How to get the time to display as1:04 instead of 1:4
How can I pad an integer with zeros on the left?
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer let $a_{i},i=1,2,\cdots,n$ be postive integer ,show that $$1^{n-1}2^{n-2}\cdots (n-2)^2(n-1)|\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$$  I know this $\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$ is  Vandermonde  determinants,and I found $$1^{n-1}2^{n-2}\cdots (n-2)^2\cdot (n-1)=1!2!3!\cdots (n-1)!=\prod_{1\le i&lt;j\le n}(j-i)$$ we only prove $$\prod_{1\le i&lt;j\le n}\dfrac{a_{j}-a_{i}}{j-i}$$ is integer  maybe consider Vandermonde determinants ? But I can't prove this UK Standard Visitor visa application to sit for PLAB 1 without savings or job I am a medical doctor in Pakistan. I have been on a career break to allow myself to study full time for the IELTS exam (from which I recently got the required band score) and PLAB 1. I have now registered and paid for the PLAB 1 exam in UK for June 2016, as the next sitting in Pakistan is in November 2016 and I feel like I am ready to do the exam sooner.  Due to having no current employment, my savings are limited (around 25,000 Pakistani Rupees) but I live with my parents and do not have any financial commitments at home.  My savings have depleted in the past ten months whilst I have taken a career break and the money has been used for my own personal expenses. My trip to the UK is being funded by my grandfather who is a British citizen. He is a retired doctor with a good NHS pension. He has provided me with:   6 months bank statements which clearly show his pension deposits   Letter from NHS Pensions stating his pension   Sponsorship letter stating that he will pay for my PLAB exam fee, travel, accommodation and subsistinence costs whilst in the UK   Copy of British passport  Document confirming that he owns the house he lives in mortgage-free Confirmation email from GMC stating he has paid the PLAB exam fee.   Without large personal savings and no current job (but I have job offers now) would my application be rejected or is the strong sponsorship going to be good enough?  Are there any other documents I should consider submitting that may help me get a visa? Hill cipher, unknown letter value I've been struggling on this problem for a while now : the Hill cipher is well-known to be vulnerable to known-plaintext attack due to its linearity. Given a key matrix $K$ of size $n\times n$, one can retrieve the key with as little as $n^2$ plaintext/cipher text couples.  All examples found on the Internet assume an alphabet where $A=0, B=1 \dots Z=25$, but how could we break the Hill cipher using a know-plaintext attack without any clue over the alphabet permutation nor the key matrix ?  I've tried several things such as  the whole set of equations together, however it requires several divisions in $\bf{Z}_{26}$ which aren't possible (i.e. division by even numbers or 13) Display lost/negative reputation in topbar achievements When you get reputation, you get a +X green spot on your reputation feed telling you that you gained reputation and if you drop down the menu, you get more detail.  How about we make it that when you lose more than you got since the last time you checked, you see it red with a little -X.  For example, let's say you've just looked at the reputation bar so any old rep notification is gone and you ask a new question. 3 users downvote your question and 1 upvotes it. You will see it green because you gained 5 rep but you should see it red because you are at -1 rep.   This would help people improve their questions / answer by seeing, as soon as they get on the site, that they got negative feedback and that something needs to be checked / changed.    It shows here so it could very well be applied to the notification count: What's the difference between align and align*? After some brief searching I can't find the difference between align and align*. Google summarily ignoring the * is making it harder I think.  Can you tell me the difference between these two?  Moreover, can you tell me where you generally go for this type of information? As a relatively new user I'm still building up my resources. Book series my dad told me about. It involves space travel, clones, and an indigenous people with kangaroo tails My dad read a book series that he recommended to me last year. Now that I am ready to start it, neither of us can recall the title. He said there were several in the series but he can't recall how many.   The book is about traveling to a new planet, presumably with the goal of colonizing it. The crew are clones who have no memory. I think the goal was for the older original versions of the clones to transfer their consciousness into the clone bodies to be able to live on the new planet but something goes wrong.   There is an indigenous species on the planet who are humanoid but have kangaroo like tails.   The clone crew has markings on them that they don't understand until late. Apparently they are markings to indicate status or role on the new world. The person who they voted as there leader, it turns out, is marked as a servant or slave class. How can I enable Ctrl+Alt+Backspace? Ctrl+Alt+← can usually be set to restart X, however I can't find the option to allow this (it is disabled by default).  I have looked in System-&gt;Preferences-&gt;Keyboard and System-&gt;Preferences-&gt;Keyboard Shortcuts but I can't find an option to enable it.  Where can I change this setting? How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple? What is a simple way to create a binary relation symbol on top of another? What is a simple way to have \ll on top of \gg with equal size and vertically center aligned and have them work as a binary relation symbol like \lessgtr? The commands \underset and \overset cannot be used because they do not treat the two symbols equally, and they do not vertically center. Why are p-values uniformly distributed under the null hypothesis? PS4 Controller not connecting to PS4 and won't reset? I was playing my PS4 two days ago and then packed it up with two controllers that were both connected to this PS4.   I got to where I was going, set everything up and now the controllers won't connect. They show pulsing orange when they plug in, but when I hit the PS Button to connect, it blinks white 1-2 times and goes back to orange.   I have tried resetting them both.  Can anyone help? In ideal gas model,  is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?  Furthermore, if we accelerate a block of metal with ultrasonic vibrator so that the metal is vibrating in very high speed with cyclic motion, can we say the metal is hot when it is moving but suddenly become much cooler when the vibration stop? Best practices for storing UI settings? Find this integral $$\operatorname I=\int\limits_{0}^{1}\dfrac{\arcsin{\sqrt{x}}}{x^4-2x^3+2x^2-x+1}\operatorname d\!x$$  My try: let $$f(x)=x^4-2x^3+2x^2-x+1$$ I found  $$f(1-x)=(1-x)^4-2(1-x)^3+2(1-x)^2-x+1=x^4-2x^3+2x^2-x+1=f(x)$$ so $$I=\int_{0}^{1}\dfrac{\arcsin{\sqrt{(1-x)}}}{x^4-2x^3+2x^2-x+1}dx$$ so $$2I=\int_{0}^{1}\dfrac{\arcsin{\sqrt{x}}+\arcsin{\sqrt{(1-x)}}}{x^4-2x^3+2x^2-x+1}dx$$ then I can't,Thank you very much Ubuntu open to black screen with blinking underscore character after release upgrade I upgraded my Ubuntu OS from 12.10 to 13.04 and after the process of upgrading it via Software Updater, it requested me to restart the computer. I rebooted and on boot I proceeded to a purple screen with Ubuntu text and 5 dots below it and continued to a blank black screen with a blinking underscore character (_).  I have all my files in there and I can't access them. I tried the grub boot menu edit that other questions pointed out, but it didn't seem to do anything. How can I start automatically a command on Ubuntu 18.04? Transaction log reported full but is not Will the Android app be receiving any future updates? Will there be a new version of the Android app? It's been without any update for a long time and it doesn't seem to be working really well. Why do non-hydrogen atomic orbitals have the same degeneracy structure as hydrogen orbitals? IEEEtran - How to include ORCID in TeX/PDF with PdfLatex This question led to a new package:   I would like to display the ORCID id in an author list in an IEEEtran pdf, like that:  Is there a standard way to include it in an IEEEtran article with PdfLaTeX? I used two approaches from , but I failed. One is to insert the ORCID icon in the author list. I used the blow code: \author{Ali Al-Obaidi \href{https://orcid.org/0000-0000-0000-0000}{\includegraphics[scale=1]{figures/orcid_16x16.png}}}  where orchid_16x16.png is provided in the link . But the result is that the icon is not clear enough, even I replaced it with a different size. The other approach is to use the  package, like that: \usepackage{academicons} \definecolor{orcidlogocol}{HTML}{A6CE39} \author{AAA \href{https://orcid.org/0000-0000-0000-0000}{\textcolor{orcidlogocol}{\aiOrcid}}}  However, the result is like that:  And I also got two errors: &quot;Latex Error: Encoding scheme 'TU' unknown&quot; and &quot;Bad character code (59865)&quot;. In the latest academicons.sty (see ), academicons use the font TU. However, it seems that the compiler PdfLateX cannot support this font. Thus, is there anyone that knows a standard way to include it in an IEEEtran article with PdfLaTeX? Please help me.