Does the following series converges or diverges?
Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
I'm using Java, and need to generate a simple, standards-compliant RSS feed. How can I go about this? Prediction in Cox regression I am doing a multivariate Cox regression, I have my significant independent variables and beta values. The model fits to my data very well.   Now, I would like to use my model and predict the survival of a new observation. I am unclear how to do this with a Cox model. In a linear or logistic regression, it would be easy, just put the values of new observation in the regression and multiply them with betas and so I have the prediction of my outcome.  How can I determine my baseline hazard? I need it in addition to computing the prediction.  How is this done in a Cox model? What is the most effective way for float and double comparison? What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it. How to get exact camera view? I'm currently a beginner when it comes to 3D modelling but doing okay so far. I'm struggling a bit when it comes to the final renders of my scene, specifically on the camera view I want. Sometimes its to zoomed in and sometimes to zoomed out that it's gone out of the environment of the blender. I realized the settings for the camera on blender are for actual cameras / photography and I'm no expert on that too. A tip on how to control them precisely would be nice. Thank you. Raised index of partial derivative I am having a really hard time wrapping my head around component notation for tensor fields. For example, I do not know exactly what the following expression means $$\partial_\mu\partial^\nu \phi, \tag{$\#$}$$ where $\phi$ is a scalar field. On the one hand $\partial^\nu=g^{\lambda\nu}\partial_\lambda$ where $g_{\mu\nu}$ is the Minkowski metric, and hence we could write explicitly $$\partial_\mu\partial^\nu \phi=\sum_{\mu,\nu,\lambda}g^{\lambda\nu}\partial_\mu \partial_{\lambda}\phi=\sum_{\mu,\nu}\partial_{\mu}\partial_{\nu}\phi=\partial_\mu\partial_\nu\phi. \tag{$*$} $$ On the other hand, we may think of $\partial_\mu\partial^\nu=g(\partial_\mu,\partial^\nu)=\delta_\mu^\nu;$ so that $\partial_\mu\partial^\nu\phi=\phi?$ Maybe? I am actually not sure of what this would mean. I am really confused. Any help is appreciated. Edit: To give context of where this expression comes from: I was computing the Lagrangian $$\mathcal L=\frac{1}{2}(\partial_\mu\phi)(\partial^\mu \phi) $$ considering an infinitesimal spacetime translation $x^ \mu\to x^\mu-\alpha a^\mu$. The scalar field thus transforms like $\phi(x)\to \phi(x)+\alpha(\partial_\mu\phi(x))a^\mu.$ Plugging thins into the Lagrangian yields the term I am referring to. Edit 2: The change in placement of indices are actually my doubts. I try to elaborate. I do not have any background in using indices to talk about tensors. I am used to interpret the expressions $\partial_\mu$ as the local vector field defined in some chart (local coordinates). I think about vector fields $X$ as abstract section of the Tangent bundle, which restricted to local coordinates can be expressed as $X=X^\mu\partial_\mu$. In the context of QFT, as far as I understand, the symbol $\partial_\mu$ denotes  $(\partial_t,\nabla)$ in the local coordinates $(t,x,y,z)$. So that $\partial_\mu\phi=(\partial_t \phi,\partial_x \phi,\partial_y\phi,\partial_z\phi)$. This was supposed to be my justification on why I wrote the summation on $\mu$ and $\nu$ in $(*)$, but now I note that this only applies when $\mu$ or $\nu$ appear twice, indicating the scalar product; which leads me to the last remark. I think of $g_{\mu \nu}$ as the component of the matrix $$g=\begin{pmatrix} 1&amp;0&amp;0&amp;0\\ 0&amp;-1&amp;0&amp;0\\ 0&amp;0&amp;-1&amp;0\\ 0&amp;0&amp;0&amp;-1\\ \end{pmatrix}$$ which represents the pseudo-Riemmanian metric, which by definition acts on tangent vectors, i.e. linear combinations of the $\partial_\mu$ applied to a point. This is where my doubt comes, in which was the right way to interpret the notation; in particular what is the expresion $(\#)$ in explicit coordinates? Chi-squared test when two vectors have different lengths I want to compare two groups (vectors) having different lengths to see if their distributions differ considerably. However, when I use chisq.test, I get an error due to inequalities of lengths:  &gt; chisq.test(factor(Group1), factor(Group2))   results in:  Error in chisq.test(factor(Group1[, col]), factor(Group2[, col])) :  'x' and 'y' must have the same length   Could someone help me with this? Thanks. I have a 64-bit (amd64 a.k.a. x86_64) Debian or Ubuntu installation. I need to run 32-bit (i386/i686) programs occasionally, or to compile programs for a 32-bit system. How can I do this with a minimum of fuss?  Bonus: what if I want to run or test with an older or newer release of the distribution? Usage of Some: Does "some" require a plural or singular verb? $(a^{2^n}+1,a^{2^m}+1)=1 or 2$ Prove that if $m\not =n,a$ are positive integers then $(a^{2^n}+1,a^{2^m}+1)$ is $1$ if $a$ is even and $2$ if $a$ is odd.    I solve the problem in the following way: I assume that $m&gt;n$ then  $$a^{2^m}+1=a^{2^m}-1+2$$ With this expression if I take a divisor prime $p$ of $a^{2^n}+1$ then if $p|a^{2^m}+1$ this prime must divide 2 and the result follows.   But, how can I prove this statement without use of primes? This exercise appears before the concept of prime is introduced then I prefer do not use it.    Any idea?   Thanks! Why use the 'ref' keyword when passing an object? Prove $\limsup_{n \rightarrow \infty} a_n\geq1$ if $\lim_{n \rightarrow \infty} a_na_{n+1}=1$ Let $\{ a_n \}_{n=1}^{\infty}$ be a bounded sequence s.t. $a_n&gt;0,\ \forall n \in \mathbb{N}$. Suppose $\lim_{n \rightarrow \infty} a_na_{n+1}=1$, prove $\limsup_{n \rightarrow \infty} a_n\geq1$.   I tried to prove by contradicition using subsequence, but couldn't work it out.  Any help appreciated. I'm trying to create a pmatrix whose components are rather complicated fractions (Christoffel symbols), and the line spacing is too small making the whole thing a bit cramped and hard to read.  Is there any easy way to increase the spacing (about 1.5 the default would be perfect)? Is "TABLESAMPLE BERNOULLI(1)" not very random at all? What is the fate of the Asgardians at the start of Avengers: Infinity War? Thor: Ragnarok ends with the remaining people of Asgard aboard a refugee ship that meets Thanos' ship. Avengers: Infinity War opens with      Thanos and his minions having commandeered the ship and several bodies can be seen on the floor.   This begs the question, what happened to these characters:   Korg Miek Asguardian extra #3 Valkyrie How to divide aleph numbers Recently, I was wondering how division of aleph numbers would work. First, I thought about how finite cardinality division would work. What I came up with was that the result of $A/B$ where $A$ and $B$ are both cardinalities, is the number of times that each element of $B$ had to be mapped to an element of $A$ in order to ensure that all elements of $A$ were mapped to.  Extending this to aleph numbers, specifically, I thought that $\aleph_1/\aleph_0$ would be $\aleph_1$. The reasoning behind this is that there are an infinite ($\aleph_1$) number of real numbers between any two natural numbers. As such, that mapping would need to be applied.  Can anyone validate this idea? Is this how division of aleph numbers actually works, or am I totally off base?  Thanks. I would like to associate the last installed version of my Mac OS X application with a certain type of file. A little experimentation shows that the info.plist file seems to be read and interpreted by the operating system when launching the application, not when dragging the application bundle to the disk.  does not say much on that topic.  Is there any way, using a simple .dmg image as installation medium, to make sure the system associates that particular file type with my newly installed app without having to launch it first?  I should clarify that I want this to be done automatically during the installation (I don't want my users to have to do it themselves). I will be writing scripts for ArcGIS Desktop in Python with ArcPy.   Is there a community or open source project where code and models can be shared? Why is Euler's Totient function always even? I want to prove why $\phi(n)$ is even for $n&gt;3$.  So far I am attempting to split this into 2 cases.  Case 1: $n$ is a power of $2$. Hence $n=2^k$. So $\phi(n)=2^k-2^{k-1}$. Clearly that will always be even.  Case 2: $n$ is not a power of $2$. This is where I am unsure where to go. I figure I will end up using the fact that $\phi(n)$ is multiplicative, and I think I'll get a $(p-1)$ somewhere in the resulting product which will make the whole thing positive, as $p$ is prime implies $(p-1)$ is even. How to code an automated bot that can browse and do operations on a webpage