I don't know how to prove this example. Let $y(t):\mathbb{R}^+ \to \mathbb{R}^+$ be a nonincreasing function. Assume that there is a constant $A&gt;0$ such that \begin{equation} \int_{s}^{+\infty}y(t)dt \leq Ay(s), \quad 0\leq s&lt;+\infty \end{equation} then $y(t)\leq y(0)e^{1-\frac{t}{A}}$ for all $t&gt;0$.
I don't know how to prove this example. Let $y(t):\mathbb{R}^+\to \mathbb{R}$ be a nonincreasing function. Assume that there is a constant $A&gt;0$ such that \begin{equation} \int_{s}^{+\infty}y(t)dt \leq Ay(s), \quad 0\leq s&lt;+\infty \end{equation} Then $y(t)\leq y(0)e^{1-\frac{t}{A}}$, for all $t&gt;0$.
Direct "rate in iTunes" link in my app? Wifi disabled, no hardware switch available, rfkill list reads "Hard Blocked" anyway on an Acer Aspire One How to perform hard / cold reboot of iPhone or iPad? How do I choose an element from a non-empty set? Suppose I have a non-empty set $A$.     How do I choose an element $x\in A$?   More precisely, I believe I would like to find a formula $P(x,y)$ of ZF such that for every non-empty set $y$ there is exactly one $x\in y$ such that $P(x,y)$ is true.  I have thought about this for a while without success and I am beginning to doubt such a formula is even possible. But in mathematical proofs it is quite common to "choose a fixed element" from a non-empty set. So how exactly do we achieve such a thing? Am I missing something?  Thank you in advance. MSO Review Queue Privileges are Misleading Why is everybody so concerned about etc/passwd? Here is the content of my vagrant machine of this particular file:  root:x:0:0:root:/root:/bin/bash daemon:x:1:1:daemon:/usr/sbin:/usr/sbin/nologin bin:x:2:2:bin:/bin:/usr/sbin/nologin sys:x:3:3:sys:/dev:/usr/sbin/nologin sync:x:4:65534:sync:/bin:/bin/sync games:x:5:60:games:/usr/games:/usr/sbin/nologin man:x:6:12:man:/var/cache/man:/usr/sbin/nologin lp:x:7:7:lp:/var/spool/lpd:/usr/sbin/nologin mail:x:8:8:mail:/var/mail:/usr/sbin/nologin news:x:9:9:news:/var/spool/news:/usr/sbin/nologin uucp:x:10:10:uucp:/var/spool/uucp:/usr/sbin/nologin proxy:x:13:13:proxy:/bin:/usr/sbin/nologin www-data:x:33:33:www-data:/var/www:/usr/sbin/nologin backup:x:34:34:backup:/var/backups:/usr/sbin/nologin list:x:38:38:Mailing List Manager:/var/list:/usr/sbin/nologin irc:x:39:39:ircd:/var/run/ircd:/usr/sbin/nologin gnats:x:41:41:Gnats Bug-Reporting System (admin):/var/lib/gnats:/us$ nobody:x:65534:65534:nobody:/nonexistent:/usr/sbin/nologin syslog:x:100:103::/home/syslog:/bin/false   Could anybody explain me why it is bad if some evil guy could get this file of my production server? linux find command to move files What is the purpose of the first test in an inductive proof? Learning about proof by induction, I take it that the first step is always something like "test if the proposition holds for $n = \textrm{[the minimum value]}$"  Like this:       Prove that $1+2+3+...+n = \frac{n(n + 1)}{2}$ for all $n \ge 1$.   Test it for $n = 1$:  $$n = \frac{n(n + 1)}{2} \implies 1 = \frac{2}{2}\textrm{, which holds.}$$  * The rest of the proof goes here *    So, I do it all the time (like a standard). But I never really thought about why. Why do I do such test? I can see that if the test does not hold, it cannot be proven by induction, I guess. But is there another reason we do this? Gparted: move extended partition on the left I have some free disk space on the left of my ubuntu (sda5)  What is best solution to extend sda5 ?  I can    copy sda3 or sda5 with dd to bigger disk. delete sda3,5,swap create sda3,5,swap dd original partition.   Not sure how to do it properly.  May be there is a simpler solution. Often I need two (or more) map frames in map layout to present different data next to each other. It is easy to make multiple map frames in QGIS Print Composer. BUT...  It is in the nature of my work that very often I need to update some map frames because data I am presenting in map changed or I need to add/remove layer, change scale, projection etc.  So if I create one map frame, lock it (Lock layers for map item), create second map frame with different layers, scale,projection etc. and than realize I need to change something in first frame, I can't find a simple way to do it...  To simply do that in Mapinfo, there are more Map Windows, in ArcGIS there are multiple Data Frames. What is in QGIS to achieve that? How can I prove these statements? SaveAsActivity is not allowed with whatId that is not supported as a task whatId Let $V,W$ be nonzero normed spaces over $\mathbb{K}$ such that $V$ is finite-dimensional.  Let $E$ open in $\mathbb{K}$ and $p\in E$.  Let $f:E\rightarrow W$ be Gâteaux-differentiable at $p$.  Is $f$ necessarily Fréchet-differentiable at $p$ in this case?  I think this is not true in general, but cannot find a counterexample. What would be a counterexample? bash regex with quotes? The following code  number=1 if [[ $number =~ [0-9] ]] then   echo matched fi   works. If I try to use quotes in the regex, however, it stops:  number=1 if [[ $number =~ "[0-9]" ]] then   echo matched fi   I tried "\[0-9\]", too. What am I missing?  Funnily enough,  suggests this should work.  Bash version 3.2.39. extracting energy from cosmological expansion This question is a more concrete reincarnation of an .  Are there mechanisms to extract energy from the cosmic rate of expansion? putting some extremely long ropes across the universe and extract work from their increase of separation?  assuming this is possible ( i don't see why it would not ), what form would take the back-reaction force? in all physics, every time you extract work from some system by some force, this system will exert a force back. Can we slow down cosmic expansion by variations of these mechanisms? This post is an expansion of  For many graduated sites (eg Physics), moderators do not want to apply the unilateral close vote in all cases--it is better to let some community votes pile on first.  We only use the unilateral in obvious cases then. This renders the CV queue useless to us. If we &quot;skip&quot; something, we can't get back to it. If we say &quot;do not close&quot;, it's removed from the queue and our community can't see it. If we use &quot;close&quot;, we are using a unilateral mod vote--we don't want to do that. What I propose is a set of &quot;next/previous&quot; buttons, that let us navigate the queues, looking for closeable questions, and coming back to the others later. Thoughts? Update and bounty reason Due to the recent Great Flag Overhaul, mods no longer see close flags in the flag queue. Which means that the only way to get to them is via the review queue 1 Shog's solution is ideal in this case; let mods view the close queue as a list. (In fact, a list similar to the old flag queue -- which shows a list of mods who have seen the post and what mod actions have already been taken -- would be great) On Physics, the majority of the flags that we get are VTC flags. And the community isn't always able to close things on their own, so we have to step in. However, powering through the close queue isn't an option; because &quot;skip&quot;ing a post2 leads to it being dumped into the void (I can't get back to it unless I have a link). Extremely inconvenient. Could the workflow here be improved? 1. The /tools listing for posts with outstanding close votes doesn't work because it doesn't list posts which have been flagged but not VTCd 2. which I may want to take a closer look at later; gotta be careful with the binding votes. What is the difference between "owing to" and "due to"? What are the similarities/differences between the behaviors of Quantum particles and bouncing droplets? Why is orbital angular momentum not 0 when spin and linear momentum are not collinear?   Why can it be 0 when spin and linear momentum are parallel?  Like in the example of a scalar field at rest decaying into an electron and a positron via interaction $\frac{1}{2}g\phi \bar{\Psi}\Psi $   If spin is along x axis and three-momenta is along z axis, decay rate will be 0 if two spins are opposite because orbital momentum is not 0 after decaying. How do I stop my rim brakes making a squeaking/squealing sound? I bought a Schwinn Frontier Sport few months ago and started riding happily. After a few weeks my front rim brakes started creaking. It's so annoying in public places. My rear brake doesn't produce any sound but isn't as powerful as the front brake.  The retailer says cleaning would solve the front brake's issues and I got it cleaned, but nothing changed. Is there something I can do something myself to fix this?