Get Files and their directory in Powershell
Get full path of the files in PowerShell
Are there infinitely-many numbers that are both square and triangular? I just started to read "Friendly Introduction to Number Theory" but I am getting stuck in the first exercises.     1.1. The first two numbers that are both squares and triangles are 1 and 36. Find the next one and, if possible, the one after that. Can   you figure out an efficient way to find triangular–square numbers? Do   you think that there are infinitely many?     I found how to find out the number which is both square and triangle. (don't know if this is effective way)    However how can I answer "Do you think that there are infinitely many?"? I think I need to find the formula but no idea yet. Can you please help me? What inspired Tauriel's story arc? I know Tauriel is a Jackson created character, but I wondered if anywhere in the legendarium there was fodder for the story arc between her and Kili.  I do not have access to all my books for the time being and recall stories of love between men and elves in the Silmarillion and Appendices but don't remember any such stories between elves and dwarves and wondered if there was any basis of inspiration for this aspect of their relationship within Tolkien's works.   This movie, of course, departs even further from the original than those made before it, but as a story unto itself, I can still appreciate the ride, so if there is no Tolkien basis, what inspired Jackson, Boyens, and Walsh to create this particular arc?  Is there interview info or anything? I try to find a good proof for invertibility of strictly diagonally dominant matrices (defined by $|m_{ii}|&gt;\sum_{j\ne i}|m_{ij}|$).  There is a proof of this in  but I'm wondering whether there are are better proof such as using determinant, etc to show that the matrix is non singular. How to draw a Sankey Diagram using TikZ Primes congruent to 1 mod 6 I came across a claim that I found interesting, but can't seem to prove for some reason. I have the feeling it should be easy  a prime $p$ can be written in the form $p = a^2 -ab +b^2$ for some $a,b\in\mathbb{Z}$ if and only if $p\equiv 1\bmod{6}$ I have Windows 8 Pro activated with kms. when I open windows store, it doesn't show "win8.1 available". clicking on ms-windows-store:WindowsUpgrade just brings me to windows store main screen  slmgr /dli shows volume_kmsclient channel  I can upgrade it to WMC. Laptop is W8Pro WMC and update is available, it's retail channel  Is W8 for KMS clients delayed or what? First Order Time-Variant System : Picard Method I looking at a time variant first order system. I am trying to prove that a sequence of functions $x^{[k]}(t)$ generated using Picard iterations converges uniformly on some interval $[0,T]$.  Given:  $\dot{x}(t)=A(t)x(t)$ where $x(0)=x_0$  $x(t)=x∈R^n$ where $A(t)$ is a $n×n$ matrix  Assume there exists $M$ such that $||A(t)||\le M$ for all $t\ge 0$ and that $A(t)$ is a piecewise continuous function. Show that, for any $T &gt; 0$, a solution exists in the interval $[0,T]$.  I know that $x(t)=x_0+\int^t_0A(τ)x(τ) dτ$ must be satisfied if the solution does indeed exist.  I am supposed to use Picard iterations to prove this, which I am not familiar with yet. But I know that they are of the form: $x^{[k+1]}=x_0+\int^t_0A(τ)x^{[k]}(τ) dτ$. Where $x^{[0]}(t)=x_0$  Can I use the standard Picard proof to prove this or do I need to start somewhere else?  I was also asked to show that this method satisfies  $|x^{[k+1]}(t)-x^{[k]}(t)|\le |x_0| $$\frac{π^{k+1}(t)}{(k+1)!}$ where $π(t)=\int^t_0||A(τ)||dτ$.  I have no idea where to start with this, but hopefully it will become clearer once I finish the first part. How to change the href for a hyperlink using jQuery How can you change the href for a hyperlink using jQuery? Show that there's no continuous function that takes each of its values $f(x)$ exactly twice. I need to prove the following:  There's no continuous function $f:[a,b]\to \mathbb{R}$ that takes each of its values $f(x)$, $x\in [a,b]$  exactly twice.  First of all, I didn't understand the question. For example $x^2$ takes $1$ twice, in the interval $[-1,1]$. Is it saying that it does not occur for all $x$ in the interval? But what about $f(x) = c$? Is it saying that it does not occur only exactly $2$ times, then? I have no idea about how to prove it. I know that for $f(x)$ such that $f(a)&lt;f(x)&lt;f(b)$, if $f$ is continuous then there is a $c\in [a,b]$ such that $f(c) = f(x)$.  Now, there's the following proof in my book and I really wanted to understand it, instead of just getting a new proof  Since the interval $[a,b]$ has only $2$ extreme points, then the maximum or minimum of $f$ must be in a point $c\in int([a,b])$ and and in another point $d\in [a,b]$. Then, there exists $\delta&gt;0$ such that in the intervals $[c-\delta, c), (c,c+\delta)$ (and if $d$ is not extreme of $[a,b]$, $[d-\delta, d]$) the function takes values that are less than $f(c) = f(d)$. Let $A$ be the greatest of the numbers $f(c-\delta), f(c+\delta), f(d-\delta)$. By the intermediate value theorem, there are $x\in [c-\delta, c), y\in (c, c+\delta]$ and $z\in [d-\delta, d)$ such that $f(x)=f(y)=f(z)=A$. Contradiction.   Well, why the last part? Why is it that I can apply the intermediate value theorem to these values? For example, $&lt;f(c-\delta)&lt;p&lt;f(c)$, then by the theorem I know that there exists $m\in [c-\delta, c)$ such that $f(m) = p$. Same for the other intervals. But what guarantees thhat the greatest of the values between  $x\in [c-\delta, c), y\in (c, c+\delta]$ will be inside the intervals $[c-\delta), c), (c,c+\delta), [d-\delta, d)$? Why didn't Dumbledore just hunt Voldemort down? How can I cure lycanthropy? I really want to get rid of it. I've been through the whole companion’s quest line and cured Kodlak's. I killed all 5 witches and have 4 of the heads left in my inventory.  I've been back to that same flame and tried to use it with the head, but nothing going; activating it does nothing. I've heard this is how you cure it; however I have not heard a first-hand account of anyone actually curing it.  If you have, can you explain what you do? Do you go to the same tomb where you fought Kodlak's beast form? Do you do something special with the witch head in your inventory, or just have it in there and activate the harbinger flame or whatever? Writing test code for wrapper class I created a controller which looks like this  public with sharing class EventRegistrationController {      // A CONTROLLER FUNCTION     // FUNCTION RETURNS A LIST OF cSession      public List&lt;cSession&gt; getSessions() {            //DO STUFF       }     //A PUBLIC CLASS WITHIN CONTROLLER    @TestVisible public class cSession      {         public Session__c con {get; set;}         public Boolean selected {get; set;}          //This is the contructor method.          public cSession(Session__c c) {              con = c;             selected = false;         }     }  }   I need to write a test code for the controller, how can I create a list of cSession and call getSession function? I am trying to work through Hartshorne's book and while working through one of the exercises, I need to show the following:  Let $k$ be an algebraically closed field. Let $Y \subseteq A^3$ be the set $Y=\{(t,t^2,t^3)\;|\;t \in k\}$. Show that $Y$ is an affine variety.  The rest of the problem I have completed. I'm just not sure how to show that this set is closed and irreducible. I assume that they intend for $A^3$ to have the Zariski topology. Using "of" or apostrophe, which is more common? How to modify function argument? Is "of" instead of "have" correct? How to view the user's status? Passive POE: Need 5V @ 2A at the destination 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. When ever I save a gedit file in a directory, two copies of it get saved with identical content. Ex: If the gedit file is named as file_name and saved in Home directory then when u ls the Home directory you get file_name and file_name~ in the list. When the file command is run against them I get ASCII text, with very long lines for both of them when I view their contents using the less command they seem to largely contain identical content. The ~ file is a copy of the file when it was saved for the penultimate time. Can someone please help me in understanding as to why such a file (the file with a trailing ~ mark in its name ) is created?