I recently heard someone say 'between he and I there's difference' Is it correct not to use him and me?
When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I".
How long does the new dwellers queue last? When clicking the radio room icon that attracts a new dweller to your vault, how long will they stay queued out in front of the vault for before giving up?  Or will they?  I'm at max population and would rather not kill existing dwellers to accommodate them in my vault. Fermi's golden rule and infinite probablity? I am slightly confused about the application of . Which during standard derivations indicates a probability of transitioning from the state $|i \rangle$ to the state $|f\rangle$ of: $$P=\frac{2\pi t}{\hbar^2} | \langle f | \hat V | i \rangle|^2 \delta(E_f-E_i-\hbar \omega)$$ This holds for large values of $t$ but for arbitrarily large values of $t$: $$P&gt;1$$ Which (to me anyway) makes no physical sense since there can't be a probability greater then 1 of been in the final state. If my interpretation is right then how is this problem resolved/allowable? and if it is wrong what part of what I have said is wrong? Any data for average number of papers per year at different career stages? MySQL: LEFT JOIN not working as expected Mean and variance of inverse of a normal RV My random variable $X$ is normally distributed with mean $b$ and variance $p$. I defined a new RV, $Y$, such that $Y=1/X$. Does anyone know how to find the mean of $Y$ and $Y^2$? How do I find a recursion formula to solve the following question:  In how many sequences of length $n$, with elements from $\{{0,1,2,3,4}\}$, the difference between every 2 adjacent elements is $1$ or $-1$?  I've been trying to solve the problem for the last 5 hours maybe, I'm sure that I'm missing something..   This is a problem in combinatorics, and the solution must be by finding a recursion formula for the problem.   best solution I've come so far is that if we say that $a_n$ is the solution to the question, so let's count how many sequences of size $n-1$ there are that meet the requirement, and we complete the first element to make it a sequence of $n$ elements. so for $n-1$ there $a_{n-1}$ sequences, and for each sequence we have $2$ options to choose the first element (one option is to take a plus $1$ number from the number that start the $n-1$ sequence, and the other option to to take a minus $1$ number from the number that start the $n-1$ sequence), only problem as you figured out is that if the $n-1$ sequnce starts with $0$ or $4$ there is only $1$ option left for the first element in the sequnce.. so $a_n=2a_{n-1}$ won't work.  I think that the solution may involve using $2$ or maybe $3$ recursion formulas.  Hope I was clear enough. How do you forcefully remove apps in Windows 10? How can I remove apps that Windows doesn't seem to allow to be uninstalled, like Xbox and Groove Music? How to throttle callback of jQuery event? Chrome 100% CPU usage, again - software_reporter_tool.exe software_reporter_tool.exe belonging to Chrome running at 100% cpu, fan full speed.  Deleting it doesn't fix anything, because it gets redownloaded again! Disabling "Protect me from bla bla" doesn't make it stop running.  Please anyone have any solutions? Infinitely many primes for quadratic residues Skype app in my Ubuntu system work perfectly. But today when I run the app, I see this:    How Can I fix this? I just installed Ubuntu 16.10 on my desktop and have a USB deathadder. The problem is I can't see where the cursor actually is because it appears only in the top left of my screen. The mouse still moves but the cursor graphic doesn't follow How to connect two parents to the same child, with parents not in the same tree? I'm trying to draw a specific tree, with two parents node linked to the same child. The problem is that one of the parent is outside the main tree.  Here's the code I have for the moment:  \documentclass{article} \usepackage{tikz-qtree,tikz-qtree-compat} %\usepackage{gb4e} \usepackage{forest}  \begin{document}  %\begin{exe} \begin{forest} qtree edges/.style={for tree= parent anchor=north, child anchor=south}    [A, grow=north        [C, name=C, grow'=north            [D, grow=north ]            [E, name=t5, grow=north ]        ]        [B, grow=north ]    ]    \hspace{0.8cm}    [$F$, name=F, grow=north ]    %\draw (F.north) -- (C.south); \end{forest} %\end{exe}  \end{document}   I'd like the nodes F and C to be connected. I don't know why, but if I delete the dollar signs, node F doesn't even appear on my document.  Another thing is that I want the forest environment to be embedded in an example environment, but this doesn't work either.  Thanks in advance for your help! How do I install Adobe Flash player? How can I change the page URL without refreshing the page? In general what is the approach to switch the desktop environment or window manager on Ubuntu? The main difference between stock Ubuntu, Kubuntu and Lubuntu is supposedly the use of Unity vs. KDE vs. LXDE.  However, in order to try various desktop environments and window managers I don't want to have to reinstall the respective flavor from scratch just to get a particular desktop environments or window manager. There probably is an easier method than that.  The question: How can I easily test different desktop environments and respective compatible window managers (say KDE, LXDE, Unity, GNOME, XFCE and StumpWM)? Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$ Given measure space $(X, \mu)$ and measurable function $f$. If $p \in (0, +\infty]$, below are the facts I know about $\Vert f \Vert_p$:  (log convex in $\frac 1 p$) $\forall p_1, p_2\in (0, +\infty] \text{ such that } p_1 &lt; p_2. \forall t \in(0, 1), \text{ let } \frac 1 p = \frac t {p_1} + \frac {1-t} {p_2}$, then $\Vert f \Vert_p \le \Vert f \Vert_{p_1}^t\Vert f \Vert_{p_2}^{1-t}$ ($0\cdot(+\infty)$ is defined to be $0$). (lower semi-continuity) $\forall p_0 \in (0, +\infty], \liminf_{p\to p_0}\Vert f\Vert_p \ge \Vert f \Vert_{p_0}$. If $0&lt;\mu(X) &lt; +\infty$, then $ \Vert f \Vert_p/\mu(X)^{\frac 1 p}$ is monotone increasing in $p$, combine it with (2) we get $\lim_{p\to p_0-}\Vert f\Vert_p = \Vert f \Vert_{p_0}$.  From (1) we know the set of $p$ such that $\Vert f \Vert_p &lt; +\infty$ is an interval $I$ (possibly empty or a singleton).  If $I \not\in a = \inf I$ and $a \neq 0$, from (2) we know $\lim_{p\to a+} \Vert f \Vert_p = +\infty$. If $I \not\in b = \sup I$, then $\lim_{p\to b-} \Vert f \Vert_p = +\infty$.  From (1) and the dominated convergence theorem we know that if $I \ni p_0 \neq \inf I$ and $p_0 &lt; +\infty$, then $\lim_{p\to p_0+} \Vert f \Vert_p = \Vert f \Vert_{p_0}$. If $I \ni p_0 \neq \sup I$, then $\lim_{p\to p_0-} \Vert f \Vert_p = \Vert f \Vert_{p_0}$.  If $I$ is nondegenerate and $+\infty \in I$, then $\lim_{p\to +\infty}\|f\|_p = \|f\|_{\infty}$.  If $\inf I = 0$, from (1) we know $\lim_{p\to 0+}\|f\|_p$ exists.   Question: How $\Vert f \Vert_p$ behaves when $p$ is the endpoint of $I$? To be more precise, assume $I$ is nonempty. Let $p_0 = \sup I$ (only right endpoint is considered for simplicity):  $p_0\in I$ or $p_0 \not\in I$? Can $I$ be a singleton? What if $p_0 = +\infty$? What if $0&lt;\mu(X) &lt; +\infty$?  Please also notify me if there is any mistake above. Can you grapple/shove with the Hunter Ranger's Whirlwind Attack? The  states:     You can use your action to make a melee attack against any number of creatures within 5 feet of you, with a separate attack roll for each target.   The rules on "" state (the rules in shoving are effectively identical):     When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.   I couldn't find any other features spells or abilities that allow a creature to make a flat "melee attack". If they had said "melee weapon attack" instead this would have meant the same thing but specifically have excluded grapple/shove as an option.  I am unsure whether the rules on grappling/shoving mean that the only time you can grapple/shove are when you take the Attack action, which you are not doing when using the Whirlwind Attack feature.   I would like answers to assume that the following ruling made in the  is correct:     Whirlwind Attack is unusual, in that it’s a single attack with multiple attack rolls... Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$ Verify the identity: $\tan^{-1} x + \tan^{-1} (1/x) = \frac\pi 2, x &gt; 0$  $$\alpha= \tan^{-1} x$$  $$\beta = \tan^{-1} (1/x)$$  $$\tan \alpha = x$$  $$\tan \beta = 1/x$$  $$\tan^{-1}[\tan(\alpha + \beta)]$$  $$\tan^{-1}\left [{\tan\alpha + \tan\beta\over 1 - \tan\alpha \tan\beta} \right]$$  $$\tan^{-1}\left[ {x + 1/x\over 1- x/x }\right]$$  $$\tan^{-1}\left[{x + (1/x)\over 0} \right]$$  I can't find out what I'm doing wrong.. Let $N$ be a normal subgroup of $G$. Let $G/N = \{gN : g \in G \}$. Show that the $(G/N, \circ, 1_{G/N})$ is a group, where:  $\circ : G/N \times G/N \rightarrow G/N$ is defined by $(gN \circ hN) = ghN$ and $1_{G/N} = 1*N$.  Thanks for your help.