How to set DisplayFormulaNumbered Font style to Times New Roman?
Change font of formula number in DisplayFormulaNumbered
Let's say I have two planets that are one hundred thousand lightyears away from each other. I and my immortal friend on the other planet want to communicate, with a strong laser and a tachyon communication device.  I record a message on the tachyon communication device and release the message at exactly the same time as I activate the laser, both of which are directed to the other planet which is one hundred thousand lightyears away. Say it is the year 0 for both of us at the time I did this.  If tachyons existed, then the message would arrive to my friend before the photons in the laser. It would arrive, say, a thousand years earlier. From my vantage point, that message will arrive to her at year 99,999; the same would be true for my friend's vantage point. However, she will only see the laser at year 100,000.  So since she got the message at year 99,999, she immediately sends me a reply back going through the same procedure as I did. She records a message and releases it at the same time as the laser. The tachyons will arrive 1,000 years earlier than the laser, so for me, I will receive the message at year 199,998. I will receive the laser, however, at year 199,999.  It seems to me that communication this way does not violate causality. I will still have received the message after I had sent it.   If tachyons truly violated causality, though, I realize it should arrive at year -1 for her, and so she can reply to me at year -2, which would mess me up by year 0 as I will ask her how she knew I was planning on sending her a message before I sent it. I could send her a different message, which she would end up receiving at year -1, and will end up confusing her as she would have received one message asking her out, and the other asking her how did she know I was asking her out. She then decides I am crazy and sends me a message at year -2 that she does not want to date me, and so she will have both turned me down and entertained me before I have even asked her out.  On the other hand, let's go back to year 0 and add a third device to our list: an Alcubierre drive. After I send out the message and the laser, I get impatient and do not feel like waiting 99,999 years, so I get on my Alcubierre drive spaceship and arrive on her planet at the same year 0. My friend is not in her office, so I leave a note to her also immortal secretary saying I dropped by and that she should expect a message for her in year 99,999.  I then get back on my Alcubierre drive and land back on my planet, still on year 0. Meanwhile, the tachyons and photons I sent out are still racing to arrive to her. By year 99,999, she receives the message just as I Alcubierre drive back to her, and I pick her up for dinner.  But the point of my question is, it seems to me that just going faster than light, if that alone was what you had, would not violate causality. It must be something else. I understand time dilation and that things with mass cannot travel at the speed of light, but using the Alcubierre drive, hypothetically speaking, I was still able to outpace the photons while also having mass. It still did not produce causality problems. Alcubierre drives are also valid solutions to GR.  It seems circular to me to say that what makes traveling faster than light violate causality is because it violates causality (if faster than light communication was divorced from causality problems, then the causality problem would cause itself -- thereby violating causality and, hence, we would scrap it and conclude that there is no causality problem after all).  What is it that I am missing? If someone could help me out, that would be excellent. I've been itching to ask my friend out for a few millenia now. :) What are reaching fouls in the NBA? I would like to align the view straight on to a face, perpendicular to the normal. How do I align the 3D viewport to the face of a mesh? Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$ Using $\text{n}^{\text{th}}$ root of unity  $$\large\left(e^{\frac{2ki\pi}{n}}\right)^{n} = 1$$  Prove that   $$\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$$ How can I send an email using a template? I have created a email template in ExactTarget API and I want to use it executing XML from SoapUI.  Is there any tutorial or examples of how can this be done?  I'm new at this and I'm not sure how ExactTarget really works. Why do modern mountain bike forks no longer use boots on fork stanchions? Older mountain bikes used to have them on the forks, and lefty and headshocks still do. Why have these fallen out of fashion and would putting aftermarket fork boots on your stanchions be productive or not? Switch statement fallthrough in C#? Switch statement fallthrough is one of my personal major reasons for loving switch vs. if/else if constructs. An example is in order here:  static string NumberToWords(int number) {     string[] numbers = new string[]          { "", "one", "two", "three", "four", "five",            "six", "seven", "eight", "nine" };     string[] tens = new string[]          { "", "", "twenty", "thirty", "forty", "fifty",            "sixty", "seventy", "eighty", "ninety" };     string[] teens = new string[]         { "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen",           "sixteen", "seventeen", "eighteen", "nineteen" };      string ans = "";     switch (number.ToString().Length)     {         case 3:             ans += string.Format("{0} hundred and ", numbers[number / 100]);         case 2:             int t = (number / 10) % 10;             if (t == 1)             {                 ans += teens[number % 10];                 break;             }             else if (t &gt; 1)                 ans += string.Format("{0}-", tens[t]);         case 1:             int o = number % 10;             ans += numbers[o];              break;         default:             throw new ArgumentException("number");     }     return ans; }   The smart people are cringing because the string[]s should be declared outside the function: well, they are, this is just an example.  The compiler fails with the following error:   Control cannot fall through from one case label ('case 3:') to another Control cannot fall through from one case label ('case 2:') to another   Why? And is there any way to get this sort of behaviour without having three ifs? Exporting animation created with animate package Consider the following minimal working example.   It's great to have an animation in pdf format.   But sometimes it would be good to be able to export it into an animated gif or something else (swf, video file, svg?).  How do I achieve this?   Note: I often have animations together with pgfplots.     \documentclass{article}  \usepackage{animate}  \usepackage[active,tightpage]{preview} \PreviewEnvironment{animateinline}  \begin{document}  \begin{center} \fboxsep1mm     \begin{animateinline}[autoplay,loop]{2}     a     \newframe         b     \newframe       c                      \end{animateinline} \end{center}  \end{document}   Remark   The animation is not visible in all PDF viewers. It surely works with a current Adobe Reader. How can I display a short chapter name in the header and a long chapter name in the ToC? I am writing a book and one of my chapters has a very long title. As it can't be displayed correctly on the top of even pages, I provide a "short title name" via the   \chapter[short title]{long title}   command. But then, "short title" appears in the table of contents instead of the original/true/long one.  How can I have the "short title" in the header of even pages, and the "long title" in the ToC and in the "Title header"?  For reference, here is the code I use:  \documentclass[11pt,a4paper]{book} \begin{document} \tableofcontents  \chapter[Short title]{Very vey very very very very very very long title     i can't display in the header} Lorem ipsum dolor sit amet, consectetur adipiscing elit. \end{document} Why is there a factor of $4\pi$ in certain force equations? I mean to ask why there is $4\pi$ present in force equations governing electricity? Though all objects in universe are not spherical and circular, the constant of proportionality in both equations contain $4\pi$. Why? Regression with only categorical variables Is it possible to conduct a regression if all dependent and independent variables are categorical variables? How does "virus been detected" on android pop up on chrome when visiting some sites? What is the cause of this chrome bug on android? The last site I went to was www.destructoid.com and all of a sudden it gets redirected to the following url. This happened previously awhile back, but I didn't document everything as I did today. I'm also on android chrome canary if that matters.   I took some screenshots before closing out of that tab. But my question is:   What chrome bug or malware is causing these random redirects? How can one detect if they have this vulnerability?   The url is: I have hundreds of excel files which are all of the same format (i.e. 4 worksheets per Excel file). I need to combine all the files into 1 all singing and dancing file which must have the same format as the originals (i.e. maintain the four separate worksheets, which are all identically named).  While each file is structured the same, the number of columns (and the heading names) between sheet 1 and 2 (for example) is different. So it can’t be combined into one file with everything in one sheet!  There are two complications:   I need to create an EXTRA column in the merged file (on EACH sheet) to identify the source file (“file name”). The files contain a lot of zero data entries (e.g. 55 rows of useful data followed by hundreds of rows of zeros) which I need to remove from the merged file.   I’ve never used VBA, but everyone has to start somewhere I suppose. need to move a domain controller, the first in the forest that holds all the fsmo roles, to another location in a clients building. it will require turning off this dc, call it dc1 for this question. i want to transfer the fsmo roles to a new domain controller call the new one dc2. dc2 is already on the network and has been promoted and made a domain controller, it's dns settings are set and it is also a global catalog (GC). the work is scheduled to be done after hours and i am also planning on moving the dhcp server to dc2.  i am looking for a best practices checklist of things to verify prior to moving fsmo roles and turning dc1 off? as far as i know there are no issues with replication between the dc's. my biggest worry is if i turn on dc1 after moving it and i have hardware issues or boot issues, i would rather move the fsmo roles to a known good one that is a few months old (dc2) vs still using a 5yr old box (dc1), this is part of my migration strategy too.   thanks for the help. Restoring open software after a restart event in windows I find that at the end of a long day, I sometimes have a large number of programs running. All which I will need to use tomorrow. Normally, this isn't an issue, I can simply lock the machine and come back tomorrow. My problem arrises when windows update launches in the middle of the night and force restarts my computer. That in turns closes all my open software. I of course save everything regularly so I don't loose anything, but I waste time reopening all of those resources whenever there is a restart.   [EDIT]  I should clarify that I still want to be able to restart my computer when an update comes down. Preventing the restart only delays the problem until later. I should have been more specific in that I want to be able to recover my working environment after a restart for any reason. Things like scheduled maintence, power loss, updates, and software installs.  [EDIT]  I can't simply have them setup to launch at startup becasuse those files change from week to week. So I need something that monitors what I have open, and gives me the option to "recover" those software sessions when I log back in.  Anyone have any suggestions on what I can do? I'd even be willing to purchase software to do this for me if that is the only option.  Thanks How can one Identify a Magic Item? I had a disagreement with one of my groups recently: They believe that the  spell is the only way to identify a magic item, while I believe a high enough Intelligence (Arcana) check is able to do the same.   What I came here to ask is: What are all the possible ways to identify a magic item? How to update kernel to the latest mainline version without any Distro-upgrade? Currently I'm running Linux-3.0 and I want to update it to Linux-3.3.1 the latest stable kernel release as mentioned at . Can I update to 3.3.1 in Ubuntu without any risk of crashes? I'm updating my kernel regularly as provided by the Update Manager..Currently I have Linux-3.0.0.17..Can I update?  NOTE:  The latest kernel version any user is supposed to use in Ubuntu is updated automatically via the Update Manager, so no action is normally required by user regarding kernel upgrades. What the question author is referring to is mainline kernel, see: Modelling a spiral around a sphere I'm trying to figure out the best way to model the sphere-spiral here:    Is it possible to make this shape directly? Or do you have to make it as a cylinder and wrap it to a sphere? Two homologous but not homotopic loops on a closed surface of genus greater than one Suppose $S$ is a closed surface with genus greater than $1$. Give an example of two loops on $S$ which are not homotopic, but are homologous to each other.   I need help solving this question. I have read the Wikipedia page on it and I realize that it does not contain the necessary knowledge to visualize this problem.  And I was also wondering the relation between the fundamental group $\pi_1(S)$ and the first homology group $H_1(S)$? Some restrictions is that $S$ is a closed surface and the genus is greater than $1$. Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic. Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.    This is a question from page $181$, Chapter $3.4$ Elements of Modern Algebra ($8^{th}$ Edition) by Linda Gilbert.  My intuition tells me that the given statement is false, however, I cannot seem to find a rigorous argument (or counterexample) to disprove the statement. Can anyone please point me in the right direction?  I know that if a group $G$ is cyclic, then every subgroup is cyclic. This is not an if and only if statement - hence my intuition telling me the above mentioned statement is false.