I have two align environments which do not quite lead to a good looking result, and I don't know why. To the best of my knowledge, I did not alter anything about the alignment, and the problem also occurs when I copy the equations in a completely empty document.   How can I achieve a the "right", aesthetically pleasing typesetting of those equation?  Right Align  I do not understand why the rightmost term is aligned to the right. And I also think that the position of the = is wrong.  \begin{align} A \qquad &amp;\longrightarrow \qquad B &amp;= C \\ AA \qquad &amp;\longrightarrow \qquad BB &amp;= ABCDE  \end{align}     Huge Space  I'm not sure why it introduces such a huge space before the rightmost term.   \begin{align} A &amp;=  \begin{bmatrix} b \end{bmatrix} &amp;=  \begin{bmatrix} C + D \end{bmatrix} \end{align}
I asked this question at stackoverflow and have been kindly redirected here.  I'd like to align some equations in Latex using the AMS packages. Each equation has two equal signs that need to be aligned. So something in the line of  A = B = C D = E = F   I've tried using the align-environment like this  \begin{align} A &amp;= B &amp;= C \\ D &amp;= E &amp;= F \end{align}   This works in principle (it aligns), however it adds ridiculously large spaces before the second equal sign in each line. But I just want the line to runs as if there was no additional alignment tab. Only when I replace for example "B" by "BBB" I want the equal sign before "F" to shift to right the exact amount of space.  Could anyone help me out on that one? It's kind of driving me crazy since I don't get the idea of that strange behavior and I just can't find any solution. Maybe alignat could help, but I don't really get how that environment works.  Cheers, Oliver
What are the existing datasets of world maritime routes? Update Windows 10 to 1809 manually How to resize partitions? Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions? How to remove link for an application in new Google Launcher? Why would the First Order have lightsaber-resistant batons? In The Force Awakens there is a new Stormtroopr who is equipped with a lightsaber-resistant baton.    Except for one thing:   In Revenge of the Sith, most of the Jedi are killed. During the original Star Wars trilogy the last few remaining Jedi — except for Luke Skywalker — die.     And before The Force Awakens Kylo Ren kills off everyone at Luke’s school and drives Luke into exile.    There are practically no lightsabers in existence, so why are these weapons deployed at all if their only use is in counter-lightsaber combat? Is it possible to bake dupliverts into one mesh for the BGE? (I have a large ground landscape that I use as the parent to duplicate trees, and the BGE doesn't support most modifiers.) What causes "java.lang.IllegalStateException: Neither BindingResult nor plain target object for bean name 'command' available as request attribute"? I have a question about calculating the degree of a finite field extension over $\mathbb{Q}$.  This is problem 18 in chapter 1 of Patrick Morandi's Field and Galois Theory. The problem asked to show that $$ \left[ \mathbb{Q}{ \left( \sqrt[4]{2},\sqrt{3} \right):\mathbb{Q} }\right] =8 $$ Here's my work : First, we have $$  \left[ \mathbb{Q} ( \sqrt[4]{2},\sqrt{3}):\mathbb{Q}\right] = \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] . \left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right]$$ It's easy to show that $\left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right] =4 $ because the minimal polynomial of $\sqrt[4]{2}$ over $\mathbb{Q}$ is $x^4 -2$. Next, I'm going to show that  $$ \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] =2$$ Consider the polynomial $f(x) = x^2 -3$. It's monic and $\sqrt{3}$ is a root of $f$, but I'm stuck in proving $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ (hence $f$ is irreducible over $\mathbb{Q}(\sqrt[4]{2}))$.  My question is: Is there any proof to show that $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ or another way to caculate the degree of this field extension?  Thank you for your help. How to sum a variable by group Does C# have an equivalent to JavaScript's encodeURIComponent()? In JavaScript:  encodeURIComponent("©√") == "%C2%A9%E2%88%9A"   Is there an equivalent for C# applications? For escaping HTML characters I used:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"&amp;#" + ((int)m.Value[0]).ToString() + ";");   But I'm not sure how to convert the match to the correct hexadecimal format that JS uses. For example this code:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"%" + String.Format("{0:x}", ((int)m.Value[0])));   Returns "%a9%221a" for "©√" instead of "%C2%A9%E2%88%9A". It looks like I need to split the string up into bytes or something.  Edit: This is for a windows app, the only items available in System.Web are: AspNetHostingPermission, AspNetHostingPermissionAttribute, and AspNetHostingPermissionLevel. Has a free neutron ever been shown to absorb/emit/interact with a photon? Protons only 'interact with' very high-energy photons, whether inside a nucleus or free, right?  I'm assuming the same about neutrons....  Neutrons have a small magnetic moment and a slight electric 'moment' (dipole?), correct?  They are sometimes considered to consist of a negative charge surrounding a positive charge?  I would assume that neutrons, in a nucleus or free, interact with photons even less often than protons, and that the gamma photon has to have an even higher energy than one interacting with a proton....  Lastly, I have read about 'photodisintegration', in which a nucleon is kicked out of a nucleus by a gamma ray.  It seems to happen to neutrons sometimes...  But, I am mostly curious about experimental evidence of free neutrons interacting with photons, how often it happens compared to free protons, and whether the interacting photon's energy has to be extremely high, higher even than a photon interacting with a proton... As far as I know, only a player character's non-temporary ability scores are considered for taking feats, taking prestige classes, etc. Meanwhile, any ability bonus that comes from spells, or magic items that are in effect only while worn, is not counted (except tomes which increase abilities permanently).  So a Fighter with low Int who wants to qualify for Combat Expertise can't use spells or items that gives an Int bonus to raise it high enough to qualify. Is that right?  For example:  Say our fighter has Str 12, so he can not take the Power Attack feat. Suppose he asks for a spell from the wizard to make his Str 16, or to borrow a ring which provides +4 Str from another character. (Or any other method that will provide him a non-permanent bonus). His Str is now 16. Can he take Power Attack with that non-permanent bonus now? Because after the spell duration ends or he takes off the ring, his Str score will be to low again to qualify for Power Attack. After using the simple LM317 on breadboard variable power supply for a while, a need for a more rugged and reliable bench power supply has arose.    Short on money, i decided to build it as many other amateurs like me did. The thing is that, for my current needs i don't need a giant digitally controlled multi-channel 500 watt beast or something like that.  Instead what i really want is a low wattage positive and negative low voltage ouput -12v-0v-12v for example. However i really like that my power supply to be safe, reliable and fool-proof as far as possible. So after searching the web here and there, i found many designs that from my point of view fell in one of two divisions:-   Ones that use discrete op-amps and transistors. And ones that use integrated voltage regulators.   So -at least for me- i think that the ones with discrete op-amps and transistors are more prone to malfunctions and issues compared to the integrated ones with all of their internal over current and thermal protection circuits which would need to be discretely implemented in the bench power supplies that utilize discrete op-amps, however those designs have the advantage of ease of customization and more importantly that it is easier to have 0V output compared to 1.2V in integrated voltage regulator ones.    So i like advice to help me choose between circuits that utilize discrete op-amps like this circuit for example:-  Or ones that use integrated voltage regulators with their intrinsic robustness and low form factor.    Also as a side but related question i have seen many designs on the web that utilize negative voltage fed to the adjust or like pins to achieve 0V output from integrated voltage regulators like this single positive power supply:-     Or a positive and negative channels power supply that i really like its design because of simplicity (not because of laziness but to avoid the drawbacks that may come with complex designs especially when implemented by an amateur like me):- And the question is      Is it wrong or a system safety and reliability lowering act to feed negative voltage to adjust pin for LM317 for example?     I ask this question because the datasheet clearly states that the working output range is 1.2V-37V for LM317 for example, also no similar circuit is mentioned in the Typical Applications section except for the following one:- And even in that circuit, however the adjust pin is tied to the negative rail, it does't regulate during this interval instead it is shut until the next half wave at least that what i understand.    So at last to sum it up which alternative is best suited for my needs, its pros and cons and suggested circuits if possible. NVMe PCIe x4 SSD on M.2 PCIe x2 slot? i'm about to get a new SSD for my PC, and before spending the money i have some doubts about my decision i would like to clarify First, my mobo is a B450 Aorus Pro Wifi, it has 2 M.2 slots, one of them full length (22110) compatible with PCIe 3.0 x4 and the other one standard length (2280) and support only for PCIe 3.0 x2 About the drive, i'm aiming for a 1tb XPG SX8200 Pro , which is a PCIe 3.0x4 SSD My first M.2 slot is already taken by the main SSD, which i use for the OS and other stuff, i can't really use it. Will a PCIe x4 SSD work on a PCIe x2 slot? How much performance will be lost if it does? Will it be worth it? How can I find a mentor to critique my work? Not enough space on /tmp I'm not able to run update manager as I get an error saying that there is not enough free space in the /tmp directory. I've practically cleaned out the tmp directory but the error persists.  here's df-h  /dev/loop0       13G   11G  952M  92% / udev            2.0G  4.0K  2.0G   1% /dev tmpfs           785M  920K  784M   1% /run none            5.0M     0  5.0M   0% /run/lock none            2.0G  584K  2.0G   1% /run/shm /dev/sda6        20G   14G  6.4G  68% /host  overflow        1.0M   16K 1008K   2% /tmp Create terrazzo material/pattern with the standard textures is it possible to create this kind of material with the standard textures? The Voronoi texture (set to cells) is coming close but I don’t know if it is possible to a) set the single cells apart from each other and b) to give them seperate colors. Windows 10 100% Disk Usage after Startup After startup for 5 minutes my system is very slow. The Task Manager shows that the disk usage is at 100%. (Later this number is around 2-4 %, but sometimes for 1-2 minutes go up again at 100%.)  I searched a lot on Google. For example I read , and also other pages. I opened two topic on Microsoft answer.  and one in Hungarian.  But I didn't found the solution yet. So I would like to ask Community's help. :)  Here the steps I already done:   I disabled everything at startups (including services) and the issue is the same.  I disabled Prefetch and Superfetch, the Baground Intellingent Transmission, Windows Search and Windows Defender but the issue is still persists. I made a health check on HDD, I made defrag and file system error check, but there are no errors. Also I tried to reinstall the HDD's driver. I made a full hardware check up, with no errors. The Windows and all the drivers are up-to-date. I tried a clean start. The issue is the same. I deleted Dropbox and all antivirus. I turned of the MSI mode.      I using also Linux, where this error is not occurs. Good to know, that Windows had 4 partitions, but I deleted 2 of them for the Linux. I don't know what partitions was these but both was only 10 - 20 MB.  I using a Dell Inspiron 15R SE 7520 with Windows 10 Home.  Personally I think it can be the Intel Rapid Store Technology "driver", because the problem started around when I installed it. (However I'm not sure.) And my hardware not supported yet by Intel, so I have no the newest driver. However I deleted Intel's software and driver and the issue is the same.    Thank you in advance for your assistance! Find asymptotic of recurrence sequence Given a sequence $x_1=\frac{1}{2}$, $x_{n+1}=x_n-x_n^2$. It's easy to see that it limits to $0$.  The question is: is there exists an $\alpha$ such, that $\lim\limits_{n\to\infty}n^\alpha x_n\neq0$.  I tried to find explicit formula for $x_n$, but did not succeed. I stucked at that point: if $a_1=(\frac{1}{4})^2$, $a_n=(a_{n-1}+\frac{1}{4})^2$, then $x_n=-a_{n-2}+\frac{1}{4}$ for $n\ge3$.   Thanks for any ideas and help. I'm writing a contribution for a double-blind submission system.   Since I would like to supply more data than I could show on a small number of pages, I'm looking for a way to reference supplemental data in my manuscript, such as software scripts, figures or databases.  I could upload on GitHub, RPubs, Figshare and Zenodo, but all of these would expose my real user name (and I don't feel like making a throwaway e-mail account with a new repository for every anonymous publication that I intend to write).  Is there any way to get the above services to do what I want? Or is there a similar service that would allow anonymous hosting of research data?   It would be even better if I could later (e.g. after publication) declassify the information, with the link from the manuscript still being intact.