I have no idea what I'm doing and need help please
How to remove Ubuntu and put Windows back on?
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer let $a_{i},i=1,2,\cdots,n$ be postive integer ,show that $$1^{n-1}2^{n-2}\cdots (n-2)^2(n-1)|\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$$  I know this $\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$ is  Vandermonde  determinants,and I found $$1^{n-1}2^{n-2}\cdots (n-2)^2\cdot (n-1)=1!2!3!\cdots (n-1)!=\prod_{1\le i&lt;j\le n}(j-i)$$ we only prove $$\prod_{1\le i&lt;j\le n}\dfrac{a_{j}-a_{i}}{j-i}$$ is integer  maybe consider Vandermonde determinants ? But I can't prove this Assurance that ST_Envelope works with geography as expected Using PostGIS, I have a table of data with geographic points defined as last_known_coordinates GEOGRAPHY(POINT,4326). I want to find all of these within a geographic bounding box with given top left and bottom right geographic coordinates, and be sure that the calculations are geographic, not geometric, e.g. that the results account for the curvature of the earth. The query I'm using contains the fragment: last_known_coordinates &amp;&amp; ST_MakeEnvelope(?, ?, ?, ?, 4326)::geography As you can tell I'm a bit new to this, and I know what I want, but not necessarily how to do it correctly. Other answers hint that this is correct, but I'd like to know for sure: Will this point data and SQL fragment take into account the curvature of the Earth in the bounding box? Why doesn't Ubuntu 16.04 in Windows have ubuntu.exe? What is the white smoke-like fog called? Proving $\arg(zw)=\arg(z)+\arg(w)$ I have a large table that is already partitioned by an identifier (CustomerId). I have created new customers, and want to add new partitions to the table, and want to confirm the correct way to do this. My predecessor set this up and is no longer available so I cannot confirm.  There are currently partitions for 60 distinct CustomerIds (let's say 1-60), and a filegroup and file for each. I have created new filegroups and files for the new customers (61-68) and need to partition the existing data already in this table. So, the data that's already in the table, with customerId 61-68 needs to be moved into separate partitions.   I tried to use the partition wizard, but couldn't find an option for what I wanted. As far as I can tell, I need to run something like:  ALTER PARTITION SCHEME PS_Details  NEXT USED Filegroup61 ALTER PARTITION FUNCTION PF_Details ()  SPLIT RANGE (61)   I'm looking for someone to point me in the right direction as to best practice for this sort of thing. Do I take the data out of the table, into a new table stored in the Filegroup61 then switch the partition in? Not really sure how to approach this. 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. I just installed Ubuntu and it is great.  However, I installed in beside the Windows Vista OS.  I now want to remove Windows in an effort to improve performance.  What is the easiest way to do this? How is light affected by gravity? How can I modify title page so that it looks like it is in  video. Please seek to 16 seconds and watch title page. I do not have permission to post images. I liked this theme and I want to make a beamer theme that looks similar. I tried with beamercolorbox but I failed to position the box to the bottom.      Edit: Here is my minimum working example  \documentclass[xcolor=dvipsnames]{beamer} \defbeamertemplate*{title page}{customized}[1][] { \usebeamerfont{subtitle} \usebeamercolor[fg]{subtitle}  {\flushright \setbeamercolor{author}{bg=white,fg=Red} \usebeamerfont{author} \insertauthor\par \usebeamerfont{institute}\insertinstitute\par }  \vspace{0.2in}  \setbeamercolor{postit}{fg=white,bg=YellowOrange}  \begin{beamercolorbox}[sep=1em,wd=1.062\textwidth,ht=3cm,dp=3cm,right]{postit} \usebeamerfont{title} {\huge \inserttitle}\par \usebeamerfont{subtitle} {\insertsubtitle} \end{beamercolorbox} } \usecolortheme[named=YellowOrange]{structure} \useoutertheme{infolines} \setbeamertemplate{navigation symbols}{}  \institute{Harvard College Professor and\\ Johnstone Family Professor in Psychology, Harvard University}  \title{SAY WHAT?} \subtitle{Linguistics as a Window to\\ Understanding the Brain} \author{Steven Pinker}  \begin{document} { \setbeamertemplate{footline}{} \begin{frame} \titlepage \end{frame} } \end{document} Meaning of different Orders of Derivative I have been trying to analyse the meaning of higher order derivatives and their geometrical significance.  Given a function $f(x)$ what are the unique geometric interpretation of its higher orders?   $f'(x)$ - slope (rate of change of x w.r.t y) $f''(x)$ - convexity / concavity of $f(x)$ based on $sign(f''(x))$ $f'''(x)$ - increasing / decreasing slope of $f'(x)$ $f''''(x)$ - ?? ... $f^n(x)$ - ??   I apologize if this question is rudimentary. Can massive damage knock out rather than causing instant death? Suppose, as happened last night, a character intends to subdue rather than kill an opponent. She made a melee attack, hit, declared her intent to knock out. The damage roll was enough to reduce the opponent to zero and the remaining damage exceeded the opponent's maximum HP. Now we would seem to have two rules invoked:  Instant Death. Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum. (PHB p.197) Knocking a Creature Out. When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable. (PHB p.198)  So which rule takes precedence? Or is it neither? I just did a clean install of 20.04 and I noticed that no key shortcuts for files manipulation work when my focus in on Desktop (not in Nautilus).   When I have copied a file to clipboard, I cannot Ctrl+V it to Desktop, when I click on a file on Desktop, I cannot Ctrl+C it, or I cannot Delete it with keys. Only ways to do it is either navigate to the Desktop folder in Nautilus, or right-click the file on the Desktop and copy/move to trash/paste...  Sorry if I'm missing something obvious, all the key shortcuts worked normally for me in 18.04. What is the difference between a homepage link with or without a trailing slash? Random place change in row with restrictions How could I randomly change places of characters in a text file, with some probability (say 10%)?  file:  1  34567 2  12356 3  16987   outcome:  1  35674 2  12653 3  61987 Characterizing non-constant entire functions with modulus $1$ on the unit circle Is there a characterization of the nonconstant entire functions $f$ that satisfy $|f(z)|=1$ for all $|z|=1$?   Clearly, $f(z)=z^n$ works for all $n$. Also, it's not difficult to show that if $f$ is such an entire function, then $f$ must vanish somewhere inside the unit disk. What else can be said about those functions?  Thank you. What is the default root password? I installed  (Precise Pangolin), 64 bit. Nowhere was I asked to set password for root.  I just installed  software. It was installed under the /root folder by default. Now I try do something on that folder. I tried with su to switch to root, but I don't know its password.   Should I always use sudo or get the default root password, if any?  How do I create a  for software installed inside the /root directory? Is there a good reason to use "printf" instead of "print" in java? Can I clear an area of my prison for everyone BUT max security prisoners? How can I make sure that only low and medium security inmates are in a specific area? Is it possible to reverse the overlay you can set? It seems like you are only able to clear areas for low OR medium security prisoners, but sharing is not possible. The thing I want here is to make sure that max security prisoners are not in certain areas. Windows 7 File Explorer search not working