How to demonstrate potential for securing external funding in faculty applications?
How to respond to "How much funding will you bring?" as an interview question for a faculty job?
Which render engine renders faster? Blender Internal or Cycles? I wonder which render engine is faster? I mean, you have 2 identical scenes and render it using BI and Cycles. Which image will be generated faster? What will be the time difference?  Do you know any site (please post a link) which shows the results of such comparison? I want to create a table like this using Latex        ---------------------------------       |               sets            |       ---------------------------------       | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | --------------------------------------- | I1  | * |   | * | * |   | * |   | * | ---------------------------------------   Here is what I wrote  \begin{table} \caption{Multiprogram sets} \label{multiprogram}  \begin{tabular}{| c | c | c | c | c | c | c | c | c |}   \cline{3-9}   \multicolumn{8}{}{}    &amp;   Sets  \\   \hline   \multicolumn{1}{}{}   &amp; 1 &amp; 2 &amp;  3 &amp; 4 &amp; 5 &amp;  6 &amp; 7  &amp; 8 \\   \hline    astar         &amp;  &amp; * &amp;  &amp; * &amp;  &amp;  &amp; * &amp;   \\   \hline  \end{tabular} \end{table}   But it doesn't work! The output look like            -----------------------------                                  sets | ---------------------------------------         1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | --------------------------------------- | I1  | * |   | * | * |   | * |   | * | ---------------------------------------   Any way to fix that? I'm currently a Combinatorics student trying to parse through this solution. I do not understand the proof currently. Any help understanding it is greatly appreciated.    Question Let the number of partitions be given by the function $p(n)$, i.e. the number of ways of writing the integer $n$ as a sum of positive integers. Prove that that if $g$ is any polynomial function in $n$, then there exists an integer $N$ such that $g(n)&lt;p(n)$ for all $n&gt;N$. Do not use the asymptotic Hardy-Ramanujan formula.    Provided Proof.    Enough to show $n^a&lt;p(n)$ for fixed positive integer $a$. (This is just saying that we want to show $p(n)$ grows faster than any degree polynomial of $n$, right?) We have that $(i_1,i_2,\ldots,i_{a+1},1^{n-i_1-\cdots -i_{a+1}})$ is a partition of $n$ as long as $i_{a+1}\leq i_a\leq \cdots i_1 \leq \lfloor\frac{n}{a+1}\rfloor$. (I really don't understand this step. What is this partition? Of the coefficients or terms of polynomial $p(n)$? And how do we know this is $\leq \lfloor\frac{n}{a+1}\rfloor$?) The number of partitions $n$ of this form is multiset binomial coefficient $$\left(\dbinom{\lfloor \frac{n}{a+1}\rfloor}{a+1}\right)=\frac{\lfloor\frac{n}{a+1}\rfloor(\lfloor\frac{n}{a+1}\rfloor+1)\cdots(\lfloor\frac{n}{a+1}\rfloor+a-1)}{(a+1)!}$$ (I'm assuming that if I can understand (2.) then I can understand this line) This means $p(n)&gt;\left(\binom{\lfloor \frac{n}{a+1}\rfloor}{a+1}\right)$ for all $n&gt;0$. Since $a$ is constant, the given fraction grows with order $n^{a+1}$, which means $p(n)&gt;n^a$ for $n$ sufficiently large. (Why does it grow with order $n^{a+1}$?)   Thanks all again in advance! Permanent xmodmap in Ubuntu 13.04 I cannot make xmodmap run on login in Ubuntu 13.04. I have searched around, including in askubuntu and all answers I found do not work.  I have a file named .Xmodmap in my home folder which contains the desired mappings. If I run it manually it works fine, so there is no error there. In order to make it run on startup, I have tried:     Using various .xinitrc containing one of the following commands:      xmodmap .Xmodmap xmodmap ~/.Xmodmap   /usr/bin/xmodmap /home/NAME/.Xmodmap if [ -s ~/.Xmodmap ]; then xmodmap ~/.Xmodmap fi  Using .Xresources instead of .xinitrc with the same variations. Setting it as a startup application.   None of the above works in Ubuntu 13.04 (64-bit). I also saw a few ideas about globally changing the keyboard mappings, but most of them were not applicable in Ubuntu 13.04 (i.e. the corresponding files did not exist where specified) and I prefer not to touch the global settings anyway. Terminating with Master's after several years in a PhD program. How to indicate on CV/Resume? I am not happy with my PhD program, and after several years I am graduating with a master's this month. I earned the M.S. along the way as a PhD student, but have never formally requested it before this semester. What is the best way to indicate this situation on a CV or resume? I don't want to put just M.S. because then it looks like it took me a really long time to get a master's and I can't put that I am a PhD student because I no longer am.  Right now, I am thinking something like  M.S. in &lt;field&gt;, &lt;University&gt;, May 2016 PhD student in &lt;field&gt;, &lt;University&gt;, Aug. 2011 - May 2016 B.S. in &lt;field&gt;, &lt;Undergrad University&gt;, Aug. 2007 - May 2011   Would that be clear what's going on? Alternatively, should I list PhD above M.S. even though I didn't complete it? Should I list both M.S. and PhD in same line since it is the same university and span of time? Preview of CAD files in format .dwg I'm looking for a utility or a program for Ubuntu, and possibly even for Windows that is able to convert a CAD file format .DWG to PDF.   My need is to provide a preview of CAD files, and I thought that the easiest way is to convert them into PDF format, but I'm open to suggestions, even if there is only the possibility to convert them to JPG image file type or PNG would be fine.  What interests me is only to find some solution, no matter if it is commercial or free Are console games locked to a certain region? I'm going on a vacation from Europe to the US and was planning of bringing along some Xbox360 or PS3 games, but now I'm curious if they will be compatible with my European Xbox.  In that past there would be a clear difference between NTSC and PAL games, but is this still the case with the current gen of consoles? Displacement currents, aren't really currents? Find a bijection from $\mathbb R$ to $\mathbb R-\mathbb N$ Find a bijection from $\mathbb R \to  \mathbb R-\mathbb N$. I want to set my function up such that all natural numbers get mapped to $n+.1$ and reals of the form $n+.1$ to $2n+.1$ is this correct? What is the domain of $x^x$ as a real valued function? Consider the function $f(x) = x^x$.  Wolfram alpha tells me that this function's domain is $x : x&gt;0$, $x \in \mathbb{R}$. I can't see why it cannot be defined for a number like $(-2)$. I mean $(-2)^{-2}=0.25$, the same Wolfram Alpha told me. I realize that fractional powers for negative numbers may cause problems, but it could be defined for integers. Thanks for any help. Average arc length of a uniformly distributed points Suppose I have $N$ points on a unit circle. I am aware that for a uniform distribution the average angle of one point is not defined, but I want to calculate the average arc length between nearest-neighbors. I disregard arc lengths larger than $\pi$.  For $N = 2$ I am formulating the problem as: \begin{equation} \langle \Delta x \rangle = \frac 1 {\pi^2}\int\limits_0^\pi \int\limits_0^\pi  dx_1 dx_2 \, |x_1-x_2| = \frac \pi 3. \end{equation}  This answer does not make sense to me. Did I make a mistake constructing this integral?  What would happen to $N = 3$, etc? Write access without read access Is it possible for a user to have a write access to a file and not be able to read it? How is it possible?   I tried the following commands:  debianbox@debian:~/posix/io$ touch filetest debianbox@debian:~/posix/io$ ls -l filetest -rw-r--r-- 1 debianbox debianbox 0 14 oct.  03:10 filetest  debianbox@debian:~/posix/io$ echo "Hello World" &gt; filetest debianbox@debian:~/posix/io$ cat filetest Hello World  debianbox@debian:~/posix/io$ chmod u-r filetest debianbox@debian:~/posix/io$ cat filetest cat: filetest: Permission forbidden  debianbox@debian:~/posix/io$   As you can see here, I have write but not read access on this file. How can this be possible? Is this considered as a bug? If not, in what situation would this be useful? Meaning of symbols $\vdash$ and $ \models$ I'm confused about the use of symbols $\vdash$ and  $ \models$. Reading the answers to  and  I see that:  the turnstile symbol $ \vdash $ denotes syntactic implication. Then $ S \vdash \psi$ means that $\psi$ can be derived from the formulae in $S$  the double turnstile $ \models $, denotes semantic implication. Then the notation $A \models B$ means simply that B is true in every model in which A is true.  So I understand that, e.g., $(ZFC+ A) \vdash B$ means that $A \Rightarrow B$ is a theorem in ZFC and, in this sense $\vdash$ is a mathematical symbol for a theorem. While $(ZFC+ A) \models B$ means that $ B$ is true in every model of ZFC in which $A$ is true, and, in this sense $\models$ is not a mathematical but a metamathematical symbol.  I understand correctly? And those are the only uses of the two symbols? Printing reverse of any String without using any predefined function? Lookup list dependant on the contents of another cell hope someone can help to crack this one?  I've got a table on my data entry tab (sheet 1) where each row includes two data validation drop down lists (source is on sheet2). I want the options in the second drop down list (k13) to be dependant on what is selected in the first drop down list (g13)...  ie. if you select 'Diary' in the first drop down box then the second drop down only has 'Cheese', 'Milk' and 'Yogurt' - likewise, if you select 'Fruit' in the first box - I want the only options to be available specific to that categories column in the lookup table on sheet 2 (which are 'apple', 'pear' and 'banana' in this case)?  Please help - i think this is a vlookup indirect formula?? I've just installed Ubuntu 14.04 and am trying to install php 5.3. But when I run   apt-get install php5    it's installing php 5.5.9-1ubuntu4. I need to use php 5.3 in the system because the application I'm working on is built with php 5.3.   How can I achieve this? How to detect the presence of URL in a string How do I install a fingerprint reader on Lenovo ThinkPad? I've heard that ratios or inverses of random variables often are problematic, in not having expectations. Why is that? The title is the question. I am told that ratios and inverses of random variables often are problematic. What is meant is that expectation often do not exist. Is there a simple, general explication of that? I am making a regex expression in which I only want to match wrong tags like: &lt;p&gt; *some text here, some other tags may be here as well but no ending 'p' tag* &lt;/p&gt;   &lt;P&gt;Affectionately Inscribed &lt;/P&gt;&lt;P&gt;TO &lt;/P&gt;&lt;P&gt;HENRY BULLAR, &lt;/P&gt;&lt;P&gt;(of the western circuit)&lt;P&gt;PREFACE&lt;/P&gt;   In the above same text I want to get the result as  &lt;P&gt;(of the western circuit)&lt;P&gt; and nothing else should be captured. I'm using this but its not working:  &lt;P&gt;[^\(&lt;/P&gt;\)]*&lt;P&gt;   Please help.