Will a shutterstock image work for this or do I need a better quality image?  This is shutterstock info: Large  |  10297 px x 3433 px  |  87.2cm x 29.1cm @ 300 dpi  Is my calculation correct: DPI will be 34? Is that too low if people will be standing 1m from artwork?
For wall-sized graphics and large banners (e.g. 3m × 5m), what is an acceptable PPI for print? As I understand it 300 ppi is the typical for 'small' artworks (esp. for clean text resolution). However, for small artworks, the audience usually engages at a much closer distance. Therefore, in the interests of keeping a bitmap file down to a reasonable size, can you get away with a much-reduced PPI for a large format/banner print?
What is $i^i$ and $(i^i)^i$ What is $i^i$ and $(i^i)^i$. I fond some answers  but is there a clearer explanation of this? Maybe something help me to understand. How can I pass a class member function as a callback? I'm using an API that requires me to pass a function pointer as a callback. I'm trying to use this API from my class but I'm getting compilation errors.   Here is what I did from my constructor:  m_cRedundencyManager-&gt;Init(this-&gt;RedundencyManagerCallBack);   This doesn't compile - I get the following error:      Error  8 error C3867: 'CLoggersInfra::RedundencyManagerCallBack': function call missing argument list; use '&amp;CLoggersInfra::RedundencyManagerCallBack' to create a pointer to member   I tried the suggestion to use &amp;CLoggersInfra::RedundencyManagerCallBack - didn't work for me.   Any suggestions/explanation for this??  I'm using VS2008.  Thanks!! How do I rip audio from a DVD? Windows registry entries for default explorer view PHP parse/syntax errors; and how to solve them Zero-dimensional ideals and finite-dimensional algebras I encountered in the literature the term zero-dimensional ideal, however I can not find a relevant definition anywhere in Atiyah-MacDonald or Matsumura. In fact, I encounted the statement:      $I$ is a zero-dimensional ideal of $k[x_1,\dots,x_n]$ $\Leftrightarrow$ $k[x_1,\dots,x_n]/I$ is a finite-dimensional $k$-vector space, where we assume that $k$ is algebraically closed.   Question 1: What is the definition of the dimension of an ideal?  Question 2: How do we prove the above statement?  Question 3: Is $k$ being algebraically closed a necessary condition for the statement to be true? Where and why do I have to put the "template" and "typename" keywords? In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template &lt;typename T, typename Tail&gt; // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template&lt;typename U&gt; struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion&lt;U&gt; dummy;      };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; }; template &lt;typename T&gt; // For the last node Tn. struct UnionNode&lt;T, void&gt; {     // ...     template&lt;typename U&gt; struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template&lt; &gt; struct inUnion&lt;T&gt; {     }; };   The problem I have is in the typedef Tail::inUnion&lt;U&gt; dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion&lt;U&gt; names a type and not a function? How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$? Let $R$ be a UFD. Then for any two elements $a,b \in R \setminus \{0\}$ $ab \sim \gcd (a,b){\operatorname{lcm} (a,b)}$.   My attempt :  Let $d = \gcd (a,b)$.Then $d|a$ and $d|b$.Then $\exists x,y \in R$ such that $a = dx$ and $b = dy$.Now it is to be shown that $c = dxy$ is the lcm of $a,b$.Which I find difficulty to show.It is clear that $a|c$ and $b|c$. Now if $u$ is any common multiple of $a$ and $b$.Then $dx|u$ and also since $y|b$ we have $y|u$ i.e. $dxy|u^2$ $\implies c|u^2$.But I have to show $c|u$ to complete the proof which I fail to prove.Please help me to complete the proof.  Thank you in advance. Why are memory statistics in top and htop different? Whenever I use top and htop commands to see memory stats, they are always different as shown in figures. Which should I trust? Why do airplanes experience negligible Coriolis force while bullets experience the Coriolis force in long range shooting, even though the mass of airplane is much bigger than a bullet? How to pass multiple operator properties via UI layout? PhD without previous academic degree: truth or myth? Disable the guest user completely in El Capitan without having to disable 'Find My Mac' I know it should be straight forward but unfortunately, it  isn't.  I did disable the guest user in the System Preferences by unchecking the checkbox for Allow guests to login in to this computer, but it still shows up on the login screen.  I have heard that disabling 'Find My Mac' would fix it for OS X Lion, but I want to keep it.  Is there a way to do this? Create violine plots I use pgfplots for most of my plots. Now I need to add a . Is this possible with pgfplots or any other package? Rendering an animation the way 3D view looks I get the following error when I try to typeset a beamer document.  kpathsea: Running mktexpk --mfmode / --bdpi 600 --mag 0+525/600 --dpi 525 mathkerncmssi8 gsftopk: fatal: map file `cid-base.map' not found. mktexpk: don't know how to create bitmap font for mathkerncmssi8. mktexpk: perhaps mathkerncmssi8 is missing from the map file. kpathsea: Appending font creation commands to missfont.log.  ) !pdfTeX error: pdflatex (file mathkerncmssi8): Font mathkerncmssi8 at 525 not found  ==&gt; Fatal error occurred, no output PDF file produced!   But if I remove sansmathaccent.sty from the TeX Live tree, the document typesets fine. Here is a minimal working example.  \documentclass[10pt]{beamer}  \begin{document}  \begin{frame}{A very short beamer document}  $e^{i\pi}+1=0$  \end{frame}  \end{document} Why does "kill -9 0" end my console session? I just wonder why kill -9 0 ends my tty console session?   What exactly is PID 0, it is not listed on a ps aux? Array initialization syntax when not in a declaration 80's Animated movie: An old man joins mission to save a boy stranded on a hostile world Strange folder in my home folder after a failed run of BleachBit