TIKZ MODULO inside of FOR LOOP
Using modulo operation to draw graph
Where did my default brushes go? I was working on a logo design for a client in Illustrator CS4 when suddenly the default brushes were no longer there. The brush files are still in place but they do not show up in the brushes panel. The options to show the brushes by type are checked but greyed out.   I tried a preference reset, that didn't fix it. I haven't tried any new brushes because the brush I needed was in the stock set. I know its bad form not to try everything but I needed one of the stock brushes to tweak an existing design. Installing Wi-Fi driver for Realtek Semiconductor RTL8723DE Device [10ec:d723] How do I install Wi-Fi drivers for Realtek RTL8723DE device in Ubuntu 16.04?  lspci -v | grep -i network 02:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device d723 I have been playing with Ubuntu for a few weeks now, and I'd like to revert my computer back to it's original - factory - defaults.   On the computer I have a recovery partition (it's a netbook). I went through the process of recovery and everything seemed fine. However, when I restart the computer I'm presented with   grub rescue &gt;   Now, my understanding is that when I installed Ubuntu "side by side" it replaced the MBR or something like it, with GRUB.   I've read on a slew of forums, that I need to use a Windows Recovery Disk.   Here are my issues:   a) I don't have a recovery disk, I have a recovery partition - it's a netbook. b) I don't have an external cd drive.   What I do have is a USB key that has about 1gb of space on it.   Thanks in advance. Is a semigroup with unique right identity and left inverse a group? We know that a semigroup with a right identity and right inverse for all elements is a group (e.g. see ). Symmetrically, also a left identity together with a left inverse implies a group. We also know that a semigroup with a right identity and a left inverse is NOT necessarily a group (see ). My questions are:   in a semigroup, is the existence of a UNIQUE right identity together with the existence of a left inverse enough to have a group? in a semigroup, is the existence of a right identity together with the existence of a UNIQUE left inverse enough to have a group?   I think both these claims are false,  ut haven't found a counter-example so far. I have to find the limit of this sum: $$\sum_{r=1}^{\infty}\cot ^{-1}(r^2+\frac{3}{4})$$  I tried using sandwich theorem , observing:  $$\cot ^{-1}(r^3)\leq\cot ^{-1}(r^2+\frac{3}{4})\leq\cot ^{-1}(r^2)$$  Now when I was calculating the limit of left hand expression, I convert it to $\tan^{-1}$, by using:  $$\tan^{-1}\frac{1}{x} = \cot^{-1}x$$  but couldn't sum up the terms of arctan series.     How can I proceed?   Is there any better way ? The Center of $\operatorname{GL}(n,k)$ The given question:  Let $k$ be a ﬁeld and $n \in \mathbb{N}$. Show that the centre of $\operatorname{GL}(n, k)$ is $\lbrace\lambda I\mid λ ∈ k^∗\rbrace$.  I have spent a while trying to prove this and have succeeded if $ k \subseteq \mathbb{R}$. So I imagine there is a nicer way to go about this. I have seen people saying take matrices where every element except one is zero in proving similar results but such matrices are not in $\operatorname{GL}(n,k)$ as they are not invertible.  What I have done.  I have said let $B \in$ Center then $B$ commutes with everything in $\operatorname{GL}(n,k)$. So take a permutation matrix, $P$ which swaps rows $i,j$ $P \neq I$. From this you can deduce that $B^T = B$ and that $B_{ii} = B_{jj}$. We can use the fact that $B$ is symmetric to find an orthogonal diagonalisation of $B$ by the spectral theorem.  This gives $QBQ^T = D \rightarrow B=D$. And as $B_{ii} = B_{jj}$ we can say $B = k * I$.   But the spectral theorem requires $B$ to be a real matrix.   How do I prove this for a general $k$?. How to generate XML file dynamically using PHP? indefinite article before proper names Kafka, discovered in the 1920s by the Expressionists, damned by the Nazis in the 1930s and by the Marxists at more or less the same time, was reinvented after World War II by the French Existentialists. They saw in him the father of Angst and the Angst for the father: an Albert Camus before his time.   Can you tell me what the purpose of using the indefinite article before the proper name is in the sentence above. What it be a mistake to write just "Albert Camus" without the article? How to get permanent token? I really need to get permanent token or dynamic generator. We set job in the server and this service will come to salesforce and get the data. To provide this, I created connected app, got the token from postman by myself and gave it. After a while (approximately 1 day), we faced with session id problem.   What can I do? $|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts $(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula] How to achieve nomenclature entries like: symbol, Description, Dimension and unit, etc? The title is pretty much I want to ask. More detail, the nomenclature entries should be sorted in groups like:   Nomenclature     Acronyms     Symbol  Description     % no Dimensions and Units      ...     Greek Symbols     Symbol  Description             Dimensions     Units     ...     Roman Symbols     Symbol  Description             Dimensions     Units     S       Surface area vector     L^2            m^2     ...    Superscripts     Symbol  Description     % no Dimensions and Units      ...    Dimensionless Numbers     Symbol  Description     Definition     ...   e.g. expected entries like this:       My current nomenclature settings for grouping [book class]:  %---------------------------------------------------------- %                        Nomenclature %---------------------------------------------------------- %\renewcommand{\nomname}{List of Symbols and Abbrev.} \renewcommand\nomgroup[1]{%   \ifthenelse{\equal{#1}{A}}{%    \item[\textbf{Acronyms}] }{%                  A - Acronyms     \ifthenelse{\equal{#1}{R}}{%      \item[\textbf{Roman Symbols}]}{%            R - Roman       \ifthenelse{\equal{#1}{G}}{%         \item[\textbf{•} Symbols }]}{%          G - Greek           \ifthenelse{\equal{#1}{S}}{%            \item[\textbf{Superscripts  }]}{{%          S - Superscripts         \ifthenelse{\equal{#1}{U}}{%          \item[\textbf{Subscripts }]}{{%                 U - Subscripts         \ifthenelse{\equal{#1}{X}}{%          \item[\textbf{Other Symbols }]}%            X - Other Symbols                     {{}}}}}}}}}} %\ifpdf \renewcommand{\nomlabel}[1]{\hspace{1 em}#1}%{\hspace{1.5 em}#1} \renewcommand*{\nompreamble}{\markboth{\nomname}{\nomname}}   But how to extend it with Dimensions and Units? By accident, I messed up a configuration file. How do I recover the default version without reinstalling or affecting other things? Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution? Is volunteer work allowed in the US while visiting under the VWP or a B1/B2 visa? If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc? I have data in an Excel file that I want to join with a shapefile in my project. The Excel file contains values like volumes. The Excel file and the shapefile I want to join it with both contain the same property names.  The problem is, when I join the two, I get too many decimals in the attribute table. I get six, but I only want it to be one.  I tested to change the format of the cells to one decimal, and then I saved the file as *csv. But, somehow I seem to loose data in the process? It should be 42 rows that contains data in the column i am working with, but I end up with only like 10?  Another thing is that my property names contains the letters Å. Ä and Ö, perhaps this complicates things?  I read the question , but it doesn't mention the problem with the data loss.  My question was tagged with , but I didn't write what version I'm using. I use QGIS 2.2.0. Would it help to upgrade to the latest version? Using local OpenStreetMap (*.OSM) map with Openlayers 3? What do I need to load a .OSM map in a client side javascript app? (Imagine an offline webapp). The value of a, b and c for this integral Find out the value of $a, b$ and $c$, for which $$ \lim _{x\to 0}\:\:\frac{1}{x^5}\left(\int _0^x\:\left(a+b \cos\left(t\right)+c \cos\left(2t\right)\right)dt\right)=\frac{1}{5} $$  My first thought was to separate the integral into multiple ones because i thought that it is pretty clear that each integral is a common one and a,b,c are constants and can be taken out . After I solved the integral, that's where I had the problem. I couldn't do the limit of the result that I've got in order to find out the value of $a,b$ and $c$ . The browser's "Back" button cause problems with the review buttons