I am trying to run bash script:  export LD_LIBRARY_PATH=/usr/lib/fsl/5.0:$LD_LIBRARY_PATH export SUBJECTS_DIR=/output timefmt="%C --- CPU:\t%E real,\t%U user,\t%S sys\t%P\tMem:\t%KkiBavg.,\t%MkiB max.\tExit:\t%x" all_ids=() for dirname in /input/*; do  id=${dirname#/input/}    # remove "/input/sub-" id=${id%/}             # remove trailing "/"  printf 'Adding ID to recon-all processing list: %s\n' "${id}" &gt;&amp;2 if [ ! -e "/output/$id" ]; then     # no output file corresponding to this ID found,     # add it to he list            all_ids+=( "$id" )     /usr/bin/time -f "$timefmt" \     recon-all -s "${id}" -i /input/${id}/unprocessed/3T/T1w_MPR1/${id}_3T_T1w_MPR1.nii.gz -i /input/${id}/unprocessed/3T/T2w_SPC1/${id}_3T_T2w_SPC1.nii.gz     printf 'Series with t1 found, subjects matched: %s ; %s ; %s\n' "${id}" fi done  printf 'Found ID: %s\n' "${all_ids[@]}" &gt;&amp;2  printf '%s\n' "${all_ids[@]}" | parallel --jobs 6 --timeout 300% --progress recon-all -s {.} -all -qcache   I made a docker container and it executed without any result, it just goes to the place and prints printf 'Adding ID to recon-all processing list: %s\n' "${id}" &gt;&amp;2, how ever if i run it with entrypoint=bash option with seperated command it executed properly.  Output of bash -x script.sh:  + for dirname in '/input/*' + id=102311 + id=102311 + printf 'Adding ID to recon-all processing list: %s\n' 102311 Adding ID to recon-all processing list: 102311 + '[' '!' -e /output/102311 ']' + all_ids+=("$id") + /usr/bin/time -f '%C --- CPU:\t%E real,\t%U user,\t%Ssys\t%P\tMem:\t%KkiB avg.,\t%MkiB max.\tExit:\t%x' recon-all -s 102311 -i /input/102311/unprocessed/3T/T1w_MPR1/102311_3T_T1w_MPR1.nii.gz -i /input/102311/unprocessed/3T/T2w_SPC1/102 311_3T_T2w_SPC1.nii.gz  + printf '%s\n' 100408 100610 101006 101107 101309 101410 101915 102008 102109 102311 + parallel --jobs 6 --timeout 300% --progress recon-all -s '{.}' -all -qcache
Suppose the default shell for my account is zsh but I opened the terminal and fired up bash and executed a script named prac002.sh, which shell interpreter would be used to execute the script, zsh or bash? Consider the following example:  papagolf@Sierra ~/My Files/My Programs/Learning/Shell % sudo cat /etc/passwd | grep papagolf [sudo] password for papagolf:  papagolf:x:1000:1001:Rex,,,:/home/papagolf:/usr/bin/zsh # papagolf's default shell is zsh  papagolf@Sierra ~/My Files/My Programs/Learning/Shell % bash # I fired up bash. (See that '%' prompt in zsh changes to '$' prompt, indicating bash.)  papagolf@Sierra:~/My Files/My Programs/Learning/Shell$ ./prac002.sh  Enter username : Rex Rex # Which interpreter did it just use?   **EDIT : ** Here's the content of the script  papagolf@Sierra ~/My Files/My Programs/Learning/Shell % cat ./prac002.sh  read -p "Enter username : " uname echo $uname
Why do we care about eigenvalues of graphs?  Of course, any novel question in mathematics is interesting, but there is an entire discipline of mathematics devoted to studying these eigenvalues, so they must be important.  I always assumed that spectral graph theory extends graph theory by providing tools to prove things we couldn't otherwise, somewhat like how representation theory extends finite group theory.  But most results I see in spectral graph theory seem to concern eigenvalues  not as means to an end, but as objects of interest in their own right.  I also considered practical value as motivation, e.g. using a given set of eigenvalues to put bounds on essential properties of graphs, such as maximum vertex degree.  But I can't imagine a situation in which I would have access to a graph's eigenvalues before I would know much more elementary information like maximum vertex degree.  (EDIT: for example, dtldarek points out that $\lambda_2$ is related to diameter, but then why would we need $\lambda_2$ when we already have diameter?  Is this somehow conceptually beneficial?)     So, what is the meaning of graph spectra intuitively?  And for what practical purposes are they used?  Why is finding the eigenvalues of a graph's adjacency/Laplacian matrices more than just a novel problem? Why won't SparseArray let me store values with the head List? Intuition for groups This is quite a non-standard question, certainly for mathematics, though I believe it is no less important (for me and my peers, i.e. grads).  The course I am reading so far introduced us to Groups, rings, fields, etc. in the first year, progressing to characters, reps etc in the latter years.  However, even with representation theory I still don't feel like I have a good intuition.  How do you gain intuition in such an area. I know there will be a response of doing examples, but this doesn't really help - I've done lots already.  Am I doomed. calculating resistance for LED strips to use as parking lamps and turn signals I'm installing LED strips in my car's tail lamps to convert it from conventional bulbs to LEDs. I have a understanding of what I'm doing but not the complete knowledge to make the circuit work correctly without doing some guessing so I figured I would ask here.   I'm planning on working with and I need a length of 16", 15" and 14" to make then look correct in my housings. When I did the math the 19.7" strips have about 1.5 LEDs per inch and need to be segmented into 3 LED groups so I may have to get creative with the placement.   Ffom what I understand I need 2 diodes and a resistor. One diode on the parking lamp power, and one on the turn signal/brake power and then a resistor on the parking lamp  wire to step down the voltage enough to make them dim enough to use as a parking lamp and distinguish it from the brighter turn/brake lamps.  Does anyone know what size resistor and what size diode to use in this project? The voltage, with the car running, is around 13.8V to the rear lamps. I figure it should be running around 7V to the LEDs to light them as parking lamps.  Also will leaving out a cluster of 3 LEDs change the strips intensity to where I'll need different resistors for each strip? Example where convergence in mean does not imply convergence in quadratic mean Is there an example where convergence in mean does not imply convergence in quadratic mean. $E|X_n-X|\rightarrow 0$ but $E|X_n-X|^2 \nrightarrow 0$.  It seems like this should be fairly straightforward, but I cannot really come up with an answer.  I'd imagine the answer would look something like   $$X_n=\begin{cases}a &amp; \text{with probability } \frac{1}{n} \\\  0&amp; \text{with probability } 1-\frac{1}{n} \end{cases}$$ I've been reading , and I would like to know why the Lasso provides variable selection and ridge regression doesn't.  Both methods minimize the residual sum of squares and have a constraint on the possible values of the parameters $\beta$. For the Lasso, the constraint is $||\beta||_1 \le t$, whereas for ridge it is $||\beta||_2 \le t$, for some $t$.  I've seen the diamond vs ellipse picture in the book and I have some intuition as for why the Lasso can hit the corners of the constrained region, which implies that one of the coefficients is set to zero. However, my intuition is rather weak, and I'm not convinced. It should be easy to see, but I don't know why this is true.  So I guess I'm looking for a mathematical justification, or an intuitive explanation of why the contours of the residual sum of squares are likely to hit the corners of the  $||\beta||_1$ constrained region (whereas this situation is unlikely if the constraint is $||\beta||_2$). Problem from Herstein on group theory Please revoke badges gained by abusive voting In  (not feature request), :  ... if we find that people are abusing the system their accounts may get suspended. I would consider that kind of behavior abuse.  Well  sure qualifies. He has 11 Stack Exchange accounts and has in the last day spammed at least 8 of them to gain the Suffrage and sometimes Vox Populi badges. That's over 250 votes† in just a few hours! (And  -- while voting on other user's posts too.) I guarantee that he's not voting on those posts for/by their merits. Here's when he scammed the Suffrage badge per site (while also gaming the Vox Populi on some sites):                      - 2017-03-11 16:23:15Z                     - 2017-03-11 17:41:41Z                     - 2017-03-11 18:08:13Z                           - 2017-03-11 19:25:10Z                  - 2017-03-11 19:55:16Z                               - 2017-03-11 20:00:49Z               - 2017-03-11 20:03:13Z  - 2017-03-11 21:11:40Z  Note that he got the badge on three sites within an 8 minute span (but that might just be job run times). Please revoke badges gained through improper voting. And, maybe also warn/suspend such abusive voters.   † His account vote totals don't show all votes as some serial voting was reversed -- but none of the ill-gotten badges were. For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$ Here are my thoughts so far:    $C_p = \langle x \mid x^p =e\rangle$ $C_q = \langle y \mid y^q =e\rangle$ $C_p \times C_q$ has elements of the form $(x^a,y^b)$ There are $p$ possible values for $x^a$ and $q$ possible values for $y^b$. So there are $pq$ possible elements in $C_p \times C_q$. $C_{pq} = \langle z\mid z^{pq} = e\rangle$ and there are $pq$ elements in this group. For an isomorphism from $C_p \times C_q$ to $C_{pq}$ we send $(e,e)$ to $e$ to ensure that the identities are mapped to each other. However, I'm not sure how to define an isomorphism for the other elements. Whenever I am given a system type with a certain transfer function, I am always asked to proceed to find out the 1. impulse response and 2. step response of the system. My question is, what is so special about these two response types that other responses, like for example parabolic response, is not what I am asked to find out? I need a little hint in a proof on convergence of a sequence. The problem I have is: Suppose $(x_n)$ is a monotone decreasing sequence of real numbers such that $\sum x_n$ converges, prove that:  $$\lim_{n \to \infty} nx_n=0$$  My idea is: proving this fact aims to prove that given $\epsilon &gt;0$ there's some natural $n_0 \in \mathbb{N}$ such that if $n &gt;n_0$ we have $|nx_n|&lt;\epsilon$.  Now, I know that $\sum x_n$ converges, so that given $\epsilon'&gt;0$ there's some $k_0 \in \mathbb{N}$ such that if $k &gt; k_0$ we have:  $$\left|\sum_{i=1}^{k}x_i - S\right|&lt;\epsilon'$$  Where $S = \sum x_n$. Now, since $(x_n)$ is monotone decreasing we know that we must have $x_1 &gt; \cdots &gt; x_k$ so that the sum of all $x_i$ should be less or equal to $k x_k$. So I know that I have:  $$\left|\sum_{i=1}^{k}x_i - S\right|\leq\left|\sum_{i=1}^{k}x_i\right|+|S|\leq|kx_k|+|S|$$  I feel that the proof will come from this, however I'm stuck at this point. Can someone give just a little hint on how to proceed from here?  Thanks very much in advance for your help. Rename ToC, List of Figures, References I would like to know how to rename the standard list of figures, table of contents, and references. What I saw so far relying on \renewcommand{\contentsname}{name} did not work so far.  Here's the list of preambles I use:  \documentclass[12pt]{report} \usepackage[utf8]{inputenc}  \usepackage{fourier} \pagestyle{headings} \usepackage{marvosym} \usepackage[pdftex]{graphicx} \usepackage[margin=2.5cm]{geometry} \usepackage{rotating} \usepackage{amsmath} \usepackage{booktabs} \usepackage{url} \usepackage{natbib} \usepackage{setspace} \linespread{1.5} \newenvironment{remark}{\par\mbox{}\par\noindent{\bfseries             \emph{Remark}\/}:\normalfont}{\par} \newenvironment{defin}{\par\mbox{}\par\noindent\bfseries \emph{\Pointinghand\     }\normalfont}{\par} \setcounter{toc**strong text**depth}{2}  \usepackage[colorlinks=true, a4paper=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue]{hyperref} \pdfcompresslevel=9 \setstretch{1.0} %vertical stretch \usepackage{fontspec} \setmainfont[BoldFont       = AvenirNextRoundedPro-Bold.otf , ItalicFont     =AvenirNextRoundedPro-Italic.otf]{AvenirNextRoundedPro-Reg.otf} \defaultfontfeatures{Mapping=tex-text} \usepackage{multirow} \usepackage{array} \usepackage{booktabs} \usepackage{hyperref} \hypersetup{ hidelinks, } \usepackage{ragged2e} \usepackage{euler} \usepackage[euler-digits,euler-hat-accent]{eulervm} \usepackage[labelfont=bf]{caption} \usepackage{wrapfig} \usepackage{amsmath} \usepackage{amssymb}  \usepackage[english]{babel} \usepackage[nottoc]{tocbibind} %Adds "References" to toc \usepackage{titlesec} \titleformat{\chapter}[display]{\bfseries\huge}{\filleft\Large\chaptertitlename~\thechapter}{1ex}{\vspace{1ex}\filright}[\vspace{0.5ex}\titlerule] \usepackage{float} \usepackage{etoolbox} \makeatletter \patchcmd{\@caption}{\csname the#1\endcsname}{\csname fnum@#1\endcsname:}{}{} \renewcommand*\l@figure{\@dottedtocline{1}{2em}{6em}} \let\l@table\l@figure  \makeatother % default for 3rd arg: 2.3em - for list of figures and tables \usepackage{background} \definecolor{textcolor}{HTML}{000000}             \newcommand\Text{c\quad o\quad n\quad f\quad i\quad d\quad e\quad n\quad t\quad i\quad a\quad l} \SetBgColor{textcolor}\SetBgOpacity{0.3}\SetBgAngle{90}         \SetBgPosition{current page.center} \SetBgVshift{-0.33\textwidth} \SetBgScale{1.8}         \SetBgContents{\sffamily\Text} %for confidential   I also use TexMaker. I do not know how relevant it is, but here my document language is set to English (even if it's not the language I write in, in that document, but it isn't a problem seemingly). What I also saw is that, if I remove babel and the references, I can rename my ToC and LoF, LoT. But I need the references though. Any tip would be very welcome!  Edit: I cannot provide text data from my project, because it is confidential. Here's what I can provide from the main document. Here is what I can include more.  \begin{document} \include{02_front}  \setcounter{page}{0} \pagenumbering{roman} \tableofcontents \listoffigures \listoftables \newpage \setcounter{page}{0} \pagenumbering{arabic} \chapter{blabla} \section{test é è åøæ î} \appendix \bibliographystyle{plain}  \bibliography{80_refs}   \end{document}   Also, I actually finished writing my thesis but I need to summarize it briefly in another language, am would be extremely unwilling to test and remove packages that "might be" not very useful. I literally only have to change these names of ToC, LoF, ToF and references. Is trace invariant under cyclic permutation with rectangular matrices? I'm working with trace of matrices. Trace is defined for square matrix and there are some useful rule, i.e. $\text{tr}(AB) = \text{tr}(BA)$, with $A$ and $B$ square, and more in general trace is invariant under cyclic permutation. I was wondering if the formula $\text{tr}(AB) = \text{tr}(BA)$ holds even if $A$ and $B$ are rectangular, namely $A$ is $n$-by-$m$ and $B$ is $m$-by-$n$. I figured out that if one completes the involved matrices to be square by adding zero entries in the right places, then the formula still works... but I want to be sure about this! Cannot reach public WIFI login page in Ubuntu 18.04 Captive Portal Issue Show that the operator norm is submultiplicative We had in our lecture on numerical analysis the following: Let $\mathrm{Lin}(X,Y)$ be the set of all linear maps $X\rightarrow Y$. Let $A\in\mathrm{Lin}(\mathbb R^l,\mathbb R^n)$ and $B\in\mathrm{Lin}(\mathbb R^n,\mathbb R^m)$ and $\|C\|_{op}:=\max_{\|x\|\leq1}\|C(x)\|$. Then our lecturer followed $\|A\circ B\|_{op}\leq\|A\|_{op}\cdot\|B\|_{op}$. So he didn't prove it and so I've tried it by my own. My attempt: $$\begin{aligned} \|A\circ B\|_{\mathrm{op}} &amp;= \max_{\|x\| &lt; 1}\|(A \circ B)(x)\| \\ &amp; \leq \max_{\|x\| &lt; 1} \|A\|_{\mathrm{op}} \|B(x)\| \\ &amp;= \|A\|_{\mathrm{op}} \max_{\|x\|\leq1}\|B(x)\|\\ &amp;= \|A\|_{\mathrm{op}}\|B\|_{\mathrm{op}} \end{aligned}$$ But this seems too easy. I am really interested in a nice proof so anybody could help? Thanks a lot! How do I show that a two-qubit state is an entangled state? The Bell state $|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle )$ is an entangled state. But why is that the case? How do I mathematically prove that? How do I distinguish between a command, utility, or builtin for getting documentation? How to pause with specific time between two command in script? I want to do such as following:  #!/bin/bash command1 pause 30 seconds command2 exit   This is only example script with pause of 30 seconds between run of 2 command.  How to do this? UK Visa in an expired Nigerian passport - what to use? I am in Nigeria, my passport will expire in 4 months and I have a document to apply for a UK visiting Visa with that passport number.  Should I use it like that or go for another passport. If I choose to get another passport, how will I use it because of the passport number on the about to expired one in the document I want to use for Visa. $P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$ Here is the theorem and proof in my textbook.     Thm.  Let $P$ be an ideal of a commutative ring $R$ with identity $1$.  Then $P$ is a prime ideal of $R$ if and only if $R/P$ is an integral domain.   Proof.   Suppose that $P$ is a prime ideal of a commutative ring $R$ with $1$.  Then $P$≠$R$ implies $1+P≠0+P$. Hence $R/P$ is a commutative ring $R$ with identity.  Assume that $(a+P)(b+P)=0+P$.  Then $ab+P=0+P$ and $ab∈P$.  By the definition of a prime ideal P we get $a∈P$ or $b∈P$.  That is, $a+P=0+P$ or $b+P=0+P$.  Thus $R/P$ is an integral domain.   Conversely, if $R/P$ is an integral domain, then $1+P≠0+P$ and $R/P$ is a commutative ring $R$ which has no zero divisors.  Hence $P≠R$.  Assume $ab∈P$.  Then $ab+P=0+P$ and $(a+P)(b+P)=0+P$.  Since $R/P$ is an integral domain, we get $a+P=0+P$ or $b+P=0+P$.  So $a∈P$ or $b∈P$.  Thus $P$ is a prime ideal.    I am having problems understanding proof with "Conversely, if $R/P$ is an integral domain, then $1+P≠0+P$.".  I know that $R/P$ has an identity. (cause it is ID)  But, why doesn't "$P$" have an identity?  Isn't there a case $P=R$?  Please help me understanding. I think $P≠R$ should be with condition of Thm..  Thank you in advance.