Let $\{a_n\}\in\mathbb R^{\mathbb N}$. Does there exist $h\in C^\infty(\mathbb R)$ with $h^{(n)}(0)=a_n$ for every $n$?
Every power series is the Taylor series of some $C^{\infty}$ function
Why is 24.0000 not equal to 24.0000 in MATLAB? I am writing a program where I need to delete duplicate points stored in a matrix. The problem is that when it comes to check whether those points are in the matrix, MATLAB can't recognize them in the matrix although they exist.  In the following code, intersections function gets the intersection points:  [points(:,1), points(:,2)] = intersections(...     obj.modifiedVGVertices(1,:), obj.modifiedVGVertices(2,:), ...     [vertex1(1) vertex2(1)], [vertex1(2) vertex2(2)]);   The result:  &gt;&gt; points points =    12.0000   15.0000    33.0000   24.0000    33.0000   24.0000  &gt;&gt; vertex1 vertex1 =     12     15  &gt;&gt; vertex2     vertex2 =     33     24   Two points (vertex1 and vertex2) should be eliminated from the result. It should be done by the below commands:  points = points((points(:,1) ~= vertex1(1)) | (points(:,2) ~= vertex1(2)), :); points = points((points(:,1) ~= vertex2(1)) | (points(:,2) ~= vertex2(2)), :);   After doing that, we have this unexpected outcome:  &gt;&gt; points points =    33.0000   24.0000   The outcome should be an empty matrix. As you can see, the first (or second?) pair of [33.0000 24.0000] has been eliminated, but not the second one.  Then I checked these two expressions:  &gt;&gt; points(1) ~= vertex2(1) ans =      0 &gt;&gt; points(2) ~= vertex2(2) ans =      1   % &lt;-- It means 24.0000 is not equal to 24.0000?   What is the problem?    More surprisingly, I made a new script that has only these commands:  points = [12.0000   15.0000           33.0000   24.0000           33.0000   24.0000];  vertex1 = [12 ;  15]; vertex2 = [33 ;  24];  points = points((points(:,1) ~= vertex1(1)) | (points(:,2) ~= vertex1(2)), :); points = points((points(:,1) ~= vertex2(1)) | (points(:,2) ~= vertex2(2)), :);   The result as expected:  &gt;&gt; points points =      Empty matrix: 0-by-2 TV identification: Short-lived TV show about a time traveller with a super-computer disguised as a credit-card It might have only been a pilot or a made for TV movie, but I remember a male time traveller who was for some reason in 90s US from a semi-distant future. He had in his possession a super-computer disguised as a regular credit card, which could hack things and I think spoke to him in a female voice.   Note: Not Quantum Leap - the time traveller and "credit card computer" might be keywords that people would hit upon, but 'Ziggy' the computer in QL was non-speaking, operated by a hologram and did not resemble a credit card - this one had its own voice and was disguised as a CC. Remove association with blank file extension? I no longer use the service that I originally used to register, and would like to change the service I use to log in, or at least add a second account.  Is this possible? How do I change my login provider or associate a backup method to log in?     For more information, see "" in the . How can I output a list of all installed packages with installation date and additional information? Script to convert filenames to lowercase depending on extension What is this agglomeration of pink cells I found attached to a stone? NVIDIA Driver Install Fails Class teardown in junit 3? Some questions and answers are marked Community Wiki and are owned by a community wiki user:  (In fact, this very question is one of them)  Why have Community Wiki posts? How do Community Wiki posts work? How does a post become a Community Wiki post? How can the Community Wiki status be removed from a post? How can I find Community Wiki posts? I'm looking for a single line regex which does the following:  Given a HTML tag with the "name" attribute, I want to replace it with my own attribute. If that tag lacks the name attribute, I want to implant my own attribute. The result should look like this:  &lt;IMG name="img1" ...&gt; =&gt; &lt;IMG name="myImg1" ...&gt; &lt;IMG ...&gt; =&gt; &lt;IMG name="myImg1" ...&gt;   Can this be done with a single line regex? Cannot find Underground Jungle Temple On my 1.2 Terraria Map I have been mining from left to right in my large underground jungle using my rocket launcher. Despite this, I have had no luck on finding the Underground Jungle Lihzahrd Temple. I have been searching the layer above where lava constantly spawns. Have I simply spawned in a world without one or am I searching in the wrong place? I have also considered using the clentimator with Dark Blue ammo to provide light, should I do that? Some movies feature child characters put in violent situations. This can range from crude language to extreme horror (e.g. torture, gore, etc.). As an example,  and its sequel has plenty of those scenes. It looks like a paradox that children can be actors in movies that are definitely not for children.  Do the directors usually try and avoid exposing the very young actors to the violence of such scenes, e.g. by clever dubbing and editing? Are there laws that require them to do so, just like there are ratings that prevent children from seeing some movies? How does QGIS Zonal Statistics handle partially overlapping pixels? There are a couple Stackexchange posts asking this question, but neither of them were sufficiently answered:       I am writing Python scripts that perform essentially the same operations as Zonal Stats, and I have been using Zonal Stats to check my scripts' outputs.   I have noticed that when there are many cells in the polygon being queried, my results match perfectly, but there are discrepancies when there are only a few raster cells in the polygon. The following is an example of this. I am computing "count" for each polygon.  Exhibit 1:   The returned count is 0.45, which looks roughly correct if pixels can be treated fractionally rather than simply in/out.  Exhibit 2:   Similar result; count is 0.39.  Exhibit 3:    With a larger poylgon, now we see the count is exactly 2. Note that there are exactly 2 pixel centers contained in the polygon.  Exhibit 4:    Here, only one pixel center is within the polygon. The count is 1.008, though. If you exclude the polygon area from the pixel whose center is in the polygon, the remaining area is obviously greater than 0.008 of a pixel.   From these exhibits, it seems that Zonal Statistics treats these cases specially. It looks like to me that if there are less than 2 pixel centers within the polygon, it performs some kind of averaging such as polygon_area/raster_cell_area to return the count. I should note that I have 48 of these polygons, and all returned counts greater than or equal to 2 are integers; fractional counts are only returned for &lt;2.  How are these fractional-pixel counts incorporated into the other statistics output by Zonal Stats?    indicates strange behavior with max/min when using large raster cells, and my own testing returns mean values not congruous with simple "pixel center in/out of the polygon." To reiterate, I get exact agreement when the underlying raster contains many pixels within the polygon. I couldn't find any documentation about this, and it may be important when people have never had problems with Zonal Stats but use a coarse raster and remain unaware that there is a different behavior when there are only a few pixels within the polygon. How to align floating point variables in Latex3 I would like to have the variables (defined in Latex3) aligned in a table with the decimal point. Of course, without using the &quot;trial and error&quot; extra space &quot;,&quot;. Is there any possibility? Thank you very much. \documentclass{article} \usepackage{xparse} \usepackage[version=4]{mhchem}  \usepackage{siunitx,booktabs}  % \ExplSyntaxOn \NewDocumentCommand{\calcnumd}{o m}   {\IfValueTF{#1}      {\num[round-mode = figures, round-precision = #1, round-integer-to-decimal]{\fp_to_decimal:n{#2}}}      {\num{\fp_to_decimal:n{#2}}}   } % data \fp_set:Nn \dhfbiox {33.18} \fp_set:Nn \dhftetrox {9.16} \fp_set:Nn \dgfbiox {51.31} \fp_set:Nn \dgftetrox {97.89} \fp_set:Nn \cpbiox {37.20} \fp_set:Nn \cptetrox {77.28} % calculations % \ExplSyntaxOff % \begin{document}  \begin{center} \begin{tabular}{l|ccc}    &amp; $\Delta_f H^{\ominus}$ &amp; $\Delta_f G^{\ominus}$ &amp; $C_P$ \\    &amp; \si{\kilo\joule\per\mole} &amp; \si{\kilo\joule\per\mole} &amp; \si{\joule\per\kelvin\per\mole} \\ \midrule \ce{NO2} &amp; \calcnumd{\dhfbiox} &amp; \calcnumd{\dgfbiox} &amp; \calcnumd[4]{\cpbiox} \\ \ce{N2O4} &amp; \,\,\,\calcnumd{\dhftetrox} &amp; \calcnumd{\dgftetrox} &amp; \calcnumd{\cptetrox} \\ \bottomrule \end{tabular} \end{center}  \end{document} Possible Duplicate:          I'm working on a website that displays distance to various locations to the nearest 1/10 mile. One of the developers (a non-native speaker) asked me an interesting question: If the distance is 1.0 mile(s), is that singular or plural? Clearly, anything other that 1.0 is plural, but is it:     1.0 miles away   or     1.0 mile away   The first option sounds more correct to my ear, but the voice of my elementary school language arts tells me that the latter option is correct.  Edit: Added the word 'away' to the example. It doesn't change the question, but might provide clarity for the answer. Also, regarding numbers between 0 and 1, after more thought, I'm not sure that the answer is as clear as I originally thought. See . Can a class overload methods that also exist in the publicly inherited interface? It seems like this is unambiguous and useful, but compilers (VC, Intel, GCC) all complain, at least by my construction. Below is a toy example. The inherited rebound() function has two clear overloads, yet this will not compile.  If you rename the rebound() method in either class, it works fine, but if they share the same member function name (even though they're overloaded with different argument types!) you get a fatal error of "too few arguments to function call."  The workaround is trivial (I'll just rename the methods) but I'm just trying to understand if this is a C++ restriction (and why it would be).   #include  class Bound { public:   Bound() : x0(0.0), x1(0.0) {};   Bound(double x) : x0(x), x1(x) {};   double width() const {return x1-x0;}   void rebound(const Bound *a, const Bound *b); private:   double x0, x1; };  void Bound::rebound(const Bound *a, const Bound *b) {   if (a && b) {     x0=std::min(a->x0, b->x0);     x1=std::max(a->x1, b->x1);   } }  class Node : public Bound { public:   Node(double x) : Bound(x), left(0), right(0) {};   Node(Node *a, Node *b) : left(a), right(b) {rebound();}   void rebound() { rebound(left, right); } private:   Node *left;   Node *right; };   int main() {   Node A(1.0);   Node B(2.0);   Node C(&A, &B); } Sometimes when adding an object to the scene I see that all options (on toolbar or in window after pressing F6) are disabled. Can anyone tell me when can this happen? What is causing it and how to revert it - make it enabled again. It worked for me when I restarted Blender and reloaded the scene. However I would really like to know what can cause it? Reflection to Identify Extension Methods In C# is there a technique using reflection to determine if a method has been added to a class as an extension method?  Given an extension method such as the one shown below is it possible to determine that Reverse() has been added to the string class?  public static class StringExtensions {     public static string Reverse(this string value)     {         char[] cArray = value.ToCharArray();         Array.Reverse(cArray);         return new string(cArray);     } }   We're looking for a mechanism to determine in unit testing that the extension method was appropriately added by the developer.  One reason to attempt this is that it is possible that a similar method would be added to the actual class by the developer and, if it was, the compiler will pick that method up. OK guys I have this problem:  For $x,y,p,q&gt;0$ and $ \frac {1} {p} + \frac {1}{q}=1 $ prove that $ xy \leq\frac{x^p}{p} + \frac{y^q}{q}$  It says I should use Jensen's inequality, but I can't figure out how to apply it in this case. Any ideas about the solution?