I'm not sure which one is correct: "The Physical Therapist Organization" or "The Physical Therapists' Organization".  I'm leaning more towards without the plural-possessive but will I be grammatically wrong? Please don't respond with saying that I can use "Therapy" instead. I need to use the word "Therapist" or "Therapists'". Any help will be well appreciated.
I know that children’s books is correct, but for some reason I want to say kids books, even though I know that it’s a plural possessive noun ending in an s.   A quick search on the web turns up Barnes &amp; Noble, who have a web page title that reads “Children's Books, Kids Books”.   Is the major bookseller wrong here? Or is there some exception I don’t remember?  More simply, is it kids books or kids’ books — and why?
How do I blend multiple photos to remove random people from the background? I'm very excited about the new  for Android/iPhone. Let's say you're taking a picture of your friend in front of a landmark with several people walking by. The app allows you to remove the people from the photo, leaving only the background and your friend. The app isn't just doing a clone of the surrounding image to paint over unwanted subjects. It's actually taking multiple images, detecting which objects are moving, and letting you select them for removal. This sounds awesome! But I don't want to be limited to taking pictures with a smart phone.  I would like to take multiple photos of the same scene. (Maybe with a tripod, but it would be better if I didn't have to use a tripod.) Then I would somehow blend them together to remove unwanted elements. How do I do that? I know there are tons of photoshop tutorials out there, but all the ones I find just tell you how to use the clone tool. How to handle :java.util.concurrent.TimeoutException: android.os.BinderProxy.finalize() timed out after 10 seconds errors? Exercise $1.8$ of chapter one in Hartshorne. In exercise 1.8 of chap I in Hartshorne algebraic geometry,       Let $Y$ be an affine variety of dimension $r$ in $\mathbf A^n$. Let $H$ be a hypersurface in $\mathbf A^n$, and assume that $Y \nsubseteq H$. Then every irreducible component of $Y \cap H$ has dimension $r-1$.     I refered to a . In this solution, why $f$ is not a unit in $B$? How to partition for Windows/Ubuntu dual boot on same SSD I have a 500GB SSD in which i would like to have both Windows and Ubuntu. My plan is to have something similar to this: Windows 8.1 and ubuntu 14.04 Uefi boot   an efi partition (created by windows installer) which will have Grub as bootloader 150GB ntfs for Windows 15GB ext4 for Ubuntu (root) 35GB ext4 for Ubuntu (home) ~8-16GB swap for Ubuntu (I have 16GB RAM) ~284-292GB ntfs for Data shared for both Windows and Ubuntu   My current setup is   200GB ntfs Windows 300GB ntfs for Data   I plan to shrink both the Windows and the data partiton in order to achieve my desired plan.  My questions:   Does the order of partitions matter? Does it matter if the ubuntu partitions are not at the end/beggining of the drive? Does the swap partition behaves better if its the last/first partition? Can I use the shared NTFS Data partition between windows and ubuntu without encountering problems? Do I have enough space for my ubuntu /home partition (thinking that I'll have access to the ntfs shared partition)?   Edit: Laptop, Asus N56jr, i7, 16Gb Ram, SSD samsung 850 evo 500gb  Windows 8.1 and Ubuntu 14.04 What's the terminal command for finding out a process's id I want to exit a process using the command line, but I can't recall the command to look up the process's ID.  Does anyone know it? Is there a ZIP code I can enter when paying-at-the-pump in the USA with a foreign credit card? If $p$ is a prime such that $p≡1\pmod 7$ then $p ≡1\pmod{14}$ Prove or disprove the following:  1)  if $p$ is odd prime such that $p≡1\pmod 7$ then $p ≡1\pmod{14}$  2)  if $p$ is odd prime such that $p≡4 \pmod 7$ then $p ≡4\pmod{14}$  I think that both statement are true and have a similar proof  1) $p≡1\pmod 7$ so $p≡8\pmod 7$ then $7|p-8$ so $p-8= 7 k$ where $k$ is an integer so $p=8+7k$, so $p ≡1\pmod {14}$  It is that a correct proof? Thank you. Find number of files with a specific extension, in all subdirectories Is there a way to find the number of files of a specific type without having to loop through all results inn a Directory.GetFiles() or similar method? I am looking for something like this:  int ComponentCount = MagicFindFileCount(@"c:\windows\system32", "*.dll");   I know that I can make a recursive function to call Directory.GetFiles , but it would be much cleaner if I could do this without all the iterating.  EDIT: If it is not possible to do this without recursing and iterating yourself, what would be the best way to do it? How do I fill a shape with text, like a circle? How do I confine text within a shape such as a circle or triangle?  I don't want text along the perimeter, I would like it to break appropriately at all the inner edges. Changing "index.php" Within The Address Polynomials, prove exercise question about question There is a polynomial P with integer coefficients and with pairwise different integers $a,b,c$ . Prove that it is not possible for $P(a) = b$, $P(b)=c$, $P(c) = a$  First off I don't understand "pairwise different" part - what does it mean ,can you show me this as an equation? After that I'd like to get a hint in case I don't make it. + I'd prefer to have hints/answers written more algebraically without $\sum$ etc. (It helps me get better understanding what's going on under the hood) How to create a timeline with LaTeX? How to get instance variables in Python? How do I do a case-insensitive string comparison? strictly positive elements in $C^*$-algebra Let $A$ be a $C^*\text{-algebra}$ and $A_+$ denote the positive elements. An element $a\in A_+$ is called strictly positive if $\overline{aAa}=A$. Want to find the following:a)What are the strictly positive elements of $C_0(\Omega)$ where $\Omega$ is locally compact Hausdorff space, and $C_0(\Omega)$ is the space of continuous complex valued functions that vanishes at $\infty$.b)If $A$ is unital, then $a\in A_+$ is strictly positive iff $a$ is invertible.c)if $(e_n)$ is an approximate identity of $A$, then $a:=\sum_{n=}^{\infty}\frac{1}{2^n}e_n$is strictly positive.What I tried and know:a) I know that positive elements in this space are functions with positive images, and thus, strictly positive elements are functions with positive images and now real root. is this correct? and how can I show that the positive elements are these kind of functions.b) I figures out that if $a$ in invertible then $a$ is strictly positive, but no idea how to do the other direction.c)I did this but using another characterization of strictly positive elements but want to do it with this one, and I don't know how.Thank you for your help. General theorems for consistency and asymptotic normality of maximum likelihood I'm interested in a good reference for results concerning asymptotic properties of maximum likelihood estimators. Consider a model $\{f_n(\cdot \mid \theta): \theta \in \Theta, n \in \mathbb N\}$ where $f_n(\mathbf x \mid \theta)$ is an $n$-dimensional density, and $\hat \theta_n$ is the MLE based on a sample $X_1, \ldots, X_n$ from $f_n(\cdot \mid \theta_0)$ where $\theta_0$ is the "true" value of $\theta$. There are two irregularities I'm interested in.    The data $X_1, \ldots, X_n$ are not iid and, as a result, the Fisher information about $\theta$ accrues at a rate slower than $n$.  $\Theta$ is a bounded set, and with positive probability $\hat \theta_n$ lies on the boundary. The boundary corresponds to a "simpler" model, and so there is particular interest in whether or not $\theta_0$ lies on the boundary.    My particular questions are   Letting $J_n(\theta)$ denote the observed Fisher information corresponding to $\theta$, and suppose $\theta_0$ lies in the interior of $\Theta$. Under what conditions is $$\left[J_n(\hat \theta_n)\right]^{1/2}(\hat \theta_n - \theta_0)$$ asymptotically normal as $n \to \infty$? In particular, are the regularity conditions similar to the usual ones, with the relevant modification being $J_n(\hat \theta_n) \to \infty$ in some sense? Suppose instead that $\theta_0$ is on the boundary, and again recall that $\hat \theta_n = \theta_0$ happens with positive probability - for concreteness, in a mixed effects model $Y_{ij} = \mu + \beta_i + \epsilon_{ij}$ we can have $\hat \sigma_{\beta}^2 = 0$. Under what conditions does $\hat \theta_n \to \theta_0$ (almost surely or in probability) and under what conditions will $\hat \theta_n = \theta_0$ eventually (this probably fails for the mixed effects model, but corresponds to "oracle" properties for the LASSO and related estimators, so perhaps it is too much to ask for general results)?   Again, just a pointer to a text with results at this level of generality would be greatly appreciated. A matching or independent edge set in a graph is a set of edges without common vertices.    A perfect matching (also called 1-factor) is a matching which matches all vertices of the graph.    a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets and (that is, and are each independent sets) such that every edge connects a vertex in to one in.    Now imagine a bipartite graph like G which has a perfect matching. Prove that there exists a vertex in G like V such that every edge connected to G is in a perfect matching.  Note : I tried to prove it but i have nothing to start with ! Thanks in advance.  Edit : The graph is a simple undirected graph and i don't know anything about "strongly" connected graphs. How to Expand , Resize "extended partition"? MacOS 10.14 Mojave public beta public Wi-Fi problem I can not connect to a single public Wi-Fi hotspot that does not require a password but instead shows a pop-up window pointed to captive.apple.com  The pop-up opens blank with the error "The web page couldn't be loaded"  Any idea on how to fix this? $k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$ I would like to prove the following equality: $$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}$$if $\gcd(l,k)=1$. What methods can I use? Thank you for your help.