If $f$ is continuous function and $g(x):=f(x)\int_{0}^{x}f(t)dt$ given $g$ is non-increasing. Prove that $f(x)=0$, for all $x$.
A question about $f(x)\equiv 0$
Hide/Show field on list form based on value from another field I need to hide field 'B' when the value in field 'A' is NOT equal to 'Other'.  This is a custom list form.  Is jquery the way to go? I was wondering if there is any rule in English that forbids us to say A Happy New Year when we wish someone Happy New Year? I know that we just say it like that, but I was trying to find the rule which would explain this. Thank you for your help. sed one-liner to delete everything between a pair of brackets? I am working with some text that is full of stuff between brackets [] that I don't want. Since I can delete the brackets myself, I don't need the one-liner to do that for me, but I do need a one-liner that will remove everything between them.  What about parentheses () instead of brackets? If $n\ne 4$ is composite, then $n$ divides $(n-1)!$. I have a proof and need some feedback. It seems really obvious that the statement is true but it is always the obvious ones that are a little trickier to prove. So I would appreciate any feedback. Thank you!  Here is what I am asked to prove:     If $n$ is composite then $(n-1)! \equiv 0 \pmod n$.   Proof:  $n$ is composite $\implies n=ab$ where $a,b \in \mathbb{Z}$ and $0&lt;a,b&lt;n$.  Case 1: If $a=b$ then $n=a^{2}$. Now $n \mid (n-1)! \implies a \mid (n-1)!$, so $$\begin{aligned} (n-1)! &amp;\equiv 1\times 2\times \dotsb \times a \times\dotsb\times (n-a)\times\dotsb\times (n-1) \\ &amp;\equiv 1\times 2\times \dotsb\times a \times\dotsb\times -a\times\dotsb\times -1 \\ &amp;\equiv 0 \pmod n \end{aligned}$$  Case 2: $0&lt;a&lt;b&lt;n$.  Then, since $a \mid n$, $b \mid n$ and $n \mid (n-1)!$ we have that $a \mid (n-1)!$ and $b \mid (n-1)!$.  So this implies $(n-1)! \equiv 1\times 2\times \dotsb\times a \times\dotsb\times b\times\dotsb\times (n-1) \equiv 0 \pmod n$, Q.E.D. Get width of a given text as length PHP: Static and non Static functions and Objects Deleting Individual SE Accounts What is the Big-O time complexity of the following nested loops: for (int i = 0; i &lt; N; i++) {     for (int j = i + 1; j &lt; N; j++) {         System.out.println(&quot;i = &quot; + i + &quot; j = &quot; + j);     } }  Would it be O(N^2) still? How to make a file (e.g. a .sh script) executable, so it can be run from a terminal Proof of inequality using AM-GM inequality prove that $x^2 + y^2 + z^2 \ge xy + xz + yz$  I tried proving it the way I prove $x^2 + y^2 \ge 2xy$. But it just doesn't seem to work. I tried using AM-GM. Should I be using GM-HM or AM-HM? I really don't know what the problem is and I'd appreciate any help and a full proof explanation. Thanks. A characterisation of quadratic extensions contained in cyclic extensions of degree 4 How to do one-class text classification? I have to deal with a text classification problem. A web crawler crawls webpages of a certain domain and for each webpage I want to find out whether it belongs to only one specific class or not. That is, if I call this class Positive, each crawled webpage belongs either to class Positive or to class Non-Positive.  I already have a large training set of webpages for class Positive. But how to create a training set for class Non-Positive which is as representative as possible? I mean, I could basically use each and everything for that class. Can I just collect some arbitrary pages that definitely do not belong to class Positive? I'm sure the performance of a text classification algorithm (I prefer to make use of a Naive Bayes algorithm) highly depends on which webpages I choose for class Non-Positive.  So what shall I do? Can somebody please give me an advice? Thank you very much! Does *first of all* always go with *second of all*? According to , first of all is twice as popular as firstly, but secondly is a hundred times more popular than second of all.  When I present two points, do I have to be consistent in the choice of these phrases (if I use firstly, should the other be secondly)?  Because If I choose the most popular, my sentence would be like "First of all he is rich, secondly he is also smart." Which exhibits kind of inconsistency. How does it sound? 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'} What are the limits on how I can cast, change, and retract votes? Optimal tiling of polygon using ArcGIS Desktop? I am trying to tile a polygon with a minimal number of fixed sized squares.  Currently I am creating a fishnet over my polygon then spatially joining the squares that intersect the polygon. This is not optimal.  Also note the squares can be shifted vertically/horizontally but not rotated.  My end goal: The polygon represents a clipped image and I want a tiling of the clipped image. Where each tile is 300px by 300px. Some overlap is fine if that makes the problem easier.  Current    Manually optimized    Are there any tools or algorithms that would help with this? I am proficient with Python and ArcMap.  The polygon was created from line features so I also have access to those segments. Maybe that would will help for generating the squares.  The entire polygon must be covered. Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$? I wonder  whether there is a function $f\colon\Bbb R\to\Bbb R$ with the folowing characteristic?   for every two real numbers $\alpha,\beta,\alpha\lt\beta$,  $$\{f(x):x\in(\alpha,\beta)\}=\Bbb R$$   I can't  say such a function does not exist, neither can I construct a example  Thanks a lot! If $f,g : [a,b] \to (0,\infty)$ are continuous functions, prove that there exists $c \in (a,b)$ such that: $$\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$$ Dini's Theorem - Proof. I'd like to prove the following:  If $f_j$ are continuous functions on a compact set $K$, and $f_{1}(x) \leq f_{2}(x) \leq \dots$ for all $x \in K$, and the $f_j$ converge pointwise to a continuous function $f$ on $K$ then in fact the $f_j$ converge uniformly to $f$ on $K$.  Attempt:  Let $g_{j}(x) = f(x) - f_{j}(x)$ for all $j$. Then, since $f_j \rightarrow f$ pointwise, we see $g_j \rightarrow 0$ pointwise.  Now, let $\varepsilon &gt; 0$ . And examine { $x \in K : g_{j}(x) &lt; \varepsilon$ }.  I've been told that the next step should be to  show that { $x \in K : g_{j}(x) &lt; \varepsilon$ } is equal to the intersection of $K$ with some open set $U_j$. But I'm not certain why this is true?   Advice? Insight? How to list files installed by a snap package? After a snap has been installed with sudo snap install [package] how can I list the files which have been installed by the snap?