I'd like to draw vertical border lines in merged cells, but now merged cells do not have any vertical border line.  How can I add lines?  \begin{table}[htbp] \centering \caption{policy} \label{tab:mutationoperators} \begin{center} \begin{tabularx}{\textwidth}{|c|L|} \hline ope                 &amp; Description               \\ \hline \multicolumn{2}{l}{Category1 }               \\\hline   d                       &amp;       d                    \\\hline \multicolumn{2}{l}{Category2}                \\\hline                      f    &amp;         f                  \\\hline                        f  &amp;         f                  \\\hline \multicolumn{2}{l}{Category3}                \\\hline                      f    &amp;       f                    \\\hline                       f   &amp;        f                   \\\hline \multicolumn{2}{l}{Category4}              \\\hline                    f      &amp;        f                   \\\hline                    f      &amp;        f                   \\\hline                     f     &amp;        f                   \\\hline \multicolumn{2}{l}{Category5} \\\hline                      f    &amp;       f                    \\\hline                      f    &amp;        f                  \\ \hline \end{tabularx} \end{center} \end{table}
I tried to use this for the last part of my table, but I can't get a vertical line at the end. Does anyone know?   \begin{tabular}{|CC|C|C|C|C|C|C|C|C|C|C|}\hline \Tab{Method Based on \\\hline       Radiography\\Magnetic Particle (A.C.)\\ \\Eddy Current\\Dye Penetrants\\ Ultrasonics} &amp; \Tab{ \\\hline \\ Wet \\ Dry \\ \\ \\ \\} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Minute Surface Cracks }~}  \\\hline       N\\ G\\F\\F\\F\\P}  &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Deeper Surface Cracks      }~}  \\\hline            F\\G\\G\\G\\G\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Internal Cracks      }~}  \\\hline            F\\N\\N\\N\\N\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Fatigue Cracks      }~}  \\\hline            P\\G\\G\\N\\G\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Internal Voids      }~}  \\\hline            G\\N\\N\\N\\N\\G}           &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Porosity and Slag in Welds      }~}  \\\hline            G\\N\\N\\P\\N\\F}           &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Thickness      }~}  \\\hline            F\\N\\N\\P\\N\\G} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Stress Corrosion      }~}  \\\hline            F\\G\\F\\N\\G\\F} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Blistering      }~}  \\\hline            P\\N\\N\\N\\N\\F} &amp; \Tab{\rotatebox{90}{~\parbox{5cm}{Corrosion Pits      }~}  \\\hline            G\\N\\P\\N\\F\\P} \\\hline &amp; \multicolumn{11}{l}{G=Good;F=Fair;P=Poor;N=Not suitable.} \\ \hline \end{tabular} \label{tab:NDETechniques} \end{table}   It comes out like this:
17.10 Super key to open applications Please clarify how entropy increases when matter gravitationally coalesces On John Baez's website, , he discusses the problem of how entropy increases when a cloud of ideal gas collapses gravitationally (no black holes - keeping it simple).  But he doesn't give away the answer - instead he implies that, I presume, either gravitons or photons are released during collapse and these increase the overall system entropy.  Can someone please answer which it is, gravitons or photons?  If gravitons (or gravity waves), then does this mean that pre-20th century physicists, with no notion of gravity waves, would have concluded that gravitational attraction violates the 2nd law?  And if photons, then what about if the gas particles were totally neutral - wouldn't they not emit any EM radiation in that case?  Or am I wrong that gravitons or photons are the answer? Thanks! Assigning values to divergent series I have been looking at divergent series on wikipedia and other sources and it seems people give finite "values" to specific ones. I understand that these values sometimes reflect the algebraic properties of the series in question, but do not actually represent what the series converges to, which is infinity. Why is it usefull to assign values to divergent series?  The only theory I could come up with, is this:  Say you have 2 divergent series, series' A and B, and you assign each a value,   Series ($A= \sum_{n=0}^\infty a_n$), which I assigned the value Q  and series ($B= \sum_{n=0}^\infty b_n$ ), which I assigned the value P  But it just so happens that series $C=A-B= \sum_{n=0}^\infty (a_n-b_n)$ converges. Could that imply that the actual value of series $C$ is the difference of the two assigned values to $A$ and $B$, that is $\sum_{n=0}^\infty (a_n-b_n)=Q-P$ ?  If so, then that would make some sense to me, as to why people sometimes assign values to divergent series. What are SPF records, and how do I configure them? This is a  about setting up .     I have an office with many computers that share a single external ip (I'm unsure if the address is static or dynamic). Each computer connects to our mail server via IMAP using outlook. Email is sent and received by those computers, and some users send and receive email on their mobile phones as well.  I am using  to generate an SPF record and I'm unsure about some of the fields in the wizard, specifically:   Enter any other domains who may send or relay mail for this domain Enter any IP addresses in CIDR format for netblocks that originate or relay mail for this domain Enter any other hosts which can send or relay mail for this domain How stringent should SPF-aware MTA's treat this?   the first few questions i'm fairly certain about... hope i have given enough info. From the :  [1,4,9].map(Math.sqrt)   will yield:  [1,2,3]   Why then does this:  ['1','2','3'].map(parseInt)   yield this:  [1, NaN, NaN]   I have tested in Firefox 3.0.1 and Chrome 0.3 and just as a disclaimer, I know this is not cross-browser functionality (no IE).  I found out that the following will accomplish the desired effect. However, it still doesn’t explain the errant behavior of parseInt.  ['1','2','3'].map(function(i){return +i;}) // returns [1,2,3] Let $E=l^p=\left\{x=\left(x_n\right): x_n\in\mathbb{R}, \sum_{1}^{\infty}\left|x_n\right|^p&lt;\infty\right\}$ with $1\le p&lt;\infty$, $\left\|x\right\|_E=\left(\sum_{1}^{\infty}\left|x_n\right|^p\right)^{1/p}.$ Let $\left(\lambda_n\right)$ is a bounded sequence in $\mathbb{R}$ and consider the operator $T$ defined by $$T(x)=\left(\lambda_1x_x,\ldots,\lambda_nx_n,\ldots\right)$$ where $x\in l^p$. Prove that $T$ is a compact operator from $E$ to $E$ iff $\lambda_n\rightarrow 0$.  Can anyone give me some hints to solve this problem? Thank you! Can you launch Remote Desktop via URL? What is the formula for this numerical series? Check if convergent in the end points of the convergence interval I have to find the radius of convergence for $\displaystyle\sum_{n=0}^{\infty}\frac{n}{n+1}x^n$, for x$\in$R. I think it is $r^{-1}=\lim_{n\to\infty}\frac{a_{n+1}}{a_n}=\lim_{n\to\infty}\frac{ \frac{n+1}{n+2} }{ \frac{n}{n+1}}=1$ so r=1. Then I have to find out if $\displaystyle\sum_{n=0}^{\infty}\frac{n}{n+1}x^n$ is convergent in  the end points of the convergence interval. I think I have to check for $|r|$. But we can't use ratio test (L=1) or integral test(not decreasing) for $\displaystyle\sum_{n=0}^{\infty}\frac{n}{n+1}$. How can I then check if it's convergent in the end points of the convergence interval? Which style is preferred? Is there a good reason for one vs. the other?  Thanks in advance!  1) cmds.each do |cmd|    end  2) cmds.each { |cmd|    }   Example code:  cmds = [ "create", "update", "list", "help" ]  # Block style one # cmds.each do |cmd|   puts "loop1, cmd: #{cmd}" end  # Block style two # cmds.each { |cmd|   puts "loop2, cmd: #{cmd}" } $\exp(A)$ is orthogonal iff $A$ is skew symmetric Let $A \in M_n(\mathbb R)$ and $\exp(A)=\sum_{i=0}^{\infty}\frac{A^i}{i!}$. How to prove $\exp(A)$ is an orthogonal matrix iff $A^t=-A$?  I can get that $\exp(A)$ is an orthogonal matrix iff $\exp(A^t)=\exp(-A)$, but how to get $A^t=-A$ from it?  What's more, is $\exp(A)$ injective or not? Extracting numbers from vectors of strings The StackExchange™ MultiCollider SuperDropdown™ says I've got replies, but I've already viewed those. After creating some hi-poly model, i'm always creating low-poly model by approximating that hi-poly mesh with triangle-by-triangle LP mesh - with snap to face mode turned on.   So the process looks like CTRL + RMB (x times), and hitting F on keyboard, so the new face was made.  Then I'm using this low poly model to texture baking, mainly for gamedev purposes.  This method is very time consuming, so how to make retopology process easier and quicker? Do the electric and magnetic components of an electromagnetic wave really generate each other? Frequently when EM waves are taught, it is said that the change in electric field causes a change in the magnetic field, which then causes a change in the electric field, and so on and so forth.   But from my understanding of basic electromagnetics, it is not necessarily a changing electric field that creates a change in magnetic field, but instead an accelerating charge. and it is this charge that creates both the electric and magnetic field. Again, from my understanding, a changing magnetic field is not generated by a changing electric field, but instead just happens to always be present perpendicular to a changing electric field due to the laws of electromagnetism.   Am I wrong? Or is the "mutual generation" concept between the electric and magnetic components of an EM wave an actual thing? Why does a window become a mirror at night? In day, when you look in the room through the window out, you can clearly see what happens outside. At night when it's dark outside but there's light inside you can look in the window but it becomes a mirror.  Why? When installing user applications, where do "best practices" suggest they be located? Occasionally I install applications manually, rather than using apt or another package manager.   What location (/usr/, /usr/local/, /opt/, /home/, etc.) is suggested by "best practices" for the installation of user applications? How do I read and parse an XML file in C#? How can one make Firefox ignore my GTK theme entirely? Check out the below program.   try {     for (String data : Files.readAllLines(Paths.get("D:/sample.txt"))){         String[] de = data.split(";");         System.out.println("Length = " + de.length);     } } catch (IOException e) {     e.printStackTrace(); }   Sample.txt:   1;2;3;4 A;B;; a;b;c;   Output:   Length = 4 Length = 2 Length = 3   Why second and third output is giving 2 and 3 instead of 4. In sample.txt file, condition  for 2nd and 3rd line is should give newline(\n or enter) immediately after giving delimiter for the third field. Can anyone help me how to get length as 4 for 2nd and 3rd line without changing the condition of the sample.txt file and how to print the values of de[2] (throws  ArrayIndexOutOfBoundsException)?