The best way to combine two m4v files on Catalina
Best way to merge mp4 files
Was Stack Exchange named after Experts Exchange? Was Stack Exchange named after Experts Exchange, or is the former using the word "Exchange" a coincidence? How can I restrict the Normal user to run the only limited set of commands in RHEL? Let $R$ be a commutative ring with unit, $I$ an ideal of $R$ and consider the following three constructions.   The  $R_I$ of $R$ at $I$ (i.e. the localization of $R$ at the multiplicative system $R\setminus I$) gives a morphism $$ f_1:\operatorname{Spec}(R_I)\to \operatorname{Spec}(R)=:X $$ The  $\widehat{R}_I$ of $R$ at $I$ gives a morphism $$ f_2:\operatorname{Spec}(\widehat{R}_I)\to X $$ For the special case $I=(a)$, the localization $R_a$ (i.e. the localization of $R$ at the multiplicative system $\{1,a,a^2,\ldots\}$) gives a morphism $$ f_3:\operatorname{Spec}(R_a)\to X $$   My question is:     What is the geometric meaning of all three constructions and how are they related?   This is what I ''know'' already or describes at least the style of answer I would appreciate. As remarked in the comments, $I$ has to be a prime ideal.   $R\to R_I$ is injective iff $R\setminus I$ contains no zero divisors which is the case if $I$ is a prime ideal. The scheme $\operatorname{Spec}(R_I)$ is the intersection of all the neightbourhoods of $I$ in $X$. This is a little contra-intuitive for me since the last statement sounds like ''$f_1$ is injective'' but the $\operatorname{Spec}$-operator should turn 'injective'' and ''surjective'' around somehow (I know this is literally not true but I only want to get a feeling like ''is contained'', ''is bigger'', ''is smaller'', etc.). $\operatorname{Spec}(R_a)$ is somehow the opposite of $\operatorname{Spec}(R_{(a)})$ (= the intersection of all the neightbourhoods of $(a)$ in $X$) because $\operatorname{Spec}(R_a)$ seems to be something like the union of all the open sets of $X$ not containing the point $(a)$. $R\to\widehat{R}_I$ is injective iff $\cap I^n=(0)$ and this holds very often (e.g. for $R$ noetherian and either an integral domain or a local ring). Hence (this is probably false intuition as remarked before), $f_2$ should be something like a ''projection'' (from something ''big'' into something ''small''). But what is geometrically the difference between localization and completion. I don't have a geometric idea of completion at all.   As remarked by Qiaochu Yuan in the comments below, one should not think of $\operatorname{Spec}$ as injective-surjective switching. I get this error in the deployment step of a share-point farm based project. Most of the suggested solutions on the net are a simple Visual Studio re-start, however, a simple VS restart won't fix this.   Any ideas on what might be causing this? For all $x,y\in\mathbb{R}$   define that $x\equiv y$   if $x^{2}=y^{2}$  . Then $\equiv$  is an equivalence relation on $\mathbb{R}$  , there are infinitely many equivalence classes, one of them consists of one element and the rest consist of two elements.  Solution  True. To show that \equiv  is reflexive we need to show that \forall x\in\mathbb{R}  :x=x.  Let x\in\mathbb{R}  , x\equiv\mbox{\ensuremath{x}}  if x^{2}=x^{2},   which is obvious.  [x]  ={y\in\mathbb{R}  |x\equiv y}  =[0]={y\in\mathbb{R}|0\equiv y}={0}  . Hence y^{2}  =0^{2}   =0   which implies that y=0  . Store won't open after upgrade When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$ When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$, where $f_{xy}$ and $f_{yx}$ denote the mixed (second) partial derivatives of a multivariable function $z=f(x,y)$. how many permutations of {1,2,...,9} How many permutations of {1,2,…,9} are there such that 1 does not immediately precede 2, 2 does not immediately precede 3, and so forth up to 8 not immediately preceding 9? One obvious example of such a permutation might be 987654321, but there are many others, such as 132465879 or 351724698. Numerical integration of divergent function I am having trouble with the numerical integration of a divergent function. For example, \begin{equation} n= \int f(x)\,dx = \displaystyle\int \dfrac{\Theta(x-\varepsilon)\,dx}{\sqrt{x-\varepsilon}} \end{equation} is not behaving good when calculated numerically: \begin{equation} n_\text{numerical} \approx f(x_j)(x_j-\varepsilon) + \sum_{k=j+1}^N f(x_k)\Delta x \end{equation} with \begin{equation} x_i = x_\text{min} + i\Delta x \end{equation} and $x_j$ being the smallest point larger than $\varepsilon$. Due to the divergent behavior of $f(x)$ near $\varepsilon$, the numerical result has discontinuities and jumps at every $\varepsilon=x_i$ when I sweep $\varepsilon$. The smoothness of this integration is crucial in the convergence of my simulations. Can anybody suggest a simple trick to solve the problem? All I need is to have a continuous numerical result by continuously changing $\varepsilon$. Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space? I have a non homework related question from a text and require a nice clear proof/disproof please  Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?  my ideas:  if $H$ is the subset of the topological space $X$  if the subset is closed in the closed subspace, the complement is open in the subspace, which means the complement is of form $U\cap H$ for some $U$ open in $X$  if the subspace is closed the complement is open which means complement of $H=U$ for some open $U$ in $X$  kind thanks Splitting a semicolon-separated string to a dictionary, in Python I have a string that looks like this:  "Name1=Value1;Name2=Value2;Name3=Value3"   Is there a built-in class/function in Python that will take that string and construct a dictionary, as though I had done this:  dict = {     "Name1": "Value1",     "Name2": "Value2",     "Name3": "Value3" }   I have looked through the modules available but can't seem to find anything that matches.    Thanks, I do know how to make the relevant code myself, but since such smallish solutions are usually mine-fields waiting to happen (ie. someone writes: Name1='Value1=2';) etc. then I usually prefer some pre-tested function.  I'll do it myself then. 12 hours delay with ATmega16A I am trying to turn on a LED for 5sec every 12 hours. I tried:  #include &lt;mega16.h&gt; #include &lt;delay.h&gt;  void main(void) {     DDRC.0 = 1;     PORTC.0 = 0;      while(1)     {              unsigned long i;        unsigned long j;        PORTC.0=1;         for(i=1; i&lt;432; i++)        {              delay_ms(100);          }         PORTC.0 = 0;         for(j=1; j&lt;100; j++)        {            delay_ms(50);          }     } }   but the LED was on for about 2 hour every week. How can I use Web.debug.config in the built-in visual studio debugger server? Backup GNOME-Terminal Error : Warning: strpos() [function.strpos]: Offset not contained in string - can not find solution Is it possible to play FIFA 2015, 4v4 on 2 Consoles? I've the following situation: My friends and I, we're 8 in total, want to play Fifa 15 4v4. I know that the Playstation 4 just supports 4 controllers and thats why we think about a 2 console + 2 TV's setup, so 4 players per console.   So my question is: Is it possible or is there a game mode available were we could play such a setup?  Update: After I got the first answer I've to add that I know that the only way to play on 2 consoles would be through the psn online features. So we did not plan to play on Lan. We just want to sit in the same room with 2 consoles and play against each other over psn. I found the following blog title without a question mark from :     How to ease Afghanistan’s progress in cricket   Is it grammatical, if we don't put question mark in questions of titles? I think this blog title should have been like this:     How to ease Afghanistan’s progress in cricket?   I also found the following blog title from  without a question mark:     Election rigging 101: How to steal a mandate   However, I found a question mark from other blog title of :     Elections 101: What is the ECP and what does it do on election day? After turning census block data into a raster, how do I redistribute the density to reflect land cover types I plan on rasterizing (terminology?) census block data relating to density to a regular 30 m by 30 m grid for use with NLCD data.  I then hope to distribute the density of the original census block among each result set of grid cells within the original polygon according to the land cover type dictated by the NLCD dataset.  For example, let's imagine a string of city blocks with a park, all found within one census block.  If within this census block the average density is 1000 people/km^2, we ultimately would want the resulting grid cell containing the park to have a lower population density than the grid cells containing the surrounding apartments.  This information may be captured by the NLCD dataset, with the park being classified as '21' (open but developed land) versus 24 for apartment buildings which could be classified as '24' (high density development).  Is there a method, or set of methods, within ArcMap that would allow me to:   Redistribute the density based on the NLCD value Perform this redistribution only within the original census block polygon   I don't know if this is possible, but I figured I would ask.  Edit  Here's what I have been trying:  I converted the census block data to a raster, snapping it to the NLCD land cover data and ensuring the output grid cells were the same size.  Each cell contains the same info as the original census block (housing umbers, population, etc). I have been trying to figure out a way to edit the new grid so that if the NLCD grid cell contains a land cover type that doesn't support a business or housing (park, forest, farm, etc.) that it's housing and population values area set to 0.  My next move was going to be figuring out how to subtract the non-residential/non-business grid cells area from the area of the original census block, and force a recalculation of the density.  Converted the altered census block layer to grid cells again, with each having the new density value, and once again set the cells' housing, population, and density values that don't support a business or housing (park, forest, farm, etc.) to 0.  Kind of circular, and I'm not sure of all the steps (raster calculator for editing individual grid cells based on another raster's grid cell value?), but it seems to logically work out if I can get the parts to work.  On the other hand, @dof1985's answer seems to simplify the first part of my workflow (by directing me to the correct toolset), but I will still have to nullify the grid cells where parks, etc., do exits after the density has been recalculated for the census data. Splitting ethernet cable I have one ethernet cable that runs into my TV cabinet. It comes from a router in my closet. The router splits the main feed into the home into six runs that run through out the house. I now have several components in my TV cabinet that work best if they are connected to a hard line and not WiFi. Can I split the one cable in my TV cabinet into three or four lines to run to these other components, i.e.: playstation, Receiver,TV antenna box etc. If so, what items do I need to purchase? Thanks for your help. Earning a PhD help you learn tools and techniques in your field, and lets you become an expert in a very specific field of science. However, once you get your degree and try to enter the labor market, you're competing against people who are younger than you (i.e. recently graduated non-phd engineers) and may have actual work experience (i.e. non-phd engineers with a few years in the market).  There are, of course, some positions in which they cannot compete, including research and teaching position. Those are the minority, though... in most other fields it seems that holding a PhD is not as important as (for example) work experience.  So, I would like to know:   Is work experience more important than having a PhD in the many work environments? What skills can I acquire/demonstrate during my PhD to become more "valuable" than a non-PhD candidate for the same job?