ERROR: 'Could not compile stylesheet' FATAL ERROR: 'java.lang.NullPointerException'
What is a NullPointerException, and how do I fix it?
The sign in the formula for the voltage across the inductor This question is about voltage induced in a inductance.  I know the rate of change of current induces EMF in the inductor. The direction of the induced EMF will be opposite to the change that is causing it. The EMF induced is given by the following formula.  $$V_l = -L \frac{dI}{dt}$$  The negative sign indicates direction of induced emf across the coil is opposite the current change.     In the picture I have drawn current direction and \$V_l\$ direction.  If \$\dfrac{dI}{dt}\$ is postive, \$V_l\$ will be negative according to formula right? Or does the direction of \$V_l\$ has to be reversed?  In many Internet references I found \$V_l = L \dfrac{dI}{dt}\$. Which one is correct?  I hope they reversed \$V_l\$ reference points and removed the negative sign in the formula. Please clarify. Blackboard bold variants for Greek letters It is common (or it used to be) to use a blackboard-bold variant of \mu to denote roots of unity in some mathematical papers.  However, despite searching (several times, periodically over several years) I have never been able to locate any package or technique that makes this possible, other than using Metafont or possibly hunting through the font definitions to see if it is something I can create a variant of (along the lines of the suggestions in Section 8 of the Comprehensive LaTeX symbol list).  Thus far, I haven't been sufficiently motivated to learn how to do any of this (although it probably would have resulted in a net time savings), and I feel like I cannot be the only person who would have tried.  Is anyone aware of an existing way to produce this character? Photons acting as carriers of both attractive and repulsive forces I understand, in basic terms, how a photon, whilst not being electrically charged itself, is viewed as creating electrical repulsion by means of positive momomentum transfer between two negatively charged electrons.  In most introductory quantum mechanics and basic quantum field theory textbooks this repulsive momementum transfer picture is almost always used as a (in classical terms) billiard ball type illustration for electrical repulsion, the Compton effect and so on.  As a photon is a photon is a photon..... I would like to know how it also has the ability to produce atttraction and how negative momentum transfer (such as that between a positively charged object, say a positron and an electron) is explained in any sort of visualisable picture. I'm guessing this may involve Feymann diagrams and the use of time reversal but I'm on shaky ground from there on. Is there a simple reason why the expected number of coin flips till getting $m$ more heads than tails or $n$ more tails than heads should be $mn$? I flip a coin until I get $m$ more heads than tails, or $n$ more tails than heads. Let the expected number of flips of the coin before stopping be $f(m,n)$.  I obtained $f(m,n)=mn$ from the recursion $f(m,n)=1+\frac{f(m-1,n+1)+f(m+1,n-1)}2$ with $f(k,0)=f(0,k)=0$ for all $k$.   Other than going through this recursion (and either solving by inspection or by writing as linear recurrence in single variable and solving brute force), is there an intuitive reason you should expect this process to take $mn$ flips? I was thinking about the more general problem with probability $p$ of getting heads and was struck by how simple the formula became when handling, what turned out to be a special case (general formula broke down) of $p=\frac12$. Why is the net speed of Stack Overflow so fast? This question is about the net speed.  I'm from China, and I find that opening pages on Stack Overflow is very fast, normally within a range of 1 to 4 seconds. This speed is very good for a website outside China; it's even faster than some native websites.  Not every website outside China has such good speed, so I am wondering why and how Stack Overflow manages to be so quick. Agreement With Compound Subjects Joined by And I was surfing the internet the other day when I found this phrase: Instead your precious time and attention is wasted. To my ears, it sounds wrong. But I'm not a native English speaker, so I consulted with a number of them, and some of them said that it was "is" because the adjective modifies only the noun "time" and not "attention". Others said it "is" because that's just how it is. But I still believe it should be "are". Any help is appreciated. If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general? How do they film continuous blood pooling? Do we actually get more sick (flu/cold) during winter? The word flu derives from the Italian phrase "influenza de freddo" meaning "influence of the cold".  Indeed it is that time of the year when my colleagues seem to have the flu/cold more often than not. I remember during university, winter lectures would be riddled with people coughing and sneezing - the so called "freshers flu"  Questions   Is there statistical evidence for this claim? If so, what are the causes/factors involved?   asks why our noses get runnier during cold whether, is this related? How to use only part of screen, as if the monitor was a smaller one? Water was sprayed on my 19" monitor and damaged some parts of it. I need a solution that will let me specify the screen area to be used by Windows, as if it was a smaller monitor. Its default menu doesn't have this option. How to read a windows registry file using java? So far, I didn't have the chance to use either of these services. Before starting, I would like to hear your opinions. What are the advantages and disadvantages? Why should I choose one over the other? I am mainly interested in the technical side, but I would also love to hear comments also regarding the plans and prices. How to write startup script for Systemd? I have 2 graphics cards on my laptop. One is IGP and another discrete.   I've written a shell script to to turn off the discrete graphics card.  How can I convert it to systemd script to run it at start-up? The differences between TeX engines I am confused about what TeX and its offspring (LaTeX, pdfTeX/pdfLaTeX, e-TeX, ConTeXt, LuaTeX, etc.) are.  Some, like LaTeX, seem like add ons to TeX (maybe a change to the eyes and mouth, but not stomach). Others, like pdfTeX, seem like changes to the underlying system (i.e., a change to the stomach).  Is there a good reference that explains the differences and the evolution? What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something }; What is the difference between a URI, a URL and a URN? People talk about URLs, URIs, and URNs as if they're different things, but they look the same to the naked eye.  What are the distinguishable differences between them? What is the difference between "var=${var:-word}" and "var=${var:=word}"? If I design a PC for use as an NPC, how much XP should he give when killed? Dark Energy / Accelerating universe: naive question How do I identify the C terminal on my HVAC? How do I identify the C terminal on an HVAC, furnace, or boiler? If the terminals don't have a screw labeled C what should I look for on the wiring diagram? What steps should I take if a wiring diagram cannot be found or if it indicates that a C terminal doesn't exist?  Note: This is an extension to  which asks about running the wires through the wall. This question is about where to connect the wire at the HVAC.