RELEVANT DEFINITIONS  We define the floor of a real number $x$ to be the unique integer $n = \lfloor x \rfloor$ such that $n \leq x < n$.  We define the modulo of a real number $x$ with respect to a real number $w$ to be the real number value $y = x \% w = x - w \lfloor \frac {x}{w} \rfloor$.    MATHEMATICAL CONTEXT  Integration is a useful tool by which to analyze functions. The derivative is similarly a useful tool as well. Determining a means by which to integrate and differentiate functions that are trickier than most functions or requiring a different skill set than normally taught in a calculus course is therefore beneficial to others.    POTENTIAL USAGE  The modulo function or "saw tooth wave" (as some sites such as Wolfram Alpha appear to call it) can be used to represent discrete wave functions which are sometimes used in signal processing.  I'm not entirely sure what the floor function might be useful for in the real world other than for approximating functions. For example, $x \lfloor x \rfloor$ approximates the general shape of $x^2$. Therefore it stands to reason that there are cases for which clever replacement of $x$ with $\lfloor x \rfloor$ (or something similar) may be useful in coming up with a decent approximation of a function that could potentially be integrated more easily than     KNOWLEDGE LEVEL  At the time I made this post according to the date I was in a calculus 2 course that covered your standard integration methods and other single dimension function related things such as polar coordinate integrals. There was defintiely no interaction between that course or it's predecessor with the two titular functions.  As for my knowledge level at this time... if I were asking this question now I wouldn't be asking it at all because I'd already be able to figure it out myself.    REASON FOR ASKING  Nothing ever talked about how to deal with floor or modulo when combined with integration/differentiation, so I wanted to know how.    THE PROBLEM STATEMENT  Let $f(x)$ and $g(x)$ be functions of $x$. For simplicity's sake and because of the knowledge level being considered let us also assume they can be written as an expression of $x$, $+$, $\cdot$, $\^$, $\ln$, $\cos$, and $\sin$. We don't want them to be anything real unusual, but an answer is allowed to treat them as continuous differentiable and integrable functions if that makes the answer simpler (for example if the reasoning generalizes in some fashion).  Is there a reasonably simple identity that allows one to find the solutions to:  $\int \lfloor f(x) \rfloor dx$  $\int f(x) \% f(y) dx$  $\frac {d}{dx} (f(x) \% f(y))$   $\frac {d}{dx} (f(x))$  If there isn't such a rule or identity or integration method, could someone explain why? Is it simply because they aren't useful enough to warrant messing with and therefore the knowledge base regarding these functions is limited at best, or is there something deeper here that makes the existence of such an identity impossible?    MY ATTEMPT(S)  I honestly had no idea how to solve this when I originally asked it. I recall that in the original post was some really horrible hand-waved reasoning about asymptotes and such that I think ultimately just boiled down to "I can do this if the number of discontinuities work out to being finite because then I just know the answer" - that's equivalent to saying I can find some integrals in very niche specific cases by flat out guessing. While that's a valid way to find integrals in the real world if you're dealing with a problem that you might be able to make an educated guess about, it is not real helpful here as an attempt. That's why I'm not rewriting it.  As for an attempt now... I think the expiration date has already passed on that. Providing an attempt 4 years later (actually a solution) would be best done in an answer.

[This answer has been heavily edited in response to a long chain of comments on Eric Stucky's answer.]  I came up with these few theorems and I am curious whether or not my hypothesis are true. I don't really have a method for proving these, mind you. I'm more considering these as things I've noticed to be true. I just don't know whether they are always true.  Some of these are definitions to which I will append "def." to the end of the title. Think of these as a given. It's like how the integral is defined abstractly as area. I'm defining terms.  Jump Series Theorem def.  A function $f$ [consisting of floor] is said to have a jump series if there is a series $\Sigma=\sum_{n=1}^\infty a_nH_n$ of scaled step functions such that $f+\Sigma$ no longer has any discontinuity attributable to floor. The sequence of scaling factors $a_n$ is called the jump sequence for the function.  Definition of Implied Derivative def.  We define the evaluation of the implied derivative of a function $y$ at the point $x$ as the set of values $y^{\to}(x) = \{y | y = \lim_{h \to 0^+} \frac {y(x+h) - f(h)}{h} \lor y = \lim_{h \to 0^-} \frac {y(x+h) - f(h)}{h}\}$. It is in this sense that the implied derivative has the potential of being a multi-valued operator.  Jump Series Resolution Theorem  [The original wording is preserved; I have a formalism but it assumes that having a jump function is equivalent to being piecewise continuous, which I'm not sure is true.]   The integral of a floor-based function is floor treated as a constant minus the appropriate jump series of the integral.  Integration Continuity Theorem  The (ordinary) indefinite integral of any function $f$ having a jump series must be continuous (or fixably discontinuous) on the domain of $f$. However, this can vary for the implied indefinite integral.  Calculus Jump Theorem def.  [Again, the original wording is preserved; the meaning of this phrase has not been properly illuminated]  Any form of jumping within a function representable as a floor function can be considered as a portion of the constant of the implied integration for floor.  Jump Location Theorem  For any function $a(x)$ with a jump series, the function $\lfloor a(x)\rfloor$, has points of discontinuity precisely at those $x$ such that $a(x) - [a(x)] = 0$.  Composite Floor Function Jump Sequence Theorem One  If $a$ is a function such that $a(x) - \lfloor a(x) \rfloor = 0$ when $x - \lfloor x \rfloor = 0$, then the jump sequence of the composite function $f(x - \lfloor a\rfloor)$ is a constant value $f(0) - f(1)$.  Implied Differential Equations Conjecture  Any continuous solution to an equation constructed with implied derivatives of various orders is the same as the solution to the similarly constructed differential equation.


I am facing an issue with my brand new MacBook Air 2019 Retina True Tone model  When I put my Mac to sleep, close off the lid and let it stay like this overnight (roughly for about 6-7 hours), when I open the lid again, my Mac doesn't starts automatically. Even when I press the trackpad, spacebar etc, it doesn't wake up. I have to press the power button to turn it back on.  However, during the day, in my breaktime I leave it on sleep mode and close the lid for about 1-2 hours, opening the lid wakes up the MacBook normally.  This machine is working just fine for me except for when I wake up every morning and see that I can't start my work from where I left because my MacBook doesn't comes out of sleep.I have to shut down using the power button and then turn on my Mac.  Can someone tell me a concrete solution to this? Because I can't test each solution separately because it would consume too many days since the only time I can leave my Mac on sleep for about 5-6 hours is when I sleep.  Note : Yesterday I had updated my OS to Catalina as per the recommendation of apple chat executive, but the same problem happened today morning aswell and right now my software is up to date.

When I close my MacBook Pro in the evening, and then open it in the morning, the display is illuminated and the apple is bright but nothing is happening. So I need to push the power button to restart it. When it restarts, Google Chrome crashes and virtualenv is logged out.   I thought that the problem is with hibernation so I set the hibernation to 0 in pmset. My current pmset parameters are as follows:   standbydelay         10800  standby              1  womp                 1  halfdim              1  hibernatefile        /var/vm/sleepimage  powernap             1  gpuswitch            2  networkoversleep     0  disksleep            10  sleep                1  autopoweroffdelay    86400  hibernatemode        0  autopoweroff         1  ttyskeepawake        1  displaysleep         10  acwake               0  lidwake              1    2018-10-05 12:50:03 -0700 Assertion status system-wide: BackgroundTask 0 ApplePushServiceTask 0 UserIsActive 1   PreventUserIdleDisplaySleep 0 PreventSystemSleep 0 ExternalMedia 0 PreventUserIdleSystemSleep 0 NetworkClientActive 0   Listed by owning process: pid 94(hidd): [0x0000000e00098030] 00:00:00   UserIsActive named:"com.apple.iohideventsystem.queue.tickle.4294968174.3" Timeout will fire in 600 secs Action=TimeoutActionRelease pid 188(mds_stores): [0x00000115000b80fd] 00:00:00   BackgroundTask named: "com.apple.metadata.mds_stores.power"   Kernel Assertions: 0x100=MAGICWAKE id=503 level=255 0x100=MAGICWAKE mod=31.12.1969, 16:00 description=en0 owner=en0   Idle sleep preventers: IODisplayWrangler   If I close the lid shortly everything is okay. Any ideas on what is going on?


I am dynamically loading functions as needed in my web app. When I request these functions as I need them, I'd like to check if they already exist. So I pass in an array of the function names such as ['Result','Question']. I then loop through that array and would like to see if it's typeof is a function, if so, then I know I don't need to load it.  Here is a simplified version:  function Result(){} var functionName = 'Result'; if (typeof functionName == 'function'){     alert('function exists, don't load it'); else     alert('function does not exist, load it');   I know the above example doesn't work because I need the value of functionName, not functionName itself. Any ideas how to do this?

I have the name of a function in JavaScript as a string. How do I convert that into a function pointer so I can call it later?  Depending on the circumstances, I may need to pass various arguments into the method too.  Some of the functions may take the form of namespace.namespace.function(args[...]).


Show that F = $\{a + b\sqrt{3}\} | a, b \in \mathbb Q\}$ is a field under the operations + and $\cdot$, where + is given by $(a + b\sqrt{3}) +(c + d\sqrt{3}) = (a + c) + (b+d)\sqrt{3}$ and $\cdot$ is given by $(a + b\sqrt{3}) \cdot(c + d\sqrt{3}) = (ac + 3bd)+ (ad + bc)\sqrt{3}$  Do I just have to show it satisfies all the $A1 - A4, S1 - S4$ axioms?    For example:  $A1 = u + (v + w) = $  $$=(a + b\sqrt{3} + ((c + d\sqrt{3}) + (e + f\sqrt{3})) = (a + b\sqrt{3}) + ((c + e) + (d + f)\sqrt3{}))$$  $$= (a + c + e) + (b + d + f)\sqrt{3}$$  Also:  $$(u + v) + w = ((a + b\sqrt{3}) + (c + d\sqrt{3}) ) + (e + f\sqrt{3})$$  $$= (a + c + e) + (b + d + f)\sqrt{3}$$  Satisfies one of the eight of the axioms. Is this what I am suppose to do?    If so, I don't get how to check the scalars for example  S1: $r(u + v) = ru + rv$  $$= r((a + b\sqrt{3}) + (c + d\sqrt{3}))$$  $$= r((a+c) + (b+d)\sqrt{3})$$  Unsure what to do after this

Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field  I am having a little trouble proving that for each non-zero $b\in\mathbb{Q}(\sqrt{p})$, there is $d\in\mathbb{Q}$ such that $b\cdot d=1$.  My attempt:  Let $b=a_1+b_1\sqrt{p}$  Let $d=a_2+b_2\sqrt{p}$  We want $$b\cdot d=(a_1+b_1\sqrt{p})(a_2+b_2\sqrt{p})$$ $$=a_1a_2+a_1b_2\sqrt{p}+a_2b_1\sqrt{p}+b_1b_2p$$  $$=(a_1a_2+b_1b_2p)+(a_1b_2+a_2b_1)\sqrt{p}$$ $$=1$$  Am I following the right approach? What should be my next step


I know these layouts have two-letter codes like us for the US layout. I need a list of all the layouts available and also to pair the two-letter codes to the proper names of the layout to get the not so trivial ones.

Is there a way from command line to retrieve the list of all available keyboard layouts and relative variants?  I need to list all the valid layout/variants choices to be used then from setxkbmap.  Also about the layout toggle options, is there a way to retrieve a list of all available choices (e.g. grp:shift_caps_toggle , ...)  I know that with  setxkbmap -query   I retrieve the list of my current ones, but I need the whole list of options.  UPDATE:  I've been told about the command  man xkeyboard-config   which provides all the info to the command line.  Furthermore, using  man -P cat xkeyboard-config   the output goes to stdout and can be parsed with scripts or c code


As we all know: $$\mathcal F\{\delta(t)\} = 1$$ and: $$\mathcal F\{x(t-k)\}=X(f)e^{-i2\pi fk}$$  However when I try to use these properties to calculate the Fourier transform (FT) of an impulse train, $x(t) = \sum_{n=-\infty}^{\infty}\delta(t-nT)$, I get: $$\mathcal F\{x(t)\}=\mathcal F\{\sum_{n=-\infty}^{\infty}\delta(t-nT)\} = \sum_{n=-\infty}^{\infty}e^{-i2\pi nTf}$$ As far as I know, the FT of an impulse train should be another impulse train, but the RHS in the expression above doesn't look like it. What am I doing wrong?  Thanks for your time!

Let $f(x) = \sum_{n=-\infty}^{\infty} \delta(x - n)$, where $\delta$ is the Dirac delta function. This function $f$ (a "comb function") is important in signal processing because evenly sampling a function $g$ can be viewed as multiplying $g$ pointwise with $f$. This idea is the first step towards understanding how to approximate the Fourier transform of $g$, given evenly spaced samples of $g$. The next step is to note that $\hat{gf} = \hat{g}*\hat{f}$, where $\hat{f}$ is the Fourier transform of $f$ and $*$ denotes convolution.  Is it true that $\hat f$ is also a comb function? If that statement isn't quite right, what is the correct statement?  I would like to see: 1) an informal, intuitive, nonrigorous but easy derivation of the Fourier transform of $f$ . 2) A rigorous version of the same calculation.  (How would you even define $f$ rigorously, is it a distribution?)  (I'd also be interested in recommendations of math textbooks that cover this topic, including the Nyquist sampling theorem, even if it's only an exercise or series of exercises in an analysis textbook.)


I am examining a string of text, and I am looking to change certain words in the text, ignoring anything inside quotation marks.  Example:  If I wanted to replace "my" with "MY"  Hello my name is "Tom, and my favourite sport is football"   Would become  Hello MY name is "Tom, and my favourite sport is football"   I am using regex to search for the words to be replaced.   I'm writing this script in Python.  Edit: I will be searching the original text for words from a list, not literal words.  It is also important to match 'whole words'.

I would like to find a regex that will pick out all commas that fall outside quote sets.   For example:  'foo' => 'bar', 'foofoo' => 'bar,bar'   This would pick out the single comma on line 1, after 'bar',  I don't really care about single vs double quotes.  Has anyone got any thoughts? I feel like this should be possible with readaheads, but my regex fu is too weak.


Given that it's very useful to generate minimal reproducible examples when asking for help, it seems like a online LaTeX sandbox would be beneficial.  For those unaware,  and similar sites allow users to mock-up minimal reproducible examples of javascript code that is useful for debugging on sites like StackOverflow.

I have heard rumors that you can compile documents online, and more specifically that Google has a free online compiler, but I have never been able to find any. Is there a way to compile documents online, so that I can write and compile documents even if I don't have a TeX distribution installed on my computer?


Let $V$ be an inner product space, and $F :V\to V$ a linear map.   Some say that $F$ is an isometry when $\langle F(u),F(v)\rangle = \langle u,v\rangle \forall u,v\in V$. Others say that $F$ is an isometry when $||F(u)||=||u||$ $\forall u\in V$.     Show that these two meanings are equivalent.

Consider a map $T:\mathbb{R}^2\to\mathbb{R}^2$ such that $\lVert T(x)\rVert=\lVert x\rVert$.   Is this equivalent to stating that $\langle x, y\rangle=\langle T(x), T(y)\rangle$ for all $x,y\in\mathbb{R}^2$, where $\langle\cdot,\cdot\rangle$ denotes the usual inner product?


Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $$f(x^2 + y + f(y)) = 2y + (f(x))^2$$  I tried something like  but that inner $f(y)$ makes things worse to my opinion. Any help is appreciated.

I want to find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for all $x,y\in\mathbb{R}$: $$f(x^2+y+f(y))=2y+f(x)^2.$$  Suppose we have given a solution $f$. Then $f$ is surjective (set $x=0$). Moreover, I have shown that $f(-x)^2=f(x)^2$ for all $x\in\mathbb{R}$ as well as $f(x)=0\Rightarrow x=0$. But I could not make any progress.  I tried for example $y:=-f(x)^2/2$. Then we get $x^2-f(x)^2/2+f(-f(x)^2/2))=0$. Can someone tell me how to proceed?  Best wishes


When the number of observations is even, say 2n, it is customary to define the median as the average of the nth and (n +1)st rank-ordered values.  The clause 'say 2n' between two comma appears to be grammatically wrong since it neither contains subject nor has reduced relative clause structure. What structure is this?

The narrator, in the quote, said that things turned out to be   horrible.   According to the question I previously posted, this parenthetical prepositional phrase "in the quote" is made possible by whiz deletion. But when I applied whiz deletion to it, it turned out to be a disaster.     The narrator, who was in the quote, said that...   Surely, what I was trying to say was that narrator said something in the quote, not that narrator was PHYSICALLY in the quote.  Here is another example.     They, (who were) after so much thinking, finally decided.   Now it is just not right.   So my another interpretation was that there was an absolute phrase with "being" deleted, but it brought about the same result. You can see what I mean if you substitute who was/were for being.   So, why is it possible to use parenthetical prepositional phrase in the middle of sentence? Is there anything deleted?


I recently installed my ubuntu and am new to it. I have some projects with me related to video editing and since you can see, I have switched from windows to linux. I wanna know the best video editor for Ubuntu/Linux  thanks in advance for your suggestions.

What video editing software would you recommend on Ubuntu (or Linux in general) and why?  It can be for either beginners or experienced users.  Please only place one piece of software per response and include details to what makes it great!


in my view controller.m i have a string like this   NSString *valueToSave = @"someValue";   and would like to safe the text with NSUserDefauls in Appdelegate.m   [[NSUserDefaults standardUserDefaults]  setObject:valueToSave forKey:@"preferenceName"];   how can i use the NSString in the other file?  This doesn't work:  #import "viewcontroller.m";

I'm developing a  application, and I'm using constant NSStrings as ways to store key names for my preferences.  I understand this is a good idea because it allows easy changing of keys if necessary. Plus, it's the whole 'separate your data from your logic' notion.     Anyway, is there a good way to make these constants defined once for the whole application?     I'm sure that there's an easy and intelligent way, but right now my classes just redefine the ones they use.


I'm almost sure I read it in english, in a collection, more than 40 years ago. It was just possibly a shortish novelette, probably a short-story.  A plague has decimated mankind. Even though a cure did exist, only a single man managed to get access to it before everybody else was killed. He still has occasional fits of paralysis, prelude to death, but since the amount of medicine he has access to is huge, meant for a whole city, he can inject it over and over for his life-time and more.   The only other survivor was a woman who happened to be immune. The man wants to restart the human species. He hopes their future children can get the cure for long enough that eventually the plague will be definitely eliminated.  But he has to convince the woman. And she is very puritan. She wants a big marriage before starting a family. His arguments that there could be no priest or pastor to marry them leaves her undeterred : he can perform the rites himself, but she wants a white dress, flowers, and so on. So he manages to get all she wants, and they are about to enter together the big empty church. At the last minute, he has a pressing biological need. And since he is wearing a tuxedo, no pockets, he does not carry with him the medicine to inject in case of crisis.   Once in the toilet, he has a sudden attack of paralysis. He cannot get out but he can still call. The woman is within hearing distance, she knows where the medicine is, she has the skill to inject him, there is still time before paralysis kills him. The door to the toilets is not locked.  But he knows he is going to die, and mankind will not survive.   He is in the men's toilets. She won't get in.

It's a short short. Humanity destroyed by a disease (virus?) that causes temporary paralysis. Written from pov of last man about to marry last woman who is devout (Christian?) and very proper. Man suffers paralysis in the men's room of a restaurant and humanity is doomed because she will not dare go in to rescue him.


I am unable to connect my external hard drive with Ubuntu. It shows the bellow error again and again.   Error mounting /dev/sdb1 at /media/h/H: Command-line `mount -t "exfat" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,iocharset=utf8,namecase=0,errors=remount-ro,umask=0077" "/dev/sdb1" "/media/h/H"' exited with non-zero exit status 32: mount: unknown filesystem type 'exfat'

When trying to mount an exfat filesystem, I get the following error:  Error mounting /dev/sda6 at /media/gkp/Backup: Command-line  `mount -t "exfat" -o "uhelper=udisks2,nodev,nosuid" "/dev/sda6" "/media/gkp/Backup"'  exited with non-zero exit status 32: mount: unknown filesystem type 'exfat'   Exfat is used on some USB sticks and camera sd cards. What can I do to mount this type of filesystem?


I recently installed virtualbox Ubuntu on host Windows. I am new to Ubuntu and virtualbox. I made two changes and I would like help to understand which one (and why) it messed up Ubuntu.   I had downloaded an email attachment file 5MB large. I kept getting an error that the disk space was running low. I allocated storage 8GB at start (dont know where it has gone!) The screen resolution was like 640X480, so I adjusted the virtualbox-guest-dkms option, and it got fixed.   I restarted the guest session to effect the changes of the sizing. Now I am getting a pixelated screen for the login.     When I enter the password, I am able to get into the machine. I know this because the screen pixels change to what the desktop must be looking like.

Inside a VirtualBox VM, I have installed myself an Ubuntu 16.04.1 LTS Server installation. However, when I installed the ubuntu-desktop package and rebooted, this happened:    Exact command I used: sudo apt-get update; sudo apt-get install ubuntu-desktop ..and then a reboot command.  This just seems like a corrupted top-left portion of the screen, as my cursor can appear in view (but corrupted):    This is a purely graphical issue because I can use the keyboard to successfully progress to a desktop:    Note: On startup it shows correct graphics for a split-second then reverts to glitch.    Any help on this?


I have a .CSV file that have an arabic data and i need to import this file into the sql database using PHP. my code doing it just fine except that the arabic characters inserted into the database as 'ËËËË','ÚÚÚÚ'.  what should i do to insert that data right.  any ideas?   $filename = $_FILES['upload']['tmp_name'];   $file = fopen($filename, "r");   while (($emapData = fgetcsv($file, 1000, ";")) !== FALSE){   $emapData[0];   var_dump($emapData[0]);   //'ËËËË','ÚÚÚÚ'   }

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


Please give me an advice to create this effect to text as shown in the picture.

I am working on a print for my wall and I am trying to create something like this:      I have already created the letters in Illustrator and now I am adding the colors in Illustrator and then exporting everything to Photoshop and then using the liquify tool to blend the colors to create a similar effect. I also used the healing patch tool to blend in the hard edges.  Is that the right way of doing it? Or is there another way?


It's not that I feel bitter when somebody else's answer is upvoted above my own, but it's when a user with a high rep answers a question and their answer seems to attract an immediate barrage of upvotes.  Now I'm not saying that these votes are always unwarranted, but by simply observing this behavior, I think the system seems flawed.    The concept of reputation (or at least one of the concepts) is to give users a sense of trust in the reputed user's answers.  But this should be trust, not blind faith.  I know that this problem doesn't exist for every question asked on SO, but it's definitely present.  I'm sure this is a contentious question, as it might seem overly critical, but does anybody else agree with me and, if so, does anybody have any thoughts on how this problem could be alleviated? It's a great shame when a new or less active user's answer is stifled by the reputation-rich user's answer.

The question by  got me thinking. This has been raised on , but has been declined. Would someone with lesser rep or a less famous name have received the same number of votes/answers as Joel? I know the question was briefly closed, but it got reopened when the intent was made public. I think someone did try it, but I don't think their question was suitable for the experiment and it was soon closed. Similarly, do answers by Jon Skeet and others with > 20K rep garner more votes than equally correct answers by others less notable? Is this because of their name, their rep, or the fact that the answer is correct? I would hope it's the latter, but perhaps we ought to find out. I wonder if the following experiment would yield any useful information: If Jon created a second account under a pseudonym and posted a few answers along side slightly "worse" answers credited to Jon so we can see which ones garner the most votes. Another experiment (though this would require a change to SO) could be to hide the identity of the poster for a period (a day?) but leave the (approximate) rep score visible. This might show whether people were using the rep as a guide. On a personal note, if there are two equally correct answers I tend to award my up-vote to the one with the lowest rep score - to spread "the love" around (so to speak). NOTE I'm not saying that questions and answers should be permanently anonymous, or that there shouldn't be a way of finding out the identity of a poster straight away. I just feel that the question or answer should be judged on its own merits rather than the perceived merit of the poster.


All the volcanoes in middle earth are a throw back to Melkor trying to trash middle earth (executive summary of this ).  Would any other volcano contain enough 'power' from Melkor to do likewise? Or was mount Doom merely the closest?

I was recently reading some Lord of the Rings/Stargate SG-1 crossover fanfiction. It is a guilty pleasure, I admit :) In this story, it was suggested by Col. O'Neill to destroy the Ring using a nuclear device. Truth be told I stopped reading at this point, as it was getting to be a little much even for me.  Obviously, this is not canonical in either universe, but it made me wonder: When Elrond said that "only in the fires of Mt. Doom may it be unmade," was he speaking literally? Or was this merely the only known active volcano in Middle Earth? In other words, was whatever magic that protected the One Ring from damage location-based or did it just make it very resistant to destructive force, and Mt. Doom just happened to be hot enough to do this? I know there is (understandably) little information about such technicalities of how magic works in Middle Earth, but I'll accept any reasonable conjecture/consensus as an answer.


How can I show that $\sum \limits_{i=1}^n \log(i)$ is $O(n \log n)?$ (Log in base 2).

Let   $$f(n)=\sum_{x=1}^n\log(x)$$  What is $O(f(n))$?  I know how to deal with sums of powers of $x$. But how to solve for a sum of logs?


My issue is that I want to set a click event dynamically. So imagine I have a button. Clicking that button shows a popup box.  In that box I have a text like this:  "Men in Bulgaria"   But the issue is that I don't have access to the button event. So I would like to set the click event with an regex like this:  $("[class*='timelineplace']").click(function () {     var object = $(this);     alert(object.attr("class").match(/timelineplace-(.*?)(?:\s+|$)/)[1]); });   But yeah this only works when the popup box already existed when jQuery loading finished. So the issue is that the popup is dynamically loaded. And the click event is set when the site has finished the loadings.  So Is there a way to set a click event also at runtime to any regex matching class? Or do I really have to go to the button click event and set the onclick there.

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I'm not sure what commands are issued when trying to launch a program from the dash.  How can I determine this and modify the commands of these short cuts?  For example, I would like to change the command to launch skype from:  skype   to  LD_PRELOAD=/usr/lib32/libv4l/v4l1compat.so skype   I'm not sure which command is issued when I click on the icon in the dash and I'm not sure how I would change it.  Changing it using gnome menu editor does not seem to have any effect.

Will Unity allow making custom launcher icons from .desktop files or via menu editing system? (Right now the launcher doesn't give the option to "keep in launcher" on all programs.  For some programs I use, I have to make custom launchers or .desktop files.  For instance, daily blender builds are generally just folders with an executable.  In basic Gnome or KDE, I can make a new menu entry with the menu editing system. Then, I can also add it to Docky either from the menu or by dragging a .desktop file to it. Unity launcher doesn't support drag and drop, so thats not a bug or anything, but when I open a .desktop file, it has unpredictable results. Most time it will not have "keep in launcher". Sometime it will have a pinnable item without the .desktop's icon, and if I pin the item to the launcher, it will not call upon the program again after closing it. I've also gotten it to just work with a .desktop file for celtx.


I tried to rig but always fail. Failure message is Bone Heat weighting:failed to find solution for one or more bones.

Here is the .  Picture:   It's nothing special but I cant figure out why I get problems rigging this mesh. It would be important and a great Help! Thanks for reading and I know there are a lot of guides answering this question but I tried all and it doesn't seem to work.


I am trying to build a line-following robot with the schematics I found below. I have just started to understand the use of feedback in op-amp. Ie. The continuous balancing mechanism creates a very stable gain determined by resistors connected to the op-amp.  I have tried to trace the current path marked in green and orange lines for the respective op-amp. Both lead to the same inverting and non-inverting input terminal of different op-amp.  I am kind of puzzled by this.  1) What is the point to have feedback to the different input terminals?  2) Because of the different input terminals used, how do I know which is the negative feedback? And is there even a thing like "positive feedback" happening here?  3) Or could it be a schematic drawn wrongly because it is just not technically practical nor possible to have the feedback wired in this manner?  Many thanks in advance.

I am studying the function and characteristic of an op-amp to build a line-following robot with the schematics below. However, in many tutorials, the way to differentiate an inverting and non-inverting op-amp is by looking at the connection to ground via the inverting or non-inverting terminal.  However, in the schematics, the op-amp is considered to have connections to ground, thus in this case, how do I differentiate it then?  I may have understood the whole concept wrongly. Pls help!    EDIT: Please ignore the switch as it may have been drawn wrongly by the supplier.


I am using my email address rather than profile name but it isn't working...I thought that maybe I was using the wrong password, so I changed it, but it still isn't working.  I don't know why.   My internet connection is great.  If there is anything I am doing wrong please let me know. I have had my account for less than a month and I am very irritated.  Is it possible there is an error on Mojang's side??

I am using a premium legit version of Minecraft that I purchased. I can log into minecraft.net as well as mojang.com but I am unable to login to Minecraft the game through the minecraft.exe or the Technic launcher. The Minecraft servers are up and running fine. My internet connection is also fine. I double checked my credentials and even tried changing my password. I tried using both my username and my email. I tried all of this on two separate accounts that I own. I tried deleting my login, launcher, launcher.pack.lzma, and launcher_profiles.json and then reopening Minecraft. I tried re-downloading minecraft.exe.   Nothing has worked and I seem to have run out of options. I sent a help request to Mojang but in the meantime I was hoping that maybe you guys could offer some advice.


We define the relationship between the two sets $S_1≡S_2$ if and only if $|S_1|=|S_2|$.  How to show that $≡$ is an equivalence relation ?  sorry I'm from Iran and Basic my English is poor.

A relation is a subset of the Cartesian product of two sets, if "have the same cardinality", denoted as $R$, is a relation, then there must exist set $A, B$, such that $R \subset A \times B$. What are $A, B$ then? They cannot be "set of all sets", because there is no such set according to axiom of regularity (ZFC set theory).  Did I miss something?  Thanks.


Please help me with a solution to this problem.  Let $R$ be a commutative ring. Let $A_1, A_2$ be two ideals of $R$, and $P_1, P_2$ two prime ideals of $R$.  Assume that $A_1 \cap A_2 \subseteq  P_1 \cap P_2$. Show that there exist $i, j \in \{1,2\}$ such that $A_i \subseteq P_j$.

Let $A_1$ and $A_2$ be two ideals, and $P_1$ and $P_2$ be two prime ideals in a commutative ring $R$. Assume that $A_1 ∩ A_2 ⊆ P_1 ∩ P_2$. Is there at least an $i$ and $j$ such that $A_i ⊆ P_j$ is true?


This is question numebr 13 exercise 3.1 wayne patty topology.  Let $p$ a cut point of a connected space $(X, \mathcal{T})$ and suppose $A$ and $B$ form a separation  of $X-\{p\}$. Prove that $A \cup \{p\}$ is conected.  Attempt: I proved A and B are connected using contradiction. Now , For A$\bigcup ${p} to be connected I need to  only prove that  $Closure (A) \bigcup ${p} $\neq \phi$.  I assumed let p doesnot belongs to closure of A and trying to get some contradiction but I am unable to do so. Please help!

Let $p$ a cut point of a connected space $(X, \mathcal{T})$ and suppose $C$ and $D$ form a separation  of $X-\{p\}$, i.e $$X-\{p\}=C \cup D$$ Prove that $C \cup \{p\}$ is conected. I have this idea: Since $p$ is a cut point then $X-\{ p \}$ is not connected, and since $C$ and $D$ form a separation of $X- \{p \}$ then $X-\{p \} = C \cup D$, and also $C \cup D$ is not connected. And also $$C \cap \overline{D}= \overline{C} \cap D= \emptyset$$ I need an idea to continue please


I have a doubt for a long days.Today I got a chance to clear it.  What is the right Past tense usage of a verb "Learn"?  Is it Learnt or Learned?

In my very first question, Carlo made an edit stating that learnt is a rare past tense of learn. I am accustomed to using learnt for past tense and learned as an adjective (as in He is a learned scholar.) I checked into a couple of dictionaries and they say both are valid past tenses. Do I stand a risk of not being understood if I use learnt?  In a similar vein, should dreamed be used as a past tense for dream instead of dreamt? I can't think of other such conflicts, but I guess there must be more.


I am writing a LaTeX document with AMS Euler math as math font. I need to produce some figures with Inkscape, I for consistency I want to use the same font for numbers in my figures. However, I cannot find AMS Euler math in the list of fonts installed in my system (Ubuntu 18.03). Is there any possibility to install AMS Euler math as a system font as well? Thank you!

I use  on Windows 7 platform. The principle to enter integrals and other mathematical symbols in Inkscape seems that the best thing to do and write them in a LaTeX compiler and cut them in Adobe PDF and paste it into Inkscape as figures.   Seems to be how you make pictures like this in Inkscape:    Is there any way to type LaTeX code directly into the text boxes Inkscape?   I know this question is ultópica but it never hurts to try.


I am trying to see if two "circles" intersect. The data I have is  two points and two radii (in meters). I am using srid 4326.  My main issue (i think) is getting the radius in meters.  SELECT (ST_Buffer('POINT (-104.949517 39.740264)',300) &&            ST_Buffer('POINT (-104.999924 35.000089)',300))   My questions are   Is there a more clever way to do this? Or how do I convert the radius from dd to meters to get correct buffers?

I'm using PostGIS 1.5.2, with geometries in SRID:900913. I need create a circles using a list of points as centre, with a radius of 600 kilometers. I'm using this query:  INSERT INTO circles (geom) (    SELECT ST_Buffer(point, 600000, 'quad_segs=8')     FROM points );   But circles created have not 600 kilometers of radius (radius is near this length, but not exactly).  Are there other methods to create circles in PostGIS?  NOTE: Information represented is from Spain. Correct projection is 4326, but client use Google rasters, so I am storing data in 900913 to avoid reprojections and increase performance.


He suffers terribly with his feet.   Why not use the preposition "from"?  What is the meaning of "with" here?

Not every job will end up with a success.   What is the meaning of "with" here? Why not use other preposition?  Could native speakers please describe the scene of this sentence for me? Thx.


When stating a book title, is the comma before or after the quotations?

The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)?     When my friends ask, "What do you want for your birthday?", I never know how to respond.   It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?


Will Stack Overflow have a close question option once I create a question?

Why is it possible to flag and close my own question?   The only realistic usage I could think of is when I see that my question is a duplicate, but it has already got some great answers. So instead of deleting the question, I would vote to close it as a duplicate.   But still, I can't see how flagging my own question would be useful.


Is there a possibility to 'render' latex code with your browser?  I have some *.tex files which I would like to render a HTML version of (with HTML-navigation, hyperlinks, etc). However - running some tex2html converter everytime is quite annoying, especially since I use a lot of special packages that are not supported by most converters I tried so far, so I would need to post-process the files everytime I change something in my source document, which happens very often.  What I would really like to have is a javascript library that parses a TeX file and renders an HTML webpage from it using DOM. It doesn't need to be complete in the sense that all CTAN packages are supported, but it should be extendable in the sense that I can plug in my own javascript code to render some self-defined environments and commands.  So what I'm looking for is a javascript to HTML interpreter. Is there such a thing, or would I need to write something up myself?  PS: I know about MathJax, which does an excellent job at rendering math, but I would like to render whole documents, including preamble and custom command definitions.

Is there a converter that will convert LaTeX to HTML? I have tried several services but the LaTeX diagrams and some of the maths came out weird.  I actually converted the Latex to PDF without a problem. Then I used  to convert from PDF to HTML. The square root signs did not appear properly and some of the Cartesian coordinate plane diagrams had nothing on them except the grid.   \documentclass[12pt,a4paper]{report} \usepackage{amssymb} \usepackage{amsthm} \usepackage{amsmath} \usepackage{pstricks,pst-plot} \usepackage{pst-eucl} \addtolength{\hoffset}{0.2cm} \addtolength{\textwidth}{1.1cm} \addtolength{\textheight}{1.0cm} \addtolength{\voffset}{-0.7cm} \linespread{1.3} \begin{document}  If $x$ is non-positive then $x \leq -\sqrt{\frac{1}{2}}$     $\hspace{30 mm} $     (6)\\  (4) and (6) tell us that\\  (4)  $-1 \leq x \leq 0$  \\  (6)  If $x$ is non-positive then $x \leq -\sqrt{\frac{1}{2}}$\\  Therefore $-1 \leq x \leq -\sqrt{\frac{1}{2}}$\\  \vspace{50 mm}  \begin{align*} \psgrid[unit=2cm](0,0)(-2,-2)(2,2) \pnode(-1.8,.87){b}\uput[50](b){b} \pnode(-1.8,1.8){a}\uput[50](a){a} \psset{linecolor=green} \psline[linewidth=1pt](-1.8, 0)(-1.8,4) \psset{linecolor=green} \psline[linewidth=1pt](-1.8, 0)(-1.8,-4) \psset{linecolor=blue} \psellipticarc(0,0)(2,2){0}{180} \psset{linecolor=red} \psline[linewidth=1pt,linestyle=dashed,dash=2pt](-2,2)(-1.41,1.41) \psset{linecolor=red} \psline[linewidth=1pt](-1.41,1.41) \psset{linecolor=red} \psline[linewidth=1pt]{->}(4,-4) \psset{linecolor=red} \psline[linewidth=1pt]{->}(-2,2)(-4,4) \end{align*}  \end{document}   PDF output:    PDF->HTML output:


Is it always true that product of eigenvalues is determinant of a matrix ? what if one of the eigenvalues are same and matrix is not diagonalizable ? Is this statement is still true ?

Show that the determinant of a matrix $A$ is equal to the product of its eigenvalues $\lambda_i$.   So I'm having a tough time figuring this one out. I know that I have to work with the characteristic polynomial of the matrix $\det(A-\lambda I)$. But, when considering an $n \times n$ matrix, I do not know how to work out the proof. Should I just use the determinant formula for any $n \times n$ matrix? I'm guessing not, because that is quite complicated. Any insights would be great.


I have a circuit breaker panel with 2 supply wires (2.5-4mm2 400V). I noticed that there is some oily substance dripping out of the supply contact of my circuit breaker. What is this substance and is it dangerous? The circuit breaker does not trip. Because I live in a rather old building where the heating does not work well I often rely on electrical heaters, so I use much electricity, but the circuit breaker never trips. It is also a model without residual current circuit breaker. It is more or less this model...

I'll be replacing my electrical panel soon and I noticed that the new breakers and panel have a brown goo on them where they connect to one another. I'm guessing it is lubricant .. similar to what goes in the aluminum wires but I rather make sure than end up with fireworks.  Should I leave the brown goo in place before I plug the breakers to the new panel or should I wipe it out? Thanks.


Why is the var type still str in Case 1?. Shouldn't it be int? In Case 2 when I'm not using the function it changes to int.  #CASE 1 num1=str()  def suma():      num1=int(7)  suma()  print(type(num1)) # <class 'str'>  #CASE 2 num1=str() num1=7  print(type(num1)) # <class 'int'>

How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access?


May somebody explain why this expression results into "$x$"?  $$\frac{x(x-1)}{x-1} = x$$     Note: This is the final simplification in the problem described .

Hello,  in the picture there is an equation I can not understand. What I do not understand is how to get to the first step. I have been thinking and thinking but can not find an explanation. Could somebody please explain? Thanks.


I have been trying to remove characters from a string without using extra memory and soing it in place. I just tried removing character 'a' from a given input string but my code gives a segmentation fault .   Input- abca  Output-bc Debugger says the segmentation error is in line "str[j]=str[i]". Please help me out :) Thanks  Here is the code   #include<stdio.h> #include<string.h>  void removest(char *str)  {   int i,j=0;   int len=strlen(str);   for(i=0;i<len;i++)     {        if(str[i]=='a')     {       i=i+1;     }       str[j]=str[i];       j++;     }   str[j]='\0';   printf("%s \n",str); }  int main() {   char *str="abca";   removest(str); }

The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC.


I am learning Linux.  I was surprised to see that the parameter order seems to matter when making a tarball.  tar -cfvz casual.tar.gz snapback.txt bucket.txt   gives the error:  tar: casual.tar.gz: Cannot stat: No such file or directory tar: Exiting with failure status due to previous errors   But if I issue the command like this:  tar -cvzf casual.tar.gz snapback.txt bucket.txt   the tarball is created without errors  Can anyone explain to me why the parameter order matters in this example or where I can find that information to learn why myself?  I tried it the way I did in my first example that received an error with the logic of putting the required parameters c and f first followed by my other parameters.  I want to completely absorb Linux, which includes understanding why things like this occur.  Thanks in advance!

I am wondering to ask the difference of these two commands (i.e. only the order of their options are different):   tar -zxvf foo.tar.gz tar -zfxv foo.tar.gz   The first one ran perfectly but the second one said:  tar: You must specify one of the `-Acdtrux' or `--test-label'  options Try `tar --help' or `tar --usage' for more information.   And tar with --test-label and -zfxv said :  tar (child): xv: Cannot open: No such file or directory tar (child): Error is not recoverable: exiting now tar: Child returned status 2 tar: Error is not recoverable: exiting now   Then I looked at tar manual and realised that all the example there are using switch -f in the end!!  AFAICT there is no need for this restriction, or is there?! because in my view switches should be order free.


Consider this:  0^0 = 1 0^1 = 0 0^2 = 0 0^n = 0 (for int n > 0)   So how come 0^0 = 1, how can you get something out of nothing? Isn't it a mathematical heresy?  Also what does it mean to raise something to the power of 0? Like 2^2 = 2 * 2 = 4, I understand that, but what 2^0=? in that case?

Could someone provide me with a good explanation of why $0^0=1$?  My train of thought:  $x>0$  $0^x=0^{x-0}=0^x/0^0$, so  $0^0=0^x/0^x=\,?$  Possible answers:   $0^0\cdot0^x=1\cdot0^0$, so $0^0=1$ $0^0=0^x/0^x=0/0$, which is undefined   PS. I've read the  on mathforum.org, but it isn't clear to me.


How can I prove that     $$1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$$    for all $n \in \mathbb{N}$? I am looking for a proof using mathematical induction.  Thanks


Though seemed to be a common question, I couldn’t find any information on that. I can’t imagine the Euclidean function would be like, if there exists one, so my guess is not. But how to prove it?

Hi I don't know how to show that $\langle 2,x \rangle$ is not principal and the definition of a principal ideal is unclear to me. I need help on this, please.   The ring that I am talking about is $\mathbb{Z}[x]$ so $\langle 2,x \rangle$ refers to $2g(x) + xf(x)$ where $g(x)$, $f(x)$ belongs to $\mathbb{Z}[x]$.


My main suspicion is that i am meant to null terminate the string i'm returning or is it already terminated ?. Here's my code:  #include <stdio.h> #include <string.h> #include <math.h>  char* reverse(char*);   int main(void) {  printf("%s",reverse("abcde")); return 0; }  char* reverse(char* string){   int length = strlen(string);   int limit = (int)floor(length/2);   char temp;  for(int x = 0;x<=limit;x++){     temp = string[x];     string[x] = string[length-x-1];     string[length-x-1] = temp;  }  return string;   }


Given the following matrix, I was asked to tell whether the matrix is the square of some matrix or not.  $$ \begin{pmatrix} 1 & 0 & 0\\ 0 & -1 & 0\\ 0 & 0 & -1 \end{pmatrix} $$  Since this matrix is diagonal, a square root is  $$ \begin{pmatrix} 1 & 0 & 0\\ 0 & i & 0\\ 0 & 0 & i \end{pmatrix} $$ Am I right?

Prove that matrix   \begin{bmatrix}1&0&0\\0&-1&0\\0&0&-1\end{bmatrix}  can be square of matrix with all real entries.  I have found one such matrix to be   \begin{bmatrix}1&0&0\\0&1&-1\\0&2&-1\end{bmatrix} but is there an elegant way to do it without any trial and error?


I just upgraded my computer to Windows 8. Then I logged on, disconnected it from the domain, and rebooted. Now when the computer boots, I have to log in as Administrator. I cannot change and log in as something else.  The problem is that I don't have the password.. I have tried not typing anything as a password. I cannot get OPHCrack to work either.. It just doesn't boot from the LiveCD. (Others do, but they haven't been free.)  What is the default password of the admin account?

I got a brand new Windows 7 machine, installed the operating system, created one account and forgot its password. What can I do?  There is no external CD, the operating system is loaded from somewhere inside the machine.  I already tried to remember passwords and tried all candidates with all possible combinations of caps lock, num lock etc.


If G be a non-trivial group with no non-trivial proper subgroup, show that G is a group of prime order.  Attempt:  Given $G\neq \{e\}$ and let $a\in G, a\neq e$. Then $H=<a>$ is a subgroup of G. Then by the hypothesis, $H= \{e\} ~or~ G$. But $H\neq <a>, ~as ~a\neq e$. So G is generated by $a$.  I can show also that G is finite (if G is infinite, considering group $<a^2>$).     Let if possible, $o(G)=n=composite=kl, ~k,l>1$ are intergers. As $G=<a>$, $o(a)=n$. As $<a^k>$ is a subgroup of G, $(a^k)^l=a^{kl}=a^n=e\implies o(a^k)=l<n$, i.e $<a^k>$ is a subgroup of order $<n$, but G cannot have a non-trivial subgroup. So $l=1 ~or~ l=n$. How to conclude the rest?   The problem is in the shaded portion only. Please correct it.

This is something I'm supposed to be able to prove for an upcoming test, but I can't find anything to help me prove this in my notes or the chapter, which is on cosets and Lagrange's theorem. If all I start with is the group having no proper subsets, then that means any subset is the whole group. By Lagrange's theorem, that means the index is $1$, but that doesn't get me anywhere. Where do I start?


I need to add an event listener on paste to all elements with a specific class.   I used this simple javascript:  var fields = document.getElementsByClassName('ui-inputfield');   to get all the elements, and then for each element this one:  addEventListener('paste', handlePaste);   Where is the problem:  The funtion starts on page load, but at that moment, i don't have all the elements rendered.  When some conditions render another element with that class, this element doesn't have the paste event handled.  I use Primefaces to render or not the elements.  Someone can suggest any solution?  Thanks in advance!

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


When I run sudo apt-get update on Ubuntu 19.04 it results in:  Err:1 http://lt.archive.ubuntu.com/ubuntu disco InRelease   Could not connect to lt.archive.ubuntu.com:80 (193.219.61.87). - connect (111: Connection refused) Cannot initiate the connection to lt.archive.ubuntu.com:80 (2001:778::87). - connect (101: Network is unreachable) Err:2 http://lt.archive.ubuntu.com/ubuntu disco-updates InRelease                 Cannot initiate the connection to lt.archive.ubuntu.com:80 (2001:778::87). - connect (101: Network is unreachable) Get:3 http://deb.playonlinux.com trusty InRelease [2,590 B]                     Hit:4 http://security.ubuntu.com/ubuntu disco-security InRelease                Ign:5 http://ppa.launchpad.net/gnome3-team/gnome3/ubuntu disco InRelease Err:6 http://ppa.launchpad.net/gnome3-team/gnome3/ubuntu disco Release   404  Not Found [IP: 91.189.95.83 80] Ign:7 http://download.opensuse.org/repositories/home:/strycore/xUbuntu_16.04  InRelease Get:8 http://download.opensuse.org/repositories/home:/strycore/xUbuntu_16.04  Release [986 B] Get:9 http://deb.playonlinux.com trusty/main amd64 Packages [564 B] Get:10 http://download.opensuse.org/repositories/home:/strycore/xUbuntu_16.04  Release.gpg [481 B] Get:11 http://deb.playonlinux.com trusty/main i386 Packages [564 B] Get:12 http://download.opensuse.org/repositories/home:/strycore/xUbuntu_16.04  Packages [831 B] Reading package lists... Done      E: The repository 'http://ppa.launchpad.net/gnome3-team/gnome3/ubuntu disco 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 cannot install any program with sudo apt-get install. How can I fix this situation?

I just installed a fresh version of Ubuntu 19.10 today, and the first thing I decided to do was to install GNU Screen, using sudo apt-get install screen. my output was: Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package screen  I figured the package archives were not quite updated as it was a clean install so I tried sudo apt-get update. This is what I got: Get:1 http://security.ubuntu.com/ubuntu eoan-security InRelease [97.5 kB]       Err:2 http://au.archive.ubuntu.com/ubuntu eoan InRelease   Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Could not connect to au.archive.ubuntu.com:80 (202.158.214.106), connection timed out Err:3 http://au.archive.ubuntu.com/ubuntu eoan-updates InRelease      Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Err:4 http://au.archive.ubuntu.com/ubuntu eoan-backports InRelease   Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Fetched 97.5 kB in 31s (3,106 B/s) Reading package lists... Done Building dependency tree        Reading state information... Done All packages are up to date. W: Failed to fetch http://au.archive.ubuntu.com/ubuntu/dists/eoan/InRelease  Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) Could not connect to au.archive.ubuntu.com:80 (202.158.214.106), connection timed out W: Failed to fetch http://au.archive.ubuntu.com/ubuntu/dists/eoan-updates/InRelease  Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) W: Failed to fetch http://au.archive.ubuntu.com/ubuntu/dists/eoan-backports/InRelease  Cannot initiate the connection to au.archive.ubuntu.com:80 (2001:388:30bc:cafe::beef). - connect (101: Network is unreachable) W: Some index files failed to download. They have been ignored, or old ones used instead.  I'm really not sure why it would be doing this, other than maybe some first-use hiccups? The computer is definitely connected to the internet, as I am writing this from that machine, and I have tried running the commands after rebooting and it still gives the errors. I can't seem to be able to connect to au.archive.ubuntu.com at all. ping au.archive.ubuntu.com just sits there without a response. If anyone could help, that would be great! If any extra information is required I'd be happy to edit it into the question.


Could someone walk me through this problem from my Discrete Mathematics textbook? It states: Prove that $\forall x, \forall y \in Z^+$ such that $x|y$ and $y|x$ implies $x=y$, or in English for every x,y in the Positive Integers such that x divides y and y divides x, implies x=y.  Proofs are not my strong-suit by any means, my go to usually being to attempt a proof by Contradiction. However, for this one I'm just stuck with the statement being true because, as my instructor likes to say, "Clearly Obvious"? I mean, if x=y then if x=4 and y=4, then 4/4 = 1 meaning both ways they divide the other and are equal?   Can someone explain this to me?

Prove or disprove: If a, b belong to the set of positive integers, and if a divides b and b divides a, then a=b. Does this hold if if a,b are not necessarily positive? Why or Why not?   Here is what I have:  If a and b are integers, we say a divides b if there exists an integer k so that b=ak. Thus:  $$b=ak$$  $$a=bj$$   $$a=akj$$ $$kj=1$$   Since a divides b and b divides a, we know that k,j must both be integer, which means k and j must both equal 1 or -1. This means:   $$a=b$$  This proves that a=b when we assume that a,b are both positive integers.   For the second part of the question, I am asked if I can still say a=b if the assumption about a, b is relaxed so that a,b belong to the integers (not the positive integers.) I think The answer is no, I cannot say that a=b for every case when we allow a,b to also be negative integers.   Here is my reasoning (I use the same idea that a=bj and b=ak here)   $$+/-a=akj$$  $$+/-1=kj$$   So $ |a|=|b|$ but not $a=b$  I'm very new to proofs so any suggestions or thoughts are greatly appreciated.


How can I type the underlined symbols in LaTeX? I cannot recognize what letters they are.

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


I was working on a project where i  used "SMTP Authentication Support" module to send emails. The authentications i provided were my personal gmail account details, It was working fine. Now when i am entering the site admins account details its displaying "Unable to send e-mail. Contact the site administrator if the problem persists." error. It also says that "SMTP Error: Could not authenticate." Can anyone let me where i am going wrong.

When my web form is filled and submitted, I get redirected to a page that says:     Thank you for submitting.   but theres a red warning box there that says:     Unable to send e-mail. Contact the site administrator if the problem persists.   I think its the SMTP server, but I don't know how to fix that.


I get that you need pointers for handling something that grows and shrinks dynamically. In instances where that isn't the case, to my understanding, you use pointers when: your object is too big to be stored on the stack, or when you would like a function to modify data outside of its scope (why not just use references here?). Is this line of thinking correct? Other uses I can think of are for polymorphism and forward declarations. The other example people always give is pointer arithmetic and handling array indices, but then why not just use C++ iterators which just wrap pointers... Are there any other (common) cases? I used to think that pointers were useful as they allowed for objects to be passed around without the need for a full copy to be made, but surely move semantics allow you to accomplish that without the need for handling pointers? Overall, I feel like I am using too many unnecessary pointers in my codebase and I would really appreciate it if someone could definitively clear things up.

I know this is a really basic question, but I've just started with some basic C++ programming after coding a few projects with high-level languages.   Basically I have three questions:   Why use pointers over normal variables? When and where should I use pointers? How do you use pointers with arrays?


I want to know how I can combine many commands in one command block, like setblock, fill, give and so on.

I am looking to try and set multiple commands in a single command block, but so far everything I have tried just returns "Unknown Command".  What is the format for writing multiple commands in a single command block in Minecraft 1.8?  Can I use either of the following:  Command:(command here) Command:(command here)     /command here; /command here;   Or is there another format?


Could somebody explain why ridge regression does not perform feature selection although it makes use of regularization? So, it penalizes the regression coefficients like LASSO does, but  how come we end up with using all features for all the lambda (penalty) values in range? Why don't we end up getting some zero coefficients in case of high penalization? I know this is a very basic question, but I would appreciate any response. Thanks.

I've been reading , and I would like to know why the Lasso provides variable selection and ridge regression doesn't.  Both methods minimize the residual sum of squares and have a constraint on the possible values of the parameters $\beta$. For the Lasso, the constraint is $||\beta||_1 \le t$, whereas for ridge it is $||\beta||_2 \le t$, for some $t$.  I've seen the diamond vs ellipse picture in the book and I have some intuition as for why the Lasso can hit the corners of the constrained region, which implies that one of the coefficients is set to zero. However, my intuition is rather weak, and I'm not convinced. It should be easy to see, but I don't know why this is true.  So I guess I'm looking for a mathematical justification, or an intuitive explanation of why the contours of the residual sum of squares are likely to hit the corners of the  $||\beta||_1$ constrained region (whereas this situation is unlikely if the constraint is $||\beta||_2$).


Season 1, episode 15: Leonard tries to talk to Sheldon to persuade him that he is a suitable mate for Sheldon's sister. The scene is taken in Sheldon's room.     What is that object on the wall over Sheldon's right shoulder? It looks like it moves and there could be some sort of connector? Is it mechanical or electric perhaps?

is full of interesting props. It's a pastime of mine to try to identify odd props in shows and movies.  This one has me stymied. It is in the rarely seen set of Sheldon's bedroom. I've seen it on at least two different episodes. Can anyone help?


Let's say I have two variables: height and weight. I want to produce 4 groups: high height/high weight, high height/low weight, low height/ high weight and low height/low weight. I also want to see that these four groups are significantly different from one another in terms of hight and weight. Do you suggest me to use cluster analysis (e.g., k-means) or do you know any other simpler method?

I want to produce four groups (high/high, high/low, low/high and low/low) using two continues variables and compare these groups in terms of a few dependent variables. I know that cluster analysis (k-means and hierarchical) is a type of 'end' analysis which is the main goal of the paper to reach such clusters and then discuss the nature of the clusters. However, I am willing to use this technique (k-means by using k=4) as a kind of preliminary analysis to produce the groups. I know that scatter plot and means splits are other alternatives but they have their own disadvantages that cluster analysis may resolve. What do you think?


I have problem in completely removing the duplicates string in List<String>  String [] myno1 = new String [] {"01", "02", "03", "04", "05", "06", "07", "08", "09", "10", "11", "12", "13", "14", "15"};  String [] myno = new String [] {"01", "03", "15"};  List<String> stringList = new ArrayList<String>(Arrays.asList(myno));  List<String> stringList1 = new ArrayList<String>(Arrays.asList(myno1));  stringList.addAll(stringList1);  Set<String> set = new HashSet<>(stringList); stringList.clear(); stringList.addAll(set);  System.out.println("=== s:" +stringList);   but i got this:     === s:[15, 13, 14, 11, 12, 08, 09, 04, 05, 06, 24, 07, 01, 02, 03, 10]   i want the result to be like this:     === s:[13, 14, 11, 12, 08, 09, 04, 05, 06, 24, 07, 02, 10]

I have an ArrayList<String>, and I want to remove repeated strings from it. How can I do this?


Google Searching hasn't helped me find the answer to this.  I was wondering if there is a way to make a java Applet always on top, even when there are fullscreen applications.   Specifically I want to over-lay the applet on top of a Power-Point presentation. Is this possible, and if so, how?  Thank You!

In Java, is there a way to have a window that is "Always on top" regardless if the user switches focus to another application?  I've searched the web, and all of the solutions lean to some sort of JNI interface with native bindings.  Truly this can't be the only way to do it?.. or is it?


This code is working as expected.  [user@linux ~]$ cat script.sh #!/usr/bin/bash file="$1" while read IP; do     echo xx $IP done < "$file" [user@linux ~]$   ip.txt  [user@linux ~]$ cat ip.txt 127.0.0.1 127.0.0.2 127.0.0.3 [user@linux ~]$   output  [user@linux ~]$ ./script.sh ip.txt xx 127.0.0.1 xx 127.0.0.2 xx 127.0.0.3   But when I put xx to the end, it's replacing 127.  #!/usr/bin/bash  file="$1" while read IP; do     echo $IP xx done < "$file"   What's wrong with this code?  [user@linux ~]$ ./script.sh ip.txt  xx.0.0.1  xx.0.0.2  xx.0.0.3 [user@linux ~]$   dos2unix? Tried that many times, didn't work  [user@linux ~]$ dos2unix script.sh dos2unix: converting file script.sh to Unix format ... [user@linux ~]$ [user@linux ~]$ ./script.sh ip.txt xx 127.0.0.1 xx 127.0.0.2 xx 127.0.0.3 [user@linux ~]$   p/s - not sure the best subject for this question. If you have better suggestion, let me know

Consider the following CSV file:  jdbc.driverClassName,oracle.jdbc.driver.OracleDriver  jdbc.username,kshitiz   It has to be transformed into:  -Djdbc.driverClassName=oracle.jdbc.driver.OracleDriver \  -Djdbc.username=kshitiz \   Given the following bash snippet:  while read l; do     IFS=',' read -ra arr <<< "$l"     echo '-D'${arr[0]}'='${arr[1]}' \' done <properties.txt   Bash prints:  \jdbc.driverClassName=oracle.jdbc.driver.OracleDriver   \jdbc.username=kshitiz   What's going on here?


There are 4 major sports leagues in North America: NFL, MLB, NBA, and NHL. The teams, also known as the franchises, in the league don't change. The only exceptions are when a team moves to a different city (still the same franchise) and when the league expands by adding more teams.   This is very different to European football leagues where promotion and relegation is practiced. A small number of teams that finish last in a season are relegated to the lower league, and the top teams of the lower league are promoted to replace them.  Has there been a time where the North American major leagues practiced promotion and relegation?

Promotion/relegation is a competition format that is often used in many countries for professional leagues as a way to have many teams participate and yet not dilute the top level of play, by only allowing the best teams to play in the highest division while leaving a path to the top open for lower teams, should they improve enough to reach it.  For example, in England, there are thousands of football (soccer) teams, in varying divisions from the Premier League (top 20) all the way down to "amateur" level. However, even teams at the lowest division could theoretically one day play in the Premier League if they were to be successful enough to reach that level.  Due to the size of the United States, it seems like this format would have been ideal here to allow teams to exist all over the country. Yet it seems like this kind of format has never been used for professional sports in the United States. Why is that?


My sentence is as follows:     Carol Ohmann discusses in her article Daisy Miller: A Study of Change in Intentions how the main heroine of Henry James' novella brings rise to arguments.     Do I have to set the title of the article off in commas or leave it as it is written?

I'm thinking about making a headline. I know you would use a comma here:     Professor Bill Bick then told me, "There will be more jobs when the   economy recovers."   What about here?     Read Professor Bill Bick's article, "Why There Will be More Jobs When   the Economy Recovers."   Are commas used before article titles that are quoted?


Bijection between $\mathbb{R}^2$ and the open interval (0, 1)  No ideas,if someone could point me towards the example it would help. Is this in some way related to space filling curves ?

Could any one give an example of a bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$?  Thank you.


I've done a bit of reading about the twin paradox, as well as watched a few videos and the Wikipedia page on it, however, I don’t understand how their explanations explain away the problem. They claim that the acceleration solves the issue, however, don’t we arrive at the same problem? In the earth point of view the astronaut is accelerating, but you might as well see the earth as accelerating in the astronauts view. In other words, same problem, just with acceleration rather than velocity.

I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within , others say that you need . Now, what is true (and why)?


I am writing my thesis, so it's a work in progress where I constantly change equations, put new equations, new Lemmas, Theorems and so on. The big problem is that, for instance, if I label a theorem as "theorem_4.2" or an equation as "equation_2.3" (meaning those are the second theorem of section 4 and the third equation of section 2) and then put a new equation/theorem it messes things up. The solution I've come up with is to add points to my enumeration, so between theorem 4.1 and 4.2 I would put say, a new theorem which I'd label as 4.1.1. Otherwise I would have to rename all the theorems/equations after the new one I've added and also change every \ref I've done regarding those. Is there a simpler way? Any suggestions?

Someone please help me! I have some custom environments and I want to label them according to theorem counter. Means, that I get a numbering like Def. 1.1, Thm. 1.2 and so on. Right now, I have to enter the numbers for the labels myself and with growing content of my document, this gets messy really quick.  My goal is a modified environment for definition and theorem such that it automatically includes a label with the name of the current environment (definition, theorem, …) the chapter number and the theorem counter. See my example below.  Does anyone have an idea on how to accomplish this or even a code snippet with an implementation? I am very grateful for any help. :)  Best regards, Joe  \documentclass[a4paper,12pt]{report} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath,amsthm,amssymb,amsfonts,hyperref} \theoremstyle{plain} \newtheorem{theorem}{Theorem}[chapter] \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \begin{document} \chapter{A first chapter} \section{Terminology} \begin{definition}\label{defi:1.1} Some first definition. \end{definition} \begin{theorem}\label{theo:1.2} Some theorem. \end{theorem} Definition~\ref{defi:1.1} is important for Theorem~\ref{theo:1.2}! \end{document}


I'm using USART in Keil and I saw this;  #define USART_DRV_NUM 6  #define USART_BAUDRATE 9600  #define _USART_Driver_(n) Driver_USART##n #define USART_Driver_(n) _USART_Driver_(n)  extern ARM_DRIVER_USART USART_Driver_(USART_DRV_NUM); #define ptrUSART (&USART_Driver_(USART_DRV_NUM))   Here is the thing;  #define _USART_Driver_(n) Driver_USART##n   I couldn't find any examples on the Internet. Does anyone know something about this thing?

As mentioned in many of my previous questions, I'm working through K&R, and am currently into the preprocessor. One of the more interesting things — something I never knew before from any of my prior attempts to learn C — is the ## preprocessor operator. According to K&R:     The preprocessor operator ##   provides a way to concatenate actual   arguments during macro expansion. If a   parameter in the replacement text is   adjacent to a ##, the parameter is   replaced by the actual argument, the   ## and surrounding white space are   removed, and the result is re-scanned.   For example, the macro paste   concatenates its two arguments:      #define  paste(front, back)  front ## back      so paste(name, 1) creates the token   name1.   How and why would someone use this in the real world? What are practical examples of its use, and are there gotchas to consider?


Ok,this my question.If my laptop can run window vista,can i run ubuntu desktop 14.04 as well.Just want be sure.

I'm thinking about installing Ubuntu Desktop, but I don't know what flavor is the best for my system. What are the minimum and recommended hardware requirements? What kind of CPU? How much memory? Should I have Hardware Acceleration? What flavor should I use?  This is an attempt of a canonical answer. My answers have the "official  requirements", the recommended are a mix of official sources and opinion based (along with the answer it's told the source). You can comment or edit if you feel that the information is obsolete or incomplete. It is a good rule of thumb that any system capable of running Windows Vista, 7, 8, x86 (Intel) OS X will almost always be a lot faster with any Ubuntu flavor even if they are lower-spec than described below.


I'm new for blender and I'm searching or any advice as solution for my question. my question is, Is there any system or any tool that we can use to transfer jpeg image file to 2d animation stroke file. currently im using images as reference and creating stroke layers on it. but when it come to create the faces my out come of drawing was terrible. so please advice how I can fix this.

Say I want to automate making extruded-text or a 3d logo from an image.    An answer that uses extruding a monochrome image of the ubuntu logo to an arbitrary number of units with a python script taking only the number of units and the monochrome image as a starting point will receive extra this was awesome re-posts from me.  This could be useful for lots of things.


I am importing a csv into QGIS 2.4 with a csvt file that specifies for percent columns Real(2.1) to limit it to 1 decimal place. It imports fine. When I join it to a shapefile, it looks fine. But when I save the shapefile with a new name and bring it back in (or use it in another program), all the numbers have about 10 decimal places. The extra 0s don't show, but some wind up as xx.x99999999999.   Is there a way of limiting the number of decimal places in those columns to just 1?

I have a database in txt format made of several columns of real numbers. Two column are integer, 17 are real (rounded to the first decimal) and 17 are real rounded to the second decimal.   If I import it through a txt format QGIS identified the integer columns properly, but also assign a width of 24 and a field precision of 15.   How can I limit it?


I have got no clue of how to start with the problem .Now I know that an ideal is a kernel of a ring homorphism but why would it be a principal ideal in $F[x]$.What is the intuition behind this ?(I would like to know why is it happening instead of a formal proof)

If $F$ is a field, then $F[x]$ is a principal ideal domain.  Conversely, if $F[x]$ is a principal domain does $F$ have to be necessarily a field?  My Thoughts: Suppose instead of $F$, we take the set of polynomials $R[x]$ over a commutative ring $R$ with unity. Then, suppose $I$ is an ideal of $R[x]$. Let $g(x) \in I$ such that $g(x)$ is the polynomial of the lowest degree in $I$. Then: $ \langle g(x) \rangle \subseteq I .......... (1)$ Let $f(x) \in I$. Then $f(x) = p(x)g(x) + r(x)~~|~~p(x),r(x) \in R[x], \deg r(x) < \deg g(x)$ Since, $I$ is an ideal $\implies f(x) - p(x)g(x) = r(x) \in I$ But, $g(x)$ is of the lowest degree in $I \implies r(x) = 0 \implies f(x) \in \langle g(x)  \rangle \implies I \subseteq \langle g(x)  \rangle ......(2)$ Then from $(1),(2) : I = \langle g(x) \rangle$ Does the Presence of zero divisors in $R[x]$ really make a difference? The only advantage I see is that if there are no zero divisors in $R[x]$ then $I=\{0\} \implies I= \langle 0  \rangle$. But, every ideal contains the zero element. Why is there the condition of a field specifically given in textbooks for $F[x]$ to be a principal ideal domain? Thank you for your help.


I am not being able to access the partition which is used by Ubuntu. In fact I don't know how to mount that partition from Windows 8. Hope folks may help me.

I am running a dual-boot with Windows XP and Ubuntu 11.04.  Ubuntu has Open Office as part of the install. Occasionally, when using XP, I need to work on a spreadsheet or other Open Office document but can't seem to access them while using Windows XP. Is there a way that XP can crossover to Ubuntu documents?  Are two different versions of Adobe also needed?


I want to ask:  "If .us is a suitable suffix for a us located non-profit organization instead of .org, in a situation that .org is not available."  However, I don't see clearly where it would fit into...

I was wondering if there is a site by Stack Exchange, where one could ask hosting/domain related questions.


i have a file in which i have to change a word and then save it by same name.  for ex-  for file "name"-  my name is joe (original data) my name is roy (changed data)   how to do it in best possible way?

Replacing strings in files based on certain search criteria is a very common task. How can I    replace string foo with bar in all files in the current directory? do the same recursively for sub directories? replace only if the file name matches another string? replace only if the string is found in a certain context? replace if the string is on a certain line number? replace multiple strings with the same replacement replace multiple strings with different replacements


I am using SQL Trigger to update updatedAt column if there is a new data inserted/updated in PG 9.6. Here is the function that will be called by trigger CREATE FUNCTION sp_updatedatstamp() RETURNS trigger AS $updatedat_stamp$   BEGIN     NEW."updatedAt" := now();     RETURN NEW;   END; $updatedat_stamp$ LANGUAGE plpgsql;  Here is the trigger script create trigger tg_de_installment_cdcupdatedat before insert or update     on     public.table for each row execute procedure sp_updatedatstamp()  Here is the Table Definition CREATE TABLE table (     id serial NOT NULL,     "type" text NULL,     "transactionDate" timestamptz NULL,     remark text NULL,     "createdAt" timestamptz NULL,     "updatedAt" timestamptz NULL,     "deletedAt" timestamptz NULL,     CONSTRAINT table_pkey PRIMARY KEY (id) );  This code is working fine with small data, until an application execute bulk update query (100K+ rows will be updated) that takes 30 minutes. The trigger will makes all 100k+ rows uses updatedAt of first rows, which makes the other rows updatedAt not correct. At the end, our data pipeline with schedule 5 min, will lose this data. Is there a way to makes the SQL Trigger uses it actual timestamp for huge data?


If $f$ continuous at $x_0$ and $f(x_0)>0$   then how to show there exist $\epsilon>0$ and $\delta>0$ such that $f(x)>0$ for $|x-x_0|<\delta$.  I don't know to start proving and then i use definition continuous function at $x_0$ is  $\forall\epsilon>0, \, \exists\delta>0 \, \text{such that if }|x-x_0|<\delta\implies |f(x)-f(x_0)|<\epsilon$

Pretty much the problem asks if a function is continuous at the point $c$ and $f(c) > 0$ then there exists a $d > 0$ such that $\forall x$, $f(x) > 0$ with $|x-c| < d$.   I can understand what the problem means. That if a function is positive at a point then there is another point that's really close that'll also be positive. I can not prove this in a formal way though. I've tried using the intermediate value theorem and I do not know hot to implement it. Any ideas?


Let $E/F,L/E$ be normal field extensions.  What would be an example such that $L/F$ is not normal?

If $F\supset E$ and $E\supset k$ are normal extensions. I want a counter-example where $F\supset k$ is not normal


I am an alien towards compelx analysis, with very little know I am posing a question, who someone may want to help with.  Evaluate:   $$\frac{1}{4}\cdot \sum_{n=1}^{\infty} \frac{(-1)^n}{n^2}$$  In disguise this is similar to $\zeta(2)$  but how can this be done using residues, and complex analysis?  I need some help. I am just interested.   The answer is $\displaystyle \frac{\pi^2}{48}$

Most of us are aware of the famous "Basel Problem":  $$\sum_{k=1}^\infty \frac{1}{k^2} = \frac{\pi^2}{6}$$  I remember reading an elegant proof for this using complex numbers to help find the value of the sum.  I tried finding it again to no avail.  Does anyone know a complex number proof for the solution of the Basel Problem?


Currently installing a replacement power supply for my old 24V LED Strip lights in the kitchen. Almost got it fully connected, but on the DC end I hit a snag:  I made a small error in my wiring reference, the picture of the cables running from the PSU to the LEDs is from an angle that does not tell me which of the white cables is the V+, and which is the V-. I only noticed this after I disconnected the old PSU from the connectors. The new PSU is NOT the unknown, it has clear labels.  So in short: What polarity does White cable with a Black Stripe running along its side usually indicate?   I referred to  but this in-question had black wire with white stripes.   I have a suspicion that it is Positive, due to white cable with yellow or red stripe being the positive, but I am unsure because its black stripe.  EDIT: Adding to the issue:  A potential Answer would always be use a "multimeter": However how do you use a multimeter to distinguish is for an input cable? A multimeter doesn't really output power to power the strip.  Second problem is that the wires in the PCB do not seem to be the wires I am getting on the other side. So would the best course of action be disassemble half the kitchen to rewire everything?

What do solid or dashed lines on a wire indicate?  Is there a difference between the solid and dashed indicators?


My teacher requested that I create a duplicate of a Stack that returns a new Stack containing the same elements and in the same order as the specified Stack.  If I am only able to use methods that are unique to Stack, I would pop every element off the Stack and onto a que. Then I would pop from the bottom of the que onto a new Stack and return the new Stack.  However, I figured that since Stack inherits from Vector I could just use the addAll() method from Vector!  Here is the Java code implementation:  public class DuplicateStack {  private Stack backStack;  public Stack duplicateStack(Stack s) {     backStack.addAll(s);     return backStack; }   This would seem to do all the work for me. Only problem is, I keep getting a nullPointerException when I run this in my main:  Stack s1 = new Stack(); s1.push("c"); s1.push("b"); s1.push("a");  DuplicateStack dup = new DuplicateStack(); Stack s2 = dup.duplicateStack(s1);  while(!s2.empty())     System.out.println(s2.pop());   The error comes from the addAll() call in my DuplicateStack class. So my question is why am I getting a nullPointerException from the addAll(), and is there any way to make a duplicate copy other than using the method stated earlier (using only Stack unique methods)?

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


I had a linux plain text document file with close to 100000 lines, a size of 10 Mb. I accidentally overwrote the file via python code. But I got an exception in the middle of the code and think the file socket did not get closed properly. The new file has a few new lines (250) ,BUT the size of the file corresponds to the old one. I was wondering if the old content will still be there within the file and any chances of recovering the same. I tried using TestDisk and poked around a little bit. But it did not have any option for working on a particular file or maybe I am doing it wrong. I dont have any expertise in file systems and would really appreciate any pointers on how to proceed. Thanks

I accidentally deleted a file from my laptop. I'm using Fedora. Is it possible to recover the file?


An exercise from "Mathematical Analysis" of T. M. Apostol.     Let $f$ be an increasing function defined on $[a, b]$ and let $x_1, ... , x_n$ be $n$ points in the interior such that $a < x_1 < x_2 < ... < x_n < b$.      a) Show that $\sum_{k=1}^n [f(x_k+) - f(x_k-)] \leq f(b-) - f(a+)$.       b) Deduce from part (a) that the set of discontinuities of $f$ is countable.       c) Prove that $f$ has points of continuity in every open subinterval of $[a, b]$.   Here $f(x-)$ and $f(x+)$ mean the left-hand and right-hand  limit of $f$ in $x$.  Solution for (a)  For (a), by $f$ increasing, we have $f(b') - f(x_n) + \sum_{k=1}^{n-1} [f(x_{k+1}) - f(x_k)] = f(b') - f(x_1) \leq f(b') - f(a')$ for every $a' \in (a,x_1)$ and $b' \in (x_n, b)$. Hence taking the supremum of $f(b')$ for $b' \in (x_n, b)$ and the infimum of  $f(a')$ for $a' \in  (a,x_1)$, calling $b'=x_{n+1}$, we have:  $\sum_{k=1}^{n} [f(x_{k+1}) - f(x_k)] \leq f(b-) - f(a+)$  Notice that $f(b-)$ must exist and can't be infinity because $f(b') \leq f(b-) \leq f(b)$, the same for $f(a+)$.  For $f$ is increasing, $f(x_{k+1}) \geq f(x_k+)$ and $f(x_{k}) \geq f(x_k-)$ hence $f(x_k+) - f(x_k-) \leq f(x_{k+1}) - f(x_{k})$, and we have:  $\sum_{k=1}^{n} [f(x_k+) - f(x_k-)] \leq f(b-) - f(a+)$  Solution for (c)   From (b) is trivial, if $f$ is disconitnuous everywhere in an open subinterval of $[a, b]$ the $f$ has uncountable many points of discontinuity.  I'm asking for a solution for (b).

If $f$ is an increasing function defined on $[a,b]$ . Then show that the set of discontinuities of $f$ is countable and that $f$ has points of continuity in every open subinterval of $[a,b]$  Attempt: I have trouble understanding why the number of discontinuities of $f$ should be countable. For example, if we define a function which is increasing but different at each point in the interval $[0,1]$, then, there can be uncountable number of discontinuities.  I think if we prove that the number of discontinuities is countable, then we can prove that the function has points of continuity in every open interval of $[a,b]$.  Please help me understand intuitively why $f$ must necessarily have countable number of discontinuities. Suppose, $f$ has an uncountable number of discontinuities, then what can happen?  Thank you for your help.


Here's my list : list = [(a,1,2),(b,3,4),(c,5,6),(d,7,8),(e,9,10)]  I want to fetch the second element of the first three tuples. In this case it would be 1,3,5. Here's what I did : [item[1] for item in list]  But this would return all the elements, while I only need the first three. How do I do that?

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


I have plenty of cemeteries and crematoria, and no significant traffic issues. Why so many dead people?

I have been playing cities skylines for a while now and every now and again my city goes through the 'plague', where pretty much the entire city falls sick (see image below).   My water pollution is 0% and have more than sufficient crematoriums to accommodate the dead.   A few google searches point to water pollution but that is not the issue here... Any ideas what could be going on?


I'm learning calculus and I saw the following statement:     If $|a|+1>0$ then $\sqrt{|a|+1}>0$. By same logic we get $\sqrt{|b|+1}>0$. Then we get $\sqrt{|a|+1}+\sqrt{|b|+1}>0$.   I don't understand why $\sqrt{|a|+1}>0$. It could be a negative number no? For example if $a=3$ then we get $\sqrt{|3|+1}=\pm2$.

Lets say I have a function defined as $f(x) = \sqrt {x^2}$. Common knowledge of square roots tells you to simplify to $f(x) = x$ (we'll call that $g(x)$) which may be the same problem, but it isn't the same equation. For example, say I put $-1$ into them:  $\begin{align} f(x) &= \sqrt {x^2} \\ f(-1) &= \sqrt {(-1)^2} \\ f(-1) &= \sqrt {1} \\ f(-1) &= 1 \end{align}$  $\begin{align} g(x) &= x \\ g(-1) &= -1 \end{align}$  thereby, we conclude that $f(x)$ and $g(x)$ do not produce the same results even though they are mathematically the same. This is also shown when we try to graph the functions:  :    :    :    From this, we can see that given $f(x) = \sqrt {x^2}$, when simplified is not the same as $f(x) = x$. So, is there any way to prove that $y = \sqrt {x^2}$ is not the same as $y = x$ for negative values, but is infact the same as $y = \mid x \mid$?


The scenario is that both Alex and Yuval need to review the pull request. What is the correct way to write it in English?   Pull request awaits Alex and Yuval reviews. Pull request awaits Alex's and Yuval's reviews. Pull request awaits Alex and Yuval's reviews.   The preference on  seems to be the last option, but logically, shouldn't the second option be preferred (as Alex and Yuval play the same role).

Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better.


Having an infinite supply of water and two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters?  Each step in the solution can be one of three things: Fill up a container all of the way, empty a container completely, or use one container to fill up another as much as possible.  The solution to the original problem is: Fill the 5 litre bucket (completely). The buckets are now 5/5 and 0/3. Pour the 5 litre bucket into the 3 litre one. They are now 2/5 and 3/3. Empty the 3 litre bucket. They are now 2/5 and 0/3. Pour the 5 litre bucket into the 3 litre one. They are now 0/5 and ⅔. Fill the 5 litre bucket. They are now 5/5 and ⅔. Pour the 5 litre bucket into the 3 litre one. They are now 4/5 and 3/3. Now, you have one bucket with the required amount of 4 litres.  Is there a standard algoritm to determine a possible solution, or even the shortest solution?

I am reading a computer science puzzles book.   And I get the following question -  "You have a five quart jug, a three quart jug and unlimited supply of water. How would you come up with exactly four quarts of water ?"  The question is pretty simple and I figured the sequence of "water transfers" to solve it.  But there was an interesting side-note that I did not know.  The side-note said that as long as the two jugs size relatively prime, it is possible to find a pour sequence for any value between one and the sum of the jug sizes.  It is true for 5 and 3.   But I want to know if it is really generally true or not ? If it is, it is really cool! What is the theorem called ? Who discovered it ?


I'm trying to draw a lady that will get printed on a t-shirt. The lady will be positioned around the heart and will be around that size, so just a lady on the center of the chest. What size should i make the file where i will draw in Photoshop. What resolution. Thanks!

I made some designs for T-Shirts and I want to print them.  I want to know what's the best printing resolution for the best quality  And what's the ideal type of printers should I use if I want to market them.


Lets say a creature is attacked by an adventurer with a net.  Can the creature free themselves from the net with misty step?

Can a character escape the  (DMG p. 177, listed in the SRD as the ) with the  spell? To clarify, I am not asking if the bands prevent teleportation. I am asking whether the bands are teleported with the character as he teleports using misty step.


we pull data into excel from a web source. It fills a column all the way to row 2000. In the shortest possible way I want to spilt the data so that it fills column B, C, D, E, etc so when printing we are printer fewer pages. I would rather not cut and paste.

In my excel sheet I have three columns A, B, C that are very thin, but have a lot of lines (>500). Now if I print this out, I get 10 pages that are almost empty. Only at the left border of each page I see this three columns.  What I want to do, is to print that whole sheet in a multicolumn layout. 2 or 3 columns per page would be enough. Currently, I'm doing it by copying the values out of Excel, inserting it into a Word document and then use the multi-column layout function of Word. Isn't there a way to achieve that directly in Excel?  To clarify my problem: Currently my pages look like that  A B C A B C A B C A B C . . .   But what I want is this:  A B C     A B C     A B C A B C     A B C     A B C A B C     A B C     A B C . . .     . . .     . . .


If a object is in uniform circular motion, I know there is a acceleration directed radially inward. If that's the case, shouldn't there be a velocity radially inwards at some time. If that's true. Why does it not fall in that direction? know that i am a idiot. Please help me see how it works.

Why does the object not go inward, into the circle if the acceleration is inward? I think its because the velocity to outward? So they sort of cancel each other out? But if the speed is kept constant and the acceleration is inward, won't the object eventially move inward?   Also, what keeps the direction of acceleration always point inward?


I have few files that I need to extract from the file extension and remove the number at the end of each file  test1.alarms abcd1.alarms test2.alarms abcd2.alarms   Below is the code I used. The first part worked which removed the file extension and inserted back into the file, however, I was not able to remove the number of each file. After obtaining the result, I would then insert that back into the file.   for f in *.alarms; do base=$(basename "$f" '.alarms') sed --i "s/^/$base\:/" $f db_name=`echo $base | grep -o [a-z]` sed -ie "s/^/$db_name\:/" -i $f done   result should be   test abcd test abcd

Given a string file path such as /foo/fizzbuzz.bar, how would I use bash to extract just the fizzbuzz portion of said string?