Assigning correct permissions on a shared web server
FTP and Apache permission issues
If $f:E\rightarrow S$ is an elliptic curve over a scheme $S$ (so $f$ is proper and smooth of relative dimension one with geometrically connected fibers of genus one, equipped with a section $0:S\rightarrow E$), then is the sheaf $\underline{\omega}_{E/S}:=f_*\Omega_{E/S}^1$ actually free of rank one? According to the statement of Grothendieck-Serre duality in Hida's book Geometric Modular Forms and Elliptic Curves, there should be a canonical isomorphism $\underline{\omega}_{E/S}\cong\mathcal{Hom}_{\mathscr{O}_S}(R^1f_*\mathscr{O}_E,\mathscr{O}_S)$, and the first result on elliptic curves in this book is that $R^1f_*\mathscr{O}_E\cong\mathscr{O}_S$. It's also not clear to me whether $S$ is being assumed (locally) Noetherian, but if that's necessary for Grothendieck-Serre duality to hold, then I'm fine with assuming it. I can't find another reference with a statement of Grothendieck-Serre duality in this generality which does not use the language of derived categories (which I unfortunately don't understand).  The reason I'm kind of skeptical about this is that in Hida's book, as well as in Katz-Mazur, it is said that $\underline{\omega}_{E/S}$ is invertible, so that an $\mathscr{O}_S$-basis $\omega$ for $\underline{\omega}_{E/S}$ can be found locally on $S$. If the invertible sheaf in question were really trivial then one would be able to choose a global $\mathscr{O}_S$-basis for $\underline{\omega}_{E/S}$, and there would be no reason to talk about doing so locally. Hida goes on to say that, choosing an $\mathscr{O}_S$-basis $\omega$ locally on $S$ allows one to regard $(\Omega_{E/S}^1,\omega)$ as a relative effective Cartier divisor in $E/S$, which also doesn't make complete sense to me because if we can only find $\omega$ locally, how are we getting a global section $\omega\in H^0(E,\Omega_{E/S}^1)=H^0(S,\underline{\omega}_{E/S})$ (unless $\underline{\omega}_{E/S}$ really is trivial)? Positive series problem: $\sum\limits_{n\geq1}a_n=+\infty$ implies $\sum_{n\geq1}\frac{a_n}{1+a_n}=+\infty$ Export File Dialog in Blender 2.80 How can I get bring up a popup file browser in Blender 2.80 invoked by a button click in my addon, to define the name and location of a file to be exported?  In Blender 2.7x, I did this via the context window manager in the invoke function, but it is very possible that this hasn't been the preferred method for years, as I'm not finding useful documentation when I search for how to update this.  class MYTOOL_OT_write_data(bpy.types.Operator):     bl_idname = "mytool.write_data"     bl_label = "Write data file"      directory: bpy.props.StringProperty(subtype="FILE_PATH")     filename: bpy.props.StringProperty(subtype="FILE_NAME")      def invoke(self, context, event):  # 2.7x method         WindowManager = context.window_manager         context.window_manager.FILEBROWSERect_add(self)  # &lt;-- error here         return{"RUNNING_MODAL"}      def execute(self, context):         directory = self.directory         filename = self.filename         # Write csv data file using normal python functionality         return{'FINISHED'}   In Blender 2.80, I am getting the error "AttributeError: 'WindowManager' object has no attribute 'FILEBROWSERect_add'".  Thanks for your help.    UPDATED SOLUTION based on brockmann's solution below.  The trick is to use the ExportHelper util (which existed long before Blender 2.80):  from bpy_extras.io_utils import ExportHelper  class MYTOOL_OT_write_data(bpy.types.Operator, ExportHelper):     bl_idname = "mytool.write_data"     bl_label = "Write data file"      filename_ext = ".csv"  # ExportHelper mixin class uses this     def execute(self, context):         filepath = self.filepath         # f = open(filepath, 'w')         # f.write(stuff)         # f.close()         return{'FINISHED'} Value of $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}}$ Here is the question:     $$\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}} = \;?$$   ()  I think we need to simplify it writing it in summation sign as you can see here:  $$\frac{\sum\limits_{n=1}^{99} \sqrt{10 + \sqrt{n}}}{\sum\limits_{n=1}^{99} \sqrt{10 - \sqrt{n}}}$$  or in Wolfram Alpha input in comments.  I can compute it too! It's easy to write a script for this kind of question. I need a way to solve it. How would you solve it on a piece of paper? Error in fontspec (my first question here) I'm using xelatex to compile this code:  \documentclass{book} \usepackage{fontspec}  \begin{document}  %This is a Greek text ``Ελλάδα'' text  \end{document}   and receive this error :  ("C:\Program Files\MiKTeX 2.9\tex\latex\fontspec\fontspec.cfg") ! Undefined control sequence. &lt;argument&gt; \LaTeX3 error:                             Erroneous variable \c__fontspec_shape_n_n_tl used! l.3806 \emfontdeclare{ \emshape, \eminnershape }   My aim is to make LaTeX compile greek letters properly in my pdf, but that's a different issue. How should I transform non-negative data including zeros? If I have highly skewed positive data I often take logs. But what should I do with highly skewed non-negative data that include zeros? I have seen two transformations used:   $\log(x+1)$ which has the neat feature that 0 maps to 0. $\log(x+c)$ where c is either estimated or set to be some very small positive value.   Are there any other approaches? Are there any good reasons to prefer one approach over the others? I am trying to print a List of Appendices (LoA) for my thesis, separate from the Table of Contents (ToC).   I wish for my ToC to look like this, with depth up to subsections (2?):  CONTENTS  CHAPTER   I. Introduction......1    1.1 Section title...1     1.1.1 Subsection...1  Appendices ..... 2   and for an LoA on a new page, with depth 0, thus:  APPENDICES  APPENDIX A. Proof of Theorem 1...1 B. Proof of Theorem 2...1   I am trying to achieve this using the report class, in a way that allows me to type appendices using the hierarchy that I obtain from the chapter, section commands. This is as opposed to defining a custom myappendix command into which I insert my appendix content. (I realize that I only need the titles from the appendix chapters for the LoA, but I'd like for the appendix content to have such structure.)   For instance, this approach would solve my problem:   \chapter{Introduction} \section{Section title} \subsection{Subsection} % \begin{appendices} is also acceptable \appendix   % Some settings are changed now \chapter{Proof of Theorem 1} \chapter{Proof of Theorem 2} % \end{appendices} if environment is begun   whereas the following approach would not:  \chapter{Introduction} \section{Section title} \subsection{Subsection} \myappendix{Proof of Theorem 1} \myappendix{Proof of Theorem 2}   I realize several questions have been asked regarding this before, but none of them quite solved my problem. Notably,  defines a custom appendix command;  defines two custom commands to maintain some hierarchy, but I will have to do more work to handle the inclusion of another layer (subsection) into the appendix.    is the closest to what I want: it does give me a separate LoA, but it also adds appendices to ToC and I can't quite figure out how to suppress the entires in ToC. The moment I use   \addcontentsline{toc}{\setcounter{tocdepth}{-1}}   the line   \xpatchcmd{\@chapter}{\addcontentsline{toc}}{\addcontentsline{toa}}{}{}%   fails because I am not adding anything to the ToC anymore.   My approach: Since I was using titlesec and tocloft packages anyway, I tried to do the following:   Stop ToC once appendix command is issued Start a new counter for appendices using tocloft Using the &lt;after-code&gt; option of titlesec, add contents line after every chapter.    My MWE   \documentclass[a4paper]{report} \usepackage{lipsum} % for arbitrary text  \usepackage{tocloft,etoolbox,titlesec} \newcommand{\listappendixname}{List of Appendices} \newlistof{appendix}{apc}{\listappendixname}  \makeatletter \g@addto@macro{\appendix}{     \clearpage     \addcontentsline{toc}{chapter}{Appendices}     \addtocontents{toc}{\protect\setcounter{tocdepth}{-1}}     \titleformat      {\chapter}      [display]     {\huge\bfseries\filcenter}      {\Large \MakeUppercase{\@chapapp} \thechapter}      {1.5ex}{}     {\refstepcounter{appendix} \addcontentsline{apc}{appendix}{\protect{\@chapapp \thechapter}}} } \makeatother  \title{Title} \author{Author}  \begin{document} \maketitle \tableofcontents \clearpage \listofappendix  \chapter{Introduction} \lipsum[1] \section{Section} \lipsum[2] \subsection{Subsection} \lipsum[3]  \appendix  \chapter{Proof of Theorem One} \lipsum[4] \chapter{Proof of Theorem Two} \lipsum[5]  \end{document}   produces the following LoA:  List of Appendices  Appendix...... 5   It doesn't get the Appendix title or number, and fails after the first one.  Could you please help me obtain a separate LoA in a way that I can still use LaTeX's chapter, section, ... hierarchy? (I am okay with using different packages, the book class, or any approach other than mine.) When trying to deploy the converted metadata using VS code sfdx force:mdapi:deploy deploy to my Production Org and I get the error Property 'itemInstances' not valid in version 48.0 and Property 'processOrder' not valid in version 48.0. But when I go to Developer Console and open a class, even though it says 48.0, I have the option to select 49.0, so I am assuming I have 49.0. Yet I get this error. Pretty much all my classes, trigger and components are version 48.0, but I am not sure how that affects flexipages and Approval processes. Why None is the smallest in python? Irreducible cyclotomic polynomial Show the two fields are not isomorphic Let $p,q,r$ be prime integers with $q\neq r$. Let $\sqrt[p]q$ denote any root of $x^p-q$ and $\sqrt[p]r$ denote any root of $x^p-r$. Please show that $\mathbb{Q}(\sqrt[p]q)\neq\mathbb{Q}(\sqrt[p]r)$.  By Eisenstein we know the two polynomials are irreducible and so they are minimal polynomials and both have degree $p$. How do I execute PHP that is stored in a MySQL database? I'm trying to write a page that calls PHP that's stored in a MySQL database. The page that is stored in the MySQL database contains PHP (and HTML) code which I want to run on page load.  How could I go about doing this? Zombies are always after human beings. How do Zombies differentiate between a zombie and a human being? Why don't zombies eat each other? I am making a test where I am asked to add the missing words.     [...] chair is [...] useful piece of furniture.    I would have said that a is the missing word in both the cases, but the test says the words I should have added are the and a respectively.     [...] last time I saw [...] bear, I was travelling in [...] Europe.   I would have added: nothing, a, nothing. The correct answer is: the, a, nothing.  Why is the the correct article to use in both the sentences? What are the technical differences between using a DSLR viewfinder and live view? The earlier question  asks for practical advantages of optical viewfinders. But what's the technical difference, and why does a camera behave differently in each mode?  For example, on my Nikon D5100:   Slower auto-focus — I saw this explained in the related issue, but just partially: "The other major drawback of live view is that because it requires the mirror to be locked up, it means that the auto focusing mechanism is unavailable."  option not available. No . The manual says that it's dangerous to shoot direct light, when it's on live-view. There's no range finder available.   Why are all these things different?  Live view also has some advantages, like:   automatic scene selection grid lines on the screen other smaller things, like possibly easier operation on a tripod where the viewfinder might be inconvenient to look through   Some of these things, like the tripod operation, are natural. But are there technical reasons the others can't be done with an optical finder? Are there other advantages enabled by live view for technical reasons? How do I evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.  I have tried to use binomial expansion and combine factorials, but I have gotten nowhere. I don't really know how to start this problem.  The answer is ${n+m \choose n}$. Any help is greatly appreciated.  EDIT: I'm looking for  a proof of this identity. Square version of \cdot (small black square)? I'm looking for the symbol that's similar to \cdot in math mode, but instead of a small circle, it's a square. Like this: Compute: $\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)$ where $A_n = \frac{1}{n}(a_1 + a_2 + \cdots + a_n)$ Invalid token 'while' in class, struct, or interface member declaration in very simple code I am not sure what the problem is but I keep receiving this error when I try to use a while statement in my code.     Invalid token 'while' in class,   struct, or interface member   declaration   I want to use a while loop to have something continuously update while a statement is true.  The rest of my code is rather long but whenever I type in the syntax:  while(a&lt;b) { //do whatever i want it to do here }   It gives me that compiler error right off the bat. Not quite sure what the problem is. I am doing this in a C# windows application under the Form1.cs file with all the other event handlers (for buttons and such).  Thanks!    I was unaware that loops had to be placed within a method (fairly new to c#), but I tried it and no errors were returned. Thanks for your help everybody!  Previously, I just had the loop within the main class of the program. Why are SMD LEDs shipped in a sealed bag containing desiccant? I had a selection of 0805 LEDs in my last Mouser order and was a bit surprised to discover they arrived in heat-sealed (rather than folded and taped with sticker) bags containing a desiccant bag and some sort of litmus-esque paper indicator saying something about baking them if the dots on it went pink (instead of blue).    A quantity of through-hole LEDs I had in the same order just came in the regular ESD-protective bag, folded over with a sticker.  What's up with SMD LEDs that they work so hard to keep them dry? Surely their dryness can't be assured once they're installed. Does it have to do with their solderability or something? Why would that be different than other SMD parts?