Will gravitational field of a body increase if the body is accelerated?
If a mass moves close to the speed of light, does it turn into a black hole?
Time complexity function in terms of theta notation sum = 0;  for (i = 0; i &lt; n; i++)    for (j = 1; j &lt; n^3; j = 3*j)                  sum++;   what is the time complexity (in $\Theta$-notation) in terms of $n$?  so far, this is what i've done: The running time is $\Theta(N^4)$  Because the for loop’s condition is depend on $n$ and is incremented by $1$, and  then inside running time is $\mathcal{O}(1)$. i feel i'm wrong here. any help would be appreciated. How to set a font for math mode? I would like to have something like Segoe UI of something similar. Thank you  \documentclass{article} \usepackage{fontspec} \usepackage{firamath-otf} \begin{document} \begin{equation} x+y=45 \end{equation}  \end{document}   Error: I have a Python script that will need to be given to a client.   We are currently evaluating what license level the client will need in order to run the script for their software acquisition purposes.   We all have ArcGIS 10.1 Advanced license in our company.   I checked all the tools and extensions used in the script against the web help and found that they should work on the Standard license level.   Is there a way I can test the script against the Standard license level, when we have no Standard license level in or company (only the higher Advanced level)? Infinite Series Convergence Verification I'm currently tackling the following infinite series in order to determine if it converges or not:  $$\sum_{n=1}^\infty \frac{\sqrt{n+1}-\sqrt{n}}{n}$$  What I've done is rearranged this to make use of the comparison test, shown below:  $$= \frac{\sqrt{n+1}-\sqrt{n}}{n} * (\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}})$$  $$= \frac{(n+1)-(n)}{n(\sqrt{n+1}+\sqrt{n})}$$  $$= \frac{1}{n(\sqrt{n+1}+\sqrt{n})}$$  $$= \frac{1}{n^{3/2}+\sqrt{n+1}} &lt; \frac{1}{\sqrt{n+1}} &lt; \frac{1}{\sqrt{n}} $$  However, $\frac{1}{n}$ is smaller than $\frac{1}{\sqrt{n}}$, therefore:  $$  \frac{1}{n}   &lt; \frac{1}{\sqrt{n}}$$   This implies divergence by the comparison test due to the fact $\frac{1}{n}$ diverges, and if a smaller series diverges any larger series must as well.  Is this right? If I've made any mistakes in any part, please tell me! Connecting subplots Is there a way to draw a sort of connection between subplots in TiKz/pgfplot, like in this ? I'm looking to achieve something like this:    But I would need to draw the "x 2000" line between the plots.  EDIT: So right now I have something like this:    Coming from my main.tex:  \input{aipcheck}  \documentclass[final]{aipproc}  \layoutstyle{8x11single} \usepackage[utf8]{inputenc} \usepackage{algorithm2e} \usepackage{color} \usepackage[usenames,dvipsnames]{xcolor} \usepackage{cleveref} \usepackage{pgfplots}  \pgfplotsset{ tick label style={font=\tiny}, %axis numbers label style={font=\small}, %axis labels legend style={font=\tiny} }  \begin{document}  (...)  \begin{figure}     \centering     \newlength\figureheight      \newlength\figurewidth      \setlength\figureheight{5cm}      \setlength\figurewidth{5cm}     \input{figs/_ddmp2d.tikz} \label{fig2D} \end{figure}   with _ddmp2d.tikz, originally created from matlab2tikz, but already modified, containing:  % This file was created by matlab2tikz v0.3.3. % Copyright (c) 2008--2013, Nico Schlömer &lt;nico.schloemer@gmail.com&gt; % All rights reserved. %  % The latest updates can be retrieved from %   http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz % where you can also make suggestions and rate matlab2tikz. %  %  %   \begin{tikzpicture}  \begin{axis}[% width=\figurewidth, height=\figureheight, scale only axis, xmin=0, xmax=15, xlabel={Number of iterations}, ymin=0, ymax=16000000000000, name=plot1, after end axis/.append code={\coordinate (a) at (axis description cs:1,0);}]  \addplot [ thick, color=red, dash pattern=on 1pt off 3pt on 3pt off 3pt, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 25160000000\\ }; \addplot [ thick, color=black, dashed, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 52501000000\\ }; \addplot [ thick, color=blue, dotted, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 5324200000\\ }; \addplot [ thick, color=green, solid, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 551920000\\ }; \addplot [ thick, color=green, solid, forget plot ] table[row sep=crcr]{ 3 0\\ 3 16000000000000\\ };  \addplot [ thick, color=blue, dotted, forget plot ] table[row sep=crcr]{ 4 0\\ 4 16000000000000\\ }; \addplot [ thick, color=black, dashed, forget plot ] table[row sep=crcr]{ 5 0\\ 5 16000000000000\\ }; \addplot [ thick, color=red, dash pattern=on 1pt off 3pt on 3pt off 3pt, forget plot ] table[row sep=crcr]{ 8 0\\ 8 16000000000000\\ }; \end{axis}  \begin{scope}[xshift=5cm] \begin{axis}[% width=0.35\figurewidth, height=\figureheight, scale only axis, xmin=995, xmax=1000, xtick={997,998,999,1000}, xticklabels={$997$,$998$,$999$,$1000$}, ymin=0, ymax=8000000000, at=(plot1.right of south east), anchor=left of south west, yticklabel pos=right, axis x discontinuity=crunch, after end axis/.append code={\coordinate (b) at (axis description cs:0,1);} ] \addplot [ thick, color=red, dash pattern=on 1pt off 3pt on 3pt off 3pt ] table[row sep=crcr]{ 995 6093100000\\ 996 6093100000\\ 997 6093100000\\ 998 6093100000\\ 999 6093100000\\ 1000 6093100000\\ };  \addplot [ thick, color=black, dashed ] table[row sep=crcr]{ 995 1577100000\\ 996 1598000000\\ 997 1598500000\\ 998 1628600000\\ 999 1631000000\\ 1000 1595900000\\ };  \addplot [ thick, color=blue, dotted ] table[row sep=crcr]{ 995 2592000000\\ 996 2591900000\\ 997 2591700000\\ 998 2591600000\\ 999 2591500000\\ 1000 2591400000\\ };  \addplot [ thick, color=green, solid ] table[row sep=crcr]{ 995 391810000\\ 996 391810000\\ 997 391810000\\ 998 391810000\\ 999 391810000\\ 1000 391810000\\ };  \end{axis} \draw[gray] (a) -- (b) node[pos=0.5,sloped,fill=white] {$\times$2000}; \end{scope}  \end{tikzpicture}% Why does second pre-image resistance imply pre-image resistance I am studying hash functions. I can understand why collision resistance implies second preimage resistance, but I don't get why second preimage resistance should imply first preimage resistance. Could anybody be help me with this argument from Introduction to Modern Cryptography by Katz &amp; Lindell, please?   Collision resistance: This is the strongest notion and the one we have considered so far.  Second pre-image resistance: Informally speaking, a hash function is second pre-image resistant if given $s$ and $x$ it is infeasible for a probabilistic polynomial-time adversary to find $x' \ne x$ such that $H^s(x') = H^s(s)$.  Pre-image resistance: Informally, a hash function is pre-image resistant if given $s$ and $y = H^s(x)$ (but not $x$ itself) for a randomly chosen $x$, it is infeasible for a probabilistic polynomial-time adversary to find a value $x'$ such that $H^s(x') = y$. (Looking ahead to later chapters in the book, this essentially means that $H^s$ is one-way.)   [...] Likewise, any hash function that is second pre-image resistant is also pre-image resistant. This is due to the fact that if it is possible to invert $y$ and find an $x^\prime$ such that $H^s (x^\prime ) = y$ then it is possible to take $x$, compute $y = H^s (x)$ and invert it again obtaining $x^\prime$. Since the domain of $H$ is infinite, it follows that with good probability $x \neq x^\prime$. We conclude that the above three security requirements form a hierarchy with each definition implying the one below it. Journal of Finance Template German '*.bst' How to compare two time series? I have collected temperature readings for 4 locations on a beach in Cornwall UK using data loggers. The loggers recorded temperature every 15 mins accurate to .1 of a degree (Celsius). The loggers collected data for 10 days with a one day break to calibrate the sensors. In total I used 30 sensors with 6-7 sensors in each position.  I have now downloaded the data and have produced time-series for temperature over the 10 day period. Visual inspection of the time-series shows how the temperature changes with tides and night and day. I want to investigate whether the time-series differ significantly from one another. Please could someone point me in the direction of a technique to do this in SPSS? How do I use subprocess.Popen to connect multiple processes by pipes? How do I execute the following shell command using the Python  module?  echo "input data" | awk -f script.awk | sort &gt; outfile.txt   The input data will come from a string, so I don't actually need echo.  I've got this far, can anyone explain how I get it to pipe through sort too?  p_awk = subprocess.Popen(["awk","-f","script.awk"],                           stdin=subprocess.PIPE,                           stdout=file("outfile.txt", "w")) p_awk.communicate( "input data" )   UPDATE:  Note that while the accepted answer below doesn't actually answer the question as asked, I believe S.Lott is right and it's better to avoid having to solve that problem in the first place! How to make a through hole using inward extrusion in Blender 2.8? I am trying to make a through hole using inward extrusion. I enterd into edit mode, then I drawed an outline of my hole using knife tool. then I turn into wireframe shading, rotate my view an select snap to faces and then extrude the hole outline inward  so the hole is created successfully, but I still have a face at the hole bottom. I can select this face separately  But If I try to delete it, I siply delete this face (I can't select it anymore after deleteting), but I do not see through hole, so the basic cube face is still here. So how to remove the hole bottom? a command to list all packagas installed on the system and their installed files, how? I have to figure out a way to count how many sequences are there s.t:   My alphabet is $1$ up to $49$. Each number that is chosen, is chosen only once. The sequence is $6$ digits long. The sequence is in increasing order.  e.g that is a valid sequence: $(1, 2, 40, 42, 43, 49)$  and this is not: $(1, 2, 40, 25, 25, 12)$   I know that for the first 3 rules the answer is: $\binom{49}{6}\cdot 6!$  How do I deal with the fourth? "Can’t help but" vs. "can help but" Is "can’t help but" considered to be a confused mix of the expressions "can but" and "can’t help"? If not, what is the difference between "can help but" and "can’t help but"? How can I set desktop defaults for new users? How can I set up desktop defaults, much like most distributions do, for every new user? (ex. default wallpaper, apps, etc) How to combine low sample renders? Rotate only one screen If I have only the internal monitor (LVDS1) with an xrandr -o left command. Now I want to attach a second monitor, say to HDMI1. Then I'd like to rotate only the internal monitor, but not the external one. I tried the following (with no external attached though, since I am mobile currently), but that does not do anything:  xrandr --output LVDS1 -o left   How can I rotate only one monitor?  I do need some command line, since I want to put this into a script. Why do we say that the Earth moves around the Sun? Reputation for graph is off by a day So when we view reputation, there is graph view. However, it seems to be off by a day. Here's what I mean:   I'm sure 70 + 20 + 15 is not 15. Its 105, which is what we see below:   And 40 + 10 is NOT 105, unless you did  :)     Anyways 40 + 10 is 50:   So yeah. Did you do what that post on codegolf says? Devs better fix that :) Calling Table with custom iterator I was going through the topic "formation of comparative and superlative".       The rule says     When two objects are compared with each other, the latter term of comparison must exclude the former, as in "Iron is more useful than any other metal". If we say "Iron is more useful than any metal", that is the same thing as saying    "Iron is more useful than iron", since iron is itself a metal.   I am finding difficulty to relate the rule with example.