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How do I create bookmarks with pdfLaTeX? I'm using MiKTeX and using pdfLaTeX. I can generate the PDF, but there are no bookmarks. In the .tex-file it is using:  \chapter \section \subsection   (with labels)  I originally used make with sphinx to output LaTeX. It must work somewhat or I wouldn't get the PDF. When I say bookmarks, I mean when you are in Acrobat and the left side has the Bookmarks panel.  I am reading   But I am not sure where to apply this.  EDIT:  I applied this, \usepackage{bookmark}, and got bookmarks, but I never get the subsection bookmarks. What color codes can I use in my PS1 prompt? I used several colors in my PS1 prompt such as   \033]01;31\] # pink \033]00m\]   # white \033]01;36\] # bold green \033]02;36\] # green \033]01;34\] # blue \033]01;33\] # bold yellow   Where can I find a list of the color codes I can use?  I looked at  but it didn't answer my question about a list of the actual codes.  It would be nice if there was a more readable form also.  See also Ubuntu server: Cannot setup dummy driver alsa (LXC container) // modprobe issue I often see questions on Stack Exchange sites which I presume are written by non-native English speakers who use the word "doubt" in place of the word "question". Is this a case of misunderstanding the correct meaning or are people being taught that this is correct usage? I have set theme handler for a form in Drupal and this handler has a template file. What is the easiest way to send a value from PHP to JavaScript in that include file? Why do light disappears the moment we switch off the source (inside the wooden box)? How to reinstall Windows 10 on new hard disk I've been using Windows 10 for a couple of month now (joined the Insider Preview).  Now my hard drive started ticking so I've bought a new SSD and I want to move the windows installation to the new hard drive, which has been connected to the computer (unpartitioned). I don't mind and I even prefer reinstalling it over again.   Since I have the free version of Windows 10 pro, can I still reinstall it anew? Does the windows 10 installation offer disk management and partition like the older Windows installations used to? How should I reinstall Winodws 10 x64 the easiest but still remain on free mode? Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots. Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.  My attempt:  Consider the polynomial $g=(x-1)(1+x+x^2+x^3+\cdots+x^n)$  As $f\mid g, g$ all the roots of $f$ are roots of $g$.  This means I have to prove the statement:  If $c$ is a multiple root of $f \Longrightarrow c$ is multiple a root of $g$.  Equivalently:  If $c$ is not a multiple root of $g \Longrightarrow c$ is not a multiple root of $f$.  I'll try to prove this last statement:  Suppose $\exists c$ such that $c$ is a multiple root of $g$, then   $$g(c)=0 \implies g'(c)=0$$  $$ g=(x-1)(1+x+\cdots+x^n) \implies  g'=nx^n $$ $$ g'(c)=nc^n=0 \implies c=0 $$ But  $$ g(0)\neq 0 $$ And we've found the contradiction: $\not \exists c: g(c)=g'(c)=0$. Then $f$ has no multiple roots.  Is this correct?   Also: Assuming this is correct, is it possible to prove $\sum_{k=0}^n \frac {x^n}{n!} $ has no multiple roots in a similar manner? $x^2$ is congruent to $-1 \bmod p$ In general, how do you solve $x^2$ is congruent to $-1 \bmod p$, where $p$ is an odd prime and $x$ is an integer.  Specifically, I need to solve $x^2\equiv-1 \pmod{29}$ Mathematical symbol for "and" I have found some pretty complete lists (I think) of mathematical symbols  and , but I don't see a symbol for the word "and" on either list.  A person could easily just write the word "and" or use an ampersand, but I was wondering if there was an actual mathematical symbol for the word "and".  Also, if anyone knows any lists that are more complete than the ones I have linked to please provide a link. Runtime error : ERROR 000358: Invalid expression using SelectLayerByAttribute in ArcPy? I cannot for the life of me persuade SelectLayerByAttribute to work (I need to automate this for a complex script).  Working in ArcMap's python console on already loaded shapefile, the format below:  import arcpy from arcpy import env arcpy.env.workspace = r"C:/Users/.../working" arcpy.SelectLayerByAttribute_management("layer", "NEW_SELECTION", " 'ATTRIBUTE' = 'Criterion' ")   results in error:     Runtime error : ERROR 000358:   Invalid expression Failed to execute (SelectLayerByAttribute).   An alternative method:  import arcgisscripting import arcpy gp = arcgisscripting.create(9.3) gp.workspace = "C://...//working" sFile = "C://...//working//shapefile.shp" lyr = "layer" gp.makefeatureLayer_management(sFile, lyr) gp.toolbox = "management" gp.SelectLayerByAttribute("layer", "NEW_SELECTION", " 'ATTRIBUTE' = 'Criterion' ")   .. selects everything, including features that don't meet the criterion!  Does anyone have any idea what's going wrong?  I've read some pages on , but found no solution that works here. The working directory is correct. The attribute field and criterion are correctly specified (case sensitive etc), etc. Its very confusing. How do I add VBA in MS Office? I've seen posts showing answers which use VBA () code/macros, however, I've also noted additional comments afterwards about how to use the VBA (how to implement and execute it). I'm hoping this will help just to get the code executed.   So, my question is:  I have some VBA code. How do I add VBA to my MS Excel or Word or Outlook project? First and foremost I am sorry for this; in order to make the questions clear I must first upload the lecture notes from my institution $^\zeta$ for the derivation of Hydrostatic Equilibrium:          $^\zeta$ Lecture notes courtesy of Imperial College London, Astrophysics dept, 2017-2018 edition.    Firstly, in equation $(3.1)$ why is there no negative sign for $F_g$? Last time I checked, Newton's law of gravitation told us that   $$F=-\frac{GMm}{r^2}$$  Nextly, I have a conceptual problem with equation $(3.2)$; when they use the term 'pressure' I am going to assume that they are referring to the radiation pressure that is released due to nuclear fusion reactions taking place in the sun. In that formula it must be the case that $P(r) \gt P(r+\delta r)$ if this is the case then $(3.2)$ should read $$F_p=-\left(\frac{dP}{dr}\right)\delta r\,\delta A $$   Correct me if I'm wrong but Hydrogen nuclei are fused together to generate the more stable Helium and hence lots of radiation pressure acting outwards from the centre of the star. If this is correct then $P(r+\delta r)=0$, since the outside face of that cylindrical volume element in Figure $3.1$ will not 'feel' any of this radiation pressure because this pressure only acts on the inner face. What am I not understanding here?  Moving on to equation $(3.3)$, let's suppose the sign of the gravitational force in $(3.1)$ really is neglected. Does this mean that the negative sign in $(3.3)$ is due to $P(r+\delta r) \lt P(r)$ and hence $$\frac{GM(r)\rho(r)}{r^2}=-\left(\frac{dP}{dr}\right)\,?$$ I know this is the same equation as in $(3.3)$ but I have written it with the negative sign next to the pressure differential as I would like to know where this minus sign originates from. Does anyone know?  My final concern is the sign in $(3.4)$ as last time I checked $$g=-\frac{GM}{r^2}$$ and not $$g=\frac{GM}{r^2}$$  Hence, equation $(3.4)$ should read  $$\left(\frac{dP}{dr}\right)=\rho(r)\,g\,?$$     I forgot to mention that I have done some research and  is the closest derivation I could find, which, needless to say is no less helpful than the notes I have. What antivirus programs are available for Ubuntu?  We previously used Symantec Endpoint Protection but it does not work in Ubuntu. I found the following blog title without a question mark from :     How to ease Afghanistan’s progress in cricket   Is it grammatical, if we don't put question mark in questions of titles? I think this blog title should have been like this:     How to ease Afghanistan’s progress in cricket?   I also found the following blog title from  without a question mark:     Election rigging 101: How to steal a mandate   However, I found a question mark from other blog title of :     Elections 101: What is the ECP and what does it do on election day? Inconsistent accessibility error with the following c# code. Why? Conditional formatting of an entire row based on multiple cells I'm trying to make a conditional formatting rule in Google Spreadsheet that would highlight a row green based on text in multiple cells.   If cells L2, M2, and N2 = APPROVED; and cell O2 = X; then row 2 = highlighted green. I am fairly sure that I understand the how Monte Carlo integration works but I am not understanding the formulation of how it is used to estimate Pi.  I am going by the procedure outlined in the 5th slide of this presentation   I understand the preliminary steps.  Pi is equal to 4 times the area of a quarter of the unit circle.  And the area of the top-right quarter of the unit circle centered at (0,0) is equivalent to the integral of the curve that is the top-right quarter of the unit circle in $0&lt;x&lt;1$ and $0&lt;y&lt;1$.    What I don't understand is how this integral is  $\iint I((x^2+y^2)&lt;1)P(x,y)dxdy$  where $P(x,y)$ is uniformly distributed in the unit square around the quarter circle (i.e. it is always equal to 1 if $0&lt;x&lt;1$ and $0&lt;y&lt;1$ and 0 otherwise).  So this would mean that  $I((x^2+y^2)&lt;1)P(x,y)$ is the function that is the top-right quadrant of the unit circle at $0&lt;x&lt;1$ and $0&lt;y&lt;1$ but I do not understand how this is true since the indicator function can only be 1 or 0.  I understand that it is probably written in this way to make Monte Carlo sampling easy (i.e. it is an expectation so just sample from $P(x,y)$ and get the average of the samples applied to $I((x^2+y^2)&lt;1)$) but it just does not make intuitive sense to me why that integral represents the area under that curve.  Could someone provide an intuitive explanation of this.  Maybe show how that integral was derived in a step-by-step way?  EDIT:  I was able to gain a better understanding by relating the expectation to an area.  I will explain it here in case it helps anyone.  First start with relating Pi to the area of the top-right quadrant of the unit circle  $\pi=4\times A_{tr}$  Then we place the top-right quadrant into the unit square.  And under a uniform distribution over the unit square, the area of the circle quadrant is proportional to the probability of obtaining a sample from it.  It follows that the following equality holds  $P(x^2+y^2&lt;1)=\frac{A_{tr}}{A_{square}}$  and $A_{square}=1$ so  $P(x^2+y^2&lt;1)=A_{tr}$  And substituting into the original equation  $\pi=4\times P(x^2+y^2&lt;1)$  and it is also true that $P(x^2+y^2&lt;1)=E[I(x^2+y^2&lt;1)]$ which is equal to the original double integral.  So I understood it by relating the area to a probability then relating that probability to an expectation that is equivalent to the integral.  Let me know if I have made any mistakes. An explanation of Hawking Radiation Could someone please provide an explanation for the origin of ? (Ideally someone who I have been speaking with on the h-bar)  Any advanced maths beyond basic calculus will most probably leave me at a loss, though I do not mind a challenge! Please assume little prior knowledge, as over the past few days I have discovered that much of my understanding surrounding the process as virtual particle pairs is completely wrong. Format a date in XML via XSLT