I am currently writing a paper in Latex. I am using \section, \subsection, etc. for sections. In each section I use  \begin{equation} bla... \end{equation}   for equations I have.  I want my equation to be numbered like (3.3.1), (3.3.2), ... for section (3.3) and so on, but the code I used just gave me equations numbered (1), (2), .... I am wondering how to change the way I number my equations.
Some document elements (e.g., figures in the book class) are numbered per chapter (figure 1.1, 1.2, 2.1, ...). How can I achieve continuous numbering (figure 1, 2, 3, ...)?  And vice versa: Some document elements (e.g., figures in the article class) are numbered continuously. How can I achieve per-section numbering?  \documentclass{book}% for "vice versa" variant, replace `book` with `article`  \begin{document}  \chapter{foo}% for "vice versa" variant, replace `\chapter` with `\section`  \begin{figure} \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure}  \end{document}   Bonus question: Is it possible to adjust the numbering of the sectioning headings themselves? Can I, e.g., switch from per-chapter to continuous numbering of sections in the book class?
How do I run a program in the background of a shell, with the ability to close the shell while leaving the program running? Lets say my UI is having problems or for some reason, I need to boot up a program from the terminal window, say, nm-applet:  nm-applet   When it's started, it occupies the foreground of the terminal window.  Is there any simple way to run the program in the background without needing to leave the terminal open or have it occupy the whole terminal?  On that note, I did find a way to run programs from the terminal and have it allow for other inputs, by appending an ampersand (&amp;) to the command as such:  nm-applet &amp;   But this isn't much use as any processes started in the terminal are killed once the terminal is closed. I host am ExpressionEngine based website on a single Amazon EC2 instance in the US East (Virginia) region. I use Ubuntu.    The website allows members to post their content, and displays it for other members and for users who are not logged in.   Goal: I need to begin serving the same website across the globe, equally fast to Hong Kong, New York, and Los Angeles.   I considered two solutions:  1.Setting up three separate EC2 instances for three regions: Virginia, Oregon, and Singapore. Use Amazon Rot53 Geo Location to direct traffic to instances based on the browser's IP address.   Pro: the website will load fast for the region.   Contra: these will be essentially three separate websites. Unless I am mistaken?   Setting up one instance in a region equally remote from all three locations: (Ireliand), and boost the server to the highest performance available.    Pro: It will be the same website for all regions.   Contra: it will cost a lot to make it fast enough.   My challenges:   a) I do not know a way to sync server settings, database, and content between multiple Ubuntu instances in real time. If a knowledgeable person could explain to me how to do that, I would be most grateful.   b) I am not thoroughly familiar with all Amazon AWS resources. Does AWS has a built-in method that would allow me to achieve my goal of serving a single PHP / MySQL based membership website across the globe equally fast in all three chosen locations? I've already taken my calculus sequence and I'm interested in brushing up and staying sharp on the basics. So far, my calculus background is limited to single-variable calculus, which I applied in my physics sequence and engineering statistics. I learned a little bit of vector math in physics as well, but I'm not strong in it. My mathematical strengths lie in the discrete mathematics.  I'm particularly interested in studying for my IEEE Certified Software Development Associate exam - 10% of the exam is mathematics (calculus, differential equations, and statistics). Calculus is one of the mathematics knowledge areas that a software engineer should be competent in, so I'm looking for not only solidifying the courses that I've already taken, but moving forward with slightly more advanced topics, at an undergraduate mathematics level.  I'm currently using the textbook from my calculus sequence, but I'm interested to know what books other people used to learn calculus and if the book is potentially worth checking out.  What books are available to help me? How to Create a Grid Inside a Polygon that is Oriented with the Longest Side? I have been using a process called "Create Polygon Graticule" to create a grid within a polygon with assigned row and column attributes. It is a SAGA tool which I have been running in QGIS. It generates a grid based on the extent of the input polygon with the cell running N to S and E to W. It would be better for my analysis if the direction of the grid was parallel to the longest edge of the polygon. For reference I have attached images of the current automated output and an output that I manually altered to align the grid with the polygon. The grids originally covered the entire extent of the polygon but have been clipped to show only the cell parts that are inside.    Above image is what the tool out puts by default.   This is an image of a grid that was edited manually to fit the necessary parameters.  My question is, is there a way to produce grids that are aligned such as the one in the second image in an automated fashion? I will need to generate grids for a few thousand polygons. Been looking to pivot rows (progress_check) into columns check 1, check 2 etc... No sum or totals required, just to display the results hopefully... Can anyone help, Thanks Ad Since the final Black Hole (BH) had 3 solar masses less of mass than the original binary BH, it seems the 2 BHs lost mass, and with it event surface area, entropy, and information. If that came from inside the BHs it seems that it would be a contradiction of what a BH is --'nothing escapes its event horizon'. Some may say that came from the rotational energy of the pair, but the new BH now seems to have less than the two original ones summed. So, did some of that escape the horizons? Irreducibility check for polynomials not satisfying Eisenstein Criterion. My Question is to check Irreducibility for polynomials not satisfying Eisenstein Criterion.  As an Illustration, to check whether $x^{p-1}+.....+x+1$ for p a prime is irreducible or not, we replaced $x$ by $x+1$ and by using Eisenstein's Criterion for the resulting polynomial we conclude that resulting polynomial is irreducible and so is the original polynomial.  In general, for a given irreducible polynomial $f(x)$ with coefficients in a known U.F.D, is there some element $a$ such that we can apply Eisenstein's criterion to $f(x+a)$?  I am sure there would be no general structure for this but I expect there to be at least some special cases.   Any Reference/suggestion would be appreciated.  Thank You. How can I take pictures through a skyscraper, airplane, or train window? Evaluate the integral $\int_0^\infty \frac{dx}{\sqrt{(x^3+a^3)(x^3+b^3)}}$ Python program to calculate harmonic series Does anyone know how to write a program in Python that will calculate the addition of the harmonic series. i.e. 1 + 1/2 +1/3 +1/4... What does increased caster level affect? A  adds +1 caster level, what does this affect?   Damage from spells? (Like fireball) Duration and area of effect? "Amount" of effect (Like number of missiles from magic missile) Spells known by a wizard (ie +1 caster level mean a level 2 wizard gets the spells as if they were level 3?) Anything else? Order of automorphism group of cyclic group Let $G$ be a cyclic group of order $m$. What is the order of $\text{Aut}(G)$?  I want to know the proof as well (elementary if possible). I would still accept the proof if one answers with $m = p$, a prime. Or on top of that, I would accept the answer with extra assumption: $q \equiv 1$ mod $p$ with another prime $p$. Why are we limited to six questions per day? Can I ignore coefficients for non-significant levels of factors in a linear model? After seeking clarification about linear model coefficients  I have a follow up question concerning non-signficant (high p value) for coefficients of factor levels.  Example: If my linear model includes a factor with 10 levels, and only 3 of those levels have significant p values associated with them, when using the model to predict Y can I choose to not include the coefficient term if the subject falls in one of the non-signficant level?  More drastically, would it be wrong to lump the 7 non-significant levels into one level and re-analyze? When a holomorphy ring is a PID? I will use the notation and language of Stichtenoth, Algebraic Function Fields and Codes.  Let $F$ be a function field over a finite field $\mathbb F_q$, $S$ a non empty set of places (possibly infinite) and $O_S$ the holomorphy ring of $S$, i.e., $O_S:=\bigcap_{P\in S} O_P$ (being $O_P$ the valuation ring of the place $P$).  Give necessary and sufficient conditions for $O_S$ to be a Principal Ideal Domain.  Many thanks in advance!  G. Starting digits of $2^n$. Couldn't find hvm kernel for Ubuntu tree This command:  virt-install   \    --name bla  \    --ram=1024  \    --disk path=/home/me/libvirt/images/bla.qcow2,bus=virtio,size=10  \    --location /home/me/Downloads/ubuntu-18.10-desktop-amd64.iso   Reports:  ERROR    Couldn't find hvm kernel for Ubuntu tree.   How can I fix this?  (Since there are many duplicate posts and answers with regard to this issue, I am answering it, too.) The boundary of union is the union of boundaries when the sets have disjoint closures Assume $\bar A\cap\bar B=\emptyset$. Is $\partial (A \cup B)=\partial A\cup\partial B$, where $\partial A$ and $\bar A$ mean the boundary set and closure of set $A$?   I can prove that $\partial (A \cup B)\subset \partial A\cup\partial B$ but for proving $\partial A\cup\partial B\subset \partial (A \cup B)$ it seems not trivial. I tried to show that for $x\in \partial A\cup\partial B$ WLOG, $x\in \partial A$ so $B(x)\cap A$ and $B(x)\cap A^c$ not equal to $\emptyset$ but it seems not enough to show the result. 16.04 VirtualBox VM (from vhd file) hangs at "non blocking pool is initialized" I'm trying to boot Canonical's Azure 16.04 .vhd file in a VirtualBox VM and it hangs at "non blocking pool is initialized".  It works in Hyper-V, so it may only be a bug in virtual box (5.0.20). How do I troubleshoot high 'svchost.exe' usage in Windows 7?