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What are the complexity guarantees of the standard containers? Why does water pouring from a glass sometimes travel down the side of the glass? If you have a glass of water, say, three quarters full and you pour it at an angle of say, $45^{\circ}$ with respect to the the table, the water comes out of the glass and goes directly down towards the floor.  However, when the glass is more full, or even three quarters full and the 'angle of pouring' is far less with respect the table, when the water comes out of the glass, rather than going straight down it kind of stays stuck to the glass and travels down the outside of it.  Why does this happen? (I'm sure many of you have observed it yourself by accident and ended up making a mess). Dependency is not satisfiable: libtiff4 when trying to install Lightworks on Ubuntu 14.04 I was trying to install Lightworks 11.5.1 (amd64) on Ubuntu 14.04(amd64) but there's a notice: Dependency is not satisfiable: libtiff4. Is there anyway to solve this dependency issue?  Thanks in advance. pgfplots: lines and markers in different colors With pgfplots, I am creating a simple coordinate plot with error bars like this:    \documentclass[crop,10pt]{standalone} \usepackage[english]{babel} \usepackage{pgfplots}      \begin{document}%         \setlength{\linewidth}{246pt}%              \begin{tikzpicture}             \begin{axis}[             width=\linewidth,             ytick pos = left,             xtick pos = left,             clip=false,             axis on top,             tick align = outside,             yticklabel style={%             /pgf/number format/fixed,             /pgf/number format/precision=1,             /pgf/number format/fixed zerofill         },             ytick scale label code/.code={},             xlabel={X},             ylabel={Y},     ]             \addplot[mark=*]             plot[             error bars/.cd,             y dir=both,             y fixed=0.0001     ]             coordinates{(1,0.0005) (1.1,0.0013) (5,0.0015)};             \end{axis}             \end{tikzpicture}     \end{document}   In the original plot I have a lot more points. I would now like the line and the markers (including the error bars) to have different colors to better distinguish the line from the error bars. Is that somehow possible? The only way I found so far is to plot the data just as a line in one color and then plot it again just as markers in another color. This works, but I guess there must be some better solution to this. Thanks for the support, John How can I replace a string in a file(s)? Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges Let $t\in \mathbb R$. Prove that $\displaystyle{\sum_{n=1}^{\infty}n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+t}$ converges iff $t=\frac{1}{6}$.  While the $(\Rightarrow)$ direction was fairly easy (as $a_n$ should converge to $0$, forcing $t=\frac{1}{6}$), i'm facing some hard time trying to prove the second direction, that is $\displaystyle{\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})}$ converges. I did notice that $a_n=a_{-n}$ and tried to write this series as a Leibnitz series, but had no luck since the sequence doesn't decrease. I also tried to prove absolute convergence but then again, no luck. Thanks. Maybe a stupid question but how can I tell if I have a static IP address or a dynamic IP address? Running Fedora-13 Automatically set description list `labelwidth` based on widest label? How do I create a description list where the item text is automatically indented to the width of the widest label?  This is the same question as  but I would like the width of the widest label to be automatically calculated.  For example, I'd like the following output:    to be produced by the following input:  \documentclass{article} \usepackage{calc} \usepackage{enumitem} \usepackage{lipsum} \usepackage[margin=1em,papersize={4in,2.2in}]{geometry}  \newenvironment{mydescription}{%   \begin{description}[     leftmargin=!,     labelwidth=\magicgoeshere,     ]% }{%   \end{description}% }  \newcommand{\text}{long long long long long long long long long long   long long long long long long long long long long long long long   long long long long long long long text}  \begin{document} \begin{mydescription} \item[The longest label] text \item[Short] \text \end{mydescription} \hrule \begin{mydescription} \item[Medium label] text \item[Short] \text \end{mydescription} \end{document} Use spray paint to make mask for pre-sensitised board? I'm about to etch my first simple board for a project. I have a pre-sensitised board that (as I understand the process) you expose to UV light, then develop the board in a sodium hydroxide solution, then etch. The UV light will negatively affect the protective lacquer and developing it after exposing washes away the lacquer, making the board ready to etch.  I got the lye and I got sodium persulfate for the etching but I did not have any transparent paper as I thought I did! And it's impossible for me to get a hold of it in time (= this weekend, I live far from the city and it's a small one and I haven't found any place that stocks it so I have to order online and that's sometime next week I'd get it at the fastest).   So I am looking for an alternative solution. What I am considering is printing the design to regular paper, cut out a mask carefully from this paper and place it over the board and paint a mask on. Spray paint most likely, then in theory I would have a UV mask.  Anyone see any flaws in this plan? I have 100 files with 57,816 rows each.I want to do an outer join of these files by merging on basis of the common column.  I am using R programming for this but this is very slow.  fileList &lt;- list.files(, pattern=".txt") pm_list=lapply(fileList, read.table) merged_pm=merge_all(pm_list, by = "gene_short_name")   Is there any quick way to do this in bash? The other method that I can use is SQL but I have to create 100 tables first and then load them up before join,which is not very efficient way to do.  The number of rows are equal in each file, thats why I want to merge  based on common column and can't use cbind from R as the constants in the common column are a bit up and down in different files and not present at same location in each file.Below are two sample files.I want to join based on 'gene_short_name'  gene_short_name FPKM56  MT-TF   0.90 MT-TV   0 MT-RNR1 310.015 MT-TL1  0 MT-TM   0   File 2 is below:  gene_short_name FPKM53  MT-TF   0 MT-TV   0.344 MT-TM   0.10 MT-TL1  0 MT-RNR1 0 MT-ND2  158.332 What's the derivative of: $ \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$? let $ y=\displaystyle \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$, i'm really interesting to know how do I find :  $\displaystyle \frac{dy}{dx}$ ?.  Note: I have used the definition of derivative of the square root function but i don't succed .  Thank you for any help Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$ What is the number of Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$? I have this alias set in my system /etc/bashrc file:  alias root="sudo !!"   The intention of this being to run the last used command using sudo of course. When used, it of course appears to substitute the last command in history to the bashrc file upon shell initialization, and not the actual command that you would get if you were to run sudo !! in an interactive shell. I've also tried alias root="sudo fc -s" to no avail.  I realize this is probably something to do with how the BASH does command substitutions, but can someone explain why this is, and provide a usable substitute?  I'm running BASH version 3.2.51(1)-release (x86_64-apple-darwin13). How do I call one constructor from another in Java? I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of R gives me Negative Binomial as the best-fit. Now from the  page, the definition is given as:     NegBin(r,p) distribution describes the probability of k failures and r   successes in k+r Bernoulli(p) trials   with success on the last trial.   Using R to perform model fitting gives me two parameters mean and dispersion parameter. I am not understanding how to interpret these because I cannot see these parameters on the wiki page. All I can see is the following formula:    where k is the number of observations and r=0...n. Now how do I relate these with the parameters given by R? The help file does not provide much information either.   Also, just to say a few words about my experiment: In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment.   Now, if the model fits the Negative Binomial, I can blindly say that it follows that distribution but I really want to understand the intuitive meaning behind this. What does it mean to say that the number of people contacted by my test subjects follows a negative binomial distribution? Can someone please help clarify this? Prove Borel Measurable Set A with the following property has measure 0. This question is exercise 4.10 of Richard F. Bass's Real Analysis for Graduate Students, 2nd edition.  Let $\epsilon \in (0,1)$, let $m$ be Lebesgue measure, and suppose $A$ is Borel Measurable subset of $\mathbb R$. Prove that if $$ m(A\cap I)\leq (1-\epsilon)m(I)$$  for every interval $I$, then $m(A)=0$.  Collection of my thoughts  1. Try to prove by contradiction, suppose $m(A)=a&gt;0$ Borel Measurable Set satisfies the condition given. A property of any Borel Measurable Set on $\mathbb R$ is $A$ contains a closed set $F$ and is contained in open set $O$, and the measure of $F$ and $O$ can be arbitrarily close to $a$. 2. Obviously $A$ contains no interval, but it does not lead to contradiction, because we can find an example of $m(A)&gt;0$ that contains no interval(fat Cantor Set(remove middle 1/4 each time) has measure $1/2$ and contains no interval).  2'. For fat Cantor Set $C$ and given $\epsilon&gt;0$ how could we construct an interval I satisfies $m(C \cap I)&gt;(1-\epsilon)m(I) ?$   Maybe try to write Borel measurable set as countable union/intersection of intervals.   I'm stucked here and will appreciate any help, some examples/special case will be great too. Keyboard shortcut for switching between different keyboard layouts in Ubuntu Mate Is there a pre-assigned keyboard shortcut for switching between different keyboard layouts in Ubuntu Mate? What should I do if I have two libraries that provide functions with equivalent names? Number of $n^2\times n^2$ permutation matrices with a 1 in each $n\times n$ subgrid I found the following question in a paper I was trying to solve:  The following figure shows a $3^2 \times 3^2$ grid divided into $3^2$ subgrids of size $3 \times 3$. This grid has $81$ cells, $9$ in each subgrid.    Now consider an $n^2 \times n^2$ grid divided into $n^2$ subgrids of size $n \times n$. Find the number of ways in which you can select $n^2$ cells from this grid such that there is exactly one cell coming from each subgrid, one from each row and one from each column.  My try:  Since we have $n^2$ rows, $n^2$ columns and $n^2$ subgrids in total, we have to choose one and only one cell from each of them. Let's choose them one at a time. We can choose the first cell in $n^4$ many ways. Then, we'll have to avoid that subgrid, that column and that row that we've chosen the first one from when choosing the second cell. So, we have $n^4-n^2-2n(n-1)$ choices. We can continue this to get the total number of possible ways. But, I think there's a hole. Say, we've chosen the first cell from the subgrid of the up-left corner and the second from the subgrid just right to it so that it doesn't violate any rules. Then, when finding the number of ways we can choose the third cell, we would have substracted some of the cells twice. I think you get it. Please, if anyone can help me solving this problem, it'd be greatly appreciated. SQL Query; Admin Log System; Foreign Keys; Retriving multiple rows form different tables at once Table A (users)  id     | name   | ip 52433    Yashas   1.1.1.1 512      Admin    5.6.7.8   Table B (admin_record)  id    | admin | time    | date    | reason | action  52433   512     2312352   1213213   Test     WARN   id is FOREIGN key  Table B keeps a log of all actions an administrator takes on his users. And the table A stores the account information of the users &amp; administrators.  I am trying to display a list of actions taken by a administrators on a user.   I want to write a query which gets me all the rows of table B where id = fixed number.  Here is what I want to display:  "Administrator1 [Name]" took action on "User Name" for "[Note]" on XX/XX/XXXX. "Administrator2 [Name]" took action on "User Name" for "[Note]" on XX/XX/XXXX. "Administrator3 [Name]" took action on "User Name" for "[Note]" on XX/XX/XXXX.   All I have is the user's id using which I need to obtain all the entries in the log along with the administrator names. I need to obtain the admin's name, users name and all the contents of table B related to a particular user in one single query. If possible, I want the to change the field name(not literally change, but want the SQL server to send the data with new field names to separate admin name &amp; user name) of the admin's name to admin_name and user's name as . I mean something like this  SELECT users.name AS admin_name WHERE users.id = %i  AND SELECT users.name AS user_name WHERE users.id = %i   (the query isn't correct,it us just an example to show what I am trying)  Progress so far:   SELECT player.name, player.ip, admin.name, record.date, record.time, record.action, record.reason FROM admin_record AS record JOIN users AS player ON player.id = record.id JOIN users AS admin ON admin.id = record.admin WHERE player.id=%i   where admin_record is table B &amp; users is table A.