Where do I ask questions about the Windows OS?
Are there 'stack' sites for Mac or Windows?
According to the , /opt is for "the installation of add-on application software packages".  /usr/local is "for use by the system administrator when installing software locally".  These use cases seem pretty similar.  Software not included with distributions usually is configured by default to install in either /usr/local or /opt with no particular rhyme or reason as to which they chose.  Is there some difference I'm missing, or do both do the same thing, but exist for historical reasons? Search and replace registry entry value using powershell This is an exercise in some textbooks.     Let $E$ be an algebraic extension of $F$. Suppose $R$ is ring that contains $F$ and is contained in $E$. Prove that $R$ is a field.   The trouble is really with the inverse of $r$, where $r\in R$. How to prove that $r^{-1}\in R$, in apparent lack of a characterization of $R$.  It occurred to me to use the smallest field containing $R$ ($R$ is easily shown to be an integral domain), that's the field of quotients, and proving that it's $R$ itself, but I don't really know how to proceed.  A not-too-weak, not-too-strong hint will be much appreciated.   Beware $ $ Readers seeking only hints should  beware that there is now a complete answer. How do I make my textures show in cycles? I am admittedly new to Blender, and of course cycles. I am working on a scene and I have textures set to my objects that render with internal engine just fine. However, when I go into cycles, everything is greyish. I have two light sources that should be sufficient (I think), I just don't know what I'm doing wrong. This is a screenshot of the cycles result. For some reasons, homomorphism is a very hard area for me to make improvements. I've been hitting the brick wall for almost 2 hours.   Prove that no homomorphism exists from $Z_{16}\oplus Z_2$ onto $Z_4\oplus Z_4$.  Assume a homomorphism $\phi$ exists from $Z_{16}\oplus Z_2$ onto $Z_4\oplus Z_4$. Then $\phi$ is an isomorphism.  Note that the $\left | \ker \phi \right |=2$ The $\ker \phi$ is also a normal subgroup for $Z_{16}\oplus Z_{2}$. We want possible normal subgroup of order 2. I.e., 2 elements in each normal subgroups.  By Lagrange's theorem, the order of each element in a group divides the order of a group so the possible order of the elements are 1 or 2. If the elements has order 1, then the Ker \phi cannot have 2 elements.  Hence, $\ker\phi$ = $\left \{ (0,0),(8,0) \right \}$ ,$\left \{ (0,0),(0,8) \right \}$,$\left \{ (0,0),(8,1) \right \}$, possibly.  By the First isomorphism theorem:  $\phi: Z_{16}\oplus Z_2 \rightarrow Z_2\oplus Z_2$  $\Psi: G/\ker \phi \rightarrow \phi\left ( Z_16\oplus Z_2 \right )=Z_2\oplus Z_2$  $g\ker \phi  \mapsto \phi(g)=\Psi(g\ker \phi)$  Any help is appreciated.  Edit: I know that $(2,0)$ has order $8$ in $Z_{16}\oplus Z_{2}$ but any elements in $Z_{4}\oplus Z_{4}$ does not have order $8$ which would have solved the question at the outset. But I would like a different route. How to sum $\sum_{x=0}^{N-1} \cos{\left( \frac{2\pi x}{N} \right)}^{2}$? I've tried solving it, but I'm not familiar with these kind of progressions and I couldn't get to a result. Also, I've found that the result is just $N/2$, but I don't get why would that be the answer, as it doesn't work for $N=1$ or $N=2$. Appreciate your help :) Why time is considered a dimension? At the moment, I have created a code that retrieves data from the database and displays it. However, for some reason, I cannot see the files I want to retrieve on my page. My goal is that the data gets retrieved from the database, and is displayed on the webpage. I do not need to make a connection with the database since Wordpress does that automatically.  My code:  &lt;?php  global $wpdb; // this adds the prefix which is set by the user upon instillation of wordpress $table_name = $wpdb-&gt;prefix . "wpex_programma"; // this will get the data from your table $retrieve_data = $wpdb-&gt;get_results( "SELECT * FROM wpex_programma; " ); print_r($retrieve_data); ?&gt; &lt;ul&gt; &lt;?php foreach ($retrieve_data as $retrieved_data){ ?&gt; &lt;li&gt;&lt;?php echo $retrieved_data-&gt;column_name;?&gt;&lt;/li&gt; &lt;li&gt;&lt;?php echo $retrieved_data-&gt;another_column_name;?&gt;&lt;/li&gt; &lt;li&gt;&lt;?php echo $retrieved_data-&gt;as_many_columns_as_you_have;?&gt;&lt;/li&gt; &lt;?php  } ?&gt; &lt;/ul&gt;   My question: the data is not shown and I believe it is not retrieved. How can I fix that? The table name is correct, and I have data in my database tabel. The print_r($retrieve_data)returns the following: Array ( [0] =&gt; stdClass Object ( [id] =&gt; 35 [naam] =&gt; /public_html/wp/wp-content/plugins/AbonneerProgrammas/FilesUpload/Country Kickin 1.mp3 ) )  My query log:    My database structure:   New:  &lt;?php  global $wpdb; // this adds the prefix which is set by the user upon instillation of wordpress $table_name = $wpdb-&gt;prefix . "wpex_programma"; // this will get the data from your table $retrieve_data = $wpdb-&gt;get_results( "SELECT * FROM wpex_programma; " ); print_r($retrieve_data); ?&gt; &lt;ul&gt; &lt;?php foreach ($retrieve_data as $retrieved_data){ ?&gt; &lt;li&gt;&lt;?php echo $retrieved_data-&gt;id;?&gt;&lt;/li&gt; &lt;li&gt;&lt;?php echo $retrieved_data-&gt;naam;?&gt;&lt;/li&gt; &lt;?php  } ?&gt; &lt;/ul&gt; I'm trying to run down a memory leak in a windows forms application.  I'm looking now at a form which contains several embedded forms.  What worries me is that the child forms, in their constructor, take a reference to the parent form, and keep it in a private member field.  So it seems to me that come garbage-collection time:  Parent has a reference to the child form, via the controls collection (child form is embedded there).  Child form is not GC'd.  Child form has a reference to the parent form, via the private member field.  Parent form is not GC'd.   Is this an accurate understanding of how the garbage collector will evaluate the situation?  Any way to 'prove' it for testing purposes? What is the best method of re-rendering a web page on orientation change? In Xubuntu 16.04.3 (and several previous versions aswell) it is not possible to have no power icon in the notification area.  A power icon is displayed even though 'Show system tray icon' is unchecked in Xfce Power Manager.  When 'Show system tray icon' is checked, there are two power icons displayed.  (See screenshots)  I've searched and I can't find any information related to this in Xubuntu/Xfce.  Is there a way to fix or work around this bug? Java: Load class from string Construct a Borel set on R such that it intersect every open interval with non-zero non-"full" measure Everytime I sudo apt-get update it always not complete and will say in the end  E: Read error - read (5: Input/output error) E: The package lists or status file could not be parsed or opened.   Same goes, when I try to install something and do sudo apt-get install &lt;some app&gt;  What should I do ? I admit, that my drive has bad sectors, could that be the reason? Is there anything else I can do? On the meta home page I noticed the  is listed as doing something, but cannot figure out what it is.  There is nothing on the  or its , but the recent activity is listed with the same timestamp. It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? Is an Anti-Symmetric Relation also Reflexive? According to the definition of an Anti-Symmetric Relation if xRy and yRx then x = y  Which means, effectively, x is in relation with itself. Does this mean that anti-symmetry implies reflexive property as well? Generate random numbers uniformly over an entire range I need to generate random numbers within a specified interval, [max;min].  Also, the random numbers should be uniformly distributed over the interval, not located to a particular point.  Currenly I am generating as:  for(int i=0; i&lt;6; i++) {     DWORD random = rand()%(max-min+1) + min; }   From my tests, random numbers are generated around one point only.  Example min = 3604607; max = 7654607;   Random numbers generated:  3631594 3609293 3630000 3628441 3636376 3621404   From answers below: OK, RAND_MAX is 32767. I am on C++ Windows platform. Is there any other method to generate random numbers with a uniform distribution? What immigration and customs checks are performed for passengers leaving the U.S.? Compact topological space with closed graph implies continuity Let $X,Y$ be topological spaces and $f:X \rightarrow Y$  If $Y$ is compact and $G(f)$ (graph of $f$) is closed, show that $f$ is continuous.   I consider an open set in $X$, and as $G(f)$ is closed, $(X \times Y)-G(f)$ is open. And I guess I need to do something here. Then I can get some open sets. Also, I notice that compact is something relate to "finite". I guess I can use the compactness to do finite intersection or union and get the result finally.  But what should I do in the middle or I am not even on a right track.