NullPointerException Error when calling fillTable()
What is a NullPointerException, and how do I fix it?
How do Prestige Classes that advance spellcasting interact with racial spellcasting ability? For example Lets use the Marrutact from Sandstorm, it can cast as a 5th level wizard. if it then takes a prestige class that requires the ability to cast 1st level Arcane spells and advances arcane casting such as Abjurant Champion. assuming it meets all other prerequisites does the Marrutacts spellcasting improve when it takes a level in Abjurant Champion or does it gain no benefit? How can I depict vehicle traffic during daytime in a long exposure without washing out the vehicles? 3.8 GPA, but 3 Fs and 1 D on transcript I have scripts that expect specific drive letters for hard drives. Windows sometimes assigns the different drive letters (e.g. I expected my Maxtor drive to be E:, but it's now F:, therefore my scripts will fail), depending on the order of how the drives are plugged into my laptop.  In Windows 7, how do I assign a permanent drive letter to a drive? Site-specific spellcheck? I often see misspelled words in titles and bodies of questions, only to see them spelled properly in the tags. I have to imagine that tags are always spelled right because it's hard to type arbitrary text into the tag box. I also have to imagine that sometimes autocorrect and spellcheck provided by browsers tend to turn programming terms and package names into English words. For example, see   Would it be possible to have some sort of spellchecker that compares text of titles (and maybe bodies) to known tags and offers some sort of correction (maybe red squiggles or something) when there's some statistical probability of a misspelling?  Since this would be using a site's tags, "magneto" would get corrected to "magento" on SO, while "magento" would get corrected to "magneto" on aviation.stackexchange.com.  In theory this could reduce a lot of stupid typos and prevent trivial edits just to fix the spelling of key words.  Note that this is not solving a problem that a user's browser can already solve because browsers ship with English dictionaries, not dictionaries of programming terms. In fact, it's potentially correcting a problem created by the browser (which might have already autocorrected "magento" to "magneto"). Prove that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ converges absolutely I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? Generating samples from singular Gaussian distribution Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula $m + Lr$, where $L$ is the Cholesky lower factor so that $S=LL^T$ and $r = (r_1,...,r_n)^T$.  What about if one wants samples from singular Gaussian i.e. $S$ is still symmetric but not more positive definite (only positive semi-definite). We can assume also that the variances (diagonal elements of $S$) are strictly positive. Then some elements of $x$ must have linear relationship and the distribution actually lies in lower dimensional space with dimension $&lt;n$, right?  It is obvious that if e.g. $n=2, m = \begin{bmatrix} 0 \\ 0 \end{bmatrix}, S = \begin{bmatrix} 1 &amp; 1 \\ 1 &amp; 1\end{bmatrix}$ then one can generate $x_1 \sim N(0,1)$ and set $x_2=x_1$ since they are fully correlated. However, is there any good methods for generating samples for general case $n&gt;2$? I guess one needs first to be able identify the lower dimensional subspace, then move to that space where one will have valid covariance matrix, then sample from it and finally deduce the values for the linearly dependent variables from this lower-dimensional sample. But what is the best way to that in practice? Can someone point me to books or articles that deal with the topic; I could not find one. Sum of the series $1+\frac{1\cdot 3}{6}+\frac{1\cdot3\cdot5}{6\cdot8}+\cdots$ Recording claimable expenses in GnuCash I am new to accounting and trying to learn a few things as my accounts get more and more complicated.  I currently use GnuCash to record simple income/expenses/assets/liabilities and have had a new situation I don't know how to record.  I am currently billing some expenses for work and for my kayak club to my personal credit card.  Under normal circumstances I would do the following (my +/- may be backwards):  Expense +$100 Credit Card -$100  and then when the credit card bill comes I would pay it off  Credit Card +$100 Chequing Account -$100  For expenses that I get reimbursements for I would like to be able to note that I paid for the expense with my credit card and that I paid off my credit card with my chequing account.  At the same time, I would like to be able to create another parent account (maybe "claimable expenses") that shows that I purchased the item, and was then reimbursed so that an individual expense for work or my club has a zero balance.  I tried to look this up in previous threads but didn't quite understand how to apply this to my situation Any advice would be appreciated. How do I install different (upgrade or downgrade) PHP version in still supported Ubuntu release? Moderncv package - cventry date width I am writing my CV using moderncv package, everythig is nice but I have a problem with \cventry command. I have something like this:   (it means 2010 - now)  I would want to have this in one line, rather than in two lines. I tried looking into the moderncv style files but with no success. What can I do to achieve the effect I want? How to convert a HEIF/HEIC image to JPEG in El Capitan? So, here’s the thing. I have a new iPhone and an old Mac. iOS 11 (still in beta as of today) and El Capitan (no more updates for this Mac). I use iCloud photo library in both devices. When I take a photo in the new format with my iPhone 7, is there any way to use it right away in my mac, without having to convert it in my iPhone first? I mean, can I get those photos synced through iCloud and converted locally on my Mac?  I have tried to find a third party software that could do that kind of conversion, but was not able to find any that would work on El Capitan. Any idea? Is there any way to increase the drop rate of items? Some items in Terraria drop only very rarely from certain enemies. It's a pain having to farm so many enemies to try to get these rare items. Is there any way to make them drop more often? I'm trying to create globally-unique identifiers in JavaScript.  I'm not sure what routines are available on all browsers, how &quot;random&quot; and seeded the built-in random number generator is, etc. The GUID / UUID should be at least 32 characters and should stay in the ASCII range to avoid trouble when passing them around. Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit given a sequence $a_n=a^{\frac{1}{n}}$ for $n\in\mathbb{N}^*$, $a\in\mathbb{R},a&gt;1$ then proof that $\lim\limits_{n\to+\infty}a_n=1$ by definition.   proof:  given $a_n=a^{\frac{1}{n}}$ for $a\in\mathbb{R},a&gt;1$.  for $n\in\mathbb{N}^*,n+1&gt;n\Rightarrow \frac{1}{n+1}&lt;\frac{1}{n}$ and because $a&gt;1$ we gets $a^{\frac{1}{n+1}}&lt;a^{\frac{1}{n}}$, since $\frac{1}{n+1}&gt;0$, then $1=a^{0}&lt;a^{\frac{1}{n+1}}&lt;a^{\frac{1}{n}}\Rightarrow 1&lt;a_{n+1}&lt;a_{n}$.  then we proof that $\lim\limits_{n\to+\infty}a_n=1$ we need to show that $\forall\epsilon&gt;0,\exists N,\forall n&gt;N,|a_n-1|&lt;\epsilon$  then for $\epsilon&gt;0$, choose $N=\frac{1}{\log_a(\epsilon+1)}$, since $a&gt;1$ we gets that $$\forall n&gt;N,1&lt;a^{\frac{1}{n}}&lt;a^\frac{1}{N}\Rightarrow0&lt;a^{\frac{1}{n}}-1&lt;a^{\frac{1}{N}}-1\Rightarrow |a^{\frac{1}{n}}-1|&lt;|a^{\frac{1}{N}}-1|=|a^{\log_a(\epsilon+1)}-1|=|\epsilon+1-1|=\epsilon\Rightarrow |a^{\frac{1}{n}}-1|&lt;\epsilon$$  wich implies that $\lim\limits_{n\to+\infty}a_n=1\square$  my proof to the limit is correct? This question aims to create an &quot;&quot;  of numerous questions that ask about determinants of specific matrices (I may have missed a few):              The general question of this type is  Let $A$ be a square matrix of rank$~1$, let $I$ the identity matrix of the same size, and $\lambda$ a scalar. What is the determinant of $A+\lambda I$?  A clearly very closely related question is  What is the characteristic polynomial of a matrix $A$ of rank$~1$? match first column of file a with paragraphs of file b I have 2 files. The first, fileA looks like  TCONS_00000066  XLOC_000030     -       u       q1:XLOC_000030|TCONS_00000066|0|0.000000|0.000000|0.000000|0.000000|- TCONS_00000130  XLOC_000057     -       u       q1:XLOC_000057|TCONS_00000130|0|0.000000|0.000000|0.000000|0.000000|- TCONS_00000395  XLOC_000206     -       u       q1:XLOC_000204|TCONS_00000393|0|0.000000|0.000000|0.000000|0.000000|-   FileB looks like:  &gt;TCONS_00000001 gene=XLOC_000001 AGATGAGCTGGTGGGGATGCTCTAAGAGAACGAGAGAAGCACAGAGCAGATAAACCACACCCACAGGCAC CACCGTCCTTGTTGGTAATGAAGAAGACGAGACGACGACTTCCCCACTAGGAAACACGACGGAGGCGGAG ATGATCGACGGCGGAGAGAGCTACAGAAACATCGATGCCTCCTGTCCAATCCCCCCATCCCATTCGGTAG TTGGATTGAAGACTACCGAATAAGAGAAGCAGGCAGGCAGACAAACCCTTGAACCAAGGAGTCCTCGCTG AGGAAGCTTTGGATCCACGACGCAGCTATGGCCTCCCCGCCCACCAGGCCGCCAGCCACAACCAGCTGAC TAGGTCGCATGCATCATCAGATTTCAATCTCCCTTCGTTCCCTGTCCCTAATCCAATACCAATAGGGAGC AATCAGCTGCTCCTCGACGGCGAGGGAGATGTCGTCGGCCGCGGGCCAAGACAACGGAGATACCGCTGGG GACTACATCAAGTGGATGTGCGGCGCCGGTGGCCGTGCGGGCGGCGCCATGGCCAACCTCCAGCGCGGCG TTGGCTCCCTCGTCCGTGACATTGGCGACCCCTGCCTCAACCCATCCCCCGTTAAGGGGAGCAAAATGCT CAAACCGGAAAAATGGCACACATGTTTTGATAATGATGGAAAGGTCATAGGTTTCCGTAAAGCCCTAAAA TTCATTGTCTTAGGGGGTGTGGATCCCACTATTCGAGCTGAAGTTTGGGAATTTCTTCTTGGCTGCTATG CCTTGAGTAGTACCTCAGAGTATAGGAGGAAACTAAGAGCTGTTAGAAGGGAAAAATATCAAATTTTAGT TAGACAGTGCCAGAGCATGCACCCAAGCATTGGTACAGGTGAGCTTGCTTACGCTGTTGGATCAAAGCTA   Now, fileA contains selected transcript numbers in the first column and fileB contains sequences of all transcripts. I want to scan fileB for the first column of fileA and print the trailing sequences of matching transcripts along with the transcript number. We use unit length Quaternion to represent rotations. Following is a general rotation matrix obtained ${\begin{bmatrix}m_{00} &amp; m_{01}&amp;m_{02} \\ m_{10} &amp; m_{11}&amp;m_{12}\\  m_{20} &amp; m_{21}&amp;m_{22}\end{bmatrix}}_{3\times 3}\tag 1 $.   How do I accurately calculate quaternion $q = q_1i+q_2j+q_3k+q_4$for this matrix?Means   how can we write $q_i$s interms of given $m_{ij}$  accurately? How to make hair material different from the plane itself? In Cycles Render, I added hair to a plane (as I was making a grass field) and I don't seem to know how to make the actual flat plane's material different from the hairs themselves, because I'd like to make the plane have an image texture and the hairs have a yellow-like color to them, but of course, if I attempt to make the material yellow-ish, the plane AND the hairs will become yellow. I'm done with the plane, I just want to control the hairs' materials. How do I reference photographs with a separate numbering system to figures in latex? I am writing a book, and would like to be able to have the photographs labelled with an independent numbering system to my figures.  In the text I would refer to, for example, figure X and separately to photograph X, so I want them to have different numbering systems, just as equations and figures do.  Is it possible to have a different \begin{figure} environment so that the numbering can be separated?