Spectrum of a positive operator
Positive operator has a positive spectrum?
Seeking open source solution to access rasters in File Geodatabase? I'm looking for a way to access raster layers in an Esri File-GeoDatabase without using ArcObjects or ArcPy, specifically I would like to access the raster layers with GDAL. I understand that the GDAL FileGDB and OpenFileGDB give access to vector datasets within File-GeoDatabases, and that ESRI's own FileGDB C++ API does not support raster access.   Is anyone out there aware of any open source solutions? Why Listen to Music, why not Listening Music Maximum time I face this problem by saying listening music. Is there any traditional cause behind this?  Can we use listen music or listening music?  Seems there is only a slight difference, but why is listen to music the right way to say it? Unwanted faint lines connecting dashed double line Building on the answer  by wrtlprnft, I have the following code     \documentclass[tikz,margin=1cm]{standalone}    \usetikzlibrary{decorations.markings}    \begin{document}    \begin{tikzpicture}         \tikzstyle{arrowed double line}=[             dashed, double distance between line centers=3pt,             postaction=decorate,             decoration={                 markings,                 mark=between positions 10pt and -10pt step 20pt with {                     \arrow[thin,yshift= 1.5pt,xshift=.8pt]{&gt;}                     \arrow[thin,yshift=-1.5pt,xshift=.8pt]{&lt;}                 },             },         ]         \draw[arrowed double line] (0,0) --  (1,2);     \end{tikzpicture} \end{document}   which produces this:    I am unhappy with the faint transverse lines between the dashes. I don't even know why tikz decides to draw them.  Is there a way to get rid of them?  Thanks in advance to all replies.  PS the same thing occurs at the caps of double solid lines Books for Condensed Matter after Ashcroft/Mermin What are some good condensed matter physics books that can fill the gap between Ashcroft &amp; Mermin and research papers? Suggestions for any specialized topics (such as superconductivity, CFT, topological insulators) are welcomed. I recently reviewed a paper (general applied mathematics context). During the review, I realized that the fairly general ideas introduced in the paper can potentially be applied to a specific problem in a similar context. The authors did not mention this application in their paper, so I suggested to add a short comment about it in my review.  I later started thinking about the application in more detail and tried out some things, which actually seem to work quite well for this application. Now, the paper is still in the review process and might take some time until it gets published. What is the proper way how to proceed here in order to use the ideas and results which I in my exclusive position as a reviewer saw? How can I refer to the paper that is still under review? How can I best discuss the ideas with my co-workers (and potential co-authors) without disclosing that I reviewed the paper?  The paper under review is not available online on any preprint servers such as arXiv etc Faithful group actions for singleton group or for empty set Let $G$ be a group, possibly a singleton. Let $M$ be a set, possibly empty. Let $\mu: M \times G \to M$ be a right group action. Let $1_G$ be the identity of $G$.  I understand 's second definition of faithful as follows:     $\mu$ is faithful if for each $g \in G$ such that $g \ne 1_G$, there exists $x \in M$ such that $\mu(x,g) \ne x$. $\tag{1}$   Later  says if $\mu$ is free and $M$ is a non-empty set, then $\mu$ is faithful.  Question: Given the idea that we can have $M$ as an empty set, I would like to clarify: Are these correct?   If $G$ is a singleton, then every action $\mu$ is faithful, whether or not $M$ is empty. If $G$ is not a singleton, but $M$ is empty, then every action $\mu$ is not faithful. Regex exec only returning first match Are if and whether equivalent in sentences like the ones below?     How to determine if my saddle is too high?   How to determine whether my saddle is too high?         We should check if everything is okay now.   We should check whether everything is okay now. If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed I'd like to know if the following proof is valid.  The only thing I'm not sure about (though I can't see why it's invalid if it is) is if we can always use the Hausdorfness of $Y$ to separate an open set from $f(C)=g(C)$.  "Let $X$ be a space, $Y$ a $T_2$-space, and $f,g:X \to Y$ continuous functions.  Prove that $C:=\{x \in \,|\,f(x)=g(x)\}$ is a closed subset of $X$."  Let $x \in X$ be such that $f(x) \ne g(x)$.  Since $Y$ is $T_2$, there are open sets $U_\alpha \ni f(x)$ and $V_\alpha \ni g(x)$ such that $U_\alpha \cap O_\alpha=V_\alpha \cap O_\alpha=\varnothing$ for all $\alpha \in A$ where $A$ is the set indexing the points of $f(C)=g(C)$, and $O_\alpha$ is an open set containing $x_\alpha \in f(C)=g(C)$.  Let $U:=\displaystyle\bigcap_{\alpha \in A} U_\alpha$ and $V:=\displaystyle\bigcap_{\alpha \in A} V_\alpha$.  Then $U \cap f(C)=V \cap f(C)=\varnothing$.  Therefore, since $f,g$ are continuous, $f^{-1}(U)$ and $g^{-1}(V)$ are open sets in $X$ disjoint from $C$.  Since $X\setminus A$ is the union of such open sets, it is open itself and therefore $C$ is closed.  Thanks. How does the coin limit work? I would be happy to get some hints on the following integral: $$ \int_0^1\frac{x^{19}-1}{\ln x}\,dx $$ Few application icons not appearing in Ubuntu Dock after upgrading to Ubuntu 17.10 Is there PvP in Diablo 3? How does it work? How can I change the local origin of an object, without changing the object location in the world space.  This is the object located at position (0,0,0) in the world space    This is the same object located at position (0,1,0) in the world space, but with its local origin offset so that the object is in the same place    Is there a way to do this in a single step? In a triangle $\angle A = 2\angle B$ iff $a^2 = b(b+c)$ Prove that in a triangle $ABC$, $\angle A = \angle 2B$, if and only if:  $$a^2 = b(b+c)$$  where $a, b, c$ are the sides opposite to $A, B, C$ respectively.   I attacked the problem using the Law of Sines, and tried to prove that if $\angle A$ was indeed equal to $2\angle B$ then the above equation would hold true. Then we can prove the converse of this to complete the proof.   From the Law of Sines,   $$a = 2R\sin A = 2R\sin (2B) = 4R\sin B\cos B$$  $$b = 2R\sin B$$  $$c = 2R\sin C = 2R\sin(180 - 3B) = 2R\sin(3B) = 2R(\sin B\cos(2B) + \sin(2B)\cos B)$$  $$=2R(\sin B(1 - 2\sin^2 B) +2\sin B\cos^2 B) = 2R(\sin B -2\sin^3 B + 2\sin B(1 - \sin^2B))$$  $$=\boxed{2R(3\sin B - 4\sin^3 B)}$$  Now,   $$\implies b(b+c) = 2R\sin B[2R\sin B + 2R(3\sin B - 4\sin^3 B)]$$  $$=4R^2\sin^2 B(1 + 3 - 4\sin^2 B)$$  $$=16R^2\sin^2 B\cos^2 B = a^2$$  Now, to prove the converse:  $$c = 2R\sin C = 2R\sin (180 - (A + B)) = 2R\sin(A+B) = 2R\sin A\cos B + 2R\sin B\cos A$$  $$a^2 = b(b+c)$$  $$\implies 4R^2\sin^2 A = 2R\sin B(2R\sin B + 2R\sin A\cos B + 2R\sin B\cos) $$  $$ = 4R^2\sin B(\sin B + \sin A\cos B + \sin B\cos A)$$  I have no idea how to proceed from here. I tried replacing $\sin A$ with $\sqrt{1 - \cos^2 B}$, but that doesn't yield any useful results. Classical car collision I have a very confusing discussion with a friend of mine.  2 cars ($car_a$ and $car_b$) of the same mass $m$ are on a collision course. Both cars travel at $50_\frac{km}{h}$ towards each other.  They collide. Ignoring any shreds and collateral damage, what is the speed of collision that the driver of $car_a$ felt?  What I mean is, if $car_a$ were to be driven into an infinite mass wall, what would the velocity be to replicate the damage caused by the initial collision? I recently upgraded a c# windows service to run as a 64 bit .net process. Normally, this would be trivial, but the system makes use of a 32-bit DLL written in C++. It is not an option to convert this DLL to 64 bit, so I wrapped the DLL in a separate 32 bit .net process and exposed a .net interface via remoting.  This is quite a reliable solution, but I would prefer to run the system as a single process. Is there any way I can load my 32 bit DLL into a 64 bit process and access it directly (perhaps through some sort of thunking layer)? PlotLegends won't generate automatically more than 15 labels in v10 How can I view all of the flights between two cities across all dates? I believe that the standard routes of carriers between two semi-major US cities always maintain the same route number (e.g. UA3271), and day of the week. I'm looking at planning travel for an interview, so dates are [currently] quite flexible (as in at least one month's range). Since that's the case, there are other constraints that go into my choice of flights. One would be the option to fly out of my home city, land in the interview location, conduct the interview, and fly out in the same day. I figure: if I can view the schedule for flights (i.e. routes) between the two cities, I can make an educated request for days of travel. Yes, I could likely work with the interview scheduler (and I will), but I'd like to be proactive in suggesting some dates to achieve my goal, as well as learn this skill for myself in the future. Thus:  Where can I view the daily routes and times for flights between two cities, on whatever rotating basis (e.g. day of the week) they may be on? I love making our own bread - we rarely buy shop bought, but it tends to go off very quickly. Part of the appeal is that it doesn't have any "junk" in it - artificial preservatives - which I'm sure contributes to the lovely flavor. Is there anything natural I can add to it to stop it going moldy so fast?