For a math assignment that I am giving my students, I have included a problem from Spivak Calculus. I have the following two issues and I do not know what I should do:   If I do not acknowledge the source, it seems that I have committed plagiarism.  And if I acknowledge the source, then the students will go and perhaps find the solution manual and give the same solution as in the solution manual.   Can anyone please discuss what is the best thing to do in my case?

This question was raised by Dave Clarke .  When a textbook author approaches a topic in a novel way or presents a particularly interesting example, I believe that a teacher who creates lecture notes using this novel approach or interesting example would be doing the right thing to cite the originator of the approach or the example.  Similarly, whenever I copy a clever (and clearly unique) problem from a textbook and give it as a question in an exam or an assignment, I try my best to indicate (in the exam or assignment paper itself) the source of the original problem.  Does anyone know of any written document indicating whether or not it is considered unethical to copy a published problem and put it in an exam or an assignment without citing it?


I am trying to create an under water scene but it is not turning out like the tutorial I am following. My main issue is when I come to rendering the image it is extremely grainy and I cant get it to look realistic. Would someone be able to help me with this problem and explain in really basic terms as I have no other experience with these kind of projects. Thanks in advance!

I know that this question is a bit old or maybe overdone, but I'm running the latest edition of Blender and when I use the Cycles engine I get really fuzzy results and I can't find a simple, non-compromising solution to the quality.  I don't know exactly what I'm doing wrong here, but I'm sure others share my frustration.  Leaving everything in default settings, I started a new project and switched to the Cycles render.  I duplicated the cube and set colors for two Diffuse BSDF shaders, then went ahead and made walls and a floor all sharing the same diffuse shader.  I made two windows to emit blue light.  The screenshot has gaps between the walls because of the setup:  I'm aware that it's considered very incomplete and many have come to terms with some amount of noise, but is this normal?  Furthermore, with default settings or not, I can't change the amount of noise produced.  Supposedly, using "progressively refine" in the rendering tab should make it refine itself indefinitely, however Cycles only counts to 10 refines and then stops, creating a render which is a pixel-perfect match of the ordinary rendering method when it's completed.  I understand that there are tricks that can be used to reduce noise, but at the cost of extra processing time and usually small quality conflicts, like blurring.  My question essentially boils down to is this Cycles' current limit?


Let $(X_1, \mathcal{F}_1)$, $(X_2, \mathcal{F}_2)$ be two measure spaces. Suppose $D_i$ is the generator of the $\sigma-$algebra $\mathcal{F}_i$, $i=1, 2$.   Question:(1) Is $D_1\times D_2=\{A\times B: A\in D_1, B\in D_2\}$ a generator of $\mathcal{F}_1\otimes \mathcal{F_2}$?  (2) What if in addition $D_i$ is closed under intersection?

Let $(X, \mathcal{J})$ and $(Y, \mathcal{F})$ be two measure spaces. Let us assume that $J$ is a collection of subsets of $X$ which generates $\mathcal{J}$, i.e. $\sigma(J)=\mathcal{J}$. Similarly, assume $\sigma(F)=\mathcal{F}$. Is it always true that $$ \sigma(J)\times\sigma(F)=\sigma(J\times F)? $$ Here, $J\times F$ is the set of all cartesian products of sets in $J$ with sets in $F$.   Please note: in the above expression the two product signs mean different things. On the left I am considering the product sigma algebra $\mathcal{J}\times \mathcal{F}$, while on the right I am considering the $\sigma$-algebra generated by the cartesian products of my ``elementary sets.''


I have created a model, in it there is a transparent object. I made it transparent by changing both the alpha values as well as the Blend Mode. My problem now is that I can't retain transparency when exported to an .fbx file. I have to re-change the Blend Mode each time after importing the .fbx. Can anyone please help me to retain transparency settings, so that as soon as I import the file, I get a transparent object the same way it was before export?  I am using eevee. if someone could help, i'll be really grateful.

I used node textures in a mesh I exported to .FBX.  I then imported it into Unreal Engine 4 and it didn't import any textures; I clicked the Upload Textures option in Unreal Engine.  Is there something I'm doing wrong or is it Blender?


I installed Ubuntu in a 50 GB partition. I felt so good with the system that I decided to use it as the main OS so I erased the other OS. I deleted everything in Windows partition. Now, how do I add those 110 GB to the Ubuntu's partition.  I am using Ubuntu 18.04.1, downloaded from the official website on a HP system.

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I am trying to kill all entities that are not a player and a sheep called test catch but I can't use   /kill @e[type=!Player,!sheep]   so how could it be done WITHOUT scoreboard because I don't want to keep doing scoreboard for everything that deserves and that doesn't. and please don't judge me because I don't want to use scoreboard.

I've asked this question towards a developer for Minecraft and I thought I'd ask here too since they might not see the question.  How do I select all but two types of entities in Minecraft?  For example, something like: /say @e[type=![Player,Item],r=50] (to clarify I also tried type=Item,Player, type=Item,type=Player etc)  Should select any entity that does not match players or items, so things like Creepers, Ghasts, XPOrbs, PrimedTNT and so on within a radius of 50 blocks and print them to the chat.  Instead it ignores one of the flags, and works with the other instead.


Is there a length limit for a URL (especially for an embedded image) in Google Sheets?  I'm trying to create a cell with an image by a specific URL, in the following way:  =IMAGE(URL)   It works at the creation moment, but a short time afterwards it's not showing the picture anymore. I checked a few times a day later, and the image was missing, although the URL is valid.  Tried to both give IMAGE a direct URL (with quote marks), and also pointing it to a cell that contains a URL.  https://lh3.googleusercontent.com/-mK3Eid7Vg8ytUbbe3W7x-0ZrFE_nXPMrYpIG8ZfhkCop1lSVv8PrY00YGrt_sqLOEaHnqdb0zRft-2YviQ1R_1HPkVxM9U8Ryb8pNFZzy-GHYHEBFWjUByFf-8ifYye1OqvL_Bo287cF6TPLJZx8l9zK6hB6TKVjDQdTqBv9g_vMoyH1oV_OzVPsXfGkqYSgENyviTXjvEeLZjv1HEIx0dFEMVxBULhdY6VaQgNcwHXiMiUf552Z-wA3AXLSA7vZ8d3oZgwb6cEB0d4JwwSGugR-wO0_QtMo6CZGuwe-gddNBiPEhCjs93UqzhAxAfYfC2NHEsgcQN7tor84CNRnbSUoxGh3Ee3YXMvzXlXRL9yWEdX2q7OgG7wzMz0sTEZt81BxlzVeY2g2tvHAB5Hp_HpzTEbGN0dBp3tMWuE-bkf3jbCHOGag70H8ti-8p82ZVjF6Evn9Wk8OZEhAcW9u_04DpTFrIQj_zUw3cl6E4BMkM3iVvFzoOdUNZC60O1ID453BEi9EWGP7_DneZ7-mjl2MFqinXM0GvhEMq4_NYljU-uNM704fOrD49O0GaGJatY7RfkRwocVc4ZTjcq_DF2ozhSeV8q5kbH1y7S_=w728-h947-no   - all worked on creation.  The URLs that I tested with, were 663 chars long.

I want to add an image stored in my Google Photos. How can I get the direct link to an image in my Google Photos? The links I copied are not direct.


Given infinite sets $X$ and $Y$ such that $X$ has strictly smaller cardinality than $Y$, is it the case that the power set of $X$ has strictly lower cardinality than the power set of $Y$?

The following is my rewrite of  for the following assertion :     For infinite sets $A, B$, $|A| = |B| \Longrightarrow  \require{cancel} \cancel{\Longleftarrow} |P(A)| = |P(B)|$.    $\bbox[2px,border:1px solid black]{\text{ Proof Strategem : }}$ We are given that $f :A \rightarrow B$, is a bijection. How do we construct a bijection between subsets of A and subsets of B? We need a rule whereby, if we take one subset of A, then we can use the rule to uniquely construct a unique subset of B. My intuition on this is to take all the elements of the subset of A, and map them under $f$ to elements of B, which will form a subset of B.  $\bbox[2px,border:1px solid black]{\text{ Proof : }}$  In mathematical notation, we define $g$ as:  $g : P(A) \rightarrow P(B)$ by means of $\color{#009900}{g(S) = \{f(x) : x ∈ S\}} \; \forall S \subseteq A$.  $\bbox[2px,border:5px solid grey]{\text{ $g$ onto ? }}$ For all $T \subseteq B$, does there exist $S \subseteq A$ such that $\color{#009900}{g(S) = \{f(x) : x ∈ S\}} \; = T$?  Since $f^{-1}$ exists, define $S = \{f^{-1}(x) : x ∈ T\}.$ We must prove $\color{#009900}{\{f(x) : x ∈ S\}} = T$.  $\bbox[5px,border:1px solid grey]{T \subseteq g(S)}$ Take $y \in T \iff  f^{-1}(y) ∈ S \iff  \color{ #FF4F00}{f}[f^{-1}(y)] ∈ \color{ #FF4F00}g[S] \iff y \in g[S]. $  $\bbox[5px,border:1px solid grey]{{g(S)} \subseteq T}$ Take $y \in g(S)$ which means there exists $x \in S \ni f(\color{#C154C1}{x}) = y $. Since $x \in S$ means there exists $t \in T \ni \color{#C154C1}{f^{-1}(t) = x}$, substitute this into the previous equation: $f(\color{#C154C1}{f^{-1}(t)}) = y \implies t = y $. Since $t \in T$, thus $y \in T$.  $\bbox[2px,border:5px solid grey]{\text{ $g$ 1-1 ? }}$ Suppose we have $G,H ⊆ A$ such that: $g(G) = g(H)$ which means $\{f(x) : x ∈ G\} = \{f(x) : x ∈ H\}$.  $\bbox[5px,border:1px solid grey]{\{f(x) : x ∈ G\}  \subseteq \{f(x) : x ∈ H\}}$ Take $g \in G \implies f(g) ∈ \quad g(G) = g(H) \quad \implies f(g) ∈ g(H)$. Thus there exists a $h ∈ H$ such that  $f(g) = f(h)$ $\implies g = h$ because $f$ is a bijection.  Since $g ∈ G$, thus $g ∈ H$.  We can prove the other direction by the same argument, just with $G$ and $H$ swapped around.  $1.$ In the proof for $g$ onto, how would you (fore)know (ie: divine or presage) to define $S = \{f^{-1}(x) : x ∈ T\}$?  $2.$ Would someone please explain the step $f^{-1}(y) ∈ S \iff  \color{ #FF4F00}{f}[f^{-1}(y)] ∈ \color{ #FF4F00}g[S] $?  $3.$ Are there easier proofs? The result seems intuitive but the proof is complex.  $4.$ Are there any pictures?  $5.$ My course doesn't include $ZFC$. So what's the intuition why ?


I have 2 HDD in my computer at the moment... One 2TB HDD that is running Windows 8 and one 1TB HDD that I would like to install Ubuntu on. I bought the second HDD so that the two don't have to conflict with each other at all!  How do I install Ubuntu onto my second HDD, without affecting my first, and then when I boot up my computer, how can I choose between which OS to use? I have seen it at a friends house: they have a black screen on startup which they can then choose whether they want Windows or Linux.

I have two hard drives. One is used for Windows and one is empty. I want to install Ubuntu on the empty hard drive. The Windows hard drive is disk0 in Windows and the empty hard drive is disk1. When I install Ubuntu and it asks where I want to install it, I choose "Something Else" but I am stuck there. What do I choose for "boot loader installation"?


This seems such a simple thing, I can't believe I can't work out how to do it or find the solution on the net. My partner's MACbook Pro (running 10.15) laptop was on the lock screen, and I stupidly pressed "switch user" and got to the switch-user screen with login user/password boxes and  "sleep", "restart", "shutdown" as other options.  Turns out she doesn't know her username (it is a work's machine) and has been logging in with a password only on the locksceen since receiving the machine.  So my simple question is, how do I return to the lock screen after "switching user"?  It would seem so obvious, but I'm in real trouble if I don't find the answer in the next 24 hours...

Is there a keyboard shortcut to lock the screen on macOS 10.14 Mojave like Command + L or something easy without setting up Hot Corners/Spaces etc.  The app  used to work fine till maOS High Sierra, but isn't starting up on macOS Mojave. It is showing this popup as soon as I try to run it:    Is there an app that works on Mojave which helps to customize the lock keyboard shortcut to Command+L? I am used to using Command+L on windows and older Mac OS (using "Lock me now" app).


I have a document library with multiple level folder structure, I want to fetch the server relative URL of individual folder by their name. For example: Folder structure in lib like this: Document Library > Folder => subfolder1 => subfolder2 If I pass Name='Folder', it should return /Document Library/Folder If I pass Name='subfolder2', it should return /Document Library/Folder/subfolder1/subfolder2 I tried below restAPI: _api/web/lists/GetByTitle('Documents')/RootFolder?$expand=Folders/Folders&$Filter=Name eq 'subfolder2'  But it returns extra folder details as well. Any extra parameter I can add to my rest URL to filter out extra folder details?

I have a site which is running under SharePoint 2013. Via REST I am trying to retrieve the file and folder directory for that site. There are several similar questions on this site related to recursively retrieving all of the files and folders for a given a folder:       The answers provided therein led me to the following URI:     /_api/web/Lists/GetByTitle('Documents')/Items?$expand=Folder&$select=Title,FileLeafRef,Folder/ServerRelativeUrl   Which from what I can tell does retrieve all of the files and folders from the given starting path.  However, I am missing something. When reading through the returned XML I cannot figure out where a given file goes. Meaning that I have info on how to retrieve file bros.pdf, but cannot determine that it is in the documents/super/mario/ folder.  For the file items I've tried to retrieve the ServerRelativeUrl property, but have not succeeded though the folders seem to. Is there some identifier in the XML that I am missing? When doing a recursive RESTful query how do I determine where a given file belongs?


I want to compute the following integral for an arbitrary $k \in \mathbb{N}$.  $$ \int_{-\infty}^{+\infty} \frac{\sin^k(x)}{x^k} dx$$  For $k = 2$ I computed:   $$ \int_{-\infty}^{+\infty} \frac{\sin^2(x)}{x^2} \, dx = $$  $$ \lim_{n\rightarrow\infty} \int_{-\frac{n\pi}{2}}^{+\frac{n\pi}{2}} \frac{\sin^2(x)}{x^2} \, dx = $$  (Substitute $x = \frac{nt}{2}$)  $$\lim_{n\rightarrow\infty} \int_{-\pi}^{\pi} \frac{\sin^2(\frac{nt}{2})}{(\frac{nt}{2})^2} \frac{n}{2} \, dt = $$  $$\lim_{n\rightarrow\infty} \int_{-\pi}^\pi \frac{2\sin^2(\frac{nt}{2})}{nt^2} \, dt = $$  $$\lim_{n\rightarrow\infty} \frac{1}{2\pi} \int_{-\pi}^\pi \frac{\pi\sin^2(\frac{t}{2})}{(\frac{t}{2})^2} \frac{1}{n} \left( \frac{\sin(\frac{nt}{2})}{\sin(\frac{t}{2})}\right)^2 \, dt = $$  $$\frac{f( 0^{+})- f(0^{-})}{2} = \pi$$  (where $\lim_{t\rightarrow0}\frac{\pi\sin^{2}(\frac{t}{2})}{(\frac{t}{2})^{2}} = \pi$ and $\frac{1}{n} (\frac{\sin(\frac{nt}{2})}{\sin(\frac{t}{2})})^{2}$ represents the Fourier-kernel)  Now for an arbitrary $k \in \mathbb{N}_{\geq3}$ I have tried to use the recursion formula for the sine, but I did not get very far.   I would appreciate any help or ideas!

(Edit: Thank you Vladimir for providing the references for the closed form value of the integrals. My revised question is then to how to derive this closed form.)     For all $n\in\mathbb{N}^+$, define $\mathcal{I}_n$ by the definite integral,   $$\mathcal{I}_n:=\int_{0}^{\infty}\frac{\sin^n{(x)}}{x^n}\mathrm{d}x.$$   Prove that $\mathcal{I}_n$ has the following closed form:   $$\mathcal{I}_n\stackrel{?}=\pi\,2^{-n}\left(n\sum_{k=0}^{\lfloor\frac{n-1}{2}\rfloor}\frac{(-2)^k(n-2k)^{n-1}}{k!(n-k)!}\right),~~\forall n\in\mathbb{N}^+.$$     Integrals of small positive integer powers of the $\operatorname{sinc}$ function come up on a regular basis here, but it occurred to me that while I probably know the derivations for the $1\le n\le 4$ cases like the back of my hand, I can't recall ever working the integrals wfor any value of $n$ higher than that. The values of the first four integrals are,  $$\mathcal{I}_1=\frac{\pi}{2},\\ \mathcal{I}_2=\frac{\pi}{2},\\ \mathcal{I}_3=\frac{3\pi}{8},\\ \mathcal{I}_4=\frac{\pi}{3}.$$  So I set out to first calculate $\mathcal{I}_5$ to see if any obvious pattern jumped out (and see if the trend of being equal to rational multiples of $\pi$ continued). I wound up getting frustrated and asking WolframAlpha instead. It turns that while the first four cases hinted very much at the possibility of a simple pattern relating the values of $\mathcal{I}_n$ for different positive integers $n$ (or possibly two separate patterns for even and odd $n$), the next few values most definitely did not:  $$\mathcal{I}_5=\frac{115\pi}{384},\\ \mathcal{I}_6=\frac{11\pi}{40},\\ \mathcal{I}_7=\frac{5887\pi}{23040}\\ \mathcal{I}_8=\frac{151\pi}{630}.$$  So my questions are, 1) is there a systematic way to compute these integrals for all $n$?; and 2) is there an elegant way to represent these values in closed form for general $n$?


Let $X$ be any arbitrary set. Set $X$ exists. Now assume on the contrary that $\mathscr{P}(X) \subseteq X$. Since $X \in \mathscr{P}(X) $, we have $X \in X$. But this is not allowed by the axioms. So we reach contradiction and hence,  $\mathscr{P}(X) \nsubseteq X$ for any set $X$. Is this a valid proof ?

Now let set $A$ be arbitrary. So set $A$ exists. Using axiom of pairing $\{A\}$ exists. And then using axiom of regularity, we can argue that $A \notin A$. So, there is some $x$ such that $x \notin A$. Is this a valid proof ? Thanks


Let $\{f_k\}_k\in L^{1}_{loc}(\mathbb R)$ be a sequence of real value functions such that $\mathrm{supp}f_k\subset \{|x|\leq\frac{1}{k}\}$ and $\int f_k(x) dx = 1 \,\, \forall k$.     How to prove that $\{f_k^2\}_k$ doesn't converge in distribution? That is, for some $\phi\in C^{\infty}_c(\mathbb R)$, $\lim_{k\rightarrow \infty} \int f_k^2(x)\phi(x) \,dx $ doesn't exist.   Intuitively I tried letting $F_k(x)= f_k(1/k)/k$ just like when dealing with dirac funtion, then get $\int F_k(x)\, dx =1$ and $\int f^2_k(x)\, dx= k\int F_k^2(x)\, dx$, but it doesn't seem working.

Let $\{f_k\}_{k=1}^\infty\in L^{loc}_1(\mathbb R^n)$ be a sequence of real value functions such that  $\mbox{supp}(f_k)\subseteq\{|x|\leq k^{-1}\}$, $\quad \int f_k(x)dx=1$ $\quad for\quad all \quad k=1,2........$  show that the sequence $\{f_k^2\}_{k=1}^\infty$ does not converge in $\mathscr{D}^\prime(\mathbb R^n)$ $as \quad k\rightarrow \infty$


I'm moving into a new house. We have pretty much thrown out all of the bed furniture's and have not seen any bugs in the sheets or anything like that.  But, while preparing for painting, I saw this little guy on the wall and I've never seen one of those before.  Know what it is?  Is it a bed bug?    The plastic thing you see here is an electrical outlet wall plate. I would say the insect is about 2 mm. I live in Quebec, Canada  (Edit: i understand there is  like mine but his pictures show an adult bed bug while my pictures show what I think is either a nymph or a book lice or something else). Thanks!

I have a large wooden cutting board which is used in my kitchen mainly for preparing egg pasta. The wood type is Populus (poplar or aspen or cottonwood).  The main ingredients used with the cutting board are: flour (mainly soft wheat flour), hens' eggs, white sugar, butter, and baking powder.  After the food preparation, the cutting board is cleaned by scraping away the ingredients remains.  The board has some cracks and some small unknown insects are living inside the cracks.   The board has also a lot of holes due to woodboring beetles but I think the woodworms operated long time ago and they no longer live in the cutting board.  The unknown insect has an approximate length of 1 mm (along the direction of their movements) and a width of 0.3 mm. The unknown insects do not have wings, they just walk. I am not able to see how many pairs of legs they have.  The color of the insect is pale brown.  The cutting board was free from these unknown insects some months ago but then they appeared.  My questions:   What insects are they? Are these insects poisonous to humans? How can I get rid of them?   Update  The unknown insects could be Acarus siro, I will try to get a picture of the insects.  Update 2  Here is a picture. The bottom part of the image is a one Euro coin, the top part of the image is a caliper (each bright area is one mm tick).   Some more pictures:


I need to programmatically list all the currently in progress bulk api jobs. I don't see any API methods available to do this.  The goal here is to be able to wait till there are no in progress bulk api jobs and then kick off a new one.  This is not a duplicate. I don't really care if I use APEX or the bulk api or what I use, but I need to be able to get a list of all jobs or ideally of all in progress jobs. Once I have the job ID I can get all the info I need. What I don't know how to do is get a list of all bulk api jobs.

I have a requirement where, we need to send an Email on the status of failed Bulk Data Load jobs. But I am not sure the Object Name or how to refer those jobs programatically in my APex code. When I use 'AsyncApexJob', it's referring to Scheduled Apex Jobs. But I want the reference of Bulk Data Load Jobs. (Bulk Data Load jobs will be submitted by Mule ESB process using Salesforce Connectors.) Any info on this helps. Thanks.


I got 3 appimage I'd like to launch via the Ubuntu dock on 20.04. I've manage to add them to the dock, with the correct icons I've downloaded apart. I'm sure it is possible to find the icon in the appimage, I've to check.  My issue is, when I click on the launcher (which works), the dock adds a new instance of the launcher, so that I've 2 launchers (one is permanent, the one I created and the other is temporary and will be removed when the application is closed).  Is there a mean to avoid the second temporary launcher to be created? Appimage concerned are CURA, REPETIERHOST, PRUSASLICER, all in last available version.

I'm using Ubuntu 17.10 with GNOME shell and Numix-Circle icon theme.   When I hover over the Numix icon for Nightly Web Browser, which is pinned to the dock I get the title "Nightly Web Browser".      But when I launch the program, another icon pops up at the bottom, with the name "Nightly".


I'm not sure if this is a problem being caused by Windows 8, the asus power-management programs, or what. Whenever my screen is displaying something darker, specifically the Steam client or in games/movies/other media, the screen dims, and when i go back to a brighter program like skype or firefox, it brightens.   I have disabled adaptive brightness multiple times, and it claims to be off. My power plan should have the screen remaining at 100% brightness all the time, and it doesn't put itself to sleep or anything. It's only when my screen attempts to display darker colors, it also dims.   It's becoming a problem in games with bright flashes because the entire screen will brighten and dim back and forth repeatedly.   Is there a setting I have missed?

I am not talking about adjusting screen brightness through power management (this is a laptop), I'm not talking about how the screen brightness setting may be different between 'plugged in' and 'battery powered', and unplugging the laptop will suddenly change the brightness. I'm talking about:  I have a Dell XPS 15 (L502X), and with intell hd graphics driver installed (from a vanilla win7 64 bit install), I start to see a brightness change. (This is also before the nvidia driver install).  I set my desktop to black, and open notepad, fullscreen. Now the entire screen is a bright white. I then alt-tab back to desktop, all black.  This is the interesting part:  I alt-tab back to notepad (all white, fullscreen), and the brightness of the white slowly, every so slightly, incrementally steps up (less than even one brightness adjust as you would do via the power settings). Then you swith back to the black desktop, and barely you can tell it steps back down (the backlight on the black grows a bit darker). It is a small change, but noticeable in a dark room. Again back to white, and a step up to a brighter white.  It. drives. me. crazy. :)  It is very annoying googling for info (everyone has something about power management). I can't find any setting in the intel hd graphics properties that affects this. Oddly enough, I have an older install of windows on this same machine which doesn't do it, I fixed it once about a year ago and I can't remember how I did it (I work on quite a few pc's, I THOUGHT I tweeked something in the intel hd graphics properties, but nothing seems to stick this time).   What is this feature called? How do I disable it?   EDIT  This does behave a lot like the automatic brightness adjustment that my smart phone exhibits. Ironically, that annoyed me as well (fixed with root and app)  I have tried to disable this feature, but here is a screenshot of my "Power" tab:    // The brightness feature is missing  I'm going to check what this tab looks like on my other disc (where I believe i once 'fixed' this)  EDIT 2  Turns out it was in the same view, but you have switch to change the power source to 'on battery' and disable "DIsplay Power Saving Technology"    Thank you.


As per title - I have a server running wherein I can access index.html placed in the document root (/var/www/html), but not any subdirectories within the document root.  Permissions on root index:  $ namei -l /var/www/html/index.html f: /var/www/html/index.html dr-xr-xr-x root   root   / drwxr-xr-x root   root   var drwxr-xr-x root   apache www drwxr-x--- myuser apache html -rwxr-x--- myuser apache index.html   Permissions on subdirectory index:  $ namei -l /var/www/html/foo/bar/index.html           f: /var/www/html/foo/bar/index.html dr-xr-xr-x root   root   / drwxr-xr-x root   root   var drwxr-xr-x root   apache www drwxr-x--- myuser apache html drwxr-x--- myuser apache foo drwxr-x--- myuser apache bar -rwxr-x--- myuser apache index.html   Security context info on /var/www/html:  $ ls -Z /var/www/html drwxr-x---. myuser apache unconfined_u:object_r:httpd_sys_content_t:s0 cszg -rwxr-x---. myuser apache unconfined_u:object_r:httpd_sys_content_t:s0 index.html   Security context info on /var/www/html/foo/bar:  $ ls -Z /var/www/html/foo/bar                         -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 3rdpartylicenses.txt -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 es2015-polyfills.24633e0ae24ffe204041.js -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 favicon.ico -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 index.html -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 main.38de9b2b74351642ba79.js -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 pdfjsWorker.382cb0cf8fa9c06b8500.js -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 polyfills.e1e93dfb20909209aa48.js -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 runtime.1f744383c7edc51f6732.js -rwxr-x---. myuser apache unconfined_u:object_r:user_home_t:s0 styles.9e51190222492c49b9b3.css   Finally, here's the relevant parts of httpd.conf:  User apache Group apache  DocumentRoot "/var/www/html"  <Directory />     AllowOverride None     DirectoryIndex index.html     Require all denied </Directory> <Directory "/var/www/html">     Options FollowSymLinks     Require all granted </Directory>   The error logs indicate this is a permissions problem (AH00132), but as far as I can see the permissions are exactly the same for the root index and the subdir index?

I've got this one file, favicon.ico. It's actually a large group of nested files, but purely for example, just this one.  If I do cp favicon.ico favicon2.ico, Apache can read the second one just fine.  If I do mv favicon.ico favicon3.ico, Apache throws a 403 on favicon3.ico.  If I su apache, I can read the file as apache.  stat says both files are identical, except for the inode number.  Is there some hidden flag somewhere or something that I'm missing? I've never seen anything like this.  error_log says (13)Permission denied: access to /favicon3.ico denied


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?


All dictionaries I consulted say that "nog" is not an English word.   （self-made)   Will this kind of entanglement of tenses be acceptable for English? At first, I used past tense, then switched to present tense immediately. But I think it fits well into the reality,my action of consulting a dictionary has become the past, whereas the dictionaries themselves still remain the same, and say the same thing about that word.

I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense?


How would you describe someone doing something that is for the common good (well-intended), but is very inefficient, and possibly even harmful to what they're trying to achieve?  e.g.   The new mayor is finally serious about climate change, but he wants charge all petrol cars $2000 a month, starting today! To incentivise more women to join our company, the CEO is offering double the men's salary for women who apply for the same role. The IT department so paranoid about company security that every website must first be signed off by the IT manager before entering.   Pretty much situations that make you think "I agree with what you're trying to do, but that's not how you do it! You'll only end up upsetting people, and make them NOT want to support your ideals."  I've looked at: Counterproductive, hindering, Barking up the wrong tree (too focused on being wrong), misguided, off the mark, carry water in a sieve, bikeshedding, etc., but nothing fits.  Thanks in advance!

Consider the case where a professor is erasing a board and one of the teaching assistant tries to help him by erasing part of the board.   Unfortunately, while trying to pick up the eraser, the teaching assistant bumps into the professor and they both drop their erasers.  An outside observer sees this and says the TA is ______, rather than helping.   The missing word or phrase would capture the good intentions but also express the fact that the intended help had the opposite of the intended effect.  In Mandarin Chinese, the phrase 帮倒忙 comes to mind, but the Google translation "disservice" does not quite capture it.


When I click some links in chrome (trusted websites), I get redirected to 'spam' websites that say "your computer has viruses" or something stupid like that. How do I stop it from doing this? I have run  numerous virus removal tools including:  AVG  Norton  Malwarebytes  Trojan Killer  Google's software removal tool  Adwcleaner  Ccleaner  Windows Defender  I also reset chrome  I did find a number of viruses, but got rid of them. This is still happening and is starting to get annoying. Anyone know how to fix this?

What should I do if my Windows computer seems to be infected with a virus or malware?  What are the symptoms of an infection? What should I do after noticing an infection? What can I do to get rid of it? how to prevent from infection by malware?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


n = int(input())  # number of strings for _ in range(n):     string = input()     print(string[::2], string[1::2])  # print even letters, odd letters   Why inside of string[1::2] has a 4 property. So must be 3 property start, end, increment step. And the code running with nothing wrong. Can explain why the string had 4 property not 3, it same thing or different?

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


I am not able to delete one folder on the desktop....if i try to delete i get the message as "Access is denied".  I tried running the command from cmd prompt as an administrator:   RD /S /Q "C:\Users\username\Desktop\folder"   Still the same error.  I tried to change the permissions on the folder but still I am not able to do the changes I again get access denied. Any help will be much appreciated.

There's a folder on my desktop called like 'example' and when I try to delete it it says "You require permission from the computer's admistrator to make changes to this folder" when checking the properties; the Current owner says "Unable to display current owner."  I have tried many solutions found online, including enabling & signing into the adminstrator account, but haven't been able to fix it. My situation is extremely similar .  I can't even open the folder. I am running Windows 7 x64 Home Premium. I can't do anything to the folder because I need permission from my 'computer administrator' It's extremely weird, and I can't fix it. Thanks in advance!  UPDATE: Yes, I'm adminsitrator on my computer.


Someone  in one of my posts.  Much appreciated, but it was just deleting one character. How could he do that? I thought there was a minimum of 6 characters for an edit to go through? (A rather silly rule if I may say so, but how did the user bypass the rule?)

I'm currently a >20K user, with the  badge on Super User (in short, I don't actually have any reason to edit, other than an error of some sort bugging me). I just did a one character edit (bad geek, no cookie) on  - primarily because I recall this happening before.  As I understand it, this is a minor edit and should have been automatically rejected. It's however an accepted edit.  Did the edit get counted as a legitimate 7-8 character edit, or is there something else at play here?


I am trying to make a set of flashcards using beamer. I want the page size to be well suited for my phone. But I am not able to change the page size of the beamer presentation. Can you suggest something?

In the Beamer class, is it possible to change the height of a page and frame? I'm producing a document for web display and would like it to be on a continuously scrolling format so I would like to have frames with height 4 times taller than the current default height. I tried something like the MWE below but I get "Missing \begin{document} error"...    \documentclass{beamer}   \usepackage[papersize={12cm,30cm}]{geometry}   \begin{document}    \begin{frame}{test}    \end{frame}{test}    \end{frame}   \end{document}


Black holes are caused by massive curvature of the fabric of space-time. Is it right in believing theoretically that forces of electromagnetic origin could also lead to distortion of the fabric of space-time, (though it may not be as tremendous as the extent to which distortion is brought about by gravitational forces)? If it is right, then could we venture on the existence of tiny holes in space-time due to electromagnetic effect on space-time fabric?

It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to other forces or aspects of bodies?  Why isn't it that there are curvatures related to the charge of a body or the spin of particles or any other characteristics?


As a novice I am trying to understand a particular part of len() . friends = ["Alice", "Bob", "Carl", "John"] print(len(friend))                         # answer = 4 (number of items in list) friend.extend([1, 2, 3])   print(len(friend))                         # answer = 7 (where does the "7" come from and what is it                                             # telling me?

What's the difference between the list methods append() and extend()?


I am looking for good solutions to this problem. Could you please help me with this? Any solution would be appreciated.  Let $\mathscr{G}$ be the smallest $\sigma-algebra$ on $\mathbb{R}$ containing all single points. Let f(x) be a function that is measurable with respect to $\mathscr{G}$, that is, for any Borel set B on $\mathbb{R}$, $f^{-1}(B) \in \mathscr{G}$.    Show that there is a countable set A on $\mathbb{R}$ such that f is a constant on $\overline{A}$ (the complement of A).

I found a interesting problem that says: Let $(X,S)$ be a measurable space where $X=\mathbb R$ and $S$ is the countable co-countable $\sigma$-algebra in $\mathbb R$, i.e. $S=\{A\subset\mathbb R: A\ \lor\ \mathbb R-A\ \ is\ finite\ or\ countable\}$. So the point is to describe the S-measurable functions $\ f:X\to \Bbb R^*$, where $\Bbb R^*$ are the extended real numbers.


I did some mathematical induction problems on divisibility   $9^n$ $-$ $2^n$ is divisible by 7. $4^n$ $-$ $1$ is divisible by 3. $9^n$ $-$ $4^n$ is divisible by 5.   Can these be generalized as $a^n$ $-$ $b^n$$ = (a-b)N$, where N is an integer? But why is $a^n$ $-$ $b^n$$ = (a-b)N$ ?  I also see that $6^n$ $- 5n + 4$ is divisible by $5$ which is $6-5+4$ and $7^n$$+3n + 8$ is divisible by $9$ which is $7+3+8=18=9\cdot2$.  Are they just a coincidence or is there a theory behind?  Is it about modular arithmetic?


While not all yokai wear masks, many do, such as the 3 yokai serving as Natori Shuuichi's shiki. Many of the other yokai that meet Natsume also wear masks.  In the story where Natsume was taken by some yokai to be presented to their boss, after he broke out of his confinement, he wore a mask to disguise himself. He also wore a mask for the same purpose when he joined the festival to take a magical kimono that enables the wearer yokai to be seen by humans. Thus it can be concluded that when a human wears a mask, it is to prevent yokai from learning that they are human.  Yet, why do yokai wear masks? What is the mythological background behind yokai wearing masks?

In Natsume's Book of Friends, some of the human-looking Youkai wear masks, or at least obscure their sight. For example:   Tsubame   Hotaru   Hiiragi   Tsuyukami   Sasago     I am wondering if there is a reason for this as none of these Youkai seemed to be affected by their obscured vision. For Tsubame and Hotaru, they are both shown to be able to show their full face. And for Kiiragi, after she was attacked, we can see one of her eyes though her broken mask and there seemed to be nothing wrong with it.


I am retrieving object arraylist of a recyclerview item ,my function on the fragment is updated ,but my arraylist on oncreateview remains null, how can i observe the updated value on realtime ?   public void gettolist( ArrayList<Profilefire> profilesingle) {     profilestoinvoice=profilesingle;     Log.v("listtocheck",profilestoinvoice.size()+" ");  }   -----> this shows size is updating    facture.setOnClickListener(new View.OnClickListener() {         @Override         public void onClick(View v) {               Log.v("listtocheck",profilestoinvoice.size()+" ");          }     });   ------> but here on the main onCreate method where i am handling my button click,the array keeps showing null    @Override   public void onBindViewHolder(@NonNull UserHolderFacture userHolderFacture, int i) {     final Profilefire profilefire =profiles.get(i);     userHolderFacture.updateUI(profilefire);      if (!isSelectedAll) userHolderFacture.checkall(false);     else userHolderFacture.checkall(true);        userHolderFacture.getFacturecheck().setOnCheckedChangeListener(new CompoundButton.OnCheckedChangeListener() {         @Override         public void onCheckedChanged(CompoundButton buttonView, boolean isChecked) {              if(isChecked){                 profilestoinvoice.add(profilefire);                 invoicingFragment.gettolist(profilestoinvoice);              }else {                  profilestoinvoice.remove(profilefire);                  invoicingFragment.gettolist(profilestoinvoice);              }            }     });    }

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


I was trying to overload controller method or action I am able to write controller action and compile but still I am not getting result.     public ActionResult Contact()     {         ViewBag.Message = "Your contact page.";          return View();     }     public ActionResult Contact(string str)     {         ViewBag.Message = "Your contact page by overloaded method";          return View();     }   but still I am getting following Error Server Error in '/' Application

I'm curious to see if you can overload controller methods in ASP.NET MVC.  Whenever I try, I get the error below.  The two methods accept different arguments.  Is this something that cannot be done?     The current request for action 'MyMethod' on controller type 'MyController' is ambiguous between the following action methods:


I was just wondering if it would be possible to put 12.04 on my Dell Studio 1558. I was poking around the Ubuntu website, and other websites and was unable to find any specific drivers for this model of laptop.  Does anyone know where I could find the appropriate drivers so I can get a better grip if ubuntu is right for me?  Thank you

I want to ask a question I am a new user to Ubuntu and I am    going to install it on my PC and Remove Windows as I have read a lot    about Ubuntu and how it's solid based system and that it's more    stable and stronger but to be honest I am a bit afraid of installing    it as I don't have the drivers CD so Does Ubuntu need drivers or not    ? and how do I check that all the drivers are installed and updated    and work correctly ? and If I want to install a driver will Ubuntu    help me to search for it and install it ?  and will Ubuntu install the sound card . the internet card and the graphics etc. automatically or not waiting for your replies    cheers :)


From , Carmichael numbers are (1) "composite numbers $n$ which divide  $b^n  −  b$  for every integer  $b$ .   OR equivalently (2) Carmichael numbers have the property that  $b^{n  − 1}  ≡   1  \pmod n$  for all bases  $b$  coprime to  $n$."  So essentially my question is: why  does the second definition requires $b$ to be coprime to $n$ and the first doesn't?  I tried to go from $b^{n-1} \equiv 1 \pmod n$ (with $b$ coprime) to $b^n \equiv b \pmod n$ for ANY $b$  but I hit a lot of dead ends.

In Burton's Elementary Number Theory, when introducing absolute pseudoprimes (also called Carmichael numbers), the author states that they are composite numbers $n$ such that $a^{n-1} \equiv 1 \pmod n$ for all integers $a$ with $\gcd(a,n) = 1$.   When showing that 561 is an absolute pseudoprime, he then concludes that $a^{561} \equiv a \pmod{561}$ for all $a$.   I searched a bit on the internet, and it seems that these two are actually equivalent definitions of a Carmichael number. However I have not been able to find a proof; the fact that the implication in the title of the post is stated so plainly in my textbook makes me think it is quite simple to see, but I can't seem to understand the argument.


No matter how I try I end up with nodejs 4.2.6. Is it a joke?  $ nodejs -v v4.2.6   Uninstall and 4.2.6 returns like a virus  $ sudo apt-get install nodejs Reading package lists... Done Building dependency tree        Reading state information... Done The following packages were automatically installed and are no longer required:   gyp libjs-inherits libjs-node-uuid libjs-underscore libuv1-dev Use 'sudo apt autoremove' to remove them. The following NEW packages will be installed:   nodejs 0 upgraded, 1 newly installed, 0 to remove and 73 not upgraded. Need to get 0 B/3 161 kB of archives. After this operation, 13,2 MB of additional disk space will be used. Selecting previously unselected package nodejs. (Reading database ... 434000 files and directories currently installed.) Preparing to unpack .../nodejs_4.2.6~dfsg-1ubuntu4.1_amd64.deb ... Unpacking nodejs (4.2.6~dfsg-1ubuntu4.1) ... Processing triggers for doc-base (0.10.7) ... Processing 1 added doc-base file... Registering documents with scrollkeeper... Processing triggers for man-db (2.7.5-1) ... Setting up nodejs (4.2.6~dfsg-1ubuntu4.1) ... update-alternatives: using /usr/bin/nodejs to provide /usr/bin/js (js) in auto mode

I noticed over at the  website that node is currently at v 0.12.0.  Can someone let me know how to install the latest version of node together with npm (terminal commands please)?


my method is supposed to compare a cat's name from the entire cat array. This is because my array will have nulls between created objects. for example [0(cat 0), 1(cat 1), 2(cat 2), 3( empty null), 4(cat 4), 5(cat 5)] I think the reason I am getting a null pointer exception is because I try to return a null and compare it to the param (String catName). How could I avoid this while still searching the entire array? /**  * @param catName to search for cat name  */ public void searchCatByName(String catName) {      if (cats[0] != null) {          if(catName != null) {             int index = 0;             while (index < cats.length) {                                   if(cats[index].getName() != catName) {                      if(index == cats.length - 1) {                          System.out.println(catName + " was not found in the cattery.");                         break;                     }                     index++;                 }                  else {                      System.out.println(cats[index].getName() + " is in cage " + index);                     break;                 }              }         }     } }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I am from Minnesota and have always pronounced GROCERY as GROSH-RY. I teach grammar and pronunciation online, and I recently encountered much controversy regarding what is the correct or incorrect pronunciation of this word. According to  which offers a multitude of real-life examples, my pronunciation is not in the minority. If it is so widespread, why insist that it is wrong? If English is a fluid language, and a high percentage of otherwise well-educated people pronounce a word in a specific way, wouldn´t that make it correct?

I caught myself pronouncing the "c" in "grocery" as an "sh" sound.  Is this commonplace/accepted, or is it perhaps geographic?  Does this occur with "c" in other words?  As background, I was raised in Cincinnati, OH and now live in western New England.


Ubuntu shows only login console but no gui login. Even though I entered right login user name and password, I can't login. I can't do anything with this. How can I resolve this problem?

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


I am a green card holder based on asylum and hold a US refugee travel document. Can I travel to Hungary visa-free for a short stay?

I just want to double check to make sure I won't run into any issues at the border of entry.  I'm a permanent resident of the USA with a green card and I have a travel document issued by the USA (I-571). Will I have any issues traveling around in the Schegen countries?  Do I need a visa? Do I have to pay any fees?


For example:   I have a sister named Charlotte Martin has a brother named William Charlotte is married to Martin   Martin is my brother-in-law, but what is William to me?  I originally posted  on English.StackExchange. A commenter referred me to ask it on this stack.

Here at the Genealogy and Family History Stack Exchange we see many questions about relationship mapping which is also known as:   relationship calculation kinship terminology etc   If you are just trying to understand how to calculate "cousins and removes" then  provides an excellent guide.  However, if you are seeking an English term for a more complicated relationship between two members of an extended family, rather than asking a question like:          site users are encouraged to first review the answers below.    Note: This Q&A arises from  and is set to  to help make it canonical.


Okay, so I followed some tutorials, but I could not get it to work still...... I just need a walkthrough or something for me and my Hp windows 8.1 laptop.

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?


I am entering the details (Username and password) in the login page and then I am displaying all the details of all the users registered in the application in a ListView.  I am populating the ListView with an ImageView , username and password.  When I am redirecting the page from the Login page to the HomePage (in which I am having the ListView) I am getting this error of null exception.  Homepage.java  public class HomePage extends AppCompatActivity {       @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);          ListView listView=(ListView)findViewById(R.id.listUserDetails);          DBhelperClass obj1=new DBhelperClass(this);         Cursor f=obj1.display();          AdapterForHomePage obj=new AdapterForHomePage(this,f,0);         listView.setAdapter(obj);      } }   AdapterForHomePage.java (this is a custom CursorAdapter for populating the ListView).  public class AdapterForHomePage extends CursorAdapter {       LayoutInflater inflater;      public AdapterForHomePage(Context context, Cursor c, int i) {         super(context, c);         inflater=LayoutInflater.from(context);     }      @Override     public View newView(Context context, Cursor cursor, ViewGroup parent) {          View v= inflater.inflate(R.layout.homepagelist,parent,false);         return  v;      }          @Override         public void bindView(View view, Context context, Cursor cursor) {          TextView name=(TextView)view.findViewById(R.id.displayName);         TextView emailId=(TextView)view.findViewById(R.id.displayEmail);            // ImageView phoneCall=(ImageView)view.findViewById(R.id.displayCallImage);             TextView phoneNumber=(TextView)view.findViewById(R.id.displayPhone);                String n=cursor.getString(cursor.getColumnIndex("NAME"));             String e=cursor.getString(cursor.getColumnIndex("EMAILID"));             String p=cursor.getString(cursor.getColumnIndex("PHONENUMBER"));              name.setText(n);             emailId.setText(e);             phoneNumber.setText(p);          } }   My DBhelper  This is the display function which is called in the HomePage.java class  public Cursor display()     {         SQLiteDatabase db=this.getReadableDatabase();         Cursor cs=db.rawQuery("SELECT * FROM USERINFO",null);         return cs;       }   The error which I am getting is :  Java.lang.RuntimeException: Unable to start activity     ComponentInfo{com.example.hsports.bandpop/com.example.hsports.bandpop.HomePage} java.lang.NullPointerException: Attempt to invoke virtual method 'void     android.widget.ListView.setAdapter(android.widget.ListAdapter)' on a null object    reference   I am getting the error in the CustomAdapter object. How can I resolve this problem?


Let $F$, $K$, and $L$, be fields, and suppose we are given maps $F\to K$ and $F\to L$. I claim that there exists some field $\Omega$, and maps $K\to\Omega$ and $L\to\Omega$ such that $F\to K\to\Omega = F\to L\to\Omega$.  Why is this true though?

Let $K$ be a field having two field extensions $L\supseteq K$ and $M\supseteq K$. Does there exist a field $N$ along with embeddings $L\to N$ and $M\to N$, such that the diagram $$     \require{AMScd} \begin{CD}     K @>>> L\\     @V  V V @VV  V\\     M @>>> N     \end{CD} $$ is commutative? To put it less formally, do $L$ and $M$ have a common field extension $N$ (with $K$ lying in the intersection)?  If yes, consider this side question (but do leave an answer even if you can only answer the main question!): Does the above property of fields generalise to the following, stronger property? Let $p$ be either $0$ or a prime number. Does there exist a sequence of fields $$ \mathbb F_p = L_0\subseteq L_1\subseteq L_2\subseteq L_3\subseteq L_4\subseteq\cdots$$ (where I use the convention $\mathbb F_0 = \mathbb Q$) such that any field $K$ of characteristic $p$ has an extension field among the $L_\alpha$? This sequence should be understood as enumerated by ordinal numbers. In other words, what I need is a function that assigns to each ordinal number $\alpha$ a field $L_\alpha$ containing all $L_\beta$ with $\beta < \alpha$. (Intuitively, I suspect that this might depend on the Axiom of Choice.)  If the second property holds, it shows that you can essentially only extend a field in one "direction." It also shows that the class (it is obviously not a set) $\mathbb M_p = \bigcup_\alpha L_\alpha$ is a field (class). We can define all the usual field operations (addition, multiplication, division) here since all pairs of elements lie in $L_\alpha$ for a sufficiently large $\alpha$. This "monster field" of characteristic $p$ then contains all other set fields of that characteristic.


I noticed something odd while messing around on my calculator.  $$\lim_{n\to \infty} \cos^n(c)=0.7390851332$$ Where $c$ is a real constant.  With $$\cos^n(c) =\underbrace{\cos \circ\cos \circ\cos \circ \cdots \circ \cos \circ \cos}_{n \text{ times}}(c)$$  My calculator is in radians and I got this number by simply taking the cosine of many numbers over and over again. No matter what number I use I always end up with that number. Why does this happen and where does this number come from?

There is an unique solution with $x$ being approximately $0.739085$. But is there also a closed form solution?


For any $m×n$ matrix $A$, where $n>m$ and $\mathrm{rank}(A)=m,$ show that $$\mathrm{rank}(I_n-A^TA)-\mathrm{rank}(I_m-AA^T) \geq n-m$$   Using the hint by Omnomnomnom, I've known that $AB$ and $BA$ have the same nonzero eigenvalues with the same geometric multiplicity when they are both square. It seems that I should consider geometric multiplicity of eigenvalue $1$ of $A^TA$ and $AA^T$, but I couldn't see how to make it. Any help will be appreciated.

Let $A$ be $m \times n$ matrix, and $B$ be $n \times m$ matrix. Then  Show that $$\det\begin{bmatrix}I_{n} & B\\ A & I_{m} \end{bmatrix}=\det\begin{bmatrix}I_{m} & A\\ B & I_{n}\end{bmatrix}$$  Show that $$\det(I_{m}-AB)=\det(I_{n}-BA)$$  Is it true that $I_{m}-AB$ and $I_{n}-BA$ have the same rank?    Someone please show me a way to start proving. I tried to use formulas for calculating block matrix with square matrices, but it didn't help me on this one. I really don't know where to start.


Quick summary: Forwarded port works from the outside world, but from the internal network using the external IP the connection is refused.  This is a simplified situation to make the explanation easier:  I have a computer that is running a service on port 12345. This computer has an internal IP 192.168.1.100 and is connected directly to a modem/router which has internal IP 192.168.1.1 and external (public, static) IP 1.2.3.4. (The router is TP-LINK TD-w8960N) I have set up port forwarding (virtual server) at port 12345 to go to port 12345 at 192.168.1.100.  If I run telnet 192.168.1.100 12345 from the same computer everything works. But running telnet 1.2.3.4 12345 says connection refused. If I do this on another computer (on the same internal network, connected to the router) the same thing happens. This would seem like the port forwarding is not working. However...  If I run a online port checking service on my external IP and the service port it says the port is open and I can see the remote server connecting and immediately closing connection. And using another computer that is connected to the internet using a mobile connection I can also use telnet 1.2.3.4 12345 and I get a working connection.  So the port forwarding seems to be working, however using external IP from the internal network doesn't. I have no idea what can be causing this, since another setup very much like this (different router) works for me. I can access a service running on a server from inside the network both through the internal and external IP.    Note: I know I could just use the internal IP inside of the network to access this service. But if I have a laptop that must be able to do this both from inside and outside it would be annoying to constantly switch between 1.2.3.4 and 192.168.1.100 in the software configuration.    Router output:  > iptables -t nat -L -n Chain PREROUTING (policy ACCEPT) target     prot opt source               destination          ACCEPT     all  --  0.0.0.0/0            224.0.0.0/3          DNAT       tcp  --  0.0.0.0/0            0.0.0.0/0           tcp dpt:25 to:192.168.1.101  DNAT       udp  --  0.0.0.0/0            0.0.0.0/0           udp dpt:25 to:192.168.1.101  DNAT       tcp  --  0.0.0.0/0            0.0.0.0/0           tcp dpt:110 to:192.168.1.101  DNAT       tcp  --  0.0.0.0/0            0.0.0.0/0           tcp dpt:12345 to:192.168.1.102  DNAT       udp  --  0.0.0.0/0            192.168.1.1         udp dpt:53 to:217.118.96.203   Chain POSTROUTING (policy ACCEPT) target     prot opt source               destination          MASQUERADE  all  --  192.168.1.0/24       0.0.0.0/0             Chain OUTPUT (policy ACCEPT) target     prot opt source               destination

This is a  about Hairpin NAT (Loopback NAT).   The generic form of this question is:  We have a network with clients, a server, and a NAT Router. There is port forwarding on the router to the server so some of it's services are available externally. We have DNS pointing to the external IP. Local network clients fail to connect, but external work.   Why does this fail? How can I create a unified naming scheme (DNS names which work both locally and externally)?   This question has answeres merged from multiple other questions. They originally referenced FreeBSD, D-Link, Microtik, and other equipment. They're all trying to solve the same problem however.


I am trying to follow this , but I am encountering some problems with how it is displayed.  I have the following CGI script located in a folder scripts in my html folder that Apache serves to me.     #!/usr/bin/perl  # hello.pl -- my first perl script!  print "Content-type: text/html\n\n";  print <<"EOF";    <TITLE>Hello, world!</TITLE>
Hello, world!
    EOF   When I run this script in the console (with ./hello.cgi), I get the following correct output:  Content-type: text/html     <TITLE>Hello, world!</TITLE>
Hello, world!
      I am trying to access this on my ec2 instance with a URL like this: http://<ec2-address>.compute-1.amazonaws.com/scripts/hello.cgi. However, this is what I see:    It is printing out the HTML correctly, but it is also printing everything else out as well.  What am I doing wrong here? Why am I getting a different output when I run the script on the server versus when I run it on the console in the server?

I would like to configure Apache 2 running on Kubuntu to execute Perl CGI scripts. I've tried some steps that I came across by googling, but nothing seems to work.  What is the right way of achieving this?


I've killed a whole lotta monsters in the RUINS and I'm on lvl 3 already. I'm just where you pick up the Toy Knife but I still haven't had the 'but nobody came' encounter yet. Also, I've gone back but had no more encounters.  What should I do?

So, I have just completed the True Pacifist run in the game Undertale, and am now attempting a Genocide run. I understand that I need to kill everything, but I'm not sure if I've activated Genocide mode yet. How long does it take for the save points to start telling me how many enemies I have left to kill in the Ruins? And for that matter, how many enemies are in the Ruins?


I've come across a weird paradox that I can't answer, I will explain it via the following thought experiment:  There is a space-train and an observer 1 light year apart with synchronised clocks. The train travels to the observer at just below the speed of light. In the reference frame of the observer the train is subject to time dilation and length contraction. When it arrives its clock reads 1 second as its time was basically standing still and the observers clock reads one year. From the trains reference frame it sees the 'observer' travelling towards the train at near light speed, so the train should expect to read the observers clock as 1 second and the trains clock as a year as the train sees the observer to have undergone time dilation. So what do the clocks actually read and why? The only way I can imagine the paradox with relativity not occurring is if both clocks read the same otherwise you could tell what speed you were going?

I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound.  What if there is strictly no acceleration?   Peter is on a space ship, traveling 99% of light speed.  He is exactly 20 years old.   Michael is on Earth (or a planet similar to Earth, but with a radius so small that any centripetal acceleration is negligible... or consider him standing just on a piece of concrete in space with an oxygen supply) Michael is also exactly 20 years old. According to time dilation, Peter's clock in the spaceship is slower than Michael's clock. According to time dilation, Michael's clock on Earth is slower than Peter's clock.  (since motion is relative, if we consider Peter to be stationary, and Michael is traveling) Peter's spaceship is traveling towards Michael. After 30 years on Earth, Peter's spaceship went past Michael's face, so Peter and Michael are 1 cm apart, face to face and eye to eye. Now, would Peter see Michael quite older than him, and also, Michael sees Peter quite older than him?


I understand the idea and concept of XOR outside of code. But I wanted an easy explanation when it's used in code. Let me give you a few examples of what I'm having trouble understanding.   Say we wanted to Swap internet values in C++ with out using a third temp variable and by using XOR, like so:  int a = 1; int b = 3;  int *x = &a; int *y = &b;  *x ^= *y; *y ^= *x; *x ^= *y;    Now I understand that *x ^= y translates to *x = *x ^ *y But I just need to understand one line only to understand the rest. Basically, in *x = *x ^ *y why is *y always being set to *x in order to being the swap sequence? (Or am I getting that part wrong too?) How is *y being exclusively chosen and on what criteria?

Can someone explain to me how XOR swapping of two variables with no temp variable works?  void xorSwap (int *x, int *y) {     if (x != y) {         *x ^= *y;         *y ^= *x;         *x ^= *y;     } }   I understand WHAT it does, but can someone walk me through the logic of how it works?


We're trying to block the users from accessing to local files from Chrome.   We've disabled the access from Windows Explorer. However, if the users use Google Chrome, then they can easily type C: in the address bar, following which they can access local files. You can see an example below:    Does anyone know how to block the access?  I've been looking options such as:    Block the file system Configuring the user agent stylesheet, default styles, as well as the main set-up.    I'm looking in the JavaScript to edit it but I haven't found a solution. This image below is what I see, but I don't know the location for the file that gives a style or format to the local directory and I haven't found such a file in the latest Chrome version.

Is there a way to disable file:/// protocol in google chrome?  Is there some option, or some switches that can disable this feature?  Please help


This is my usual experience:  "I want to post a question but I don't know what kind of questions are within the rules on this site. And since I don't want a question that took me 10 minutes to write to be instantly flagged as off-topic, deleted or down-voted into oblivion I won't post until I know the rules."   But the rules are nowhere to be found. The short site description is often not enough and doesn't include any extra information, for example Server Fault says "Q&A for server administrators" and nowhere does it say "Don't post questions about home servers on Server Fault" etc.  With the increasing amounts of new users wouldn't it be a good idea to have the rules defined on the front page of each site like on reddit for example?

Important: This question is being asked here, and not on the Programmers Meta,  because I believe that several SE sites suffer from this same, specific problem.    On Programmers, I see a pattern emerging.   New User sees the "Programmers" site title, and asks their incomplete, "fix my broken code" question. Community members comment that their question is off-topic, and recommend Stack Overflow.  New User says "thanks" and leaves, leaving their undeleted question for the community to clean up.    What seems clear to me is that:   New User has never seen the "What kinds of questions can I ask about here" page, or if they have, they've clicked through it without reading it. New User doesn't know how to move their question to the right place properly  (i.e. post on new site, delete from old site). Community cleanup of such questions is onerous.  The moderators on Programmers, following the principle that the community should moderate itself for the most part, are not proactive about removing such questions unless they're especially egregious. Migration is even more onerous.   OK, so we have the .  Here's what it says about topicality, about halfway down the page:    Note to those who are confused about Programmers' site scope: it's all right there, in black and white.  However, I do notice a problem.  It's circled in red.  That's our fault, the fault of the Programmers community.  What we really meant to say was "Don't ask your code troubleshooting questions here; those belong on Stack Overflow."  Coding tools deserves its own bullet.  We should fix that.  However, what are the chances that the user is actually seeing this, and evaluating whether or not they should ask their question based on this?  So here's my question, in two acts:  ACT I:  Is there a way to highlight the pain points of a particular site to new users specifically, so that we can be very clear that we don't want those questions that are clearly and unambiguously off-topic on our site, before they ask their question?  ACT II: Failing that, is there a way that we can fast-track the removal of such questions so that they no longer pollute our front page?


The only issue I can see is the text entry box: there's just a blank space where the it should be. It's actually still there, though, just invisible. If I tap it, the keyboard comes up and I can type, but I can't see the text I've entered either.    I can only reproduce this in Android Chrome Beta (67.0.3396.29), and this is on a Pixel 2. Everything's fine in default Android Chrome (66.0.3359.126).

Which browsers are officially supported by Stack Exchange?  Also, what else is needed in order to use every feature of the site?


I am struggling with proving the theorem that if $A$ and $B$ are $n\times n$ matrices, then:     $$\operatorname{rank}(AB)\leq \operatorname{rank}(B)$$   Could anyone suggest me a hint? Any help is greatly appreciated, thank you very much.

Let $A$ and $B$ be two matrices which can be multiplied. Then $$\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B)).$$   I proved $\operatorname{rank}(AB) \leq \operatorname{rank}(B)$ by interpreting $AB$ as a composition of linear maps, observing that $\operatorname{ker}(B) \subseteq \operatorname{ker}(AB)$ and using the kernel-image dimension formula. This also provides, in my opinion, a nice interpretation: if non-stable, under subsequent compositions the kernel can only get bigger, and the image can only get smaller, in a sort of loss of information.  How do you manage $\operatorname{rank}(AB) \leq \operatorname{rank}(A)$? Is there a nice interpretation like the previous one?


I accidentally put the wrong boulder in the wrong hole and now I’m stuck in the Distortion World. I tried saving and reloading my game and leaving the area and coming back but the boulder wont reload. How can I reset the puzzle? Do I need to restart the whole game?

In the part where you have to solve the boulder puzzle, I accidentally dropped the first boulder in to the wrong hole (the one to the left of the boulder). Is there any way I can undo this action? I do not have a savestate from before this happened.


I found lots of references that say, "the probability that a continuous random variable equals some single value is always zero". Why is that?  Here is a counterexample I thought of: supposing $X\sim N(0,1)$, define $Y=min(X,0)$. Then Y is a continuous random variable but the probability of $Y$ at a single point $0$ should be $0.5$, not zero.  Also, I think any CDF would be left continuous if "the probability that a continuous random variable equals some single value is always zero".  What is wrong with my thoughts?   P.S. Examples of the references are:

I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ?


I did this:$ uname -r 4.15.0-041500-generic $ git clone  Cloning into 'rtl8723de'... remote: Counting objects: 536, done. remote: Total 536 (delta 0), reused 0 (delta 0), pack-reused 536 Receiving objects: 100% (536/536), 2.41 MiB | 356.00 KiB/s, done. Resolving deltas: 100% (195/195), done. Checking connectivity... done. $ sudo dkms add ./rtl8723de Creating symlink /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/source ->                  /usr/src/rtl8723de-5.1.1.8_21285.20171026_COEX20170111-1414 DKMS: add completed. $ sudo dkms install rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414 Kernel preparation unnecessary for this kernel.  Skipping... Building module: cleaning build area.... 'make' all KVER=4.15.0-041500-generic....(bad exit status: 2) ERROR (dkms apport): binary package for rtl8723de: 5.1.1.8_21285.20171026_COEX20170111-1414 not found Error! Bad return status for module build on kernel: 4.15.0-041500-generic (x86_64) Consult /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/make.log for more information.I suspect is because the kernel 4.15 but i wanted to see what you think it is, im struggling with this the whole daythanksEDIT:make.log$ cat make.log  DKMS make.log for rtl8723de-5.1.1.8_21285.20171026_COEX20170111-1414 for kernel 4.15.0-041500-generic (x86_64) mar ini 30 14:47:00 PET 2018 make ARCH=x86_64 CROSS_COMPILE= -C /lib/modules/4.15.0-041500-generic/build M=/var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build  modules make[1]: Entering directory '/usr/src/linux-headers-4.15.0-041500-generic'   CC [M]  /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/core/rtw_cmd.o In file included from /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/include/osdep_service.h:42:0,                  from /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/include/drv_types.h:32,                  from /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/core/rtw_cmd.c:22: /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/include/osdep_service_linux.h: In function ‘_init_timer’: /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/include/osdep_service_linux.h:287:8: error: ‘_timer {aka struct timer_list}’ has no member named ‘data’   ptimer->data = (unsigned long)cntx;         ^ /var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/include/osdep_service_linux.h:288:2: error: implicit declaration of function ‘init_timer’ [-Werror=implicit-function-declaration]   init_timer(ptimer);   ^ cc1: some warnings being treated as errors scripts/Makefile.build:316: recipe for target '/var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/core/rtw_cmd.o' failed make[2]: * [/var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build/core/rtw_cmd.o] Error 1 Makefile:1514: recipe for target 'module/var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build' failed make[1]: * [module/var/lib/dkms/rtl8723de/5.1.1.8_21285.20171026_COEX20170111-1414/build] Error 2 make[1]: Leaving directory '/usr/src/linux-headers-4.15.0-041500-generic' Makefile:1884: recipe for target 'modules' failed make: *** [modules] Error 2

How do I install Wi-Fi drivers for Realtek RTL8723DE device in Ubuntu 16.04?  lspci -v | grep -i network 02:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device d723


Hello soo im having a problem, i shot in raw a picture for a contest, days ago i asked a question about this. However, now that I finally took the shot and it was in B&W with the camera and also edited in lightroom B&W the image when i export it and set it to 300resolution dpi and 12.0mp it comes out getting 5MB or 6mb and thats not enough for the contest since 9MB = 12 MP. I appreciate any help guys please.

I am submitting a photo for an exhibit.  They require a jpeg to be evaluated and then a print, if accepted.  The rules indicate "Entries must be in JPEG format sized at 300 dpi on a CD (4” width of image 1,200 pixels at 300 dpi is the largest dimension please)." The final submission will be a maximum of 36" x 36".  I don't see any of this in the photo's properties.  What exactly are they looking for?


I have an arc with start and end points and also I have width and height of the ellipse. Using these can I find center of the ellipse?  hi Stefan,  how can i calculate $(x,y)$ center , can u give idea?

I have the following data:-   I have two points ($P_1$, $P_2$) that lie somewhere on the ellipse's circumference. I know the angle ($\alpha$) that the major-axis subtends on x-axis. I have both the radii ($a$ and $b$) of the ellipse.   I now need to find the center of this ellipse. It is known that we can get two possible ellipses using the above data.  I have tried solving this myself but the equation becomes so complex that I always give up.  This is what I have done till now:-  I took the normal ellipse equation $x^2/a^2 + y^2/b^2 = 1$. To compensate for the rotation and translation, I replaced $x$ and $y$ by $x\cos\alpha+y\sin\alpha-h$ and $-x\sin\alpha+y\cos\alpha-k$, respectively. $h$ and $k$ are x and y location of the ellipse's center.  Using these information I ended up with the following eq:- $$a B_1\pm\sqrt{a^2 B_1^2 - C_1(b^2 h^2 - 2 A_1 b^2 h)} = a B_2\pm\sqrt{a^2 B_2^2 - C_2 (b^2 h^2 - 2 A_2 b^2 h)} \quad (1)$$  where $A = x\cos\alpha +y\sin\alpha$, $B = -x\sin\alpha+y\cos\alpha$ and $C = a^2 B^2 + A^2 b^2 - a^2 b^2$.  Now the only thing I need to get is $h$ from (1). All other values are known, but I am not able to single that out.  Anyway if the above equations looks insane then please solve it yourself, your way. I could have drifted into some very complicated path.


While running the below code getting java.lang.NullPointerException: . Let me know how to resolve this package login; public class an { public WebDriver driver; @BeforeTest public void setup() {     System.setProperty("webdriver.chrome.driver",             "C:\\Users\\chromedriver.exe");     WebDriver driver = new ChromeDriver();     driver.manage().window().maximize(); } @Test public void url() {     driver.get("https://www.google.com/"); }  } error

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


okay so I've beaten the 'Four and have caught Mewtwo and Zygarde. I've done the Looker Quest, and I'm working on getting all mega stones, and the legendary bird. is there anything else to do on the game? thanks for the help c:

I've defeated the Elite Four and the Champion. The credits rolled and I've been teleported to my home in Vaniville Town. What is there to do now? Any specific events/features that are unlocked now?  I already know of and caught Mewtwo and Zyrgarde.


I'd like to summon a Goblin Army, and I know that I need 200 Health and a Shadow Orb. But how do I get a Shadow Orb without an op pickaxe? Also, I have a Crimson biome, not a Corruption so how do I get a Shadow Orb? In addition, do I need anything else to spawn a Goblin invasion other than 200 Health and a shadow orb?

I'm trying to get a Goblin army to spawn.  Thus far I have:   Destroyed 1 Shadow Orb Have at least 200 HP currently and have not seen an invasion yet this game.   At what time does the Goblin Army usually spawn?  When I say time, I mean what time in the night (i.e. 12am, 1am, 2am, etc...).  Am I missing any pre-requisites to getting the army to spawn?


We all know that birds don't get electrocuted while standing on a single power line, but if the bird touched the ground while holding the power line, it will die instantly.   One thing that riddles me is that I don't understand why the bird doesn't act as "ground" while touching the power line with voltage of 120v while the bird has a voltage of 0v. the potential between the two is 120v. why is it that only when the bird touches the ground that also have voltage of 0v the bird dies?

At the voltage levels of typical overhead transmission lines in the US, a bird can land on one and be just fine (as long as it doesn't do something like spread its wings and touch a tree or something else at lower electric potential).  However, what about a hypothetical powerline at much higher voltage (as in tens of megavolts). Could landing on such a powerline fatally-shock the bird even though it does not complete a circuit for sustained current? (Assume that the distance is long enough that electrical arc'ing is impossible.)  NOTE: My understanding of what happens when a bird flies from an earth object to a powerline (please correct me if I'm wrong) is that - upon contacting the wire - its electric potential changes from earth-potential to the powerline's potential. In order for this to happen, there is an initial transfer of electrical energy (i.e. flow of charge i.e. current) from the powerline to the bird which "equalizes" their electric potential, which happens nearly instantaneously. If this is correct, then my question can be restated more generally as "Can an 'equalization charge' such as this result in a fatal shock, if the potential difference that it's equalizing is high enough?"


An involution is a function that satisfies the following: $f = f^{-1}$  MY question is how many involutions can you find in the set of real functions, and how would you go about solving that problem?  EDIT: $f$ does have to be in the family of continuous functions.

Just recently I read up something about involutions (functions $f: A \rightarrow A$ such that $f(f(x))=x$, for all $x$ in the domain of $f$), and was wondering how many (if there is a small set of general functions) such involutions exist for $A = \mathbb{R}$, or maybe $A = \mathbb{R} - S$, where S is some set of points that would make the involution work if they were left out of $A$. In general I'm interested in real functions that are involutions, continuous or otherwise.  There were some examples I found , but any more would be certainly very interesting!


There are options to flag questions, answers and comments but I do not see any options for flagging a user.   The main reason I can see for that is when someone is suspected of gaming the system or using tactics to force answers or bounties to go their way.

I think the community does a great job policing questions/answers, etc. and the community has some good tools available to do this.  Between flagging questions with some reasons behind it and editing posts, closing them, and deleting them, the only thing that seems to be missing to me is the ability to flag a user.  Reasons to flag a user as abusive:   Duplicate User Abusive Behavior Offensive user name or profile User profile consists of spam Others?


I'm using matlab2tikz to export imagesc figures into TikZ/pgfplots code. This process gives me a TikZ file and a rasterized png version of the image with colours matching the colourbar at the time of execution.  The problem is that the resulting image is upside-down and displays a blurred colormap, as shown below.  This is the tikzpicture:    while this is how it should look like (screenshot from Matlab R2013a):    The file produced by matlab2tikz is as follows  \begin{tikzpicture}  \begin{axis}[% width=5.296in, height=4.747in, at={(1.01in,0.641in)}, scale only axis, point meta min=1, point meta max=8.715, axis on top, separate axis lines, every outer x axis line/.append style={black}, every x tick label/.append style={font=\color{black}}, xmin=0.05, xmax=1.05, every outer y axis line/.append style={black}, every y tick label/.append style={font=\color{black}}, y dir=reverse, ymin=0.05, ymax=1.05, axis background/.style={fill=white}, colormap/jet, colorbar, colorbar style={separate axis lines,every outer x axis line/.append style={black},every x tick label/.append style={font=\color{black}},every outer y axis line/.append style={black},every y tick label/.append style={font=\color{black}}} ] \addplot [forget plot] graphics [xmin=1.05,xmax=0.05,ymin=1.05,ymax=0.05] {ainf-1.png}; \end{axis} \end{tikzpicture}%   while the Matlab code that generates the figure is  figure imagesc([1 0.1], [1 0.1], mean_e_range) colorbar   My primary concern is how to sharpen the blurred surface of the colormap. As for the other problem, at worst I can plot the upside-down figure in Matlab and then get the upside-down TikZ version of such upside-down figure, which is the final picture I want.

I'm using matlab2tikz to export imagesc figures into TikZ/pgfplots code. This process gives me a TikZ file and a rasterized png version of the image with colours matching the colourbar at the time of execution.  The file produced by matlab2tikz is as follows:  \begin{tikzpicture}   \begin{axis}[     axis on top,     xmin=75,     xmax=575,     xlabel={$x$},     y dir=reverse,     ymin=-0.045,     ymax=0.955,     ylabel={$y$},     colorbar,     point meta min=0,     point meta max=80000000]    \addplot graphics [xmin=75,xmax=575,ymin=-0.045,ymax=0.955] {p.png};   \end{axis} \end{tikzpicture}%   The problem is that because I'm doing this for multiple figures, I need to be able to switch the colourbar upper and lower bounds. Therefore, the rasterized png images do not match the modified colourbar.  The output I'd like to get is:    I was wondering whether it is possible to produce the exact same figure (ticks centered on the square etc.) with TikZ/pgfplots, while retaining the ability to change the colour of each square to match the colourbar --- ideally, the colour will be determined by the value loaded from a text file and the colourbar ranges.  Edit: Sample data can be found . First two columns are the x and y axes and the fourth column (or third) will be what decides the colour of the square.


As the title explained, I'm eager to find an alternative software on Ubuntu which can make my screenshot floating on the screen, just like the snappy application on macOS. But after googling for a while I didn't manage to get a good answer. Would you like to give me some advice? Thanks for your time.

On Mac OS X, there is a handy key combo for taking a screenshot of any arbitrary rectangle section of the screen(Command-Shift-4).   Is there something similar(maybe Compiz plugin) for Ubuntu/Gnome?


Most of us will know that tapping "build number" a few times in "about device" gives us access to developer settings.  Is there a way to reverse this, and hide developer settings from the menu without doing a factory reset?


In the first image, the laser colour is green.  When it is shined on the plastic cap of the pink highlighter, the colour changes, why has this happened?  Tech Details about the Laser Source are; Max output <1mW Wavelength 532nm +_10  Class II laser product

My friend recently bought a high-powerd pocket laser pen (from China). It is green, and reflects off most surfaces as green.  On some orange surfaces, it reflects orange instead. That is to say, we see an orange dot instead of a green one.  It seems to be certain hard, shiny plastics (for example a Kryptonite bike lock). Orange fruit peel, for example, reflects green, and most orange fabrics reflect green.  I suspect it's some kind of pigment that is reflecting this way.  When the reflection is orange, the intensity of the reflection is subjectively about the same, i.e. it doesn't seem to be losing much energy. If one shined light from a green incandescent bulb onto an orange surface, one would expect that surface to be lit less intensely than a white surface. Not so the laser.  So it seems to be that the photons are being re-emitted at a different wavelength than they were absorbed at.  How can this happen? And why is it only orange?


I have an infinite set $X$, I need to take a proper (countable or not) infinite subset of $X$ so there are theorems that guarantee its existence but it's not clear what set of axiom I need to take, maybe ZFC. Besides, how do I know the complement of that subset is also infinite?

Let $X$ be a set and consider the collection $\mathcal{A}(X)$ of countable or cocountable subsets of $X$, that is, $E \in \mathcal{A}(X)$ if $E$ is countable or $X-E$ is countable. If $X$ is countable, then $\mathcal{A}(X)$ coincides with the power set $\mathcal{P}(X)$ of $X$. Now suppose that $X$ is uncountable. Assuming the axiom of choice, we can conclude that $\mathcal{A}(X) \ne \mathcal{P}(X)$, since $|X| = |X| + |X|$. So the question is:     Can we prove in ZF that $\mathcal{A}(X) \ne \mathcal{P}(X)$ for every uncountable set $X$?   I'm assuming that a set $X$ is uncountable if there is no injective function $f : X \rightarrow \mathbb{N}$.


Given that I have a fair coin which I toss three times, how do I:  a) Find three events $A$ , $B$, and $C$ such that no two are independent but $P( A  \cap B \cap C) = P( A ) P( B) P( C)$ ?  b) Find three events $A$ , $B$, and $C$ such that every two are independent but all three are not independent: $P( A  \cap B \cap C) \not= P( A ) P( B) P( C)$ ?  How would I approach a problem like this ? I started by drawing a binary tree that ended up with 8 leaves but I have no idea how to use it to get the answers. Any help would be appreciated.

I've seen the statement:     It's possible that random variables $X_i, X_j$ are independent for $i≠j$, but $X_1, X_2, X_3$ are dependent.   I haven't been able to find examples of this though.  Any examples?


Let $g\colon \mathbb{R} → \mathbb{R}$ be differentiable with bounded derivative. i.e. $|g'(x)| < M$ for all $x ∈ \mathbb{R}$. Let $\epsilon$ be a positive number satisfying $0 < \epsilon < 1/M$. Let $f(x) = x+\epsilon g(x)$.    How can I prove that $f$ is one-to-one (injective)? I really have no idea how to solve hint. Any hint would be appreciated.    Thank you :)

Let $g:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that   $|g'(x)|\le M$ for all $x\in \mathbb{R}$. For what values of   $\epsilon$ will the function $f(x)=x+\epsilon g(x)$ will be   necessarily one-one?   Not getting any idea how to proceed, maybe Mean value theorem will work.


I am trying to install Ubuntu 14.04 from a bootable USB (tried from CD - same problem) on my laptop. At boot, the GRUB opened:    And then it's like the installation have stopped or something. I see only a black screen:    My laptop is an ACER Aspire E15 (E5-573G-504H).

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I'm on some (single) SX site, call it foo.stackexchange.com . There used to be a user named JoeUser, with number 1234. That user has left, deleting their account.  Their questions and answers don't disappear, but I do not seem to be able to search for them: https://foo.stackexchange.com/search?q=user%3A1234 doesn't work.  Can I effect this search somehow?

We can do searches for content by user with the syntax user:xxx where xxx equals the user number. However, this does not work with deleted users.  This could be useful for the same reasons the user-based search is useful in general, of course. In the case of deleted users, this can sometimes be especially useful, though; for 10k and diamond users doing moderation duties, in particular.  In fact, this would also be a great thing to simply link directly to on the moderator's page for deleted users (perhaps in conjunction with showing deleted posts)


I have just came across a site saying that when we touch a good conductor and if it's temperature is a lower than our body we feel it cold as heat starts flowing from our hands to it. On the other hand if we touch something which is cold but is a bad conductor of heat we will not feel it that cold.  So does this translate to that we will make an error in judging whether the object is really cold or not if it is a worse thermal conductor and it's temperature is considerably lower than our body?

(I apologize for this elementary question. I don't know much about physics.)  Let's say that I put a metal pot in the refrigerator for several hours.  At this point, I guess, the pot and the air (in the refrigerator) have the same temperature.  Now, I touch this pot. It feels very cold. But when I "touch" the air (that is inside the fridge) it doesn't "feel" as cold. I don't feel the same "ouch!" that I feel when I touch the pot.  Why is that? Why does the metal seem colder than air although they both have the same temperature?  (I know that gas has less particles in it in one unit of volume compared to solids and liquids, but since "temperature" means "the average kinetic energy", these fewer air particles are supposed to hit my hand in a velocity that's going to compensate for their lower number, aren't they?)  A related question, for clarification:  If I use a thermometer to measure the temperature of the pot & air (let's assume it's a thermometer that has a probe that can touch objects), will it show the same reading for both? If so, what makes the thermometer different than my hand? I mean, my hand is sort of a thermometer, so why would it fail whereas a non-human thermometer would work?


When I was in college, in a small town, there was a radio station in town that would play old time radio shows.  One night I heard one that has stuck in my mind ever since.  While I have a lot of OTR (old time radio) shows in files, most files have air dates and series names, but not show titles, so I'm still working my way through them.  This story had a small family living in an apartment I think they called "The Nest."  Earth was bitter cold by then, cold enough for oxygen to freeze.  (I think that was because the Sun had gone out or, more likely, Earth had left its orbit.)  This family didn't have anything fancy, no hermetically sealed walls or doors, just a LOT of blankets hung all over.  Instead of space suits, they had home made suits they could use for a short while (I think - maybe they had space suits).  They survived by going out, periodically, and scooping up "snow crystals" of frozen oxygen and bringing a bucket full of oxygen like that back to the nest where they could thaw it by the fire (which they had to keep burning continuously for warmth).  I'm working my way through these OTR shows, but I haven't found it yet.  It's also possible this was based on a short story, since a lot of the OTR shows were based on stories in print at the time.  Can anyone tell me the name of the story or who wrote it or anything else to identify it?

This is a short story I read maybe in the '80s.  Earth has been thrown away from the Sun, probably due to a very large object passing through the Solar System, and the atmosphere has frozen in layers. There is a small family - father, mother, two children, who live in a room they have made airtight by hanging many layers of material to slow the loss of air. They keep warm with a 'camp-fire'. The father goes out every day in a suit of some sort to find food and mine frozen oxygen. It ends when they are found by another, larger group of survivors.  Does anybody know the title and author?


I want to google if fluorine has more s-character. So which one is more correct 'Does fluorine has more s-character' or 'Does fluorine have more s-character'. Both sound unnatural to me when I read them.  Also, are there other ways to ask this same questions without adding new chemical terms?

Generally we use "hads* with he , she , and it.   So which one is correct to say ?  Does this phone has / have xyz function ?   Does his father has / have a car ?


I'm using a state machine to learn C++ and I want to provide an overloaded operator << to return the respective string instead of an int. Apologies for the length ...  #ifndef STATEMACHINE_H #define STATEMACHINE_H  #include <map> #include <string>  namespace statemachine{     using namespace std;      enum State { ON, RESTING, SLEEPING, LOCKED, OFF };      struct StateMap : map<unsigned int, string>     {         StateMap()         {             this->operator[]( ON ) = "ON";             this->operator[]( RESTING ) = "RESTING";             this->operator[]( SLEEPING ) = "SLEEPING";             this->operator[]( LOCKED ) = "LOCKED";             this->operator[]( OFF ) = "OFF";         };          ~StateMap(){};     };  struct Machine {      Machine(State state) : statemap() {         m_currentstate = state;     }      //  trying to overload the operator -- :(     //  Error   1   error C2676: binary '<<' : 'std::ostream' does not define this operator or a      //  conversion to a type acceptable to the predefined operator **file** 38 1 statemachine_01     ostream& operator << (ostream& stream){         stream << statemap[m_currentstate];         return stream;     }      State state() const {         return m_currentstate;     }      void set_state(State state){         m_currentstate = state;     }  private:     State m_currentstate;     StateMap statemap; };  }  #endif   What am I doing incorrectly?

I am writing a small matrix library in C++ for matrix operations. However my compiler complains, where before it did not. This code was left on a shelf for 6 months and in between I upgraded my computer from debian etch to lenny (g++ (Debian 4.3.2-1.1) 4.3.2 ) however I have the same problem on a Ubuntu system with the same g++.  Here is the relevant part of my matrix class:  namespace Math {     class Matrix     {     public:          [...]          friend std::ostream& operator<< (std::ostream& stream, const Matrix& matrix);     } }   And the "implementation":  using namespace Math;  std::ostream& Matrix::operator <<(std::ostream& stream, const Matrix& matrix) {      [...]  }   This is the error given by the compiler:     matrix.cpp:459: error: 'std::ostream&   Math::Matrix::operator<<(std::ostream&,   const Math::Matrix&)' must take   exactly one argument   I'm a bit confused by this error, but then again my C++ has gotten a bit rusty after doing lots of Java those 6 months. :-)


I have created a simple age calculator. I want to remove decimal places but the problem is when I substract now to bday.     example : I input 2012, 10 and 23 and the date now is 2014-10-22, So when 2014.1022 - 2012.1023 the result would be 1.9999... I want to remove all decimal places and remain the whole number 1, but the time I use String.Format("{0:00}" It rounds off the result to 02even when I use ConvertToInt32, I don't want to use  it needs a lot of code.  Any Ideas?   static void Main(string[] args)         {             string year, month, day = string.Empty;             Console.WriteLine("Enter your Birthdate:");             Console.WriteLine("Year :");             year = Console.ReadLine();             Console.WriteLine("Month :");              month = Console.ReadLine();             Console.WriteLine("Day :" );             day = Console.ReadLine();             try             {                 DateTime date = Convert.ToDateTime(year + "-" + month + "-" + day);                  var bday = float.Parse(date.ToString("yyyy.MMdd"));                  var now = float.Parse(DateTime.Now.ToString("yyyy.MMdd"));                  if (now < bday)                  {                      Console.WriteLine("Invalid Input of date");                      Console.ReadLine();                   }                  Console.WriteLine("Your Age is " + (String.Format("{0:00}", (now - bday)))); //it rounds off my float                  Console.ReadLine();             }             catch (Exception ex)             {                 Console.WriteLine(ex.ToString());                 Console.ReadLine();             }          }   }

Given a DateTime representing a person's birthday, how do I calculate their age in years?