My C drive has 100 GB capacity with around 60 GB free space. Two months ago I created an imaginary drive Y with 2 GB capacity to copy certain files from another computer. The files are being copied by Robocopy upon running a small batch file.   One week ago I noticed drive Y is almost full and the C drive was also full. I tried to delete the drive Y, but Y didn't go that time. When I restarted the computer the Y drive disappeared but C was still almost full. I did some clean-up and now the empty space is just 4 GB. C drive Properties shows data only for 32 GB. Out of 100 GB the empty space should be around 60 GB. This is my office computer and only essential office work software is installed. How to recover the full free space?

If I enable both hidden and system files, and then select them all while in the C:\ Drive, the properties window adds their data up to 220 GB. However, if I right click on the C:\ Drive itself and select properties, I have 300 more GB than what was shown previously.    Where is this other 300 GB of data coming from? Is it something vital to the OS? Is it something that's still hidden somehow?


Consider this sentence:     I want to join the contest..   Which is more correct, "so bad" or "so badly"?  I'm leaning towards the latter because it is an adverb and an adverb is required to describe a verb or an adjective. As with the case above, badly should describe want.  I am not sure though if the former is acceptable. And if it is, why so?

What is the correct usage? Apparently it is "I feel badly", but but wouldn't that mean you have an inadequate ability to feel?


For which values of $x$ such that  $0$°$≤x<360$°, we have: $\sin x > \cos x$?   The answer is "When $45$° $< x < 225°$, the $y$-coordinate of the point on the unit circle is greater than the $x$-coordinate", but I don't understand why this is the answer and how the book got it.

Prove that Sine is algebraically less than Cosine for any angle between $2n\pi-\dfrac{3\pi}{4}$ and $2n\pi+\dfrac{\pi}{4}$.   My attempts:  $\sin \bigg(-\dfrac{3\pi}{4}\bigg)=\cos \bigg(-\dfrac{3\pi}{4}\bigg)=-\dfrac{1}{\sqrt{2}}$.  Now when moved further  $\sin$ will starts increasing in magnitude (till $\dfrac{-3\pi}{2}$) and $\cos$ will decrease, hence because they are in $3^{rd}$ quadrant $\implies\sin<\cos$.  Now if we enter  $4^{th}$ quadrant $\cos>0$ and $\sin<0$ till $2\pi$ $\implies\cos>\sin$.  Now if we cross $4^{th}$ quadrant $\sin\uparrow$, from $0$ and $\cos\downarrow$, from $1$, and becomes euqals at $\dfrac{\pi}{4}$, will imply $\cos>\sin$ till $\dfrac{\pi}{4}$. Hence the results.  But is there any way to do this with pure algebra, without these intuitions.  Please help.


The "Add" button is either truncated or altogether hidden when editing favorite tags:   On Unix & Linux, English Language & Usage, Super User and Biology the right hand side border is not shown:   On Ask Ubuntu, it is much worse, I can't even see the word Add itself:     I also checked on Science Fiction and Fantasy which has the old CSS style and there, the button is displayed correctly. I have the same issue on Chromium 45.0.2454.85 and Firefox 41.0 (slighlty worse on FF, I can only see about 2 pixels worth of the A in Add), both running on Debian.      I expect this is a duplicate but I can't seem to find one. Was there a recent change in the CSS style?

I appear to have found a bug, when adding Favorite tags, I find that the buttons are half off the page (this is of the  site):    Although on other sites it looks more like this:    I am running Ubuntu GNOME 15.04 with Firefox 41.0.1+build2-0ubuntu0.15.04.2.


I've got scripts that run nightly that need access to a mapped drive.  I would like to avoid having the script manually map the drive as I don't want to have to dump my credentials into it.    The problem is with the drive mapped as it is, by the time the scripts run, the mapped drive can't be found.  I've got the server configured to never go to sleep and net config server autodisconnect is set to -1.  This is on win server 2008r2  Can anyone help me figure out a way around this?

I have 4 mapped drives to a "SimpleShare" network storage device. 2 have no passwords and 2 have passwords. On Windows 7 Pro PCs, Randomly, 1 of the password protected drives loses connection. The dropped drive changes on different PCs.


A non-participating user did a drive-by edit of an answer, changing the answer. It was in my review queue and I rejected it. However, 3 other users with high accept-reject rates accepted it. I rolled back the edit because it was invalid, and commented on the answer accordingly.  As it turns out, the OP of the answer accepted the change. That was not apparent to me.  Either   it needs to be more obvious that this drive-by change (which should be rejected) was accepted by the OP, or if the OP accepts an edit, it should be removed from the Suggested Edit queue and be auto-accepted, or changes accepted by OP should look like OP edited the question themselves, or something.

When clicking "edit" I see:  Your edit will be placed in a queue until it is peer reviewed. We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.  Like:     Likewise, when I am not logged in, clicking "improve this question" or "improve this answer" shows:  You are not . Your edit will be placed in a queue until it is .  And when I click 'Save', I get:  Thanks for submitting an edit. It is only visible to you until it's been approved by trusted community members  Like:     Who can suggest an edit? Where do suggested edits go? Who can vote on a suggested edit? How do suggested edits get reviewed? Can I earn reputation? What about abuse or bad edits? Sometimes the Community user approves or rejects my edit. Why is that? When can I not suggest an edit? Is there a minimum change requirement for a suggested edit? How do I check my suggested edit history? I disagree with the reasons why my suggested edit was rejected. What can I do? How do I know whether there are edits waiting for review? Someone suggested an edit to my own post, and the reviewers took the wrong action. What can I do? Are tag wikis included in this scheme? What do the "Improve Edit" and "Reject and Edit" buttons do? Why are apparently valid links to rejected edits resulting in 404 errors?   For more information about editing, see "" in the .


Let $p$ be a prime number and $V$ an $n$-dimensional space over $\mathbb{F}_p$. For $r \le n,r \in \mathbb{N}$ find the number of $r$-dimensional subspaces of $V$.  I suspect we can choose an $r$-dimensional subspace in $\binom{n}{r}$ ways. Is this reasoning correct?

Let $V_{n}(F)$ be a vector space over the field $F=\mathbb Z_{p}$ with $\dim V_{n} = n$, i.e., the cardinality of $V_{n}(\mathbb Z_{p}) = p^{n}$. What is a general criterion to find the number of bases in such a vector space? For example, find the number of bases in $ V_{2}(\mathbb Z_{3})$. Further, how can we find the number of subspaces of dimension, say, $r$?   I need a justification with proof. I have a formula, but I am unable to understand the basic idea behind that formula.


The sentence is below (standalone sentence, no context)     Bears often hide themselves in places ____ hunters can't find.   My teacher said the answer was "that/which". I feel totally OK with that, but am confused about why which is also applicable here.  IMHO, which leads a non-restrictive clause while that leads a restrictive clause. Since hunters can't find isn't an additional description of the noun places, which is not suitable here. And because it restricts places to those that hunters can't find, that should be OK here. Am I right?

What is the difference between the words which and that?  For example I have the following sentences:   “I have a car which is blue.” “I have a car that is blue.”   Are there any rules specifying usage of which and that?


How does the combination of different medium affect the force? How do we calculate the equivalent dielectric constant? Say, two charges are separated by 100 cm, first 10 cm is a slab of dielectric constant 100, the last 10 cm is another slab of constant 50, rest is air.

I am given two charged particles of same charge at a distance of $r$. They initially apply force $F$.  Now an infinite dielectric (of dielectric constant $4$) of width $\frac{r}{2}$ is introduced between the particles. What will be the new force?   I find this problem confusing because I have only been told about forces when its either fully dielectric or fully vaccum given by Coulomb's law. How do we get forces when only partial space is dielectric?


I have a textbox, I want to check if it has focus (User clicks on textbox) in plain javascript . How can I do that in javascript not JQuery ?

I would like to find out, in JavaScript, which element currently has focus. I've been looking through the DOM and haven't found what I need, yet. Is there a way to do this, and how?  The reason I was looking for this:  I'm trying to make keys like the arrows and enter navigate through a table of input elements. Tab works now, but enter, and arrows do not by default it seems. I've got the key handling part set up but now I need to figure out how to move the focus over in the event handling functions.


I'm trying to install Wacom Tablet Drivers on Ubuntu 18.04, Code:   sudo add-apt-repository ppa:doctormo/wacom-plus   However, I keep getting the error:   E: The repository 'http://ppa.launchpad.net/doctormo/wacom-plus/ubuntu bionic Release' does not have a Release file.  N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details`   I have tried --allow-unauthenticated But it doesn't work. I also have deleted the Docker repository, as Raffa said in comments. Still no dice. Does anyone know any fixes? Thanks!

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


I have a collection of unique ints which is always unsorted, something like   [1, 56, 78, 89, 887, 98, 100, 0, 23, 114, 900]   I would like to quickly remove an element from the container, say 887 and the result should be   [1, 56, 78, 89, 98, 100, 0, 23, 114, 900]   I am currently using a vector and using this code to erase the element.  container.erase(std::remove(container.begin(), container.end(), elem), container.end());   where elem holds the value to be removed. This works but I have do this operation a million times or more and hence I would like to see if I can use any other algorithm or container to remove elements faster.

I've been reading up on STL containers in my book on C++, specifically the section on the STL and its containers. Now I do understand each and every one of them have their own specific properties, and I'm close to memorizing all of them... But what I do not yet grasp is in which scenario each of them is used.  What is the explanation? Example code is much prefered.


I'm trying to create "/tmp/pwet/foo bar" with this:  DIR="/tmp/pwet/foo bar" ARGS="-p ${DIR}" mkdir $ARGS   For integration reasons, I have to keep the ARGS building in 2 steps: ARG = some_options + $DIR This code create 2 dirs: /tmp/pwet/foo and ./bar. this is not what I want.  I've tried a lot of escaping things, without results. I run the script with bash. What's the good solution?

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


A website I'm building has a product search page with many options. Name, size, category, etc.   Currently the url is search.php and the GET string (when the user submits the form) effectively just returns search.php?name=abc&size=3,6,8&category=12&available=yes etc.   Is this best for SEO or should I construct some URL like search/name/abc/size/3,6,8/category/12/available/yes or similar? I could just exclude the entire search.php page in the robots file, which seems sensible, as it's not a massively optimised page for any particular keywords.

I am having a home page where I can search on multiple tags. How should I construct the URL? Suppose I search for tag = test_1 and tag = test_2  Should I construct the url like   http://www.example.com/tag/test-1,test-2   or  http://www.example.com/tag/?tag=test-1,test-2   or  www.example.com/tag/test-1-test-2   or  any other option?  I know query params are generally ignored by search engines and I should not put comma in URL so according to it "www.example.com/tag/test-1-test-2" is best option but I am afraid that www.example.com/tag/test-1-test-2 and www.example.com/tag/test-2-test-1 will generate the same result.


This is the code I have right now and can't figure out why this while loop isnt ending when there is a period entered. while (emailTxt!="."){   emailTxt = "";   emailTxt = scanner.nextLine();   totalText.add(emailTxt); }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


In radioactivity we know that a parent nucleus can disintegrate into daughter nuclei by emitting alpha or beta particles. If this is true then how can the daughter nucleus have as many electrons as protons?  For example, suppose a parent nucleus emits an alpha particle. Its mass number gets decreased by 4 and its atomic number gets decreased by 2 as it converts into a daughter nucleus. Now, how can the number of electrons and protons be the same?

When an alpha particle is emitted, two protons and two neutrons leave the nucleus but the electrons remain the same in number. Why does the atom remain uncharged although it appears it should have a net charge of $-2e$?


i have transit 6 hours in aljazeera terminals kuwait with 1 year old kid.How can reach any aiport lounge (Sheikh Saad Terminal) or (terminal M)

I'm traveling to Rome from Delhi, India, via Kuwait. What are the options available to spend the transit time (approximately 6 hours) in the airport? I also have a 5-year-old kid with me. Are there some affordable sleeping places? And the entire transit time is at night.


I had a paper accepted at a conference in theoretical computer science. However while revising the final version I found an error in the proof of an important lemma. Although I believe the error is fixable, It will require some effort. I will not be able to fix the error before the deadline for the final version.   1) Should I withdraw the paper?  2) Should I leave the lemma without proof, and add the corrected proof at the final version.  What would be the best thing to do? Would I be able to resubmit the paper to some other conference? What would be the damage for my reputation?

I have submitted a paper to a conference with a scientific error in it.  Essentially I have a concept and I have claimed it works in two conditions. Actually it only works in one of them. Technically, my experimental results are correct, but its only a small test and when extrapolated to full scale the error can be found and also actually predicted theoretically. The overall concept is still correct however for the other condition and I am still working on it in future research.  Should I ask for the paper to be changed? The conference isn't until 25th August but the submission deadline has passed.  I don't want a public document where people will repeat my experiments and find that some of what I have claimed is incorrect.


I have a wildcard domain certificate from StartSSL for a site ().  When I check it in any browser on my home PC, it's all good. (Green lock in Chrome.) When I check it in Chrome on my work PC, it's not good:    The page loads like no problem. There are no other requests, so nothing over HTTP. It uses safe protocols etc. I checked the connection on  and  and they agree it's perfectly safe.  On the same computer, other browsers are fine with it. On other computers, Chrome is fine with it too. I tried restarting, flushing caches, incognito mode, etc. Nothing changes.  It's no real problem for me, because I know it's safe, but it's still annoying.  Any ideas?  PS. Chrome did something like this a while ago with Windows XP: suddenly websites were 'unsafe' because Windows protocols were unsafe. Both PC's are Windows 7 and the same version of Chrome, so that's probably not it...  More info:    For some reason the 2 computers have different certificate chains. The domain certificate and root certificate are the same, but the intermediary is different. On my home PC it uses sha2, on my work PC it uses sha1. The intermediary is included in the server cert (which has sha2), so that's weird. All the SSL checkers only detect the sha2 intermediary cert. What's going on!?

We're using an AWS ELB to do SSL termination and are having an issue where Chrome is displaying "https" in red with a strikethrough.  It says "The site is using outdated security settings that may prevent future versions of Chrome from being able to safely access it." but it doesn't explicitly call out what setting it doesn't like.  How can I find out what Chrome is having a problem with so that our users will get a green checkmark?  An example URL producing the error is here:     I ran our site through SSL Labs and it gave us an "A" Grade:


I understand that to many this will be a frustratingly basic question which will not require much thought, but hopefully there are a few who can answer it anyway.  I have various sets of data on spreadsheets. Some worksheets have 900 rows of data and some have 15,000. There are many columns to each row, but essentially one row is one 'record'. The significant thing is that for each set of data, there is a finite and known population size.   I want to set up a 'checking' plan to provide me with a level of confidence (ideally without a tolerance, but if I have to have one then I have to have one). Each row (i.e. each record) on each worksheet can be correct or incorrect. There is no numerical variance, it is simply whether the data provided on each row accords to the various hard copy documents, data and calculations which feed into it.  My objective is to be able to state that I have reviewed the data and can say, with a given % confidence (and potentially tolerance, but ideally not), that the sample size I have examined (n) represents the larger population (N).  The ideal answer would provide me with a simple worked solution, but also a reference or several references to the genre of statistics that this exercise belongs in, so that I can go on to research it further and understand the basis for the worked solution provided.  I understand that I may be looking at a huge sample size, but I want to investigate the various possibilities, for instance to be able to work the formula (optimistic that one exists) backwards to determine what % confidence I could have with an n sample size.    EDIT:   I have a spreadsheet with 1000 rows on it. In each row there is an invoice number and an invoice value, just two columns. I want to know whether all 1000 rows are correct, but I don't want to check all 1000 rows manually. How would I calculated a sample size for this (say 20, 50 or 75?) and what confidence level could I have that all 1000 were correct, if for example I checked 20 invoices and all 20 were correct.

I have read through existing answers on CrossValidated (plus elsewhere online) and can't find what I'm looking for, but do please point me to existing sources if I've missed them.  Let's say I have a data set of N=1000 records, each of which can be manually sampled and labelled as either 'Valid' or 'Invalid' (or True/False, Right/Wrong, etc).    I want to achieve a given level of confidence that all records in the data set are Valid.  As I sample records, if I find a single Invalid one I would go back and amend how the data set is created to rectify that and similar problems.    So, after some iterations of spotting Invalids, fixing and recreating the data set, I do some sampling that only includes Valid records.  If I want to be (say) 99% or 95% sure that all records are Valid, how big does my sample have to be? (Ideally as a function of N.)  I've tried playing around with Hypergeometric tests () - in that context I want to know what k should be, but I don't have a fixed value of K. Rather I want to choose k such that K is likely to be equal to N - but setting K=N obviously works out to a Probability of 1! I'm also wondering if I need to use a Bayesian approach but I don't understand Bayesian stats enough.


I am trying to understand Rudin's remark 4.12 on pages 88-89. What Rudin says is that, though we can talk about continuity of $f$ on $E \subset X$, the complement $E^c \subset X$ plays no role, unlike in the limit definition. I'm not able to understand exactly why this is, other than that we restricted ourselves in the case of limits to letting $x \to p $ for a limit point $p$. I'm assuming the continuity definition is "vacuously true" for $x \in E^c$, but I'm not totally sure. Could someone shed some light on this?

"We defined the notion of continuity for functions defined on a subset $E$ of a metric space $X$. However, the complement of $E$ in $X$ plays no role whatever in this definition (note that the situation was somewhat different for limits of functions). Accordingly, we lose nothing of interest by discarding the complement of the domain of $f$. This means that we may juct as well talk only about continuous mappings of one matric space into another, rather than of mappings of subsets."  I have one question:  Why $E^c$ in $X$ plays no role in definition of continuous function but it's material in definition limit of function?


fast question what does this do in c++;  auto asd = (1,2,3,4,5);   note: this does note emit an error  Is this a class? If it is a struct of data or class or array, can you tell me how to get the individual element value;  When i cout << asd ; It return always the last number, in this case 5  thanks in advance

How does the comma operator work in C++?  For instance, if I do:  a = b, c;     Does a end up equaling b or c?   (Yes, I know this is easy to test - just documenting on here for someone to find the answer quickly.)  Update:  This question has exposed a nuance when using the comma operator.  Just to document this:  a = b, c;    // a is set to the value of b!  a = (b, c);  // a is set to the value of c!   This question was actually inspired by a typo in code.  What was intended to be  a = b; c = d;   Turned into  a = b,    //  <-  Note comma typo! c = d;


I asked a similar question about the Principle of Univariance yesterday, but now I have another one.  According to the Principle of Univariance, the input to a photoreceptor differs along two dimensions (wavelength and intensity) but the output can only vary along one dimension (the cell's graded potential).  This means that there is inherent ambiguity in the output of the photoreceptor. What I do not understand then is how it is possible for a rod (or cone) to ever distinguish between intensities (or wavelengths) when each photopigment can absorb a range of wavelengths at different probabilities.  For example, say a rod cell absorbs $50\%$ of all photons at wavelength $x$ and $25\%$ at wavelength $y$. If 100 photons reach the rod cell at wavelength $x$ we can roughly assume that $100*0.5=50$ isomerizations will occur. Equally, if 200 photons reach the rod cell at wavelength $y$ then we can roughly assume that $200*0.25=50$ isomerizations will also occur. From the perspective of the cell's synaptic activity, the two responses will be the same despite the large difference in intensity.  Clearly there are an infinite number of permutations to this basic pattern. It is thus unclear to me how the visual system is able to obtain any information about the intensity of light in rod cells.  The same issue also appears present to me in cone cells (the usual explanation is that the relative amount of excitation/inhibition can be compared between cone cells, but this does not seem to solve my overall question).

Here is my confusion: we can see colored light of different wavelengths: form red to violet. To my understanding, these stimuli cause a confirmational change in the photoreceptors in our eyes and results in a STP that eventually leads to an "all or nothing" action potential that sends another signal, again an all or nothing action potential through the optic chiasm to the occipital lobe and we perceive the colors as we see them.   My question is *how does this signaling work? *; How can a minor stimulus, resulting in an "all or nothing" chain of action potentials be converted into something as specific as the vision of color?   Asked another way, how does variation in a confirmational change at a receptor that results in "all or nothing" signaling lead to specific signals being sent such as colored vision ?  PS: I dont know jack about sensory physiology


Let $g(x)=a_1\sin x+a_2\sin 2x+\ldots+a_n\sin nx$, where $a_1,a_2,\ldots,a_n\in \mathbb{R}$ such that $|g(x)|<|\sin x|\;\forall x\in\mathbb{R}$. Then, can we prove that $|a_1+2a_2+\ldots+na_n|<1$.   I think yes, because we may apply the triangle inequality repeatedly and the boundedness of $\sin$ function. Any ideas. Thanks beforehand.

Let $a_1,a_2,\ldots,a_n\in \mathbb R$ and $f(x)=a_1\sin x+a_2\sin 2x+\ldots+a_n\sin nx$  such that $|f(x)|\leq|\sin x|$ for every $x\in \mathbb R$. Prove that $|a_1+2a_2+3a_3+\ldots+na_n|\leq1$.  Solve: I solved it very simple. $$|a_1+2a_2+\ldots+na_n|=\lim_{x\to 0}\frac{|a_1\sin x+a_2\sin 2x+\ldots+a_n\sin nx|}{|\sin x|}=\lim_{x\to 0}\frac{|f(x)|}{|\sin x|}\leq1.$$


Where are the settings as modified by "unity-tweak-tool" stored?  Can they be edited with a text editor?  Is there documentation, manual or help on the available options? Are there options not available in the GUI? which?  Where is the documentation available?  Are there system wide pre-sets possible? Are there automation guidelines?  This question is different from this  because unity-tweak-tool is not mentioned there, and thus that question and answer can not be found by simply search for unity-tweak-tool.

Mark Shuttleworth  about the decision to include the Qt libraries in the 11.10 release, with a  Jono Bacon. Mark states that the biggest challenge to integrating apps written in Qt into the larger Ubuntu system is Qt's current non-compatibility with dconf.  What is dconf, and what is the role it plays in Ubuntu?


This question on Multilayer intersection in QGIS was asked by "julsbreakdown" a year go. But I am a newbie and I am not really sure how it works with SQL as suggested in the responses. And I am using the same image posted by "julsbreakdown." Here is the link of the previous thread:   Using QGIS (or its plug-in) or python script, how do I get the polygon (x) which is the intersection of four polygons?

I am trying to find a way with QGIS to get the intersection area of more than 2 layers.  All the tools in QGIS take just the 2 input layers.  For example in the image below, I have 4 layers and I want to retrieve just the black area.   Furthermore, I need to retrieve the count attribute and add it to the intersected area attribute table (in this case 4)    I know there is a tool that does the trick in ArcGIS, but is there a QGIS solution?


Suppose that a fair die is rolled repeatedly; different rolls are   independent.   N is the minimum number of rolls till each of the six faces of the die shows up at least once.       Suppose that i distinct faces have already shown up, i = 1; 2; 3; 4;   5. N_i is the minimum number of additional rolls after i distinct faces have shown up till another distinct face (one of the remaining 6   - i faces) shows up. Derive the pmf.   I know that N is Geometrically distributed by 1/6, however, I am having trouble figuring out if N_i is geometrically distributed like N, and why is that different if not? How would the p.m.f of N_i be derived?

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?


Let $X \sim exp(\lambda)$ be independent of $Y \sim exp(\lambda)$ compute $E[X|X+Y]$  I have tried to do this in a couple different ways and all of them have either led to an indefinite integral or a bad answer (illogically $-\lambda$).   Let $Z := X+Y$  The first way I tried to do it was,   $ \begin{align} E[X|Z] &= \int_0^{\infty} x p_{x|z}dx\\ \end{align}$  Then I found $p_{x|z}$ to be   $ \begin{align} p_{x|z} &= \frac{P(X=x, X+Y=z)}{P(Z=z)}\\ &= \frac{P(X=x)P(Y=z-x)}{P(Z=z)}\\ &= \frac{\lambda^2 e^{-\lambda x} e^{-\lambda (z-x)}}{\lambda e^{-\lambda z}}\\ &= \lambda  \end{align}$  So,  $ \begin{align} E[X|Z] &= \int_0^{\infty} x p_{x|z}dx\\ &= \int_0^{\infty} x \lambda dx \end{align}$  Which doesn't coverage, can anyone help?

Being $X$ and $Y$ independent random variables distributed as $\mathrm{Exponential}(1)$ and let $T=X+Y$ Calculate $E(X|T)$.  This is my attempt at solving this:  Being $Z=\sum_{i=1}^{n}P_{i}$ where $P_{i}$~$\mathrm{Exp}(\lambda)$ then using it's MFG you have that $$M_{P_i}(t)=\frac{\lambda}{\lambda-t}$$ then $$M_{Z}(t)=M_{\sum{P_{i}}}(t)=(M_{P_{1}})...(M_{P_{n}})=(\frac{\lambda}{\lambda-t})^n$$ with this being the MFG of a $\mathrm{Gamma}$ distribution with parameters $(n,\lambda)$  With this result is easy to see that $T$~$\mathrm{Gamma}(2,1)$  Now $E[X|T]=\int xf_{X|T}(x|t)dx$  Then using Bayes' theorem we can make $$f_{X|T}(x|t)=\frac{f_{T|X}(t|x)f_{X}(x)}{f_{T}(t)}$$ then $$f_{T|X}(t|x)=Pr(T=t|X=x)$$ $$=Pr(X+Y=t|X=x)$$ $$=Pr(x+Y=t|X=x)$$ $$=Pr(Y=t-x)=f_{Y}(t-x)$$  Using this result we can now rearrenge $$f_{X|T}(x|t)=\frac{f_{Y}(t-x)f_{X}(x)}{f_{T}(t)}$$ $$=\frac{e^{-(t-x)}.e^{-x}}{\frac{te^{-t}}{\Gamma(2)}}$$ $$=\frac{1}{t}$$ then $$E[X|T]=\int (x)(\frac{1}{t})dx$$  And this where I got stuck because $1_{x\epsilon(0,\infty})$, I made this explanation step-by-step hoping that someone can se easily check where I went wrong. I would aprecciate a step-by-step answer, thanks.


When $() or `` is used bash can't overwrite it. Here is the code: #!/usr/bin/env bash  multiply() {     it=0     for i in ${arr[*]}; do         arr[$it]=$((i * 2)) # change the global array         it=$[ $it + 1 ]     done      echo ${arr[*]} }  arr=(1 2 3 4 5 6 7 8 9 10) new_arr=($(multiply))  echo "Before: " ${arr[*]} echo "After:  " ${new_arr[*]}  output: Before:  1 2 3 4 5 6 7 8 9 10 After:   2 4 6 8 10 12 14 16 18 20  Why it works like that? Aren't the just supposed to assign output to array/variable?

The following code works differently depending on which way Parse_Short_Switches() is called.  After calling the function 'Parse_Short_Switches' by using result=$(Parse_Short_Switches), the value of $error_flag is NOT set to -1 as I would expect.  After calling the function 'Parse_Short_Switches' by simply using Parse_Short_Switches, the the value of $error_flag is set to -1 as I would expect.  Any help would be greatly appreciated.  Thanks  #!/bin/bash  function Parse_Short_Switches() { echo "error_flag inside of the function= $error_flag" 1>&2 error_flag="-1" echo "blah blah ..." }  # --- MAIN --- error_flag="999" echo "error_flag= $error_flag" #result=$(Parse_Short_Switches) Parse_Short_Switches echo "error_flag= $error_flag"


I am searching for a column header and return a value under it.  Example:  _|A|B|C  1|X|Y|Z  2|1|2|3   If the value is Y, it must return 2. I tried =SUMIF(A1:C1,"B", A2:C2), but realized that IFSUM does not support searching horizontal.  I would appreciate an alternative solution!


Evaluate $$\lim_{n\to\infty}\frac{\sum_{k=1}^n\sqrt{k}}{\sum_{k=1}^n\sqrt{n+k}}$$  I can't seem to remove the $\frac{1}{n}$ term in order to use the riemann integral any help?

Use Riemann integral to evaluate the limit $$\lim_{n\to\infty}\frac{\sum_{k=1}^n \sqrt k}{\sum_{k=1}^n\sqrt{n+k}}$$


I would like to trim subsections length in my table of contents despite of the title of subsection will be so long. Something like in this pic, I mean, trim this reference but keeping my subsection without changes.    Produced by this code:  \documentclass[8pt,a4paper,dvipsnames]{article} \usepackage[utf8]{inputenc} \usepackage[spanish]{babel} \usepackage[left=2cm,right=2cm,top=2cm,bottom=1.5cm]{geometry}  \begin{document} \tableofcontents \section{blablablablablablablablabla} \subsection{blablablablablablablablablablablablablablablablablabla blablablablablablablablablablablablablablablablablabla blablablablablablablablablablablablablablablablablabla blablablablablablablablablablablablablablablablablabla blablablablablablablablablablablablablablablablablabla blablablablablablablablablablablablablablablablablabla blablablablablablablablablablablablablablablablablabla}  \end{document}   Thank you so much! :D

Sorry if this question already appears elsewhere, I couldn't find it.  Is there a way to label a section in the text but give it a different name in the table of contents?  I have very long section titles but would like to give them nicknames in the TOC. I tried using \section*{A} then \addcontentsline{toc}{section}{B} but this removes the numbering of the section from the body of the text.  I'm very new to LaTeX so sorry if this is an annoying question!


I'd like my program to find location from which it was run, i.e. program uses txt file and I'd like it to look for this txt file in the same directory as jar file.  I am aware of the existence of Path class, but I don't have a clue how to use it in this situation. For the time being I'm using a fixed path, but it's not good enough.  package readsqlfromfile; import java.io.*; import java.util.Scanner;   public class ReadSqlFromFile {  static File file = new File ("C:\\sql\\sql.txt");  public static void main(String[] args) throws FileNotFoundException  {       Scanner input =new Scanner(file);      String linia = new String ("");  while (input.hasNextLine()) {     linia = input.nextLine();     if (linia.length()>4) {     if (linia.substring(0, 4).equals("sql:")) {        //some database logic here    }    }        }  } }

I've recently searched how I could get the application's directory in Java. I've finally found the answer but I've needed surprisingly long because searching for such a generic term isn't easy. I think it would be a good idea to compile a list of how to achieve this in multiple languages.  Feel free to up/downvote if you (don't) like the idea and please contribute if you like it.  Clarification:  There's a fine distinction between the directory that contains the executable file and the current working directory (given by pwd under Unix). I was originally interested in the former but feel free to post methods for determining the latter as well (clarifying which one you mean).


Can I use they in the following fashion when referring to oneself?     [Name] is a Web Developer at [company Name]. They holds a B.S. in Computer Science.    The emphasis here is when one tries to refer to themself without using she/he or her/him.      [Name] is a Web Developer at [company Name]. They hold a B.S. in Computer Science.    Turns it into an Illeism and sounds somewhat pompous.   Is there any way to use they in a singular form to refer to oneself? Something along the lines of      Name is a Web Developer at companyName. Xe holds a B.S. in Computer Science.   but that is more recognized.

Is there a pronoun I can use as a gender-neutral pronoun when referring back to a singular noun phrase?  Each student should save his questions until the end. Each student should save her questions until the end.


When I use free -h -l  command I see 1.8G in use where system monitor app shows me 1.1G in use.               total       used       free     shared    buffers     cached Mem:          1.8G       1.7G       161M       245M        67M       553M Low:          853M       735M       117M High:         1.0G       963M        44M -/+ buffers/cache:       1.1G       783M Swap:         3.8G       1.4G       2.4G

I am using System Monitor 2.28.0.  When I look in the Resources tab, I see a nice graph with for memory and swap.  Memory is about 60% 2.3 GiB of 3.8.  When I type the command free, I got :               total       used       free     shared    buffers     cached Mem:       3994908    3962396      32512          0     100852    1477032 -/+ buffers/cache:    2384512    1610396 Swap:      8000328      28468    7971860   cat /proc/meminfo | grep MemFree give  MemFree:           34536 kB   The situation has remained the save for several minute.  I started a lot of process with a script and the script is waiting for the free memory to get lower.  According to what I am seeing in the Process tab (or with top), the number in System Monitor seem a lot closed to the total of the memory of the process that the one reported by free.   Thanks


I'd like to downgrade from Ubuntu 13.10 back to an older version. i.e. 13.04.  Can I just boot ubuntu installer, uninstall Ubuntu 13.10 and install 13.04 without any problems to my home folder?

I just installed a new version of Ubuntu and I want to roll it back to the previous version.  How can I do that? Is that even possible?


Using XeTeX(xelatex) [i got the same using pdflatex] on Debian I am trying to save some compilation time using tikz external. Yet, the figures are never updated unless I delete the corresponding files. Otherwise I get     ===== Image 'figures/mwe-figure0' is up-to-date. ======   eventhough I changed something, e.g. labels or coordinates  \pgfversion gives me 2.10  mwe:  \documentclass{scrartcl} \usepackage[english]{babel} \usepackage{tikz} \usetikzlibrary{external} \tikzexternalize[prefix=figures/] \tikzset{external/system call={% xelatex \tikzexternalcheckshellescape -halt-on-error -shell-escape -interaction=batchmode -jobname "\image" "\texsource"}} \begin{document} \begin{tikzpicture} \node (f) at (0,0){d}; \end{tikzpicture} \end{document}   Interestingly, when I add   \tikzset{external/up to date check=md5}   to the preamble I get     ! Package pgfkeys Error: I do not know the key '/tikz/external/up to date check   'and I am going to ignore it. Perhaps you misspelled it.   What could be the cause of that?  PS: If it provides any insights to you, the *.dpth files are empty.

I am using the external library to avoid recompiling tikz figures unnecessarily in a large document. Every now and then I have to change some details of some selected pictures. After the modifications it is necessary to recompile only those figures that have been modified. My aim is to do that automatically.   From Christian Feuersänger's answer to , I have interpreted that pictures whose content change can be remade automatically. I have not found however a simple MWE in which a tikz figure is recompiled only when its content is changed. It would be useful to have one.  The following MWE does not work, in the sense that changes in figure.tikz do not trigger re-compilation of the figure.  \documentclass{article} \usepackage{pgfplots} \usetikzlibrary{external} \tikzexternalize[prefix=tikz2pdf/]  \begin{document} \begin{figure}   \tikzsetnextfilename{figure}   \input{figure.tikz} \end{figure} \end{document}   figure.tikz  \begin{tikzpicture}  \draw (0,0) -- (1,0); \end{tikzpicture}   From the logs of pdflatex I can see  ===== Image 'tikz2pdf/figure' is up-to-date. ======   which tells that the file checked against being up-to-date is the generated pdf, not the original tikz. Obviously I am missing something.  How do I specify that the file to be checked is the original tikz?  For the background, I use pdflatex and tikz/pgf 2.10.


I have 2 computers connected to the same router. Ip config of one says    Connection-specific DNS Suffix  . : www.tendawifi.com    Link-local IPv6 Address . . . . . : fe80::3804:2d04:a591:7142%6    IPv4 Address. . . . . . . . . . . : 192.168.0.108    Subnet Mask . . . . . . . . . . . : 255.255.255.0    Default Gateway . . . . . . . . . : 192.168.0.1   Ipconfig of another is similar except that it's 192.168.0.106  C:\Users\vbcbu>ping 192.168.0.106  Pinging 192.168.0.106 with 32 bytes of data: Request timed out. Request timed out. Request timed out. Request timed out.  Ping statistics for 192.168.0.106:     Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),  C:\Users\vbcbu>  They're connected to the same router.   Why can't they ping each other? I can however, ping my android phone C:\Users\vbcbu>ping 192.168.0.103  Pinging 192.168.0.103 with 32 bytes of data: Reply from 192.168.0.103: bytes=32 time=212ms TTL=64 Reply from 192.168.0.103: bytes=32 time=100ms TTL=64 Reply from 192.168.0.103: bytes=32 time=61ms TTL=64 Reply from 192.168.0.103: bytes=32 time=134ms TTL=64  Ping statistics for 192.168.0.103:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 61ms, Maximum = 212ms, Average = 126ms  This is tracert result Tracing route to DESKTOP-MNQO6R4 [192.168.0.106] over a maximum of 30 hops:    1     *        *        *     Request timed out.   2     *        *        *     Request timed out.   3     *        *        *     Request timed out.   4     *        *        *     Request timed out.   5     *        *        *     Request timed out.   6     *        *        *     Request timed out.   7     *        *        *     Request timed out.   8     *        *        *     Request timed out.   9     *        *        *     Request timed out.  10     *        *        *     Request timed out.  I can ping gateway C:\Users\vbcbu>ping 192.168.0.1  Pinging 192.168.0.1 with 32 bytes of data: Reply from 192.168.0.1: bytes=32 time=5ms TTL=64 Reply from 192.168.0.1: bytes=32 time=6ms TTL=64 Reply from 192.168.0.1: bytes=32 time=12ms TTL=64 Reply from 192.168.0.1: bytes=32 time=4ms TTL=64  Ping statistics for 192.168.0.1:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 4ms, Maximum = 12ms, Average = 6ms  C:\Users\vbcbu>  I can do this from both computers

Ipconfig says that my IP is 192.168.0.108 C:\Users\vbcbu>Reply from 192.168.0.108: Destination host unreachable.ip 'Reply' is not recognized as an internal or external command, operable program or batch file.  C:\Users\vbcbu>ipconfig  Windows IP Configuration   Ethernet adapter Ethernet:     Media State . . . . . . . . . . . : Media disconnected    Connection-specific DNS Suffix  . :  Wireless LAN adapter Local Area Connection* 12:     Media State . . . . . . . . . . . : Media disconnected    Connection-specific DNS Suffix  . :  Wireless LAN adapter Local Area Connection* 13:     Media State . . . . . . . . . . . : Media disconnected    Connection-specific DNS Suffix  . :  Wireless LAN adapter Wi-Fi 2:     Connection-specific DNS Suffix  . : www.tendawifi.com    Link-local IPv6 Address . . . . . : fe80::3804:2d04:a591:7142%6    IPv4 Address. . . . . . . . . . . : 192.168.0.108    Subnet Mask . . . . . . . . . . . : 255.255.255.0    Default Gateway . . . . . . . . . : 192.168.0.1  Ethernet adapter Bluetooth Network Connection:     Media State . . . . . . . . . . . : Media disconnected    Connection-specific DNS Suffix  . :  C:\Users\vbcbu>  I can ping router at 192.168.0.1 I can't ping 192.168.0.108 C:\Users\vbcbu>ping 192.168.0.1  Pinging 192.168.0.1 with 32 bytes of data: Reply from 192.168.0.1: bytes=32 time=2ms TTL=64 Reply from 192.168.0.1: bytes=32 time=24ms TTL=64  Ping statistics for 192.168.0.1:     Packets: Sent = 2, Received = 2, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 2ms, Maximum = 24ms, Average = 13ms Control-C ^C C:\Users\vbcbu>ping 192.168.0.8  Pinging 192.168.0.8 with 32 bytes of data: Reply from 192.168.0.108: Destination host unreachable. Reply from 192.168.0.108: Destination host unreachable. Reply from 192.168.0.108: Destination host unreachable. Reply from 192.168.0.108: Destination host unreachable.  Ping statistics for 192.168.0.8:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),  C:\Users\vbcbu>ping 192.168.0.8  Pinging 192.168.0.8 with 32 bytes of data: Reply from 192.168.0.108: Destination host unreachable. Reply from 192.168.0.108: Destination host unreachable.


Suppose an object A is traveling towards black hole. For an observer outside it looks like A almost reached even horizon and is still trying to reach it.  So from point of view of an observer all the matter is on even horizon (we don't see all of it due to severe severe redshift making black holes invisible in all EM spectrum that we can detect). And all observers being equal, this view is also correct.  So which one is true, did A cross horizon or not? Or somehow both is true? Which leads to this question do blackholes contain matter? Or they are just a void out in both time and space. Because for all practical and theoretical purposes all curved spacetime ends at event horizon. We simply don't know what lies beyond.

The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through?


I am running a logistic regression in SAS where the outcome variable is a binary on sale success (IVs are: location of the customer, Vendor, handling time, experience level of sales person etc.). Either an offer was applied (sale) or it wasn't (no sale). However, the cases with the event of a sale amount to 500 and the one with no sale amount to 10k. Is that a problem? And if it is, how does site affect my estimates/odd ratios and what are possible solutions?

Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables.   My problem is the following: whatever set of predictor variables I use, the classifications never get better than a specificity of 100% and a sensitivity of 0%. However unsatisfactory, this could actually be the best possible result, given the set of candidate predictor variables (from which I can't deviate).   But, I couldn't help but think I could do better, so I noticed that the categories of the dependent variable were quite unevenly balanced, almost 4:1. Could a more balanced subsample improve classifications?


I installed openvpn on my Ubuntu 16.04.2 LTS System, but I can't add a connection, because the field is greyed out.   I've tried this:  sudo apt-get install network-manager-openvpn network-manager-openvpn-gnome   Is there maybe any super secret file I have to edit?  Edit: Also tried to solve it via installing the following packages:  network-manager-openvpn network-manager-openvpn-gnome network-manager-pptp network-manager-vpnc   Edit 2: The suggested solution in the comment from alfred worked for me:     I'm on 16.04.2, but I don't see "Add a VPN connection" option on nm-applet. > However I can add a VPN connection by choosing "Edit conections..." -> "Add" > – alfred Mar 17 at 23:55

When I choose the Connection Type in VPN Connections, I have only PPTP and I can't find OpenVPN, but I already installed it via terminal with the command sudo apt-get install openvpn easy-rsa  Why I can't find it?


I have a table data as shown below.  +---------+----------+-------+--+ |  Name   | Semester | Score |  | +---------+----------+-------+--+ | John    | Sem 1    |    80 |  | | Michael | Sem 1    |    90 |  | | Dennis  | Sem 1    |    65 |  | | Peter   | Sem 1    |    70 |  | | John    | Sem 2    |    65 |  | | Michael | Sem 2    |    85 |  | | Peter   | Sem 2    |    95 |  | | George  | Sem 2    |    85 |  | | Michael | Sem 3    |    80 |  | | Peter   | Sem 3    |    70 |  | | George  | Sem 3    |    75 |  | | Dennis  | Sem 3    |    70 |  | +---------+----------+-------+--+   I want to execute a query and get the following resultset.  Name    Sem 1   Sem 2   Sem 3   Avg Total John    80      55              67.5 Michael 90      85      80      85 Dennis  65              70      67.5 Peter   70      95      70      78.33 George          85      75      80   Help me to build the query.  Thanks in advance

I have a TEMPORARY table containing pairs of key/value as  id   col1      col2        type         pair 1    key1      key2        key          1 2    value1    value2      value        1 3    key3      key4        key          2 4    value3    value4      value        2 5    key5      key6        key          3 6    value5    value6      value        3   I want to mix the key/values as  pair    key_col1     key_col2      value_col1      value_col2 1       key1         key2          value1          value2 2       key3         key4          value3          value4 3       key5         key6          value5          value6   Since, it is a temporary table, I cannot use JOIN. How can I SELECT from this table to have pairs of key/value in each row?


In HP7, Umbridge, with the locket, says that she is related to Selwyn with the "pure-blood chains."  Is this true?

Dolores Umbridge's dislike of Muggles, Muggle-born witches and wizards and half-breeds is quite obvious. In Order of the Phoenix she takes a particular dislike to Hagrid due to his giantess mother (and his allegiance to Dumbledore), as well as to the centaur Firenze who takes over as Divination teacher after Professor Trelawney is sacked. And, of course, during Deathly Hallows she is made Head of the Muggle-Born Registration Commission.  In Deathly Hallows, when Hermione (under the effects of Polyjuice potion) comments on the locket she's wearing, Umbridge says this:     "That's - that's pretty, Dolores," she said, pointing at the pendant gleaming in the ruffled folds of Umbridge's blouse.      "What?" snapped Umbridge, glancing down. "Oh yes - an old family heirloom," she said, patting the locket lying on her large bosom. "The S stands for Selwyn... I am related to the Selwyns... Indeed, there are few pure-blood families to whom I am not related. ..."   That seems a rather large and contrived lie to tell just to explain her possession of the locket, considering her blood status had never been questioned by the Ministry. I don't remember it being covered anywhere in the books (which I just recently re-read, so I'd hope I'd remember if it had been!), but I was wondering if there was any other evidence (interviews, etc) to say whether Umbridge was Pure-blood, Half-blood or Muggle-born?


I need to find two infinite fields of characteristic $p$ which are not isomorphic.

Can you give me an example of infinite field of characteristic $p\neq0$?  Thanks.


I am new to Java and I am trying to solve an exercise given by my professor. He has given this class  public class MioPunto { public int x; public int y; public String toString() {     return ("[" + x + "," + y + "]");   } }   and I am supposed to write another class with a main method. Into the main I have to print the coordinates without explicitly calling the "toString" method. I unconsciously solved it in this way  public class TestMioPunto{ public static void main(String[] args){     MioPunto inizio = new MioPunto();     MioPunto fine = new MioPunto();     inizio.x=10;     inizio.y=10;     fine.x=20;     fine.y=30;     System.out.println("Inizio: " + inizio + "\n" + "Fine: " + fine);   } }   and the output is  I can't understand how Java automatically called the toString method (brackets and commas), can you please explain?

I used to use the implicit call of toString when wanting some debug info about an object, because in case of the object is null it does not throw an Exception.  For instance:    System.out.println("obj: "+obj);   instead of:  System.out.println("obj: "+obj.toString());   Is there any difference apart from the null case? Can the latter case work, when the former does not?  Edit: What exactly is done, in case of the implicit call?


As we know for synchronous operation while creating singleton class we make whole method as synchronized or only block of statements which are responsible for creation of object as synchronized.But, among these two approaches which one is better and why?  Approach 1  public static A getA(){       if (obj == null){           synchronized(Singleton.class) {             if (obj == null) {                 obj = new Singleton();//instance will be created at request time               }           }        }       return obj;   }    Approach 2  public synchronized static A getA(){       if (obj == null){           obj = new Singleton();//instance will be created at request time       }        return obj;   }

What is an efficient way to implement a singleton pattern in Java?


How can we prove that the series $\displaystyle \sum^{\infty}_{n=1}\frac{n}{1+n^2}$ is convergent or divergent?  Solution I try:  $$\lim_{m\rightarrow \infty}\sum^{m}_{n=1}\frac{n}{1+n^2}<\lim_{m\rightarrow \infty}\sum^{m}_{n=1}\frac{n}{n^2}$$  Did not know how I can solve that problem from that point.

I'm trying to show that the series $\sum_{n=1}^\infty\frac{n}{n^2+1}$ is divergent.   I'm trying to use a comparison test to do so. To do so, I first can see that $\sum_{n=1}^\infty\frac{n}{n^2+1} \geq \sum_{n=1}^\infty\frac{n}{n^2+n} = \sum_{n=1}^\infty\frac{1}{n+1}$ And I can use a change of variable $k = n+1$, so show $\sum_{n=1}^\infty\frac{1}{n+1} = \sum_{k=2}^\infty\frac{1}{k} = \infty$. Then since $\sum_{n=1}^\infty\frac{n}{n^2+1} \geq \sum_{k=2}^\infty\frac{1}{k}$ it must be that $\sum_{k=2}^\infty\frac{1}{k}$ also diverges to infinity. Is this a valid way to show it?


A user  which gets rejected as being too minor. 7 minutes later the same edit gets  by the same user on the same post and gets approved.  So actually this means that someone can repeatedly re-suggest the same edit until it bumps into a set 5 reviewers, from which the 3 of them will approve it. Wouldn't it make more sense if, after having a suggested edit being rejected on post, lose the right to edit this post again (at least for a time period)?  I know that this isn't really important and adding too much complexity in the system just for these rare occasions is not a good idea, but nevertheless it's worth to give it a quick thought :)

It seems that when a user’s suggested edit gets rejected they can simply re-suggest it, and given the  of affairs of the suggested review queue the suggested edit is quite likely to be approved (or if not this time, then it will almost certainly be approved if they are persistent).    As an example I saw the following  which was rejected, very shortly after I saw almost the  suggested again, this time it got two approvals.  Should there perhaps be some sort of delay until a user can suggest an edit after their suggestion was rejected for the same post? Perhaps a check can be made how large of a difference there is between the two suggestions (though I’m not sure it’s worth doing just for this, and a delay is probably sufficient)?   I do understand that a user should be able to re-suggest an edit after it was rejected, since after all perhaps they made a better suggestion after seeing that it was rejected, however in cases like these I don’t think that is what is happening.  I did see  saying that after some rejected edits a user cannot suggest any further edits until a week has passed, but as this is clearly not happening here I guess that may have changed since that post.


I've got a 'ul' list at the top of my page that is used for the navigation bar:    This is currently set using a fixed width div and fixed margins around each of the items. How could I go out making the spaces between the 'menu items' fluid so that page width changes would increase/decrease the margins between them?  For example when the window is pretty wide:    And this when the window is shrunk:    I've been using @media CSS queries so far, but it's pretty messy and not fluid/dynamic. I'll paste the CSS i've currently got:    ul.header_items {     list-style:none;     position:relative;     width: 1250px;     line-height:50px;     margin-left: auto;     margin-right: auto; }  .header_items li{     display: inline;     list-style-type: none;     font-family: 'cabinbold', sans-serif;     color: #ffffff;     padding: 5px 2px 5px 2px;     background-color: #7E489C;     font-size: 14pt;     text-align:center;     text-transform: uppercase;     height: 31px;     box-shadow: 0px 0px 18px 1px rgba(0,0,0,0.2);     transition: 0.4s; }
         <li class="<?php echo $active_page_home ?>" id="header_item_first">Home
         <li class="<?php echo $active_page_dance ?>">Dance &amp; Performance
         <li class="<?php echo $active_page_adult ?>">Adult &amp; Fitness
         <li class="<?php echo $active_page_workshop ?>">Workshops
         <li class="<?php echo $active_page_corp ?>">Corporate &amp; Celebrations
         <li class="<?php echo $active_page_gallery ?>">Gallery
         <li class="<?php echo $active_page_shop ?>">Shop
         <li class="<?php echo $active_page_contact ?>">Contact Us

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      Thanks for your help in advance! If you want to see the navigation bar in action, the url is

You find plenty of tutorials on menu bars in HTML, but for this specific (though IMHO generic) case, I haven't found any decent solution:  #  THE MENU ITEMS    SHOULD BE    JUSTIFIED     JUST AS    PLAIN TEXT     WOULD BE  # #  ^                                                                             ^  #    There's an varying number of text-only menu items and the page layout is fluid. The first menu item should be left-aligned, the last menu item should be right-aligned. The remaining items should be spread optimally on the menu bar. The number is varying,so there's no chance to pre-calculate the optimal widths.   Note that a TABLE won't work here as well:   If you center all TDs, the first and the last item aren’t aligned correctly. If you left-align and right-align the first resp. the last items, the spacing will be sub-optimal.   Isn’t it strange that there is no obvious way to implement this in a clean way by using HTML and CSS?


I have several screen layouts that I have defined:  default, animation, UV, etc.    In some of them, after working in the layout for some time, some of my objects disappear from the scene, and won't show even if I unhide them.  They still show up in other screen layouts and in my outliner.  I assume I'm hitting a button or something, and it's not random, but I haven't been able to figure out what I'm pressing.  I have been able to get around this by deleting my screen layouts and remaking them, but I'm getting tired of doing this.  The objects are all on the same layer, and they won't show up even when I render.    Does anyone know what's happening?

as the title states I am suddenly unable to create any new objects, when i select a mesh from the "create" bar nothing noticeably happens, other than the object name appearing in the list in the top right hand corner of the screen, i cannot edit the object, view the object, or do anything at all to it, this happened suddenly part way through a project and has caused me to be unable to continue, it's driving me nuts and I cannot for the life of me see why this has suddenly happened, im sure i must have accidentally pressed a keyboard shortcut for something, but i do not know what, any ideas?


Under the axiom of choice,  $\mathbb{R}$ and $\mathbb{C}$ are both $2^{\aleph_0}$-dimensional vector spaces over $\mathbb{Q}$. Because they have the same dimension, they are isomorphic as vector spaces. That vector space isomorphism is also a group isomorphism between them.  The proof is clearly non-constructive. Is there a way to explicity construct such an isomorphism, or do we need the axiom of choice?

Consider the abelian groups $G_n=(\mathbb R^n,+)$ for $n\geq1$.     Claim: For any $n$ and $m$ the groups $G_n$ and $G_m$ are isomorphic.   This claim is true if one assumes the axiom of choice, and I have sketched a proof below. But this claim seems much weaker than the axiom of choice, which brings me to the following questions:   Are there any milder extensions of ZF that make the claim true? If the claim can be proven with some other axioms, what does the proof look like? Are there any known  axioms that make the claim false? Does the claim have any interesting (set-theoretical) corollaries?   This claim was also considered in  earlier post, but from a different point of view.    A sketchy proof of the claim:  $\newcommand{\Q}{\mathbb Q}$ The groups $G_n$ are naturally vector spaces over $\Q$. It is easy to check that the claim is equivalent with $G_n$ and $G_m$ being isomorphic as vector spaces over $\Q$.  All vector spaces have a Hamel basis; let the basis of $G_n$ be $B_n$. Thus $G_n=\Q^{(B_n)}$ (brackets meaning only finitely many nonzero components). But $|\Q^{(B_n)}|=|B_n|$ since the basis is infinite, so $|B_n|=|G_n|=|\mathbb R|$.  There is a bijection between the bases of the vector spaces $G_n$ and $G_m$ since they have the same cardinality. This gives a linear bijection between them.


This is a generalization of:    Suppose I'm flying with a certain airline from point A to point C via point B. The maximum luggage allowance on this flight is, say, 2 pieces (never mind the exact weight and dimension limits). At A, I check in 1 piece of such luggage. The plane takes off and puts me in B, where I disembark and go into the airport.  At this point, one of the following happens:   I purchase a bunch of items in the duty free shops, including, say, a suitcase into which I put them. A mysterious stranger somehow hands me a suitcase. The airport has a luggage holding service past its security check and passport control area (I'm not sure there are such airports at all in the world), and I have deposited a piece of luggage there at an earlier time. A friend of mine on the other side of the security, passport and customs checks walks up to the airline's counter, with a duly signed and notarized letter from me asking that they carry a second piece of luggage.   Let's assume my new suitcase is under the weight & dimension limits, but is too large and/or heavy to be carried on board. Assume also that I don't cross into the sovereign territory, i.e. don't pass passports, security and customs control.  Will I be able to have the airline carry my second piece of luggage from B to C? Or rather, are there combinations of airline, airport and scenarios from the above list for which I'll be able to have my second piece of luggage carried to C?

I will have a 10 hour layover in Seoul (ICN) and I want to go out and do some shopping. Is it possible to check in a bag during my layover?  I will be traveling on Korean Air.  I will only have 1 checked bag, and international flights allow 2 bags free.


I have a little trouble understanding how to write a mathematically notation for r = x%n. How should I write this in math notation if I want to get the remainder value, after dividing by $n$? $r$ is also not just an integer in this case, just the rest of $x$ (double) divided by $n$ (integer), "$r = \operatorname{mod}(5.4, 3) = 2.4$" in this case. I think $x \equiv r \mod n$ means something different. Edit: After thinking a while, I am still confused by the notation. Why is the notation $x \equiv r \mod n$ used at all? If $\operatorname{mod}$ is a mathematical operator like $\sin$ or $\cos$, why is the notation $r = \operatorname{mod}(x,n)$ not used always?

Is there an equivalent in mathematical language to the modulo (or mod) function in computing?


I have completed my master's degree year ago and took a gap of 2-3 years before committing to the Ph.D. Right now my financial condition is worse and I don't want to make any decision in any urgency. My peers are getting enrolled for Ph.D. and I am getting worried by watching them. I am 27 right now and planning to collect enough money and build my resume strong to get into a decent Ph.D. program in Europe or Asia. Is my decision wrong? I need some advice from experienced peoples.   Thank you.

Are there any age limits (formal, informal, or guidelines) that schools use when deciding to accept someone into a PhD program? I'm most curious about the upper age limits. For example, will most schools accept someone in their 40's? How about their 50's?


I need to know whether using short URLs to back-link to pages affects your website ranking in the Google search results.

When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs?


I perfectly understand the permutations formula i.e. if you have $n$ things how many ways can you rearrange it if taken $k$ at a time (or if you have $k$ slots)? So you draw the following tree. And the formula comes out naturally. $$^nP_k = \frac{n!}{(n-k)!}$$  I get that it is including all of the duplicates, too. And to get rid of them we use the combinations formula: $$^nC_k = \frac{n!}{k!(n-k)!}$$ Can somebody explain why we have to divide by the "number of ways to re-arrange the slots" to get rid of the duplicates? I understand that it works and the division is used to scale a number down but I am not getting that "aha moment" of why we do it. Can somebody explain it?

I'm reading an algorithm book. In which it mentioned:     Imagine (once again) you have n people lined up to see a movie, but   there are only k places left in  the theater. How many possible   subsets of size k could possibly get in? That’s exactly $C(n,k)$, of   course,  and the metaphor may do some work for us here. We already   know that we have $n!$ possible orderings of  the entire line. What if   we just count all these possibilities and let in the first $k$? The only   problem then is  that we’ve counted the subsets too many times. A   certain group of k friends could stand at the head of  the line in a   lot of the permutations; in fact, we could allow these friends to   stand in any of their $k!$  possible permutations, and the remainder of   the line could stand in any of their $(n–k)!$ possible  permutations   without affecting who’s getting in. Aaaand this gives us the answer!       $$C(n,k)= \frac{n!}{k!(n −k)!}$$      This formula just counts all possible permutations of the line (n!),   and divides by the number of  times we count each “winning subset,” as   explained.   I'm not quite understand why the reminder can in any $(n-k)!$ permutation, if he stands at the end of the queue, won't he let all these people in?  And why I should use $n!$ to divide by $k!(n-k)!$ ? Didn't see that consequence from the metaphor.  If you have better ideas to explain this formula, you can use them of course.


So, I was resolving the equation $xy''+y'-y=0$ by calculating Frobenius series, and I got that the first linear independent solution is $y_1(x)=\sum_{n=0}^{\infty}\frac{x^n}{(n!)^2}$, which kind of looks like the power series for $e^x$, but I don't know what to do to the other $\frac{1}{n!}$.  Does this series converges to a function or should I just leave it indicated as the series?

Does the following series have a closed-form expression:  $$\sum_{k=0}^{\infty} \frac{z^k}{(k!)^2}$$  I know that it must converge because:  $$\sum_{k=0}^{\infty} \frac{z^k}{k!} = e^z$$  and the $(k!)^2$ denominator obviously increases more quickly than the $k!$ denominator.  This problem came up in computing the probability of a draw in a football match with each team's goal scoring modeled as a Poisson process.  Thanks,  John


I've got a 20k bounty and every guard and jarl just try to kill me so I cant speak to them to go to prison or pay it off

I accidentally killed a noble, now every guard wants to kill me. Is there any way I can get rid of the bounty?


Let $F: C \rightarrow D,\ G: D \rightarrow C$ be an adjunction of functors. My goal is to construct an isomorphism  $$Hom_D(F(x), y) \simeq Hom_C(x, G(y))$$  So given a morphism $f(x): F(x)\rightarrow y$, I can form a morphism $g: x \rightarrow G(y)$ by  $$G(f)\circ e_x: x \rightarrow GF(x) \rightarrow G(y)$$  Conversely, given $g: x \rightarrow G(y)$, I can form some $f': F(x) \rightarrow y$, by   $$\epsilon_y \circ F(g): F(x) \rightarrow F(G(y)) \rightarrow y$$  I feel to see why $f = f'$, ie why these two mappings of morphisms I defined are inverses of each other. I'm looking for an answer that carefully spells out why this is the case.

Let a unit-counit adjunction between the categories $C$ and $D$ be defined as a pair of functors $F: D\rightarrow C$ and $G: C\rightarrow D$ with natural transformations $\varepsilon : FG \rightarrow 1_C$ and $\eta: 1_D \rightarrow GF$ such that $$G\varepsilon \circ\eta G=1_G$$ and $$\varepsilon F \circ F\eta = 1_F$$ i.e. for all objects $A\in C$, $G(\varepsilon_A)\circ \eta_{G(A)}=1_{G(A)}$ and for all objects $B\in D$, $\varepsilon_{F(B)}\circ F(\eta_B) = 1_{F(B)}$.  How would I prove that a unit-counit adjunction has the following universal properties?   Given $B\in D$, $A\in C$, and $f:B\rightarrow G(A)$, there exists a unique morphism $g: F(B)\rightarrow A$ such that $G(g)\circ\eta_B = f$. Given $B\in D$, $A\in C$, and $g: F(B)\rightarrow A$, there exists a unique morphism $f: B\rightarrow G(A)$ such that $\varepsilon_A \circ F(f)=g$.   I can see how to prove (say) property 1 for $B,f\in \textrm{Im} G$, which would be a complete proof iff $G$ was surjective: Let $B=G(B_0)$, $f=G(f_0)$. Then $g=f_0 \circ \varepsilon_{B_0}$ works: $G(g)\circ \eta_B=G(f_0)\circ G(\varepsilon_{B_0}) \circ \eta_{G(B_0)}=G(f_0)\circ 1_{G(B_0)}=f$.  But I can't see how to do this for all $B,f\in D$.


I have slow VPN connection to another computer, which is also connected to internet as my computer is.  When this connection is active, all browsing traffic goes via remote computer, although it is slow.  How to say Windows NOT to use this VPN connection with internet at all?  Setting higher metric does not help.

I want to use a Windows VPN but only for a particular network, so that it doesn't take over my entire network connection.  e.g., Instead of the VPN becoming the default route, make it only the route for 192.168.123.0/24  (I can see that there is a solution for this for Ubuntu , but sometimes I have to do this on Windows too)  Can this be automated so that whenever I connect to the VPN it does this?


In The Force Awakens, we see a rogue stormtrooper. This could be explained as a "glitch in the code" and many may have passed it by, but then he says something about being taken away from his family - which is a bit odd, if they were a clone, unless they were given fake families which I highly doubt. This made me wonder if the Empire have stopped using the clones for their storm troopers, and if this is the case, why?

Reading this article about , my nerd-rage started flaring as they claimed that Stormtroopers were still Fett-Clones 20 years after the rise of the Empire.  As I started thinking about it, I realized that everything I had read saying that Modern-Day Stormtroopers not being clones was from the EU - C Level books or games.   One of the quotes often cited for backing the idea that the Stormtroopers are clones comes from Princess Leia:     Aren't you a little short for a Stormtrooper?   But through the movie, paying close attention, Stormtroopers are often shown to be slightly different heights. One even hits his head in the doorway while others walk through uninjured.                                  Is there any G Canon fully canon (non-Legends/Infinities) evidence to support the idea that Stormtroopers are, or are not still clones at the time of Episode IV?


I have geometric network and try to launch Python script with tracing    gdb = "C:/Users/my_user/Documents/ArcGIS/gn/gn.gdb" gdb += "/gn/" geometric_net = gdb + "gn_Net" flags = gdb + "flags" result_name = "gn_Net2"  mxd = arcpy.mapping.MapDocument("CURRENT") df = arcpy.mapping.ListDataFrames(mxd)[0]  result = arcpy.TraceGeometricNetwork_management(geometric_net,                                        result_name,                                        flags,                                        'FIND_CONNECTED'                                        )  gl = arcpy.mapping.Layer(result_name) arcpy.mapping.AddLayer(df, gl, "BOTTOM")   This script do nothing (as I see in ArcMap) - no new group layer in ArcMap, no new layers/feature classes/other instances in current geodatabase.  result variable have some value after last row execution, but I can't determine its type - debugger says thatresult.__class__ returns <class 'arcpy.arcobjects.arcobjects.Result'>, and result returns {geoprocessing server result object} gn_Net2  From  I presumed that result is group layer that I must to add to map. But I can't find Arcpy method which can add group layer to map - only layer adding to map or existing group layer (arcpy.mapping.AddLayer).  What really arcpy.TraceGeometricNetwork_management returns? Did I understood correctly that it's group layer? And it's ready for add to ArcMap via arcpy.mapping.AddLayer method? If no, where is tracing result? How can I see it? What is the arcpy.TraceGeometricNetwork_management result?  Edits: I added   ArcMap document (mxd) and data frame (df) getting Group layer adding   to script. I launches my script from ArcMap via toolbox-script object.  Result of my changes is: Group layer adds to ArcMap document, but without found path (no new layer, selectiong or highlighting). Only geometry network and its layers was added. When I run geometry tracing manually with same conditions (Utility Network Analyst - Solve), found way highlights at map.

I'm trying to make a Python script tool which uses the Trace Geometric Network tool (10.3). My script works in the Python window, but as a script-tool, it runs and NOTHING HAPPENS. Messages state: Executing..., Start time..., Running script..., Completed script... Succeeded at... It acts like the tool executed with no errors, but there's no visible output.   The Trace Geometric Network tool refuses to work inside a Python script tool the way it does in the Python window.  I tried playing with the parameters, data types in of parameter settings, and deleting and remaking the tool several times. I even tried using other geometric networks with the tool. Finally, I made a bare-bones script with only the trace tool to troubleshoot, and NOTHING. I get the same action as above.  Here's my bare-bones script:   geoNetwork = arcpy.GetParameterAsText(0)  inflags = arcpy.GetParameterAsText(1)  barriers = arcpy.GetParameterAsText(2)  arcpy.TraceGeometricNetwork_management(geoNetwork, "Trace", inflags, "TRACE_DOWNSTREAM", barriers)   Here's a screen shot of how I'm setting my parameters in the tool properties:    How can I to get this to work as a Python script tool?  Here's the actual code. As this tool executes, I can see it looping over the flags and selecting them one by one. No output group layer files are added to the map and no apparent traces are made. Again, these functions work as intended if pasted in the python window, but misbehave as python-script tools.   inflags = arcpy.GetParameterAsText(0) geoNetwork = arcpy.GetParameterAsText(1) barriers = arcpy.GetParameterAsText(2) outPath = arcpy.GetParameterAsText(3) outName = arcpy.GetParameterAsText(4)  def makeFullPath(path, name):     return path + "\\" + name  def TraceCapture(inflags, geoNetwork, barriers, outPath, outName):       mxd = arcpy.mapping.MapDocument("CURRENT")     df = arcpy.mapping.ListDataFrames(mxd)[0]     flagList = list(arcpy.da.SearchCursor(inflags, 'UNITID'))     trace = 1     segmentCapture = []     for flag in range(1, len(flagList)+1):          try:             outputLayer = "Trace_" + str(trace)             expression = '"OBJECTID" =' + str(trace)             arcpy.SelectLayerByAttribute_management(inflags, "NEW_SELECTION", expression)             arcpy.TraceGeometricNetwork_management(geoNetwork, outputLayer, inflags, "TRACE_DOWNSTREAM", barriers)             arcpy.AddMessage("Trace_" + str(trace) + " complete")              for lyr in arcpy.mapping.ListLayers(mxd, "", df):                 if lyr.name == "Sewers":                     pipesCursor = arcpy.da.SearchCursor(lyr, 'ASSETID')                     for i in pipesCursor:                         segmentCapture.append((flagList[trace - 1][0], i[0]))                 if lyr.name == outputLayer:                     arcpy.mapping.RemoveLayer(df, lyr)             trace += 1         except RuntimeError:             print "Flag " + str(trace) + " was invalid and skipped."             trace += 1             continue      arcpy.CreateTable_management(outPath, outName)     outFile = makeFullPath(outPath, outName)     arcpy.AddField_management(outFile, "manholeID", "TEXT", "", "", 10)     arcpy.AddField_management(outFile, "pipeID", "TEXT", "", "", 10)      with arcpy.da.InsertCursor(outFile, ["manholeID", "pipeID"]) as cursor:         for row in segmentCapture:             cursor.insertRow(row)  TraceCapture(inflags, geoNetowrk, barriers, outPath, outName)


About everything (even clear and open) is giving 'Command Not Found' on the Terminal.  If I do and echo $PATH, it gives me this. /Users/username/Documents/android/android-sdk-macosx/platform-tools:/Users/merck/Documents/android/android-sdk-macosx/tools  The /.profile file is not even there in the Finder.  The environment.plist file in .MacOSX has this value. bplist00—_SENCHA_CMD_3_0_0_$/Users/username/bin/Sencha/Cmd/4.0.2.67E  Can anyone give some pointers.

I'm really new to Mac OSX and UNIX based systems. I wanted to run a few Windows games on my Mac Mini so I started installing Wine and MacPorts. I think the installs are correct, but when I type sudo port install wine I see a not found error in my terminal. I tried other basic commands like say and clear and all of them return the same not found error. My research shows that my PATH might be incorrectly set, but it lacks steps I can implement. Specifically, I ran this command: echo $PATH and it returned:  /opt/local/bin:/opt/local/sbin:/opt/local/bin:/opt/local/sbin:/opt/local/bin  I'm a complete newbie to mac and have no idea where .bash_profile or any of those files are. My skills let me install Xcode and the Command Line tools for Xcode and I sense I need to level up on path management. At this point I need help managing my dot files and changing my path to fix these specific errors on Mountain Lion. What are my next steps?


The covariance (and correlation) are described as the strength of a linear association between variables. Is there a way to see where the 'linear' part comes from in the formula?

1) What is meant by linear dependence?  2) How can I convince myself that covariance measures linear dependence?   3) How I can convince myself that non-linear dependence is not measured by covariance?


Prove that: $x^2+y^2+z^2=2xyz$ has no answer over $\Bbb{N}$   $$LHS=(x+y+z)^2-2(xy+yz+xz)=2xyz \implies (x+y+z)^2=2(xy+yz+xz)+2xyz$$ now what??

Calculate all integer solutions $(x,y,z)\in\mathbb{Z}^3$ of the equation $x^2+y^2+z^2 = 2xyz$.   My Attempt:  We will calculate for $x,y,z>0$. Then, using the AM-GM Inequality, we have  $$ \begin{cases} x^2+y^2\geq 2xy\\ y^2+z^2\geq 2yz\\ z^2+x^2\geq 2zx\\ \end{cases} $$  So $x^2+y^2+z^2\geq xy+yz+zx$. How can I solve for $(x,y,z)$ after this?


I have tried many times on my realm to set keepinvintory to true using a command block and changing the capitalization  but it wont work. Whenever I /kill I still lose my stuff. Is it possible to do on a realm? Or what am I doing wrong?

I once played a vanilla Minecraft adventure map (called "Herobrine's Mansion") that prevented the player from losing their items on death. Which commands can be used to prevent the player from losing their items on death (in vanilla Minecraft)?


There seems to be a paradox which shows up when defining set theory and logic. On one hand, set theory appears to be grounded in logic. However, on the other hand, sets are required to define necessary properties of logic. Have I misunderstood something? Because from my perspective, it seems that a set would need to exist before it can be defined...

I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.  Now is the "=" taken as undefined? I have seen it been defined in terms of the identity relation.  But in order to talk about functions and relations you need set theory.  However,  seems to be a part of mathematical logic.  Does this mean that (naive) set theory comes before sentential and predicate logic? Is (naive)set-theory at the absolute bottom, where we can define relations and functions and the eqality relation. And then comes sentential logic, and then predicate logic?  I am a little confused because when I took an introductory course, we had a little logic before set-theory. But now I see in another book on introduction to proofs that set-theory is in a chapter before logic. So what is at the bottom/start of mathematics, logic or set theory?, or is it circular at the bottom?  Can this be how it is at the bottom?  naive set-theory $\rightarrow$ sentential logic $\rightarrow $ predicate logic $\rightarrow$ axiomatic set-theory(ZFC) $\rightarrow$ mathematics  (But the problem with this explanation is that it seems that some naive-set theory proofs use logic...)  (The arrows are of course not "logical" arrows.)  simple explanation of the problem:  a book on logic uses at the start: functions, relations, sets, ordered pairs, "="  a book on set theory uses at the start: logical deductions like this: "$B \subseteq A$", means every element in B is in A, so if $C \subseteq B, B \subseteq A$, a proof can be "since every element in C is in B, and every element in B is in A, every element of C is in A: $C \subseteq A$". But this is first order logic? ($(c \rightarrow b \wedge b \rightarrow a)\rightarrow (c\rightarrow a)$).  Hence, both started from each other?


public class ParametricIndicators {     static Method GET_PARAMETRIC_INDICATOR; //equal to a double number (as parameter)      static {         try {              GET_PARAMETRIC_INDICATOR = ParametricIndicators.class.             getDeclaredMethod("getParametricIndicator", new Class[]{ArrayList.class, short.class});          }          catch (Exception e) {             System.out.println("Predicate.static: " + e);         }     } }   I am new to Java, and I am converting a java codebase to C#. I want to know what type of code is this? Is it a getter?   static {             try {                  GET_PARAMETRIC_INDICATOR = ParametricIndicators.class.                 getDeclaredMethod("getParametricIndicator", new Class[]{ArrayList.class, short.class});              }              catch (Exception e) {                 System.out.println("Predicate.static: " + e);             }         }

My question is about one particular usage of static keyword. It is possible to use static keyword to cover a code block within a class which does not belong to any function. For example following code compiles:  public class Test {     private static final int a;         static {         a = 5;         doSomething(a);     }     private static int doSomething(int x) {         return (x+5);     } }   If you remove the static keyword it complains because the variable a is final. However it is possible to remove both final and static keywords and make it compile.   It is confusing for me in both ways. How am I supposed to have a code section that does not belong to any method? How is it possible to invoke it? In general, what is the purpose of this usage? Or better, where can I find documentation about this?


The manga makes it plenty clear that Sasuke can/does not use Tsukuyomi. Both his eyes have powers related to Amaterasu only. But why? Madara and Kakashi could use Kamui using Obito's eyes and Danzo could use KotoAmatsukami using Shisui's eyes. Then why not Sasuke? We have seen that during fight with Kabuto, he uses ordinary sharingan genjutsu on Itachi when freeing him from Kabuto's sound genjutsu.  Does this mean that once you achieve your own MS powers, implanting someone else's eyes does not grant you their power but just give you EMS?  Does the eye transplant work differently for non-Uchihas, as in they just gain the original eye power?  But this still does not explain Madara's using Kamui.  Edit: People seem to be confused about the fact that Sasuke can NOT use Tsukuyomi. Here is the detailed answer I wrote:   Here is a  that clearly states the only user is Uchiha Itachi

The question is based on my theory from the recent manga chapter (Naruto 661):     Sasuke, when stabbed by Madara is the effect of Tsukuyomi from Sasuke.   Now, to prove my theory, is there an episode in manga/anime that Sasuke used Tsukuyomi?


Recently, I saw a video showing a penalty kick replayed twice because the goalkeeper advanced from the goal line.  My question is: what is the distance allowed for the goalkeeper to be off the line during a penalty kick? And generally, have these kind of incidences happened before?

The laws of the game prohibit encroaching on a penalty kick whether it is an attacking player or defending player.  The keeper is supposed to remain on the line until the kick is taken but in practice this is a loose interpretation; movement off the line is common.   My question is: if another player (besides the keeper and penalty taker) has a foot on/over the line of the 18 yard box or the arc, what grounds are there for a retake or an indirect kick out?  Is it a similar loose interpretation which goes unpunished or shall it be referenced as an offside play or simply an infringement?


My screen on HTC Wildfire has gone blank and so have got my phone upgraded. Whilst the guy in the shop was able to transfer my pictures and video, when he tried to transfer my contact phone numbers he said he couldn't do that without putting the phone into debug mode, and he could only do that if he could see what he was doing on the screen.  Is there any way of getting a HTC Wildfire into debug mode without having to use the screen?

The screen of my phone is physically broken, so it doesn't display anything, but the touch aspect does seem to be working, as I can unlock my phone, and get haptic feedback.  Before I go to get it replaced, I'd like to back up some personal data from the built-in memory to the SD card. I'm fairly certain that if I can get adb to recognize the device, then I can use  to see where I am touching the screen and do what I need to do. Problem is, when I plug it in, it's not recognized, while my emulator is.  I suspect that I might not have USB debugging enabled, which I think is necessary for adb to work. If this is the case, can someone give me screenshots of their Droid X (running 2.3.X) going from the home screen, through all the menus, to activating debug mode? Hopefully I can do it by dead reckoning and adb from there.  Edit: I haven't changed anything about the ROM or launcher; it's all stock.


I have a URL, for example: http://www.di.fm/calendar/event/40351  I want to parse this URL with a regular expression, and retrieve the part after domain.  In this case :calendar/event/40351  There can also be additional information after a hash: (e.g., calendar/event/40351#event-info)

Given the URL (single line):   How can I extract the following parts using regular expressions:   The Subdomain (test) The Domain (example.com) The path without the file (/dir/subdir/) The file (file.html) The path with the file (/dir/subdir/file.html) The URL without the path () (add any other that you think would be useful)   The regex should work correctly even if I enter the following URL:    http://example.example.com/example/example/example.html


Let $f:[0,1] \to R$ be a continuous function. Then prove   $\int_0^1f^2(x)dx \ge (\int_0^1|f(x)|dx)^2$.    I am getting a lot of problems of this type and I don't know how to even begin solving this type of problems.   Can anyone please tell me how to approach problems of this type?  Thank you.

$f:[0,1]\to \mathbb R$ , be continuous function then prove that    $$\int_0^1f^2(x)dx\geq \biggl(\int_0^1|f(x)| \biggr) ^2$$   I tried this for $x^2$  For that above is true   But I checked following proof Which is complete opposite to above.   Please help me to find that where is I am making wrong ?  Any help will be appreciated


The bottom of the reputation card on the activity page is all squished together:     The "next privilege" seems to be overlapping with the rep graph or something...is this on purpose? Has it always been and I just haven't visited my profile in forever? Or is it a bug?  I'm on Chrome on a Mac booting Windows. The track a tag badge is looking good for me on Sci-Fi and Fantasy (where the above pic is) but on Quantum Computing where I'm a mod there's no button to switch back to the rep-next-privilege dealio, which I guess is because there's no more privileges for me to get as mod? (But what about rep milestones?)

It seems "See votes, expandable user card" goes on a second line on the activity page of the user profile resulting in a pretty bad look:    You can see it live on  (though of course that may change any day now depending on their rep-growth).  I'm using Chrome Version 67.0.3396.99 (Official Build) (64-bit)


In the view of the recent Worldbuilding election, I wanted to check the profile of the voters (based on Constituent badges awarded). And one idea was to look at the reputation of the users.  However some users have a rather low reputation on Worldbuilding (specifically) whereas they have a high reputation on other site. Is there a way to run a query on Worldbuilding, and see, for all users, their network reputation?

I think it would be useful if we could join across databases in the data-explorer.  For example, I'd like to query up a list of questions that I had a hand in migrating away from SO, and see what percentage of them were subsequently closed or re-migrated.  I realise I could download the various data dumps and do this on my own machine, but it would be nice if it were allowed on the online version.  Is this possible/practical?


I'm planning to study Java EE but I do not know where to start.   Based on  there are technologies present in lower versions which are not available in the higher version. Do I need to learn J2EE 1.4 before learning Java EE 5 or 6? Or is it better to learn the latest version since their purpose of doing it is to improve the previous version.   Can you also suggest some resources on Java EE?

I am about to start a web project and have been working almost exclusively with a LAMP stack for the past 5 years.  I would like to build something larger and more scalable and hence have been looking into Java EE.  The division of logic between JSP and EJB seems ideal for what I want to do.  Can anyone recommend resources for getting familiar with Java EE?  And perhaps if anyone knows of technologies that are more scalable than PHP that I should consider as well, I'm all ears.  Thanks a lot!


I found the information to know ++i is more efficient, so I wrote a piece of code.  long iStartTime = System.nanoTime(); for (int i = 0; i < times; i++) { } long iEndTime = System.nanoTime(); System.out.println("i++: " + (iEndTime - iStartTime));  long startTimeI = System.nanoTime(); for (int i = 0; i < times; ++i) { } long endTimeI = System.nanoTime(); System.out.println("++i: " + (endTimeI - startTimeI));   when times is 100:  i++: 3911 ++i: 3632   when times is 999999:  i++: 4242438 ++i: 3434235   but when times is 1000:  i++: 11734 ++i: 32406   Why this happend?

How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related:


Find all $ f : R\rightarrow R $ such that $f(x^2+f(y))=(f(x))^2+y, \forall\text{ x,y}\in R$  Thanks in advance!

How to solve the following functional equation:  Find all $f:\mathbb{R}\to\mathbb{R} $ such that: $$ f\left(x^2+f(y)\right)=y+f(x)^2 $$ Holds for every $x,y\in\mathbb{R}$.  A friend gave it to me, probably its an olympiad question.  I started with the equation $f(f(y))=y+f(0)^2$ which seems to be quite helpful, but I couldn't do it effectively. How to solve it properly?


For an illustration, see the following MWE.  MWE  \documentclass{article} \usepackage{etoolbox}  \newcommand\Push[1]{\gappto\Array{#1}}   \newcommand\NewItem[2]{%     \expandafter\newrobustcmd\csname#1\endcsname{#2}%     \Push{#1}% }  \newcommand\PrintOut{%  % for each <x> in \Array, call \<x> }  \NewItem{Books}{There are 3 books in stock.} \NewItem{Pencils}{There are 2 pencils in stock.}  \begin{document} \section{Manually printed} \begin{enumerate}     \item \Books     \item \Pencils \end{enumerate}  \section{Automatically printed by iterating \textbackslash Array} \end{document}   Questions  How to iterate the list \Array and call the corresponding macro for each element?

How can I iterate, loop, process, or otherwise do something, with each element from a comma separated list of things?  This question       , and the are already lots of very good answers everywhere. However I think it would also be valuable to have a single reference point where all such alternative techniques are explained in detail, with their advantages and disadvantages discussed.  All of plain-TeX, LaTeX, LaTeX3, LuaTeX, Context, etoolbox, pgffor, etc. answers are invited. Please consider explaining, for example:   How does the command/method deal with whitespace around items? How does the command/method deal with empty/missing items? (e.g. a,b,,c) How does the command/method deal with a trailing comma? Can the command/method work of a list stored on a macro? Is each iteration evaluated globally or on a local group? (i.e., if a command is defined during an iteration, does the command survive the loop?) Do items get expanded or somehow mangled before being processed? What about lists where items are key=value or some other kind of pairs? Does the method work for lists separated with something other than a comma? Any other thing I should know before deciding to use this method?


After a few hours I am about to give up on finding a kind of documentation for the QGIS Python API that actually works/gives the correct information. It is obvious that there is no actual code documentation besides the one for the C++ API which differs from what works in Python. Ok, there is the help()-function, too, to get information about classes which is more than ust tedious to use. As an entry point, I thought I could use the tutorials/cookbook: . Even simple things like adding features does not work the described way in the current QGIS Version 2.4.0-Chugiak (there is no addFeature-function for example).  I wonder how working with the Python console and writing plugins makes sense under such unfavorably conditions.  What sources can actually be used to lookup and learn the Python API for QGIS for current versions?

I'm looking for some resources for learning PyQGIS.  It would be interesting having a collection of books or websites that provide some practical examples for learning the syntax or accomplishing specific tasks.  Ideally, these resources should give a general guidance for both beginner and experienced users.   is a very similar question, but it gives help for learning QGIS, and not specifically PyQGIS (in fact, it doesn't have the PyQGIS tag).  Any help?


I have multiple servers which host several sites, some of them being QA environments.  Unfortunately, Google has found its way to some of them, and it is displaying results which are in fact competing with the corresponding live site URLs, for multiple sites.  Is there a way I can tell google, via analytics or something similar, to simply delist all of the existing information for subdomains *.a.example.tld or *.b.example.tld?

My code base is shared between several environments (live, staging, dev) & sub-domains (staging.example, dev.example, etc.) and only two should be allowed to be crawled (ie. www.example and example). Normally I'd modify /robots.txt and add Disallow: /, but due to shared code base I cannot modify /robots.txt without affecting all (sub)domains.  Any ideas how to go about it?