Opposite of Torricelli's trumpet (or Gabriel's horn) is an example of a solid figure with infinite surface area and finite volume.  Is it possible to build the opposite (finite surface area but infinite volume) in an n-dimensional space? If not, how do we prove it?  More formally:   Let $S$ be an open subset of $\bf{ℝ^n}$ that is homeomorphic to $\bf{ℝ^n}$  and $S$ has infinite volume. If $T\cap \overline S\setminus S$  has a definable finite surface for every closed bounded $T\subset \Bbb R^n$, is it possible for $S$  to have finite area?
Infinite Volume but Finite Surface Area Is there any pathological shape that has a finite surface area but an infinite volume? Sort of like the opposite of a Gabriel's horn.
Making leaflet control open by default I'm using leaflet to display a map.  I have a control section that I'd like to be open by default, but I can't find a way to do it through the . Is there a way to do this? I want a true deep copy. In Java, this was easy, but how do you do it in C#? Percentage of overlapping regions of two normal distributions I was wondering, given two normal distributions with $\sigma_1,\ \mu_1$ and $\sigma_2, \ \mu_2$   how can I calculate the percentage of overlapping regions of two distributions? I suppose this problem has a specific name, are you aware of any particular name describing this problem?  Are you aware of any implementation of this (e.g., Java code)? pwd without symlinks How to programmatically login/authenticate a user? I am looking for a list of all English words that are their own antonyms. Off the top of my head, I can only think of "either", "fast", "to dust" and "to lease", but there must be dozens more. Can you provide a link to a comprehensive list, if such exists?  Also, what are such words most commonly called? I like the term "Janus word" I once heard, but is that widely understood?  Edited by popular demand to make it absolutely clear that this is not a community wiki poll. Array slices in C# How do you do it? Given a byte array:  byte[] foo = new byte[4096];   How would I get the first x bytes of the array as a separate array? (Specifically, I need it as an IEnumerable&lt;byte&gt;)  This is for working with Sockets. I figure the easiest way would be array slicing, similar to Perls syntax:  @bar = @foo[0..40];   Which would return the first 41 elements into the @bar array. Is there something in C# that I'm just missing, or is there some other thing I should be doing?  LINQ is an option for me (.NET 3.5), if that helps any. Show that the range of $p(z)e^{q(z)}$ for nonconstant polynomials $p$ and $q$ is all of $\mathbb{C}$. Visiting two Schengen countries, coming back home in between, do I apply for single-entry or multiple-entry visa? I am a resident of Turkey and I will go to Austria for 6 days beginning of June and then I will come back to Turkey. After staying 10 days I will go to Italy for 11 days at the end of June. Do I need two single-entry visa, or a multiple-entry visa, and which country do I apply to? (My first destination is Austria but I will stay more in Italy) My work has decided to issue their own  (CA) to handle different aspects of our work securely without paying for certificates.   Cryptographically sign emails Encrypt email contents Make access to things like the company  client-certificate based. Revoke the keys of former employees automatically   They sent me a .pem file, and I'm not sure how to add it to my Ubuntu install. The instructions sent were: "Double-clicking on it on a Mac should install it."&nbsp;  How do I proceed? Do I need to do something with  to create a .key, .csr, or .crt file? (Revised) Prove that $\phi$ is a group homomorphism and find the kernel. Quoting " Let $\phi : \Bbb Z \rightarrow \Bbb Z$ be given by $\phi(n) = 7n$. Prove that $\phi$ is a group homomorphism. Find the kernel, and the image of $\phi$."   My understanding:  Part 1:   Given $n,m \in \Bbb Z$, let's check that $\phi(n+m) =\phi(n)+\phi(m)$  $$\phi(n+m) = 7(n+m) = 7n + 7m = \phi(n)+\phi(m)$$  Therefore as the group operation in $\phi$ is preserved, $\phi$ is a group homomorphism.  Part 2 (revised):   $\phi$ is one-to-one as:  $\space \space \phi (n) = \phi(m) \Rightarrow 7n =7m \Rightarrow n=m  $. We also know that $\phi(e)=e$ by the property of homomorphism. Therefore, no other object than $0$ in the domain can map to $0$ in the codomain. It follows that: $$\ker(\phi)=\{ x \in \Bbb Z : \phi(x)=e\}=\{e\}$$   Part 3 (revised):  I claim that the only possible image-elements of $\phi$ are the multiples of $7$ in $\mathbb Z$ denoted $7\mathbb Z$.   To prove this I have to show that Im$(\phi) \subset 7 \Bbb Z$ and that $ 7 \Bbb Z \subset $ Im$(\phi)$.  Proving Im$(\phi) \subset 7 \Bbb Z$ :      $\forall y \in $ Im$(\phi)$ such that $  y =\phi(x)$ where $x \in 7 \Bbb Z$. It follows that $y \in 7 \Bbb Z$, therefore Im$(\phi) \subset 7 \Bbb Z$   Proving $ 7 \Bbb Z \subset $ Im$(\phi)$:   $\forall y \in  7\Bbb Z$ such that $  y =7x$ where $x \in \phi(x)$. It follows that $y \in \phi(x)$, therefore $ 7 \Bbb Z \subset $ Im$(\phi)$.   Any input to my understanding is much appreciated. Given two ciphertexts $c_1 = enc(p_1)$ and $c_2= enc(p_2)$ using any additive homomorphic encryption scheme (or specifically Paillier).   Can we find out whether the underlying plaintexts $p_1,p_2$ are equal without decrypting $c_1,c_2$ i.e. homomorphically? setSystemUiVisibility(SYSTEM_UI_FLAG_LAYOUT_HIDE_NAVIGATION) does not work Android app should send edits to edit queue if necessary rather than rejecting them I edited a question, on Stack overflow and when submitting preview, got red bar telling me my account isn't allowed to make suggested edits.  On the Sandbox android question it works fine, but that is editing an answer to my question.   The message I receive is:     Account is not allowed to suggest edits   Are the rules for suggested edits different for Android app? When using the \cite command in figure captions and the ieeetr bibliography style, then  BibTeX numbers the citations as appearing earlier than they do in reality (i.e. the first citation in the document ends up being [42]).  Is there any way to get BibTeX to ignore the \listoffigures section when numbering? An awful identity We take place on $\mathbb C(x_1,...,x_r,x'_1,...,x'_p,u_0,...,u_r,u'_0,...,u'_p)$ with $r,p\in \mathbb N$     Show that :   $$\displaystyle{\sum_{i=1}^r \left(   \frac{\prod_{j=0}^r (u_j-x_i) \prod_{j=1}^p (x'_j-x_i) }{  \prod_{1\leq j\leq r, j\neq i     }(x_j-x_i) \prod_{j=0}^p (u'_j-x_i)}      \right)}-\displaystyle{\sum_{i=0}^p \left(   \frac{\prod_{j=0}^r (u'_i-u_j) \prod_{j=1}^p (u'_i-x'_j) }{  \prod_{0\leq j\leq p, j\neq i     }(u'_i-u'_j) \prod_{j=1}^r (u'_i-x_j)}      \right)}=\displaystyle{\sum_{i=1}^p x'_i +\sum_{i=0}^r u_i -\sum_{i=1}^r x_i-\sum_{i=0}^p u'_i}$$   I have seen this exercise in an old book at the library. Unfortunately there was no indication how can I solve the problem.   Anyway if someone can give me some ideas it will be greatful.   NB: Sorry for the title, I have not had other ideas Expected Value of the maximum of two exponentially distributed random variables I want to find the expected value of $\text{max}\{X,Y\}$ where $X$ ist $\text{exp}(\lambda)$-distributed and $Y$ ist $\text{exp}(\eta)$-distributed. X and Y are independent. I figured out how to do this for the minimum of $n$ variables, but i struggle with doing it for 2 with the maximum.  (The context in which this was given is waiting for the later of two trains, with their arrival times being exp-distributed).  Thanks! I got a brand new Windows 7 machine, installed the operating system, created one account and forgot its password. What can I do?  There is no external CD, the operating system is loaded from somewhere inside the machine.  I already tried to remember passwords and tried all candidates with all possible combinations of caps lock, num lock etc. If I use  two different router in the same network while both are running in the default router mode then we can access the setup page or setup interface from browser just by IP address of corresponding router. But when I use one of the router as repeater then I can only enter the setup page of the router which is running in router mode. Why router's setup page cannot be accessed when using the router as repeater? Now how can I change the settings of the router in repeater mode? The only way is to reset router with the hardware key then setup again. If the Standard Normal PDF is $$f(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2/2}$$  and the CDF is  $$F(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-x^2/2}\mathrm{d}x\,,$$  how does this turn into an error function of $z$?