Show that an expansion map is an isometry
Is an expanding map on a compact metric space continuous?
How to identify predatory publishers/journals For creating the graphics for my thesis (function graphs, flow charts, line art sketches) I've chosen to use the sans serif font by  \renewcommand\familydefault{\sfdefault}    However when I use mathematical symbols like $p_{s}$, they are still typeset in roman font and that looks weird:    So I wonder:   how could I force mathematical expressions also be typeset in \sfdefault if I do, are there any negative sideeffects to expect (with greek signs or other special symbols?) OR should I typeset all "mathematical" graphs (axis labels etc.) in roman font, and only make the other graphics like flow charts and sketches with sans serif font? How to convert date to timestamp in PHP? How do I get timestamp from e.g. 22-09-2008? Looking for a post-apocalyptic trilogy where pilot is nursed back to health by natives of the land I read a series of books around 2005. I think it might have been a trilogy.  Basic story line is in a post apocalyptic world. The main character is a pilot for the Federation or something similar to that. He crash lands, is nursed back to health by the natives, comes to like and respect them, and does not want to fight against them.  Also in the later book I think it also involves another race who are very Japanese-ish. They drink sake and the "clan" names are things like Fu-Jitsu and Mitsu-Bishi. Proper use of the IDisposable interface What does a de Broglie wave look like? What does a  wave look like? Are de Broglie waves transverse or longitudinal?   Can they be polarized?    What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom?   What experimental evidence do we have that supports the detailed nature of a de Broglie wave?     I have always assumed that de Broglie waves were mathematically  identical to electromagnetic waves, but I just realized there is no basis for this assumption, and in fact it must be false, unless there is an analogue to both the magnetic and the electric components of the electromagnetic wave.  So what does a de Broglie wave "look like"? Show that holomorphic $f_1, . . . , f_n $ are constant if $\sum_{k=1}^n \left| f_k(z) \right|$ is constant. While studying for an exam in complex analysis, I came across this problem. Unfortunately I was not able to solve it. Any help would be greatly appreciated.  Let $U ⊂ \mathbb{C}$ be a domain and $f_1, . . . , f_n : U \rightarrow \mathbb{C}$ holomorphic functions, such that $\sum_{k=1}^n \left| f_k(z) \right|$ is constant on $U$. Show that $f_1, . . . , f_n$ are constant. SFDC DKIM Setup - Production or Sandbox? Cannot figure out this via SFDC documentation. Need someone who have setup this before to advise.  Basically we want to enable DKIM for our SFDC org. In testing Sandbox and production, the from email address is using the same email domain. For example, "test@abc.com" for sandbox and "contact@abc.com" in production.   Question: shall we setup DKIM in both sandbox and production or just need to setup in production since sandbox and production are actually using the same domain "abc.com"? I was wondering if there are functions for which $$f'(x) &gt; f(x)$$ for all $x$. Only examples I could think of were $e^x - c$ and simply $- c$ in which $c &gt; 0$. Also, is there any significance in a function that is always less than its derivative?    Edit: Thank you very much for all the replies. It seems almost all functions that apply are exponential by nature...  Are there more examples like - 1/x?  Again are there any applications/physical manifestations of these functions? [for example an object with a velocity that is always greater than its position/acceleration  is always greater than its velocity] How do you use a variable in a regular expression? Can I travel to Canada with valid visa on old/expired passport? How did Sauron remain in control of the Nazgûl? The One Ring gave Sauron control of the Nine, yet when it was taken from him he still possessed the power to control them (or, at least he regained it towards the end of the third age).  Why is this?   mentions that he drew the Nine to him, but not how. How does one add boarding passes to Apple Wallet? How to prove that $E[Y]=E[E[E[Y|X_1, X_2]]]$ ?  PS. I don't see how $E[E(Y|X_{1},X_{2})|X_{1}]=Y[Y|X_{1}]$ and $E[Y]=E[E(Y|X_{1})]$ can be used here. But it feels close. Please help, I'm stuck PPS. Thanks @Deep North. Let's consider the case when X1 is independent of X2 I'm getting the following error when i try and install MSSQL 2008 on Windows Server Standard 2008 R2: We will make the convention that exact categories be skeletally small.   Is this construction (used in a mathematical context) correct? There is something that strikes me as odd in that "be". Should it be "are"? I know I've seen a similar way of using "be" like that, without conjugating the verb, but I'm not completely sure when it should be used. How can I uninstall software? Seeing there are various ways to install on Ubuntu. What are the various ways to uninstall items?  Which ways always work? How can I be sure something was uninstalled? How do you use Excel server-side? A client wants to "Web-enable" a spreadsheet calculation -- the user to specify the values of certain cells, then show them the resulting values in other cells.  (They do NOT want to show the user a "spreadsheet-like" interface. This is not a UI question.)  They have a huge spreadsheet with lots of calculations over many, many sheets.  But, in the end, only two things matter -- (1) you put numbers in a couple cells on one sheet, and (2) you get corresponding numbers off a couple cells in another sheet.  The rest of it is a black box.  I want to present a UI to the user to enter the numbers they want, then I'd like to programatically open the Excel file, set the numbers, tell it to re-calc, and read the result out.  Is this possible/advisable?  Is there a commercial component that makes this easier?  Are their pitfalls I'm not considering?  (I know I can use Office Automation to do this, but I know it's not recommended to do that server-side, since it tries to run in the context of a user, etc.)  A lot of people are saying I need to recreate the formulas in code.  However, this would be staggeringly complex. Why is there no last activity message? How to stop people from using my domain to send spam? I receive Mailer Daemon messages saying certain emails fail. My domain is itaccess.org which is administered by Google apps. Is there any way I can identify who is sending emails from my domain, and how they are doing it without me creating an account for them?  Delivered-To: 7e949ba@itaccess.org Received: by 10.142.152.34 with SMTP id z34csp12042wfd;         Wed, 8 Aug 2012 07:12:46 -0700 (PDT) Received: by 10.152.112.34 with SMTP id in2mr18229790lab.6.1344435165782;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Return-Path: &lt;whao@www20.aname.net&gt; Received: from smtp-gw.fsdata.se (smtp-gw.fsdata.se. [195.35.82.145])         by mx.google.com with ESMTP id b9si24888989lbg.77.2012.08.08.07.12.44;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Received-SPF: neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) client-ip=195.35.82.145; Authentication-Results: mx.google.com; spf=neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) smtp.mail=whao@www20.aname.net Received: from www20.aname.net (www20.aname.net [89.221.250.20])     by smtp-gw.fsdata.se (8.14.3/8.13.8) with ESMTP id q78EChia020085     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:43 +0200 Received: from www20.aname.net (localhost [127.0.0.1])     by www20.aname.net (8.14.3/8.14.3) with ESMTP id q78ECgQ1013882     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:42 +0200 Received: (from whao@localhost)     by www20.aname.net (8.14.3/8.12.0/Submit) id q78ECgKn013879;     Wed, 8 Aug 2012 16:12:42 +0200 Date: Wed, 8 Aug 2012 16:12:42 +0200 Message-Id: &lt;201208081412.q78ECgKn013879@www20.aname.net&gt; To: 7E949BA@itaccess.org References: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; In-Reply-To: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; X-Loop: whao@whao.se From: MAILER-DAEMON@whao.se Subject: whao.se:  kontot avstängt - account closed X-FS-SpamAssassinScore: 1.8 X-FS-SpamAssassinRules: ALL_TRUSTED,DCC_CHECK,FRT_CONTACT,SUBJECT_NEEDS_ENCODING      Detta är ett automatiskt svar från F S Data - http://www.fsdata.se      Kontot för domänen whao.se är tillsvidare avstängt.     För mer information, kontakta info@fsdata.se      Mvh,     /F S Data      -----    This is an automatic reply from F S Data - http://www.fsdata.se    The domain account "whao.se" is closed.   For further information, please contact info@fsdata.se    Best regards,   /F S Data