CSS challenge, can I do this without introducing more HTML?
CSS technique for a horizontal line with words in the middle
Finding a set of continuous functions with a certain property 2 I need help finding the set of continuous functions $f : \Bbb R \to \Bbb R$ such that for all $x \in \Bbb R$, the following integral converges:  $$\int_0^1 \frac {f(x+t) - f(x)} {t^2} \ \mathrm dt$$  I think it might be the set of constant functions but i havent been able to prove it :(   I was thinking that you can use the stone weiestrass theorem considering the set of continuous functions on a closed  interval(non trivial) ,and a subset which contains the set of continuous functions whose integral above diverges in some point in that interval along with  with the set of constant functions. So in order to solve the problem i need only to prove that if two functions do not meet the condition of the problem then their product does not as well .  I hope you can provide some insight and thank you . What is the difference between 'can', 'could', 'may' and 'might'? I'm a native English speaker and I've been doing some research into English grammar for a programme I'm working on. However, on looking into modal verbs, I've only just come to appreciate how subtle and complicated they are.  What is the difference between these sentences? What possible different response might one have to each?        I can go to the cinema tonight.   I could go to the cinema tonight.   I may go to the cinema tonight.   I might go to the cinema tonight.      Granted, the first of these looks more like a statement of ability or possibility than the three that follow. But in what ways does it differ from the others, since all suggest ability and possibility? And crucially, what distinguishes the other three.  Perhaps it's a matter of tone, of context, of the speaker... The question may appear quite simple but I haven't found a satisfactory answer elsewhere.    looked quite useful in that it covered levels of confidence and certainty but it was talking about the potential state of something rather than the possibility for the person who is speaking. Are there any differences in that sense?   looked at these verbs used in question form (e.g., differences between 'Can I...?' and 'May I...?') but I'm not so interested in that for now.  Any thoughts appreciated. Connected graph with colored edges We have connected undirected graph with colored edges in two way (green or blue). And also each vertex have the same number of green and blue edges. How to prove that there are alternate colored (green-blue) path between any two nodes? I am trying to build a computer, placing an  in a custom .  The case is an extra small form factor which can accommodate the Mini ITX board, but it requires an external power supply, similar to the power-bricks that laptops use.  I am looking at different power supplies and like , but I cannot figure out whether/how to power this system, because they provide a 24-pin connector, but the motherboard has a 4-pin connector as well.  Is the 4-pin connector optional or is it required? If it is required, how can I provide power for this system? How do you take off body armor in GTA Online? It's kind of hard to shop for clothes with a big bullet proof vest on.  Is there a way to take off the armor after missions, or at least hide it? Two functions $f:A\rightarrow B$ and $g:B\rightarrow A$. Can someone give me an example where $g\circ f=id_A$ but $f\circ g\neq id_B$? Is there a way to test an application where you simulate a hundred different clients connecting to a IIS server and asking the same data? At the customer where our project is running they have 400 computers and they often do stress tests with all computers. I on the other hand have only got my laptop... (and a development server).  (In my case the data is asked through a WebORB Gateway). I want to see if my process makes a lot of context switches. I also want to see how manpulating task groups affects the number of context switches. Correlation between dichotomous and continuous variable I am trying to find the correlation between a dichotomous and a continuous variable.  From my ground work on this I found that I have to use independent t-test and the precondition for it is that the distribution of the variable has to be normal.  I performed Kolmogorov-Smirnov test for testing the normality and found that the continuous variable is non-normal and is skewed (for about 4,000 data points).   I did the Kolmogorov-Smirnov test for the entire range of variables. Should I split them into groups and do the test? I.e., say if I have risk level (0 = Not risky, 1 = Risky) and cholesterol levels, then should I:    Divide them into two groups, like  Risk level =0 (Cholestrol level) -&gt; Apply KS Risk level =1 (Cholestrol level) -&gt; Apply KS  Take them together and apply the test? (I performed it on the whole dataset only.)   After that, what test should I do if it is still non-normal?    EDIT: The above scenario was just a description I tried to provide for my problem. I have a dataset which contains more than 1000 variables and about 4000 samples. They are either continuous or categorical in nature. My task is to predict a dichotomous variable based on these variables (maybe come up with a logistic regression model). So I thought the initial investigation would involve finding the correlation between dichotomous and a continuous variable.  I was trying to see how the distribution of the variables are and hence tried to go to t-test. Here I found the normality as an issue. The  Kolmogorov-Smirnov test gave a significance value of 0.00 in most of these variables.  Should I assume normality here? The skewness and kurtosis of these variables also show that the data is skewed (>0) in almost all cases.  As per the note given below I will investigate the point-biserial correlation further. But about the distribution of variables I am still unsure. "How" vs. "that" in "You know how we have pizza on Thursdays, right?" From time to time I hear sentences like this:      You know how we have pizza on Thursdays, right?   Here, how doesn't mean exactly how those guys eat pizza, it is something like "that" in this context.   So what is the difference between using how, that or just skipping the conjunction? Can I connect to a sandbox using JWT Flow and Prod connect app? I'm trying to connect to a sandbox using the sfdx cli and the JWT flow through force:auth:jwt:grant. According to , we can use the same connected app information from Production to connect to our Scratch Org.  Is it something that should work for sandbox too ? I'm getting a "Failed: Not approved" error.  Connected app in sandbox comes from the refresh but has a different consumer key. The Permission set is set correctly on my user.  Is there a way to connect to a recently refreshed sandbox using the JWT flow (without manually changing something like the consumer key) ? Various \textcolor within lstlisting? Zero module of differentials implies finite extension? I had one batch class in which i am passing some data required for creating object record.But when i call that batch class from parent class variables are initialized but start method are not called as there is no record to query i also tried with iterable object but not able to do that.My code is as below  global class testBatchClass implements Database.Batchable&lt;SObject&gt;,Database.Stateful{     public List&lt;sObject&gt; sObjectList;     public string objectName;     public String dataList;      public testBatchClass(String objectName,String inputdata){          String listType = 'List&lt;'+objectName+'&gt;';         system.debug('list type value is'+listType);         List&lt;SObject&gt; castRecords = (List&lt;SObject&gt;)Type.forName(listType).newInstance();         this.sObjectList = castRecords;         this.objectName = objectName;         this.dataList = inputdata;      }     global Iterable&lt;SObject&gt; start(Database.BatchableContext batchableContext) {         return new sObjectList{};     }     global void execute(Database.BatchableContext batchableContext, List&lt;sobject&gt; scope){          List&lt;OpportunityRenewal__mdt&gt; mdtList = new List&lt;OpportunityRenewal__mdt&gt;([Select id,Api_Name_of_Fields__c,Sobject_Name__c from TestFileUploadCustomSetting1__mdt where Sobject_Name__c=:objectName]);         List&lt;String&gt; fieldName = new List&lt;String&gt;();         for(OpportunityRenewal__mdt md : mdtList){             if(md.Sobject_Name__c == objectName){                 fieldName = md.Api_Name_of_Fields__c.Split(',');                 break;             }         }         List&lt;String&gt; dataRowsSplit= dataList.split(',');         dataRowsSplit.remove(0);         for(String eachRow: dataRowsSplit){             List&lt;String&gt; splitString = eachRow.Split(',');             sObject sobj = Schema.getGlobalDescribe().get(objectName).newSObject();             for(Integer i=0; i &lt;= splitString.Size(); i++){                 sobj.put(fieldName[i],splitString[i]);             }             scope.add(sobj);         }         if(scope != Null &amp;&amp; scope.Size() &gt; 0){             upsert scope;         }     }      global void finish(Database.BatchableContext batchableContext) {} }   Thanks In the Wikipedia article , it says     After Newtonian gravitation was found to be inconsistent with special relativity, . . .   I don't see how Newtonian gravitation itself is inconsistent with special relativity.  After all, Newton's Universal Law of Gravitation is completley analogous to Coulomb's Law, so it would seem that, if there were an analogous "gravitational magnetic field", one could formulate a theory of gravitation in exact analogy with Maxwell's Theory of Electromagnetism, and of course, this would automatically be consistent with Special Relativity.  What about this approach to gravitation does not work?  The only problem I could see with this is the lack of evidence for a "gravitational magnetic field".  That being said, gravity is "weak" as it is, and my guess is that it would be extremely difficult to set up an experiment in which a massive body were moving fast enough for this "magnetic field effect" to be obsevable.  EDIT:  As has been pointed out to me in the answers, Newton itself is inconsistent with SR.  Similarly, however, so is Coulomb's Law, yet, electromagnetism is still consistent with SR.  Thus, how do we know that it is not the case that Newton's Law is the special "static" case of a more general gravitomagnetic theory exactly analogous to Maxwell's Theory:  Let $\mathbf{G}$ be the gravitation field, let $\rho$ be the mass density, and $\mathbf{J}$ be the mass current density, let $\gamma _0$ be defined so that $\frac{1}{4\pi \gamma _0}=G$, the Universal Gravitation Constant, let $\nu _0$ be defined so that $\frac{1}{\sqrt{\gamma _0\nu _0}}=c$, and suppose there exists a field $\mathbf{M}$, the gravitomagnetic field, so that the following equations hold: $$ \vec{\nabla}\cdot \mathbf{G}=-\frac{\rho}{\gamma _0} $$ $$ \vec{\nabla}\cdot \mathbf{M}=0 $$ $$ \vec{\nabla}\times \mathbf{G}=-\frac{\partial \mathbf{M}}{\partial t} $$ $$ \vec{\nabla}\times \mathbf{M}=\nu _0\mathbf{J}+\gamma _0\nu _0\frac{\partial \mathbf{G}}{\partial t} $$ where theses fields would produce on a mass $m$ moving with velocity $\mathbf{v}$ in our inertial frame the Lorentz force $\mathbf{F}=m\left( \mathbf{G}+\mathbf{v}\times \mathbf{M}\right)$.  This theory would automatically be consistent with SR and would reduce to Newton's Law of Gravitation for the case of gravitostatics:  $\frac{\partial \mathbf{G}}{\partial t}=\frac{\partial \mathbf{M}}{\partial t}=\mathbf{J}=0$.  (To be clear, you can't just set the time derivatives equal to $\mathbf{0}$ as it seems I have done.  Upon doing so, you obtain the corresponding static theory, which is technically incorrect (as you can easily see because it won't be relativistically invariant), but is nevertheless often a useful approximation.)  My question can thus be phrased as:  without appealing directly to GR, what is wrong with this theory? Triple integral limits over pyramid Share your experiences on exploring iOS 7 with us..  Whether you found hidden or little-known feature of iOS 7 or can explain how a big feature makes a difference, we're looking for objective reports of how the new OS affects your workflow.  Also provide details on how to achieve that feature, and if possible, include a relevant image too (hold Home and Lock for a screenshot on your iOS device).    Please post one tip per answer. Please also check to see if your answer has already been posted - duplicate answers will be deleted in favour of the original answer on any given topic. To search answers for this question use inquestion:101382 (or inquestion:this, directly from the question page) in addition to your search terms in the search box in the upper right hand corner of this page. Drawing a 3D cylinder, and a circle shape on the x---y plane I'm trying to draw a cylinder on the three dimensional space, and I also want its projection on the x--y plane. I found the first answer  to be very useful. I just copy-paste it to my document, and modify it as follows (the modifications are only inside the \begin{tikzpicture} tags):   \documentclass[parskip]{scrartcl} \usepackage[margin=15mm]{geometry} \usepackage{tikz}  \pgfmathsetmacro{\xdeg}{30} \pgfmathsetmacro{\xx}{cos(\xdeg)} \pgfmathsetmacro{\xy}{sin(\xdeg)}  \pgfmathsetmacro{\ydeg}{120} \pgfmathsetmacro{\yx}{cos(\ydeg)} \pgfmathsetmacro{\yy}{sin(\ydeg)}  \pgfmathsetmacro{\zdeg}{80} \pgfmathsetmacro{\zx}{cos(\zdeg)} \pgfmathsetmacro{\zy}{sin(\zdeg)}  \newcommand{\tdcyl}[5]{% origin x, origin y, origin z, radius, height     \path (1,0,0);     \pgfgetlastxy{\cylxx}{\cylxy}     \path (0,1,0);     \pgfgetlastxy{\cylyx}{\cylyy}     \path (0,0,1);     \pgfgetlastxy{\cylzx}{\cylzy}     \pgfmathsetmacro{\cylt}{(\cylzy * \cylyx - \cylzx * \cylyy)/ (\cylzy * \cylxx - \cylzx * \cylxy)}     \pgfmathsetmacro{\ang}{atan(\cylt)}     \pgfmathsetmacro{\ct}{1/sqrt(1 + (\cylt)^2)}     \pgfmathsetmacro{\st}{\cylt * \ct}     \filldraw[fill=white] (#4*\ct+#1,#4*\st+#2,#3) -- ++(0,0,#5) arc[start angle=\ang,delta angle=-180,radius=#4] -- ++(0,0,-#5) arc[start angle=\ang+180,delta angle=180,radius=#4];     \filldraw[fill=white] (#1,#2,#3+#5) circle[radius=#4]; }       \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h         \tdcyl{0}{0}{0}{1}{3} % x y z   r h           \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}     \end{document}   I added another cylinder and tweaked the positions to fit what I need. This produces the following:      Which is almost what I want, except that I want to see the projection of that cylinder on the x--y plane, but unfortunately, the top cylinder hides the full circle. When I disable the top cylinder:      \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h            \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}   Now the projection is shown again:   But the top cylinder is missing...  How can I make the top cylinder transparent, or, alternatively, and even better; how do I create one long cylinder and emphasize its projection on the x--y plane?   BTW, what determines the position of the labels x,y,z in the above code? I want to reposition them so they won't overlap with the axis. Thanks in advanced! if $x+2y+z=4$ and $x,y,z$ are real number. then find maximum value of $xy+yz+zx$  putting $x+z=4-2z$ in $y(x+z)+zx = y(4-2z)+zx = 4y-2yz+zx$  i wan,t be able to  go further,could some help me with this How to move /usr to a new partition?