I'm thinking of installing a motion detector inside an existing recessed fixture over my front door in order to illuminate the stairs and door lock at night. Home Depot sells a small sensor that can be installed between the socket and bulb but nobody has been able to tell me if the frosted glass cover will block the sensor.
Can any one help? I purchased a solar powered PIR security light, with the intention of putting it inside my kitchen window. The PIR would be inside the window, but this does not work.  When I go outside to activate the light, it does not work. When I go inside to run my hand across the sensor, it works.  Will a PIR unit penetrate glass, or am I barking up the wrong tree?
How can I integrate $$\ln \left( x+\sqrt{1+x^2} \right) $$   The problem is from IA Maron Calculus, Problem 4.3.17. The problem is under the heading 'Integration by parts'. I have tried it, but it just leads to 2 unsolvable integrals Adventurer enters an other-dimensional realm where he repeatedly dies unexpectedly and wakes up in reality Running junit tests in parallel in a Maven build? I'm using JUnit 4.4 and Maven and I have a large number of long-running integration tests.  When it comes to parallelizing test suites there are a few solutions that allow me to run each test method in a single test-class in parallel. But all of these require that I change the tests in one way or another.  I really think it would be a much cleaner solution to run X different test classes in X threads in parallel. I have hundreds of tests so I don't really care about threading individual test-classes.  Is there any way to do this? Lenovo Y510P: Battery wont charge past 60% On my y510p, I set Lenovos battery software to "Optimize battery health" while I was in Windows 8.1. I forgot to change it before overwriting that partition with Ubuntu, and now my battery in Ubuntu never charges past 59~60%. I think this is due to something in the BIOS because it persists despite my Windows partition being gone.   I've searched the BIOS but there's no mention of battery anywhere!  I'm using Ubuntu 14.04 LTS. Let $\mathbb{F}_{27}$ denote the finite field of size 27. For each $\alpha\in\mathbb{F}_{27}$ , define $ A_{\alpha}$ $=$ { $ 1, 1+\alpha , 1+\alpha+{\alpha}^2 , 1+\alpha+{\alpha}^2+{\alpha}^3 , .... $} . Then  prove that  the number of  $\alpha\in\mathbb{F}_{27}$ such that $|A_\alpha|$=26 equals 12.  $ 0\in A_\alpha $ if and only if $\alpha\neq 0$ For the first proof , the multiplicative group of the field $\mathbb{F}_{27}$ is cyclic and its order is 26  , so there are 12 generators in that group.   Now  I need  to  show  that  $ 1+\alpha+{\alpha}^2+.. {\alpha}^{25} $ =0  , where order of $\alpha$=26 . Since   $\alpha ^{26}$ =1 ($\alpha$-1)(1+$\alpha$+${\alpha}^2$+...+${\alpha}^{25}$)=0 , since $\alpha\neq 1$  , So $ 1+\alpha+...+{\alpha}^{25} $ =0 My question is , can I write these last two  lines?  I mean are those two lines alright to write? If those two lines are invalid then I need some help to show  $ 1+\alpha+{\alpha}^2+..+{\alpha}^{25} $=0  .Thanks In ideal gas model,  is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?  Furthermore, if we accelerate a block of metal with ultrasonic vibrator so that the metal is vibrating in very high speed with cyclic motion, can we say the metal is hot when it is moving but suddenly become much cooler when the vibration stop? Why should the "H" option not be used in floats? I have been a witness to many a discussion about numbers to the power of zero, but I have never really been sold on any claims or explanations.  This is a three part question, the parts are as follows...    1) Why does $n^{0}=1$ when $n\neq 0$?  How does that get defined?  2) What is $0^{0}$?  Is it undefined?  If so, why does it not equal 1?  3) What is the equation that defines exponents?  I can easily write a small program to do it (see below), but what about in equation format?    I just want a little discussion about numbers to the power of zero, for some clarification.    Code for Exponents: (pseudo-code/Ruby)  def int find_exp (int x, int n){     int total = 1;     n.times{total*=x}     return total; } Do cell carries have access to FaceTime information? On the newest iPhone, do cell phone carriers have access to FaceTime call data (such as which caller initiated and ended a FaceTime call)? How do I interpret the Mann-Whitney U when using R's formula interface Since canonical is  Ubuntu One, what are the possible alternatives?  I currently use Ubuntu One as a backup service for my Documents folder and various other folders I deem important. Of course I have backups on an external hard drive as well, but nevertheless, I find Ubuntu One to be very useful. What I'm especially looking for is a cloud service that does not need a special folder (such as a dropbox or google drive folder); something that is able to integrate into my own file system and syncs just any folder I want to.   I am aware that this question is rather subjective, but I do guess many people who have used Ubuntu One are now in the dark. How to get Steam to recognize existing game files from a different source? Let's say I have a game bought on retail/other digital download and installed on my hard drive. I buy the same game (or a minor variant of it, say the GOTY edition) on Steam. It should be possible to use the existing installation to avoid the generally big downloads. This is very useful as it saves both bandwidth and time.   Previously, as far as I understood, Steam downloaded the game files directly to steam\steamapps\common\&lt;game_name&gt;. Since this folder would be created on starting the download, pausing and closing steam, copying the game files to this folder and then validating game files would make Steam absorb as much as possible and just download the missing files.  Currently, Steam downloads the files to steam\steamapps\downloading\&lt;game_id&gt; and then moves them over to the aforementioned folder once the download finishes. So first of all, what the final folder would be is not clear. So what would be the correct way of doing the same thing, that is, make steam use as much of the existing files as possible? Should the files be copied to downloading\*\, or should I figure out the actual folder (say via googling) and copy the files to steamapps\common\*\?  More specifically, I had a retail copy of Arkham City installed and I just bought the GOTY version on Steam. Now I tried both of the above things, in either case, the validating does not seem to do anything. Assuming I have the correct folder name steamapps\common\Batman Arkham City GOTY, according to , if I copy the files there, Steam seems to just continue with its 17GB download. If I copy it to steamapps\downloading\200260 then the download keeps stopping every few seconds with "Disk Write Error" after modifying 1 or 2 files, and I have to keep hitting resume. No Dialect mapping for JDBC type: -9 Suppose all the Associated Primes are Minimal. Let $R$ be a commutative Noetherian ring with unit and let $I$ be a fixed ideal. I am sorry if the following turns out to be a very silly question.  1) Suppose $\operatorname{Ass}(R/I)$ are all minimal, then what can we say about $R/I$?  One conclusion is that $I$ has a unique primary decomposition. If $R/I$ is CM, then $\operatorname{Ass}(R/I)$ are all minimal, but I don't think the converse is true. Can someone provide a counterexample?  2) Suppose $\operatorname{Ass}(R/I)$ are all minimal and have the same height. I still dont think we can conclude that $R/I$ is CM. Can someone provide a counterexample? Theorem 2.1.6 of Bruns and Herzog, CM Rings, gives a result in this direction but it needs additional hypothesis. It says that if every ideal $I$ is generated by height $I$ elements and $\operatorname{Ass}(R/I)$ are all minimal, then $R$ is CM.  It would be nice if someone can say something nice about the ring in the special situation described in 1) and 2).  Thanks. How can I typeset this accented, dotless i? See the rough sketch above. I am able to typeset the accented i shown in the middle (for which I used the \v macro) and, obviously, the plain and simple i shown on the left also. However, I can't figure out how to typeset the one shown on the right. How can I do that? Fix corrupt NTFS partition without Windows MY NTFS Partition has gotten corrupt somehow (it's a relic from the days when I had Windows installed).     I'm putting the debug output of fdisk and blkid .  At the same time, any OS is unable to mount my root partition, which is located next to my NTFS partition. I'm not sure if this has anything to do with it, though. I get the following error while trying to mount my root partition (sda5)  mount: wrong fs type, bad option, bad superblock on /dev/sda5,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so  ubuntu@ubuntu:~$ dmesg | tail [ 1019.726530] Descriptor sense data with sense descriptors (in hex): [ 1019.726533]         72 03 11 04 00 00 00 0c 00 0a 80 00 00 00 00 00  [ 1019.726551]         1a 3e ed 92  [ 1019.726558] sd 0:0:0:0: [sda]  Add. Sense: Unrecovered read error - auto reallocate failed [ 1019.726568] sd 0:0:0:0: [sda] CDB: Read(10): 28 00 1a 3e ed 40 00 01 00 00 [ 1019.726584] end_request: I/O error, dev sda, sector 440331666 [ 1019.726602] JBD: Failed to read block at offset 462 [ 1019.726609] ata1: EH complete [ 1019.726612] JBD: recovery failed [ 1019.726617] EXT4-fs (sda5): error loading journal   When I open gparted (using live CD), I get an exclamation next to my NTFS drive which states   Is there a way to run chkdsk without using windows ?  My attempt to run fsck results in the following :  ubuntu@ubuntu:~$ sudo fsck /dev/sda fsck from util-linux-ng 2.17.2 e2fsck 1.41.14 (22-Dec-2010) fsck.ext2: Superblock invalid, trying backup blocks... fsck.ext2: Bad magic number in super-block while trying to open /dev/sda  The superblock could not be read or does not describe a correct ext2 filesystem.  If the device is valid and it really contains an ext2 filesystem (and not swap or ufs or something else), then the superblock is corrupt, and you might try running e2fsck with an alternate superblock:     e2fsck -b 8193 &lt;device&gt;   Update: I was able to fix the NTFS partition running chkdsk off Hiren's BootCD, but it seems that the superblock problem still remains.  Update 2: Fixed superblock issue using e2fsck -c /dev/sda5 macOS Mojave won't install updates past 10.14.1 due to requirement for APFS formatting I have a MBP 2012 I upgraded from High Sierra to Mojave after it came out as GA. I don't recall if I was asked about upgrading to APFS when Id id that, but at this time the main volume is Mac OS Extended (Journaled).  My current About This Mac...version is Mojave 10.14.1 (18B75). Now, when updates are advertised from the App Store, I'm unable to upgrade because 10.14.3 is required.  No OS updates show in the App Store, and when I searched for the updaters (10.14.2 Combo, etc), I can't install because the installer reports "macOS 10.14.2 Update can't be installed on this disk. This Mac can only install macOS on APFS-formatted drives."  I tried the search results recommending to boot in Recovery Mode and use Disk Utility, but APFS is not available as a type.  I have good backups and I can reformat the boot volume if I need to, but I have not done this before. Should I get a 10.14.3 installer to do this and boot from an external drive? The only guies and message boards I've found just keep saying to install 10.14.3 (I can't) or convert the disk in Recovery Mode (APFS is not available as an option.)  Any known-good ways to get my 10.14.1 upgraded so I can keep getting App Store updates? How can we evaluate this series  $$\sum_{n=1}^\infty \frac{n^a}{b^n}?$$  Here $a$ and $b$ are positive integers. If $b=1$ then series will be diverging, in other cases, it will be converging, but how to find this sum?  Isn't there a simple solution which doesn't involve Stirling numbers? Is propagation of uncertainties linear? I'm in doubt with one thing: let's imagine that we have $n+1$ quantities, $n$ of them being directly measured, and the other one being related to the first $n$ by a function $f : \mathbb{R}^n \to \mathbb{R}$. If the $x_i$ is one of the quantities being directly measured and if $\Delta x_i$ is it's uncertainty, then I've learned that the uncertainty of the quantity $y = f(x_1, \dots x_n)$ is given by:  $$\Delta y=\sum_{i=1}^{n}{\frac{\partial f}{\partial x_i}\Delta x_i}$$  My problem in understanding this is: well, if $f$ is such a function, it's derivative is the linear transformation $df : \mathbb{R}^n \to \mathbb{R}$ given by:  $$df=\sum_{i=1}^{n}\frac{\partial f}{\partial x_i}dx_i$$  Where $dx_i : \mathbb{R}^n \to \mathbb{R}$ is given by $dx_i(a_1 \dots a_n) = a_i$. Hence, what we are saying, is that $\Delta y = df ( \Delta x_1, \dots \Delta x_n)$, in other words, we are saying that the uncertainty of $y$ is given by a linear function of the vector of uncertainties of the quantities $x_i$. Why should that be true? I mean, what's the reasoning behind this? I really didn't get the point, my teacher just gave the equation without justifying or anything like that.  Any help and reference is appreciated. siunitx tabular numbers with separated uncertainty I would like to format the space reserved for a number shown in a table with separated uncertainty. It seems that when I use the table-format option the brackets around the mantissa disappear. This is illustrated in the example below:  \documentclass{article}     \usepackage{siunitx}  \begin{document}     \begin{table}   \begin{tabular}{                   S[separate-uncertainty = true]                   S[table-format=1.1(1)e1,                   separate-uncertainty = true]                   }     {Header} &amp; {Header}\\     1.0(2)e2 &amp; 1.0(2)e2\\   \end{tabular} \end{table}     \end{document}     I have also tried to use the bracket-numbers and multi-part-units = brackets without solving this issue. Is there any workaround to center the number and keep the brackets like in the first column of the example?