How do I make a striped texture?
How to create a torus with divided cuts that correspond to the direction of the torus
If a measure only assumes values 0 or 1, is it a Dirac's delta? How do you set password-hash for OpenLDAP? What are the shortcomings of the Mean Absolute Percentage Error (MAPE)? The  () is a common accuracy or error measure for time series or other predictions,  $$ \text{MAPE} = \frac{100}{n}\sum_{t=1}^n\frac{|A_t-F_t|}{A_t}\%,$$  where $A_t$ are actuals and $F_t$ corresponding forecasts or predictions.  The MAPE is a percentage, so we can easily compare it between series, and people can easily understand and interpret percentages.  However, I hear that the MAPE has drawbacks. I'd like to understand these drawbacks better so I can make an informed decision about whether to use the MAPE or some alternative like the MSE (), the MAE () or the MASE (). Since I upgraded to the latest version of Ubuntu, I cannot install the Java OpenJDK package needed to compile Android custom ROMs. When I run sudo apt-get install openjdk-7-jdk, the following error appears:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  openjdk-7-jdk :  Depends: openjdk-7-jre (= 7u51-2.4.6-1ubuntu4) E: Unable to correct  problems, you have held broken packages.   How do I fix this problem? Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$ I am given the info that A is an invertible  m by m matrix and B is a m by n matrix. By solving for the null space $ABx=0$, I get $A^{-1}ABx=A^{-1}0$, therefore $Bx=0$. I concluded that the null spaces of A and AB must be equivalent, and therefore the nullity(AB) = nullity(B) = some number p. Therefore rank(AB) = n-p = rank(B)   (because both AB and B are m by n matrices).   Is this proof valid, specifically the null space step? Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$ I have the following homework problem:  Let $B$ be the set of rational numbers in the interval $[0,1]$, and let $\{I_k\}_{k=1}^n$ be a finite collection of open intervals that covers $B$. Prove that $\sum_{k=1}^n m^*(I_k) \geq 1$.    This is my approach, First we have that $B = \mathbb{Q}\cap [0,1]$. Now, $B \subset \bigcup_{k=1}^nI_k$, where $I_k$ are open intervals.In particular $0 \in B \wedge 1 \in B$.Now, since $B \subset \bigcup_{k=1}^nI_k$ then there exist positive numbers, $\epsilon_0, \epsilon_1$ such that: $$(0-\epsilon_0,0+\epsilon_0)\subset \bigcup_{k=1}^nI_k$$ $$(1-\epsilon_0,1+\epsilon_0)\subset \bigcup_{k=1}^nI_k.$$   Clearly, $-e_0 \notin [0,1]$ and $e_1 \notin [0,1]$.I am not sure, if so far I am in the right track. I want to prove or disprove this problem: If there exist $\lim\limits_{x\rightarrow \infty} (f'(x)+f(x))=L&lt;\infty$ then $\lim\limits_{x\rightarrow\infty} f(x) =L$.  When I assume problem below:  If there exist $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L&lt;\infty$, There exists $\lim\limits_{x\rightarrow\infty} f(x)$?  I can use mean-value theorem to show that.  So my question is:     If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x))=L&lt;\infty$, does $\lim\limits_{x\rightarrow\infty} f(x)$ exist? When customers buy things from a store, you say:  (1) Customers give ABC Store business.  If I "turn this around", can I say:  (2) ABC Store obtains or acquires business from its customers.  Do these verbs work in (2)? Would particles behave the same way as a satellite orbiting earth, only far more compact and rapid correlating to the gravitational force of the black hole? Removing unwanted appearance of underlying mesh So I'm in Linux and I want to have a program accept arguments when you execute it from the command line.  For example,   ./myprogram 42 -b -s  So then the program would store that number 42 as an int and execute certain parts of code depending on what arguments it gets like -b or -s. I'm struggling with my lab report. I have a questionnaire which contains Likert responses (1-7) as well as questions that require only yes or no answers. I want to see if there is a correlation between higher scores on the likert scale and responses to the binary answers to the other questions.   Specifically - the likert response is about anxiety levels. The binary (yes/no) answer is about negative consequences due to alcohol use. I want to just run the one ordinal likert item with all the negative consequence responses to see if there is a relationship. Can anyone help me?     Thanks so much for the fast comments. It definitely assures me that Spearman's Rho can be used but my main problem is the fact that i am mixing binary and ordinal variables together in the one correlation matrix.  I have one ordinal variable (anxiety - 1-7 on likert scale) crossed with 13 dichotomous (0 or 1 representing yes or no) to answers ("have you ever been hospitalised due to your alcohol use?). I get statistically significant answers (&lt;.05 and &lt; .01 but the Correlation coefficients are tiny (i.e o.2) at best.   the hospitalisation is the DV an the anxiety levels the IV.   I just think i'm doing something wrong here. should i collapse the 13 binary variables in to one some how?   i can't see how SPSS will recognise the values between 1-7 when correlating with binary answers. i keep thinking it will just read that there is something in that box (ordinal) but not recognise the value (i.e 1-7) . but people keep saying that SPSS does in fact recognise this difference and account for it. Why should I "watch" a nearby Pokémon? How are questions in the 'hot' tab on a site selected? I know questions on the "hot" tab of a site homepage are based on some sort of views/velocity criteria, but does anyone know the actual algorithm used?  Background: I was considering a feature-request about the "hot" tab, but I don't have enough information to speak about it intelligently. Register On-Click Event with jQuery - Not Firing Conjugation: Do we cite authors or papers? When referencing to another work in a scientific paper, do we cite the paper or its author(s)?  This question is intended to clarify the conjugation of the verb that follows the reference -- especially in these cases:   One author, two papers:     Jane Doe (2015a, 2015b) list-s the very specific conditions under which...   -> lists (singular: referencing to Jane Doe) or list (plural: referencing to both papers) Several authors, one paper:     John Doe, et al. (2015) claim-s this and that.   -> claim (plural: referencing to the multiple authors of the paper) or claims (singular: referencing to the single paper). If $m_1 , m_2, \cdots m_n$ are natural numbers where at least one of them is not a perfect square, then how do I prove that the sum $$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$$ is irrational? I'm hoping to prove this using methods from pre-calculus level algebra. rotatebox symbol in caption generates error Following minimal example doesn't work and generates an error  \documentclass{article} \usepackage{graphicx} \usepackage{amssymb} \begin{document} \begin{figure}   FIGURE \caption{$\blacksquare$ result of; \rotatebox[origin=c]{45}{$\blacksquare$}}% \end{figure} \rotatebox[origin=c]{45}{$\blacksquare$} \end{document}   The error message says:  rotatebox-in-caption.tex|7| Argument of \@caption has an extra }. || &lt;inserted text&gt;  ||                 \par  || l.7 ...; \rotatebox[origin=c]{45}{$\blacksquare$}}   Do I have to wrap the \rotatebox in a certain box to make it work? Function ereg() is deprecated Sum of derivatives of a polynomial