Is an AR(p) process with roots inside the unit circle non-stationary?
Explosive AR(MA) processes are stationary?
Why does Captain Antilles in a New Hope say they're on a diplomatic mission? Units and Nilpotents If $ua = au$, where $u$ is a unit and $a$ is a nilpotent, show that $u+a$ is a unit.   I've been working on this problem for an hour that I tried to construct an element $x \in R$ such that $x(u+a) = 1 = (u+a)x$. After tried several elements and manipulated $ua = au$, I still couldn't find any clue. Can anybody give me a hint? ZFC + $\exists$ Standard model $\rightarrow$ Con(ZFC + $\exists \omega$-model) $ZFC + \exists V_\alpha$ model of $ZFC \vdash Con(ZFC + \exists$ transitive standard model of $ZFC)$  and then  $ZFC + \exists$ transitive standard model of $ZFC \vdash Con(ZFC + \exists \omega-model$ of $ZFC)$  For the first one :   We can always find a countable extentional $M \subset V_\alpha$ elementary equivalent to $V_\alpha$. Let $M&#39;$ be the mostowski collapse of $M$. $M&#39; \approx M$ so $M&#39;$ is model of ZFC. And because $M&#39;$ is countable and transitive then $M&#39; \in V_\alpha$ (since $H_{\omega_1} \subset V_{\omega_1}$ and $\alpha$ is surely far larger than $\omega_1$).   So $V_\alpha$ is the model of '$\exists$ a standard transitive model of ZFC'.  For the second one :   I don't really know how to do it... Does anyone have an idea ? Creation of a matrix Let $H$ be a subgroup of $G$ with $[G:H]=n$. Let $N$ be the kernel of the left-multiplication action on the cosets of $H$. Show $[G:N]$ divides $n!$ Let $H$ be a subgroup of $G$ with $[G:H]=n$ and $G$ finite.  Let $G$ act on left cosets of $H$ by left multiplication.  Let $N$ be the kernel of the action.  Show that $[G:N]$ divides $n!$.  Ok so I have a theorem that says that if $G$ is simple then it embeds into $S_n$.  So if $G$ is simple than I'm done because $G$ divides $n!$ and thus $N$ divides $n!$ and hence $[G:N]$ divides $n!$.  Now I also know that $N$ is the largest normal subgroup of $G$ contained in $H$.  Thus if $G$ isn't simple then it contains some non-trivial normal subgroup $K$ and thus $K\cap H$ is normal in $H$ and by the 2nd Iso Theorem $H/K\cap H\cong KH/H$...    As you can see I'm not sure where to go from here. I was hoping to prove that $K\cap H$ wasn't trivial and thus that $N$ couldn't be trivial since it must contain $K\cap H$, but I'm not sure I can, and even if I could I'm not sure that would help me in showing that $[G:N]$ is small enough to divide $n!$.  Can anyone give some guidance?  Thanks. Installing QGIS with ECW support on Mac? Using Windows 10 in a virtual machine. Can it be done? I am currently running 8.1. I'd like to try out Windows 10 and if I like it upgrade. If not, I'll keep running as I am.   I've never used a virtual machine before: can Window 10 be used from a virtual machine as a "sandbox", and if so how? Let's have 2 numbers, N and K, where K divides N. The number of K-combinations from a given set S of N elements is a well known formula. Let's concatenate N/K groups (resulting in N elements) such as the resulting set is N. How many possibilities are there, i.e. what's the formula?  For instance:    N=4, K=2, C(4, 2) = 6 {1,2},{1,3},{1,4},{2,3},{2,4},{3,4}   The 3 possibilities are:     {1,2},{3,4}   {1,3},{2,4}   {1,4},{2,3}   I generated these combinations and I think the number goes like this:  (4, 2): 3 (6, 3): 10 (6, 2): 15 (10, 5): 126 (9, 3): 280 (10, 2): 945 (14, 7): 1716 (12, 4): 5775 (15, 5): 126126 (15, 3): 1401400   Apparently, the result always divides with (N-1). I want to combine two ffmpeg commands to a single command. I am using ready made ffmpeg binary in my Android application. I want to concat .ts files and overlay an image.  I am using following commands:   To concat .ts files:  String[] ffmpegcommand = {"ffmpeg", "-i","concat:"+input_file_path+"|"+input_file_path1, "-c", "copy", "-bsf:a", "aac_adtstoasc", output_file_path};  Apply image overlay effect:  String[] ffmpegcommand = {"ffmpeg","-y" ,"-i", input_file_path,"-strict","experimental", "-vf","movie="+AppStaticData.BASE_FOLDER_PATH + File.separator + "watermarklogo.png"+" [watermark]; [in][watermark] overlay=main_w-overlay_w-10:10 [out]", AppStaticData.BASE_FOLDER_PATH+"/" + output_file_path}; SQLite parameter substitution problem Using SQLite3 with Python 2.5, I'm trying to iterate through a list and pull the weight of an item from the database based on the item's name.  I tried using the "?" parameter substitution suggested to prevent SQL injections but it doesn't work. For example, when I use:  for item in self.inventory_names:     self.cursor.execute("SELECT weight FROM Equipment WHERE name = ?", item)     self.cursor.close()   I get the error:     sqlite3.ProgrammingError: Incorrect number of bindings supplied. The current statement uses 1, and there are 8 supplied.   I believe this is somehow caused by the initial creation of the database; the module I made that actually creates the DB does have 8 bindings.  cursor.execute("""CREATE TABLE Equipment      (id INTEGER PRIMARY KEY,      name TEXT,     price INTEGER,      weight REAL,      info TEXT,      ammo_cap INTEGER,      availability_west TEXT,     availability_east TEXT)""")   However, when I use the less-secure "%s" substitution for each item name, it works just fine. Like so:  for item in self.inventory_names:     self.cursor.execute("SELECT weight FROM Equipment WHERE name = '%s'" % item)     self.cursor.close()   I can't figure out why it thinks I have 8 bindins when I'm only calling one. How can I fix it? Another problem from quora.  What can be said about $v =\prod_{s=2}^{\infty} \zeta(s) $?  Wolfy says that $v \approx 2.294856591673313794183 $.  The Inverse Symbolic Calculator () finds nothing.  Here are the close values:  $2294856391585950 = (0064) sum((7/6*n^3-3*n^2+65/6*n-3)/(Fibo(n)+1),n=1..inf)\\ 2294856397653578 = (0001) GAM(5/6)*BesI(1,2)^{GAM(7/12)}\\ 2294856469349552 = (0006) 1/4357571\\ 2294856473388934 = (0324) 1/10*(10+14^{1/2}*10^{1/4})^{1/2}*10^{3/4}\\ 2294856488490537 = (0001) BesJ(0,1)^{GAM(1/3)/GAM(5/12)}\\ 2294856524215021 = (0314) sin(Pi*8/45)-sin(Pi*14/51)\\ 2294856591673313 \text{ would be here}\\ 2294856740350177 = (0011) sum((2*n^3-5*n^2+22*n-14)/(n!+2),n=1..inf)\\ 2294856991319600 = (0324) 23^{1/2}/(12^{3/4}-3^{2/3})^{1/2}\\ 2294857017919943 = (0001) Feig2*Li4(1/2)/GAM(5/6)\\ 2294857089879260 = (0248) F(11/26;27/50;1) \\ 2294857493303450 = (0404) Psi(1/21)+Psi(19/21)+Psi(13/14)\\ $  I tried using Euler's zeta product and partition sum, but this didn't seem to help. Here is what resulted:  $\zeta(s) =\dfrac1{\prod_p (1-p^{-s})} $.  $\begin{array}\\ v &amp;=\prod_{s=2}^{\infty} \zeta(s)\\ &amp;=\prod_{s=2}^{\infty} \dfrac1{\prod_p (1-p^{-s})}\\ &amp;=\prod_{s=2}^{\infty} \prod_p\dfrac1{ (1-p^{-s})}\\ &amp;= \prod_p\prod_{s=2}^{\infty}\dfrac1{ (1-p^{-s})}\\ \end{array} $  Euler's product identity states that $\prod_{n=1}^{\infty}\dfrac1{1-zx^n} =\sum_{n=1}^{\infty} \dfrac{x^nz^n}{\prod_{k=1}^n(1-x^k)} $. Putting $x=z=\dfrac1{p} $, $\prod_{n=2}^{\infty}\dfrac1{1-p^{-n}} =\sum_{n=1}^{\infty} \dfrac{p^{-2n}}{\prod_{k=1}^n(1-p^{-k})} $.  That's as far as I can go. I am looking for the stuff above, so I can make non-duplicate proposals on area 51. What is the purpose of the /etc/shadow file in Linux Operating system?  Also, is it same for SUSE clients? There is one shadow cache file is maintained what is purpose of that? This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the  and find the energy eigenvalues and eigenfunctions but I am confused about how exactly this should be done.  I've solved some initial value problems in the past using iterative methods such as Runge–Kutta. I've read that  is the way to solve Schrödinger's equation but Wikipedia also describes it as an iterative method for initial value problems.  How do I use it to solve an eigenvalue problem?  This confuses me for the following reasons:   Wouldn't iteratively solving the DE require knowledge of the energy eigenvalues to use as input to the calculation? I don't know the eigenvalues yet; they're precisely what I'm trying to calculate. If I did that, wouldn't I simply get a unique solution, instead of a family of eigenfunctions and eigenvalues?    I've seen some mention of "tridiagonal matrices" being generated somehow, but am not sure what the elements of that matrix would be or how that applies to the problem. Leandro M. mentioned that "the discretization defines a finite dimensional (matrix) eigenvalue problem". This seems like the correct road I should be going down, but I haven't been able to find anything that explicitly explains this process or how the matrix is constructed. If this is the correct procedure, how is such a matrix constructed? Display sheet name in Google Spreadsheets Is there any way to display a sheet name as the result of a function in a Google Spreadsheets (exactly like , except in Google Sheets)? Money transfer from India to USA My daughter is a US Citizen. We (parents)are also planning to permanently settle in US. We will go their as Permanent Resident,as per US Law. We have a house here in India worth Rs.2 Crores.  We want to sell it and take money with us. We have ordinary savings Bank account here in India.  My US Citizen Daughter is a Income Tax payer.  Now your advises are required as under:   What are the routes to take money from India to US and our tax liabilities Can I gift this whole amount to my US Citizen Daughter or what is the maximum limit of Gift amount.  What will be the tax liability on me and on my Daughter in case of Gift   Whether I have to show it in my Income Tax Return or in my Daughter's Tax Return. What US Income Tax Laws says. What will be the procedure to send money as Gift to my Daughter. Will the money will go directly from my Bank Act.to my Daughter's Bank Account. Will there will be wire transfer from bank to bank Can I send money through other money sender Certified Companies also.    Please advise. If there is something more on the subject to make me understand, please advise. Thanks, What is the difference between "Build and view" and "Compile"? set fontsize for TikZ figure How to delete OS from boot menu After installing fedora and Centos and other OS now I have them all showing in my Boot menu [F2] on start up not the menu form the OS even after deleting them and reinstaling other OS - Ubuntu -so It just shows one when the OS starts but when I go to UEFI setting I still find all the old ones they instruct you to use DEL to take them out but that does not work TeXShop and Mac preview crashing when opening latex/beamer built pdfs After updating to Sierra 10.12.4 last week, TeXShop crashes:   when opening an existing .tex document that has a pdf associated to it immediately after compiling a new document, i.e. as soon as a pdf is created.   Furthermore, preview crashes opening almost any pdf that has been created with TeXShop. There is virtually nothing on the internet about it, and the only solution seems to be a complete reinstall of MacOSX (so as to reinstall the supposedly broken preview), which I'd like to avoid if at all possible.  Someone else has described a similar issue, but has not received any responses ().  I would be very grateful for some help, as I can neither produce work, nor look at any at the moment. Many thanks!