume the code is prefix free, we will have an elegant probabilistic proof at  (consider the infinite binary sequence generated by i.i.d. binomial random variable with probability $1/2$, define $E_x$ be the event that the sequence has prefix $x\in \mathcal{C}$, then $\sum_i\frac{N_i}{2^i}\le \sum_i P[E_x]=  P[\cup_i E_x]=1$). But for the general case one will not necessarily have the events $E_i$s disjoint, I'm curious if similar argument exists for the general case. (The problem is an excercise in the probabilistic method of alon, I guess some probabilistic argument should exist)  (My attempt is that consider the product topology $T=\prod_i\mathcal C$ whose open sets generated by $E_x$s where $x$ is the concatenation codes of $\mathcal{C}$, we define a natural product measure $\mu$ over $T$ by $\mu(E_x)=2^{-|x|}$. Clearly $\mu(T)\le 1$ (as $T$ is a sub-topology of $\prod_i\{0,1\}$), I want to show $\mu(E_x\cap E_y)=0$ for $x\not=y\in \mathcal{C}$, if not we can find $E_z$ such that $E_z\subset E_x\cap E_y$ by compactness, if we can show $z$ can be write as concatenation code start with both $x,y$ we will done, but I get stuck at here.) Nonlinear function continuous but not bounded I would like an example of a map $f:H\rightarrow R$, where $H$ is a (infinite dimensional) Hilbert space, and $R$ is the real numbers, such that $f$ is continuous, but $f$ is not bounded on the close unit ball $\{ x\in H : \|x\| \leq 1\}$.  Actually, $H$ could be replaced by any Banach space (but not just a normed space-- that's too easy).  My motivation is that if $f$ is linear, this is impossible; but I have next to no intuition about non-linear functions.  Edit: Here's an example for $c_0$ which is even differentiable (disclaimer: I found it here: ).  Define $f:c_0\rightarrow F$ (where F is your field, real or complex) by $$ f(x) = \sum_{n=1}^\infty x_n^n \qquad (x=(x_n)). $$  You can estimate the sum by a geometric progression, so it does converge.  A bit of checking shows that f is Frechet differentible (so certainly continuous).  But $f(1,1,\cdots,1,0,\cdots)=n$ (if there are $n$ ones) so $f$ is not bounded on the closed unit ball.  What I don't immediately see is how to adapt this to $\ell^2$, say. How do I get a list of obsolete packages? I'm trying to figure out a way to get a list of the packages that are no longer available in the repositories that I have enabled. This workstation has been through quite a few versions of Ubuntu and has had many 3rd party repositories added and removed. I'd like to get a list of software that I have from these removed repositories, so I can clean it up or add back the appropriate repositories. How to read command line arguments of another process in C#? What's the best solution to check a users country? So this is a question with which I have been stuck for a while and it all revolves around the concept of volt.  I have posted a LOT of questions on physics forums while trying to understand the concept of volt and potential difference. This is hopefully going to be the last one.  What do you exactly mean when you say that a battery is 2.5 V. I know that it says that the potential difference between the 2 terminals of the battery is 2.5 V  but then what is the potential of the 2 ends of the battery? Is there a unit of potential and not just potential difference?  Also volt = work/charge but how can work/charge express the difference of potentials across the 2 terminals? That's really embarrassing, however I need to ask it. I could not prove that the normed space    $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle $ is complete (as a metric space), where $\| f\|_1 = \int_0^1 |f(x)|dx$. I don't really know how to explicit a continuous functions as a limit of a Cauchy sequence. I tried to prove that the pointwise limit (of the Cauchy sequence) have just a finite number of discontinuities (I don't know if it's true) and then approximate it by a continuous function.  Thanks in advance. Strict warning: Only variables should be passed by reference I get the following error:     Strict warning: Only variables should be passed by reference in include() (line 18 of /home/sites/dev/theparce/sites/all/themes/parce/block--block--3.tpl.php).   This is the block code which is causing that error.  if ($user_gallery) {   print render(node_show($user_gallery));  // Line 18   print drupal_render ($user_gallery_edit);  } else {   print drupal_render($user_gallery_new); }   Why do I get that error, even if I get all printed as expected? CDF of absolute value of difference in random variables