Some magical items, such as spell scrolls, work only if a given spell is on the caster's spell list. For example, the description of a  states:  A spell scroll bears the words of a single spell, written in a mystical cipher. If the spell is on your class’s spell list, you can read the scroll and cast its spell without providing any material components. Otherwise, the scroll is unintelligible. [...]  The 's  feature and the 's  feature (TCoE, p. 67-68) grant access to additional spells not on the general sorcerer spell list:  You learn additional spells when you reach certain levels in this class, as shown on the [Psionic/Clockwork] Spells table. Each of these spells counts as a sorcerer spell for you, but it doesn't count against the number of sorcerer spells you know.  Additionally, it is possible to swap these spells at level up:  Whenever you gain a sorcerer level, you can replace one spell you gained from this feature with another spell of the same level. The new spell must be [a divination or an enchantment spell/an abjuration or a transmutation spell] from the sorcerer, warlock, or wizard spell list.  Do the additional spells from the Psionic/Clockwork spell tables count as being on the Aberrant Mind or Clockwork Soul sorcerer's spell list? What about the spells that can be learned by swapping the Psionic/Clockwork Spells out?

I've been trying to resolve some edge cases with who can use which spell scrolls. As the DMG says in the Spell Scroll entry on page 200:  "If the spell is on your class's spell list, you can use an action to read the scroll and cast its spell without having to provide any of the spell's components. Otherwise, the scroll is unintelligible."  The issue here is the meaning of "class's spell list". It seems straightforward; surely a class's spell list is simply what is listed in the back of the PHB, from pages 207 to 211? But of course it isn't quite that simple, as clerics, druids and warlocks each get additional spells that aren't specified in these lists through domains, circles and patrons respectively. These class features seem to expand their personal spell lists directly. As an example, both Light domain clerics and Fiend patron warlocks can get the fireball spell, which isn't on the spell list of either class. On page 109 of the PHB the warlock's Fiend patron Expanded Spell List literally says:  "The following spells are added to the warlock spell list for you."  Which shows that Fiend patron warlocks have fireball in their spell lists, and so should be able to use spell scrolls of fireball. For clerics (and druids, which have almost identical phrasing), the Domain Spells class feature on PHB page 58 says:  "Each domain has a list of spells - its domain spells - that you gain at the cleric levels noted in the domain description. Once you gain a domain spell, you always have it prepared, and it doesn't count against the number of spells you can prepare each day. If you have a domain spell that doesn't appear on the cleric spell list, the spell is nonetheless a cleric spell for you."  So for a Light domain cleric, fireball is a cleric spell. These spells don't say that they're added to the cleric spell list, but they are cleric spells. So the question becomes: Are cleric spells another name for spells which are on the cleric spell list? To potentially shed some light on this, on PHB page 52 the cleric's Spellcasting feature says:  "You prepare the list of cleric spells that are available for you to cast, choosing from the cleric spell list. When you do so, choose a number of cleric spells equal to your Wisdom modifier + your cleric level (minimum of one spell). The spells must be of a level for which you have spell slots."  Which shows that clerics get cleric spells from the cleric spell list, so all spells on the cleric spell list must be cleric spells. But does that make all cleric spells part of your cleric spell list? Which leads us to: Can clerics use spell scrolls for spells they receive through their Divine domains? And would this mean a Light domain cleric could use a spell scroll of fireball?


Prof. Gilbert Strang mentions, in , that a matrix $A$ has orthogonal eigenvectors when $A^T A=AA^T$; i.e., when it is normal. Could someone provide me a (preferably intuitive) proof of this?

The problem statement is as follows:     Prove that for a normal matrix $A$, eigenvectors corresponding to different eigenvalues are necessarily orthogonal.   I can certainly prove that this is the case, using the spectral theorem.  The gist of my proof is presented below.  If possible, I would like to find a simpler proof.  I was hoping that there might be some sort of manipulation , noting that $$ \langle Av_1,A v_2\rangle  = \langle v_1,A^*Av_2\rangle  = \langle v_1,AA^*v_2\rangle  = \langle A^* v_1,A^* v_2 \rangle $$  Any ideas here would be appreciated.    My proof:  Let $\{v_{\lambda,i}\}$ be an orthonormal basis of eigenvectors (as guaranteed by the spectral theorem) such that $$ A v_{\lambda,i} = \lambda v_{\lambda,i} $$ Let $v_1,\lambda_1$ and $v_2,\lambda_2$ be eigenpairs with $\lambda_1 \neq \lambda_2$.  We may write $ v_1 = \sum_{i,\lambda}a_{i,\lambda}v_{i,\lambda} .$ We then have $$ 0 = Av_1 - \lambda_1 v_1 = \sum_{i,\lambda}(\lambda - \lambda_1)a_{i,\lambda}v_{i,\lambda} $$ So that $a_{i,\lambda} = 0$ when $\lambda \neq \lambda_1$.  Similarly, we may write $v_2 = \sum_{i,\lambda}b_{i,\lambda}v_{i,\lambda}$, and note that $b_{i,\lambda} = 0$ when $\lambda \neq \lambda_2$.  From there, we have $$ \langle v_1,v_2 \rangle = \sum_{i,\lambda}a_{i,\lambda}b_{i,\lambda} $$ the above must be zero since for each pair $i,\lambda$, either $a_{i,\lambda}=0$ or $b_{i,\lambda} = 0$.


This is Exercise EP $8$ from Fernandez and Bernardes's book Introdução às Funções de uma Variável Complexa (in Portuguese).     If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for   some $t\gt 0.$   I supposed that $|z+w|=|z|+|w|$ and by squaring it I got  $\operatorname{Re}(z\bar{w})=|z||w|$ and I am stuck.  I would appreciate a hint in this question.


How can we calculate the number of ways in which a $p$-sided polygon can be made inside a $n$-sided polygon such that no side of the $p$-sided polygon is in common with the $n$-sided polygon?

If hexagons are formed by joining the vertices of a 20 sided convex polygon such that no side of  hexagon is common with side of the polygon, then how many possible ways are there?   I have no idea where to start. I actually have difficulties when I deal with geometric applications of permutations and combinations.   My approach: Choose 1 point (20 ways), then leave two adjacent points and choose 1 out of the remaining 17 (17 ways) and so on. But I think I can't use the multiplication principle without double counting and even if I double count, I can't find the method to remove those cases. Would someone please help me to solve this question?


Why does resisting force depend on velocity? I think there is no relation between resisting force and velocity of object. Please speak about it logically.

A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the  (air resistance) which is proportional to the object's speed. By Newton´s laws this can be written as:   $mg-kv=ma$ (for low speeds)  $mg-kv^2=ma$ (for high speeds).    I assume that $k$ is a positive constant that depends on the geometry of the object and the viscosity. But how can one explain that the air resistance is proportional to the velocity? And to the velocity squared in the second equation?


How can I find all the nodes that are no longer in a menu? I've created a view that manage those nodes. Nodes can be find on a search but they are no longer in the main menu.

In the course of creating the content for a site, we've ended up with orphaned content nodes that are not linked to from anywhere. I'd like to find and examine these. Surprisingly, I can't find a module for this.  Tiny hypothetical example: I'm building a brochureware site. Someone wrote a "Contact" page, someone else wrote an "About Us", and someone else wrote "Directions". The person writing "Directions" forgot to put it in a menu link or add a link from "About Us" to "Directions". So "Directions" is orphaned: there are no links to it. I'd like to find all such nodes so I can figure out what to do with them.


I want to add nonlinear character into multi-class logistic regression. I know kernel logistic regression can do it. Is there any kind of neural network which has similar characteristic?

Suppose my training data contains ~100 variables, and each example is tagged as "success" or "failure".  I understand how a neural network can be used to try and predict success vs failure based on the variables.  However I am interested in the neural network outputting the posterior probability rather than success or failure. In fact, I evaluate the efficacy of the NN based on how accurate the probabilities are (eg. AUROC over the entire dataset) rather than % of cases with correct prediction.  Are NN's the right tool for the job here and if so how do you structure the NN to output this?  (NOTE: I'm a ML newbie!)


It's well known that if $X$ is a Banach space, then $X^{**}$ contains a copy of $X$, so we'll informally say $X\subset X^{**}$. It's also well known that in general we don't have $X=X^{**}$. So what if, starting with a Banach space $X$ such that $X\subset X^{**}$ but $X\neq X^{**}$, you considered the sequence $$X\subset X^{**}\subset X^{****}\subset X^{******}\subset\cdots$$ Not sure why this sequence would be of any interest but...is it possible that the inclusions are all strict in this infinite chain?  EDIT: Some are (justifiably) suggesting that this question is a "duplicate" of the question of whether or not $X$ is reflexive iff $X^*$ is reflexive. While, in some sense, one could make that claim based on how the answer to my question almost immediately follows from the truth of that statement, I wouldn't go so far as to claim it's a duplicate question.

How to show that a Banach space $X$ is reflexive if and only if its dual $X'$ is reflexive?


When starring messages at the side, the actual message does not star:   We can see that the message by jadarnel27 is starred at the side but not the actual message itself. (Don't suspend GnomeSlice, its a joke)

If you click to star a post on the side (in the starred list), it changes color but not the star by the main chat area (it does add one to the number, but it doesn't change the color). Then when you click the star on the main chat area, it changes color to yellow but lowers the number by one  After clicking in sidebar:     After clicking in the main chat:


I am using Ubuntu 14.04.5 LTS & I am not always connected to the internet for downloading software-packages. Suppose, for instance, I downloaded packages like VLC, Banshee etc, using synaptic package manager, and after a month or so I have to format the system.   So here are my queries :-    How to backup these 2 softwares EARLIER so I won't have to go through the pain of downloading them again? Does synaptic uses dpkg or apt-get by default? If it uses dpkg, how to change it to apt-get? Is it recommend to change it to apt-get or dpkg is good? Is there a way to ensure that after fresh installation of the Ubuntu, Synaptic only downloads the Repositories and not the Updates?   EDIT :- I KNOW THAT .deb files downloaded by Synaptic are kept at  /var/cache/apt/archives/   But you can't just randomly put any deb files there and than sew it in synaptic for installation. I've tried it.  Eg. If I have a package and all its dependencies as .deb and to install them I keep them at /var/cache/apt/archives/ and then open synaptic. But you see that software won't be visible in synaptic for installation. (won't be in search list)  I want to install backed up packages from synaptic not with  sudo dpkg -i *.deb

Where can I find the location of downloaded .deb files?  I want to copy this folder before I reinstall Ubuntu so I don't have to redownload the packages.  I am running Ubuntu 12.10 32-bit.  How can I do this?


Time is called as a measurement of difference between two or more incidents. So if we stop happening incidents can't we stop the TIME? Eventhough it's impractical, I mean if we reduce the temperature of earth to absolute zero.... isn't it stop the motion of matter and stop the time? When we start increasing temperature again isn't the time starts from where we stopped?

Time has many definitions per se, but the basic idea being it's "the measurement of change" so as we know, all matter looses it's ability of changing with the loss of kinetic energy. and the where it becomes zero is the absolute zero (−273.15°C). so my question would be, will time stop/freeze at Absolute zero? and does time get slow while reaching there?


While browsing the mobile website on an iPod touch, I encountered the following problem while trying to flag a question as too broad.  The textfield for entering an answer to the question is obscuring the last few flagging options:    I did not have any problems with the initial flag screen. Only after I selected the "It should be closed for another reason.." option did the textview obscure my view.  This was while viewing the website on Safari. Still on iOS 6.

The "Your Answer" textbox seems to be eating the flagging dialog as shown in Figure A.


I was wondering why do we use integers to get addresses in memory while memory addresses can only be positive? Why don't we use unsigned integers?  For example:  in C#, why do we have IntPtr, why not UIntPtr?  Arrays also have a limitation of Int32.Max. Still, why not unsigned since index can only be >= 0?  Also, in C++, a lot of codes assign a pointer address to ints, and not uints, is there a reason behind it? Is it bad practice?   Thank you!

Why is Array.Length an int, and not a uint. This bothers me (just a bit) because a length value can never be negative.   This also forced me to use an int for a length-property on my own class, because when you  specify an int-value, this needs to be cast explicitly...  So the ultimate question is: is there any use for an unsigned int (uint)? Even Microsoft seems not to use them.


Apparently this question has been asked many times on here, but my question is more specific.  Let $X$ be the quotient space of $S^2$ under the identifications $x \sim -x$ for $x$ in the equator $S^1$. We are asked to compute the homology groups $H_i(X)$.  The method I chose is to use cellular homology. Give $X$ the following cell structure: one 0-cell $e^0$, one 1-cell $e^1$, and two 2-cells $e_1^2$ and $e_2^2$. The 2-cells are attached via the quotient projection of the boundary $x \sim -x$. In particular, the 0 and 1 skeletons are $\mathbb{R}P^0$ and $\mathbb{R}P^1$ respectively and the 2-cells are attached in the same way as in Hatcher's computation of the homology of $\mathbb{R}P^n$ using cellular homology.  The nontrivial part of cellular chain complex is  $0 \rightarrow \mathbb{Z}^2 \xrightarrow[]{d_2} \mathbb{Z} \xrightarrow[]{0} \mathbb{Z} \rightarrow 0$.     I don't understand why $d_2$ is not multiplication by $2$ here since they are attached in the same way as in Hatcher's Example 2.42. According to another answer $d_2(e_1^2)=2e^1$ and $d_2(e_2^2)=-2e^1$ "by the cellular boundary formula". I do not see why this is the case since $e_1^2$ and $e_2^2$ have the same attaching map.

Let $X$ be the quotient space of $S^2$ under the identifications $x\sim -x$ for $x$ in the equator $S^1$. Compute the homology groups $H_i(X)$.   I wrote my solution/attempt below and I would like to know if it it correct and, more importantly, if there is a simpler solution. I tried using cellular homology but I'm not very experienced with it and kept getting nonsense.   Here is my attempt:  $X$ can be written as the following pushout: $$\begin{align*}  \require{AMScd}  \begin{CD}   P^1 @>{i}>> P^2\\   @V{i}VV @VVV \\   P^2 @>>> X  \end{CD} \end{align*}$$ where $i:P^1\hookrightarrow P^2$ is the inclusion. So by a Mayer Vietoris argument, we have $H_i(X,P^2) \approx H_i(P^2, P^1)$. This can be simplified to $\tilde{H}_i(P^2/P^1) \approx \tilde{H}_i(S^2)$. Now we consider the LES of the pair $(X, P^2)$. $$0\to H_2(P^2)\to H_2(X)\to H_2(X, P^2)\to H_1(P^2)\to H_1(X) \to 0$$ We know all homology groups involved except those of $X$, so the LES reads: $$0\to \Bbb{Z}\to H_2(X) \to \Bbb{Z}\to \Bbb{Z}_2\to H_1(X)\to 0$$  The problem lies in identifying the map $\Bbb{Z}\to \Bbb{Z}_2$, call it $f$. The LES tells us that $H_1(X)\approx \Bbb{Z}_2/\text{im }f$. On the other hand, by the Van Kampen theorem for attaching 2-cells, $X$ can be viewed as $P^2$ with a 2-disk attached along the path $aa$, hence $\pi_1(X)\approx \Bbb{Z}_2$. This is abelian, so it coincides with $H_1(X)$. Then $f$ must be the $0$ map. Using that, from the LES we can also compute $H_2(X) \approx \ker f \oplus \Bbb{Z}\approx \Bbb{Z}^2$.


I am trying to read a string that contains multiple lines \n included, and it has the following pattern:  Total     : 30 ================ Loaded    : 27 Loading   : 0 Failed    : 3  Done.. time taken : 3.49  seconds. ============= 2020-03-08 15:39:26   The line containing the time taken can sometimes be represented in milliseconds, seconds, or minutes. So I need to capture the digits before the unit, the unit itself, and the digits represented by Failed.  I was able to extract the time duration plus the unit without any issues. Maybe because they both are on the same line.  let matches = /taken\D+([\d\.]+)\s+(\w+)/g.exec(trace); matches[1];  // 3.49 matches[2];  // seconds   But when I tried to extract the Failed digit, the regular expression does not work.  /Failed\s+:\s(\d+).*?taken\D+([\d\.]+)\s+(\w+)/g   /Failed\s+:\s(\d+).*?taken\D+([\d\.]+)\s+(\w+)/gm   /Failed\s+:\s(\d+)[.\n\r]*?taken\D+([\d\.]+)\s+(\w+)/g   None of that worked. I know I can do a workaround by removing all new line \n characters before performing the regular expression, but I want to know what mistake was done from my part?    let trace = "Total     : 30\n"           + "================\n"           + "Loaded    : 27\n"           + "Loading   : 0\n"           + "Failed    : 3\n"           + "\n"           + "Done.. time taken : 3.49  seconds.\n"           + "=============\n"           + "2020-03-08 15:39:26";  let pattern = /Failed\s+:\s+(\d+)[\n\r.]*?taken\D+([\d\.]+)\s+(\w+)/gm;  let matches = pattern.exec(trace);  let failedCount = matches[1];   // should be "3" let timeTaken   = matches[2];   // should be "3.49" let timeUnit    = matches[3];   // should be "seconds"

For example, this regex  (.*)<FooBar>   will match:  abcde<FooBar>   But how do I get it to match across multiple lines?  abcde fghij<FooBar>


If $\mu^*$ is an outer measure on $X$ and $\{A_j\}_{1}^{\infty}$ is a sequence of disjoint $\mu^*$-measurable sets, then $\mu^*\left(E\cap\left(\bigcup_{1}^{\infty}A_j\right)\right) = \sum_{1}^{\infty}\mu^*(E\cap A_j)$ for any $E\subset X$.   Attempted proof - From countable subadditivity, $$\mu^*\left(E\cap\left(\bigcup_{1}^{\infty}A_j\right)\right) = \mu^*\left(\bigcup_{1}^{\infty}E\cap A_j\right) \leq \sum_{1}^{\infty}\mu^*(E\cap A_j)$$ Let $B_n = \bigcup_{1}^{n}A_j$. For each $n\geq 2$ since $A_n$ is $\mu^*$-measurable we have \begin{align*} \mu^*(E\cap B_n) &= \mu^*((E\cap B_n)\cap A_n) + \mu^*((E\cap B_n)\cap A_n^c)\\ &= \mu^*(E \cap A_n) + \mu^*(E\cap B_{n-1})\\ \end{align*} (These 2 lines above me came from part of the proof in Carthedory's Theorem and I don't really understand it at all if someone would be so kind to explain that part to me.)  By induction, $\mu^*(E\cap B_n) = \sum_{1}^{n}\mu^*(E\cap A_j)$ for all $n\geq 1$. So then by monotonocity, $$\mu^*\left(E\cap\left(\bigcup_{1}^{\infty}A_j\right)\right) \geq \mu(E\cap B_n) = \sum_{1}^{n}\mu^*(E\cap A_j)$$ for all $n\geq 1$. Thus as $n\rightarrow \infty$ we have the result.

$\mu^*$ is an outer measure on $X$ and $\{A_j\}_{1}^\infty$ is a sequence of disjoint $\mu^*$-measurable sets. Prove that $\mu^*(E\cap(\bigcup_1^\infty A_j))=\sum_1^\infty \mu^*(E\cap A_j)$ for any $E\subset X$.   This is what I have shown so far:   $\mu^*(E \cap (\bigcup_1^\infty A_j))=\mu^*(\bigcup_1^\infty (E \cap A_j))\leq \sum_1^\infty \mu^*(E\cap A_j) ;$ since $\mu^*$ is an outer measure.   If I can show the reverse inequality I will win. Can anyone help me?


$x$, $y$ and $z$ are lengths of the sides of a triangle. Prove the following and determine when both LHS and RHS are not an inequality but EQUAL. $$\sqrt{x+y-z} + \sqrt{y+z-x} + \sqrt{z+x-y} \leqslant \sqrt{x}+\sqrt{y}+\sqrt{z}$$

I did substitute $a=x+y, b=x+z, c=y+z$ and I arrived at $\sqrt{2x} + \sqrt{2y} + \sqrt{2z} \le \sqrt{x+y} + \sqrt{x+z} + \sqrt{y+z}$. However, after this, I tried various methods like AM-GM and Cauchy-Schwarz inequality for hours and I still can't prove it. Can someone help please? Thanks.


I am new in salesforce development and I am new in test classes. Now I am trying to increase code coverage for vf page controller. Now it's showing 50% but I need more than 75% .. please any one help me for giving good suggestion for increasing the code.

This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How is code coverage obtained and calculated? How do I increase my coverage?  Why can't I cover these lines? Why isn't the body of my loop or conditional statement covered?


I have windows 10 installed on my pc. It was originally windows 8. I was wondering how to dual boot with Ubuntu. I want Ubuntu to be default but I still want to keep windows so I can play video games without paying for a VM. Is it as easy as hitting the Ubuntu download button and selecting an option for dual boot? Also, why do I need to download Ubuntu to a USB drive? I just want it installed on my computer and if I need to change back to windows for gaming then have that option at startup.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


Last night when I was researching on an issue I can to a post which one of the answers had a Avatar Icon with text Moderator inside it. I cannot find that post today.  Considering that person reputation was lower than 50, I wonder if he could be a real moderator.  Do we have a guideline which explicitly ban this?(That is A none moderator uses the moderator icon?   I think no web site needs fake moderators.  The suggested(Duplicate) link says impersonation is OK. I disagree. A moderator should not be impersonated by anyone as people rely on them more than others..

The discussion in  led me to think of a real question. What display names and avatars are off-limits on the Stack Exchange network?  I think I remember seeing a fake Jeff Atwood in the past on Meta, and a fake Jon Skeet on SO. If I recall correctly, the former had to change his name and the latter got banned.  Is a fake Barack Obama okay? What about Steve Jobs? James Gosling? What if a user's legal name is William Gates, but he's not "that" Bill Gates? Does the choice of avatar make a difference?  Tangentially related:


Is there a way to download an offline copy of the Stack Overflow questions? I am hoping I can view it offline.  Thanks guys. I have found the cc-wiki-dump for Stack Overflow.  But the post in the dump XML file looks like below. I don't know where the category tag is. For example, the category tag for this question is "support".    ADD 1 - 11:22 AM 11/9/2018  I made a StackExchangeArchiver, and it can archive questions/answers of a specific user into a pure HTML offline page, including the images. It's made in a haste. But it can work. It's open-sourced here:  I hope it can be helpful to other people.

I would like to create a local MySQL copy of Stack Overflow for academic purposes (school project). As far as I know, the database dump of the  database is available only in an XML format that I will have to convert to SQL on my own with some tool.  Most of direct download links I found were broken (404). The only non-torrent source that I have found and that is still alive is  but the latest Stack Overflow dump there is from October 2009, content of which looks like this:    Where could I find a direct download link with the Stack Overflow dump?    Note: I am not able to use torrents due to network policies, yet for the completeness of this question, here's the link that might help someone:    Other related questions / links that haven't helped me:     ~ all links there give 404  ~ from September '09 with another broken link  ~ from about a year ago with a clearbits.net link  ~ also not working anymore


I have tried to evaluate the series $\sum \limits_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$. I get that it converges to $\frac{1}{2}$ but there must be a flaw in my reason since then result I get does not match that of Wolfram's Alpha.   Let me show you my work.  One good way to begin with is to recall the known Fourier series   \begin{equation} \sum_{n=1}^{\infty} \frac{\cos nx}{n^s} =\frac{1}{2} \bigg({\rm Li}_s  \left ( e^{-ix} \right ) + {\rm Li}_s \left ( e^{ix} \right ) \bigg) \end{equation}  where ${\rm Li}_s$ is the polylogarithm of order $s$. Hence  \begin{equation} \sum_{n=2}^{\infty} \frac{\cos nx}{n^s} = - \cos x + \frac{1}{2} \bigg({\rm Li}_s  \left ( e^{-ix} \right ) + {\rm Li}_s \left ( e^{ix} \right ) \bigg) \end{equation}  We differentiate with respect to $s$ , hence  \begin{equation} \sum_{n=2}^{\infty} \frac{\cos nx}{n^s \log n} =  \frac{e^{ix}}{2} {\rm Li}_{s-1} \left ( e^{-ix} \right ) + \frac{e^{-ix}}{2} {\rm Li}_{s-1} \left ( e^{ix} \right ) \end{equation}  For $x=\pi$ and $s=1$ we have that $\displaystyle \sum_{n=2}^{\infty} \frac{(-1)^n}{n \log n} = \frac{1}{2}$.  Where have I gone wrong?

The series $\displaystyle \sum_{n=2}^{\infty} \frac{1}{n \log n}$ is known to diverge. This can be seen with comparison to the harmonic series.   The other series $\displaystyle \sum_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$ converges due to Liebniz's alternating criterion. I see these two series quite often in exams' questions to examine them if they converge or not. The answers are pretty straight forward.   Now , out of curiosity , could we find a closed form for the series  $$\mathcal{S}=\sum_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$$  The interesting fact is that if we define the function   $$f(s)=\sum_{n=2}^{\infty} \frac{(-1)^n}{n^s \log n} , \; s \geq 1$$  then taking the derivative with respect to $s$ we get that   $$f'(s)=-\sum_{n=2}^{\infty} \frac{(-1)^n}{n^s} = \zeta(s) - 2^{1-s} \zeta(s) - 1$$  I don't know how to go back and evaluate $f(1)$. Has anyone done that before. Expressing the value of the series in terms of special functions will suit me. Numerically it is approximately equal to $0.526412$. That said Wolfram. So, any clues?


But latex is very difficult to use without shortcuts. I also tried to use the solutions mentioned in the last post by someone about the same problem, but still it doesn't.

Even the simple ctrl+F is not working... I tried installing texmaker from software center and , but shortcuts still doesn't work...


I'm currently following Sebastien Konig's Match Track Blend DVD and have encountered a problem where despite matching camera type, lens type and trying to solve for distortion, I'm getting the following console messages when I try to Solve Camera Motion:  bpy.ops.clip.solve_camera() Some data failed to reconstruct (see console for details)   And I'm getting an average Solve Error of 0.9561, where I'm used to getting .4 and below. So what's going on?  The related files can be found .  This may be related to another question I've asked on the site -  I figured that the issues were different enough that I should give them different questions.  Many thanks to everyone who built and everyone who visits this site. StackExchange/Answers style-sites are very useful to me and I appreciate any time spent trying to answer the questions people ask here. (Thus ends that digression!)

I added tracks and stuff, but then when I tried to solve motion track, there was a error that said:     Some Data Failed to Reconstruct   and it also said to look into the console for details, which I did. This is what the console said:    By my understanding, my video is 372 frames long, and Blender is cutting the footage at 318 for some reason. Here is the image of the scene:    Why? Here are links to  and also . Also the next morning I did a camera solve, but then most of the frames went red.


I want to prove  the following proposition.  If every Sylow subgroup of a finite group $G$ is normal for every prime $p$, then $G$ is the direct product of its Sylow groups.  IDEA. I have the idea to use the following theorem. THEOREM If every Sylow subgroup of $G$ is a normal subgroup, then $G$ is isomorphic to the product of its Sylow subgroups.

I want to prove the following:     If every Sylow subgroup of $G$ is a normal subgroup, then $G$ is isomorphic to the product of its Sylow subgroups.   So far, I have gotten to realize that for every prime factor $p_i$ of $|G|$, there is exactly one Sylow subgroup and that these form a partition of $G$. However, I am having trouble finding the isomorphism between $G$ and the product which I will call $G_1 \times \ldots \times G_r$. My idea was just to use the mapping $(g_1, \ldots, g_r) \mapsto g_1\ldots g_r$, which is a bijection, but I don't see whether it is a homomorphism. In general, not all elements of $G_i$ commute with elements of $G_j$, so one cannot simply change the order of the elements in the product.


My Schengen visa to Italy was refused in 2013; I had a previous passport back then which I no longer use. I don’t remember if there was any document attached with the reason for refusal, except for a stamp showing date. I assume my visa was refused due to insufficient finances, since I was a student at that time.  I’m now applying for a UK visit visa with a new passport to celebrate new year with my friends. I would like to ask if I should mention about the previous visa rejection in the given section of application. If I mention it on a sincere note, how will it affect the chances of getting my visa to UK? This is my first attempt to secure a UK visit visa; I can’t afford to lose this chance!  Edit  Thank you for guiding me. As I said my passport was stamped and returned without mentioning any reason. How will they verify if I say it was refused due to lack of funds ?

My Canada visa was refused; I got a refusal letter but nothing was stamped in my passport. I got rejected under section 205(a) and 186 for not demonstrating specialized knowledge.   Do I have to mention the Canadian refusal in my UK work permit visa application? Will it affect my application (it is not an offense or criminal case)?


I recently upgraded my Ubuntu installation from 16.10 to 17.04. Since then, the notification bar has not displayed some of the icons that should be present when certain programs are running.    Both Skype and Slack are running, and previously displayed their respective icons in Ubuntu 16.04, which are missing after the upgrade to 17.04. (Due to the lack of the icons, this is a bit hard to illustrate. Note that both the Redshift as well as the Dropbox icon are still there, as well as the standard notification icons.)  Also, new notifications look strange (blue box) and have become non-clickable. The image shows an incoming Skype notification, which did not look like this before.  What has happened, and how can I revert to the previous (standard, I assume) behaviour?

After playing around with the i3 tiling window manager, I had my fill and decided to uninstall it and continue using gnome. However, to my dismay, something in i3 overrode the default gnome alert box. For example, when connecting to wifi, I get a gray or blue box instead of the nice ubuntu popups. The screenshot says it all. Any ideas?    (See top right corner)


The infinite tetration of ${x}$ basically means that we take a value and we continue to raise the value to its power forever. If that sounds confusing, it can be thought of as infinite repeated exponentiation of ${x}$. Now, my question is, will this value converge for any vale of ${x}$? In other words, is there a value that this will get infinitely close to when ${x}$ is a certain value?

I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework. The problem is stated as follows. Assume we have an infinite tetration as follows $$x^{x^{x^{.^{.^.}}}} \, = \, a$$ With a given $a$ find $x$. The next part of the problem was to discuss the convergence radius of a. If a is too big or too small the tetration does not converge. Below is my humble stab at the problem.  My friend said you would have to treat the tetration as a infinite series, and therefore could not perform algebraic manipulations on it before it is know whether it converges or diverges. However my attempt is to first do some algebraic steps, then discuss the convergence radius. I) Initial discussion At the start it is obvious that the tetration converges when $a=1$ (just set $x=1$) Now after some computer hardwork it seems that the tetration fails to converge when a is roughly larger than 3. II) Algebraic manipulation $$ x^{x^{x^{.^{.^.}}}} \, = \, a$$ This is the same as $$ x^a \, = \, a$$ $$ \log_a(x^a) \, = \, \log_a(a)$$ $$ \log_a(x) \, = \, \frac{1}{a}$$ $$ x \, = \, a^{\frac{1}{a}}$$ Now, if we let $a=2$ then $x = \sqrt{2}$. After some more computational work, this seems to be correct, which makes me believe this formula is correct. III) Discsussion about convergence By looking at the derivative of $ \displaystyle \large a^{\frac{1}{a}} $ we see that the maxima occurs when $a=e$, which also seems to correspond to the inital computational work. Now I think, that the minima of $\displaystyle \large a^{1/a}$ is zero by looking at its graph, studying its derivative and the endpoints. So that my "guess" or work shows that it converges when $$ a \in [0 \, , \,  1/e] $$ VI) My questions Can my algebraic manipulations be justified? They seem rather sketchy taking the a`th logarithm and so on . (Although they seem to "magically" give out the right answer) By looking at Wikipedia it seems that the tetration converge when $$ a \in \left[ 1/e \, , \, e \right] $$ This is almost what I have, why is my lower bound wrong? How can  I find the correct lower bound?


I have just learned that . But Harry broke it in the movie. Perhaps movie makers are jerks or they did that due to marketing reasons (it looks fantastic).  Now I am curious: How many times did the movies not follow the books? Please, list up.

I know that the movies were written to be a stand alone universe on their own, but what key elements were missing in the movies that were vital in the books that viewers are missing out on?


This Q has been asked times before on here, going by a search for the message, but all the answers have been immensely convoluted and impractical in my situation. I have installed Ubuntu on many other machines over many years and know my way around it. I'll give it a quick go anyway:  I've installed Linux 18.04 from USB on a HP Pavilion desktop literally straight out of the box. During the installation I wasn't prompted for wifi details, so clearly the installation didn't pick up the Wifi adaptor. Clicking on Settings / Wifi it says "No Wi-fi Adapter (sic) Found". The adaptor definitely works in Windoze 10 so clearly Ubuntu is lacking the driver.  Linux and hardware drivers is a problem going back to when I started using it in the Jurassic, but I'd thought it had been resolved in modern versions. Are there any quick fixes to this that don't involve abstruse and complex command lines, as suggested in other Qs on this topic? Also suggested is physical connection to the router which is not a physical option as one's upstairs and one's downstairs. I do have another machine, on which I'm writing this, on which I could download drivers.  Alternatively, is it worth me downloading 2 gigs of Ubuntu 19.10 and installing that?  The installation is not important - I just want a dual-boot desktop but can live with just Windoze, inferior and insecure as it is. I don't want to spend any significant time on a fix.  If there's no relatively simple fix, can anyone advise on how to remove the Ubuntu installation, and/or replace it with another distro?

Your situation   You have successfully installed Ubuntu.  You have just downloaded and booted Ubuntu live media.  The latest LTS (see also ) or latest non-LTS release are preferred. See the list of  that are currently supported.) You upgraded your Ubuntu installation to the latest release that the software updater offered you. WiFi worked before, but not now on the new release. You  to new hardware.   Your problem   The wireless of your laptop or desktop is not working. You tried switching the wireless switch off and on and you tried rebooting several times, but you don't see any WiFi access points. You can see your wireless access point, but you cannot establish a connection. You want to analyze the problem, but you don't know where to start or what information you can provide.   This question and answer was written to give people the wireless script that will provide the information needed in most cases to diagnose their wireless issue's.   Related questions


I'm just starting to learn python. For this I want to install the latest version on Ubuntu 18.04. I have accessed the page . Python 3.8.3 should be the current verison, right? I entered the following commands and expected phyton 3.8 to be installed on my computer. sudo apt-get update && sudo apt-get upgrade sudo apt-get install python3.8  Unfortunately, this is not the case. At least this request shows me a different version number. python3 Python 3.6.9 (default, Apr 18 2020, 01:56:04)  [GCC 8.4.0] on linux Type "help", "copyright", "credits" or "license" for more information. >>>  Maybe I'm not reading it right? What do the individual numbers mean and why can't I see 3.8 anywhere?

Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.?


$$\sum_{k=1}^nk\binom nk$$ I have to write this as $n2^{n-1}$, and nothing I tried has worked so far. How should I approach this? Thank you

I want to prove the following: $$\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$$ what I did is(use binominal): $$\binom{n}{k}X^k\cdot 1^{n-k} = (X+1)^n$$ $$k\binom{n}{k}X^k\cdot 1^{n-k} = k(X+1)^k-1$$ now I replace $k$ by $n$ and insert $X=1$ , I will get now $n\cdot2^{n-1}$ what you are suggesting? there is another way to do that? thanks!


I'm flying to Kuala Lumpur from Oslo with an 8-hour stopover in Istanbul on Turkish Airlines.   Do I need a visa if I want to leave the airport? I'm travelling on a Malaysian passport.  What would I be able to see or do in such a short time?

I have an Indian passport and am planning to visit Germany with a valid visa. To book a flight for Germany (Mumbai – Dusseldorf), I came across some connected flights that stop at Istanbul.  Do I need to have visa for Turkey?  This is the first time I am travelling outside my country, and any information on this will be helpful.


I have an object that I cannot select nor manipulate. I can get into Edit Mode by using the Outliner however it is useless since I cannot Move it as an object. Seperating, duplicating etc the selection in edit mode doesn't do anything either.   See for yourself:

Okay, so this thing, is for me very strange. It still might be very obvious, but I started with blender 4 days ago.  So what is happening is that when I am rendering my animation, I have a white wall and ground where the scene grid is.  Here is a screenshot when in render mode:   And here it is in material mode:   I would really like to remove this, and I have tried for hours now with no success. I tried to unlink "world" from the scene but then it got all dark when rendered.  If you have any idea of what could be causing this?  (I am making an animated minecraft intro)  Edit: I was told to do alt + h and then the wall and the ground was visible in material mode as well. Here is a screenshot.    But I can't find a way to delete it...  :/


I want to remove the ubuntu operating system from my laptop so I formatted the ubuntu drive (previously had dual booting)  But now I run in grub rescue mode. I checked the other forums and tried the set root and set prefix with all the drives but it still shows file system not found.   Can someone help me so that I can normally boot my win 8.1 which is already loaded ?

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


After watching  I got interested in the question: For which $n \in \mathbb{N}$ is there a number $m \in \mathbb{N}$ s.t.  $$ \sum_{k=1}^nk^2=m^2 $$  Or to put it in plain english, when is the sum of the first $n$ square numbers again a square.  The surprising answer to this is that this is only the case for $n=0,1,24$ and you proof this (according to him) with the formula  $$ \sum_{k=1}^nk^2=\dfrac{n(n+1)(2n+1)}{6} $$  and the machinery of elliptic curves. My guess is that you probably want to proof that the elliptic curve $E$ given by the above equation satisfies $E(\mathbb{Q})=\mathbb{Z}_3$ (not sure here, but something along these lines).      My main question is: can somebody name a reference for a proof of this? But I would also be interested if you could shed some light on how to proceed here or how much machinery you actually need to prove this.   Edit: Since the question got closed while I was not on a computer I just wanted to point out that the other thread doesn't answer my question. The answers in the other thread answers the question: For which $n$ are there $n$ consecutive squares that sum to a square. Note that there the consecutive squares don't have to start with 1. Part of the answer is that this is always the case when $n$ is a perfect square coprime to 6 which clearly is not the case in my situation. The problem is that the answer doesn't shed light on the number $a$ in the question. In particular it is not clear when $a=0$ and when not (which would be my situation). I'm not sure why  so many people mark this as duplicate when the questions are clearly different.

We have the sum of squares of $n$ consecutive positive integers: $$S=(a+1)^2+(a+2)^2+ ... +(a+n)^2$$ Problem was to find the smallest $n$ such, that $S=b^2$ will be square of some positive integer. I found an example for $n=11$. Now, I'm trying to prove, that if $2<n<11$ there is't any solution. So I need some help with this: If $n,a,b \in \mathbb{N}$ and $n<11$ prove that equation  $$ n\cdot a^2 + n(n+1)\cdot a + \frac{1}{6}n(n+1)(2n+1)=b^2 $$  can't be solved. Or if I'm wrong, find counterexample.  The only idea I have is: to consider the remains $\operatorname{Mod}[b^2,n]$ and $\operatorname{Mod}[\frac{1}{6}n(n+1)(2n+1),n]$. For each $2<n<11$, but it is very long.


I'm working on a project where I have a GPS and two receivers to create a triangle with a transmitter. The problem I'm trying to figure out right now is how can I get the position of the two receivers?  I know it can be done, but I'm blanking on the math and Google hasn't been too helpful, maybe I'm not searching it correctly.  Here's my circumstance: GPS is reading lat: 42.331429 and lng: -83.045753. My device is sitting perfectly level and pointing due north. My two receivers are 30 inches to the left and 30 inches to the right. Can anyone help me figure out the equation to get their positions? I know these are going to be very small differences, but that's as far as I've gotten so far.  Also, if things were more complex, how would that be solved? Such as pointing North/West, and 5 degrees rotated on each axis, x, y, and z? I realize that's kind of a crazy scenario, but I like to potentially prepare for every scenario. These are based on being in fixed positions from the GPS and the plane that the GPS is on.

I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route.


With Mavericks is this still needed? Doesn't this eventually cause the battery to die faster because it means it'll have to go through more cycles frequently?

My friend told me that I need to disconnect the power cord when the battery is fully charged. Otherwise, I will shorten the life of the battery.  Other people say you should drain it once a month or point out that for long term storage, you should charge it to 50% and then periodically (3 to 6 months) bring it back to 50% and store it again.  I am going to use my laptop at home 90% of the time. So, I plan to have the power cord connected all the time.  I'd prefer to just plugging in my MacBook Pro and letting it be on charge long term and occasionally taking it away from the charger when I'm not at home or my desk.  Are these specific recommendations worth the inconvenience?


I am undertaking a course of Machine learning by Prof Ng on coursera. I wish to know what notes or any reference material I should refer as along the course there are number of doubts that I wish to understand.  So what text should I prefer for it?

I'm looking for a Machine Learning course that would give the maths behind algorithms rather than simply teach how to apply them. I've looked at Udacity Into to Machine Learning and Andrew Ng's course on Coursera, and they both seem too applied to me. Any recommendations of textbooks would also be much appreciated.


To the best of my understanding the correct contraction of "Am I not" is "aren't I". However, growing up in Scotland I very frequently heard an alternative contraction "amn't I". I think this though is extremely uncommon outside of Scotland.  Now obviously the latter uses the correct part of the verb for "I" and the former does not. I was wondering if anyone knew how we got the wrong part of the verb in the right contraction, and the right part of the verb in the wrong contraction?

Why do we say "ain't I" or "aren't I" instead of "amn't I"? What's the history of this usage? Are there any other similar patterns in English?  I'm guessing it has something to do with the dispreference of two consecutive nasal consonants, but a more authoritative answer would be great.


There is a host PC that runs VirtualBox. There are 3 Virtual Machines installed. An Ubuntu Server, an Ubuntu Desktop and a Windows 7. I have te be able to access the Ubuntu Server from a totally different PC. Not the host, not any of the guests, another one. So it has to get a fix IP. This Ubuntu Server has to function as a server in the virtual network. It has to be a DHCP and DNS server for the two other VMs. The two other VMs also have to access the internet, but across the Ubuntu Server. So that's the problem. I just have no idea what network cards and configuration file settings are needed to achieve this.

I'm trying to use VirtualBox to host a couple of VMs.  Each VM should be able to connect to the Internet (this is needed primarily to install software) My Host browser should be able to connect to the Guest VMs.  Also I need to be able to ssh to the Guest VMs.     This is why I want each VM to have a static IP address.     This will also allow the VMs to connect to each other, say for database connectivity.  I have done this with VMware Fusion.  However, VMware has lately bitten me too often and destroyed so much work that I want to try VirtualBox.  But I'm not a network guru and don't know which type of networking I want.  So what I'm asking is simple:  What are the main differences between networking types. This could help me find out which type of networking I should use in my case.  And of course if anyone has a link to any documentation of how to do what I want, that would be greatly appreciated.  Thanks, ge


I am looking for a way to use AppleScript to test my website.  Is there a way that I can make AppleScript click on different buttons and click on Text Input Fields using the JavaScript ID?  I am aware that there is a way to type using AppleScript.  Thanks!

Is it possible with AppleScript to choose a clickable element in a web page and click it and if so, can you give me an example?


I have two shape files, with the same coordinate system (File 1 and File 2). I have defined the Projection/Coordinate System of File 2 in ArcGIS using ArcToolbox using the Data Management Tools/Projections and Transformations/Define Projection.  For selecting the coordinate system. I have used the import button and have it use the same coordinate system of file 2.  Everything seems right the current coordinate system of both files is the same, but the files don’t align /overlap. What is wrong with these files?  The only strange thing that I find is the Units that in both cases are “Unknown Units”.  The data source box of both files is the same :  Data Type:  Shapefile Feature Class  Shapefile:  C:\SIG\Cartografia\Cartas_uso_do_solo\CLC06_PT\CLC06_PT.shp Geometry Type:  Polygon Coordinates have Z values:  No  Coordinates have measures:  No   Projected Coordinate System:    ETRS_1989_Portugal_TM06 Projection: Transverse_Mercator False_Easting:  0.00000000 False_Northing: 0.00000000 Central_Meridian:   -8.13310833 Scale_Factor:   1.00000000 Latitude_Of_Origin: 39.66825833 Linear Unit:    Meter  Geographic Coordinate System:   GCS_ETRS_1989 Datum:  D_ETRS_1989 Prime Meridian:     Greenwich Angular Unit:   Degree

I put 4 different layers into my ArcMap document, but only one of them will show up on the map! I should be seeing the other 3 layers as well. When I do a Zoom to layer, I can see one layer, but I cannot figure out how to make the other 3 show up at once on top of each other.  Before I opened ArcMap, I used ArcCatalog where I right-clicked 3/4 of the shapefiles and  clicked Properties → Coordinate system → Import and then clicked on my Trees layer, which has the coordinate system I want the other 3 to have. But when I opened ArcMap the 4 layers did not overlap, nor could I move them above or below each other.


I have this String c9e9a0f30c56fc4881f09b65070ecf6ad65f2a51bc910fd5 composed of hexadecimal characters only. Correct me if I'm wrong but a character on a String takes a byte for its representation right? But since a hexadecimal character fits in 4 bits I could fit two characters in a byte. Is there a simple way to do this in Java?  Thank you in advance! You guys rock!

I am looking for a way to convert a long string (from a dump), that represents hex values into a byte array.  I couldn't have phrased it better than the person that posted .  But to keep it original, I'll phrase it my own way: suppose I have a string "00A0BF" that I would like interpreted as the  byte[] {0x00,0xA0,0xBf}   what should I do?  I am a Java novice and ended up using BigInteger and watching out for leading hex zeros. But I think it is ugly and I am sure I am missing something simple.


Why it is a bad practice to synchronize on the object which are changable. How they lead to deadlock ?  For ex ::   private int count = 0; private final Integer Lock = count; // Boxed primitive Lock is shared  public void doSomething() {   synchronized (Lock) {    count++;    // ...  } }

This is a poll of sorts about common concurrency problems in Java.  An example might be the classic deadlock or race condition or perhaps EDT threading bugs in Swing.  I'm interested both in a breadth of possible issues but also in what issues are most common.  So, please leave one specific answer of a Java concurrency bug per comment and vote up if you see one you've encountered.


I was using blender and I created a little character and when it came to putting it in pose mode so I could begin to animate it, from then on the navigation around the 3D window will not work it will zoom in and out but the only way for me to navigate now is through the View menu and this obviously takes forever and I can't get the angles I want, could I have pressed something to make it this way? I just generally cannot navigate at all around my interface.

I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out – at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case?


Find the equation of the two tangent lines to the ellipse $x^2+4y^2=36$ that pass through the point $(12,3)$.   I tried using implicit differentiation, and then I didn't know where to go from there.

I was solving a few problems from a textbook and I came across this one:     Find the tangent lines to the graph of $x^2+4y^2 = 36$ that go through   the point $P=(12,3)$   I could find the tangency points $$ but my solution was completely messy (I had four equations that I had to go back-and-forth with.  Is there an elegant/simple solution to that?  Tangency points:  $$P_1 = (0,3)$$ $$P_2 = \left( \frac{24}{5} , 3-\frac{24}{5} \right)$$


The built in light meter for my Canon EOS Rebel T5 doesn't seem very good. It'll tell me that 30 seconds will overexpose my photo every time. I want to be able to do 1-8 minute exposures and have a workable image (not too under or over exposed)

One of my longstanding interests is long exposure night photography.  However, many of the situations where I am shooting require exposure lengths on the order of 10 minutes, which is far beyond what the internal meter in my camera (5DII) can handle.  Right now, I take a test exposure, extrapolate from that to guess my exposure time, try again, etc...  This works, but since the test exposure alone can be 10 minutes, and it generally takes me a few shots to get the exposure right, it can take 30 minutes to an hour just to figure out exactly how long I need to expose for.  Obviously, this is really inconvenient (fortunately, long exposure subjects don't move much, most of the time).   For instance, recently I did a series of 13 minute exposures at f4, ISO125. It came out really well, but I would up spending 2 hours to get one shot.  Anyways, is there an easier way to determine how long an exposure has to be, preferably that doesn't take multiple test exposures? I've looked at light meters, but none of them make explicit statements about how low a level of light they can handle.


I have seen in a book the following "square hat" symbol to denote the discrete Fourier transform:   I would like to use the same symbol, but I cannnot find the corresponding command. Can anyone help me, please?

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


I would like some feedback on my proof of the fact stated in the question.  First, we note that $ L = \mathbb{Q}(\zeta_5) $ is the splitting field of $ X^5 - 1 $, so it is Galois. Furthermore, we know that $ \mathrm{Gal}(\mathbb{Q}(\zeta_5)) \cong C_{4} $. By the fundamental theorem of Galois theory, the subfields of $ L $ of degree 2 are in one-to-one correspondence with the subgroups of the Galois group which have $ 4/2 = 2 $ elements. However, $ C_4 $ has only one subgroup of order 2, which is $ \{e, g^2\} $ where $ g $ is an arbitrary generator. We conclude that $ L $ has only one subfield of degree 2, and it is fixed by the aforementioned subgroup of the Galois group.  Now, the Galois group is comprised of automorphisms $\sigma_i: \zeta_5 \to \zeta_5^i $ for $1 \leq i \leq 4 $, and this group has only one element of order 2, which is $\sigma_4$. We conclude that the intermediate field $ F $ is the one fixed by the cyclic subgroup generated by $ \sigma_4 $. Now, we consider the polynomial $ P(X) = (X - \zeta_5)(X - \zeta_5^4) $. Again, by the fundamental theorem, $\textrm{Gal}(L/F) = \{\sigma_1, \sigma_4\}$. We see that the entire Galois group fixes $P$, so $P$ has coefficients in $F$. Defining $ A = \zeta_5 + \zeta_5^4 $ which is negative of the coefficient of $X$ in $P$, we see that  $ A^2 + A - 1 = \zeta_5^2 + \zeta_5^3 + \zeta_5 + \zeta_5^4 + 1 = 0 $  and therefore, by the quadratic formula, $$ A = \frac{-1 \pm \sqrt{5}}{2} $$ and $ \sqrt{5} \in F $, implying that $ \mathbb{Q}(\sqrt{5}) = F $ as $ F $ has degree 2.

I want to prove the assertion:      The unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ when $p \equiv 1 \pmod{4}$, respectively $\mathbb{Q}(\sqrt{-p})$ when $p \equiv 3 \pmod{4}$.   My first attempt is this. In $\mathbb{Z}[\zeta_p]$, $1-\zeta_p$ is prime and $$ p = \epsilon^{-1} (1-\zeta_p)^{p-1} $$ where $\epsilon$ is a unit.  Since $p$ is an odd prime, $(p-1)/2$ is an integer and  $$ \sqrt{\epsilon p } = (1-\zeta_p)^{(p-1)/2} $$ makes sense and belongs to $\mathbb{Z}[\zeta_p]$.    How do I deal with the $\epsilon$ under the square root?  I guess the condition on the congruence class of $p$ comes from that.  Is this even the right way to proceed?  Uniqueness is not clear to me either.  I thought about looking at the valuation $v_p$ on $\mathbb{Q}$, extending it to two possible quadratic extensions beneath $\mathbb{Q}(\zeta_p)$, then seeing how those have to extend to common valuations on $\mathbb{Q}(\zeta_p)$, but I didn't see how to make it work.  I would appreciate some help.


College officer wrote me: you will be receiving a new letter... Why didn't he write "you will receive"?  In addition, what is the difference between "I will wait" and "I'll be waiting"?

Could you let me know why future continuous is used in this sentence:     You will be receiving an invoice from Thomas in a few days.   Is it because it relates to a routine, or is it because of the duration (in a few days), or is it because the man who wrote the email is a different person (neither Thomas nor the man who will receive the email) and his willingness cannot influence Thomas' action meaning maybe Thomas can forget….


What would the properties of a particle be that would allow light to orbit it?  Light travels fast. Really fast. Almost to the point where we consider that it's instantaneous, and moves only in a straight line.  We know that's not true though. Light can be influenced in such a way so as to cause it to change course. "Bend" if you will.  Black holes influence light strongly enough as to cause the light to be pulled in without escaping. (at least, as far as we know. right?)  This gives me the fundamental basis for thinking that it would be possible to influence light enough to allow it to orbit a particle. I'm curious if anyone has an idea of what properties a particle like this would have, how it could be described, and whether or not it could exist in our physical reality.

The moon orbits Earth at about $380,\!000 \,\mathrm{km}$  away from it, at around $3,600 \,\mathrm{km}$ an hour.  I was thinking, with light traveling at $300,\!000 \,\mathrm{km/s}$, how close to earth (probably in the $\mathrm{nm}$ range is my guess) would light have to be to Earth to orbit it?  Update: After reading the below answers, here's my reasoning to why I thought it would be in the nanometre range.  I thought that if light was as close as possible to Earth (like, a planck length away or something), Earth's gravity would make it hit Earth immediately, but I forgot that the pull of gravity gets weaker when one is further away from Earth (i.e. at the surface of Earth is still somewhat "far away").


The voting seems to suggest that my question helped promote the other question. I don't know if chronological precedence is a criterion. I wonder if it is fair that the votes my question might have continued to receive will now most probably be received only by that question, which hadn't got too many votes before I asked my question.  I'm asking out of curiosity. I am actually pleased with the way my question was handled. And it's not like I asked it for the votes anyway.

I asked a question regarding a very specific feature of a program and whether or not it works with a larger program.  Within hours someone had marked it with "This question may already have an answer here of a similar question, but not related to my question.  The question I asked IS NOT ADDRESSED in the referred-to question. It's frustrating to spend half an hour putting together an intelligent and specific question, and then have someone mark it as a duplicate (or possible duplicate), which apparently causes people to skip over my question. I haven't received any more responses since the question was flagged.   Two questions:  (1) How do I get this flagging removed and (2) what's the best way to prevent these "helpful" flaggings in the future?


If one was to state that neither him or another person committed a certain act, how would that be phrased with proper grammar?  ex. Who broke that window?  It wasn't me or Steve.  vs.  It wasn't Steve or I.

When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I".


I have accidentally uninstalled python 2.7 and python-minimal from my Ubuntu. It gave me an error saying wicd has shut down and there are broken packages.  When I restarted the system, only the desktop is seen. No launcher or any other panels are seen. Even Alt+T is not working to open up the terminal. I have a folder in my desktop which can help in navigating to the file system.  Please help me...

I uninstalled the Python 2.7 package to try and upgrade to Python 3. I uninstalled Python 2.7, and noticed some of my launcher items were completely gone. At this point I had installed Python 3. Now on reboot, I can't log in and the background for the log-in screen is black with white dots. Any help would be greatly appreciated.  P.S. - This is running 11.10 Oneiric Ocelot. I still have the same version Live CD.  EDIT: Thanks for the feedback! But I can't boot into text mode, only boot from the Live CD, and I can't connect to the internet because I installed the Debian .tar.gz package usb_modeswitch for Mobile Broadband. Is there a way to copy the Python 2.7 parts of the OS from the Live CD and inject them into my system? The only thing I can think of is get a 12.04 Live CD and click 'Upgrade from 11.10 to 12.04' option, but for reasons I won't go into this is impractical for me.


I'm currently writing a RSS parser and I use Ractive to generate the view. I'm trying to vertically align the contents of .feed-text-offset according to the height of .feed-item.  How can I accomplish this?  Demo:   The output HTML is like this:

         Text here         1 hr

   CSS  .feed-item {     padding: 2px;     background-color: green;     float:left; }  .feed-item-since {     font-size: 0.8em;     font-weight: 400;     margin-top: 5px;     display: block; }  .news-img-container {     width: 125px;     float: left; }  .feed-text-offset {     margin-left: 130px; }

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


Let T be the line passing through the points P(-2,7) and Q(2,-5). Let $F_1$ be the set of all pairs of circles $(S_1,S_2)$, such that T is tangent to $S_1$ at P and tangent to $S_2$ at Q, and also such that $S_1$ and  $S_2$  touch each other at a point, say, M. Find the locus of point M.  Actually what i presume that the distance between the centre of the circle is $4\sqrt10$ unit , it is the distance between P and Q. But not able to proceed from here onward as i am not able to formulate it.

Q) Let T be the line passing through the points P(–2, 7) and Q(2, –5). Let $F_{1}$ be the set of all pairs of circles $(S_{1}$, $S_{2}$) such that T is tangent to $S_{1}$ at P and tangent to $S_{2}$ at Q, and also such that $S_{1}$ and $S_{2}$ touch each other at a unique point, say, M. Let $E_{1}$ be the set representing the locus of M as the pair ($S_{1}$, $S_{2}$) varies in $F_{1}$. Let the set of all straight line segments joining a pair of distinct points of $E_{1}$ and passing through the point R(1, 1) be $F_{2}$. Let $E_{2}$ be the set of the mid-points of the line segments in the set $F_{2}$. Let $C$ be the circle $x^2+y^2+6(2y+7x)=53$. The number of times $C$ intersects $E_{1}$ and $E_{2}$ is (are):


[EDIT2]  Something is wrong with answer ordering: different versions of Chrome (under different environnments) show different behaviour.  Noticed here:    WinXP(VM) and Win7, Chrome Version 33.0.1750.154 m: constant order Linux, Chrome Version 23.0.1271.95: random order   Might extends to other browsers?  [EDIT1]  In the end it looks like a browser specific issue, in the very particular case of:   a self-accepted answer with N votes, other non-accepted answers which with N votes too, sorting answers by vote, the browser is an old version Chrome, Firefox (which version?), maybe others too.   In this case, the order of the answers with N votes varies randomly at each refresh, including the accepted one. This doesn't happen on more recent versions of Chrome, accepted answer is always first and the order remains the same between refreshes.  [ORIGINAL]  I understand the choice of using random for ordering equally voted answers: a simple way of giving the same visibility without the hassle of taking rep or time into account, etc.  However I had the case where I needed to refer to an accepted answer which had the same number of votes than other, less acurate answers, and was surprised to have to search it each time I reopened the page (there can be many answers with 1 vote).  See this question for example: , where the accepted answer is not ordered at the beginning.  Do accepted answers deserve more visibility than others when votes are equal?

What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the .


I got into an argument today about the role of the Rebel Alliance and the Empire in the Galactic Civil War. My opponent posits the Galactic Empire is not inherently evil, and the Rebels would just be terrorists from their point of view. She felt the oppression and fear of violence they were fighting against were only brought on because of the existence of the Rebel Alliance in the first place.  Are there specific examples of "evil" actions taken by the Empire unprovoked, or were all their actions "justified" by rebellion? I tried to bring up , , and Alderaan, but my opponent felt they were justified because the Empire was provoked and needed to keep the peace. I also brought up Order 66, but they argued that was Darth Sidious using the Empire as a vehicle for his whims, not the empire itself.  Thank you in advance!

In the Star Wars prequel trilogy (and in the Clone Wars TV show) we see that Darth Sidious fooled the galaxy gradually. The Republic was reorganized into the Galactic Empire with the people's consent, Palpatine having convinced them that the Jedi were traitors. Aside from a small group of perceptive individuals (like Padme, Bail Organa, and Mon Mothma), we get the impression that during the reign of the Empire the average person (citizen or officer) might believe that the Empire was in the right. Consider the fact that:  the Emperor   the Emperor kept the Imperial Senate intact for a while  Tarkin seemed to discourage Vader from choking imperial officers   It seems as though the Emperor needed to keep up appearances of being good and wanted the imperials to believe that as well. However the Empire has some really evil names like Death Star and Star Destroyer that would likely tip people off that the Empire was evil. I realize that the construction (as well as probably the name) of the Death Star was  before it's completion. Star Destroyers, however, were plentiful before that. Did the average imperials (such as stormtroopers, officers, or admirals) know that they were the "bad guys"? If they don't consider the Empire to be evil, then how can they justify the Empire's action to themselves?


I use Ubuntu 20.04 dual boot. sudo apt-get update I get this: Get:7 http://security.ubuntu.com/ubuntu focal-security InRelease [107 kB]       Ign:8 http://ppa.launchpad.net/colingille/freshlight/ubuntu focal InRelease     Hit:9 http://ppa.launchpad.net/diesch/testing/ubuntu focal InRelease            Hit:10 http://ppa.launchpad.net/yann E: The repository 'cdrom://Ubuntu 20.04.1 LTS _Focal Fossa_ - Release amd64 (20200731) focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'http://ppa.launchpad.net/colingille/freshlight/ubuntu focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.```   How can I solve this?

When updating, I get the following error message:   W: The repository 'http://ppa.launchpad.net/mc3man/trusty-media/ubuntu xenial Release' does not have a Release file.   Here, I find another statement on this error:   This recommends removing certain PPAs; and, I'm not sure if I should do that since it might mean not getting the updates that I need.    Is this what I should do?


I'm doing some remodeling on a river cabin. It was built 50 years ago and most of it is not to code.  It's not mine and I'm trying to get my family to look at upgrading all the wiring. It doesn't even have outlets with grounds in them.  Also, for those who might be concerned, I do have some experience wiring. My uncle wired his whole home and came down to wire my dad's shop. He taught me and an inspector said it was wired better than some homes he'd been in. I know how to safely wire this project in, just not issue like this. If I can't find a satisfactory answer or I don't feel confident, I will call in a professional.   My issue is that I'm working on redoing a wall in the bathroom. There is currently a light fixture with a built in plug for plugging in something like a hair dryer. I'm replacing that light fixture and would like to add a gfci outlet in the wall before I add the FRP board I'm covering it with. The current gang box for the light is free floating and I'm going to replace it with a plastic one with the little wings that hold it in place. Being able to push it back I can read that the wire says 14/2.  Ideally all the wire would be 12/2, but I don't know when or if that will happen. I'll never use 14/2, so instead of buying a roll of that, can I use a piece of the 12/2 romex that I already have, and wire off the light to the outlet?  I understand that the outlet would only work when the light was on. I just want to make sure I'm not going to burn the cabin down. In my mind, it would be fine, because it's already wired correctly for 14/2, with the correct amp breaker, so if it hits a load too high for the 14/2, then the breaker shuts off. It just has the capability to run more power. I wouldn't be able to do the reverse, but this seems okay.  Am I correct on this or is there an issue I don't know about? Thanks. I did see similar questions, but none that I thought were exactly this issue.

I have 12/3 wire from a switch to 3 light fixtures; can I feed the switch with 14/2 wire from a 15 amp breaker?


I was running around the internet looking at Dihedral groups and ran into a page that claimed that $D_{10} = C_2$ $\times$ $D_5$ (I know notation for Dihedral groups is confusing - here I'm using $D_{n}$ to denote the Dihedral group of order $2n$), and was wondering as to why this is the case.  Now I've been mostly thinking about this in terms of group representations. I know $D_{10} =$ <$a, b: a^{10} = b^2 = 1,$ and $bab^{-1} = a^{9}$>, or equivalently, <$a, b: a^{10} = b^2 = (ba)^2 = 1$> ($a$ is akin to a rotation and $b$ is akin to a reflection).   I also know that $D_5 =$ <$u, v: u^5 = v^2 = 1,$ and $vuv^{-1} = u^4$>, while $C_2 = <c:c^2=1>$. Then thinking of '$\times$' as creating an ordered pair, to me it would seem that $C_2$ $\times$ $D_5$ gives us a group with 3 generators, with the relations listed as above.   I'm not quite sure where to go from here. One thing that stands out to me is the fact that we have two generators of order 2 ($v$ and $c$), and I suspect we might make use of that somehow. However, I'm still not sure how to get the group presentation to look like $D_{10}$'s. I guess thinking about it now, I'm not even really sure how to picture what $C_2$ $\times$ $D_5$ would look like (and if there even is a way to visualize it without $D_{10}$).  Any help would be appreciated, and if there is a different way to approach this problem (Isomorphism between the two groups), that would be welcome as well, though I really do want to try and figure this question out through group presentations as I feel it's a very useful tool.

Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. I define a map $$\phi:D_{2n} \rightarrow \mathbb{Z}_2 \times D_n$$ by $R \mapsto (0,r^{\frac{n+1}{2}})$ and $M \mapsto(1,m)$. Then I am stuck at showing the map is bijective. By the way, do we need to show that $(0,r^{\frac{n+1}{2}})(1,m)(0,r^{\frac{n+1}{2}})^{-1}=(1,m)$ ? If we can prove this, then what can we conclude?


I remember reading some robot stories years ago, and am trying to track down the stories to read again. Initially I though they must be Asimov stories, but I can find no Asimov story that has what I remember.  The story (or stories) is about a boy that has a robot. I part of the story the robot has only black and white vision, but someone(I forget) replaces its with a new tube, so that the robot see now see in color. The boy is disappointed as he wanted to get the tube for the robot, as soon as he had enough money saved.  In another part of the story, the robot is on his own and Is being tracked down, he is going to "Charge" (Attack) but is turned off by a switch, before he attacks. The comment is that the company says they have never seen such devotion in a robot for its owner. Story may have "Marsport" or "Marspoint" in the story.

I'm trying to find a children's/YA book.  I remember it being about a family's robot that is about to be either destroyed or have its mind wiped.  The boy that it belonged to orders it to run away to save it.  I think it was thought to be defective for not following some of its prime directives.  The story is set on either the Moon or Mars and the people live in domes.  During the story, the boy meets up with the robot and both helps and is helped.  I don't believe it was I, Robot.  It wasn't a short story or stories, but a children's book.  At a guess, I'd say it was written for 10-14 year-olds. I keep thinking the book was called "Run, Robot, Run" but I can't find it by that title.    I don't know if it had a positronic brain, but it may have been something like that.  I mostly remember that the book started off almost immediately with the child yelling "Run, robot, Run!" and most of the rest of the book being about the robot trying to escape/hide with the boy's help and a growing sense of self.  Thank you!  It is the Runaway Robot, I remember that book cover.  Greatly appreciated!


Is it possible for the program to output the entire name of data type or ?  For eg. (int, double ...)  #include <iostream> #include <typeinfo>  using namespace std;  int main(){      auto a = 5.34;     auto b = 3 ;     auto c = a * b ;      cout << typeid(a).name() <<  endl; //output d     cout << typeid(b).name() <<  endl; //output i     cout << typeid(c).name() <<  endl; //output d         return 0; }

I'm currently working on some logging code that supposed to - among other things - print information about the calling function. This should be relatively easy, standard C++ has a type_info class. This contains the name of the typeid'd class/function/etc. but it's mangled. It's not very useful. I.e. typeid(std::vector<int>).name() returns St6vectorIiSaIiEE.  Is there a way to produce something useful from this? Like std::vector<int> for the above example. If it only works for non-template classes, that's fine too.  The solution should work for gcc, but it would be better if I could port it. It's for logging so it's not so important that it can't be turned off, but it should be helpful for debugging.


On my laptop I have Xubuntu 20.04. I've noticed that running # apt update && apt upgrade -y hardly ever results in updates being applied. Upon doing a comparison of /etc/apt/sources.list between my laptop and a fresh Xubuntu (installed in a VM using the 20.04.1 point release ISO), I've noticed that the following lines are missing (as opposed to commented out) on my laptop's version of the file: deb http://gb.archive.ubuntu.com/ubuntu/ focal-updates main restricted deb http://gb.archive.ubuntu.com/ubuntu/ focal-updates universe deb http://gb.archive.ubuntu.com/ubuntu/ focal-updates multiverse deb http://gb.archive.ubuntu.com/ubuntu/ focal-backports main restricted universe multiverse  What could have caused this difference between the two installations and how can I avoid it happening in future? Edit  It has been proposed to close this question on the basis that  is a duplicate. That question asks how to restore a broken sources.list file. I already know how to do that. My question is asking why the lines are missing the in first place. The two questions are not duplicates of each other. Whilst I am grateful for efforts to locate a duplicate, please be careful to make sure that it actually is before submitting a close-vote. It was suggested in the comments that I must have edited the file myself. This is not the case. The file sources.list.save is missing exactly the same lines and has a modified date of 26 April 2020 which is the date that I installed the system (a few days after 20.04 was released in case that is significant).

There are now errors when updating and I cannot install most software due to a corrupted  /etc/apt/sources.list   file. Is there a copy I can download to replace it?  The file would be for Ubuntu 12.04 (Final Beta) in the United States.


We have created our own 2nd generation package and trying to install it in our org, but getting the following error: 1.  ORA-20001:  ORA-06512: at "HAPPY.CMETAACCESS", line 665 ORA-01403: no data found ORA-06512: at "HAPPY.CMETAACCESS", line 848 ORA-06512: at "HAPPY.CMETAACCESS", line 799 ORA-06512: at "HAPPY.CMETAACCESS", line 784 ORA-06512: at "HAPPY.SITEDEVCOMPONENT", line 718 ORA-06512: at line 1   {call SiteDevComponent.load_sitecomponents(?,?,?,?)} : ORA-20001:  ORA-06512: at "HAPPY.CMETAACCESS", line 665 ORA-01403: no data found ORA-06512: at "HAPPY.CMETAACCESS", line 848 ORA-06512: at "HAPPY.CMETAACCESS", line 799 ORA-06512: at "HAPPY.CMETAACCESS", line 784 ORA-06512: at "HAPPY.SITEDEVCOMPONENT", line 718 ORA-06512: at line 1   {call SiteDevComponent.load_sitecomponents(?,?,?,?)}  Has anyone encountered something like this before? Any tips would be helpful around the potential causes based on Oracle errors.

I'm deploying an apex class and Test class which is running successfully and covering 84% test coverage in sandbox however when deploying it in Prod, I'm running in to below issue. I have included Static Resource in the changeset. Any ideas what is wrong with it? The Static resource consist of a CSV file that includes User data (Name, email, Username , lastlogindate). istest public class TestScheduleInactiveUser {     @istest static void ScheduleInactiveUser(){              List<sObject> ls = Test.loadData(User.sObjectType, 'UserLoadTest');                          Test.startTest();             ScheduleInactiveUser fc=new ScheduleInactiveUser();             Database.executeBatch(fc);         Test.stopTest();              } }   Error: System.SObjectException: ORA-20001: ORA-06512: at "DOC.CPROFILE", line 1128 ORA-01403: no data found ORA-06512: at "DOC.CPROFILE", line 2940 ORA-06512: at line 1 SQLException while executing plsql statement: {?=call cProfile.get_user_type(?)}(00eP0000000bIq5)  Stack Trace:  Class.System.Test.loadData: line 53, column 1 Class.TestScheduleInactiveUser.ScheduleInactiveUser: line 5, column 1


If you put some XML in a code block (by indenting by 4 spaces) and one of the tags is <Style> it will mess up the syntax highlighting of the generated result.  This works:  <Style2 Foo="ThisWillWork">    <!-- Stuff in here is colored ok -->    <SomeElement Bar="Baz" /> </Style2>   While this won't:  <Style Foo="ThisWontWork">    <!-- stuff in here won't be properly colored -->    <SomeElement Bar="Baz" /> </Style>   The problem is both in the JS preview as well as the rendered result.  In case this cannot be reproduced, here's a screenshot of what I'm seeing:    For reference:   Using Google Chrome 8.0.552.215  I first saw this issue when answering  on Dec 7 2010

I noticed that sometimes my code gets highlighted in different colors when rendered.   What is syntax highlighting? How does it work? Why isn't my code being highlighted correctly? How do I report a bug or request a new language? How do I use syntax highlighting? What languages are currently available on Stack Exchange?


Q: If complex matrices $\rm{A}$ and $\rm{B}$ satisfy $\rm{rank}\ (\rm{AB}-\rm{BA})\ \le1$, then there exists a revertible matrix $\rm{P}$ such that $\rm{P^{-1}AP}$ and $\rm{P^{-1}BP}$ are both upper triangular matrices.   I have figured out the proof when the condition is restricted to $\rm{AB-BA} = 0$. Since each characteristic subspace of $\rm{A}$ is also an invariant subspace of $\rm{B}$, one can readily see that  $\rm{A}$ and $\rm{B}$ share a common eigenvector, and the conclusion can be drawn by induction. However, when it comes to $\rm{rank\ (AB-BA)= 1}$, I find it hard to find a common eigenvector of $\rm{A}$, $\rm{B}$.  Am I right in this way of thinking? Is there any other elegant proof? Thanks for any help!

Let $A$ and $B$ in $M_n(\mathbb C)$ such that the rank of $AB-BA$ is $1$. Prove that $A$ and $B$ are simultaneously triangularisable.  This generalizes the classical case $AB = BA$. By induction on $n$, it suffices to show that $A$ and $B$ have a common eigenvector. So, it would be sufficient to find a eigenspace of $A$ which is stable by $B$ since matrices are complex. Do you have ideas for that? Thank you.


Reading a text on Transformation and Variate Generation that says that if   we want to simulate V, but we know only its conditional distribution given U, and we can simulate U   then we can simulate V as follows:   Draw u_sim from the marginal distribution of U Draw v_sim from the conditional distribution of V given U=u_sim   then v_sim is a variate from the marginal distribution of V. This is the part I don't understand: why are we allowed to say we have simulated from the marginal distribution of V and not the conditional $p(v|u)$?  Maybe this is just an approximation, and this distribution converges on $p(v)$ for large samples?

I want to sample from a univariate density $f_X$ but I only know the relationship:  $$f_X(x) = \int f_{X\vert Y}(x\vert y)f_Y(y) dy.$$  I want to avoid the use of MCMC (directly on the integral representation) and, since $f_{X\vert Y}(x\vert y)$ and $f_Y(y)$ are easy to sample from, I was thinking of using the following sampler:   For $j=1,\dots, N$.  Sample $y_j \sim f_Y$. Sample $x_j \sim f_{X\vert Y}(\cdot\vert y_j)$.   Then, I will end up with the pairs $(x_1,y_1),...,(x_N,y_N)$, and take only the marginal samples $(x_1,\dots,x_N)$.  Is this correct?


As an administrator to many Ubuntu servers that run on AWS - sometimes I cannot keep track of what servers need package updates and when. Is there a way to automate this process in a sense where running sudo apt-get update and sudo apt-get upgrade is just done automatically?  EDIT: This is in question to running Ubuntu 16.04 LTS servers.

Update Manager is constantly offering me updates (e.g. security fixes, updates from PPAs).  How can I tell my Ubuntu installation to automatically download and install updates whenever they become available?


I have been trying to access a folder to install a program and I keep receiving the following error message:  bash: cd: *: No such file or directory   I then tried accessing the desktop with the command cd desktop and received the following message:  bash: cd: desktop: No such file or directory   I've tried re-installing Terminal to see if that fixes the problem but still get the same messages.  Can anyone help with this issue? Accessing files and folders works normally through the Unity user interface.  EDIT: Solution found in comments and is not part of existing command-line questions.

I am using Precise pangolin. As far as I know, commands like   cd..   or   cd-   are used to browse through folders in the terminal.  But whenever I enter one of this commands, it gives an error saying no such command or filename found. Do I have to perform any additional task before I use commands involving cd?


Is it possible to clone a running VBox machine?   I need this because I can't turn off the machine during its purpose so I was wondering if something like that is possible?   I tried by cloning the snapshot but that option is not available while the VBox machine is running.  Im using Windows7 and the machine im trying to clone Linux machine.

I am currently running a time consuming python script on a virtual machine(It has been running for ~95 hours at the moment). I have no idea how long it will take to complete and am running it on a VM because of the possibility to save the state and reboot my laptop (In case of mandatory updates). However, I just received an e-mail that I have to turn my laptop in to get an upgrade from windows 8 to windows 10 tomorrow.   Because the script has been running for quite some time now I don't want to start all over again the day after tomorrow. Is it possible to back-up the VM including the current state and get it up and running again when my machine has been updated? And if so what is the best way to do this?  Some extra information: -I am running windows 8 on the host system -The VM is running Xubuntu 16.04  Thanks in advance!  Edit: I'm not upgrading from windows 8 to 10 with the free upgrade, i will receive a clean windows 10 installation because of company policy.


I have images/files that I look at time to time inside the native Files app that I would prefer not to show up in the “Recents” area.  How do I hide files from showing up in the “Recents” area inside the files app?

I am trying to remove some files out of the 'recents' view of the files iOS app without actually deleting the file.   My 'recents' list is currently too long, for this view to be of any help for me at this point. Ideally, I can curate individual items that aren't relevant and keep the rest of the list, but if needed - can I just purge all recents and start cleanly?


I must prove, that when dividing the following by 6 it yields no remainder: $$n^2+11n $$  Is this done with mathematical induction method? and what other technique can I use?  Update: some may find this question as a potential duplicate of the correct case when we have $n^3$ instead of $n^2$. I want to clarify that this is not true.

Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.  I've started by letting $P(n) = n^3+11n$  $P(1)=12$ (divisible by 6, so $P(1)$ is true.)  Assume $P(k)=k^3+11k$ is divisible by 6.   $P(k+1)=(k+1)^3+11(k+1)=k^3+3k^2+3k+1+11k+11=(k^3+11k)+(3k^2+3k+12)$  Since $P(k)$ is true, $(k^3+11k)$ is divisible by 6 but I can't show that $(3k^2+3k+12)$ is divisible by 6


I have a log message in my application which depends on a list which may contain one or several elements. The string I am trying to create to show in the logs is like this:  "The key(s) {listOfKeys} have an odd length"  Given that the list of keys may have a minimum of 1 element, and hence I don't know if the subject will be singular or plural, should I use "have" or "has"? Or maybe something like "have/has"? Note: I know that I can rephrase the sentence to avoid this problem, maybe something like "Invalid length for the key(s) {listOfKeys}", or even introduce a condition to write the sentence one way or another depending on the length of the key list, but I'm just curious to know how this problem is solved in English if I had no other option.

Consider the following sentence:     We assume that the individual(s) possesses some general knowledge of the rules of football.   Is "possesses" correct there? Should it be "possess"? Is the rule more complex than always using one or the other?


I thought of starting from the Menger theorem which says that between every two vertices $u$ and $v$ there are $k$-edge disjoint graphs. So I think if I look at $G$ without the subset $S$ then I have $k$ paths from $S$ to $V-S$. I know for a fact that there has to be a cycle because $k \geq 2$ and between $u$ and $v$ there are at least two paths and they form a cycle. Now I was thinking about looking at $u\in S$ and $v\in V-S$. At this point I get stuck ...

Let $G$ be a $k$-connected graph. Meaning, $G$ has no fewer than $k$ vertices, and for every set of $k-1$ or fewer vertices, if we remove them from $G$, the graph stays connected (Of course, $G$ itself is also connected).  I want to prove that for any $k>1$, if $G$ is $k$-connected, then every set of $k$ vertices is contained in a cycle.  I have tried some ways - mainly using induction by removing one of the vertices of the set from the graph, and/or using Menger's theorem to construct the cycle. But I always encounter problems with making sure that the cycle I'm building deosn't have repeating edges etc.  Help would be greatly appreciated :) Thanks!


If G is a finite group generated by $a,b \in G$, both $a$ and $b$ having order 2, what can we say about the order of another element $xy \in G$?  I was thinking that we can conclude that $xy$ has finite order because it is contained in G, but nothing else can be concluded. Is this correct or am I missing something?

Let $G$ be a group and let $a,b$ be two elements of $G$. What can we say about the order of their product $ab$?   says "not much":     There is no general formula relating the order of a product $ab$ to the orders of $a$ and $b$. In fact, it is possible that both $a$ and $b$ have finite order while $ab$ has infinite order, or that both $a$ and $b$ have infinite order while $ab$ has finite order.   On the other hand no examples are provided. $(\mathbb{Z},+), 1$ and $-1$ give an example of elements of infinite order with product of finite order. I can't think of any example of the other kind! So:   What's an example of a group $G$ and two elements $a,b$ both of finite order such that their product has infinite order?     Wikipedia then states:     If $ab = ba$, we can at least say that $\mathrm{ord}(ab)$ divides $\mathrm{lcm}(\mathrm{ord}(a), \mathrm{ord}(b))$   which is easy to prove, but not very effective. So:   What are some similar results about the order of a product, perhaps with some additional hypotheses?


I would love to hide the top bar through the terminal, but don't currently know how.  Can somebody help me please?

I want a shortcut to hide the top bar and dock, so I thought the best way to do that would be to figure out a terminal command which does the same.So, can someone tell me the command to do so or another way to make the shortcut work?


I've been working on a large multiplayer world. In it, I have set up a "P.A. System" using a command block chain, with all the blocks set to use the /say command to send messages in chat.    When I send a  signal through the chain, the first block (set to impulse, not chain, and unconditional) activates. Then the second block (set to chain and conditional) activates. The signal seems to end there, as the third block (set to chain and conditional) does not activate. Why is this setup not working?  I am playing Bedrock Edition, on my phone.

So I am trying to do some stuff with command blocks in 1.10.2 . But I have come to a problem. To make things more compact I have placed command blocks like a tower. The bottom command block checks for a pushed button in a location. The top ones are suppose to do what I need but they don't. Any ideas? By the way the testforblock command is correct.


Why some people use could instead of can (in the simple present tense) For example,  Could you open the door?

Can you please explain this to me?          Could you please explain this to me?   I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.  What is correct way to use these words?


I'm writing Selenium tests, and I need to support Internet Explorer 8.  I want to use Developer Tools in Internet Explorer 8 to verify that Internet Explorer 8 can find certain elements by their XPath expressions. I can do this easily using Chrome of Firebug with Firefox, but I can't figure out how to do it with IE Developer Tools -- it feels very clunky, foreign, and unintuitive for someone coming from Chrome and and Firebug with Firefox.  I'm not trying to get an element's XPath expression with Developer Tools. (The web has plenty of links for how to do that.) I'm trying to verify that XPath expressions which I already have will work in Internet Explorer 8 using Developer Tools.  If I want to verify that an XPath expression finds an element in Chrome, I would:   Navigate to the page I want to verify Press F12 to bring up Chrome debugger Press Ctrl + F to bring up find Type or paste in the XPath expression that I want to test See if the XPath expression found an element.   Here is an image of what it looks like in Chrome:    I would like to do the same thing in Internet Explorer 8. How can I do this?  I have seen  which tries to get the XPath expression from the webelement. I'm trying to do the opposite: get the webelement from the XPath expression to verify the XPath expression is valid in Internet Explorer 8.

I have an Internet Explorer only web application.  I'm exploring what we can do to automate the testing.   Selenium looks like a good tool, but to be able to activate links etc. I need to tell it where they are. The application wasn't built with this kind of testing in mind, so there generally aren't id attributes on the key elements.  No problem, I think, I can use XPath expressions. But finding the correct XPath for, say, a button, is a royal pain if done by inspecting the source of the page.  With Firefox / Firebug, I can select the element then use "Copy XPath" to get the expression.  I have the IE Developer Toolbar and it's frustratingly close. I can click to select the element of interest and display all sorts of information about it. but I can't see any convenient way of determining the XPath for it.  So is there any way of doing this with IE?