I know that the transform form cartesian to elliptical is  $x=a \cosh \mu \cos \nu; \;\;\;\; y=a \sinh \mu \sin \nu$  How do I go back to cartesian if I have an expression in elliptical, meaning that I need the relations  $\mu = f(x,y);\;\;\;\nu=g(x,y)$?

The standard way to transform elliptic coordinates $(\mu, \nu)$ $\ to$ Cartesian coordinates $(x,y)$:  $x = a \cosh(\mu) \cos(\nu)$  $y = a \sinh(\mu) \sin(\nu)$  Is there any way to get the transformation $(x,y)$ to $(\mu,\nu)$? Meaning is there a way to find:  $\mu = f(x,y)$  $\nu = g(x,y)$  I'm guessing that it would involve $\sinh^{-1}$'s and $\cosh^{-1}$'s, if it was possible to do this at all.


Is the following proof valid? (Note: I know there is a post discussing this problem, but I am curious to see if my argument works). This problem is different from , because my proof begins with an existential neighborhood and ultimately considers a different route in proving the problem.  Let $S \subseteq \mathbb{R}$. Prove that if $x$ is an isolated point of $S$, then $x$ is a boundary point of $S$.  Suppose that $x$ is an isolated point of $S$ and assume to the contrary that $x$ is not a boundary point of $S$. Then for each $x$, there exists an $\epsilon > 0$ such that $N_{\epsilon} \subseteq S$. But because $x$ is not an accumulation point of $S$, we see that for each $x$, there exists a $\delta > 0$ such that $N_{\delta}^* \cap S = \varnothing$ where $N_{\delta}^*$ is some deleted neighborhood. Therefore, $N_{\delta}^* \subseteq S^c$.   Thus there are two intervals centered at $x$, and either $\epsilon \geq \delta$ or $\delta \geq \epsilon$, which would then imply that $N_{\delta}^* \subseteq N_{\epsilon}$ for the former and $N_{\epsilon} \subseteq N_{\delta}^*$ for the latter (it helps to draw a picture of these intervals to see why these cases arise). But in both cases we reach a contradiction, because these possibilities imply that $N \not \subseteq S$. Therefore, there are no $N_{\epsilon}$'s contained in $S$, but because $x \in S$, we deduce that every neighborhood $N$ must satisfy $N \cap S \neq \varnothing$ and $N \cap S^c \neq \varnothing$. Hence, $x$ is a boundary point of $S$.

Here is a professor's solution to the exercise which states, " Prove that if $x$ is an isolated point of a set $S \subseteq \mathbb{R}$, then $x$ is a boundary point of $S$."    The professor derived a contradiction upon assuming that for an arbitrary neighborhood $N$ centered at an isolated point $x$ of $S$, we have $N \subseteq S$, so he then proceeds in saying that every $N$ must have a noenmpty intersection with $S^c$. But I feel that there is something wrong with his argument: Using mathematical logic, we can represent his assumption that every $N$ is a subset of $S$ as $\forall \, N : p(N)$ where $p(N)$ means, "$N$ is contained in $S$." He then showed that this assumption is false, so $\sim \forall \, N : p(N) \equiv \exists \, N : \, \sim p(N)$ is true, which means there are some $N$'s that are not contained in $S$. But this information is not sufficient in concluding as to whether or not there is at least one $N$ contained in $S$; it just means not every $N$ is contained in $S$. But if I am right, how can he proceed with his proof since whatever result he deduces about $N$ after the contradiction does not necessarily apply to all $N$?  I hope what I am trying to convey is clear, and I thank you for your help


Per  on a recent Star Wars question, is the 2003 Tartakovsky "" TV series still part of the official Star Wars (Disney) canon?

For all types of derivative works, namely:   Movies Novels Comic books Other written works (including RPG materials) Cartoons Video games Derivative movies (such as the infamous Ewok movies and even more infamous )   According to what rules does something become "canon" and who is responsible for the evaluation of a published work?


Does network devices have device nodes because i have looked inside /dev directory and have not found any corresponding device node although it's up and running

I'm mostly curious, but why aren't network interfaces in /dev? Are there any other kinds of devices that aren't represented as a node under /dev?


I am trying to build the apk for the charade sample for google glass:  I am getting the error Error:Module 'gdk-charades-sample' production: java.lang.NoClassDefFoundError: com/android/resources/ResourceFolderType Does anyone have any idea what is causing the error?

I am getting a NoClassDefFoundError when I run my Java application.  What is typically the cause of this?


In reported speech we generally back shift the tense. But why in news articles do I often see that this guideline is violated?                                                                For example:     a) - The president said that he wants support from other countries to combat terrorism.      Don't you think that 'wants' should be back shifted to 'wanted'?                                               b) - Secretary said that she has faced many hurdles in her life.    Don't you think that here 'had faced' should be used instead?                          P.S. My question concerns reported speech in news articles.

In indirect speech we generally backshift the tense. For ex - Direct speech : "I am the most powerful person." Indirect speech : "He said that he was the most powerful person."  What if someone reports like -  He denied the charges claiming that he is/was the most powerful person. So here which is correct- is or was ?  Thanks in advance.


Whenever you die in Minecraft Java Edition, you get the option to respawn or quit to the title screen. You also are shown your score. What factors lead up to that score? Im thinking that stuff, like picked up XP or mobs defeated, would count towards the score, but what is the exact number of score you get for one thing that you accomplish?

When you die, 3 things happen.    You swear  A message appears in the chat log describing how you died A "You died" screen appears, with the options to quit or respawn, and a "Score".   What contributes to this score?


Please check my proof   I claim every subgroup of the integers has finite index  Suppose nZ is subgroup of integer  Then the cosets are   (n)+0,(n)+1,(n)+2,.......(n)+n-1  Since the cosets can't exceed (n-1)  therefore, every subgroup of integers has finite index

I think that this statement is false, but only in the trivial case. $\{ 0 \}$ is obviously a subgroup of $(\mathbb{Z},+)$ with infinite index.  In the case of a nontrivial subgroup of $(\mathbb{Z},+)$, intuition tells me that these subgroups will have finite index. How should I begin to prove this?  What I know:  Nontrivial subgroups of $\mathbb{Z}$ are of the for $n\mathbb{Z}$ for some $n\in\mathbb{N}$. These subgroups are infinite cyclic groups.  I read in another  posted here that I should try use the smallest positive element of $n\mathbb{Z}$ and Euclidean division to explicity describe all of $\mathbb{Z}$, but I'm not sure what that means, precisely.


I'm trying to create a tile system which creates a single instance of a tile, and adds the tile to an array of tiles, allowing you to call Tile::s_tileList[1] to get the dirt tile.  However, I'm having some issues with it. Here's the complete tile code:  tile.h  #pragma once  class Tile { public:     static const Tile s_tileList[128]      static const Tile s_dirt;      Tile(int tileId);     virtual ~Tile(); protected: private:     int m_tileId; };   tile.cpp  #include "tile.h"  #include "tile_dirt.h"  const Tile Tile::s_dirt = TileDirt(1); // This line errors  Tile::Tile(int tileId) {     s_tileList[tileId] = *this;     m_tileId = tileId; }  Tile::~Tile() {  }   tile_dirt.h  #pragma once  #include "tile.h"  class TileDirt : Tile { public:     TileDirt(int tileId);     virtual ~TileDirt(); protected: private: };   When I'm trying to assign s_dirt to TileDirt I get the following error:  conversion to inaccessible base class "Tile" is not allowed   What am I doing wrong here?  I tried doing:  static const Tile* s_dirt;   And assign it like:  const Tile* Tile::s_dirt = new TileDirt(1);   But that just adds another error: no suitable constructor exists to convert from "const Tile *" to "Tile"

Someone mentioned it in the IRC as the slicing problem.


In a recent music video I saw an effect which I found quite awesome. I tried creating it myself in Photoshop but since I'm quite inexperienced with the software I wouldn't know where to start.  What I would like to do  I have a photo of a person taken in front of a greenscreen. I would like to give it a darkish cloudy or foggy background. I would make a silhouette in the front. But I don't want the complete person to be a silhouette. I want the right to light up like a light is falling on it. So that about 15% of the right side of the person is visible.  I don't know how to better explain this but I hope you know what I mean.  Example    I mean something like the above example but with the shadow being a bit larger.

There is a technique in photography, called Invisible Black Background. You can find details about it in this blog post   An example image is this one:    I have just started using Photoshop, so I am not aware of design techniques and terms. But is there any way (or tutorial better) to replicate this effect in a portrait image with a non-black background?


I really want to know because it occurs a lot with the people I hang out with. I would do something "bad" and get in trouble, or get called out for it, but then the people who had a negative response to what I did would do the same thing as if they forgot it was bad.

I have a friend who always expects you to be fully understanding, considerate and thoughtful, but when you expect her to behave in the same way, she says you are too picky, a drama queen, and not being thoughtful by asking her to be thoughtful because she is either busy or stressed.  Is there a word that describes this type of behavior or person?


I am confused about the different syntax used for instantiating an object.   This is my class:  class Object {  private:      int field = 0;  public:      Object() = default; // Just for testing.     ~Object() = default; // Just for testing.      Object( const Object& obj ) = default; // Just for testing.  };   This is main method:  int main() {     Object b(); // ???     Object c{}; // default     Object d = Object(); // default     Object e = Object{}; // default     Object f ( Object() ); // ???     Object g { Object() }; // default     Object a; // default but avoid     Object h ( Object() ); // ???     Object i { Object{} }; // default     Object j = i; // copy     Object k( j ); // copy     Object l{ k }; // copy     Object m = { l }; // copy     Object n = ( m ); // copy     auto o = Object(); // default     auto p = Object{}; // default     return 0; }   I have no problem with the one's marked default or copy. I just want to know, which constructor is called for the one's with ??? as the default one is not called. Has it something to do with () initialization, as it can be seen.  I know this may not be important, but I am suspicious about it.  Can anyone help!

Is there any good reason that an empty set of round brackets (parentheses) isn't valid for calling the default constructor in C++?  MyObject  object;  // ok - default ctor MyObject  object(blah); // ok  MyObject  object();  // error   I seem to type "()" automatically everytime. Is there a good reason this isn't allowed?


I am applying for a Postdoc in an UK University. They are asking whether I have permission to work in UK. How can I know my eligibility to work as Postdoc in UK? What type of visa issued by UK for postdocs?  Detail:     The University of Bath is a sponsor under the Points Based System. Where there are no suitable applicants from within the EEA, we may, depending on the position, be able to issue a Certificate of Sponsorship.   For further information, please refer to the UK Border Agency website (new window).      Please select one of the following options*          I am a British Citizen/EEA National.   I am not a British Citizen/EEA National and I am not currently eligible to work in the UK.   I am not a British Citizen/EEA National, but I am eligible to work in the UK. Please give the reason below.

I have completed a Ph.D. in India, which is my native country, and am applying for post doc positions in the UK.  However, due to strict visa rules, I am not sure if my application would be shortlisted. In these types of situations, my CV and application file have already been approved by the PI.   However, do universities generally sponsor non-EU candidates like me or  is it the responsibility of the PI to make the proper arrangements? How can I ensure that my job is not denied due to non-academic reasons like visa issues?


I need to reinstall Xubuntu on a new, bigger hard drive (I can't find a way to increase the partition size, but that's a separate question). How would I go about doing this without losing data, software installed, preferences, etc.  Thanks, djtravz

I'm a new Linux user. I've reinstalled my Wubi from scratch at least ten times the last few weeks because while getting the system up and running (drivers, , etc.) I've broken something (X, grub, unknowns) and I can't get it back to work. Especially for a newbie like me, it's easier (and much faster) to just reinstall the whole shebang than try to troubleshoot several layers of failed "fixing" attempts. Coming from Windows, I expect that there is some "disk image" utility that I can run to make a snapshot of my Linux install (and of the boot partition!!) before I meddle with stuff. Then, after I've foobar'ed my machine, I would somehow restore my machine back to that working snapshot. What's the Linux equivalent of Windows disk imagers like  or ?  Note: I found a similar question:


I have a set of probability corresponding to Bernoulli experiment. How to draw Bernoulli random number given these specific probability from a uniform(0,1) distribution. I know we can draw from binom, but using uniform distribution can vectorize the operation and make it so much faster.

I was implementing a simple scheme of Bernoulli distribution sampler. $ X \sim B(p) $. I have a function that generates a uniform random number $r \in (0,1)$. Then, I set $ X = 1 $  if $p > r $, and $X =0$ otherwise. Is this correct?


I am stuck with a question $$\left(\frac15\right)\div\left(\frac15\right)\div\left(\frac15\right)\div\left(\frac15\right)$$ We can have different approach to this problem but how are we gonna apply BODMAS here.

Unlike with addition, subtraction and multiplication where the order of operations will lead to an unambiguous result when the rules of BIDMAS (or PEMDAS) are applied, this does not hold true for division.  For example:  5 + 3 x 5 x 7 - 2 = 5 x 7 x 3 + 5 - 2 = -2 + 5 + 7 x 5 x 3  Of course, BIDMAS states we must group our multiplications together but within that grouping the order of multiplications makes no difference to the result.  Furthermore, following the rules of BIDMAS and performing the multiplications first, the subsequent order of the arithmetic also makes no difference.  Right?    In the above example, for instance, 3 x 5 x 7 = 105.  So: 5 + 105 - 2 = -2 + 105 + 5, etc...  However, operation order DOES affect the result when dividing!  For example:  (1/4)/27 does NOT equal 1/(4/27).    We know this, right!  I always took it for granted that the order of operations when presented with multiple divisions must be performed in the order it is presented; ie from left to right.  That is what we were taught at kindergarten, right?  So:  a/b/c/d = ((a/b)/c)/d  Right?    Well that's what I believed all my life and took this for granted.  But now my sanity is being challenged by Casio's most recent scientific calculators which do not obey this rule!!!!  If you were to type in a/b/c/d into a modern Casio scientific calculator using its fraction key for '/' rather than the division button, the calculator yields a/(b/(c/d))!!!!!  Using the division button instead of the fraction key gives a conflicting (but what I believe to be the correct) answer; that is:  a divided by b divided by c divided by d = ((a divided by b) divided by c) divided by d  I feel sure that the older Casio scientifics (pre 1991) gave the correct result following the rules as I have explained above.  But I cannot get hold of one to check my theory.  So my question is: What is the correct order of operation with multiple consecutive divisions?  That is, what is the order of division for:  a/b/c/d   as written without any parenthesis?  Are the new Casio calculators giving the wrong answer or have I been living a lie?  PS:  I am aware that the calculators give what I believe is the correct answer if  the right cursor key is pressed after the keying in of each denominator.  Bu that is a fudge.  By using the right cursor, you are applying implicit parenthesis.  As inputted, either the calculators are giving the wrong answers or I have been living a lie.  Can someone please confirm the order of division should indeed be from left to right!  PS:  I have searched everywhere I could on the internet and in many maths text books but have not been able to find anything that addresses the ambiguity in the order of multiple consecutive division operations.


We are given a function $f$ from reals to positive reals (not including $0)$ satisfying    $$f(x)f(y)\leq |x-y|$$   for every rational number $x$ and irrational number $y$. Does this function exist?   If $f$ is continuous, it is easy to show that $f$ must be a constant zero function (So it does not exist, in this case).  Otherwise, for an irrational number $y$ it can be shown that for any sequence $x_n$ of rationals converging to $y$, $f(x_n)$ converges to zero and the same is true for rational number $x$ and the sequence of irrationals $y_n$.   Does this argument give us any information about $f$, and does it say whether $f$ exists at all?

Does there exist a  function $f:\mathbb R \to (0,\infty)$ such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$ ?


say that a watermelon is divided into three parts to be served to the guests. I should say "would you like some melons" or "would you like a melon"? I should say "the melon is sweet" or "the melons are sweet"? Which one is right?

I would like to ask how people who are familiar with English interpret these sentences regarding the nouns that can be both count and noncount nouns.  (1) I have to make more cake/cakes to offer a wide variety of bakery products for my own business.  (2) France is famously known for having more cheese/cheeses than there are days in the year.  My foreign teachers went for plural noun in (1), but they chose the bare form for (2). I have them chose only one form for each item. For me (I'm Thai), I just want some explanations because both items represent "a variety of sth", so why these two are treated differently.


How to book the tickets dispalyed by matrix.itasoftware.com When I search through any ticket booking site, the prices differs a lot. Even the airline website does not show the same.

When I find a flight I like on the , it spits out a bunch of travel agent secret codes™.  If I look for the same flight on the airline's web site, I often get much higher rates.  As an example, looking at a flight from Cape Town (CPT) to New York (JFK), on December 31, 2013, I get the following from Matrix:     Cape Town (CPT) to New York (JFK) - Tue, Dec 31   Turkish Airlines Inc.    Cape Town (CPT) to Johannesburg (JNB) - Tue, Dec 31   Turkish Airlines Inc. 41    Dep: 4:30PM Arr: 6:35PM 2h 5m   Airbus A330  Economy (T)   Stop in JNB      1h 10m        Turkish Airlines Inc.  Johannesburg (JNB) to Istanbul (IST) - Tue, Dec 31   Turkish Airlines Inc. 41    Dep: 7:45PM Arr: 5:30AM 9h 45m  Airbus A330  Economy (T)   Layover in IST   Wed, Jan 1  1h 55m        Turkish Airlines Inc.  Istanbul (IST) to New York (JFK) - Wed, Jan 1   Turkish Airlines Inc. 3 Dep: 7:25AM Arr: 11:25AM    11h 0m  Airbus A330  Economy (T)                  Cost per passenger (including taxes & fees)   $781.60   Total cost for 1 passenger  $781.60             Provide this information to a travel agent to help them match the fares found.    Make sure to provide the exact booking and fare codes shown.   Fare 1: Carrier TK TA2PXOW CPT to NYC (rules)   Passenger type ADT, ONE-WAY-ONLY fare, booking code T   Covers CPT-IST (Economy), IST-JFK (Economy) $406.54   USDA APHIS Fee (XA) $5.00   US Immigration Fee (XY) $7.00   US Customs Fee (YC) $5.50   Turkish Int'l Airport Service Charge (TR)   $6.80   (YR)    $278.40   US International Arrival Tax (US)   $17.20   South Africa Passenger Service Charge (ZA)  $32.40   South Africa Air Passenger Tax (WC) $18.70   South Africa Passenger Safety Charge (EV)   $1.60   South Africa Passenger Services and Security Charge (UM)    $2.00        Subtotal per passenger    $781.60   Number of passengers    x1        TOTAL AIRFARE & TAXES $781.60   Changes to this ticket will incur a penalty fee.   Fare construction (can be useful to travel agents)   CPT TK X/IST TK NYC 406.06TA2PXOW NUC 406.06 END ROE 10.146090 XT 1.60EV 2.00UM 18.70WC 32.40ZA 6.80TR 5.50YC 7.00XY 5.00XA 17.20US 278.40YR   For this search, I specified USD as the currency, but left the Sales City field blank.  When I try to book the same flight on the Turkish Airlines web site, I get a rate of €797 (~USD$1079), or a USD$298 difference.  By looking at the details of the two sites, I see that it is indeed selling me the same flight.  How can I take advantage of the Matrix-provided travel agent secret codes™ to book the flight at the lower price? Or must I go through a travel agent to use these codes?


I am not able to find out any example of non-commutative ring other than matrix ring which is easier to work on.please help

Looks like it is easier to find example of commutative rings rather than non-commutative rings. Prabably the easiest examples of the former are $\mathbb{Z}$ and $\mathbb{Z}_n$. We can find elaborations on these two commutative rings in various literatures including  and . These are quite simple and easy to comprehend.  However, the examples on simple (non-commutative kind) are not that easy. One example is found  and it has been mentioned as "one of the simplest examples of a non-commutative ring". This is also on the easier side.  EDIT: The following two are also commutative rings.  Other examples are given in this . But as you can see, examples like  or  are difficult for starters to comprehend.  Do you think you can give one or two simple examples on non-commutative rings, based on every day numbers?  If it is that difficult, perhaps some insight comments why this is difficult would be welcome.


I've enabled a disk partition of around 8 GB to be dedicated for .    Windows keep warning me about that disk running out of space (Low Disk Space).    How do I turn off that warning for THAT disk and ONLY that disk.  I DO want that warning, I do not want it for that disk I specifically instructed windows to completely fill.  I find it absurd that a Windows feature meant to completely fill a disk cause an annoying warning that you can't disable.

Id like to disable the low disk space warning, ideally for a single drive in Windows 8.  My gut feeling is that is it will be an all or nothing change.  Any ideas?


In Excel 2016, I would like to change the keyboard shortcut for the Search command from CTRL+B to CTRL+F so that this command has the same keyboard shortcut as in other programs. However, I could not find how to do this.  In Word, to do this, I can right click on the ribbon, select "Customize ribbon" and click on the button "Keyboard shortcuts: Customize" like in the screenshot:    However, in Excel, this button doesn't exist, or at least I couldn't find it:    I found a similar issue with Excel in Mac , but it didn't help me since the answers suggested using features that are specific for Mac and I'm using Windows.  How can I change keyboard shortcuts in Excel 2016 in Windows?

How do you customize Excel 2010 keyboard shortcuts?  This article from microsoft.com provides instructions for "Microsoft Office 2010" but seems only apply to Word, not Excel.   In Microsoft Office 2010:  Click the File tab to open Backstage view, and then click Options.  Click Customize Ribbon and then, next to the Keyboard Shortcuts heading, click Customize. You can enter the new key combination here.    Here's the dialog it points to shown in Word:  But here's the same dialog shown in Excel:  Notice it looks almost exactly the same but no "Keyboard Shortcuts: Customize.." button. So how do you customize the keyboard shortcuts in Excel?


A set $A$ is set to be infinite if it is not finite, i.e. if there exists no $n\in\mathbb{N}$ such that $|A|=n$, meaning there exists a bijection $A\leftrightarrow\{1,\dotsc,n\}$. How do I prove that for any such set there necessarily exists an injective function $f:\mathbb{N}\to A$, meaning there are no infinite cardinalities under countability?

I am comfortable with the different sizes of infinities and Cantor's "diagonal argument" to prove that the set of all subsets of an infinite set has cardinality strictly greater than the set itself. So if we have a set $\Omega$ and $|\Omega| = \aleph_i$, then (assuming continuum hypothesis) the cardinality of $2^{\Omega}$ is $|2^{\Omega}| = \aleph_{i+1} > \aleph_i$ and we have $\aleph_{i+1} = 2^{\aleph_i}$.  I am fine with these argument.  What I don't understand is why should there be a smallest $\infty$? Is there a proof (or) an axiom that there exists a smallest $\infty$ and that this is what we address as "countably infinite"? or to rephrase the question "why can't I find a set whose power set gives us $\mathbb{N}$"?  The reason why I am asking this question is in "some sense" $\aleph_i = \log_2(\aleph_{i+1})$. I do not completely understand why this process should stop when $\aleph_i = \aleph_0$.  (Though coming to think about it I can feel that if I take an infinite set with $\log_2 \aleph_0$ elements I can still put it in one-to-one correspondence with the Natural number set. So Is $\log_2 \aleph_0 = \aleph_0$ (or) am I just confused? If $n \rightarrow \infty$, then $2^n \rightarrow \infty$ faster while $\log (n) \rightarrow \infty$ slower and $\log (\log (n)) \rightarrow \infty$ even slower and $\log(\log(\log (n))) \rightarrow \infty$ even "more" slower and so on).  Is there a clean (and relatively elementary) way to explain this to me?  (I am totally fine if you direct me to some paper (or) webpage. I tried googling but could not find an answer to my question)


If there is a box on a truck. The truck is accelerating to the right. The question asks us to draw all forces applying on the box. (Free body diagram of the box)  I have done this, but I always read that friction is opposite to the direction of motion. But when I read in other places the static friction that is holding the box and the truck together is in the direction of the truck. Can you please check if I am right? Thank you.    It is not the same question, it is more simple in nature, those answers are not clear bearing this question in mind. Thank you.

In my book, the following are described to be the steps that one must follow if he wishes to find the direction of static friction force acting on an object:  "(1) Draw the F.B.D(free body diagram) of the object in question with respect to the other object on which it is kept. (2) Include the pseudo force also, if the contact surface is accelerating. (3) Decide the direction of the resultant force and resolve this force into two components; one along the surface of contact and the other along the normal to this surface. (4) The direction of static friction is opposite to the component of the result force along the contact surface."  Firstly, are these steps correct? Will I always obtain the correct answer by following these steps? Secondly, consider the following problem:  In questions like these, when I try to find the resultant force and then assign the direction to static friction, I find that my answer is incorrect! Are there some other steps to follow when I know that the object is definitely accelerating in one direction or another? Edit 1: I approached the above question by doing exactly what my book suggests; first, I identified all the forces acting on the smaller block, being the normal force applied by the block A and its weight mg downward. Adding these two forces, I get another force that actually acts on the body like so:  I wonder if I'm not supposed to take either of the contact forces into consideration when drawing the F.B.D to figure out the direction of static friction acting on the body. Also, are there other steps for finding the direction of kinetic friction? Edit 2: From Judge's answer, I have been able to figure out my mistake, it being that I completely missed step (3) and didn't resolve the resultant force into components! Sheesh. Sorry! Much thanks in advance! :) Regards.


I want to keep password for my important folder where my all the documents are kept so how can i keep password for it?

Let's say that I have a folder, within my Documents folder, that has files I want no one to access without a password.  Is there a way to lock down that folder so that it's password protected / encrypted?  In fact, is it possible to password-protect any individual folder?


$$ \begin{align}x^2&=x+x+\cdots\ (\text{$x$ times})\\ \implies \dfrac{\mathrm d}{\mathrm dx}(x^2)&=\dfrac{\mathrm d}{\mathrm dx}(x)+\dfrac{\mathrm d}{\mathrm dx}(x)+\cdots \ (\text{$x$ times})\\ \implies 2x&=1+ 1+\cdots \ (\text{$x$ times})\\ \implies 2x&= x \\ \implies 2&=1 \end{align}  $$  Which is obviously wrong. So, where am I wrong?

Consider the following:   $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$   Therefore,   $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$   Take the derivative of lhs and rhs and we get:   $\underbrace{1 + 1 + 1 + \ldots + 1}_{x \textrm{ times}} = 2x$   Which simplifies to:   $x = 2x$   and hence    $1 = 2$.     Clearly something is wrong but I am unable pinpoint my mistake.


There are 3 colleges with $n$ students each. Any student knows $(n+1)$ students of the other colleges. Prove that there exists three students from different colleges who know each other (this doesn't have direction). A knows B implies B knows A i.e. the graph is undirected.   My work: Let the colleges be $X,Y,Z$. A student (say $a$) from college $X$ knows at least $\lfloor{\frac{n}{2} \rfloor}+1$. If one of the students that are known to $a$ in $Y$ knows a student in $Z$ and that student knows $a$ then we are done! But that is not always possible. There are too many cases. I can't take them all and become confused. Please help me.

I need help for one problem.     In every of 3 schools there are n students (in total = 3n vertex, n per school).   Every student knows at least n+1 students from the other two schools.   Prove that there are 3 students, one from each school, who know each   other.   Do you have some idea for this proving?


I have 15 VMs on Google Cloud and would like to know which one is causing my egress data to china.  How can I tell which one is doing the all that traffic? It has probably been hacked and would like to fix it.

Trying out Google Container Engine, and in my 'billing' section I see some traffic 'egress' charges for data from America to China.  I have a web portal up. Does 'egress' traffic means anything that's coming out (i.e. even web traffic not just ssh/ftp or others) ?  is there a way to monitor where this traffic is going / coming from, besides the web server logs? I mean Google has a way to measure that so is there a place to look up these connections?   If that's not so obvious, what are the recommended tools to setup to log all this traffic.


Given that  $$a\cdot b=gcd(a,b)\cdot lcm(a,b)$$  How can we find all the integer solutions $(a,b)$ if $gcd(a,b)=6$ and $lcm(a,b)=540$?  The first thing I did was factorizing using the fundamental theorem of arithmetic.  $$a\cdot b=gcd(a,b)\cdot lcm(a,b)=6\cdot540=2^3\cdot3^4\cdot5$$  I also know that  $$gcd(a,b)=p_1^{min(a_1,b_1)}\cdot p_2^{min(a_2,b_2)}\dots p_n^{min(a_n,b_n)}$$  $$lcm(a,b)=p_1^{max(a_1,b_1)}\cdot p_2^{max(a_2,b_2)}\dots p_n^{max(a_n,b_n)}$$ where $a_1\dots a_n$ and $b_1\dots b_n$ are the exponents in the factorization of $a$ and $b$ respectively.  From there I am not sure where to go to obtain all the possible integers $a$ and $b$.  There is already a similar question on Mathematics SE, however the accepted solution is simply a hint towards the correct procedure to do it, while this question already acknowledged that hint.

These two exercises I encountered recently seem to develop some type of connection between GCD and LCM I can't quite figure out. Exercise 1:  Find all the numbers $x$ and $y$ such that: $a) \ GCD(x,y)=15, \ LCM(x,y)=150$ $b) \ GCD(x,y)=120 \ LCM(x,y)=1320$ $c) \ GCD(x,y)=100 \ LCM(x,y)=990$  Exercise 2:   Find all the numbers $m,n$ such that $GCD(m,n)=pq , \ LCM(m,n)=p^2qs$  where $p,q,s$ are prime  The first thing that is known to me is that $GCD(x,y) \cdot LCM(x,y)= x \cdot y$ Also $LCM(x,y)$ is at most $x \cdot y$ while $GCD(x,y)$ is at most $\max \{x,y\}$. Last thing is that $GCD(x,y)|LCM(x,y)$. Using all this I tried to solve the first exercise: $a)$ First two obvious pairs are $x=15, y=150$ and $y=15, x=150$. Now neither of the numbers can be bigger than $150$ or smaller than $15$. So we are looking for numbers in the range $15-150$ that satisfy $x \cdot y = 15 \cdot 150$ Another such pair is $(x,y)=(30,75), \ (x,y)=(75,30)$. Similarly for $b)$ we find that the only possible values are permutations of the set {$120,1320$} and in $c)$ since $100$ does not divide $990$ no such numbers exist. Now exercise 2 is what made me think there is actually another connection I'm not quite aware of since now it's about arbitrary prime numbers and the previous method doesn't work anymore. My intuition is that it has something to do with $GCD$ or $LCM$ of the $GCD(x,y), \ LCM(x,y)$


Prove that {1,sin(x),sin(2x),sin(3x),…,sin(nx)} is an independent set. I received 1 answer 3 days ago but didn't find the answer very clear.  Please advice, thanks!

Prove that {$1, \sin(x), \sin(2x), \sin(3x),\ldots, \sin(nx)$} is an independent set. I can think of the long way which is to differentiate this and put the differentiations into a matrix and row reduce it.  Please advice, thanks!


Every country is trading with other countries around the world, some more than others.  I was wondering if there would be any change to the Earth's rotation because of the imbalance of trade between countries.

We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples along with their vehicles at their maximum velocity in one line in one direction along the equator? How much effect will it make?


$F$ is a field of order $q$.  We are essentially counting the total number of possible ordered bases in the vector space $F^d$.   The first vector has $q^d - 1$ possibilities because we need to exclude the zero vector.  The second vector cannot be a scalar multiple of the first vector, and there are $q$ scalars in $F$, so once we have chosen the first vector, there are $q^d-q$ possible ways to construct the second vector such that $v_1$ and $v_2$ are linearly independent.  But what about the third vector? Why are there $q^d-q^2$ possibilities?

$F$ is a finite field of order $q$. What is the size of $\operatorname{GL}_n(F)$ ?  I am reading Dummit and Foote "Abstract Algebra".  The following formula is given:  $(q^n - 1)(q^n - q)\cdots(q^n - q^{n-1})$.  The case for $n = 1$ is trivial.  I understand that for $n = 2$  the first row of the matrix can be any ordered pair of field elements except for $0,0$. and the second row can be any ordered pair of field elements that is not a multiple of the first row.  So for $n = 2$  there are $(q^n - 1)(q^n - q)$ invertible matrices.  For $n\geq 3$, I cannot seem to understand why  the formula works.  I have looked at Sloane's OEIS A002884.  I have also constructed and stared at a list of all $168$ $3\times 3$ invertible matrices over $GF(2)$.  I would most appreciate a concrete and detailed explanation of how say $(2^3 - 1)(2^3 - 2)(2^3 - 2^2)$ counts these $168$ matrices.


A committee of three boys and three girls is to be selected from a class of $14$ boys and $17$ girls. In how many ways can the committee be selected if the girls must include either Roberta or Priya but not both?  I did $(14 C 3) \times (15 C 2) \times 2 = 76,440$  However, the correct answer is $65,520$.   Any help is much appreciated, thanks in advance.

For this question:  A committee of three boys and three girls is to be selected from a class of 14 boys and 17 girls. In how many ways can the committe be selected if:  a.) Ana has to be on the committee.  Ana is a girl so: $$(^{14}C_3)(^{16}C_2)=43680$$  b.) the girls must include either Roberta or Priya, but not both.  I basically needed help in this question (Question B)  Attempts I made so far:  1.) $$(^{14}C_3)*2(^{16}C_2)-(^{15}C_1)=87345$$ 2.) $$(^{14}C_3)*2[(^{16}C_2)-(^{15}C_1)]=76440$$  I need help in what I've been doing wrong in these workings for question B


I was curious to know if its possible to change the motherboard of an iPad to reset its software version? The iPad is locked to my friends late grandpa, and hence locked to his name.   I was using it without any problems until one fine day when the iOS upgraded from 6.0 to 7.0 and after that it was asking the iCloud password of the device, which unfortunately none of us knows. Then I kept the iPad as a decoration, until today, when it struck me, that probably changing the motherboard might help to reset the software version to an earlier iOS version.  Or are there any other possible technical solution to bring back the iPad to life, instead of running around solicitors and lawyers?   This is a genuinely bought family iPad / not stolen etc duly passed on to a family member.

My Auntie died unexpectedly without leaving her icloud information (pretty standard!) I've restored her ipad as I thought it would reset her passcode as I couldn't guess it but now it's asking for Apple ID. I've tried everything but I can't guess her secret info or get into her emails until I go see my grandad and get her phone (he literally lives at the other side of the country.) So now I have this ipad and my cousin has iPod touch which is acting as a paper weight. There must be a way around it as this must be a fairly common thing surely? I don't have her death certificate, there isn't a will and my grandad (next of Kin) is 86 and quite flustered about everything and he's about had enough.   Ive looked online for a bypass but no luck, as it's not reported stolen surely it can't have an anti theft lock?  Thank you


What is the rationale behind using a 20 amp circuit breaker with 12/2 cable for a circuit that only contains 15 amp duplex receptacles? I understand the rationale behind using 12/2 cable instead of 14/2 cable, but do not understand the rationale behind using the 20 amp circuit breaker instead of a 15 amp circuit breaker. Without understanding the rationale, I would assume it would be prudent to either:   Replace the 20 amp circuit breaker with a 15 amp circuit breaker. Replace the 15 amp duplex receptacles with 20 amp duplex receptacles.   References to the National Electric Code would be appreciated.  Edit:  I did not intended to ask if it was permissible to use a 20 amp circuit breaker.  Instead, I meant to ask "What benefit does the 20 amp circuit breaker provide if there are only 15 amp duplex receptacles?"

OK, the one answer I got was way off target, and another commenter couldn't figure out what I was asking, so I'm restating the question...  Are 15A 3-prong grounded outlets actually rated to 20A, allowing them to be used on 20A circuits? And if so, why, when the outlet can never be asked to supply more than 15A by anything that would be plugged into it?  More info:   had a comment that 15A outlets were actually rated to 20A. However, by design, there is nothing that will plug into a 15A outlet that will draw more than 15A. An appliance that draws more than 15 amps would have a "T-blade" plug that wouldn't go into a standard 15A outlet.   In addition, outlets are always wired in parallel, meaning that a 15A outlet would never have to transmit the amperage draw of a "downstream" outlet; you never "daisy-chain" outlets by connecting hot to neutral, for a number of reasons.  So, there is AFAIK no situation in which a 15A receptacle would ever have to handle more than 15A, even if installed on a 12AWG, 20A-breaker circuit.  If all the above is true, why would a 15A receptacle even have to be rated to 20A?


When using Overleaf you get quite helpful suggestions, like when you type in \beg it gives you the option to autofill the whole   \being{}  \end{}    and even adds the contents of the first bracket into the second bracket.   However, there are some options that I use quite regularly, which while being compiled by Overleaf fine are not auto-filled, for example  \textsubscript{}   Is there a way to add new options to the prediction/autofill lists in Overleaf?

For example, when I use the command (in Overleaf/ShareLaTex):  \begin{figure}[H]     \centering     \includegraphics{some_graphic}     \caption{some_caption}     \label{fig:some_label} \end{figure}   the \includegraphics{} comes without the [] parameter to change the size of the image, and \begin{figure} without the [H] option by default.   Is it possible to renew the command to make it default? By that I mean that when I type the \begin{figure} command it adds the [H] and [h] as well as [width=\textwidth] in the \includegraphics command, rather than making a global change in the preamble e.g.


Consider the elliptic curve defined by $\ y^2 = x^3 + 1\ $ over $\ \mathbb{Z}_p,\ $ where $\ p \equiv 2 \pmod{3}\ $ is prime. Prove that the number of points on the curve is exactly $\ p + 1.\ $  Hint: for $\ y \in \mathbb{Z}_p,\ $ prove that there is exactly one $\ x \in \mathbb{Z}_p\ $ satisfying the equation.  Prove without showing that $\ x \mapsto x^3\ $ is a bijection

Let $p > 3$ be a prime such that $p \equiv 2 \pmod 3$. Define the elliptic curve $E$ over $\mathbb{F}_p$ by $y^2 = x^3 + 1$. Prove that $E(\mathbb{F}_p)$ consists of $p+1$ points.  Using Fermat's little theorem you can prove that $x^3 + 1$ is a bijection on $\mathbb{F}_p$. Hence, $$\#E(\mathbb{F}_p) = \#\{(x,y) \in \mathbb{F}_p^2 : y^2 = x^3 + 1\} + \#\{\infty\} = \#\{(x,y) \in \mathbb{F}_p^2 : y^2 = x\} + 1.$$ But then I am stuck trying to prove that $y^2 = x$ has $p$ solutions $(x,y) \in \mathbb{F}_p^2$.


Obviously, if $F$ is a field, and $I$ is it's nonzero ideal, then it contains an invertible element of $F$(any nonzero element of $F$). Denote this element as $a$. Since $I$ is ideal, $aa^{-1} = 1 \in I$. Hence, $I = F$.  But I'm not sure how to prove that any commutative ring with identity without nonzero proper ideals is a field.

Let $R$ be a commutative ring with identity. Show that $R$ is a field if and only if the only ideals of $R$ are $R$ itself and the zero ideal $(0)$.  I can't figure out where to start other that I need to prove some biconditional statement. Any help?


I'm having a problem. Can't set dhcp and static IP on the same interface at the same time.  My interfaces file:  auto eth0 allow-hotplug eth0 iface eth0 inet dhcp  iface eth0:0 inet static address 192.168.1.253 netmask 255.255.255.0   I followed a tutorial but still no use. Only DHCP address is being displayed. I'm trying to make it without GUI.

We can use multiple IP addresses for a single interface in Linux (eg. eth0:0, eth0:1). But can we use DHCP and static IP at the same time? eth0:1 should have a static IP address and eth0:0 should be configured using DHCP.  How can we accomplish both?


Is the number 3776543210123456773, in base 8, divisible by 7?  I started by expanding the number: 3 * $8^0$ + 7 * $8^1$ + 7 * $8^2$ + ... 3 * $(7 + 1)^0$ + 7 * $(7 + 1)^1$ + 7 * $(7 + 1)^2$ + ...    Then, by using Newton's Binomial Theorem, I reasoned that for each binomial, only the first term wouldn't be divisible by 7 since it would be equal to 1. This led me to the conclusion that each digit of the initial number would be multiplied by one once. Therefore, if the sum of all digits was divisible by 7, the number would also be divisible by 7.  However, I converted this number to base 10 and the remainder of the division by 7 was equal to 2, instead of 0, which was the result I found using the reasoning above.  I can't seem to find where I made a mistake. :c

I was showing my son how to cast out nines the other day.  He noted that based on the way it worked, we should be able to cast out 7s when we work with octal.  We tested this in several bases and it seems to work.  I am assuming the chance for false positives increases with the decrease in radix (but I don't actually understand the theory well enough to be sure).  But then we got to binary where everything seemed to be a false positive (my son got a huge kick out of the false positive when I showed it to him).  First question:  Are there any articles on check sums (like casting out nines) for other radix and their false positives.  And other methods that avoid the false positives?    Second question:  Is there any check sum for binary that doesn't take longer than the actual calculation (right now we convert to another base and check it, but that takes longer than actually doing the operation)?  Third question: Also, I have seen one book that talked about casting 11s (alternate subtracting and adding the number up starting from the right, and adding 11 if it is negative).  Has anyone seen a detailed explanation of it?  We could not make it work in other bases--any suggestions?


I came across this oddity when I ran , sorted by votes:    That question has zero answers, but its search result summary is formatted as though it has an accepted answer (green box, yellow-highlighted text).  In fact, the CSS class on that div is class="status answered-accepted">.  Perhaps the Skynet Exchange Stack Exchange system has become so intelligent, that it knows the OP solved their own problem (answering it in the question portion of the post), and thus it's marked as "answered-accepted."  Or maybe, after over 5 years, the question has just accepted the fact that it isn't going to get any answers.   Regardless, this seems like a display bug =)

On , the accepted answer (with 23 votes) is deleted. But it is still pinned to the top. (10k required to see deleted answer)    By the looks of it, the answer was deleted from the "low quality posts" review queue. But it never got unpinned when upon deletion.


I'm probably overthinking this, but I can't decide if it should be "was" or "were" in this case. Can someone explain to me which is correct and why? I think part of my problem is that, assuming were/was is the verb, I'm not sure what the subject is. Should it be conjugated to match "donuts"? Thanks.

I've recently read a  from a local paper that included the following:     The pair was drinking prior to the shooting.   To me, this appears wrong and I would say that the proper way to make the statement would be:     The pair were drinking prior to the shooting.   Is the original article correct?


I don't know why or when it started. I just noticed that the laptop where I have Windows 8 has an absurdly short timeout to lock the screen. The screen that is shown is the picture of the current user prompting for password.  I have tried many things in an attempt to get rid of it. Note that this version of Windows 8 is not Pro or Enterprise and It does not have the gpedit.msc tool:   In the screen options, in screensaver, no screen saver is set, but the timeout field steel controls when the screen will be locked or turned off, so I set value 0 there, and it changes to the string "(Never)". Also I unchecked "prompt for password". But screen steel locks.  Googling I found that there is a policy, editable in gpedit (no available in this edition of Windows), to set the timeout to lock the screen. Then I looked for the registry key that sets that policy and changed it (but it seems that it has no effect at all, screen still locks with a timeout of 1 min approx). The key I edited is "HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Policies\System\InactivityTimeoutSecs". I didn't existed, so I created It as DWORD with a large value.   Machine is SAMSUNG ATIV Book 2, in case somebody knows of any software that comes by default that may be causing this. I uninstalled the trial security software and I'm using Windows alone with Windows Defender and my common sense.

I recently got a new laptop (Lenovo T440p with Windows 8.1 Pro) and was having the following issue: the screen would lock (screen would go black and require a password to get back in) after 1 minute. I would prefer something more like 10 or 15 minutes. So, I tried the obvious changes (check the screensaver settings, power management settings for sleep, turning off the screen, etc.), with no success. I did, however, notice a rather odd behavior: if I changed the screensaver timeout from 1 minute to anything else (say, 15 mins), clicked OK, and re-opened the screensaver settings window, it would be back to 1 minute. Odd.  At that point, I turned to Google. I found posts ( in particular was helpful) suggesting all sorts of causes and resolutions:   If you have Cisco AnyConnect VPN client (which I did), try uninstalling it. I uninstalled, rebooted, no change. Open the User Accounts control panel and, on the left side of the screen, click Reset Security Policies. My User Accounts control panel, however, has no such link. Reboot into a repair console and run "sfc /scannow". It did indeed find and repair some issues, but didn't fix the screen timeout problem. Edit the Group Policy to force a particular timeout time; the setting showed up correctly (15 mins) in screensaver settings, power management settings, etc., but the screen would still go black and lock after 1 minute. In the registry, manually change the screensaver timeout and the "turn off the screen" timeout. No luck.


I am trying to make a function that will count how many lines starts with & in given file. So far i came up with following function    public int CountNumberOfTexts(String filename)  {          try{              File file = new File(filename);              if(file.exists()){                  FileReader fr = new FileReader(file);                 LineNumberReader lnr = new LineNumberReader(fr);                  int linenumber = 0;                  while (lnr.readLine() != null){                     if (lnr.readLine().substring(0,1) == "&") {                         linenumber++;                     }                 }                  Log.d("Count", "NUMBER OF LINES: " + linenumber);                  lnr.close();                  return linenumber;              }else{                 System.out.println("File does not exists: " + filename);             }          }catch(IOException e){             e.printStackTrace();         }          return 0;     }   Current Function error is: Not recognizing lines starting with & character.

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


I would to ask if it is possible to integrate Office Online from O365 with SharePoint 2016 instead of using Office Online Server?  Thank you,

I just wondering if we can use existing Office Online Server in Office365 for SP2013 on premise. If yes, how this can be achieve?   In SP2013 we normally run Get-SPWOPIBinding to find out the server binding and to connect to Office web App we normally run  New-SPWOPIBinding -ServerName. Is this the same command if I want to connect to the existing new Office Online Server in Office365?  Thanks


I take a string with integer count  int count=0; string s="wow"   and i am using foreach loop to count number of characters in a  specified string   foreach(char ch in s) {  count++ }   so how can i count those characters which are repeated in my string like 'w'.

I am doing something where I realised I wanted to count how many /s I could find in a string, and then it struck me, that there were several ways to do it, but couldn't decide on what the best (or easiest) was.  At the moment I'm going with something like:  string source = "/once/upon/a/time/"; int count = source.Length - source.Replace("/", "").Length;   But I don't like it at all, any takers?  I don't really want to dig out RegEx for this, do I?  I know my string is going to have the term I'm searching for, so you can assume that...  Of course for strings where length > 1,  string haystack = "/once/upon/a/time"; string needle = "/"; int needleCount = ( haystack.Length - haystack.Replace(needle,"").Length ) / needle.Length;


$\forall (x_n),(y_n)\ge0$,pf:  $$(x_1\cdot...\cdot x_n)^{1/n}+(y_1\cdot...\cdot y_n)^{1/n}\le((x_1+y_1)\cdot...\cdot (x_n+y_n))^{1/n}$$  I've turned it into: $$log(1+(z_1\cdot...\cdot z_n)^{1/n})\le\dfrac1 n\sum_{k=1}^{n} log(1+z_k)$$  Look like the average of a function with the function over an average now, but it's not convex...  Could someone give a simple proof to this inequality(even without Jensen's) :)  Thanks~

consider positive numbers $a_1,a_2,a_3,\ldots,a_n$ and $b_1,b_2,\ldots,b_n$. does the following in-equality holds and if it does then how to prove it  $\left[(a_1+b_1)(a_2+b_2)\cdots(a_n+b_n)\right]^{1/n}\ge \left(a_1a_2\cdots a_n\right)^{1/n}+\left(b_1b_2\cdots b_n\right)^{1/n}$


I have a question about the calculation of RSA decryption with the help of the CRT (Chinese Remainder Theorem).  If $c$ is the crytogram, $m$ the message, $d$ the private key and $p, q$ the primes. Then in RSA with CRT they use:  $m_1 = c^d \bmod p = c^{(d \bmod (p-1))} \bmod p$ with the help of .  But for FLT you need that $\text{gcd}(c,p)=1$ That is given if $c$ is less than $p$ because $p$ is a prime. But what is, if $c$ is bigger (because $c = m^e \bmod p*q$)? Then we can have $\text{gcd}(c,p)=p$  Does FLT also apply in this case? Or did I do something wrong?

I decided to read the original RSA paper A Method for Obtaining Digital Signatures and Public-Key Cryptosystem because of a question I had about RSA (which is not the question I'm about to ask, but may be a question on here at some time) and came across something I had never seen before in any textbook description of RSA (Note: this comes from the beginning of ).  for any integer (message) $M$ which is relatively prime to $n$, $M^{\phi(n)} \equiv 1\pmod{n}$  The part I don't recall ever hearing in class, or coming across in a text book, or seeing in any description of RSA I've ever read is that $M$ and $n$ must be relatively prime. So, I decided to play around with a toy example of RSA to see what would happen. I use $p=13$, $q=31$, $e=7$ and $M=2p=26$ (for completeness: $d=103$, $\phi(n)=360$, $n=403$). I observed the following using my toy instance of RSA: $M^e\equiv M\pmod{n}$, $M^e\equiv 0\pmod{p}$ and $M^e\equiv M\pmod{q}$. Do these equivalences hold for all $M,p,q$ when $M$ and $n$ are not relatively prime? How would I prove this? What is the real-world effect of this?


Is this supposed to happen? Why would conquering a duchy in war via claim work differently than usurping the title (if a count usurps a duchy and you are king they stay your vassal normally)?

I'm King.  A Count under a Duke vassal of mine, inherited a Duke-level title (Petty Kingdom)… and now he's independent.  I assumed that since King>Duke, he would still be my vassal, but this didn't happen.  Is that because he's not my direct vassal, and his liege was a Duke, ignoring that that Duke herself had a King liege?  Or would that have happened anyway for other reasons?  (maybe my Duke was a Grand Mayor actually, in case this changes anything, while the Count was a regular noble)


I have a computer that is kinda stumping me. It has something that has hijacked the browser with ads by dealpeak.  I have checked browser extensions, hosts files, proxy servers, scanned with malwarebytes, MSE and spybot all to no result. Malwarebytes was set to scan for rootkits as well.  Also manually scanned over task manager to see if anything was out of the ordinary and did not see anything but did not do more than check the folder anything I did not recognize was running out of. I may have to go back and check all those that were in safe folders(ie c:\program file\lenovo).  Lenovo running windows 7. Can't give more specs because it is not right in front of me.

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


Suppose that a group $G$ has order $p^{3}$ where $p$ is prime. How would I prove that $p$ divides $|Z(G)|$?

I'm trying to understand the proof of a Burnside theorem (as stated in Beachy's Abstract Algebra p. 328): Let $p$ be prime number. The center of any $p$-group is nontrivial.  Now, In the proof they say that if we let $G$ be a $p$-group, then in the class equation $$|G| = |Z(G)|+\sum [G:C(x)]$$ for all $x$ that is not in the center and represent a conjugacy class, we see that every term in $\sum [G:C(x)]$ is divisible by $p$ since $x\not\in Z(G) \implies [G:C(x)]>1$. This last statement is what I do not understand, how do we know that $p \mid [G:C(x)]$ for any conjugacy class?  I know that the elements in the conjugacy class of $x$ is in bijection with the cosets of $C(x)$, i.e. $[G:C(x)]$, but how can we be certain that the number of elements in a conjugacy class of $x$/cosets of the centralizer of $x$ is divisible by $p$?  Best regards.


Whenever I did calculations in high school physics involving gravity, it was either "a ball falling to the earth" type scenario, or a basic measurement of the gravitational attraction between two planetoids.   I think I read somewhere recently that gravitational changes "aren't reflected instantly across the universe but instead propagate at the speed of light" somewhat like the ripples in a pond expanding.   Is this true? Is there experimental evidence to confirm or deny this? What is the theoretical basis for it?

A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth.   However, what about the Sun's gravitational effect? If gravity propagates at the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent, so we could observe the Sun's disappearance more quickly.  What is the state of the research around such a thought experiment? Can this be inferred from observation?


I am not yet a Linux guy and I have some problem trying to add a new permanent environment variable.  So I have to set a new environment variable named CATALINA_HOME with this value: /opt/apache-tomcat-8.0.23  What can I do to set it permanently?  Tnx

I'm trying to set up Apache Tomcat on my pc, and it wants me to set up an environment variable for CATALINA_HOME.  Does any know how to do this?


My understanding at this point is that to assign a probability measure to a random variable defined on the real line, we need a Borel $\mathscr{B}$ sigma algebra, because otherwise we wouldn't be able to find a bijection from every subset of the power set ($2^\Omega$) to the Lebesgue measure, due to the fact that the cardinality of $2^\Omega$ is not just greater, but much greater than the subsets of the Borel algebra.   On the other hand, the Borel sigma algebra, even though it contains every number in the real line as a singleton set, has that same cardinality as $\mathbb{R}$.  How can this be proven? Is there a way to see this through the concept of standard topology?

Second countability by itself doesn't restrict the cardinality of a topological space, since every set with the trivial topology is a second countable space, but it seems natural to ask whether second countability restricts the cardinality of the Borel $\sigma$-algebra of the space.  Can the cardinality of the Borel $\sigma$-algebra of a second countable space be arbitrarily big? If this is the case is there a simple construction for a second countable space with an arbitrarily big Borel $\sigma$-algebra?


my niece is due to travel for a visit in April 2019 for 3 weeks to the uk and we are a bit concerned about what travel documents she can travel on due to the uk leaving the EU with or without a deal on the 29th of march any help would be appreciated.

I am traveling as a Belgian citizen after 28 March (brexit). Can I still enter with my identity card?


Say I have the top mesh in the image. If I subdivide it, I'll have the second mesh in the image. But what I want is the third. It has vertical subdivisions, but not horizontal. Is there a way to do this?

I have a plane that has a scale of x: 100, y: 5, z: 1, and I want to split it into squares that have a scale of x: 5, z: 5, but when I do subdivide, I get a result like this:     When in reality, I'd rather have something like this:    How can I do this? (Sorry for the badly sketched pictures.)


im currently creating a Menu Screen for my libgdx Game. I want to draw a Rectangle to dectect if my Menu Play Button is touched. Unfortunately by unprojecting the camera i get a Exception even tough i initialized the camera and checked muliple times for mistakes. Dont wonder about the OrthoCamera Class it just inheriting from the OrthographicCamera class and has some additional Functions.   Menu Class:  public class MenuScreen extends Screen {   private OrthoCamera cam;  private PlayButton pb; private ExitButton eb; private Background bg;  @Override public void create() {     // TODO Auto-generated method stub     cam = new OrthoCamera();      cam.resize():      pb = new PlayButton();      eb = new ExitButton();      bg = new Background();   Play Button Class:  public class PlayButton  {  Texture texture; Sprite sprite;  public PlayButton(){      texture = new Texture("button.png");      texture.setFilter(TextureFilter.Linear, TextureFilter.Linear);     TextureRegion region = new TextureRegion(texture, 59, 52, 300,250);      sprite = new Sprite(region);     sprite.setSize(sprite.getWidth() / 2, sprite.getHeight() / 2);     sprite.setOrigin(-sprite.getWidth() / 2, -sprite.getHeight() / 2);      sprite.setPosition(MyGdxGame.WIDTH / 2  - 317, MyGdxGame.HEIGHT /2 -110);     }      public void render(SpriteBatch batch) {     // TODO Auto-generated method stub     System.out.println("es wird gerendert");     sprite.draw(batch); }      public void update(OrthoCamera cam) {          // Source: http://stackoverflow.com/questions/24834399/how-to-detect-if-a-texture-has-been-touched-libgdx-without-scene2d          System.out.println("update");          if(Gdx.input.isTouched())          {        Vector3 tmp = new Vector3(Gdx.input.getX(),Gdx.input.getY(),0);        cam.unproject(tmp);       Rectangle textureBounds=new Rectangle((MyGdxGame.WIDTH / 2-317),            (MyGdxGame.HEIGHT /2 -110), 300, 250 );             if(textureBounds.contains(tmp.x,tmp.y))               {                ScreenManager.setScreen(new GameScreen());               }          }            }    }  @Override public void render(SpriteBatch batch) {      batch.begin();     bg.render(batch);     pb.render(batch);     eb.render(batch);      batch.end();  }    public void update(OrthoCamera cam) {     // TODO Auto-generated method stub     //cam.update();     pb.update(cam); }        If i click on the screen the Game crashes and the console says:         Exception in thread "LWJGL Application" java.lang.NullPointerException at buttons.PlayButton.update(PlayButton.java:58) at screen.MenuScreen.update(MenuScreen.java:109)

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've tried what seems to be everything.  Changing permissions in the home folder to my user ownership.  Installing the manager Eiciel it won't let me change permissions on apps since everything belongs to root!  And I can't find a way to login to Ubuntu Studio as sudo or any other way to grant permissions.  How does one fix this issue?    I tried adding my username user to visudo from su.  After running a terminal and typing: sudo shutdown now, it seems to save files now and actually allows me to shutdown the system in Ubuntu Studio, but the permissions app Eiciel still won't allow me to add permissions to any apps.  Synaptic Package Manager won't let me select downloaded .deb files in my Download directory to install either (could be another problem IDK).  Geany located in /usr/bin/geany found with: locate -e geany from the root directory.  Tips?  UPDATE, NOT A GREAT (BUT WORKING) SOLUTION: I ran this (I'm sure it's not the proper way to give permissions) from a su terminal in the root directory; the program I want to give write access to is in usr/bin: chown -R usr user:user  Now Geany shows up with check boxes and I can edit permissions.  There has to be a better way to do this.  Doesn't seem like this is in line with how security should be setup.

Despite the fact that I didn't run any chmod or chown commands, I seemed to have lost the ability to cd into some folders in my home directory. So I ran according to various answers on this forum since I have no clue about linux permissions:  sudo chmod -R 666 /home/rasmus/ sudo chown -c rasmus /home/rasmus/ sudo chown rasmus:rasmus /home/rasmus/ chmod 750 /home/rasmus/ sudo chown -R rasmus:rasmus /home/rasmus/ sudo chmod a+rx /home sudo chmod u+w /home   leaving my home dir in this state:  10:57:35: 8𝌆𝌆𝌆D:[~] ls -l total 52 drw-rw-rw- 2 rasmus rasmus 4096 Apr 15 10:43 catkin_ws/ drw-rw-rw- 2 rasmus rasmus 4096 Apr 14 16:31 Desktop/ drw-rw-rw- 3 rasmus rasmus 4096 Apr 15 09:31 Documents/ drw-rw-rw- 4 rasmus rasmus 4096 Apr 14 14:55 dotfiles/ drw-rw-rw- 3 rasmus rasmus 4096 Apr 14 15:27 Downloads/ -rw-rw-rw- 1 rasmus rasmus 8980 Apr 14 14:03 examples.desktop drw-rw-rw- 2 rasmus rasmus 4096 Apr 14 16:31 Music/ drw-rw-rw- 2 rasmus rasmus 4096 Apr 14 16:31 Pictures/ drw-rw-rw- 2 rasmus rasmus 4096 Apr 14 16:31 Public/ drw-rw-rw- 2 rasmus rasmus 4096 Apr 14 16:31 Templates/ drw-rw-rw- 2 rasmus rasmus 4096 Apr 14 14:22 Videos/   Apparently, I can read the folders, but not cd into them:  10:58:54: 8𝌆𝌆𝌆D:[~] ls Desktop/ 10:58:58: 8𝌆𝌆𝌆D:[~] cd Desktop/ bash: cd: Desktop/: Permission denied   What do I need to do to fix this?


Suppose $(x_n)$ is a sequence that satisfies $$ |x_m - x_n| \leq \dfrac{1}{1+|m-n|} $$ for all $m$ and $n$. Find (with proof) $\lim x_n$ ATTEMPT: If we put $m = n+1$, then $$ |x_{n+1} - x_n | \leq \dfrac{1}{1+n} $$ From this condition we see that $\lim x_n = L$ exists. On the other Hand, if we choose $n=m-1$, we obtain $$ |x_{m} - x_{m-1} | \leq \dfrac{1}{2} $$ And, as $m$ can by any number, then we may not conclude that the sequence converges as it may oscillate. Can I get some hints on how to solve this? Is my reasoning reasonable? or am I overthinking and it is a simple exercise.

Let $\{z_n\}$ be sequence of complex numbers such that   $$ |z_n - z_m| < \frac{1}{1+ |n-m|} $$ for all $n,m$  Given this information, can we compute $\lim_{n \to \infty} z_n $?  Attempt:  For sure the sequence is bounded since the RHS is always $\leq 1 $. IF $z_m = 0$, then we have   $$ |z_n | < 1 $$ for all $n$. I claim that the limit is $1$. How can I prove this ?


Suppose $S$ is a finitely generated $A$-algebra. I'd like to describe a natural morphism between $\operatorname{Proj}S$ and $\operatorname{Spec}A$. In exercise 6.3.F in Vakil's AG notes, we show that morphisms $X\rightarrow\operatorname{Spec}A$ are in natural bijections with ring morphisms $A\rightarrow\Gamma(\mathcal{O}_X,X)$. Why does this result gives us the desired natural morphism?

If $B$ is a graded ring, then for me is clear that $\operatorname{Proj}B$ with affine covering given by $D_+{(f)}\cong\operatorname{Spec} B_{(f)}$ is a scheme. The problem arises when $B$ is a graded $A$-algebra, because in this case $\operatorname{Proj}B$ should be an $A$-scheme:  clearly  we have a morphism of rings $A\longrightarrow B_{(f)}$ that induces a morphism of affine schemes ${\operatorname{Spec}{B}}_{(f)}\longrightarrow\operatorname{Spec} A$. Now, to get the structure of $A$-scheme, we must define a morphism from $\operatorname{Proj}B$ to $\operatorname{Spec} A$, and the simplest thing to do is glueing the above morphisms of affine schemes. But nobody ensures that this glueing is possible; to be precise my question is the following: why do the affine morphisms  match on the intersections?  Many thanks in advance.


In a regression what is the matrix $(X'X)^{-1}$? What do its interior elements represent?

Consider a simple regression (normality not assumed): $$Y_i = a + b X_i + e_i,$$ where $e_i$ is with mean $0$ and standard deviation $\sigma$. Are the Least Square Estimates of $a$ and $b$ uncorrelated?


i have a table fetching data in ajax. so  i want get some value return values. mainly i need check box checked count in server side data. i have try many more time. sorry i have no idea how to explain this. I'm New web development.please check my code here   this is my firt html code

      server side script   if(isset($_POST["action"])){  // fetch data in mysql      $output = '

      name	      checkbox	      Change	      Remove
   ';   while($row = mysqli_fetch_array($result))   {    $output .= '
      '.$row["SliderId"].'	      '.$row["Name"].' 	      <input type="checkbox" name="vehicle" value="abc" id="'.$row["SliderId"].'">	      <button type="button" name="update" class="btn btn-warning bt-xs update" id="'.$row["SliderId"].'">Change</button>	      <button type="button" name="delete" class="btn btn-danger bt-xs delete" id="'.$row["SliderId"].'">Remove</button>
    ';   }   $output .= '
';   echo $output;  }   when i have click  checkbox. i want alert check box checked count.

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 am currently facing some problem regarding bold numbering in algorithmic package  \begin{algorithm} \caption{Mining Three Node Root from Summary Graph}\label{algo_disjdecomp}   \hspace*{\algorithmicindent} \textbf{Input:} \\  \hspace*{1.5cm}${\cal S_G}$:Co-expression Network\\  \hspace*{1.5cm}${\gamma}$:Gamma Value of a Module\\  \hspace*{1.5cm}${d}$:frequency threshold for the graph\\  \hspace*{\algorithmicindent} \textbf{Output:} \\  \hspace*{1.5cm}$\cal{R}$: Set of three node root\\   \begin{algorithmic}[1] \Procedure {FindRoot}{${\cal S_G}$,${\gamma}$,${d}$} \State $\cal R = \emptyset            $~~~~~~~$\triangleright$Set of three node root   \State $\cal M_X =\emptyset         $~~~~~~~$\triangleright$Empty Matrix for edge count  \State $\cal M_F =\emptyset$~~~~~~~$\triangleright$Empty Matrix for frequent edge with count \State $V$=$getVertices(\cal G)$~~~~~~~$\triangleright$Set of Vertices in $\cal G$ \State  \bf{for each} $G_i  \in \cal S_G $  : \State \hspace*{1 cm} \bf{for each} $e_k\in  G_i$ : \State \hspace*{1.5 cm} {\bf if} $e_k \notin \cal M_X$: \State \hspace*{2 cm} {\bf Add} $e_k \hspace*{.25 cm} in \hspace*{.25 cm} \cal M_X$  \State \hspace*{2 cm} {\bf Set} $C_k$ to 1 \State \hspace*{1.5 cm}{\bf elseif} \State \hspace*{2 cm}{\bf Increment }  $C_i$ \State \hspace*{1.5 cm}{\bf end elseif} \State \hspace*{1 cm}{\bf end for} \State {\bf end for} \State {\bf for each} $e_i \in  \cal M_X$ : \State\hspace*{1 cm} {\bf if} $C_i$ $>$ ${d}$: \State\hspace*{1.5 cm}{\bf Add} in ${\cal M_X}$ \State\hspace*{1 cm}{\bf end if} \State {\bf end for} \State {\bf for each} $e_i\in \cal M_F$: \State\hspace*{1 cm}{\bf for each} $G_i \in \cal S_G$ : \State\hspace*{1.5 cm} {\bf Fill} $A_i$ of ${\cal M_F}$:~~~~~~~$\triangleright$ Attribute for every edge $e_i$ \State\hspace*{1 cm}{\bf end for} \State {\bf end for} \State {\bf for each} $e_i\in \cal M_F$: \State \hspace*{1 cm} {\bf for each} $e_j\in \cal M_F$: \State \hspace*{1.5 cm} {\bf if} $e_i$ and $e_j$ connected and $|  A_i \cap A_j |$ $>$ ${d}$ \State \hspace*{2 cm}{\bf Add} $e_i \cap e_j$ to \cal R \State \hspace*{1.5 cm}{\bf end if} \State \hspace*{1 cm}{\bf end for } \State {\bf end for }  \EndProcedure  \end{algorithmic} \end{algorithm}   output :

MWE:  \documentclass{article}  \usepackage{bm}  \begin{document} $$x(t), \bf{x}(t), \bf{x(t)}$$ \end{document}   Result:    Question:  Why are the second and third x(t) typeset the same? In the second  expression, it was asked to apply \bf to only x.  EDIT:  I had not payed attention to it when asking the question, but I would like to have a bold and italic x.


Which is grammatically correct?        "Request you to register me for the course"   "Request you to register myself for the course"

I'm confused by why people use the following:     It's up to yourself.   Rather than:     It's up to you.   Another example of this would be:     Please feel free to contact ourselves if you have any problems.   Rather than:     Please feel free to contact us if you have any problems.   Are both of these correct?  Is there any reason for using the former?


I deleted the /etc/passwd file and cannot login now. I don't know the root password and tried lots of passwords, but none of them worked.  How can I fix this?

I was trying to change my username and also my home directory (/home/username) and my system started to crash. I deleted the passwd file but I had a backup named passwd_bkp. I tried to rename this passwd_bkp as passwd and it did not work. No commands were being executed... I was in a terminal window.   I restarted my system and now I cannot log in. GRUB gives two options: Linux and recovery mode.   I tried to open a sessions as root but it says the filesystem is corrupted. I cannot access my files.  Did I lose all my files?


Question  Everyone knows that each utility room has a S.P.E.C.I.A.L. stat that compliments it (Waterplant-perception, etc). What I want to know is are there secondary stats that are important? Below are examples of secondaries that I'm aware of but I'm paranoid that I'm missing some.  Examples  For instance, I train everyone to have high luck because I noticed that it results in better rush-success. Obviously I'm working on my explorers having max luck, so they get the best items.  I put people with a high overall character level near the vault door, because they have more health.   My near-door room is a water plant because everyone in it has maxed perception, for more accurate shooting. Should I also train these near-door protectors in strength, to make them better fighters?  High charisma helps speed up the baby making process. But does it have any effect on happiness if everyone in a room is charismatic?  Does any skill help them put out fires faster?  Maybe high intelligence helps dwellers learn other skills faster?  Does any skill result in children being born with higher starting skill levels?

Besides its workplace uses, like Charisma in Living Quarters, Strength in Power Generators, Agility in Diners.   Do we know if Endurance increases HP in the Dwellers, or that strength helps in melee damage / survivability in the wastelands? And Perception?


It's been awhile since I've used my Kubuntu system. I'm trying to upgrade to version 16.04 - and running into a series of problems:  When attempting to upgrade Kubuntu to version 16.04, I get the error message: Required depends is not installed The required dependency 'apt (>= 1.0.1ubuntu2.13)' is not installed.   So, when I attempt to fix that in the (Konsole) Terminal, I enter: sudo apt-get install --only-upgrade apt  The response that I get is: Command 'sudo' is available in '/usr/bin/sudo' The command could not be located because '/usr/bin' is not included in the PATH environment variable. sudo: command not found   I then try to fix that by entering: apt-get install sudo  The response that I get to this is: Command 'apt-get' is available in '/usr/bin/apt-get' The command could not be located because '/usr/bin' is not included in the PATH environment variable. apt-get: command not found   I tried to address that by entering: export PATH=/usr/bin:/bin sudo apt-get install --only-upgrade apt  In response, I get: E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?   In order to identify what might be causing the problem, I ran: ps aux | grep apt  The only thing that comes up that looks like it might be a possibility is this: 4381  0.0  0.0  11740   936 pts/2    S+   23:50   0:00 grep --color=auto apt    (All the other "apt"s it finds are part of "caption"...) At this point, where should I go? What should I try?

I have been using Ubuntu 12.04 for quite a while and have never had a problem come at me out of the blue like this. I'm trying to install python 3.2 on my Ubuntu system and every time I run the code to compile the python source, I get this error:  'Command 'sudo' is available in '/usr/bin/sudo' The command could not be located because '/usr/bin' is not included in the PATH environment variable. sudo: command not found'   I've also tried running gksudo command to view what my environment shows but I pretty much get the same error.


As I understand it, Ubuntu uses lots of free (FOSS/FLOSS) software but often also some closed-source proprietary software, which is why Ubuntu is not included in the FSF list of .  While I'm not a fanatic about this, I do want to support the free software movement and use as much free software as possible. So I wonder: is there some way to get a list or overview of all non-free software and firmware that is used/installed on my Ubuntu system?

I know I can check the currently installed non-free software with the following command (assuming aptitude is FOSS):  aptitude search '?installed (?section(restricted) | ?section(multiverse))'   And I can remove the "restricted" and "multiverse" sources (and not add any PPA's) to keep that list empty. I'm assuming from this point, whenever I apt install something, that something is either in the allowed sources or it is not found.  Is this enough? Does this make sure all software I'm running (in Ubuntu) is open-source?


This is really frustrating. Having to edit a title because it was "too long" despite the title field not having a hard limit or a character count.

When asking a question the title textbox allows 300 characters max. But If I try to post such a long question title I get an error after hitting the post button:     title too long; maximum length 150   Could you please sync that?!


I am reading Lie groups, Lie Algebras, and Representations: An Introduction (2nd edition) by Brian C. Hall and I am unable to do the problem 12 in chapter 5. It says  Show that every connected Lie subgroup of SU(2) is closed. Show that this is not the case for SU(3).  Also I am wondering if the Lie algebra of SU(2) has any two-dimensional subalgebras. Is there a systematic way of listing all the Lie subalgebras of the Lie algebras of SU(2) and SU(3) ? What about Lie subgroups ?

Is there an easy way to prove that every Lie subgroup of $SU(2)$ is closed? That is, is it true that any $K=\exp_{SU(2)}(k)$ is closed for every subalgebra $k \subset \mathfrak{su}(2)$?  If there isn't, is there a reference for this fact?  I thought that this was left as an exercise on the book on compact Lie groups by Sepanski, but I cannot find the reference. Thanks.


When I bought my house last year, I had only about 8% of the purchase price for a down payment (though the bank's initial appraisal was for about $17,000 higher than the purchase price) but I figured that getting a low interest rate would offset the PMI payments if they went up.  Anyway, I can afford the total payment on the house but the PMI payment is sticking in my craw a bit.  Do I have any other options than taking out a personal loan for the ~$13,000 that it would take to pay down the remaining principal to get me to an 80% LTV on the property?

I am a relatively new home owner, having purchased my first home in October 2009. Overall, I feel I got an excellent deal on the loan, which was 5% no-cost, no points, and 12% down. I had to take on PMI (mortgage insurance) since I was unable to put down a full 20%. This mortgage insurance is costing me a hefty $1752 per year, and I am wondering if there are any options for refinancing that would allow me to remove the PMI, despite not yet reaching that 80% loan-to-value ratio.


I have found a lot instructions, but most (or all) of them use a Windows GUI application to root the device. The Linux scripts, that I found did not work.  My telephone:   Model: Xperia Mini Pro (SK17i) Android-Version: 4.0.4 Kernel-Version: 2.6.32.9-perf Build-Nummer: 4.1.B.0.587   How can I root this phone with a linux computer?  HINT This is not a duplicate question, because I want to do it from Linux (not Windows) and second the  does not contain an answer for my phone!

This is a common question asked by those who want to root their phones. How exactly do I root my Android device? Are there risks involved?


I am trying to make the pygame window background transparent. I want it to show content, but just the background fully transparent. Here is my code so far: import pygame pygame.init()  screen = pygame.display.set_mode((600, 600), flags=pygame.NOFRAME)  If you need more info just ask!

Is it possible to get a fully transparent window in Pygame (see the desktop through it)?  I've found how to create a window without a frame, but there doesn't seem to be any obvious way to make it transparent.  I'd be willing to tie into system-specific technology/frameworks as long as there are solutions for both Windows and Mac OS X, but I'm not sure which direction to be looking.  The only topic I was able to find , which isn't something I can do for this particular project (needs to be Pygame).


I bought a laptop with Ubuntu formatted the hdd through my PC put the hdd back wiped out formatted still grub remains can't let me boot from windows cd or USB !! What can I do.?

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


In trying to answer a question , I was re-reading  from .  What I followed from this is that, given a model with one dependent variable and two independent variables,  $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$  then the estimated regression coefficients, let's say for example $\hat{\beta_1}$ in the equation above, would be the same $\hat{\beta_1}$ from this equation:  $z_2 = \beta_0 + \beta_1X_1 + \epsilon$,  where  $z_2 = Y - \beta_0 - \beta_2X_2$  That is: It is my understanding that the regression coefficient $\hat{\beta_j}$ one gets in a multivariate linear regression is equal to the coefficient you would get if you took the residuals from the model where the dependent variable is regressed on all other predictor variables (besides $X_j$) and regressed those on $X_j$. However, I simulated some data and did not get this:  set.seed(1839) # setting seed x1 <- rnorm(200, 0, 1) # generating x1 x2 <- x1 + rnorm(200, 1, 3) # generating a correlated x2 eps <- rnorm(200, 0, 6) # generating error y <- x1 + x2 + eps # making y fit <- lm(y ~ x1 + x2) # fitting overall model   Looking at the summary, we can see the coefficients for x1 and x2:  summary(fit) # looking at summary      Call: lm(formula = y ~ x1 + x2)  Residuals:      Min       1Q   Median       3Q      Max  -18.4923  -4.4054   0.2954   4.0371  15.0697   Coefficients:             Estimate Std. Error t value Pr(>|t|)     (Intercept)  -0.5802     0.4462  -1.300    0.195     x1            0.1487     0.4733   0.314    0.754     x2            1.1272     0.1397   8.071 6.77e-14 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Residual standard error: 6.021 on 197 degrees of freedom Multiple R-squared:  0.2706,    Adjusted R-squared:  0.2631  F-statistic: 36.53 on 2 and 197 DF,  p-value: 3.199e-14   Now, why don't these coefficient's match these found in the equations below?  coef(lm(residuals(lm(y ~ x2)) ~ x1))[2] # not exactly equal to the x1 in the original fit         x1  0.1358402   coef(lm(residuals(lm(y ~ x1)) ~ x2))[2] # not exactly equal to the x2 in the original fit        x2  1.029427    Why are these x1 and x2 coefficients not the same as those above? They are close—is this due to rounding? Or am I missing something from Algorithm 3.1?

Not sure if normalize is the correct word to use here, but I will try my best to illustrate what I am trying to ask. The estimator used here is least squares.  Suppose you have $y=\beta_0+\beta_1x_1$, you can center it around the mean by $y=\beta_0'+\beta_1x_1'$ where $\beta_0'=\beta_0+\beta_1\bar x_1$ and $x_1'=x-\bar x$, so that $\beta_0'$ no longer has any influence on estimating $\beta_1$.  By this I mean $\hat\beta_1$ in $y=\beta_1x_1'$ is equivalent to $\hat\beta_1$ in $y=\beta_0+\beta_1x_1$. We have reduced equation for easier least square calculation.  How do you apply this method in general? Now I have the model $y=\beta_1e^{x_1t}+\beta_2e^{x_2t}$, I am trying to reduce it to $y=\beta_1x'$.


When one makes a beamer presentation with many overlays (as for a lecture), one ends up with a pdf with many pages that is hard to read through. It would make sense that someone had come up with a quick and easy way to remove all overlay behavior from a document, to make a pdf that can be quickly perused.  In the past I have tried to do some clever use of "find and replace". But that can get tricky.

Currently I am preparing a presentation in beamer. I make an extensive use of the \pause-command. However, it would be good to disable \pause temporarily to quickly go through the presentation. Additionally, I would like to send the presentation to members of the audience without all the split frames and without deleting or %-ing the \pauses manually. Does anyone has a solution?


my pdf generation works like pdflatex biber pdflatex pdflatex. In the context of final PDF generation, I checked the log file and stumbled upon several weird entries:  <graphics/measurementOverview.pdf, id=2875, 384.43625pt x 196.23312pt>   The weird thing about this is the dimension: I checked the text width (using \the\textwidth) to be 383.0pt. So I created all my pdf figures on exactly 383.0pt. Besides, I include figures like that:  \newcommand\figureFrame[3][ht]{%     \begin{figure}[#1]         \centering         \includegraphics[width=\textwidth]{graphics/#2}         \caption{#3}         \label{fig:#2}     \end{figure} }   As you can see, also there is the text width of 383.0pt used. So why the hell prints the pdflatex run this strange dimension of 384.43625pt? This happens for nearly all my figures... thank you!

recognize this simple example:  \documentclass[]{article} \usepackage[paperwidth=612.0pt, paperheight=792.0pt]{geometry}  \begin{document} Hello World \end{document}   I compiled it with pdflatex. Additionally I wrote this small Java-Programm (using the iText library):  PdfReader reader = new PdfReader("example.pdf"); Rectangle psize = reader.getPageSize(1); System.out.println(psize.getHeight()); System.out.println(psize.getWidth());   The result:  Height: 789.041 Width: 609.714   Why is the paperwidth and paperheight different to the tex?


What is the remainder when $2^{2016}$ is divided by $47$?   I have done Fermat's little theorem and I have now this:  $2^{2016} \equiv 2^{38} \pmod{47}$  My issue is that $2^{38}$ is too large of a number to work with, how do I continue?

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 .


I'm trying to prove the following statement: $P(n) = 3^{2n-1} + 2^{n+1}$ is always a multiple of $7$  $\forall n\geq1$. I want to use induction, so the base case is $P(1) = 7$ so that's okay.  Now I need to prove that if $P(n)$ is true then $P(n+1)$ is true. So there exists a $d \in \mathbb{N}$ such that  $$ 3^{2n-1} + 2^{n+1} = 7d $$ From this I need to say that there exists a $k \in \mathbb{N}$ such that: $$ 3^{2n+1} + 2^{n+2} = 7k $$ With a little algebraic manipulation, I have managed to say: $$ 2 \cdot 3^{2n+1} + 9 \cdot 2^{n+2} = 7\cdot(18d) $$ But now I am stuck. How should I keep going?

Expanding the equation out gives  $(3^{2n}\times3)+(2^n\times2^2) \equiv 0\pmod{7}$   Is this correct? I'm a little hazy on my index laws.  Not sure if this is what I need to do? Am I on the right track?


In my .bib file I have two entries as follows: @book{si20,     title = {Introduction to Econometrics with R},     author = {Schmelzer, Martin Arnold, Alexander Gerber, and Martin, Christoph Hanck},     url = {https://www.econometrics-with-r.org/},     urldate = {2020-10-02},     year = {2020} }  @Article{pcalg,     title = {Causal Inference Using Graphical Models with the {R}       Package {pcalg}},     author = {Markus Kalisch and Martin M\"achler and Diego Colombo and       Marloes H. Maathuis and Peter B\"uhlmann},     journal = {Journal of Statistical Software},     year = {2012},     volume = {47},     number = {11},     pages = {1--26},     url = {https://www.jstatsoft.org/article/view/v047i11},   }  My  document looks like this: \documentclass{article} \usepackage[utf8]{inputenc}  \title{Test citations} \author{Jaime Sevilla} \date{November 2020} \usepackage[ backend=biber, natbib, style=numeric ]{biblatex} \addbibresource{name.bib}  \begin{document}  \maketitle  \section{Introduction}  \cite{si20}  \cite{pcalg}  \printbibliography  \end{document}  At first sight I would think that both bib entries are correctly formatted. But only the second one works!  What is going on? How do I fix the first bib entry?

I use  to store all articles I need and bibtex4word add-on (in MS Word) to maintain the reference list. So, I would like to know how to properly fill the "author" field in Jabref with multiple authors to appear them correct in the reference list.  For example, I've got the article with several authors:      E. Orti, J.L. Bredas, C. Clarisse   And I would like them to appear in this manner. But instead I get this:     C. C. E. Orti, J. L. Bredas


In , the OP admitted to deleting his question and then reposting it. I feel like this user has successfully "gamed" the system. His post is not technically a dupe (since he deleted the original), and it's not offensive (in content) or spam, so it's not flag-worthy.  I left a comment attempting to educate the user. But what else can be done here? I would hate to see this catch on as a way of getting more attention for your post.

A user has asked  which did not receive much attention, and thus the user deleted the post. After some time, the user asked the  (with just slight changes to the title and a tag change), so that it could receive a bit more attention. The strange thing is that the question was not downvoted or poorly written, and yet the user deleted the original post. Now, since the original question was deleted, I could not mark the new one as a duplicate (it threw an error). My question is, how do we handle such questions? Just let them be as such or let the user know about it or is there another way to handle such situations?


I tried to shrink Windows and then expand Ubuntu. I did shrink Windows from within Windows and I boot Ubuntu from USB to add that unallocated space to Ubuntu but I cant do it.  The option doesn't show. Any idea how to complete the process?

How can I merge an unallocated partition with an extended partition ? I'm having trouble moving this unallocated space to the Linux portion. Here is my partition space:  (source: )


Is there a general procedure one can follow to find the force of constraint for a classical holonomic system with the nonconstraint forces derivable from a potential energy $U\left(\mathbf{r}_1, \dots , \mathbf{r}_n, t\right)$ where $\mathbf{r}_1, \dots , \mathbf{r}_n$ are the positions of the particles in an inertial reference frame? It seems that one can always find the force of constraint using the method of  which I am not familiar with. If there is an algorithm for finding the force of constraint, what is it?

Suppose we try to obtain the movement equation for a particle sliding on a sphere (no friction, ideal bodies...). The only forces acting on the particle are its weight and - here's my problem - a force that keeps the particle attached to the sphere*. How I am supposed to represent mathematically this kind of forces? As a restriction on the coordinates of the particle?  As a side note: My teacher refers to this, in Spanish, as a "fuerza de ligadura". I don't have a clue on its correct translation; does ligature force make any sense?


I want to know if there in big difference in Lineage OS and CyanogenMod ROM's ?

So Cyanogen Inc (cyngn), known for their support for their support for CyanogenMod and their efforts to integrate Cyanogen OS into devices such as the OnePlus One, Alcatel POP Mirage, and . Cyanogen Inc just recently .  What does this mean for CyanogenMod, Cyanogen OS, and the devices which originally shipped with Cyanogen OS? Will they no longer receive OTA updates?


I read numerous websites including wikipedia on heavy and light tail distributions. However, I am not quite understanding the distinction between the two. In some sources, it notes that light tail distribution has uniform distribution while heavy tail has a larger distribution. Hence, I am led to believe that heavy tail distributions are just distributions with greater variance than light tailed distributions. Are there more nuances to this understanding? Can someone elaborate on this concept?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation with the same person.)  Last year I was told that the gamma distribution is heavier tailed than the lognormal, and I've since been told that's not the case.   Which is heavier tailed? What are some resources I can use to explore the relationship?


I put some uncooked stew meat and veggies on this morning and left for 5 hours. When I came home I realized it was only set on warm. Is my meat safe to eat? I have now put it on the stove to cook.

I left a round steak out for 7 hours in a container of cold water.  It was wrapped very well, hadn't been opened yet.  Is it ok to cook this? I planned on cooking it in the crockpot for 8 hours.


I'm having trouble with this question, which appears in Professor Higgin's problem collection. There is an answer, though I do not really understand it. The question goes somewhat like this :  In a 10 by 10 grid, assign each square in the 10 by 10 grid a number from 1 to 100 so that no numbers are repeated. It would be ideal to choose this arrangement so that the difference of adjacent squares is as small as possible. Find a numbering that has a maximum difference between adjacent squares of 10 (which I have done). Is it possible to do better?  I am having trouble with the part of the question that ask whether you can do better, which is to say, can the maximum difference between adjacent squares on the grid be 9 or lower?  Thanks for anyone who answers!

Is it possible to write the numbers 1, 2, ..., 25 on the square of a 5 by 5 chess board (one number per square) such that any two neighbouring numbers differ by at most 4?  (Two numbers are neighbours if they are written on squares that share a side.)  Thanks, the problem was from a maths olympiad so it might prove to be quite a tricky one :/  Any help is appreciated! Thanks! :)


Is there a small package free way of implementing something like this in pdflatex and LaTeX?  I wish for the outcome of   \documentclass{article} \begin{document}     `It's a nice day!' \end{document}   To be     ʻIt's a nice day!ʼ   I know that due to there being a single apostrophe inside the quote can mess up stuff, so I'm more then happy to use a function or macro, like \apos, to insert it.  I know that the apostrophe I want has the Unicode value of 39, so is in the standard ASCII implementation. "U+0027 ' apostrophe (HTML: &#39; &apos;) typewriter apostrophe."

The question  is my question too, but the answer points to a package upquote that affects the entire document. I need to display an apostrophe (U+0027) only a couple of times within the document. Otherwise I would like the general conversion to quote to take place.  \documentclass{article} \usepackage{fontspec, xunicode, xltxtra} \defaultfontfeatures{Mapping = tex-text}  \begin{document} \noindent I would like an apostrophe to appear in the word ap'ple (U+0027), but a right quotation mark (U+2019) when I quote the word `orange'. \end{document}