New Question: Proving Divergence of a Sequence
Proof of Divergence for a Sequence
Mathematica9: NDSolve slows down after repeated calls Why does Python pep-8 strongly recommend spaces over tabs for indentation? I have the amulet of Mara but when I go to talk to maramal about a wedding nothing shows up. WHY is that. Last Logon Time of All Users - RDP server not on a domain Difference between ulimit, lsof, cat /proc/sys/fs/file-max I've been getting java.io.IOException: Too many open files while running a Kafka instance and using one topic with 1000 partitions so I started investigating the file descriptors limits in my ec2 vm. I cannot understand which is exactly the limit for open files on a Centos 7 machine since all the following commands produce different results. The commands are:   ulimit -a: open files 1024 lsof | wc -l: 298280 cat /proc/sys/fs/file-max: 758881 (which is consistent with /proc/sys/fs/file-nr)   If the actual limit is the one the last command produces then I am well below it (lsof | wc -l: 298280). But if this is the case, the output of the ulimit command is quite unclear to me since I am well above the 1024 open files.   but are there all these seemingly "inconsistencies" between these commands? Cauchy condensation test The following is Cauchy condensation test:  If $b_n \ge 0$ and $b_n \ge b_{n+1}$ then $\sum b_n$ converges if and only if $\sum 2^n b_{2^n}$ converges.  Is the following modified Cauchy condensation test possible:  Let $N \in \mathbb N$. Then if $b_n \ge 0$ and $b_n \ge b_{n+1}$ then $\sum b_n$ converges if and only if $\sum N^n b_{N^n}$ converges? Title is the question itself.  How can I show below without L’Hospital’s Rule  $$ \lim_{x\to \infty} ( 1 + x )^\frac{1}{x} = 1 $$ How to change the disk space left warning in Windows 7? my disk has over 100GB of free space, but the usage bar in Computer is displayed in red, as if it reached a low space limit. It looks like Windows applies the same 10% or 15% hard disk space value for low space warnings, regardless of if the disk is 50GB in size or 1.5TB, which is not very smart and obsolete for most recent computers.  Is there a Registry key or some place I can change this percentage so the usage bar displays in green, not red?  The hibernation and page files are already reserved (5GB together), so surely the low space warning for a 1.5TB disk should be 5-10GB, not 150GB or more. The way Windows 7 computes the low space limit seems pretty dumb, not much Intellisense there.  This is not a high priority issue, but it makes the Computer applet look pretty stupid and it's irritating every day to see that 100GB of free space is putting my computer in the red. It would also be nice to be able to edit this low limit percentage in Computer/Manage/Storage/Disk Management or directly in the disk properties ("Tools" tab). If I chose "Replace Windows with Ubuntu", do I lose the other partition too? I am a newbie in linux. I wanted to install ubuntu to my desktop. I currently have two partitions, Windows 8 in installed on one, and i have some important files in another partition. While installing ubuntu, if I chose "Replace Windows 8 with Ubuntu", do I lose the other partition too?   And are there other ways to leave the other partition as it is, and install ubuntu in the partition  where windows was installed. How can you sync Blender configs between multiple machines? I run Blender on several machines, it is a hassle to copy configs around, in order that you don't have to configure everything from scratch every time. Is there a sync functionality that does this? Why is the Earth so fat? I made a naive calculation of the height of Earth's equatorial bulge and found that it should be about 10km.  The true height is about 20km.  My question is: why is there this discrepancy?  The calculation I did was to imagine placing a ball down on the spinning Earth.  Wherever I place it, it shouldn't move.  The gravitational potential per unit mass of the ball is $hg$, with $h$ the height above the pole-to-center distance of the Earth (call that $R$) and $g$ gravitational acceleration.  Gravity wants to pull the ball towards the poles, away from the bulge.  It is balanced by the centrifugal force, which has a potential $-\omega^2R^2\sin^2\theta/2$ per unit mass, with $\omega$ Earth's angular velocity and $\theta$ the angle from the north pole.  This comes taking what in an inertial frame would be the ball's kinetic energy and making it a potential in the accelerating frame.  If the ball doesn't move, this potential must be constant, so  $$U = hg - \frac{(\omega R \sin\theta)^2}{2} = \textrm{const}$$  we might as well let the constant be zero and write  $$h = \frac{(\omega R \sin\theta)^2}{2g}$$  For the Earth,   $$R = 6.4*10^6m$$  $$\omega = \frac{2\pi}{24\ \textrm{hours}}$$  $$g = 9.8\ m/s^2$$  This gives 10.8 km when $\theta = \pi/2$, so the equatorial bulge should be roughly that large.    , the Earth is 42.72 km wider in diameter at the equator than pole-to-pole, meaning the bulge is about twice as large as I expected.  (Wikipedia cites diameter; I estimated radius.)  Where is the extra bulge coming from?  My simple calculation uses $g$ and $R$ as constants, but neither varies more than a percent or so.  It's true the Earth does not have uniform density, but it's not clear to me how this should affect the calculation, so long as the density distribution is still spherically-symmetric (or nearly so).  (Wikipedia also includes , without derivation, that agrees with mine.) Inaccurate reputation graphs - bug or as designed? I have notice two issues with the reputation graph: 1: This user has a higher score on the graph than in reality I happened to notice  where the user's graph reputation does not match their actual reputation.  The person in question was hit by a -100 penalty for an offensive answer a while back, but the graph doesn't reflect that.  I thought it just didn't update when I noticed this at the time, but the person has since gained and lost reputation and at all times the graph was +100 of their actual reputation.  It seems, based on Shadow Wizard's comment that this is because the reputation change is non-public. OK, fair enough... , which was marked as , noticed a similar phenomenon for placed DVs.  This prompted me to examine graphs more carefully.  It seems that this hidden -1 has been updated, as I checked several users and did not find any others that had lower actual reputation than graph reputation, so .  (Since the number of DVs placed is public, I can be reasonable sure that these users have placed -1 rep DVs, although strictly speaking they could be 100% question DVs.) 2: Some users have a lower score on the graph than in reality I did, however, find many users where the graph says their reputation is much lower than it actually is.  Perhaps that is from deleted downvotes turning into hidden +1s, but those should be balanced by hidden -1s, so its not clear what happened.  Seems there is some error in the logic - maybe the -1s do affect the graph now as per the , but the corresponding +1s don't?  Whatever the case, I can't imagine it is intentional. Edit: I went back to find some examples today &amp; didn't find any.  I think the issue has been resolved - either it was a caching issue or a change was made to the code after this post. Does the shebang determine the shell which runs the script? This may be a silly question, but I ask it still. If I have declared a shebang  #!/bin/bash    in the beginning of my_shell_script.sh, so do I always have to invoke this script using bash  [my@comp]$bash my_shell_script.sh   or can I use e.g.  [my@comp]$sh my_shell_script.sh   and my script determines the running shell using the shebang? Is it the same happening with ksh shell? I'm using AIX. Changing the style of the first *typeset* line of a paragraph Is it correct to use that/which in the relative clause when it is referring to the place as an object pronoun? Clone a hard disk content to another hard disk I subjected my hard disk (C drive) to a disk scan and found that there was 12 KB of bad sectors. I now consider that disk to be unreliable, and am looking forward to transferring all my data to another file.  The problem is, I want to clone the complete drive (including the apps, OSes, files and everything, verbatim) to another drive. I know there would be some crazy software activation issues, like Windows Not Genuine problem and so on. But I wonder whether is there a tool powerful enough to do the cloning and at the same time maintain the  OS and apps? Do photons truly exist in a physical sense or are they just a useful concept like $i = \sqrt{-1}$? Reading about photons I hear different explanations like "elementary particle", "probability cloud", "energy quanta" and so forth. Since probably no one has ever seen a photon (if "seen" it supposedly - and rather conveniently - ceases to exist) but many experiments seem to verify its properties (or are they maybe adjusted to fit the experiment). I thus can't help wondering if the "photon" is then just a physical/mathematical tool with inexplicable properties (like zero mass - but affected by gravity fields - and constant speed c in space) invented to explain some otherwise unexplainable phenomem and to supplement the elementary particles and their interactions. In short: Are they real or imaginary!  Does anybody know? Or maybe the answer is "blowing in the wind" because to most physicist it probably just does'nt matter as long as it works (as the alternative healers say). Sorry if I seem a little sarcastic here and there. Original sentence:     Prince Andrew, looking again at that genealogical tree, shook his head, laughing as a man laughs who looks at a portrait so characteristic of the original as to be amusing.    (War and Peace, Tolstoy, English translation)     In the sentence above, shouldn't the comma before laughing be omitted if this is about the participle clause denoting "an action that happens at the same time in the past"?  I mean it should be      Prince Andrew…shook his head laughing as a man…   Plus, shouldn't the verb laugh after a man be in the past tense in order to be in accordance (agreement) with shook his head?   You know, the whole sentence should be consistent…. Regular expression for URL Why are SMD LEDs shipped in a sealed bag containing desiccant? I had a selection of 0805 LEDs in my last Mouser order and was a bit surprised to discover they arrived in heat-sealed (rather than folded and taped with sticker) bags containing a desiccant bag and some sort of litmus-esque paper indicator saying something about baking them if the dots on it went pink (instead of blue).    A quantity of through-hole LEDs I had in the same order just came in the regular ESD-protective bag, folded over with a sticker.  What's up with SMD LEDs that they work so hard to keep them dry? Surely their dryness can't be assured once they're installed. Does it have to do with their solderability or something? Why would that be different than other SMD parts?