What am I doing wrong regarding flipping omlettes or pancakes?
How to succeed with making omelette
I want to make a logistic model from my survey data. It is a small survey of four residential colonies in which only 154 respondents were interviewed. My dependent variable is "satisfactory transition to work". I found that, of the 154 respondents, 73 said that they have satisfactorily transitioned to work, while the rest did not. So the dependent variable is binary in nature and I decided to use logistic regression. I have seven independent variables (three continuous and four nominal). One guideline suggest that there should be 10 cases for each predictor / independent variable (Agresti, 2007). Based on this guideline I feel that it is OK to run logistic regression.    Am I right? If not please let me know how to decide the number of independent variables? I'm looking for an understandable proof of this theorem, and also a complex one involving beautiful math techniques such as analytic number theory, or something else. I hope you can help me on that. Thank you very much What is the most preferred and easiest way to do pagination in ASP.NET MVC?  I.e. what is the easiest way to break up a list into several browsable pages.  As an example lets say I get a list of elements from a database/gateway/repository like this:  public ActionResult ListMyItems() {     List&lt;Item&gt; list = ItemDB.GetListOfItems();     ViewData["ItemList"] = list;      return View(); }   For simplicity's sake I'd like to specify just a page number for my action as parameter. Like this:  public ActionResult ListMyItems(int page) {    //... } Here's the information :     There are four different pairs of   opening and closing tags which can be   used in PHP. Two of those, &lt;?php ?&gt;   and &lt;script language="php"&gt; &lt;/script&gt;,   are always available. The other two   are short tags and ASP style tags, and   can be turned on and off from the   php.ini configuration file. As such,   while some people find short tags and   ASP style tags convenient, they are   less portable, and generally not   recommended.   In my experience most servers do have short tags enabled. Typing  &lt;?=   is far more convenient than typing  &lt;?php echo    The programmers convenience is an important factor, so why are they not recommended? Let $U\subset\mathbb R^3$ be an open set, and $f:U\to \mathbb R$ be a smooth function. Suppose that the level set $S=f^{-1}(\{0\})$ is non-empty, and that at each $p\in S,$ the gradient $\overrightarrow \nabla f(p)$ is not the zero vector. Then $S$ is a smooth two-dimensional surface in $U$, and $p\mapsto \overrightarrow \eta(p)=\frac{1}{||\overrightarrow \nabla f(p)||}\overrightarrow \nabla f(p)$ defines a smooth unit-length normal vector field along $S$. At each $x\in U,$ write $H(f)_{(x)}$ for the $3\times 3$ Hessian matrix specified by $$(H(f)_{(x)})_{ij}=\frac{\partial^2f}{\partial x_i\partial x_j}(x).$$   Show that, at each $p\in S$, the second fundamental form $II_p: T_p(s)\times T_p(s)\to \mathbb R$ is the symmetric bilinear map    $$II_p(\overrightarrow v,\overrightarrow w)=\frac{-1}{||\overrightarrow \nabla f(p)||}\overrightarrow v\cdot H(f)_{(p)}\overrightarrow w,$$for all $\overrightarrow v ,\overrightarrow w \in T_p(s)$.       (Here, we view the tagent space $T_p(S)$ as the two-dimensional subspace $(span\{ {\overrightarrow \eta(p)}\})^{\bot}$ of $\mathbb R^3$.      Edit: Actually my question is why the second fundamental form under the usual definition can be written in this way.      Definition: The quadratic form $II_p$, defined in $T_p(S)$ by $II_p(v)=-&lt;d  N_p(v),v&gt;$ is called the second fundamental form of $S$ at $p$, where $dN_p:T_p(S)\to T_p(S)$ is the differential of the Gauss map.   Hopefully, I express this problem explicitly. I was just wondering how to prove this statement.   I took a diffrential geometry class last semester, and when I organized my notes this morning, I found this statement, but there was no proof...  Looking forward to an understandable explaination. Thanks in advance.     Edit 2:Furthermore, show that, at each point $p\in S$, the expression   $$\phi_p(z)=det\pmatrix{-H(f)_{(p)}-zI_{3\times 3} &amp; \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)&amp; 0}$$   (the underlying matrix here is $4\times 4$) defines a second-degree polynomial whose roots $\lambda_1$ and $\lambda_2$ are $||\overrightarrow \nabla f(p)||k_1$ and $||\overrightarrow \nabla f(p)||k_2$, where $k_1$ and $k_2$ are the principal curvatures of $S$ at $p$.      Also, if a non-zero vector $\pmatrix {\overrightarrow v \\c}$ lies in the kernel of the $4\times 4$ matrix $$\pmatrix{-H(f)_{(p)}-\lambda_jI_{3\times 3} &amp; \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)&amp; 0},$$   then $\vec v$ is a non-zero element of $T_p(S)$ and lies in the "principal direction" corresponding to $K_j$. How do I properly use the "Not an Answer" flag? What is the "Not an Answer" flag and what is its purpose? When should I use this flag? When should I not use this flag? But I'm still not sure if I'm using the flag correctly... An answer is "Not an Answer", but the flag was declined or disputed!   See also: I am trying to prove the following statement but have trouble  comprehending/going forward with some parts! Here is the statement:     If $A$ is any set, then  $|A|$ $&lt;$ $|P(A)|$   Here is what I have so far:  We need to show that there is an injection from $A$ to $P(A)$ but not a surjection.   A natural choice for an injection is the function $ f(x)$ $=$ $\{x \}$, which in plain English, takes any element $x$ (that is in $A$) and sends it to the one-element set $\{x \}$. Thus $f(x)$ is injective!  To show that there is no surjection, for the sake of contradiction, assume there is a surjection. Here is where I start to have trouble. Surjectivity means that every element of the co-domain is mapped to an element of the domain, correct? Consequently, in this particular case, we are "matching" sets (from $P(A)$) to elements (from $A$) right?  If the above is correct, my problem arises here. I am not sure how to prove that $f$ is not surjective. Unfortunately, I am easily confused by notation so please explain in English.  Thank you in advance!! :) identity element of $(D_n ,\gcd)$ Let $x*y=\gcd(x,y)$ on $D_n=\{x\in \mathbb N:x |n\}$. I have to prove that $(D_n,*)$ is a commutative monoid and I have a problem when finding the identity element.  $x*e=x$  So $gcd(x,e)=x \to e=xk,k\in \mathbb N^*$ and $e \leq n$  A good $e$ is $0$ but it's not in $D_n$ General question I have an app X installed on my device in version Y. I don't want to update it to any newer version (Y+z) for some reason. Still, the Google Play Store app always lists updates for X, which keeps me from a simple &quot;update all&quot;. My question, put to a single sentence:  How to hide updates for X permanently from the &quot;available updates&quot; list?   Specific examples First, I know there are alternatives as e.g. the , which can handle this quite well (skip this update, skip all future updates). I prefer a &quot;generic solution&quot;, which does not depend on a 3rd party's market app. Second, I know that  includes a &quot;Market doctor&quot;, which can be used to disconnect an app from Google Play.1 However, in my specific case that only worked for a few hours: I disconnected GTalk, as I don't want it replaced by Hangouts. The update notification disappeared for a few hours, then it was back. No idea what restored the &quot;link&quot;. Third, just to make sure: I'm not talking about the &quot;auto update&quot; feature as discussed e.g. in . I was rather hoping for something close to , but without the need to &quot;freeze&quot; the app in question (which I still want to use, but in the version installed, not in a &quot;future version&quot; available). Fourth: No, uninstalling the app in question is no option here, though it would perfectly hide any future updates from being displayed :) Nor is &quot;freezing&quot;, as the app is used regularly. Fifth: There is a related question for my GTalk example:  However, I want the opposite: No update.  It might very well be that &quot;Google Apps&quot; (and other pre-installed apps) are handled in some specific way, and restore their &quot;market links&quot; themselves somehow. For this case, my question includes: How to prevent that from happening?  Update There's a  discussing the very same issue. Until recently, a work-around for &quot;user installed apps&quot; was to uninstall them and then sideload the .apk – but even that stopped working. Well, re-signing the .apk with a different key might work for user-apps. But both would fail for pre-installed apps (can't sideload them to override; different signature would refuse that install completely). Moreover, there's an  on this by some &quot;joel.bou..&quot;. Not hard to guess, though blanked out: that would be Joël Bourquard. If it's really him, then that's really an issue (for those who don't know: Joël is the dev behind Titanium Backup). Let me quote from the issue:  For the record: in the Android Market days it was possible to &quot;Attach&quot; or &quot;Detach&quot; apps (on rooted devices) with a system tool such as Titanium Backup. But nowadays (with the Google Play Store app) this has become nearly impossible to do, because the complete app list seems to sync from Google's servers and the user has no control over that.  Which explains why detaching with apps like Titanium Backup is no longer permanent. And I'm afraid I've asked the impossible. But I thought the same in the past with other questions, and surprisingly got solutions here. So I do not yet give up hope on this one!  1: what that does is explained by eldarerathis  (thanks to  for digging that up!) Using Windows 10, I can't run certain commands from PowerShell but they all work correctly using cmd. PowerShell: node --version: node : The term 'node' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again. At line:1 char:1 + node --version + ~~~~     + CategoryInfo          : ObjectNotFound: (node:String) [], CommandNotFoundException     + FullyQualifiedErrorId : CommandNotFoundException  node.exe --version: no output. node.exe: opens a new black console (node.exe application itself). Get-Host | Select-Object Version: Version ------- 5.1.19041.906  Get-Command node: The term 'node' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again. At line:1 char:1 + Get-Command node + ~~~~~~~~~~~~~~~~ + CategoryInfo : ObjectNotFound: (node:String) [Get-Command], CommandNotFoundException + FullyQualifiedErrorId : CommandNotFoundException,Microsoft.PowerShell.Commands.GetCommandCommand Get-Command node.exe: CommandType Name Version Source ----------- ---- ------- ------ Application node.exe 14.16.1.0 C:\Program Files\nodejs\node.exe $env:Path output has nodejs &amp; git &amp; other paths. cmd: everything works fine with any command. I have git and nodejs in my PATH env variable. What's wrong with PowerShell, what a strange behavior is this and how to fix it? if a complex function $f$ is real-differentiable, then $f$ or $\overline{f}$ are complex-differentiable This is an exercise from Remmert's Theory of Complex functions.  Let $D\subset \mathbb{C}$ be a domain and $f:D\rightarrow \mathbb{C}$ a real-differentiable function. Assume that the following limit exists:  $ \mathrm{lim}_{h\rightarrow 0} \left|  \frac{f(c+h) - f(c)}{h}   \right|.$  Show that either $f$ or $\overline{f}$ is complex-differentiable.  I've tried showing that $\frac{\partial f}{\partial \overline{z}} = 0$ or $\frac{\partial \overline{f}}{\partial z} = 0$ by using the fact that there exist continuous functions $g$ and $h$ such that in $D$ one can write   $f(z) = f(c) + (z-c)g(z) + (\overline{z} - \overline{c})h(z)$   and that  $g(c)= f_{z}(c)$ and $h(c) = f_{\overline{z}}$ and then plugging this into the limit above. Does this approach works and I just can´t see how to do it? Can someone give a hint or a guideline solution to this? Using Green's identity to show that a harmonic function with zero boundary values is identically zero I am confused how to do this question. I need to use Green's first identity and if $\nabla(f)=0$ then $f$ is constant on $\Omega$ since $\Omega$ is path connected.  I have subbed in the information into green's identity but I don't get anything useful.  $$\iiint_\Omega \nabla f\cdot \nabla g \,dV =\iint_{\partial\Omega} f\nabla g\cdot n \,dA - \iiint_\Omega f\cdot \Delta g \,dV$$   We get:  $$\iiint_\Omega \nabla f\cdot \nabla g \,dV =-\iiint_\Omega f\cdot \Delta g \,dV$$   $$\iiint_\Omega \nabla. (f \nabla g) \,dV =0$$ $$\iint_{\partial\Omega} f\nabla g\cdot n \,dA=0$$ Why do I have two docks in Ubuntu desktop (with GNOME 3) after installing Dash to Dock? What's going on here? I've installed the  on Ubuntu 17.10. Everything was cool, and as I was trying to hone and tweak the look of my desktop, at some point the shortcuts bar (dock?) on the left is duplicated.  (Click image to enlarge) The default, which normally disappears with Dash to Dock, is there underneath the one that usually shows up when I install Dash to Dock. Why? I've tried to go through the options for Dash to Dock, the GNOME Tweak Tool, and the regular Ubuntu settings, but I can't figure it out. How can I remove myself from India's visa blacklist? Why is median age a better statistic than mean age? If you look at       Or this Wikipedia page      Clearly  seems to be the statistic of choice when it comes to ages.  I am not able to explain to myself why  would be a worse statistic. Why is it so?  Originally posted  because I did not know this site existed. I use a very custom style (not mine) and very frequently I get a heading  on the bottom of a page and the next paragraph on the top of the next page. Sometimes this paragraph may be a list or similar. The same is true for listings and the listing description.   Is there a general way how I can adjust the "badness" of these events? Or can I adjust when a section heading would be on the last, say, 3cm of a page it should go to the next page? Or can I say, if a *listing description" is on the top 3cm of a page pull 5 more listing lines from the last page onto this page?   The style I use does not use standard structure tags and environments. But lets call them section, subsection, listing and I will try to migrate them to my lingo. Execute PowerShell Script from C# with Commandline Arguments I need to execute a PowerShell script from within C#. The script needs commandline arguments.  This is what I have done so far:  RunspaceConfiguration runspaceConfiguration = RunspaceConfiguration.Create();  Runspace runspace = RunspaceFactory.CreateRunspace(runspaceConfiguration); runspace.Open();  RunspaceInvoke scriptInvoker = new RunspaceInvoke(runspace);  Pipeline pipeline = runspace.CreatePipeline(); pipeline.Commands.Add(scriptFile);  // Execute PowerShell script results = pipeline.Invoke();   scriptFile contains something like "C:\Program Files\MyProgram\Whatever.ps1".   The script uses a commandline argument such as "-key Value" whereas Value can be something like a path that also might contain spaces.  I don't get this to work. Does anyone know how to pass commandline arguments to a PowerShell script from within C# and make sure that spaces are no problem? Tabs in output file written by xelatex and pdflatex are different Birthday Problem applied to collisions I'm trying to extend the birthday problem to detect collision probability in a hashing scheme. Here is my problem. I use the letters and numbers [A-Z][a-z][0-9] to make a set of keys by randomly choosing from that set 10 times and concatenating them all together. So A24cv30kf2 could be one key for example. This implies that the base set has $62^{10}$ possible keys. Next, I want to compute the probability that I would see a collision if I picked a key from that set and issued it to $n$ users. If $M$ represents the size of the set (= $62^{10}$) and $P(M,n)$ the probability then  $$P(M,n) = \frac{M!}{M^{n}(M-n)!}$$  This follows by replacing 365 in the well known birthday problem shown   What I want to understand is the following: I want to check and see if my choice of concatenating 10 is right, when I know that my $n$ is of the order of a few millions and my $1 - P(M,n)$ needs to be less than 0.0001 or some small number. The large values of M &amp; n make the above intractable to compute. Is there an easier way to compute this? Sometimes we assume that regressors are fixed, i.e. they are non-stochastic. I think that means all our predictors, parameter estimates etc. are unconditional then, right? Might I even go so far that they are no longer random variables?  If on the other hand we accept that most regressors in economics say are stochastic because no outside force determined them with some experiment in mind. Econometricians then condition on these stochastic regressors.  How is this different from treating them as fixed?  I understand what conditioning is. Mathematically, it means we make all observations and inference conditional on that particular set of regressors and have no ambitions to say that inferences, parameter estimates, variance estimates etc. would have been the same had we seen a different realization of our regressors (such is the crux in time series, where each time series is only ever seen once).  However, to really grasp the difference between fixed regressors vs. conditioning on stochastic regressors, I am wondering if anyone here knows of an example of an estimation or inference procedure that is valid for say fixed regressors but breaks down when they are stochastic (and will be conditioned on).  I am looking forward to seeing those examples!