I am learning QFT (in a path integral formalism) and one thing I'm struggling with is that self-interaction is supposed to be a quantum phenomenon, not apparent in classical non-linear field theory. I have read and understood how a perturbative construction of nonlinear field solutions give rise to tree-level (-only) diagrams (compare ) but I fail to link it to my intuitive model of waves superimposing nonlinearly. Let's calculate the 2-point function $\left<\phi(x_1)\phi(x_2)\right>$ of a classical theory. In a free theory, you'd calculate the fundamental solution to the field equation and evaluate it at $x_2$. That is, you apply a $\delta$-shaped source term at $x_1$ and calculate how the field evolves starting from there. Going to a nonlinear theory, the prementioned construction no longer yields a fundamental solution as there is no superposition principle. Still you can can calculate how the field evolves starting from a point source (where I mean "point" both in space and time) and that should yield the 2 point correlator, no? Now, my mental model is the following: the point source produces have a spherical wavefront that (freely) propagates for a bit. Now Huygens' principle kicks in and every point of the wavefront is again the origin of a new spherical wavefront. Only now we have no linear, but nonlinear superposition, i.e. interaction. Now when these different branches of the wave come together again, that is exactly self-interaction, no? and seems to produce exactly the processes that are depicted by loop diagrams? The integral $-\lambda^2 \int\mathrm{d}^4\!y_1 \mathrm{d}^4\!y_2 \; G(x_1, y_1) G^3(y_1, y_2) G(y_2,x_2)$ reads just like two elemental nonlinear superpositions, to me. How does nonlinear superposition (not) relate to self-interaction? Speaking in words of perturbation theory, how does nonlinear superposition of the different branches of a classical wave not lead to loop diagrams? What makes them appear in QFT then? How does the full propagator of nonlinear field theory look like? If it does not differ from the free one, why not?

We always say that tree levels are classical but loop diagrams are quantum.  Let's talk about a concrete example： $$\mathcal{L}=\partial_a \phi\partial^a \phi-\frac{g}{4}\phi^4+\phi J$$ where $J$ is source.   The equation of motion is $$\Box \phi=-g \phi^3+J$$  Let's do perturbation, $\phi=\sum \phi_{n}$ and $\phi_n \sim \mathcal{O}(g^n) $. And define Green function $G(x)$ as $$\Box G(x) =\delta^4(x)$$  Then   Zero order:  $\Box \phi_0 = J$   $\phi_0(x)=\int d^4y G(x-y) J(y) $  This solution corresponds to the following diagram:  First order:  $\Box \phi_1 = -g \phi_0^3   $  $\phi_1(x)=-g \int d^4x_1 d^4x_2 d^4x_3 d^4x_4 G(x-x_1)G(x_1-x_2)G(x_1-x_3)G(x_1-x_4)J(x_2)J(x_3)J(x_4) $  This solution corresponds to the following diagram:  Second order:  $\Box \phi_2 = -3g \phi_0^2\phi_1  $  $\phi_2(x)= 3g^2 \int d^4x_1 d^4x_2 d^4x_3 d^4x_4 d^4x_5 d^4yd^4z  G(x-y)G(y-x_1)G(y-x_2)G(y-z)G(z-x_3)G(z-x_4)G(z-x_5) J(x_1)J(x_2)J(x_3)J(x_4)J(x_5) $ This solution corresponds to the following diagram:  Therefore, we've proved in brute force that up to 2nd order, only tree level diagram make contribution.  However in principle the first order can have the loop diagram, such as  but it really does not occur in above classical calculation.  My question is:   What's the crucial point in classical calculation, which forbids the loop diagram to occur? Because the classical calculation seems similiar with quantum calculation. How to prove the general claim rigorously that loop diagram will not occur in above classical perturbative calculation.


Can anyone please explain when should i create communities, portals and sites for salesforce users?  How should i decide whether shoud i go with communities or portals?

After introduction with salesforce community, I am unable to clear how community is different from portal functionality. I already read  but this don't have answers of question like:   What is new things being provided by community? What are restriction we have if we use community? Advantage of community over portal. Is it capable of provide Email functionalities as same we have in other organization types? Role of chatter in communities etc. Is their difference between portal user and community user?   I already know that community is dedicated feature for portal functionality, but is it have some new functionality or only a portal part is separated?  Please provide some summary, links or answers you have.


I want to solve a problem, which needs the largest sum of the subarray and it's position. The program's solution is in pseudocode from the book Introductions to algorithms, however it contains a returning which contains 3 elements (low,high,sum). What can I do about this? How can I return three elements? The program is easily understandable, however the returning makes me unable to transform it to c++.

Is there a preferred way to return multiple values from a C++ function?  For example, imagine a function that divides two integers and returns both the quotient and the remainder.  One way I commonly see is to use reference parameters:  void divide(int dividend, int divisor, int& quotient, int& remainder);   A variation is to return one value and pass the other through a reference parameter:  int divide(int dividend, int divisor, int& remainder);   Another way would be to declare a struct to contain all of the results and return that:  struct divide_result {     int quotient;     int remainder; };  divide_result divide(int dividend, int divisor);   Is one of these ways generally preferred, or are there other suggestions?  Edit: In the real-world code, there may be more than two results.  They may also be of different types.


hello guys I am facing a problem that my Windows partition is not mounting in Ubuntu I kind of get the error that Windows maybe hibernated or has not been properly shutdown. But the thing is I have completely shutdown Windows but I'm still facing this error. Can somebody tell me why am I facing this error. I am using Windows 10

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


Well, it radiates in the infrared, I guess. But how exactly are these photons created? The atoms have some kinetic energy, which makes up the temperature. So while the atoms or molecules jitter a bit relative to each other, how does this spontaneously create a photon?

By conservation of energy, the solid is left in a lower energy state following emission of a photon.  Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium is a statement of the mean behaviour of the system, not a statement that the internal energy is constant on arbitrarily short timescales.  The energy has to come from somewhere during emission, and go somewhere during absorption.  Energy in a solid can be stored as kinetic and potential energy of electrons and nuclei, either individually or in collective modes such as phonons and plasmons.  In thermal equilibrium energy will be stored more or less in various forms depending on the temperature and material.  However, even if most of the thermal energy in a particular solid at temperature $T$ is stored in the form of phonons, it could be that phonons primarily interact with light indirectly via electrons, e.g. a phonon excites an electron in a phonon-electron interaction, which can interact with light via the EM field.  Given that light is an EM field, it makes sense to me that it is emitted and absorbed by charged particles.  The electron-photon interaction is probably dominant for visible and ultraviolet light, given that metals are opaque, while semiconductors and insulators are transparent to (visible and UV) light with energy lower than their bandgap. However, once you get into energies in the IR and below, or X-rays and above, other mechanisms apparently take over.  For example, on the high-energy end of the spectrum I've heard that gamma rays can interact directly with nuclear degrees of freedom, which is reasonable considering that gamma rays are emitted during a lot of nuclear reactions.  A review of  might give clues to important light-matter interactions over a broad range of wavelengths.  Whether all of the these processes are involved in blackbody emission is a somewhat different question.  What physical processes mediate energy transfer during blackbody emission, and in which energy ranges are the various processes dominant?


Each time I run it, I get a NullPointerException.  public StrongBuilder inorder() {     return inorder(root);  }  private StringBuilder inorder(Node root) {     StringBuilder val;     if (root != null) {         inorder(root.getLeft())      }     val = new StringBuilder().append(root.getValue().getAccountNumber()).append(root.getValue().getName());     inorder(root.getRight());     return val; }   Can anyone help spot the error for me? Thanks.

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 was directed here from lifehacks SE. Basically I am a student who would need access to gmail, Google in China (mainland).  From my past experience, Gmail is not blocked sometimes, blocked sometimes, but I would like something more reliable.  I am using MacBook Air. Does anyone know a reliable VPN that suits this purpose? I am just looking at mail/googling normal academic (English) websites on Mathematics, not searching for sensitive/prohibited content.

I will soon be spending a few months travelling across China and want to get a VPN service to get around the Golden Firewall.   When I was in China in 2014/15 the general consensus was that Astrill offered the most reliable service, but I heard that they have been targeted quite strongly by the government over the last year.   Therefore, I am wondering what is the best VPN for China these days? Is Astrill still as good as it used to be?   Any recent experiences would be very helpful!


I see a lot of templates coming with an massive slider on the top of the main page and as I was about to design my website I wanted to know if it's good for the design and UX . And as I googled it many sites says it's an bad idea but I wanted more idea of how it affects UX.

Go to just about any eCommerce site and the homepage is nearly guaranteed to feature a carousel - an auto-rotating panel, usually with some sort of small navigation, usually highlighting new product releases, sales or offers.   Are there any studies out there that look into how effective carousels actually are in terms of conversions and as compared against other ways of displaying similar information? I have a hypothesis that they might be something of a UI cliche, partially supported by looking at click data from some of our own sites.


I am looking for a traditional beginner's commentary on Aristotle's categories in order to start learning Aristotle's system of logic.  Even better would be a "road map" for studying Aristotle's logic through commentaries. I aim to eventually be able to read and understand Aquinas's commentary on the Posterior Analytics, as well as other works of Aristotle such as his Physics.

I am looking for books on Aristotle's Categories with academic commentary, preferably with references to further development of logic.


I have a server machine, with regular desktop hardware that I have obtained from my company. It is currently running Windows Server 2012 R2. The intention is to use it as a media server, connected to a TV. It works well, but the server OS is very heavy and slow to boot, also not 100% compatible with some of the applications I want to run on it, so I would like to install standard Windows 10 on it. Does anyone know if the server license will work for Windows 10, and which version of Windows 10 (home/pro/enterprise) I could install?

This is a  about Licensing.    Questions on licensing are off-topic on Server Fault.  If your question has been closed as a duplicate of this question, then this is because we want to help you understand why licence questions are off topic rather than just telling you "it just is". In all likelihood, this question will not address your question directly, it was not meant to.    I have a question regarding software licensing. Can the Server Fault community please help with the following:   How many licenses do I need? Is this licensing configuration valid? What CALs do I need to be properly licensed? Can I run this product in a virtual environment? Can I downgrade this product to an earlier version? Am I entitled to feature X with license Y?


What should the 'efficient' way of finding the last two digits of $2^{2016}$ be? The way I found them was by multiplying the powers of $2$ because $2016=1024+512+256+128+64+32$. I heard that one way would be with the Chinese Remainder Lemma but I don't really know how I should start?

How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and .


It's a well established concept in various fields of physics that the action of the field / trajectory that becomes physically real, minimizes / maximizes the action functional.  For the calculations, we only require the action to be extremal, which means, in principle if the value of the action would be kind of a "saddlepoint", this would suffice for the equations of motion to hold.   Even before asking such a question: Can there be an equivalent to a "saddlepoint" for functionals definded over a function space? If so, is it a meaningful definition to define a "saddlepoint" as the case when some trajectories in the vicinity of the extremal trajectory do have higher action, while others have lower action?  If so: are there any cases out there in any field of physics, where the extremal trajectory actually is such a "saddlepoint" trajectory?  Is there any case (from any physics field) where the choosen trajectories follow some of those saddlepoint lines?  Here, by saddlepoint I mean that some trajectories in the vicinity of the extremal trajectory do have higher action, while others have lower action.

Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in the points 1. and 2. below.  I understand that "principle of least action" is somewhat of a misnomer, since we find that to determine the path taken by a system, we need only impose the condition that the action be stationary, i.e., that $\delta S$ should vanish to first order for small variations of the path, and this leads to the Euler-Lagrange equations. In The Classical Theory of Fields, Landau & Lifshitz discuss the relativistic action for a free particle:  So for a free particle the action must have the form $$S = -\alpha \int_a^b ds$$ (...) It is easy to see that $\alpha$ must be a positive quantity for all particles. In fact, as we saw [earlier], $\int_a^b ds$ has its maximum value along a straight world line; by integrating along a curved world line we can make the integral arbitrarily small. Thus the integral $\int_a^b ds$ with the positive sign cannot have a minimum; with the opposite sign it clearly has a minimum, along the straight world line.  There is also a footnote, addressed a couple of paragraphs earlier, but which is relevant:  Strictly speaking, the principle of least action asserts that the integral $S$ must be a minimum only for infinitesimal lengths of the path of integration. For paths of arbitrary length we can say only that $S$ must be an extremum, not necessarily a minimum.  I have two questions regarding this:  How is the condition "the action must be a minimum for infinitesimal displacements" formulated? I've never heard of that outside of Landau & Lifshitz's books, and in Mechanics they mention it as well but doesn't go into detail. Is this discussed a bit more somewhere?  If for the whole path the action only needs to be stationary, how can we make the argument for the negative sign? If the action had to be a minimum then it would make sense, but surely the fact that $\delta S$ = 0 isn't affected by an overall sign?


My flight is from Chicago to Rome via Dublin Airport. Arriving and departing from the same Terminal 2. Layover is only 1 hour at 5:30 a.m. I'm a US permanent resident card holder with a Colombian passport.    Do I need a visa or transit visa?

I am Haitian, and traveling with a Haitian passport. I have to go to London with a work permit (tier 2 visa) on the 29th of July but I have 2 hour transit in Dublin.  Do I need a transit visa? Can I get it at the airport?  I also have a valid US visa.


If a moderator tries to delete a comment of a user that is not a member on the site (because the question was migrated) then the Android app crashes (app version 1.0.77).  The bug can be reproduced consistently.  Update January 14, 2020: I'm now using Android app version 1.0.95 and noticed this bug still/again is present. The app crashes every time I try to delete a comment written by people that are not a member on the site (migrated question). I tried it with 3 different users, all non-members at the time of writing, and get the same behavior every time.

I'm using the official Stack Exchange mobile app for iOS or Android, and  My app crashed! It doesn't look good on my new smartphone. It won't run after I updated my device. I noticed another bug. I have an idea for a new feature which is currently not in the app.  How do I report bugs with or request features for the iOS and Android apps? Also:  I've used the built-in functionality of the app to report a bug or submit a feature request. Did I do the right thing? The app prompted me to post on Meta after an error occurred. Should I post about it here? I'm wondering why the latest version is from 2017. I've heard rumors that the apps are no longer supported; is that true? I can't find the app on my device's app store anymore! Where did it go?     We get a lot of bug reports from users about the mobile apps, which are unsupported, and at the moment, there is no centralized Q&A pair for those to be closed as duplicates of (the relevant answers are spread across multiple unrelated questions). This question is an FAQ proposal, to serve as a directly-related duplicate target for those questions.


Given that we have a recursive function defined as $\begin{matrix} f_{0}=0 \\  f_{n}=f_{n-1}+1 \end{matrix}$ We can come up with a related non-recursive closed form function defined as $g(x)=x$ Where for every value of $n$ $f_{n}=g(n)$ Do all recursive functions defined with $\begin{matrix} f_{0}=\text{an integer} \\  f_{n}=\text{an algebraic function(1)} \end{matrix}$ (1): where said function involves only algebraic operations, like, addition, subtraction, multiplication, and division, as well as fractional or rational exponents have such a related non-recursive closed form function $g(x)$? I'm not looking for how to find $g(x)$ if it exists, I`m just wondering if one always exists.

From what I know, it is unknown whether $x_n=x_{n-1}^2 + 1$ has a closed form. Is there a recurrence relation which is known to have no closed form with a proof of inexistence?  Assuming a closed form is a non recursive description using the elementary operations of addition multiplication and power, or, assuming any other good definition of "closed form".  Edit  There are similar questions out there, but the answers are a little bit going around the question.   So is there one with proof or is it unknown? And if it depends on the definition of a closed form, then what are the (or some) options? How strong can a closed form definition be to still have a recursive relation that can be proved to not being able to have its form?  Update  Because it is a big question, and I don't want to open a new small one, I think a good representative small question about this subject is:  Is there a recurrence relation with a domain of the natural numbers, described by elementary functions, which has no closed form defined as:  A closed form of a recurrence relation with a domain of natural numbers is a function $f$ that can be described as a composition of a constant number of elementary functions without reccursion. i.e, $f(n) = f_1(f_2( \dots (f_k(n))) \dots) $ where $f_i$ is elementary for all $1 \leq i \leq k$   I think this definition is the most intuitive and basic.  For example, the relation $x_n = x_{n-1}+1$ has a closed form in this sense: $$f(n) = f_1(f_2(f_3(f_4(n))))$$  Where $f_1$ is division, $f_2(n)=(n,2)$, $f_3$ is multiplication and $f_4(n) = (n,n+1)$   Is there a recurrence relation which has no closed form in this sense?


this question arised because I'm working with Windows' CNG library and it has 4 functions for RSA:   BCryptEncrypt (private key, message) BCryptDecrypt (public key, message) BCryptSignHash (private key, hashed message) BCryptVerifySignature (public key, signature, hashed message)   So I was wondering, is there any difference between "Encrypting + Decrypting" and "Signing + Verifying"? I mean, if I hash the message and then encrypt it, wouldn't that be the same as Signing it? or Am I missing some logic that is behind that function? (talking about RSA in general, not about how windows' CNG work).  The only visible difference I see is:   For Encryption and Decryption I can use OAEP and PKCS1 padding. For Signing and Verifying I can use PKCS1 and PSS padding.   But again, is this because of how those functions are made in this library? or because the "operation" and the output are done in different ways depending on if it is Signing or Encryption?  If they are different, then why do we need the Signing part? Isn't encrypting with private and decrypting with public secure enough to "sign" it?

It is often said that RSA encryption of a cryptographic hash with a private key is the same as signing (signature generation). And that verification consists of decryption using a public key.  Is RSA encryption with a private key over a cryptographic hash equivalent to  signature generation?


I am reading the book Complex algebraic curves by Kirwan. In the exercise of chapter 2 of the book i am asked to find the tangent line at a singular point.  I was able to calculate the singular point. I want a definition of tangent line, so that i can calculate the same?  what is the geometric meaning of a tangent line here? Is it related in any way to theory of smooth manifolds?  Can someone please explain with minimal use of new math. Thank you!

Find the singular points and the corresponding tangent lines of $X^4+Y^4-X^2Y^2$.    I get that the singular points are those of the form $(a,a)$ and $(a,-a)$. The corresponding tangent lines are $X=-a, Y=-a$ and $X=-a, Y=a$ respectively. Is this correct? Thanks.


You are better than he. You are better than him.  Which one is correct? According to my views, Both are correct. "HE"is correct according to examiners. Otherwise, both are correct in conversation.

It is a well known fact that Alex is more soft-spoken than (she/her).    Why would "her" be wrong? Why must the sentence end with "she"?


Is it possible to load a backup of SQL server 2014db into SQL server 2012?  Trying to import/restore is throwing backward compatibility issues.  Thanks

What are my options if I need to move a database from SQL Server 2012(32bit) to SQL Server 2005(64bit)?  I know I cannot:   restore a backup of the database on SQL Server 2005 detach & attach   I know I can:   use import data wizard, and I tried it on one database, but it only moves data, and even that was troublesome as I needed to do a lot of work creating temp tables to maintain identity columns, recreating all FKs, indexes etc.    Is there an easier option?


In the wake of the recent news of the confirmation of the existence on gravitational waves, I was discussing gravitational waves with a friend, and he asked whether this could potentially lead to some kind of warp drive, and I pretty much immediately dismissed it. However, it got me thinking.   The gravitational waves detected by LIGO were from 2 black holes that merged and released of the order of 3 solar masses of gravitational energy (I apologise if I'm slightly butchering the science here, I'm no physicist), and it caused a "deflection" (again, please excuse, and feel free to correct, any technical ignorance on my part) of a fraction of the width of a proton.  The point of my question is this: if such an unimaginably large output of energy could cause such a tiny "deflection" at a distance of ~1.3 billion light years, what would something like LIGO (or perhaps something more like ESA's eLISA) observe at a distance of only 1 light year?

Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.  If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.  How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument?


I encountered this doubt while studying unique factorization domain (UFD): In the definition of UFD , there is a condition that every nonzero element can be written as a product of irreducible elements and a unit in the integral domain, which can be interpreted as the existential condition on factoring termination. However, in Algebra by Artin, page 364, the condition described above is replaced by that "factoring terminates", by which the author means the factoring will terminate if an element keeps being properly factored. This amounts to the universal condition, and it is equivalent to , namely ACCP. So my question is, are these two conditions equivalent, in other words, can the first (existential) one imply the second?

Let $A$ be an integral domain. We know that if $A$ satisfies ACC on principal ideals then it is a Factorisation Domain. I want to know about the converse, i.e.,      Does there exist a FD not satisfying ACC on principal ideals?   Edit. A Factorisation Domain is an integral domain whose every non-zero non-unit element is a finite product of irreducible elements.  Thank You.


I'm working on a Bubblesort that's supposed to take a random array of numbers and return them but I keep getting a 'possible loss of precision' error when compiling that tells me Math.random is returning a double and I need an integer. How can I covert this?   public class Bubblesort {    public static void main(String[] args) {      //create an int array we want to sort using bubble sort algorithm     int intArray[] = new int [Math.random()*100];   Here's my code just in case.  Edit: There was more code involved that I didn't think I would need to include. I tried casting but System.out.println isn't working now.  Rest of the code:   public static void main(String[] args) {      //create an int array we want to sort using bubble sort algorithm     int intArray[] = new int [(int)Math.random()*100];      //int intArray[] = new int [100];      //print array before sorting using bubble sort algorithm     System.out.println("Array Before Bubble Sort");     for(int i=0; i < intArray.length; i++){       System.out.print(intArray[i] + " ");     }      //sort an array using bubble sort algorithm     bubbleSort(intArray);      System.out.println("");      //print array after sorting using bubble sort algorithm     System.out.println("Array After Bubble Sort");     for(int i=0; i < intArray.length; i++){       System.out.print(intArray[i] + " ");     }

How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum.


Should I use can or may in the following sentence: "For more information on how you can help with wreath sponsorship..." ?

Which word to use when we ask for help?  Some conditions:     We know that the person asked is able to do it. We don't know if the person asked is able to do it.


I'm new to python scripting and got some task. I need to write a script that will make a GET request for all domains, parce the EXPIRES_ON date, compare with the current date, and if there is less than a month left, extend it by 1 year with a POST request. The only thing i need is to come up with right solution for parsing this date. Some people recommend me to do this with cycle. Any thoughts? language: python source: dnsimple example of date: 'expires_on': '2022-01-25'

I've got a huge list of date-times like this as strings:  Jun 1 2005  1:33PM Aug 28 1999 12:00AM   I'm going to be shoving these back into proper datetime fields in a database so I need to magic them into real datetime objects.   This is going through Django's ORM so I can't use SQL to do the conversion on insert.


I found a sentence in this :     He was determined not to complain in the presence of the nurse.   I got confused.  Was the man controlled by other people? Why the passive form? Why not:     He determined not to complain in the presence of the nurse.

How can I reliably and accurately identify the passive voice in writing or speech? I'm not interested in advice about whether or not to use it yet... I just want to know for sure what it is, so that I don't look as stupid as .


Just out of curiosity, can we make illegitimate operations with $0$, say, division by $0$ legitimate simply by imposing additional axioms? If so, then what consequences may follow? If the answer is negative, what are the differences between making operations with $+\infty, -\infty$ legitimate in the extended reals?

We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers).  Why this trick isn't performed with division by zero?


This is a practical problem born while folding a paper.  We can bisect a paper by using only hand.      $\star$ Easy, fold it so that the two ends (of the length) coincide and press   the paper to get the bisector of the length.   Repeating the $\star$ again and again we can divide the paper into $2^n$ (where $n\in\mathbb{N}$) parts using only hand.  But how can we divide the paper into some other(I mean other than $2^n$) number of parts .And particularly,       How can we divide the paper into three parts? Using only hand and instruments like ruler, compass, protractor etc and cutting away any piece of paper is banned.   I would recommend the reader to take a paper and try it!, it's really interesting!.

This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on eye estimate where to fold. Then I turn the letter over and fold bottom to top. Most of the time ending up with three different areas. There must be a way to do this exactly, without using any tools (ruler, etc.).


The TV show depicts the Dome as being perfectly round/circular when viewed from above but I'm sure in the book, it is portrayed as somehow following the shape of the town limits. That always seemed very arbitrary - how would the perpetrators (deliberately avoiding spoilers) know?  This question:  asks about the 3D shape of the Dome, but doesn't discuss what the basic 2D shape being extruded is.

What is the shape of the barrier in the TV series Under the Dome? Is it indeed a dome shape, or does it encircle the entire town like a spherical bubble, with one hemisphere above ground and the other hemisphere underground?


In the article about  thre is a following code snippet template <typename T> typename remove_reference<T>::type&& move(T&& arg) {   return static_cast<typename remove_reference<T>::type&&>(arg); }  Can please somebody explain the usage of typename (except  , it's clear)?

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I can't understand why this code returns False:  list_of_disks = [[170, 158, 470, 0.1], [135, 176, 410, 0.2], [100, 193, 350, 0.3], [170, 458, 470,       1.1]] def f1(pos):     for x in range(0, len(list_of_disks)):         if list_of_disks[x][3] == pos:             print list_of_disks[x+1][3] - 0.1, list_of_disks[x][3]             print list_of_disks[x+1][3] - 0.1 == list_of_disks[x][3] # Why is this False..?             break  f1(0.2)   When I print out the 2 values, they seem to be the same..? Hope someone can help me out here, thanks!

In follow up to , it appears that some numbers cannot be represented by floating point at all, and instead are approximated.  How are floating point numbers stored?  Is there a common standard for the different sizes?  What kind of gotchas do I need to watch out for if I use floating point?  Are they cross-language compatible (ie, what conversions do I need to deal with to send a floating point number from a python program to a C program over TCP/IP)?


I am new to java and having an issue calling a non static method  This is my main      public static void main(String[] args) {     Fish f1 = new Fish("Nemo");     Fish f2 = new Fish("Dory");     f2.setNumber(2);     Fish m = new Fish("Bruce");     m.setNumber(3);     Fish.printAllFish(); }   This is my fish class  import java.util.ArrayList; import java.util.List;   public class Fish { protected String name; protected int number; protected List<Fish> fishList = new ArrayList<Fish>();   public Fish(String in){ name = in; number = 1; fishList.add(this); }     public void printFish(){     System.out.println("the fish called" + name + " is number " + number ); } public void setNumber(int Number){     this.number = number; } public int getNumber(){  return number;    } public String getName(){  return name; } public int getFishNumOf(){     return fishList.size();  }  public void printAllFish(){     int size = this.getFishNumOf();     System.out.println("There are " + size + " fish:");     for (int i = 0; i < size; i++){         String a = getName();         int b = getNumber();         System.out.println("The Fish " + a + " is number " + b );     } } }   I  get the nonstatic error when trying to call printAllFish, I know I am probably making some rookie mistakes but I only just started to learn programming and things like classes, gets and sets still confuse me, any help would be very much appreciated!

The very common beginner mistake is when you try to use a class property "statically" without making an instance of that class. It leaves you with the mentioned error message:     You can either make the non static method static or make an instance of that class to use its properties.   Why? I am not asking for solutions. I would be grateful to know what is the reason behind it. The very core reason!  private java.util.List<String> someMethod(){     /* Some Code */     return someList;             }  public static void main(String[] strArgs){                // The following statement causes the error. You know why..     java.util.List<String> someList = someMethod();          }


I have a question. How come that the flight from Toronto to Moscow takes the same time as the flight from Moscow to Toronto. Should it take much longer because of the earth rotation?  One direction we travel in direction or an orbit and traveling back we are going against the Earth orbit...  From Toronto 9hours From Moscow 9:45 hours.  If flying from Moscow we are traveling against the Earth rotation so we should add half of the travel to our current travel. It means that the travel from Moscow should take about 13 hours...  Thanks,

Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S).  During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles turning/moving away from our position?  Or, in the opposite direction, would the flight to Sydney be faster since the Earth turns underneath us and moves Sydney closer?  ===   Please ignore jet stream effects and all other variables; this is a control case in an ideal environment. By "dramatically" I suppose I mean a delay of 1 hour or more.


I googled it, It didn't helped me a lot.  So Why cancer disease is named after sun signs ?

Origin of the word "cancer"      The disease was first called cancer by Greek physician Hippocrates (460-370 BC). He is considered the “Father of Medicine”. Hippocrates used the terms carcinos and carcinoma to describe non-ulcer forming and ulcer-forming tumors. In Greek this means a crab. The description was names after the crab because the finger-like spreading projections from a cancer called to mind the shape of a crab. –      So the cancer cells spread in a way that tumor looks like a crab. Why? Why doesn't it, for example, have a potato-like spread in which cancer cells form a sphere?


I have a large file composed of text fields separated by semicolons in the form of a large table. It has been sorted. I have a smaller file composed of the same text fields. At some point, someone concatenated this file with others and then did a sort to form the large file described above. I would like to subtract the lines of the small file from the big one (i.e. for each line in the small file, if a matching string exists in the big file, delete that line in the big file).  The file looks roughly like this  GenericClass1; 1; 2; NA; 3; 4; GenericClass1; 5; 6; NA; 7; 8; GenericClass2; 1; 5; NA; 3; 8; GenericClass2; 2; 6; NA; 4; 1;   etc  Is there a quick classy way to do this or do I have to use awk?

I have a CSV file users.csv with a list of userNames, userIDs, and other data:  username, userid, sidebar_side, sidebar_colour "John Lennon", 90123412, "left", "blue" "Paul McCartny", 30923833, "left", "black" "Ringo Starr", 77392318, "right", "blue" "George Harrison", 72349482, "left", "green"   In another file toremove.txt I have a list of userIDs:  30923833 77392318   Is there a clever, efficient way to remove all the rows from the users.csv file which contain the IDs in toremove.txt? I have written a simple Python app to parse the two files and write to a new file only those lines that are not found in toremove.txt, but it is extraordinarily slow. Perhaps some sed or awk magic can help here?  This is the desired result, considering the examples above:  username, userid, sidebar_side, sidebar_colour "John Lennon", 90123412, "left", "blue" "George Harrison", 72349482, "left", "green"


An ethernet cable is stuck in the laptop. The laptop is a Lenovo G50 and its Ethernet port is compact and sort of expands when you push the cable in. The cable is thinner and narrower than most, but the actual terminal seems to be standard. This has never happened before. I've tried really hard to get it out but it won't move. This is a silly problem. It's a "Cat 6 flat cable". Here is a picture of it stuck in the laptop (laptop is being held upside down):   Here is the picture of the other end of the cable:    I got it out :) but it looks completely fine. I'm not sure if I should try using it again:

I have plugged a network cable into my PC to temporarily adjust some settings on my router. Now I can't unplug it. The cable is physically stuck in the RJ45 port. I've tried squeezing every part of it but it won't come out.  Any suggestions for how I might remove it?


I see lot of information about the power of compound interest and how it can help money grow. I understand the mathematics of compound interest but I have no idea how to take some money and make it grow. If I am in my 20s and I have $10k to invest and I know nothing about the stock market, what can I do right now to maximize my earnings ? What can I do in the next 3-5 years ? I am living in New York, USA.

I am young, just started my career, and looking to begin investing so I can make my money work for me. I'm still living like I did in college (occasional purchase on myself, but most of it goes into savings) and I would like to take the extra money and invest it.   What would you suggest are the best options for me to begin? I was considering getting a personal investor [a financial advisor] for perhaps a year or so, but I've heard that they really are not worth the money. I wanted to get the input of the great minds here.


I would like to ask one solution regarding update and upgrade process. I am using Ubuntu 16.04 LTS xenial version. I found one problem statement:     E:The package linux-headers-4.13.0-37 needs to be reinstalled, but I can't find an archive for it.   when I try to update. I am not able to open my synaptic. Please suggest me to get rid of the problem.

From time to time, Ubuntu users encounter errors from  or , of the form:  The package some-package needs to be reinstalled, but I can't find an archive for it.  I want to know what causes this error so that I can reproduce it and try to find safe ways of fixing it, even when the broken package is important and has many dependencies.  of the  might give a bit of a clue, but I don't know how packages get the status that causes the error.  How can I produce this error for testing on my (Ubuntu MATE 17.10) system?  This is prompted by  and my long-standing discomfort with closing questions about this error against , whose answer uses dpkg --force-all to remove the offending package.  suggests this solution has worked for many users, but I am not confident that using --force-all won't cause later problems, or that it's a good idea to use this method to remove important packages like APT.


By default, diagrams in tikz and pgfplots inherit the style of the surrounding document, which is a good thing.  However, I've read that serifs are good for large bodies of printed text (the main text of the document), whereas sans-serif is more suitable for headings.  What is a good choice for labels in diagrams such as drawn with tikz and pgfplots, and why?  What is the tradition here?  \tikzset{every node/.append style={font=\sffamily}} % yes or no?   Although I realise that good may be subjective, it appears that typographers often have strong reasons to favour a particular style.  Related questions:

Question for you design-y types:  I like to use a serif font for all my text (title, headings, body). What I'd like to know is whether you think that I should go with a serif or sans serif for text in my charts (bar labels, axis labels, chart titles, etc) and figures (flowchart node and edge labels, etc).  On the one hand, serif lends a nice continuity to the feel of the document, but on the other I think sans serifs are more legible with small fonts.  I'm torn on the matter. Thoughts?


I have a SQL query that returns a list of GUIDs like this:  92bca6ba-0174-4d80-b701-8bed4b2673e0 917399f2-05d7-42ff-b84e-5f8395c8e8fd   What I need the results to be is one string of text:  '92bca6ba-0174-4d80-b701-8bed4b2673e0', '917399f2-05d7-42ff-b84e-5f8395c8e8fd'   I've looked into several options but can't seem to get it to work.

I'm trying to migrate a MySQL-based app over to Microsoft SQL Server 2005 (not by choice, but that's life).  In the original app, we used almost entirely ANSI-SQL compliant statements, with one significant exception -- we used MySQL's group_concat function fairly frequently.  group_concat, by the way, does this: given a table of, say, employee names and projects...  SELECT empName, projID FROM project_members;   returns:  ANDY   |  A100 ANDY   |  B391 ANDY   |  X010 TOM    |  A100 TOM    |  A510   ... and here's what you get with group_concat:  SELECT      empName, group_concat(projID SEPARATOR ' / ')  FROM      project_members  GROUP BY      empName;   returns:  ANDY   |  A100 / B391 / X010 TOM    |  A100 / A510   So what I'd like to know is: Is it possible to write, say, a user-defined function in SQL Server which emulates the functionality of group_concat?   I have almost no experience using UDFs, stored procedures, or anything like that, just straight-up SQL, so please err on the side of too much explanation :)


I'm creating a Toggle function I've done the bigger part (I hope). But now I'm facing two problem :  • I can Show and Hide my resume but I can't do it again (more than once in each direction).  • I Dont get how to apply this to a specific resume and not to every one; shall I use .each() ? I'm a bit lost on it I admit.  This is what I've manage to do for now :   HTML
Lorem Ipsum ....
   jQuery  $(document).ready(function(){      if($('.resume').text().length > 100)     {         complet = $('.resume').text();         complet += ' Cacher';         html = $('.resume').text().slice(0,100);         html += '...';         $('.resume').html(html);     }      $('.showMore').on('click',function(){         $('.resume').html(complet);         showLess();     });      function showLess(){     $('.showLess').on('click', function() {         $('.resume').html(html);     });     }  });   And here is the

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 can know some patterns like these.  I enjoy cooking. He wants to swim.  But for other verbs like admit, allow, agree, appear and so on. It seems that I have to remember which verbs are followed by infinitives or gerund. I know I have to listen a lot. At least I know how to use "can't help" from this song "but I can't help falling in love with you...." But for learner do we have only to remember them or are there any other solutions?

English isn't my mother tongue. I'm familiar with the notions of infinitive and gerund but I sometimes just don't know which of the two should be used in combination with which verb.  Thomson and Martinet [1986] provide some verbs that may take either infinitive or gerund without changing the meaning (advise, allow, ...).  I am looking for a list of verbs and the allowed construction (gerund/infinitive/both). Ideally this should be a text-based list so I can search it on my computer without having to use the internet.  [Thomson and Martinet, 1986] A. J. Thomson and A. V. Martinet, A Practical English Grammar, Oxford University Press, isbn: 0-19-431342-5, 1986.


Given that an arbitrary $a_n > 0$, and $\sum a_n$ converges, then does $\sum \sin (a_n)$ converge also? Honestly I don't know where to start with this question. I tried some examples like $\frac{1}{n^2}$, $\frac{n^2+n}{n^4+5}$, and they all seem to follow this statement. I am beginning to think that this statement is correct. But how?

I am given the problem: Let $a_n>0$, prove $\sum_{n=1}^\infty a_n$ converges if and only if $\sum_{n=1}^\infty \sin(a_n)$ converges.  We have this problem in a homework, and I don't believe it can be true. The statement being biconditional implies that when $\sum_{n=1}^{\infty} \sin(a_n)$ converges, so too does $\sum_{n=1}^\infty a_n$, but if we take $a_n=\pi n$ or even $a_n=\pi$, then $\sum_{n=1}^\infty \sin(a_n)$ converges while $\sum_{n=1}^\infty a_n$ diverges. Is my thinking incorrect?


I use ubuntu for downloading and I want to move the files to my C: Drive so that when I run windows I can access the files. How do I do that?

I wanted to ask, how can i view all my windows files on Ubuntu. I found out how to get my D drive folders but have yet not figured out how to get my C drive files. Please give me an easy way to find my files. For more information, i have installed ubuntu via wubi. Please answer my question ASAP.


For a metric space $X$, show that if $F \subset X$ is closed and connected then for every pair of points $a, b \in F$ and each $\varepsilon > 0$ there are points $z_0, z_1, ... , z_n \in F$ with $z_0 = a$, $z_n = b$ and $d(z_{k−1},z_k) < \varepsilon$ for  $1 \le k \le n$. Is the hypothesis that $F$ be closed needed?   Actually, I tried to prove it by contradiction, i.e. let there exists distinct $a, b \in F$ and there does not exist any finite set of points in F such that the above condition holds . Then, $\exists \varepsilon>0$  such that for any finite set of points $\{a, z_0, z_1, ..., z_n\} \in F$, there is a positive integer $k<n$ with $d(z_{k−1},z_k) > \varepsilon$ , then for any $z \in F$, $z \ne a,b$ ; either $d(a,z) < \varepsilon$ or $d(a,z) \ge \varepsilon$, now as $F$ is connected, there is a $z$ with $d(a,z) = d(b,z) = \varepsilon$, then I can't approach .

Let $F\subset X$ be a closed and connected subset of the metric space $(X,d)$ then for every pair of points $a, b\in F$ and each $\epsilon>0$ there are points $a=z_0,z_1,\ldots z_n=b$ in $F$ such that $d(z_{k-1}-z_k)<\epsilon$ for $1\leq k\leq n$.  Is the hypothesis that $F$ is closed needed?


I'm trying to typecast the uint8_t buffer to structure with bit field as below. #include<stdio.h> #include<inttypes.h>  struct msg{     uint64_t field:56; };  void main() {    uint8_t buf[8]={0x7,0x6,0x5,0x4,0x3,0x2,0x1};    struct msg *m = buf;    printf("buf=%"PRIx64"\n",m->field); }  But I'm getting the output as below.  Actual output: buf=1020304050607 Expected output: buf=7060504030201   Am I doing anything wrong while typecasting?

When asking about , people sometimes refer to the strict aliasing rule. What are they talking about?


I'm learning logistic regression on Coursera.  In the class, we say the logistic regression model is $h_\theta(x) = p(y=1) =\frac{1}{1+e^{-\theta^Tx}}$. When making predictions, we say that $y=1$ if $h_\theta(x) \ge .5$ and $y=0$ otherwise. The cost function we use to find the parameters $\theta$ given the training set is $J(\theta)=\frac{1}{2m}\sum (-y^{(i)}h_\theta(x^{(i)}) - (1-y^{(i)})(1-h_\theta(x^{(i)})))$.  But couldn't we predict the exact same thing using linear regression? Our linear model is $a = \theta^TX$ and we output $y=1$ if $a \ge0$ and $y=0$ otherwise. We could make our cost function $J(\theta)=\frac{1}{2m}\sum (-y^{(i)}g(a) - (1-y^{(i)})(1-g(a)))$ where $g$ is the sigmoid function. Using linear regression with this new cost function and a threshold of $0$ would give us exactly the same predictions as logistic regression.  So why do we use logistic regression instead of linear regression with a new cost function? Is it just because the probability in logistic regression is more easily interpretable than the real number outcome in linear regression? Or is there another reason?

Recently I began studying machine learning, however I failed to grasp the intuition behind .   The following are the facts about logistic regression that I understand.   As the basis for hypothesis we use . I do understand why it's a correct choice, however why it's the only choice I don't understand. Hypothesis represents the probability that the appropriate output is $1$, therefore the domain of our function should be $[0,1]$, this is the only property of sigmoid function I found useful and appropriate here, however many functions satisfy this property. In addition, sigmoid function has a derivative in this form $f(x)(1-f(x))$, but I don't see the utility of this special form in logistic regression.   Question: what so special about sigmoid function, and why we cannot use any other function with domain $[0,1]$? The cost function consists of two parameters ${\rm Cost}(h_{\theta}(x),y)=-\log(h_{\theta}(x))$ if $y=1, {\rm Cost}(h_{\theta}(x),y)=-\log(1-h_{\theta}(x))$ if $y=0$. In the same was as above, I do understand why it's correct, however why is it the only form? For example, why couldn't $|h_{\theta(x)}-y|$ be a good choice for the cost function?  Question: what is so special about the above form of cost function; why cannot we use another form?   I would appreciate if you could share your understanding of logistic regression.


Suppose two players in a game of poker (assume Texas Hold'em) have cards with the same values. For example, Player A and Player B have the cards 4 & 9. The board shows a 2,3,4,7, and 8 face up.  Who would be the winner, Player A or Player B?

In Texas Hold'em poker, there are some cases where a particular card, often called kicker, acts as a tiebreaker between players to determine who wins the pot, or if the pot has to be shared.  For some combinations such as three or four of a kind, there is no doubt: the kicker is the 5th card of the chosen combination, and determines the winner.  Example     Alice has 7 and 10   Bob has 7 and K   On the board are 7, 7, 2, 3, 4   In that case, both have a three of a kind. But because Bob has a king and Alice only a 10, he wins.  Most of poker websites explaining the rules clearly mention the role of the kicker applying to three of a kind and double pairs. But much fewer say something about colors, straights and full houses, and I found many contradicting answers. I also asked the question to some used online poker players and they also gave me contradicting answers.  I have tried to search for official tournament rules, but most of them only explain what happens with bad behaviors, bad deals, incorrect or confusing betting, showing cards when you shouldn't, acting when it's not your turn, etc. without mentioning subtleties about combinations at all.  To simplify my question, I will take three examples; I think it's better to start with examples before getting to the general answer if one exists. So, what's happening in the following 3 examples? Could you give a more generalized answer?  Example 1 - Flushes     Alice has 2♣ and 3♣   Bob has 4♣ and 5♣   On the board are 6♣, 8♣, 10♣, 2♥, 5♦   Contradicting answer 1: it's a tie, because the highest card included in the flush is the 10, which everybody chooses to include in their 5 showdown cards. Contradicting answer 2: Bob wins, because he has the greatest private card that is part of the flush  Example 2 - Straight     Alice has 6 and K   Bob has 6 and J   On the board are 4, 5, 7, 8, 10   Contradicting answer 1: it's a tie, because the greatest card in the straight is the 8 for both Alice and Bob Contradicting answer 2: Alice wins, because she owns an extra king, compared to the jack of Bob  Example 3 - Full house     Alice has 3 and 7   Bob has 3 and 6   On the board are 3, 3, 2, 2, 5   Contradicting answer 1: it's a tie, because one is supposed to choose only five cards to make a combination, and a full house is already five cards. There couldn't be any kicker, and thus their showdowns are strictly equals. Contradicting answer 2: Alice wins because of her extra 7, compared to the 6 of Bob  Thank you very much for your answers.  Note: I'm unable to post next to you, so I edit my own post; strange not be able to answer to an answer.  Ok, So if I summarize what you are saying :   In the flush case, Bob wins because at some point, their hand differs. Technically, I can continue comparing the highest private card to decide who wins. I had it correct. In the straight case, if the highest card of the straight is public, then it's technically always a tie, no matter what the players had as second private card (asuming that only one of the two cards was part of the straight). In a full house if both players have the same triplet and the same pair, it's always a tie, no matter what the players had as second private card (assuming again that only one of the two was part of the full house).   Please confirm me that what I summarized is correct.  Thank you for your answer.


Say you have n digits and you want to see how many different numbers you can form with these digits (i.e. all possible numbers, not only the ones that are n digits long). These digits however aren't unique. How would one approach such a question? There wouldn't be any problem if you considered only the numbers that are 8 digits long, but unfortunately that's not the case.   For example: how many numbers can you make with the following 8 digits: $1, 2, 2, 3, 3, 3, 0, 0$.  For 8 digits the answer would be quite simple: $\frac{8!}{1!2!3!2!}$  I also figured the answer above includes the answer for 7 and 6 digits because of the two zeros. But I don't know how to continue for 5 etc.. digits.

How many different numbers can you make with the following eight digits?   $1, 2, 2, 3, 3, 3, 0, 0$  The problem I encounter is how to include numbers that aren't 8 digits long? For instance the number 12.   I know the answer for 8 digit numbers (assuming zero can be a starting digit):   $\frac{8!}{2!3!2!}$  But I can't seem to figure out how to include all the other numbers that aren't 8 digits long.


Can I use "years" as a continuous variable ("years" as calendar years from 1984 to 2014) to see if NDVI (normalized difference vegetation index), of the same area at the same time (summer), has changed positively or negatively over the years, for example with a GLMM or GLM?

I'm not used to using variables in the date format in R. I'm just wondering if it is possible to add a date variable as an explanatory variable in a linear regression model. If it's possible, how can we interpret the coefficient? Is it the effect of one day on the outcome variable?   See my  with an example what I'm trying to do.


I have newly moved to a property with a small cottage. It is located in a hot desert climate, close to the sea, with occasional rain during the winter.   The cottage is made from relatively thin planks and has rain damage inside. It's cheaply built, but I would love to preserve it.  The water damage is mainly on the back wall, which is on the rainy side and leans against a stone wall which is about three feet tall.   The walls look like this. (This is one of the side walls.)    The damage from inside is visible in this terrible photograph:    It appears the water seeps through the cracks, both from the rain and perhaps from what moisture the stone wall is preserving.   What are good ways to protect a wall like this from water creeping in?   Covering it in tarboard from top to bottom seems to be an option (and is available) but I'm not sure whether it is ideal.

I have an old prefab cottage made of wood.     its walls have become leaky. When it rains sideways (happens a lot because we're so close to the sea), water seeps in from in between the beams, and through the knotholes.     This is, of course, ruining the wood inside and I need to do something.    The weather conditions here are extreme: in summer, there is zero rain, and temperatures can reach up to 40°C (104°F). In winter, there are rare but intense rainfalls. I guess the nearby sea makes the air very salty.    I have considered - and discarded - a number of options, but of course I'm open to being corrected! I am really out of my depth here.   Varnish it - the most obvious solution I guess, and would take care of the leaks, but that'd have to be sanded down every couple years, right? I'd like to avoid that as it would be a lot of work. Especially since with our extreme weather, the cycle is going to be very short. Use silicone to fix the leaks directly - I've been told that might not hold together well, and silicone that can withstand the sun is extremely expensive around here. It could be hundreds of Euros to do the job. Plaster the walls - an interesting option as it would also add a little bit of insulation (it gets mercilessly hot in the cottage during the summer), but I've never done this before, it seems tough to do and it would of course alter the look of the building.    Obviously, I'd like the solution to be as cheap as possible, and as long-lasting as possible.  What would you do?


Prove the following inequality.   $\frac1{\sqrt1+\sqrt3}+\frac1{\sqrt5+\sqrt7}+...+\frac1{\sqrt{9997}+\sqrt{9999}}>24$   I tried to rationalizing the denominator and I got the following inequality to be proved,  $$-\sqrt1+\sqrt3-\sqrt5+\sqrt7-...-\sqrt{9997}+\sqrt{9999}>48$$  Once I got that, I don't know what to do with the LHS. Hints or solution would be appreciated.

Prove the inequality $$\frac{1}{\sqrt{1}+ \sqrt{3}}  +\frac{1}{\sqrt{5}+ \sqrt{7} }+......... +\frac{1}{\sqrt{9997}+\sqrt{9999}} > 24$$   My work:   Rationalizing the denominator gives   $$\frac{\sqrt{3}-1}{2}  +\frac{\sqrt{7}-\sqrt{5}}{2}+......+\frac{\sqrt{9999}-\sqrt{9997}}{2} .$$  Now by taking two as common and separating the positive and negative terms gives  $$\frac{1}{2} [ \{\sqrt{3} +\sqrt{7}+\dots +\sqrt{9999}\} - \{1+\sqrt{5} +\dots+\sqrt{9997}\}].$$  Can we do like this please suggest. Thanks.


I have a symmetric and weighted adjacency matrix with $n$ elements. What algorithms exist to cluster the elements from this matrix?  The matrix has values between $0$ and $1$. In the case of a similarity matrix the elements in the main diagonal are $1$, in the case of a distance matrix the values in the main diagonal are $0$.  Is it possible to use $k$-means using the "adjacency" matrix?

I have a (symmetric) matrix M that represents the distance between each pair of nodes. For example,       A   B   C   D   E   F   G   H   I   J   K   L A   0  20  20  20  40  60  60  60 100 120 120 120 B  20   0  20  20  60  80  80  80 120 140 140 140 C  20  20   0  20  60  80  80  80 120 140 140 140 D  20  20  20   0  60  80  80  80 120 140 140 140 E  40  60  60  60   0  20  20  20  60  80  80  80 F  60  80  80  80  20   0  20  20  40  60  60  60 G  60  80  80  80  20  20   0  20  60  80  80  80 H  60  80  80  80  20  20  20   0  60  80  80  80 I 100 120 120 120  60  40  60  60   0  20  20  20 J 120 140 140 140  80  60  80  80  20   0  20  20 K 120 140 140 140  80  60  80  80  20  20   0  20 L 120 140 140 140  80  60  80  80  20  20  20   0   Is there any method to extract clusters from M (if needed, the number of clusters can be fixed), such that each cluster contains nodes with small distances between them. In the example, the clusters would be (A, B, C, D), (E, F, G, H) and (I, J, K, L).  I've already tried UPGMA and k-means but the resulting clusters are very bad.  The distances are the average steps a random walker would take to go from node A to node B (!= A) and go back to node A. It's guaranteed that M^1/2 is a metric. To run k-means, I don't use the centroid. I define the distance between node n cluster c as the average distance between n and all nodes in c.  Thanks a lot :)


I was trying to upgrade Ubuntu from 16.04 to 16.10, but during the upgrade process an error popped up (it said something like 'there is an error in system files' but I don't remember exactly).   The upgrade window froze and I forced quit.   Now, after restart Ubuntu is stuck at purple screen. What should I do to reach the login screen? I have important files in my system and now I can't reach them also. I also have windows 8 installed pc and I can start windows normally, if that's any use.

During upgrade from 12.04 to 12.10 there was a power failure.  computer boots to desktop but without tools and menus to navigate.  files that can be open cannot be closed.  sidebar menu does not exist.  there is no function of the DVD drive, the USB drive nor the internet.  Possible to open GRUB but I am not familiar with it's function.  Please help.


Let $$f(z)=\int _{-\infty }^{\infty }\frac{\sin\left(wz\right)}{w}\:dw$$  $$f'(z)=\int _{-\infty }^{\infty }\sin\left(wz\right)\:dw=\lim _{x\to \infty }\left(\frac{\cos\left(wz\right)}{z}\right)-\lim _{x\to -\infty }\left(\frac{\cos\left(wz\right)}{z}\right)= \cos\left(\infty \right)-\cos\left(-\infty \right)=\cos\left(\infty \right)-\cos\left(\infty \right)=0$$  $f(z)= 0 + C$;      $f(0)=\int _{-\infty }^{\infty }\frac{\sin\left(w0\right)}{w}\:dw \Leftrightarrow 0 = 0 + C \Leftrightarrow C=0 $  I should have obtained $\pi $, since $\frac{\sin\left(w\right)}{w}$ is an even function and $\int _{0\:}^{\infty \:}\frac{\sin\left(w\right)}{w}\:dw$ = $\frac{\pi }{2}$

I just need to know if this integral converges.  If it does, what is the value?  If not can anyone tell me what is the value of the $$ \int_{-\infty}^\infty 2\,\frac{\cos(w)\sin(w)}{w}\ dw ? $$


It seems that there are no badges similar to the criteria of the :     answer +5 a -3 question that goes to +3   This badge would promote users to answer many underrated good questions.  Would this make a good silver badge?

During Winterbash 2014, there was a hat called , which was earned by giving an answer scoring 5 or better to question that had a score of −3 or worse at the time of answering and later rose to a score of +3 or better.  I’ve already shared the . Those cases give me a great deal of confidence that this would be a challenging badge trigger that would produce good behavior with a minor tweak. Here are the Red Barons earned on other sites:    (Logan Maingi) Mathematics  (Mike Miller) Mathematics  (Hugo) English Language and Usage  (tchrist) English Language and Usage  (Mr. Shiny and New 安宇) English Language and Usage  (Darth Satan) Science Fiction and Fantasy  (DVK) Science Fiction and Fantasy  (rolfl) Code Review  (Heslacher and Hosch250) Code Review  (Edward) Code Review  (janos and Manny Meng) Code Review  (Mark Mayo, Rory Alsop and MeNoTalk) Travel      (DJClayworth) Christianity  (McMagister) Puzzling   Looking through the timelines, I’m convinced that the answerer’s votes should be excluded from the pre-answer question score calculation. Doing that would have reduced the number of Red Barons to 16 across the network. However, the cost of making a badge harder to obtain is worth the benefit of avoiding giving people an incentive to manipulate question scores¹.  To wrap up, the hat seemed to have encouraged a number of great answers and rescued some questions that would otherwise have been lost to time. My outstanding questions are:   Were there any problems on questions where people were attempting to earn the hat, but failed? (Or any other problems I didn’t observe.) If not, should we  or create a new badge? If we create a new badge, what should it be called?   I’m especially interested in feedback that counters my own bias in favor of this idea. If I’m missing any problems, I’d like to know about them now.    ¹ Several questions were downvoted, answered, edited (sometimes trivially)  and upvoted by the user who earned the hat.


Could you deliver an answer in a way that does not require too much special knowledge in advance, yet also deliver some deeper insight to a lesser advanced Linux User ?

What is the difference between a "job" and a "process"?


Trying to write a script which will read what a user has imput... I know it's basic but im stuck on the first if..  echo  "Please enter yes or no (y/n)?" read string if [ $string = "y" -o "n" ]    then       echo "User selected $string"    else       echo "You didn't enter y/n !!!" fi   I would like it to be if [ $backup = "y" or "n" ]  Any ideas?

I want to pause input in a shell script, and prompt the user for choices. The standard Yes, No, or Cancel type question. How do I accomplish this in a typical bash prompt?


This might be a stupid question, but what exactly is the is function, and when would one use it?  From the context, i guess i could infer that it's equivalent to ==; but if that's the case, why have both? The  shows nothing, and help(is) returns a SyntaxError.

My  has failed me.  In Python, are the following two tests for equality equivalent?  n = 5 # Test one. if n == 5:     print 'Yay!'  # Test two. if n is 5:     print 'Yay!'   Does this hold true for objects where you would be comparing instances (a list say)?  Okay, so this kind of answers my question:  L = [] L.append(1) if L == [1]:     print 'Yay!' # Holds true, but...  if L is [1]:     print 'Yay!' # Doesn't.   So == tests value where is tests to see if they are the same object?


I am looking for a module or way to use an external RSS feed in a view. I know this was easily done in Drupal 6, but I can't seem to find much on Drupal 7.  I am trying to use Views RSS, but there is very limited documentation.

I have an rss feed (facebook) (can also be output as a json). I want to import the RSS feed and have it display using a view.  I already have the Feeds module installed and the Feeds: Facebook Parser installed. I think I have everything I need but I can't figure out how put it together. Seems like this is a common need just not sure how to put the pieces together to make it happen.


Can you please elaborate on these two tendencies separately? The quotation assumes that your PhD alma mater differs from the university where you first taught. First, why less prestigious than PhD alma mater? Second, why less prestigious than the university of the first teaching position?  In 2005, thanks largely to his field experiments, List was offered a tenured professor position at the University of Chicago, perhaps the most storied economics program in the world. This wasn’t supposed to happen. It is a nearly inexorable law of academia that when a professor lands a tenured job, he does so at an institution less prestigious than the one where he began teaching, and also less prestigious than where he received his Ph.D. John List, meanwhile, was like a salmon who swam downstream to spawn, into the open water. Back in Wisconsin, his family was unimpressed. “They wonder why I’ve failed so miserably,” he says, “why I’m not still in Orlando, where the weather is really great, instead of Chicago, where the crime is really high.”  Dubner, Levitt. SuperFreakonomics: Global Cooling, Patriotic Prostitutes, and Why Suicide Bombers Should Buy Life Insurance (2009). P 118.

Recently, someone analyzed  and found that over half of the professors at the top 51 universities graduated from a top 10 university.  have also brought this up. From my personal observations, most schools do hire graduates from better ranked schools.  Is this because of the competitive job market? We have so many good applicants, we have to narrow it down some how! Or is it simply that these schools produce the most PhDs? Has this always been the case? How rare are exceptions to this? I know of a few people who graduated from a top 75 school and got hired at a top 50 school. But what about bigger gaps? The top 10 schools seem to just swap graduates, do they ever hire from a 50+ ranked school?  Update 2018: I have accepted a tenure-track position at a top 75 department at an R1 university immediately after graduating from an unranked department at an R2 university. It does happen! This may or may not generalize to other fields and countries.


I'm trying to create generic array in java but it results in error. Can any one help me on this?  Please find my code below:  public class GenericArrayTest<TKey extends Comparable,TValue>                                    implements Iterable<Map.Entry<TKey,TValue>> {   private TKey[] _arrayCOll;    public void test(){     _arrayCOll = new TKey[10];//error "Cannot create a generic array of TKey"   }    @Override   public Iterator<Entry<TKey, TValue>> iterator() {         // TODO Auto-generated method stub         return null;   }  }   Note: I could not know the class type so that i could not use the below solution   Thanks in advance. Sarath

Due to the implementation of Java generics, you can't have code like this:   public class GenSet<E> {     private E a[];      public GenSet() {         a = new E[INITIAL_ARRAY_LENGTH]; // error: generic array creation     } }   How can I implement this while maintaining type safety?  I saw a solution on the Java forums that goes like this:  import java.lang.reflect.Array;  class Stack<T> {     public Stack(Class<T> clazz, int capacity) {         array = (T[])Array.newInstance(clazz, capacity);     }      private final T[] array; }   But I really don't get what's going on.


I'm making an interpreter and I've been having trouble getting the Windows CMD to output the correct unicode characters. I understand Windows can't handle UTF8 so you have to use UTF16 but everything I have tried hasn't worked. I've tried changing the code page saving the files with specific encodings etc ... and nothing has worked. So my question is, how does Python or Ruby or Lua output Unicode characters to the command prompt?   Do they convert the characters to UTF16 or do they internally represent the characters as UTF16? I don't mind if you only give an explanation of how one of the programming languages works, I wouldn't expect you guys to go looking through the code of all of them. Any help at all would be appreciated.

We have a project in Team Foundation Server (TFS) that has a non-English character (š) in it. When trying to script a few build-related things we've stumbled upon a problem - we can't pass the š letter to the command-line tools. The command prompt or what not else messes it up, and the tf.exe utility can't find the specified project.  I've tried different formats for the .bat file (ANSI, UTF-8 with and without ) as well as scripting it in JavaScript (which is Unicode inherently) - but no luck. How do I execute a program and pass it a Unicode command line?


Should  be the appropriate term? I mean, for example, because of the quantum field theory we have been able to find the subatomic particles that it theorized and make the Standard Model. Why then is is labeled as a theory? Also wave-particle duality is widely accepted fact yet labeled as a theory. What is up with that, why call it a theory. Maybe because it promotes the fact of idealism?

Some basic Physics books are often misguiding in the sense that they don't make clear whether something is a primitive concept, a law, a definition or a theorem. This is often a little confusing. I've asked here some moments ago if there's a definition of force, and I've been redirected to a question about whether Newton's Laws are laws or definitions of mass and force.  This is just an example, but there are many others, like for instance, the conservation of energy, which some books present as a theorem, and some places says that this is a law of Physics. Time on the other hand, is something that according to Feynman's lectures on Physics, cannot be defined, so we just say how to measure it and leave it as a primitive concept.  In this context: how in general can we identify whether something is a primitive concept, a fundamental law of Physics, a definition or a theorem?


Im trying to prove or disprove the following , but I am having a hard time. It seems that the statement is true , but I have no idea how to prove it.  If   \begin{equation*} \sum_{n} a_{n}^2 \end{equation*}  is converging , then   \begin{equation*} \sum_{n} \frac{|a{_n}|}{n} \end{equation*}  is also converging. Thanks in adavance!

Problem:      Suppose that for every $n\in\mathbb{N}$, $a_n\in\mathbb{R}$ and $a_n\ge 0$. Given that   $$\sum_0^\infty a_n$$   converges, show that    $$\sum_1^\infty \frac{\sqrt{a_n}}{n} $$   converges.   Source: Rudin, Principles of Mathematical Analysis, Chapter 3, Exercise 7.


If $c$ is just an arbitrary constant, why don't we say $E=mc$ and define the value of $c$ to be $\sqrt{299 792 458} \approx 17314$ meters per second? Or, why not use $E=mc^3$?

is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is speed of light in vacuum.   What I didn't understood is how we will introduce speed of light?  Atom bomb is made using this principle which converts mass into energy; in that the mass is provided by uranium but where did speed of light comes into play? How can speed of light can be introduced in atom bomb?


I have a string with values stored as:  string formula = "(10.5+10.5)/(2*5)";   double a=convert.ToDouble((10.5+10.5)/(2*5)) is working fine but i need to solve it like double a=convert.ToDouble(formula). Is it possible? I'm geeting error input string is not in correct format.

Is there a function the .NET framework that can evaluate a numeric expression contained in a string and return the result? F.e.:  string mystring = "3*(2+4)"; int result = EvaluateExpression(mystring); Console.Writeln(result); // Outputs 18   Is there a standard framework function that you can replace my EvaluateExpression method with?


I am new to the field of electrodynamics and I recently came across the definition of capacitance as $$C = \frac{Q}{V}$$ It is said that capacitance is constant, which implies that total charge of the one conductor is proportional to the voltage difference between the two conductors. But we know that $$Q = \int ρ(\vec r')dV$$ where the integral is evaluated in one conductor, and $$V(\vec r) = \int \dfrac{ρ(\vec r')}{|\vec r - \vec r'|}dV$$ where the integral is evaluated along the two conductors. How can we prove from these that $Q$ and $V$ are proportional?

My textbook states that:  ...The capacitance $C$ depends only on the geometrical configuration (shape, size, separation)of the system of two conductors. [As we shall see, later, it also depends on the nature of the insulator (dielectric) separating the two conductors.]...  Now I wanted to know if these were the only two factors on which the capacitance of a conductor depends. So I tried thinking about it from the basic definition, which is:  Capacitance is the ratio of the change in electric charge of a system to the corresponding change in its electric potential. (Source: )  i.e., $$C= \frac {dQ}{dV}$$ where, $V$ is the potential of the conductor with respect to zero potential at infinity. Now, I can not think of why $C = f(V)$ isn't a possible scenario, assuming that shape size, etc remains constant. So:  Why cannot $C$ be a function of $V$?


I'm having trouble trying to call the override function of an object that was appended to a vector. I'm not quite sure if I just don't completely understand pointers and references, so I'm not quite sure what to look for when debugging this issue. Here is my code: #include <iostream> #include <vector>  class Task {     public:         Task(std::vector<Task> *list) {             list->push_back(*this);         }          virtual void Run() {             std::cout << "Called Task Run!" << std::endl;         } };  class OverrideTask : public Task {     public:         OverrideTask(std::vector<Task> *list) : Task(list) {}         void Run() override {             std::cout << "Called Override Run!" << std::endl;         } };  int main() {     std::cout << "Main method entered" << std::endl;     std::vector<Task> listOfTasks;      OverrideTask ot = OverrideTask(&listOfTasks);     Task t = Task(&listOfTasks);      for(int i = 0; i < listOfTasks.size(); i++) {         listOfTasks[i].Run(); // Will print "Called Task Run!" twice.     }      ot.Run(); // Prints "Called Override Run!"     t.Run(); // Prints "Called Task Run!" }  When I loop through the vectors, it seems that I can't call the override function, but when I call them directly from the object, they seem to work. Can anybody point me in the correct direction?

Someone mentioned it in the IRC as the slicing problem.


I would like one which would also emulate other features of slideshow of Microsoft Powerpoint.

I really like the way Keynote and MS Office (and also OpenOffice & similar) support a presentation mode that displays the current slide, the next (and maybe previous) slide, the elapsed and current time, and also any notes attached to the slides on one screen and the presentation itself on the beamer/second screen.  It enables me to give good, professional presentations without having to know everything by heart (I suck at that).  I found a , but I am looking for alternatives, especially OS-independent would be great. Not having to create 3 different PDFs is a boon.  Any hints?


I want to call ajax to fetch notifications in a bootstrap dropdown on clicking the bell (icon). In the code below, it works only when I click on the bell first on loading the page. If I click anywhere else and then click on the bell, the click event does not fire (and thus the AJAX). Why is it happening? PS. I am using .NET Razor views and Partials. All the notifications should load inside the class "notifications" HTML:

  JS: $(document).on('click', 'a.nav-link', function (e) {         $.ajax({             cache: false,             url: "/Notification/NotificationList",             type: 'GET',             traditional: true,             data: {                 selectedNot: checkedIds             },             contentType: 'application/json;',             success: function (response) {                 if (response.success != false) {                     if (response.message == 0) {     //If no notifications                         //append no notifications landing page                     }                     else {                         //append notifications in HTML                     }                 }             },         }); });

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.


Do I need a separate visa to visit Paris, if I have a visa to visit Belgium?

I have 6 month validity Schengen visa. I want to in how many countries I can travel?


I have problems referencing a numbered section containing a glossary from the glossaries package.  \documentclass{article} \usepackage{glossaries} \makeglossary \newglossaryentry{ge}{   name=glossary entry,   description=with a long description } \begin{document} \section{Section} This \gls{ge} is listed in the glossary in Section \ref{sec:glossary}. % 1 This reference is wrong as the glossary is actually in Section 2. \printglossary[numberedsection] \label{sec:glossary} \end{document}   While this code should reference the glossary in section 2 it actually assumes that the glossary is in section 1.

I'm trying to find a way to create a cross-reference to a particular glossary. I have several glossaries that I refer to in-text, and I would like to be able to link to a specific glossary whenever I refer to it in the text. To be clear, I don't want to link to a specific entry in a glossary, but to the glossary itself. Ideally, the link would take the reader to the first page of the specific glossary I intend.  I suppose I could get around this by cheating and linking to the first entry of the glossary and having it display the name of the glossary instead of the regular entry name, but before I did that I was hoping to find out if there is a general way to do this. Any suggestions would be appreciated.


It works with Ubuntu 12.04 (32-bit) but in 16.04 (64-bit) the V600 do not work for me.  $ scanimage -L device `epkowa:usb:001:013′ is a Epson (unknown model) flatbed scanner   Iscan or XSane do not work for me.  Installed:   Sane Epson data package Epson core package Epson plug-in package   In epkowa.conf added line: usb 0x04b8 0x013a (this was not needed in epkowa for 12.04 32-bit)  Is there a problem with the Epson 64-bit driver or what do I do wrong?  I use Epson Scanner Driver Version 1.0.1 Release date 07-04-2016   All other connected USB units works, keyboard, mouse, bluetooth and kvm-switch.  Scanner connected to USB2 at Motherboard.  Motherboard Asus H170M-PLUS  XHCI disabled.  From Bios Manual:  XHCI Hand-off [Disabled]  [Enabled]       Enables the support for operating systems without an XHCI hand‐off feature. [Disabled]       Disables the XHCI Hand-off support.

Cannot get my v600 usb scanner to work. Looking for epson drivers, I found . I downloaded drivers there :   iscan_2.29.1-5~usb0.1.ltdl7_amd64.deb iscan-data_1.23.0-1_all.deb   and installed them. But my scanner is still not recognized. I use ubuntu 13.04. simple scan, iscan or xsane scan  can not see the device.


Below code I expected 12 but I get 11:    public static int previousMonth(String format, String value) {         SimpleDateFormat sdf = new SimpleDateFormat(format);         Date date = null;         try {             date = sdf.parse(value);         } catch (ParseException e) {             e.printStackTrace();         }         Calendar calendar = Calendar.getInstance();         calendar.setTime(date);         calendar.add(Calendar.MONTH, -1);         return calendar.get(Calendar.MONTH);     }       int actual = CommonUtil.previousMonth("yyyy-MM-dd", "2021-01-01");     int expected = 12;     assertEquals(expected, actual)  ;

In java.util.Calendar, January is defined as month 0, not month 1. Is there any specific reason to that ?  I have seen many people getting confused about that...


A uniform solid body is constructed using a square-based pyramid mounted on a cube. If each edge of the solid has length $l$ show that the centre of gravity of the body lies within the cube is, $\frac {11l}{(24 + 4√2)}$from the base of the pyramid.  Now Volume of cube = $l^3$, and of the pyramid = $\frac{l^3}{3√2}$, using the height of the pyramid as $\frac{l}{√2}$, from Pythagoras. If $O$ is at the base of the pyramid we can say that for the pyramid the height above $O$ is $\frac{l}{4√2}$, as the centre of gravity (centre of mass) is  $\frac{h}{4}$ above the base, and we are expecting the centre of gravity to be in the cube. The height below the base $O$ for the cube is $\frac{-l}{2}$.  Some texts equate the centre of gravity to the centre of mass. Can we do this in this particular problem?

What is the difference between  and ?  These terms seem to be used interchangeably.  Is there a difference between them for non-moving object on Earth, or moving objects for that matter?


if fuction is defined from $N to N$ then can we say that it is not continuous as it is not defined for all $x$??a simple statement ,but this is stopping me from giving the solution to a question..pls help

I'm wondering if it's possible to have a continuous sequence $f: \mathbb{N} \to \mathbb{R}$? My intuition is telling me no because logically it would be impossible to map the natural numbers onto the real numbers but I'm not sure how to formalize it. What do you think? How would you prove that no function over the natural numbers (no sequence) is continuous?  For example, how would you prove that $f: \mathbb{N} \to \mathbb{R}$ such that $f(n) = n^{2}$ is not continuous over the natural numbers?


$$\int \frac{x-1} {1 + \sqrt{x^2+2x-3}}dx$$ The teacher advised me to calculate through Euler's substitution. Please help me to find the integral  (similar topic was created earlier but now I need Euler's substitution using)

Compute the indefinite integral  Irrational: $$\int \frac{x-1} {1 + \sqrt{x^2+2x-3}}dx$$ Help me pls. What do I need to do then? fraction isn't simplified


I'm working on an application that does some basic network management. Due to constraints outside of the scope of this application, there's a need to encode a cidr block (eg 127.0.0.1/32) into the url. For instance, an endpoint route might look something like this post "/home/network/:user/:cidr". In most cases, one could easily send the cidr as a string in the payload but that is not an option here.  I know that . is a valid url character and that / can be encoded with %2F. Naively combining these and attempting to post against that endpoint like so: /home/network/janedoe/127.0.0.1%2F32 404ed which makes me think Sinatra isn't able to properly parse that url parameter. I've also tried using the URI module to encode the cidr string with no luck so far.  Perhaps there's an easier way to think about encoding the cidr block into the url that makes for easy extraction in the endpoint.

Playing with , I'm stuck on a little problem : when I use params with slashes, it confuses the router engine. So is there a nice way to handle this kind of param without having to encode it ?  The code looks like   get 'add/:url' do    #.... end   And I intend to get something like /add/ working


I want to automatic redirect home page after click on update button, here is my handleSubmit code:  const handleSubmit = (e) => {     e.preventDefault();     // access data from backend     axios       .put(`${process.env.REACT_APP_API}/post/${slug}`, {         title,         content,         user,       })       .then((response) => {         console.log(response);         const { title, content, slug, user } = response.data;          setState({ ...state, title, content, slug, user });         alert(`Post Title ${response.data.title} is Updated`);       })       .catch((error) => {         console.log(error.response);       });   };  Here I have use a alert when my post has been updated then show me, but now I need to redirect my home page. when I click on update button Any suggestion please.

How can I redirect the user from one page to another using jQuery or pure JavaScript?


So I need to use induction to prove that $4^n<5^n$ for all natural numbers $n > 0$. I have proved the base case to be true. For the induction hypothesis, we assume that when $n=k$, then $4^k < 5^k$. However, I am stuck in the inductive step when I try to show that it needs to be true for $n+1$. Therefore, we need to show that $4^{k+1} < 5^{k+1}$. However I get stuck on the first step trying to prove it as in  $4^{k+1} = 4 \cdot 4^k$, then by substituting $5^k$ instead of $4^k$ from the inductive hypothesis and I get stuck right here and I do not know how to proceed.  Any help would be appreciated.

I have done a few normal inductions (like divisibility and sums) and know a little bit about strong induction. I can't find any problem similar to this one and am struggling to understand any intuition that would make proving this statement any easier. Here is how far I have gotten (not very much): Base Case: $4^1 < 5^1$ $4^2 < 5^2$ $16 < 25$ Induction: $4^k < 5^k$ $4^{k+1} < 5^{k+1} = 4\times4^k < 5\times5^k$ I have no clue where to go or how to force the k+1 equation to somehow equate to the k equation. Sorry if this has been asked before. Thank you.


I have the following regex:  /^([\p{L}])*[\p{L},.'-]+$/u   it is a unicode version, which I use for international firstnames.  When I try this:  const value = "Hello" const criteria = value.match(/^([\p{L}])*[\p{L},.'-]+$/u); console.log(criteria);   It always returns null, no matter which value the variable has.  I tried it in Regex Debugger / Tester on a Browser and it worked there.

How can I use Unicode-aware regular expressions in JavaScript?  For example, there should be something akin to \w that can match any code-point in Letters or Marks category (not just the ASCII ones), and hopefully have filters like [[P*]] for punctuation, etc.


Let $F$ be a field and let $f(x)$ be a polynomial of degree $n \geq 1$ in $F[x]$. Let $g(x) = f\big(\frac{1}{x}\big)x^n$. Assume $f(0) \neq 0$. Prove that $f(x)$ is irreducible over $F$ if and only if $g(x)$ is irreducible over $F$. $\mathbf{My~Attempt:}$ Prove of if: Assume that $f(x)$ is irreducible over $F$, WTP: $g(x)$ is irreducible over $F$. First, notice that $F[x] = \{ a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 ~|~ a_i \in F \text{ and for some } n \in \mathbb{N} \cup \{ 0 \} \}$. Since, we let $f(x)$ be a polynomial of degree $n \geq 1$ in $F[x]$. Then, $f(x) = b_n x^n + b_{n-1} x^{n-1} + \cdots + b_1 x + b_0$, for each constant coefficient $b_i \in F$. Since, we assumed that $f(x)$ is irreducible over $F$ and we know that $f(0) \neq 0$. Then, by defintion of irreducible, if $f(x) = h(x)j(x)$ with $h(x), j(x) \in F[x]$, then $h(x)$ or $j(x)$  is a unit in $F[x]$. Now I don't know how to prove that $g(x) = f\big(\frac{1}{x}\big)x^n = b_n + b_{n-1} x + \cdots + b_1 x^{n-1} + b_0 x^n$ whhere $g(x) \in F[x]$ is irreducible. Also, I have no idea only how to prove the only if which assume $g(x)$ is irreducible over $F$ and prove $f(x)$ is irreducible over $F$.

Given that  $f(x)=\sum\limits_{k=0}^n a_kx^k$ is an irreducible polynomial, show that $g(x)=\sum\limits_{k=0}^n a_kx^{n-k}$ is irreducible too. I don't see how this specific coefficient exchange would preserve the irreducibility. Is there something else I should be looking at?


I am trying to add some EPS  files in text but I got the following error message  ! LaTeX Error: Unknown graphics extension: .eps.   Does anyone knows how to fix it?  I installed MikTex 2.9

This question has been asked a lot, but for reason I cannot get it to work. I'd like to include a .eps image in my document - I am using pdflatex in TeXMaker. Below is the input (I am providing the whole preamble incase there is some interference.   \documentclass[11pt]{article} \usepackage{times} \usepackage{graphicx} \usepackage{epstopdf} %converting to PDF \usepackage{amssymb} \usepackage{amsmath} \usepackage{mathtools} \newcommand{\HRule}{\rule{\linewidth}{0.5mm}} \usepackage[parfill]{parskip} \setcounter{secnumdepth}{5} %how deep sections are numbers \usepackage{float} \usepackage[font={sf,footnotesize},labelfont=bf, justification=justified, singlelinecheck=off]{caption} \usepackage[font=footnotesize]{subcaption} \usepackage[scaled]{helvet}  \usepackage{titlesec}  \usepackage[T1]{fontenc} \usepackage[export]{adjustbox} %for large figures \usepackage{upgreek} \usepackage{microtype} \usepackage{setspace} \singlespacing \usepackage[defaultlines=4,all]{nowidow}  \includegraphics[scale=1]{/../model_1_2.eps}    The error I get is:      ! Package pdftex.def Error: File `/model_1_2-eps-converted-to.pdf' not   found.See the pdftex.def package documentation for explanation.Type H    for immediate help.... .../../model_1_2.eps}   I hope someone can help.


Whenever I run  mysql -u root mysql   I get an error like:   ERROR 1698 (28000): Access denied for user: 'root@localhost'   I tried running  update user set authentication_string=password('akshansh') where USER='root'   But I got   bash: syntax error near unexpected token `('   Then I ran  $ mysql>FLUSH PRIVILEGES   I still get an error:  ERROR 1045 (28000): Access denied for user: 'root@localhost' (using password: NO)   I've tried all possible solution on Stack Overflow or any other website.  I've also tried deleting and re-installing MySQL. I am still not able to reset the password.

I install mysql and phpmyadmin and in installation phpmyadmin i add config password is root but in connection with user is root and password is root i have this error


As stated in , the SE network only allows one draft per site.   However, in the iOS app, there's a folder for 'Drafts,' in which you can save multiple drafts (for questions) for each site:    With multiple drafts:    Why don't we have this functionality on the regular website? Can we please copy this feature to the website?  Or, at the very least, can we make it so we can write multiple drafts for a SE site?

The draft feature was discussed a lot  and in other posts, but I didn't see much talk about the OP's mention of being able to have multiple.     Optionally, allow multiple draft questions and a page to edit/delete them.    I think the draft feature where it autosaves and stores it server-side is great, but in most things where they have a draft feature (like email clients), they allow you to have multiple drafts (also stored server-side).  The expiration can even work the same as it does for the single draft system right now.  You wouldn't even need full page to store them, I think the user profile page could have a tab for it like it currently has for answers, questions, and everything else.    It could look very similar to how questions look, with it's title and tags listed there.


I know C++, Python, JavaScript and Prolog.  I want to learn Java.  Will my question be deleted if I ask for recommendations on StackOverflow?  If so, is there another StackExchange site I can ask on?

Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com.


an old version of R is already installed on the server I am working with, but it is not really useful for my work. I have tried to install R 3.1.1 on my own directory (/local/data/project/behi) on the server using this command :  $ wget  $ tar xvf R-3.1.1.tar.gz $ cd R-3.1.1 $ ./configure --prefix=$HOME/R $ make && make install  when I tried to run R (by just typing R in my directory) again it showed me the old version of R. would somebody please let me know what the problem is and how I can install and run the new version of R?  thanks in advance, Behi

How can I install a new version of R in my own directory, e.g., /local/data/project/behi.