Splitting a list of letters into subsequences starting with uppercase letters
Partition on sublists beginning with a certain marker elements
In electrostatics, why the electric field inside a conductor is zero? In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero.  I have 2 questions:    We know that conductors (metallic) have free electrons which randomly moves in all directions, so how come we can talk about electrostatics which by definition means stationary charges? When the textbooks try to show why the electric field inside a conductor is zero they say let us put our conductor in an electric field. What happens then is that there will be an induced surface charge density which consequently induces an electric field within the conductor such that the total electric field within the conductor will be zero. That is perfectly understood, but my problem is the following: the original claim was that the electric field within a conductor is 0, not the electric field after putting the conductor in an external electric field it became zero. I do not understand the logic! Create an instance of a class from a string Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module I installed the ubuntu 12.04 server edition for my server pc . i had installed lamp server. i need to change the var/www location to my secondary hard disk location. i was configured so many time to at gedit /etc/apache2/sites-available/default here is my code  &lt;VirtualHost *:80&gt;     ServerAdmin webmaster@localhost      #DocumentRoot /var/www     DocumentRoot /media/myserver/     &lt;Directory /&gt;         Options FollowSymLinks         AllowOverride None     &lt;/Directory&gt;     #&lt;Directory /var/www/&gt;         &lt;Directory /media/myserver/&gt;         Options Indexes FollowSymLinks MultiViews         AllowOverride None         Order allow,deny         allow from all     &lt;/Directory&gt;      ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/     &lt;Directory "/usr/lib/cgi-bin"&gt;         AllowOverride None         Options +ExecCGI -MultiViews +SymLinksIfOwnerMatch         Order allow,deny         Allow from all     &lt;/Directory&gt;      ErrorLog ${APACHE_LOG_DIR}/error.log      # Possible values include: debug, info, notice, warn, error, crit,     # alert, emerg.     LogLevel warn      CustomLog ${APACHE_LOG_DIR}/access.log combined      Alias /doc/ "/usr/share/doc/"     &lt;Directory "/usr/share/doc/"&gt;         Options Indexes MultiViews FollowSymLinks         AllowOverride None         Order deny,allow         Deny from all         Allow from 127.0.0.0/255.0.0.0 ::1/128     &lt;/Directory&gt;  &lt;/VirtualHost&gt;   and also used  sudo chown -R var/www /media/myserver/   and  chmod -R 755 /media/myserver/   still i was not able to connect my /media/myserver and my browser show the following message  Forbidden  You don't have permission to access / on this server.   Please tell anyone how to mount myserver at my var/www, thanks advance Posts flagged for attention but there are none The comment with the Flagged Posts that seems to be new as of today states there are posts with flags awaiting my attention but the counter shows zero and when I go into flagged posts there is nothing waiting for me. How do idle games handle such large numbers? Just wondering how games such as Tap titans and Cookie Clicker handle such large numbers.  I am trying to implement an idle game however the largest number format supported by C# is decimal.   I am looking to support up to 10^500; that needs to be floating point  How could I handle this?  P.S. it needs to be cross platform i.e. pc, mac, ios, android and compatible with Unity found a 1994 uncashed profit sharing retirement plan check For any natural number $n\ge 1$, given pairs $(a_1,b_1),(a_2,b_2),...,(a_n,b_n)$ of integer numbers, there exist integer number $c$ and $d$ such that  $$\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$$    My initial approach is  Base Case: $(a_1^2+b_1^2) = a_1^2+b_1^2$ which is true. (Although it is trivial)  Prove the statement is true when $n=2$: We have $$(a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2$$ (Thanks André Nicolas for pointing it out)   So if $a,b,c,d$ are integers, $ac,bd,ad,bc$ are all integers and integers are closed under addition and subtraction. Hence $(ac-bd),(ad+bc)$ are integers.   Inductive Hypothesis: $\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$ is true  Inductive Step: $$\prod_{i=1}^{n+1}(a_i^2+b_i^2) = \prod_{i=1}^{n}(a_i^2+b_i^2)\cdot (a_{n+1}^2+b_{n+1}^2) = (c^2+d^2)\cdot (a_{n+1}^2+b_{n+1}^2)$$  Where $c$ and $d$ are integers.   But when we apply $n=2$, we have  $(c^2+d^2)\cdot (a_{n+1}^2+b_{n+1}^2) = (e^2 + f^2)$ where $e$ and $f$ are integers.  Hence, by the principle of induction, the statement we needed to prove is true. What are the tools to help import my data into Salesforce I am switching from old CRM and looking for easy to use tools to import my data Editing older revision (not most recent) no longer includes older title and tags, and automatic rollback note How do I perform a redirect to a custom URL after login? I am trying to redirect users to a custom URL after they logged in, but my code doesn't work.  How do I redirect users after they logged in? Careers ads break the Android app Clicking any Careers (or Jobs) ad in the Android app feed results in an instant crash for the Android App version 1.0.89. How to create a squiggle arrow with some text on it in TikZ? I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated. Can't Add css-columns Tag I've tried at least 4 times on  to add the tag css-columns, but each time after I save it disappears. When I type it in the tag box, it shows up and even has a tag wiki associated with it, but it will not stick when I save. I love R. Courant and F. John's Introduction to Calculus and Analysis because of its wide coverage, precise description and friendly written style.  Are there any classic textbooks like it on ODE/PDE?  thanks. I care to understand the concept behind the Borel-Cantelli Lemma better, hence I would appreciate it if someone could take the time to check if my arguments below are clear and rigorous.     Statement: Let $(X_n)_{n \geq 1}$ be a sequence of non-negative random variables that are identically distributed $X_n \sim X \geq 0 $ with $E(X)&lt; \infty$, show that $ X_n/n \to 0$ almost surely     Proof: Since $X_n \sim X$ for some non negative random variables we can easily compute that for $\epsilon &gt;0$ we have $$ \infty&gt;E(X/\epsilon) = \int_0^\infty P(X/ \epsilon &gt; t) dt = \sum_{n=1}^\infty \int_{n-1}^n P(X/ \epsilon &gt; t ) dt \geq \sum_{n=1}^{\infty} P(X/ \epsilon &gt;n) $$ Thanks to the Borel-Cantelli Lemma we obtain that $$ P ( \limsup_{n \to \infty} \lbrace X_n/n &gt; \epsilon \rbrace ) = 0 \iff P ( \liminf_{n \to \infty} \lbrace X_n/n \leq \epsilon \rbrace) = 1 $$     Question: Does the $\epsilon$ in the above depend on $k$?   I think it does and I would argue as follows $$P( \liminf_{n \to \infty} \lbrace X_n/n \leq \epsilon \rbrace )= P  \left( \bigcup_{n=0}^\infty \bigcap_{k=n}  \lbrace X_k/k \leq \epsilon (k) \rbrace \right) $$ Now using the chain of inclusions that state that we have for $\epsilon &gt;0$  $$ \lbrace \limsup |X_n-X| &lt; \epsilon \rbrace \subset \liminf \lbrace |X_n-X| &lt; \epsilon \rbrace \subset \lbrace \limsup |X_n-X| \leq \epsilon \rbrace $$ We conclude that $$ P ( \lbrace \limsup_{n \to \infty } X_n/ n \leq \epsilon(k) \rbrace)=1 $$ Where I choose the same $k \in \mathbb{N}$ as above, and then choose $k^*$ large enough such that $\epsilon(k) \leq \frac{1}{k^*}$, define the set $$ \Lambda_{k^*}:= \lbrace \limsup_{n \to \infty} X_n/n \leq 1/k^* \rbrace \implies P(\Lambda_{k^*})=1$$ and also we obtain that $\Lambda:=\bigcap_{j \geq k^*} \Lambda_{k^*}$ is still an almost sure event, i.e. $P(\Lambda)=1$ but for all realizations $\omega \in \Lambda$ we have $\limsup_{n \to \infty} X_n( \omega)/n \leq 0  \implies X_n( \omega)/n \to 0$ for all $\omega \in \Lambda$ that is$X_n/n \to 0$ almost surely $\Box$  Are my arguments given above correct and more importantly complete? Are there steps where you'd use different arguments? Why are my SVG imports so small? How can I set up password-less SSH login? I want to be able to login to a remote via ssh without having to enter the password all the time.   How do I set it up? Is a different command required to execute a password-less session? Well, I already searched meta as well as cleared my browser cache.  I realize this may be a SO cache problem, but it still seems kind of strange to me.    The deleted question is (assuming it still exists).  Shouldn't deleted questions only be visible to 10k users?  I'm only at 2k. List of all "partitions"/ "cuttings" of a list