Using vector artwork for print
Do I have to create vector files at the correct print size?
consider the following subsets of complex plane $$\Omega_1=\left\{c\in\Bbb C:\begin{bmatrix}1&amp;c\\\bar c&amp;1\\ \end{bmatrix}\text{ is non-negative definite } \right\} $$  $$\Omega_2= \left\{c\in\Bbb C:         \begin{bmatrix}         1 &amp; c &amp; c \\         \bar c &amp; 1 &amp; c \\         \bar c &amp; \bar c &amp; 1 \\         \end{bmatrix} \text{ is non-negative definite } \right\}$$  Let $$\bar D=\{z\in\Bbb C:|z|\le1\}$$ Then 1) $\Omega_1=\bar D,\Omega_2=\bar D$  2). $\Omega_1\neq\bar D, \Omega_2=\bar D$  3). $\Omega_1=\bar D, \Omega_2\neq\bar D$  4). $\Omega_1\neq\bar D, \Omega_2\neq\bar D$  How to proceed? Thank you. How can I keep a folder synchronized to an external USB hard drive? I have a growing music collection which I manually keep in sync with an external USB drive. Sometimes I edit their ID3 tags, add or delete a file in either the hard drive or the USB drive, and I would like to keep those changes synchronized between both.  Does Ubuntu has something available that would help me with this scenario? Preferably something easy to use with a UI.  Update: To clarify my question, changes may happen on both the local hard drive or the USB drive, so the sync process must be on both directions. Lightning-Web-Components Select Option prepopulate value Let's say I have a Lightning-Web-Component with a select list with dynamic options where the value is a user Id and the label is the user's name:  &lt;select class="slds-select" onchange={handleSelectChange} disabled={isDisabled}                           data-value={step.selectedUser} &gt;                                 &lt;option value=""&gt;--None--&lt;/option&gt;                                 &lt;template for:each={step.approvalTemplateStep.Approval_Step_Users__r} for:item="user"&gt;                                     &lt;option key={user.key} value={user.User__c}&gt;                                         {user.User__r.Name}&lt;/option&gt;                                 &lt;/template&gt;                             &lt;/select&gt;    How do I prepopulate the select option with a value? I have the value I want to be prepopulated in the variable called step.selectedUser.  Here's what I see on page load:   Here's what I should see: How to organically merge nested associations? I have come across both the phrases - 'on the internet' and 'over the internet.'   I'm pretty sure that both are correct but then which to use when?  Please note, I'm well aware of all over the Internet which I'm not concerned about. C++ handling very large integers I am using the RSA Algorithm for encryption/decryption, and in order to decrypt the files you have to deal with some pretty big values. More specifically, things like   P = C^d % n   = 62^65 % 133   Now that is really the only calculations that ill be doing. I have tried using Matt McCutchen's BigInteger Library, but I am getting a lot of compiler errors during linking, such as:  encryption.o(.text+0x187):encryption.cpp: undefined reference to `BigInteger::BigInteger(int)'  encryption.o(.text+0x302):encryption.cpp: undefined reference to `operator&lt;&lt;(std::ostream&amp;, BigInteger const&amp;)'  encryption.o(.text$_ZNK10BigIntegermlERKS_[BigInteger::operator*(BigInteger const&amp;) const]+0x63):encryption.cpp: undefined reference to `BigInteger::multiply(BigInteger const&amp;, BigInteger const&amp;)'   So I was wondering what would be the best way to go about handling the really big integers that come out of the RSA Algorithm.  I heard that a possibility would be to declare your variables as a double long, so...  long long decryptedCharacter;   but I'm not sure exactly how big of an integer that can store.    Well for example, I try to compile and run the following program using dev C++:  #include iostream  #include "bigint\BigIntegerLibrary.hh"  using namespace std;  int main() {     BigInteger a = 65536;     cout &lt;&lt; (a * a * a * a * a * a * a * a);     return 0; }   then I get those errors.  Derek, I thought that by including the BigIntegerLibrary.hh file, that the compiler would go through and compile all the necessary files that it will use.  How should I try and compile the program above in order to resolve the linking errors? What does the notation like 8.6e-28 mean? What is the 'e' for? Where are the outliner toggles in 2.8? The selection toggle arrows in the Outliner disappeared. Is there some preference in the settings that has to be turned on? If a trait would be advantageous to an organism then why hasn't it evolved yet?  Conversely, if a trait is not advantageous or mildly disadvantageous, why does it exist?  In other words why does evolution not make the organism more "perfect"?    This is a general question that would be applicable for any kind of trait. Please keep the answers precise and scientific.   Read this meta post for more information: How can I monitor all and any Internet traffic from my home PC? I would like to monitor all and any Internet traffic from my home PC to see what programs installed on my home machine are accessing the Internet.  I thought I could use  for this, but I noticed Firefox traffic doesn't show up by default; you need .  What options do I have to monitor all traffic? When displaying the value of a decimal currently with .ToString(), it's accurate to like 15 decimal places, and since I'm using it to represent dollars and cents, I only want the output to be 2 decimal places.   Do I use a variation of .ToString() for this? I am just curious that the following format looks good to you or not? The preamble I used is just   \documentclass[12pt,a4paper]{article}  \usepackage{amsmath} \usepackage{amsthm} \usepackage{amssymb}   I don't feel it's so good because the first paragraph has no indent but the second does. If the first paragraph is much longer, than it's fine. But if not, it looks strange. Should I leave it, or you have suggestions for this? What is the purpose of the word 'self'? Unable to parse query string for function Query, when using IMPORTRANGE "Requires 50 reputation" to comment on deleted posts How to switch from Resident visa to Tourist visa status in the Schengen area? Construction of Dirichlet distribution with Gamma distribution Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$, have a joint ditribution as $\text{Dirichlet}(\alpha_1,\alpha_2,\dots,\alpha_k;\alpha_{k+1})$   Joint pdf of $(X_1,\dots,X_{k+1})=\frac{e^{-\sum_{i=1}^{k+1}x_i}x_1^{\alpha_1-1}\dots x_{k+1}^{\alpha_{k+1}-1}}{\Gamma(\alpha_1)\Gamma(\alpha_2)\dots \Gamma(\alpha_{k+1})}$.Then to find joint pdf of $(Y_1,\dots,Y_{k+1})$ I can not find jacobian i.e.$J(\frac{x_1,\dots,x_{k+1}}{y_1,\dots,y_{k+1}})$ MySQL SELECT LAST_INSERT_ID() for compound key. Is it possible? Can I get the LAST INSERT ID() for a compound key in MySQL? How to align checkboxes and their labels consistently cross-browsers How to safely upgrade from an older Ubuntu version to a newer one? How can I safely upgrade an Ubuntu installation from one release to another? What should I do before upgrading to ensure it goes smoothly, and is there any clean-up I need to do afterwards?  In particular, do I need to do anything special if I am using packages from PPAs, if I have a graphics card that needs drivers, or if I'm running a custom Linux kernel?  This is a general question , but as example we take Ubuntu 12.04 and Ubuntu 12.10