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Contraction Map on Compact Normed Space has a Fixed Point How to redirect output to screen as well as a file? Mirror modifier is not working, no mirrored object? I'm learning how to use the mirror modifier and I am having some trouble.  When I apply the modifier to my object I don't see a mirrored version of it.  What am I doing wrong? I am new to Force.com and trying to learn some concepts.  Currently I am using Single Email Message to send my emails, but I need to change that to mass email, but I don't quite understand how to do that.   I have also created a Visualforce email template, which I would like to use, but it doesn't seem to work.   It would be great if someone could help me out.  //email_disease_map contains pairs of email address and disease ID for (Id id : email_disease_map.keySet())   {     Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();     String[] defaultAddresses = new String[] {'id@test.com'};      List&lt;String&gt; toAddresses = new List &lt;String&gt; (email_disease_map.get(id));      if (!toAddresses.isEmpty())       {         //set addresses for email to be sent         mail.setToAddresses(defaultAddresses);         mail.setCcAddresses(toAddresses);         mail.setTemplateId(Notification);         //set up remaining email         mail.setReplyTo('test@mail.com');          mail.setSenderDisplayName('Ms Test');          Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });       }  } Complex towers: $i^{i^{i^{...}}}$ If $w = z^{z^{z^{...}}}$ converges, we can determine its value by solving $w = z^{w}$, which leads to $w = -W(-\log z))/\log z$.  To be specific here, let's use $u^v = \exp(v \log u)$ for complex $u$ and $v$.  Two questions:   How do we determine analytically if the tower converges?  (I have seen the interval of convergence for real towers.) Both the logarithm and Lambert W functions are multivalued.  How do we know which branch to use?   In particular $i^{i^{i^{...}}}$ numerically seems to converge to one value of $i2W(-i\pi/2)/\pi$.  How do we establish this convergence analytically?  (Yes, I have searched the 'net, including the tetration forum.  I haven't been able to locate the answer to this readily.) Does option "-h" for "ls" display size in MB or MiB and is it consistent over Unix-based systems? Can I use an inner tube that's too narrow for the tyre? I recently got a puncture and when I went to replace the inner tube I discovered that I'd bought the wrong size tube. My tyre is 700 x 40c, the tube is 700 x 28-35c.  What is likely to happen if I use this tube? Will the tube explode when I attempt to inflate it? Multiple domains for different products? I have a website with software applications. Is it good for SEO to choose one keyword rich domain name for each of our software products or should we stick to a single domain?  From a user's perspective I think it would be easier to remember a domain that is keyword rich as the user will instantly know what this product is for.  But I have read articles that the latest trend in SEO is to stick to one domain for all of your products and invest on this single domain website.  Is that true? What do you advise? Should I register a separate domain for each of our products or should I use only one single domain?  Should I do a 301 redirect with a .htaccess to a single domain? And what about the sitemaps? Should I register all sites in Google Webmaster Tools and post a separate sitemap for each one of them? should my main site sitemap include all pages or should separate domains have their own sitemaps? I'm new to Ubuntu. What's the application extension for development reasons? I know Windows is mainly .exe and Mac is .dmg or .app. Does Linux have an unique one? $x^{p-1} + ... + x^2 + x + 1$ is irreducible using Eisenstein's criterion? Eisenstein's criterion says that for a prime $p$ if the following conditions are satisfied for a primitive polynomial, $f(x)$, then that polynomial is irreducible in $\mathbb{Z}[x]$  $p \mid a_0, a_0, ..., a_{n-1}$   $p \not\mid a_n$  $p^2 \not\mid a_0^2$  Now I am almost certain I read somewhere that this lemma can be used to prove that the polynomial $x^{p-1} + x^{p-2} + ... + x^2 + x + 1$ is irreducible.  All coefficients are $1$ though and we have have an awkward amount of terms, $p - 1$ terms as opposed to $p$ terms - so how can Eisenstein's criterion be applied here? I encountered the following induction proof on a practice exam for calculus:  $$\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$$  I have to prove this statement with induction.  Can anyone please help me with this proof? How to force the browser to reload cached CSS and JavaScript files If a subsequence of a Cauchy sequence converges, then the whole sequence converges. Let $(X,d)$ be a metric space, and say $(x_n)$ is a Cauchy sequence such that it has a convergent subsequence $(x_{n_k})$ that converges to $x$. We show $x_n \to x$. Let $\epsilon &gt; 0$. Take $N &gt;0$ such that for all $n,m &gt; N$, we have   $$d(x_n,x_m) &lt; \frac{\epsilon}{2}.$$  By hypothesis, we can take also $K &gt;0$ such that for all $n_k &gt; K$, we have  $$ d(x_{n_k},x) &lt; \frac{\epsilon}{2}.$$  Put $M = \max \{N,K\}$. Therefore, for all $n,m,n_k &gt; M$, we have  $$ d(x_n,x) \leq d(x_n, x_{n_k}) + d( x_{n_k},x) &lt; \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilon.$$  Hence, $x_n \to x$ as desired.  Is this a correct approach? Thank you very much in advance. How to compare two time series? I have collected temperature readings for 4 locations on a beach in Cornwall UK using data loggers. The loggers recorded temperature every 15 mins accurate to .1 of a degree (Celsius). The loggers collected data for 10 days with a one day break to calibrate the sensors. In total I used 30 sensors with 6-7 sensors in each position.  I have now downloaded the data and have produced time-series for temperature over the 10 day period. Visual inspection of the time-series shows how the temperature changes with tides and night and day. I want to investigate whether the time-series differ significantly from one another. Please could someone point me in the direction of a technique to do this in SPSS? I had to write the proof to show that an Ideal $P$ of a commutative ring $R$ is prime Ideal if $R/P$ is an integral domain.       let $a,b\in R$ s.t. $ab\in P$ ,        $$ab+P=P\implies(a+P)(b+P)=P\implies\overline a \overline b=0$$  and as $R/P$ is an integral domain either $a=0$ or $b=0$ $\implies a+P=P$ or  $b+P=P$.        $\therefore$ either $a\in P$ or $b\in P$.   Hence, $P$ is a prime Ideal.    Am I correct in writing this or am I making some error... This song by The Rolling Stones, "(I Can't Get No) Satisfaction". As a non-native speaker, I always wondered what's the exact meaning of this phrase?   Is it "I'm not getting any satisfaction" (this seems to be the most widely met translation; double negation used where single negation should have been used). Or is it "I want my satisfaction, I cannot leave without getting some" (makes much more sense to me).   Or is it something else? I've always had troubles understanding double negation as applied to English. First I was taught it's a mistake to use double negation at all, and then I see it everywhere. Good and easy way to share files on local machine I would like to have a directory that has following properties:    Many users can copy files into it  These files can be deleted/changed by these users (user A can delete/modify file that was copied into this directory)    it cant be done using normal file permissions (because permissions are retained on copy).  Here is what I found on the net:        Some use cases:    Sharing music on local machine  Simple git repository sharing (just make a bare repository writeable to many people) --- i know that there are solutions like gitosis Allow many developers to modify test instance of php app without giving them root (i guess they would copy files) --- I'm leading a team of nonprofit junior developers and I need to keep that one simple!    EDIT  AFAIK setting SGID bit is not enugh, it only affects newly created files --- and basic workflow for these use cases ivnolves copying and other operations (which cleave file's gid unchanged) How does searching a file (locate) or autocompletion work? I am a Windows user and coming from Windows with all the indexing and eternal wait times when searching for files, I find it surprising how fast does locate work or the autocompletion (that I know) work in linux.  Is there any indexing being done in the background or how is this achieved? I still have a pretty clean installation, so maybe this goes bad with time, but in Windows the moment you want to search on a folder which is not indexed you have to wait for some seconds. If I inherit from a base class and want to pass something from the constructor of the inherited class to the constructor of the base class, how do I do that?  For example, if I inherit from the Exception class I want to do something like this:  class MyExceptionClass : Exception {      public MyExceptionClass(string message, string extraInfo)      {          //This is where it's all falling apart          base(message);      } }   Basically what I want is to be able to pass the string message to the base Exception class. how to properly save an architecture in a fpga ic forever