Certain categories have the property that for every morphism $f:A\to B$ can be decomposed into an epimorphism and monomorphism. with some intermediate object $C$. e.g. Grp has this property.  Is there a name for this so I can look it up?
The category Set has the property that any morphism f can be decomposed into an epimorphism $e$ and a monomorphism $m$ with $f$ = $m\circ e$. (The intermediary set object is the image of $f$.)  Is there a name for this construction?  Is there a name for this property of categories?  In Set, the intermediary object is unique up to isomorphism. Is this the case for all categories with the property?
From what I understand, the  states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on equipment but just a natural phenomenon.  However, isn't this just an observational limit? There is a definite velocity and momentum, we just don't know it. As in, we can only know so much about the universe, but the universe still has definite characteristics.  Considering this, how do a wide range of quantum mechanical phenomena work? For example, quantum tunneling - its based on the fact that the position of the object is indefinite. But the position is definite, we just don't know it definitely. Or the famous light slot experiment? The creation of more light slots due to uncertainty of the photon's positions?  What I am basically asking is why is a limit on the observer, affecting the phenomenon he is observing? Isn't that equivalent to saying  because we haven't seen Star X, it doesn't exist? It's limiting the definition of the universe to the limits of our observation! I have been playing with the settings for the text object recently, and every time I add a new text object, I need to change the font to my favorite one. (Eurostile LT ExtendedTwo) Is there any way to change the default font so I do not need to change it every time I add a new text object?   Example: How do I determine whether or not two lines intersect, and if they do, at what x,y point? Physical meaning of this integral in $k$-space I am trying to solve an integral in $k$-space where I want to calculate the ratio of the average energy of an arbitrary electronic band ($E(k)=k^n)$ to the square of average group velocity of electrons($v_g   = k^{n-1})$ approximately in the form of this expression given by $$L=\frac{\frac{\sum_{\mathbf{k}}k^{n}}{\sum_{\mathbf{k}}1}}{\left(\frac{\sum_{\mathbf{k}}k^{n-1}}{\sum_{\mathbf{k}}1}\right)^2}\;.$$  Now, I want to do this for $d$-dimensions, so I convert this sum to integral.  $$L=\frac{\dfrac{\int_{0}^{k_f}k^{n} d^d k}{\int_{0}^{k_f}1d^d k}}{\left(\dfrac{\int_{0}^{k_f}k^{n-1}d^d k}{\int_{0}^{k_f}1d^d k}\right)^2}$$ where $d^dk  = \dfrac{d \pi^{d/2}}{\Gamma(\frac{d}{2}+1)}k^{d-1}dk$ is the volume element in $d$-dimensional space.  I want to get a simple expression for $L$ and how it depends with $k_f,n$ and $d$. any physical insight into this integral could also be helpful. Can I, as a reviewer, tell authors to get a native English speaker to proofread their paper? I am reviewing a paper for possible publication in a respected journal. The English in the paper is very poor. The authors are clearly not native English speakers. I want to write something to the effect of the following in my review.   I advise the authors to find a native English speaker to proofread the manuscript.    My question: Is this appropriate in a review?  On one hand, I think it is good, constructive advice. The paper would be significantly clearer if someone spent a few hours helping them fix it up. I can try to help them through reviewer comments, but it would be much easier if someone could help them in person. The authors are located in a western English-speaking country, so they should be able to find someone.  On the other hand, I don't want to be "the mean reviewer." I understand that English can be difficult to master for immigrants. Perhaps there is a more diplomatic way of saying this. Temporal Table that doesn't use system time We want to implement temporal tables in SQL Server 2016. We are creating a Datawarehouse and developing Type 2 Slowly changing Dimension Tables.  For the BeginDate, we want it to be dependent on transaction date and not the current getdate time. We are reprocessing a history of transactions. Example below, customer has gym or bank status, and goes from inactive, to active, or pending, dependent on transaction date.  We currently have this.  CREATE TABLE dbo.Department (     CustomerId int primary key,     MembershipStatus int,     TransactionDate datetime  );   We we would like to create a table like this.  CREATE TABLE dbo.DepartmentHistory (     CustomerId int primary key,     MembershipStatus int,     TransactionDate datetime,     BeginDatetime datetime,     EndDatettime datetime  );   Example usage would be:   first Customer Transaction on 3/5/2018 as Pending P        +------------+--------+-----------+---------+     | CustomerId | Status | BeginDate | EndDate |     +------------+--------+-----------+---------+     | 1          | P      | 3/5/2018  | NULL    |     +------------+--------+-----------+---------+    second transaction is 4/21/2018 is Active A        +------------+--------+-----------+-----------+     | CustomerId | Status | BeginDate | EndDate   |     +------------+--------+-----------+-----------+     | 1          | P      | 3/5/2018  | 4/21/2018 |     | 1          | A      | 4/21/2018 | NULL      |     +------------+--------+-----------+-----------+ If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative. Let $R$ be a ring, where $a^{3} = a$ for all $a\in R$. Prove that $R$ must be a commutative ring. Looking for a book series about a girl and her friends captured and sold as slaves I'm trying to find the name of a book series I read about 10 years ago. It might be a children/young-adult series since I was fairly young. There is also a small chance it was written by a french author, as I read it in french. The series is composed of at least three books, maybe more. Here is what I remember :   The main character is a poor girl/young woman, but there are several point of view characters At the beginning of the first book the plot is set in a city where rich people live in the city center and the further you go from the center the poorest people are. Moreover, the houses are painted according to the wealth of the owner. It was something like : the richer had red houses, the poorer blue houses, and the moderately wealthy purple (it was not those colors in particular but it was something like that) At the end of one of the book there is some kind of uprising and the people paint all the houses in multiple colorful shades (to symbolize the new found equality between the citizen) At some point the main character and other peoples of the city get captured (maybe after some kind of war the city was involved in), separated and sold to slavery One of them, an older boy, become a soldier and learn a special fighting technique that looks like dancing (and he grows to like it) Another of the captives, a young girl (the sister of the main character if I recall correctly) get marked with a fire-heated mark to show her condition of slave   That is all I remember, I have no clue about the time or geographic setting nor the story details.  I know it's not much to go by, any help would be greatly appreciated, as I would like to find these books and read them again. When I boot in GRUB2 and press c, I have access to GRUB shell.  How to change the keyboard layout (language) of this GRUB shell?  Note that I'm booting an Ubuntu VM inside Virtualbox. How do I recover my Google account (or Gmail) password or username? I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons.  How can I recover my account?  (This Q&amp;A is meant as a general description for all Google and Gmail username/password questions. See: ) Why did they make another prequel? Star Trek: Discovery, the first new Star Trek television series in 12 years, debuted last week.  As with a number of recent Star Trek efforts, this is a prequel to the Original Series, occurring roughly one decade prior chronologically.    The Original Series, the Next Generation, Deep Space Nine, and Voyager occur in a chronological sequence that, generally speaking, moves forward (although TNG, DS9, and Voyager overlap to various degrees).  The linear trajectory of Star Trek productions took a sudden shift with the television series Enterprise, which was set just over 100 years before TOS. This was followed by J.J. Abrams' 2009 film Star Trek, which created a new timeline and which followed the characters from TOS, but at a time that is also chronologically one decade before TOS.  Given that the last few interpretations of Star Trek were prequels in one sense or another, I was disappointed that Discovery was yet another prequel.  I'd like to know why the showrunners decided to take this direction.  I haven't been able to find any statements about the rationale.    That being said, I find it interesting that Star Trek (2009) was set in 2255-2258 and Discovery is currently set in 2256, even though they are ostensibly in different timelines &mdash; the former in the reboot timeline and the latter supposedly in the original timeline.  Also, one of the showrunners for Discovery, Alex Kurtzman, was one of the principal members of the creative team behind the Abrams films.  Why did the creative staff behind Discovery decide to make another prequel?  Does it have anything to do with the fact that Star Trek (2009) and Discovery are set in roughly the same years? What is a NullPointerException, and how do I fix it? intuition on the fundamental group of $S^1$ I am familiar with the proof that the fundamental group of the unit circle $S^1$ is $\mathbb Z$, yet I couldn't develop intuition for why it is true. For example, why would I fail if I try to find homotopy from a path that circles $S^1$ once to the path that stays at one point all the time? What brakes the continuity of such a homotopy? 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 I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.  Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the same? The charges obviously lose energy in the lamp and so become SLOWER, which should mean current decreases, right?  [Edit] All answers explained a bit of everything, so it was hard to choose one. If YOU are looking for an answer, please check the others too, in case the accepted one doesn't answer your question. Finding the Dimension of a Matrix Polynomial: $W$ = { $p(B)$ : $p$ is a polynomial with real coefficients} Let $W = \{ p(B) : p \text{ is a polynomial with real coefficients}\}$, where $$B= \begin{pmatrix} 0 &amp; 1 &amp; 0\\  0 &amp; 0 &amp; 1\\  1 &amp; 0 &amp; 0 \end{pmatrix}$$  Which of the following possibilities presents the tightest bounds on the dimension $d$ of the vector space $W$?     $4 ≤ d ≤ 6$    $6 ≤ d ≤ 9$    $3 ≤ d ≤ 8$    $3 ≤ d ≤ 4$ I'm trying to install  on my Ubuntu box (11.04). The website has a Ubuntu .deb available for download (for 10.10 and 10.04 so I chose 10.10).   However,   sudo dpkg -i mysql-workbench-gpl-5.2.34-1ubu1010-amd64.deb   yields:  (Reading database ... 194069 files and directories currently installed.) Preparing to replace mysql-workbench-gpl 5.2.34-1ubu1010 (using mysql-workbench-gpl-5.2.34-1ubu1010-amd64.deb) ... Unpacking replacement mysql-workbench-gpl ... dpkg: dependency problems prevent configuration of mysql-workbench-gpl:  mysql-workbench-gpl depends on libctemplate0; however:   Package libctemplate0 is not installed.  mysql-workbench-gpl depends on libpython2.6 (&gt;= 2.6); however:   Package libpython2.6 is not installed.  mysql-workbench-gpl depends on libzip1 (&gt;= 0.8); however:   Package libzip1 is not installed.  mysql-workbench-gpl depends on python-paramiko; however:   Package python-paramiko is not installed.  mysql-workbench-gpl depends on python-pysqlite2; however:   Package python-pysqlite2 is not installed. dpkg: error processing mysql-workbench-gpl (--install):  dependency problems - leaving unconfigured Processing triggers for bamfdaemon ... Rebuilding /usr/share/applications/bamf.index... Processing triggers for desktop-file-utils ... Processing triggers for python-gmenu ... Rebuilding /usr/share/applications/desktop.en_US.utf8.cache... Processing triggers for python-support ... Errors were encountered while processing:  mysql-workbench-gpl   My question is, is there a way to tell dpkg to automatically fetch missing dependencies, or do I need to manually apt-get install missing packages like libctemplate0 and  libpython2.6?   (Or alternatively, is there some other way to get MySQL Workbench easily up &amp; running?) How do I set Windows to boot as the default in the boot loader? Can we simply rename an app if they are different versions and keep them both? For example, I have Xcode 4.4.1, and now Xcode 4.5 Golden Master (GM) version is available, but it is also called Xcode (when the .dmg is mounted as an disc image, it shows only one app (or folder), called Xcode)  I think the way is just to double click on the .dmg file, and then drag and drop that app into our Applications folder.  But since the current Xcode and Xcode 4.5GM have the same name, can the new one just be renamed and so we can have both versions on our machine?  I was worried that what if the app writes back data to the /Applications/Xcode folder, then the GM version can write unexpected data for the 4.4.1 version.  And will it work with other software, such as Xcode 3.2, Xcode 3.3, or even different versions of Microsoft Office and Adobe Photoshop? How do I check if an integer is even or odd? How can I check if a given number is even or odd in C?