What is the difference in the meaning of following sentences?        If Tom were to do my homework, I would watch a film.   If Tom did my homework, I would watch a film.      I know that both of these questions express unlikely or imagined condition. I'm not sure but I think. There's is difference in the meaning between two sentences. Here is my opinion:   In the first sentence, the speaker thinks that  it's impossible for Tom to do his homework or Tom isn't able to do his homework or Tom is a baby. So, the speaker is  imagining a impossible thing. In the second sentence, the speaker thinks it's a bit possible for Tom to do his homework.Tom is the speaker's friend and Tom is able to his homework but he isn't willing to do. So, the speaker is expressing his imagination and saying "If Tom did my homework I'd watch a film".   For more clearification of my openion i would say: I'm not sure but I'm just guessing the possible meaning of those sentences like this:  both sentences are all about imagination but first sentence indicates impossible imagination and second expresses unlikely but expected imagination. AM i correct?  Am I correct in my opinion ? If not, what is the correct meaning?    Please explain it in details.

What is the difference in the meanings of the following sentences:      If you asked me, I would say no.     If you were to ask me, I would say no.    I know that these sentences express imagination of the speaker. But they look similar to me. I don't know which one is correct to use depending on the different context. Which sentence expresses more possibility of your asking ?  I think that 'were to'  could also express the meaning 'by chance' or happen to' for example: 1."If you were to ask me (If you happened to ask me or by chance) I would say no." Am I correct here ?  My question is about difference between these two sentences and which one is correct to use depending on different context.  I'm expecting an helpfull answer. Thank you very much in advance.


How to prove the following identity: $$\sum_{k=0}^n\frac{(-1)^k}{2k+1}\binom{n}{k}=\prod_{k=1}^n\frac{2k}{2k+1}$$

Mathematica tells me that  $$\sum _{k=0}^n { n \choose k} \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}.$$  Although I have not been able to come up with a proof.  Proofs, hints, or references are all welcome.


Let $K$ be an arbitrary field, $p$ a prime and $a\in K$. Show $f=x^p-a$ is either irreducible in   $K[x]$ or has a root in $K$.   My strategy was to split this up into a case for each characteristic.   The characteristic $p$ case is easy. Assume $f$ is reducible $=gh$ both smaller degree $g$ irreducible, with $\alpha$ a root of $g$. Then in $K(\alpha)[x]$, $f=(x-\alpha)^p$. So $g=(x-\alpha)^k$, and all the other factors of $f$ are of the same form. Hence they are all equal to the $minpoly(\alpha)$ and the degree of $minpoly(\alpha)|p$ so it is $1$ or $p$ and we are done.  The characteristic $0$ case  and characteristic $q\ne p$ I get stuck on. If $K$ contains a primitive $p$th root of unity $\zeta$, then over $K(\alpha)$, $f$ splits into linear factors. So the degree of the field extension for any root of $f$ is the same, so the degree of such a root is either $1$ or $p$. If $K$ does not have a primitive $p$th root of unity, then simply adjoin one. We know $[K(\zeta):K]|p-1$ and by the previous step either $f$ is irreducible over $K(\zeta)$ or splits into linear factors. If it is irreducible we are done, if not we have it splits into linear factors of the form $x-\zeta^ia^{1/p}$, but I am unsure what to do from here. The characteristic $q$ case seems similar to the characteristic $0$ case but again I am stuck trying to finish the proof.   Some googling has lead me to believe that this problem is generally approached using the field norm and if an accessible online reference exists I would love to see it, but I feel that in the context I have seen it should be entirely possible that this is done without needing the norm. As I have not seen the field norm before, I would like to know if there is a possible way to prove this without using it and hopefully that follows in the same vein my attempt at a proof did.

Let $F$ be a field of arbitrary characteristic, $a\in F$, and $p$ a prime number. Show that $$f(X)=X^p-a$$ is irreducible in $F[X]$ if it has no root in $F$.   This  to a related question mentions the result is due to Capelli.  I can prove the result if $F$ has characteristic $p$ as follows.  Suppose $f$ is reducible: $f(X)=g(X)h(X)$ with $g(X)$ an irreducible factor of degree $m$, $1\le m<p$. Then if $\alpha$ is a root of $g$ in some extension field $K$ of $F$, we have $$f(X)=X^p-\alpha^p=(X-\alpha)^p$$ so its divisor $g(X)$ must be of the form $(X-\alpha)^m$. Since the coefficient of $X^{m-1}$ in $g$ is in $F$, we have $m\alpha\in F$.  So $\alpha\in F$ because $m$ is invertible modulo $p$.  How would you show the result in other characteristics?


In the following formula $\alpha \rightarrow \forall x \alpha$, why is it important that $x$ does not occur free in $\alpha$?  Here are my thoughts: I would like to find a countermodel and formula $\alpha$ where $x$ is free in $\alpha$ and $\alpha \rightarrow \forall x \alpha$ holds. If we take $\alpha$ to be the formula $x = 5$ in some model whose domain is $\mathbb{N}$, we see that neither $\alpha$ nor $\forall x \alpha $ is satisfied which is not what we want. I cannot see how to meaningfully satisfy $\alpha$ while not satisfying $\forall x \alpha$. Any hints?

Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?  i.e., when there are free occurrences of $x$ in $\alpha$, and, on the same point, why is the formula scheme correct when there are no free occurrences of $x$ in $\alpha$?


The following code results in node labels overlapping the graph. How can I align them depending on the graph so that '1375' und '1574' are below the node and the others still above?  \documentclass{article} \usepackage{pgfplots} \begin{document} \begin{tikzpicture} \begin{axis}[ nodes near coords, point meta=explicit, nodes near coords align={auto} ] \pgfplotstableread{ a  d 1   1557 2   1375 3   1722 4   1763 5   1574 6   1591 7   1563 }\datatable \addplot table[y = d, meta=d] from \datatable ; \end{axis} \end{tikzpicture} \end{document}

\documentclass{standalone}  \usepackage{pgfplots} \usepackage{pgfplotstable} \pgfplotsset{compat=1.10}  \pgfplotstableread{ 0.01    1.00 0.02    2.00 0.03    3.00 0.04    4.00 0.05    5.00 }\datatable  \begin{document} \begin{tikzpicture} \begin{axis}[ymin=0, ymax=6] \addplot table  {\datatable} node[pos=0.0, pin=above:"Unidentified peak"]{} % pos only allows for fractional value node[pos=0.2, pin=above:"Bragg peak"]{} % pos only allows for fractional value node[pos=1.0, pin=above:"my custom label"]{} % pos only allows for fractional value ;  \end{axis} \end{tikzpicture} \end{document}   UPDATE: A slightly shorter version of the second solution in the answer by @Matthew Leingang:  \documentclass{standalone}  \usepackage{pgfplots} \usepackage{pgfplotstable} % For \pgfplotstableread \pgfplotsset{compat=1.10}  \pgfplotstableread{ 0.01    1.00 0.011   2.00 0.012   3.00 0.013    4.00 0.05    5.00 }\datatable % \pgfplotstableread{results.dat}\datatable  \pgfplotstablegetrowsof{\datatable} \pgfmathsetmacro{\N}{\pgfplotsretval}    \begin{document} \begin{tikzpicture} \begin{axis}[ymin=0, ymax=6]   \addplot+[mark=none, forget plot] table {\datatable};   \addplot+[only marks] table  {\datatable}     % pos = (index-1)/(N-1)  (index starting from 1)     node[pos=(1-1)/(\N-1), pin=right:first point (1/\N)]{}     node[pos=(3-1)/(\N-1), pin=-45:third point (3/\N)]{}     node[pos=(4-1)/(\N-1), pin=-45:end of linear behaviour (4/\N)]{} ; \end{axis} \end{tikzpicture} \end{document}


if you write String s = new String ("abc"); two objects get created on is in non pool (heap) area and one is in common String pool (if it not exists. ) Suppose it creates two objects. Now when I create String literal String s1 ="abc"; Now according to me in string pool there is one string "abc" and has two reference s1 and s. so System.out.println(s==s1) it should give true but its giving false.. why??

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 came across this strange IndexOutOfRangeException exception. The code I am working with was originally a C code, I have managed to translate it to C#  So I the followin loop gives me the error:  for (int i = 0; i < 6; i++) {     L[0] = new double[]{ T[0] + rxp[0][i] - (p[0][i]) }   According to the 'Locals' tab, rxp has only 3 'children' with only 1 items / child.  So I guess the problem is here:  void getrxp() {     for (int i = 0; i < 6; i++)     {         rxp[0] = new double[]{ M[0][0] * (re[0][i]) + M[0][1] * (re[1][i]) + M[0][2] * 0};         rxp[1] = new double[]{ M[1][0] * (re[0][i]) + M[1][1] * (re[1][i]) + M[1][2] * 0};         rxp[2] = new double[]{ M[2][0] * (re[0][i]) + M[2][1] * (re[1][i]) + M[2][2] * 0};     } }   Am I getting this to to create a double rxp[3][6]; array wrong or there is something else?   The original code looks like this (C):  void getrxp() {   for(int i=0;i<6;i++){     rxp[0][i] = M[0][0]*(re[0][i])+M[0][1]*(re[1][i])+M[0][2]*0;     rxp[1][i] = M[1][0]*(re[0][i])+M[1][1]*(re[1][i])+M[1][2]*0;     rxp[2][i] = M[2][0]*(re[0][i])+M[2][1]*(re[1][i])+M[2][2]*0;     } }

I'm trying to create an array of arrays that will be using repeated data, something like below:  int[] list1 = new int[4] { 1, 2, 3, 4 }; int[] list2 = new int[4] { 5, 6, 7, 8 }; int[] list3 = new int[4] { 1, 3, 2, 1 }; int[] list4 = new int[4] { 5, 4, 3, 2 };  int[,] lists = new int[4, 4] {  list1 ,  list2 ,  list3 ,  list4  };   I can't get it to work and so I'm wondering if I'm approaching this wrong.   What I'm attempting to do is create some sort of method to create a long list of the values so I can process them in a specific order, repeatedly. Something like,  int[,] lists = new int[90,4] { list1, list1, list3, list1, list2, (and so on)};  for (int i = 0; i < 90; ++i) {    doStuff(lists[i]); }   and have the arrays passed to doStuff() in order. Am I going about this entirely wrong, or am I missing something for creating the array of arrays?


Someone has taken a copy of my passport and other identification.  Does that mean it's possible for someone to steal my identity?

In one of the questions on this site, it was suggested the use of  to save a backup copy of your passport, in case you need to proof who you are if your original document is lost.   I like the idea, but what if someone gets access to your Dropbox folders and is able to acquire the copy of your passport.  The same goes for when you leave a copy of your passport at a hotel receptions desk. Once someone has the info printed on that copy, would that make it easier to steal your identity?


I want to send variable from source to host, and exec host script. Here is my code :   var1=1 ssh -p 42 root@xxx /bin/bash << EOF   var2=2   echo $var1   echo $var2 EOF   Return : 1  var1=1 ssh -p 42 root@xxx /bin/bash << \EOF   var2=2   echo $var1   echo $var2 EOF   Return : 2  How to return :  1 2   ?

When executing this bash script, it only shows my local path.  ssh ${REMOTE_HOST} 'bash -s' <<EOL     set -e     source ~/.profile     echo $PATH     # Commands here don't work because $PATH is not set properly.     # How can I see what $PATH is set to here? EOL   How can I view the remote value of $PATH to debug this?


This was on my combinatorics exam. I definitely didn't answer it correctly, but I'll explain what I did.  Mary has to go to work or some bs. She needs to travel 6 blocks east and 7 blocks north. How many different routes can she take? Honestly, Mary, pick one route and stick to it. You don't need to know all the different ways you can walk to the same place.  Then they throw a wrench in the gears and tell you she has to go 2 blocks east and 4 blocks north first before she takes her daughter to preschool, and then go to work. How many ways can she do this?   First I tried 13! which seemed too large. Then I started thinking like a decision tree. I tried to imagine the scale of the tree in considering my answer. I was somehow led to thinking in terms of binary decisions. So I ended up writing $2^{13}$ because I figured she had 2 decisions to make at each block, but clearly, that's just not true. By my incorrect logic, she could go north 13 times.

I am not sure how to approach this problem.  Every day, a dance student walks from her home to dance-school, which is located $12$ blocks east and $16$ blocks north from home. She always takes the shortest walk of $28$ blocks.  $a$) How many different walks are possible?  $b$) Suppose that $5$ blocks east and $6$ blocks north of her home lives her dance friend, whom she meets each day on her way to dance school. Now how many walks are possible?  For $a$ I was thinking $P(28,12)\cdot P(28,16)$, but not sure if that would work because you can't walk the furthest block north before the closest block north.  And for $b$ I'm not really sure where to start.


Is there any regex to get the alt attribute? Example: <img src="http://static.adzerk.net/Advertisers/a61df59863ed44e59446d0b9bb805c56.jpg" title="" alt="blahblah" border="0" height="90" width="728">   I want to get the "blahblah" from above image tag.

I would like to create a page where all images which reside on my website are listed with title and alternative representation.  I already wrote me a little program to find and load all HTML files, but now I am stuck at how to extract src, title and alt from this HTML:  <img src="/image/fluffybunny.jpg" title="Harvey the bunny" alt="a cute little fluffy bunny" />  I guess this should be done with some regex, but since the order of the tags may vary, and I need all of them, I don't really know how to parse this in an elegant way (I could do it the hard char by char way, but that's painful).


Me and Energy      I'm trying to move along with my study of non-advanced physics but not grasping what energy really is, is driving me nuts.  Whenever i see anything about energy ( Kinetic, Potential, Energy in light ) i don't precisely understand what it is talking about and I can't move forward.     Begins of Understanding  After searching in  and reading a Feynman's article I was able to have a basic idea of what energy is about.         Given we determine a physical system ( a portion of the universe ), there is a quantity associated with that physical system at each instant of time that we call energy. If the physical system is isolated, that quantity shall be conserved as time passes ( Law of Conservation of Energy ).     Also, that specific quantity ( called energy ) is the sum of a set of other quantities, each of which related to mutually exclusive ( else, the sum of the quantities would be less or more than the total energy ) characteristics of the isolated physical system ( each one corresponds to a different energy form and we have formulas to calculate them ).       Doubts, many doubts But i'm still far away from grasping it.     1 - Do we have a well-defined set of mutually exclusive energy forms for each physical system, such that their sum corresponds to the total energy of the system ?      What are them, exactly ?    More detailed explanation about Doubt 1 I can read about many kinds of forms ( chemical, thermal, nuclear, electric, kinnetic, potential, mass, light, etc,etc ) but this tells me nothing about the well-defined set of mutually exclusive energy forms.     For instance, the listed ones are certainly not mutually exclusive, afterall we could just see thermal energy as a mixture of kinnetic energy ( sensible thermal energy ) and potential energy ( latent thermal energy ). Same thing for chemical and nuclear ( a kind of potential energy at the atomic-level ).    We could even extrapolate that for mass ( a kind of potential energy inside the nucleons ). In the end, almost all kinds of energy form could be viewed as Kinnetic ( related to the system's motion ) and Potential ( related to the position of the system within a force field ) , but what about light ? Are kinnetic and Potential energy forms applied to things which are always matter , so light is not included ? How does light fits in the picture of energy of physical systems, which are decomposable into mutually exclusive energy forms ?        2 - I talked so much about Physical systems but this was because i needed to refer somehow to the thing WHICH posseses energy. The problem is that i don't really know what a physical system exactly represents.Defining it as a portion of the universe ( as Wikipedia defines it ) , tells little about what it is.  Is "portion" refering to specific matter in the universe ( which might occupy different regions of the space, along of time ), or is "portion" refering to specific volume in the space-time of the universe ?   What about light ? Is it a physical system ? It better be, afterall it posses energy.        There it is ... all my doubts that are driving me crazy understanding energy.       I don't expect to fully solve the problem of defining what energy is, i just want to have a solid understanding of what people are talking about when they mention energy.      Some clarification, or suggestion of materials to read would be imensely helpful.

The simplistic undergrad explanation aside, I've never really understood what energy really is. I've been told that it's something when converted from one kind of something to another kind, or does some "work", as defined by us, but what is that something?  Moreover, if the total amount of energy in the universe is finite and we cannot create energy. Then, where did it come from? I've learned from thermodynamics where it goes, but where does it come from?  I know this sounds like something trivially simple, but there is so much going on in the physical universe and I just can't grasp what it is. Maybe it is because I lack the mathematical understanding that I can't grasp the subtle things the universe is doing. Still, I want to understand what it is doing.  How do I get to the point of understanding what it's doing?  (Note: What prompted me to ask this was . I'm afraid that it just puzzled me further and I sat there staring at the screen for a good 10 minutes.)


After a lengthy period of editing in  and finally getting it right, the OP accepted my answer        However, my activity list then showed the following entry:        which is kind of disappointing. These are probably my hardest earned 0 points so far. ;-)  My votes activity list does not show any sign of my own voting on that post:        Does anyone know what went wrong, or rather, what I did wrong?

Some questions and answers are marked Community Wiki and are owned by a community wiki user:  (In fact, this very question is one of them)  Why have Community Wiki posts? How do Community Wiki posts work? How does a post become a Community Wiki post? How can the Community Wiki status be removed from a post? How can I find Community Wiki posts?


I have a dual entry schengen visa. I want to go to Croatia first and then Italy (for which i have the schengen visa) and leave to home country after that. Is it possible to land into Croatia first using the dual entry schengen visa?  Apology for reposting but the answer was not clear from previous responses on post:

I am an Indian citizen and will be traveling to Croatia in a few days. I already have a multiple entry Schengen visa which is valid for the dates of my Croatia trip. However, my first destination from India will be Dubrovnik (Croatia) and after that I will depart for Schengen area (Austria).  Would I be able to enter Croatia before entering the Schengen zone?


So I'm a first time Latex learner and I'm still learning the roots, but I want to do something similar to the example given in the picture.

How do I produce a conditional expression with large brackets? For example: X = 0 if a=1, 1 otherwise, with a large left bracket and specifying each condition in a line?


I am trying to show that for any two real $X,Y$ iid there holds that   $$ P(|X - Y| \le 2) \leq 3P(|X - Y| \le 1) $$  I am getting nowhere with this and so I did some digging and found the following reference that proves a more general result:    However the special case that I am trying to show is just an exercise in a book that I am working through, so I suspect there must be a simpler proof for it. Also I would like to do it from first principles if possible rather then quoting a bigger result and say it's a special case.

Doing a little reading over the break (The Probabilistic Method by Alon and Spencer); can't come up with the solution for this seemingly simple (and perhaps even a little surprising?) result:     (A-S 1.6.3) Prove that for every two independent identically distributed real random variables $X$ and $Y$,   $$Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1].$$


i have a pyton script that execute with python script.py when you are in the same folder.   I want to know if it's possible to make a bash alias like alias script='command' to execute the script also when you are outside the same folder than the script?  thx

It's taken me almost 10 years of Linux usage to ask this question. It was all trial and error and random late-night internet surfing.  But people shouldn't need 10 years for this. If I were just starting out with Linux, I'd want to know: When to alias, when to script, and when to write a function?  Where aliases are concerned, I use aliases for very simple operations that don't take arguments.   alias houston='cd /home/username/.scripts/'   That seems obvious. But some people do this:  alias command="bash bashscriptname"   (and add it to the .bashrc file)   Is there a good reason to do that? I'm trying really hard, but I genuinely can't think of any circumstances in which I'd want to do that. So, if there is an edge case where that would make a difference, please answer below.  Because that's where I would just put something in my PATH and chmod +x it, which is another thing that came after years of Linux trial-and-error.  Which brings me to the next topic. For instance, I added a hidden folder (.scripts/) in the home directory to my PATH by just adding a line to my .bashrc (PATH=$PATH:/home/username/.scripts/), so anything executable in there automagically autocompletes.  If I needed to.  I don't really need that, though, do I? I would only use that for languages that are not the shell, like Python.  If it's the shell, I can just write a function inside the very same .bashrc:  funcname () {   somecommand -someARGS "$@" }   As I stated, I found a lot of this out through trial and error. And I only truly saw the beauty of functions when my computer died and I was forced to use the computers of the people around me when they weren't using them.   Instead of moving a whole directory of scripts from computer to computer, I ended up just replacing everyone else's .bashrc with my own, since they had never even made a single modification.  But did I miss anything?   So, what would you tell a beginning Linux user about when to alias, when to script, and when to write a function?   If it's not obvious, I'm assuming the people who answer this will make use of all three options. If you only use aliases, or only use scripts, or only use functions—or if you only use aliases and scripts or aliases and functions or scripts and functions—this question isn't really aimed at you.


I had been making some icing for a donut when I started to notice these evenly spaced out indentations in the texture of my object. I'm not sure if it's the result of adding a subsurf modifier to my mesh or a bad sculpting job. It looks like the pockmarks are directly related to my mesh though.

I'm currently making a donut using blender gurus tutorial. I have no idea why, but there are holes in my icing. Does anyone know what could be causing it? Thanks for any help.


When is $Aut\left(\mathbb{Z}_n\right)$ cyclic?  Where $Aut \left( G \right)$ is the group of "Automorphisms of the group $G$" under composition.     I know that $Aut\left(\mathbb{Z}_n\right) \approx U\left(n\right)$ but I don't know when $U\left(n\right)$ is cyclic.

When can we say a multiplicative group of integers modulo $n$, i.e., $U_n$ is  cyclic?   $$U_n=\{a \in\mathbb  Z_n \mid \gcd(a,n)=1 \}$$  I searched the internet but did not get a clear idea.


I am studying differential equations right now and I am confused the way $dx$ is being used.  When I learnt calculus I thought that $\frac{df}{dx}$ is just symbolic representation of derivative and we can't use it as a fraction. But when it comes to differential equation like $y = \frac{df}{dx}$ they do the following:  $$ydx = df$$  $$\int ydx = f$$  And then again I was taught that $dx$ in integral has no meaning but only convenient way to represent integral.  I am totally fine with the intuition why they do that, I can imagine $\frac{df}{dx}$ meaning small change in $f$ divided by small change in $x$ and integral meaning sum of recatngles of width $dx$ and height $f$, but what I lack is rigorous transition from $\frac{df}{dx}$ meaning just a symbolic representation of derivative to the state where we can algebraically manipulate it as a fraction. Could you please help me with that or suggest some reading?  Also, could you please recommend me some books on differential equations that teach intuition behind the equations?

I see an equation like this:  $$y\frac{\textrm{d}y}{\textrm{d}x} = e^x$$  and solve it by "separating variables" like this:  $$y\textrm{d}y = e^x\textrm{d}x$$ $$\int y\textrm{d}y = \int e^x\textrm{d}x$$ $$y^2/2  = e^x + c$$  What am I doing when I solve an equation this way?  Because $\textrm{d}y/\textrm{d}x$ actually means  $$\lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}$$  they are not really separate entities I can multiply around algebraically.    I can check the solution when I'm done this procedure, and I've never run into problems with it.  Nonetheless, what is the justification behind it?  What I thought of to do in this particular case is write  $$\int y \frac{\textrm{d}y}{\textrm{d}x}\textrm{d}x = \int e^x\textrm{d}x$$ $$\int \frac{\textrm{d}}{\textrm{d}x}(y^2/2)\textrm{d}x = e^x + c$$  then by the fundamental theorem of calculus  $$y^2/2 = e^x + c$$  Is this correct?  Will such a procedure work every time I can find a way to separate variables?


So maybe I'm reading this wrong, but my moon druid just hit level 20 and the ability seems completely over the top compared to other classes level 20 feature. Unlimited beast shapes? Am I interpreting this incorrectly? Can I really just turn into animals or even elementals (Level 10 Elemental Wild shape) AND EVEN CAST SPELLS (Level 18 Beast spell) ??   My DM for this game hates this and is trying to limit my uses to 10 per long rest, which is fine, but without this homebrew rule in place can I just make myself a meat shield and keep beast shaping into something with massive HP (e.g A giant crocodile) or even an Earth elemental every time I pop?

Page 67 of the PHB states that druids gain all the hit points of whatever creature they become when using Wild Shape, and when that shape drops to 0hp, only the excess damage carries over to the druid's original form.  Since archdruids (level 20) can use Wild Shape an unlimited number of times per day, and dismissing Wild Shape is a bonus action, could an archdruid just keep transforming into a high-HP Earth elemental over and over during a battle?    If they get near 0hp while in elemental form, they can dismiss it as a bonus action, then re-apply it as an action, all in one turn, and never take "excess damage", so their druid form would never be harmed.  Am I misunderstanding something about how hit points work between these forms, or is a level 20 Circle of the Moon druid virtually immune to all but the most insane damage spikes?


One of my friends loves puzzles-jigsaw, logic, pretty much anything. He is also addicted to reading murder mysteries and tries to figure out who killed the guy. Basically, he enjoys working things out with his own brain.  What word can I use to describe him?

What is a term or name for someone who is very adept at solving puzzles or situations that require though processing and logic.   I ran across , however this only deals with crossword puzzles. I'm looking for something that could be applied on a broader sense.


For a source with electromotive power $E$  with internal resistance $ r $ connected in series with a resistor $ R $, we have: $I = \frac{E}{r+R}$. Is there any mathematical development that describes the current value when the connection is made in parallel? As well as for which $R$ value the current and the dissipated power is maximum. I found in the books only deductions for when the connection is made in series.

I have the following homework problem.  Consider a power supply with fixed emf $ε$ and internal resistance $r$ causing current in a load resistance $R$. In this problem, $R$ is fixed and $r$ is a variable. The efficiency is defined as the energy delivered to the load divided by the energy delivered by the emf.  When the internal resistance is adjusted for maximum power transfer, what is the efficiency?  The answer is 50% but I'm confused how this is calculated. Here is my thought process so far.  The power dissipated in the load is $I^2R$ and $\displaystyle I = \frac{ε}{r+R}$ so $\displaystyle P = \frac{ε^2R}{(r+R)^2} = \frac{ε^2}{\frac{r^2}{R} + 2r + R}$ and so power transferred to the load will be maximum when $\displaystyle \frac{r^2}{R} + 2r + R$ is a minimum. Taking the first derivative $\displaystyle \frac {d}{dr}(\frac {r^2}{R} + 2r + R) = (\frac{2r}{R} + 2)$ and this equals 0 when r = -R. The second derivative is $\displaystyle \frac{2}{R} > 0$ so this point would be a minimum and therefore max power transferred when r = -R.  But having $r = -R$ doesn't make sense to me. From what I read, for maximum power transfer $r$ should equal $+R$. So I've probably done something wrong in my calculations or assumptions in the previous paragraph. Also wouldn't max power be transferred when the internal resistance is as close to zero as possible?  Can someone please show me a proof that shows why $r = R$ for max power transfer and then how to calculate the efficiency.


The Problem  I made a "Type Ahead" search feature in Javascript that returns results that match what you are typing. The search results are returned as list items (with links) and are added to the DOM, but the links do not open up on the first click, and they did not show up when I tested a mouseenter eventlistener function that logs elements you enter on the page. I thought the problem might be with z-index, but I set both the li and a to a higher index and that didn't help.    const arr = ['pink', 'blue', 'green', 'purple'];  function findMatches(wordToMatch, arr) {   return arr.filter(item => {     const regex = new RegExp(wordToMatch, 'gi');     return item.match(regex);   }); }  function displayArr() {   const matchArray = findMatches(this.value, arr)   const html = matchArray.map(item => {     const regex = new RegExp(this.value, 'gi');     const itemName = item.replace(regex, `<span class='hl'>${this.value}</span>`);     return `       <li>        <span class='name'>${itemName}</span>       </li>       `;   }).join('');   suggestions.innerHTML = html; }  const searchInput = document.querySelector('.search'); const suggestions = document.querySelector('.suggestions');  searchInput.addEventListener('keyup', displayArr);  //check for element const all = document.querySelectorAll('a, ul, li, span, form, input');  function logElement(e) {   console.log(e.target); }  all.forEach(a => a.addEventListener('mouseenter', logElement)); <form class="search-form">   <input type="text" class="search" placeholder="Search">

 </form>     As you'll see, the lowest element you can get to is the ul I'm not sure if this is a CSS or JS problem.  Thank you in advance for your help.

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.


My question concerns the problem of 'the square-sum problem' which is described in details in this video:  On this video is told  that a series of sequential numbers from 1 to 15 we can rearrange in such a way that the sum of two neighboring ones will be an perfect square. Here is a solution  {9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 1, 8}. That is not the only number with this property. The question goes like 'does there exist the biggest  N with these properties. If there is not, how to prove it?'. P.s. excuse for my not-inteligence on this comment, i'm not a student, i'm just a scholar who spent his time dealing with math and thus i don't have a perfect english and i may translate some verbs in not appropriate way. I  need your help,hope you understand the statement correctly, thanks for your attention!!!!


I executed this command from terminal:  export PATH=/home/ravinder/Java_Folder/Important_Programs/Servers/apache-maven-3.2.2/bin   So this is the only directory in my $PATH, I want to restore my path to default.

I accidentally unset all the directories of $PATH while trying to add a new one in ~/.bashrc. I opened a new terminal window as I was editing and now $PATH is empty. I'm worried if I boot from another drive to find the $PATH I won't be able to boot into this drive again.  Basically, what is the default result of echo $PATH?


Suppose we are given a set of equations of motion for $N$ bodies, which generically will go like this  \begin{equation} \frac{d^2\mathbf{r}_i}{dt^2}=\mathbf{F}_i \left((\mathbf{r}_i)_{1 \leq i \leq N}, (\frac{d \mathbf{r}_i}{dt})_{1 \leq i \leq N}, (\frac{d^2 \mathbf{r}_i}{dt^2})_{1 \leq i \leq N} \right) \end{equation} $\mathbf{r}_i$ is the position of body $i$ and $\mathbf{F}_i$ is just the sum of all the generalized force terms acting on it. $\mathbf{F}_i$ could depend on the positions $\mathbf{r}_i$ and velocities $\frac{d \mathbf{r}_i}{d t}$ of any of the other bodies, but also on powers of position and velocity, and even terms involving acceleration.   The question is: If we know $\mathbf{F}_i$, how can we know if this equations of motion can be derived from a lagrangian? Is there a systematic way to check that? Is there a systematic way of getting said lagrangian?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following:      If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always exists an action functional $A$, where    $$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$    such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?    I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all.


A friend of mine has this statement, that I cannot establish wether it is true or false.  Let us consider $\mathbb{R}$ with the euclidean topology. Let us consider $A \subset \mathbb{R}$ such as the topology induced on it is the discrete topology, so $A$ is numerable.  Actually he states that the statement holds whenever $A$ is closed, but I ignore his proof.   I tried to demonstrate, recreating something like the Cantor set, that it is false proved that there exists a non separable set $A$ with that induced topology, but I cannot prove the existence of such $A$.  With discrete topology I mean that for every $x \in A$ there exists an open neighborhood of $x$, that I'll call $I(x)$ such that $I(x) \cap A = {x} $.  Any suggestions?

Does an uncountable and discrete subspace of the reals exist?


I am studying digital electronics. A book says that "use a 0.1 μF capacitor between Vcc and ground for each IC".  What does this mean?  Why can a capacitor protect CMOS chips?  Does it mean that a capacitor should be added like in the figure?  update (7/21/2016): okay, maybe I was confused with the meaning. A chapter of the book was talking about static protection for CMOS chips and for an experiment it mentioned the quotation with a footnote.  The footnote says, "In keeping with standard practice, capacitors are specified, particularly with CMOS devices, to return switching current 'spikes' to the source through the shortest possible path"  So, I thought a capacitor should be used to "PROTECT" CMOS chips.   As I said, I am studying digital electronics. I don't know about decoupling capacitors. So still I don't know if my question is duplicate :(         – Schematic created using

What is a decoupling capacitor (or smoothing capacitor as referred to in the link below)?  How do I know if I need one and if so, what size and where it needs to go?    mentions many chips needing one between VCC and GND; how do I know if a specific chip is one?   Would an  4-bit parallel access shift register used with an Arduino need one? (To use my current project as an example) Why or why not?  I feel like I'm starting to understand the basics of resistors and some places they're used, what values should be used in said places, etc, and I'd like to understand capacitors at the basic level as well.


This is an etiquette and maybe even rules question.   I take the questions I ask seriously over at StackExchange. I form my question in an editor, I check for clarity and make edits, I take care to present my code nicely. I adhere to the idea that doing all that is like talking to the stuffed frog in the corner of the IT office analogy; I often see my own answer in my work while creating a conscientious question. I even wait to post it, and when I'm ready, it's like handing in a formal essay to me, like for grades.  The point is, it's enough of a big deal to me, and a rarity that I even post a question, that (and here's where I get to my point) ... that I stick around for five minutes, at least, me longer ... to see if anyone immediatey engages my question.  So, today ... a first time user, first question from them ever at stackexchange ... drops their fairly advanced question, upon which I engaged almost immediately. I found them an answer on the stack, and posted. I decided to explore the answer myself because I'm working with similar stuff myself, so was interested ... but did from the context of solving their problem.  I find that old answer has not just deprecated parts, but methods that don't even exist in the dependency anymore. So ... and this is now four hours later ... I post that the original answer is not cutting it, take a different path, and post the first time questioner my full code of how I do what they are trying, through a different approach.  Four hours later ... and not once had the asker engaged me. They walked across the office ... asked for help ... and while I engaged their problem, they promptly excused themselves and went for coffee. Just as I sat down and started to help them with their code. My first response was almost immediate. Four hours later, and more engaging ... first time questioner ... and silence. Nothing.  Four hours later ... in a void of silence ... I removed all my posts and code from over the four hours.  It may not be a rule ... but, as a social user, I reserve the right to take note of someone who does that; drops and leaves. I take my questions on stack exchange more seriously than that. So, I removed my answers.  What's the etiquette? What's the rule? (The two may not be the same, rule and etiquette.)

I often answer questions and wait to see if it meets the OP's requirements. Sometimes, it seems people will ask a question and not check on it until the next day.  Am I wrong to expect OPs to check on their questions when they just asked it?   Mmm... I should have left the question alone for a day or so, just for the fun of it :p


I need help using induction on a recursive sequence.  Given $S_{1}=2$ and $S_{n+1}= \frac{S_{n}}{2} + \frac{1}{S_{n}}$  I am working on the recursive convergence to $\sqrt{2}$, therefore I want to show that it is bounded below by an arbitrary lower bound, in which I chose 1. thus by induction I want to show that $S_{n+1} > 1$, $$ S_{n} > 1$$ $$\frac{1}{S_{n}} < 1$$ $$S_n +\frac{1}{S_{n}} > ?+1$$  I get stuck here. Im not to sure how to get to my end point of $S_{n+1}$.

Suppose that $S_0$ and A are positive numbers, let $$S_{n+1} = \frac{1}{2}\left(S_n +\frac{A}{S_n}\right)$$ with $n \geq 0 $.      (a)Show that $S_{n+1} \geq \sqrt{A} $ if $n \geq 0$       (b)Show that $S_{n+1} \leq S_n $ , if $n \geq 1$      (c) Show that $s= \lim\limits_{n \rightarrow \infty} S_n$ exists      (d) find s   (a) Show that $S_{n+1} \geq \sqrt{A} $ if $n \geq 0$  Given $$P_n:  S_{n+1} = \frac{1}{2}\left(S_n +\frac{A}{S_n}\right) \geq \sqrt{A}$$  $$P_0: S_{1} = \frac{1}{2}\left(S_0 +\frac{A}{S_0}\right) \geq \sqrt{A}  $$  We assume that $P_n$ is true  $$P_{n+1}: S_{n+2}= \frac{1}{2}\left(S_{n+1} +\frac{A}{S_{n+1}}\right)$$ by assumption $$S_{n+2}= \frac{1}{2}\left(S_{n+1}\left(1 +\frac{A}{(S_{n+1})^2}\right)\right) \geq \frac{1}{2}\left(\sqrt{A}\left(1 +\frac{A}{(\sqrt{A})^2}\right)\right)$$ $$ S_{n+2}= \frac{1}{2}\left(S_{n+1} +\frac{A}{S_{n+1}}\right) \geq \sqrt{A}  $$  It follows that $S_{n+1} \geq \sqrt{A} $    (b) Show that $S_{n+1} \leq S_n $ , if $n \geq 1$  $$S_{n+1} \leq S_n$$ $$\frac{1}{2}\left(S_n +\frac{A}{S_n}\right) \leq S_n $$ Dividing by $S_n$ $$\frac{1}{2}\left(1 +\frac{A}{S_n^2}\right) \leq 1 $$ $$\frac{A}{2S_n^2} \leq \frac{1}{2}$$ $$A \leq S_n^2$$ $$S_n \geq \sqrt{A}$$ As  $S_{n+1} \leq S_n$ yields a true statement, it follows $S_{n+1} \leq S_n$ is true.    (c) Show that $s= \lim\limits_{n \rightarrow \infty} S_n$ exists  Since $S_{n+1} \leq S_n$, the sequence is non-increasing,   using the non-increasing theorem stating that      if $\{S_n\}$ is non-increasing then $$\lim\limits_{n \rightarrow > \infty} S_n = \inf\{S_n\} $$     (d) find s    Is the argumentation in (a) and (b) appropriate? Also, I have to admit I m getting less confident in my argumentation (c) and (d). How to proceed in (c) and (d)?  Much appreciated for your input or help.


$a_n > 0$ and $\sum_\limits{n=1}^{+\infty} \frac{1}{a_n}$ converges. Prove $\sum_\limits{n=1}^{+\infty} \frac{n}{a_1 + \cdots + a_n}$ is convergent.  I find that this may have something to do with Stolz Theorem which says that if $\{\frac{1}{a_n}\}$ is convergent then  $$\lim_{n \rightarrow +\infty} \frac{n}{a_1+\cdots +a_n} = \lim_{n \rightarrow +\infty} \frac{1}{a_n}$$ This may implies that $\frac{n}{a_1+\cdots +a_n}$ and $\frac{1}{a_n}$ have the same declining speed so leads to the answer of the question.  However, I don't know how to turn this into correct proof.

Suppose $\sum_{n=1}^\infty \frac{1}{a_n} = A$ is summable, with $a_n > 0,$ $n = 1,2,3,\cdots.$ How can we prove that $\sum_{n=1}^\infty \frac{n}{a_1 + \dots + a_n}$ is also summable?  This question came from a problem-solving seminar, but I'm quite stuck without a push in the right direction. I tried a few things, including Cauchy-Schwarz (which says $\sum_{n=1}^\infty \frac{n}{a_1 + \dots + a_n} < \sum_{n=1}^\infty \frac{A}{n}$) and also the idea of assuming the latter series diverges and attempting to deduce the divergence of the former series from that, using facts such as $\sum a_n = \infty \implies \sum \frac{a_n}{a_1 + \cdots + a_n} = \infty$. Nothing has worked so far.


Today is the release of Ubuntu 21.04 (Hirsute Hippo). And I can't update to this version. And also I selected ‘Notify me of a new Ubuntu version’ and changed it to ‘For any new version' on the Updates tab on Software & Update, but it's still not working. In addition, in the terminal, I've written: sudo do-release-upgrade -c  And output was: Checking for a new Ubuntu release No new release found.  What should I do?

As you can see in the image above, I tried to update to 19.10 and it says that   No new release found   I checked the /etc/update-manager/release-upgrades to see if the Prompt is LTS but it is still normal.  What would be your advice?  UPDATE: I already updated the system to 19.10. Thank you very much for the advices.


One of the '?' characters in the Holiday Update is a jawa. What scene does he unlock?

No matter where I look, I haven't seen almost any indications of which characters unlock which scenes.    Put plainly: Which character/level combinations unlock a scene?


Consider a man rotating on a frictionless turntable , initially with his hands folded . When he opens his hands the moment of inertia increases and as the angular momentum is conserved the kinetic energy decreases. But energy is also conserved so where does this kinetic energy goes ?

The following quote comes from:      Consider an ice skater that has just gone into a spin with arms   stretched out.  If it helps, the skater is wearing lead bracelets on   each wrist.  As the skater spins, the angular momentum and angular   kinetic energy are constant;  friction with the air and with the ice   can be eliminated.  The skater must exert an inward centripetal force   on the bracelets to keep them rotating in the same circle, but this   force does no work, since the bracelets are not changing their radius   of rotation.      Then the skater pulls in his arms and the bracelets, closer to his   axis of rotation.      Several interrelated things happen:           since there is no external torque, the angular momentum of the system stays the same;   Since the various masses of the skater are all moving towards the axis of rotation, the total moment of inertia of the system   decreases;     Combining 1 and 2, the angular velocity of the system increases;  if the moment is halved, the angular velocity doubles   Combining 2 and 3, with some quantitative treatment, the angular kinetic energy increases;  if the moment is halved and the   angular velocity is doubled, the kinetic energy doubles;   The skater does work;  his arms are now exerting an inward force through a distance as his arms draw the bracelets inward;  the work done can be rigorously shown to be identical to the increase in   kinetic energy...      However, it only covers a case when work is done to pull arms inwards. It is understandable that the work would be done in such case.  But what is happening in the opposite case when the skater has their arms inwards and lets them go outwards? S/he doesn't do any work but kinetic energy (and total energy) is lost. Why is it lost?  E.g.  I = 2kg * (1m)^2 w = 3.14/s L = 2kg * m^2 * 3.14/s Ek = 9.869  After shifting 2kg by 0.1m outwards: I = 2kg * (1.1m)^2 = 2.42 kg * m^2 L = 2 * 3.14 = 2.42 * w w = 2.5963 Ek = 8.1566   So, where did 1.7124 J go?  The quoted answer describes the easy case and omits the hard one.


Can someone help on this. I'm stuck on this part. I am trying to find a permutation $\sigma$ such that $$\sigma(1,2)(3,4)\sigma^{-1} = (5,6)(3,1)$$. By a particular theorem, I know I can have this one $$ \sigma (1,2)\sigma^{-1}\cdot \sigma(3,4)\sigma^{-1} =(5,6)(3,1)$$Then, $$(\sigma(1) , \sigma(2)) = (5,6) $$ and $$(\sigma(3) , \sigma(4)) = (3,1) $$ Am I right on doing this? $$\sigma(1) = 5 \qquad \mbox{and} \qquad \sigma(2)=6$$ and $$\sigma(3) = 3 \qquad \mbox{and} \qquad \sigma(4)=1$$ I don't really know what to do next. I thought of making them as one permutation but it doesn't really makes sense to me. Please help.

In $S_n$ with n=10, find a permutation $a$ such that $axa^{-1} = y$ if $x=(1,2)(3,4)$ and $y=(5,6)(3,1)$  I don't know how to start doing this. I read something like I need to get, for this case, $$(a(1),a(2)) \qquad \mbox{ and} \qquad (a(3),a(4))$$ but I am not sure where will I get their equivalents. Also, will those be my permutation $a$? Please help. I have problems very similar to this.


I suppose that the #container will be centered within #main_content. However, it is not. Why isn't this working, and how can I fix it?   #main_content {   top: 160px;   left: 160px;   width: 800px;   min-height: 500px;   height: auto;   background-color: #2185C5;   position: relative; }  #container {   width: auto;   height: auto;   margin: 0 auto;   padding: 10px;   position: relative; }

How can I horizontally center a
 within another
 using CSS?

Foo foo


Using HTML5 canvas where would be the best place to start to move my 3 balls in random trajectories (along a smooth line, no jumping) and when they hit each other bounce away and then go on another path, until again they hit each other and again bounce away.  So far I have set up a simple example on   where each ball follows its own path (though they do disappear off the screen).  At the moment the trajectory is as simple as   function animate(){    // Yellow Circle   circles[0].x+=1;   circles[0].y+=-1.5;    // Blue Cirlce   circles[1].x+=-1;   circles[1].y+=-1.5;    // Red Circle   circles[2].x+=1;   circles[2].y+=-1;   draw();   }   I would love to see an example, but also to know what methods and calculations I should be looking at.

With the help of the Stack Overflow community I've written a pretty basic-but fun physics simulator.    You click and drag the mouse to launch a ball.  It will bounce around and eventually stop on the "floor".  My next big feature I want to add in is ball to ball collision.  The ball's movement is broken up into a x and y speed vector.  I have gravity (small reduction of the y vector each step), I have friction (small reduction of both vectors each collision with a wall). The balls honestly move around in a surprisingly realistic way.  I guess my question has two parts:   What is the best method to detect ball to ball collision? Do I just have an O(n^2) loop that iterates over each ball and checks every other ball to see if it's radius overlaps? What equations do I use to handle the ball to ball collisions? Physics 101 How does it effect the two balls speed x/y vectors?  What is the resulting direction the two balls head off in?  How do I apply this to each ball?     Handling the collision detection of the "walls" and the resulting vector changes were easy but I see more complications with ball-ball collisions.  With walls I simply had to take the negative of the appropriate x or y vector and off it would go in the correct direction.  With balls I don't think it is that way.  Some quick clarifications: for simplicity I'm ok with a perfectly elastic collision for now, also all my balls have the same mass right now, but I might change that in the future.    Edit: Resources I have found useful  2d Ball physics with vectors:  2d Ball collision detection example:     Success!  I have the ball collision detection and response working great!  Relevant code:  Collision Detection:  for (int i = 0; i < ballCount; i++)   {       for (int j = i + 1; j < ballCount; j++)       {           if (balls[i].colliding(balls[j]))           {             balls[i].resolveCollision(balls[j]);         }     } }   This will check for collisions between every ball but skip redundant checks (if you have to check if ball 1 collides with ball 2 then you don't need to check if ball 2 collides with ball 1.  Also, it skips checking for collisions with itself).  Then, in my ball class I have my colliding() and resolveCollision() methods:  public boolean colliding(Ball ball) {     float xd = position.getX() - ball.position.getX();     float yd = position.getY() - ball.position.getY();      float sumRadius = getRadius() + ball.getRadius();     float sqrRadius = sumRadius * sumRadius;      float distSqr = (xd * xd) + (yd * yd);      if (distSqr <= sqrRadius)     {         return true;     }      return false; }  public void resolveCollision(Ball ball) {     // get the mtd     Vector2d delta = (position.subtract(ball.position));     float d = delta.getLength();     // minimum translation distance to push balls apart after intersecting     Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d);        // resolve intersection --     // inverse mass quantities     float im1 = 1 / getMass();      float im2 = 1 / ball.getMass();      // push-pull them apart based off their mass     position = position.add(mtd.multiply(im1 / (im1 + im2)));     ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2)));      // impact speed     Vector2d v = (this.velocity.subtract(ball.velocity));     float vn = v.dot(mtd.normalize());      // sphere intersecting but moving away from each other already     if (vn > 0.0f) return;      // collision impulse     float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2);     Vector2d impulse = mtd.normalize().multiply(i);      // change in momentum     this.velocity = this.velocity.add(impulse.multiply(im1));     ball.velocity = ball.velocity.subtract(impulse.multiply(im2));  }   Source Code:     If anyone has some suggestions for how to improve this basic physics simulator let me know!  One thing I have yet to add is angular momentum so the balls will roll more realistically.  Any other suggestions?  Leave a comment!


Show that if $\mathbb{R}^n=W_1\bigcup W_2\bigcup\ldots\bigcup W_k\bigcup\ldots$, where each $W_k$ is a subspace , then $\mathbb{R}^n=W_i$ for some $i$.

I know if $W_1,\ldots,W_k$ are subspaces of a vector space, their sum is the span of their union. ie. $W_1+W_2+\cdots+W_k=W_1\cup W_2\cup \cdots \cup W_k$. But how to prove $\Bbb R^n=W_i$ holds for some $i$? Is there anything to do with direct sum? Because if $\Bbb R^n$ is the direct sum of $W_1+W_2+\cdots+W_k\iff$ the sum of the dimensions of the $W_i$ is $n$.


I've been reading more about linear regression and the assumptions it makes.  What are the consequences of violating some of the assumptions involved?  For instance, you need the dataset to exhibit little or no multicollinearity.  What happens if I ignore this?  For instance, suppose I have a dataset where x_3 and x_4 are just duplicates of each other (and thus perfectly correlated).  The only difference I can see is that, instead of having one line of best fit, I can now have infinite:  E.g. if the line of best fit without x_4 had Bx_3 in it, then I can just distribute B amongst x_3 and x_4.  So if B = 5, I could do 4x_3 + x_4 or 3.5x_3 + 1.5x_4, etc.  So, it seems like:  1) Maybe it's not disastrous to violate the multicollinearity assumption?  2) Is it much worse to violate the others / if so, what are the consequences of doing so?  Thanks!

What are the usual assumptions for linear regression?   Do they include:   a linear relationship between the independent and dependent variable independent errors normal distribution of errors homoscedasticity   Are there any others?


I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on Manifolds for me on the side.  I do like mathematical rigor, and I'd like a textbook that focuses on this aspect. Having said that, I'm ideally looking for a textbook that won't keep me densely involved with it; rather a textbook that I could hopefully juggle with the textbook on GR as well.  I looked for example at Lee's textbook but it seemed too advanced. I have done courses on Single and Multivariable Calculus, Linear Algebra, Analysis I and II and Topology but I'm not sure what book would be the most useful for me given that I have a knack of seeing all results formally.  Note: I am a student of physics with a mathematical leaning.

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would   Prove all theorems used. Use modern "mathematical notation" as opposed to "physics notation", especially with respect to linear algebra and differential geometry. Have examples that illustrate both computational and theoretical aspects. Have a range of exercises with varying degrees of difficulty, with answers.   An ideal text would read a lot more like a math book than a physics book and would demand few prerequisites in physics. Bottom line is that I would like a book that provides an axiomatic development of general relativity clearly and with mathematical precision works out the details of the theory.  Addendum (1): I did not intend to start a war over notation. As I said in one of the comments below, I think indicial notation together with the summation convention is very useful. The coordinate-free approach has its uses as well and I see no reason why the two can't peacefully coexist. What I meant by "mathematics notation" vs. "physics notation" is the following: Consider, as an example, one of the leading texts on smooth manifolds, John Lee's Introduction to Smooth Manifolds. I am very accustomed to this notation and it very similar to the notation used by Tu's Introduction to Manifolds, for instance, and other popular texts on differential geometry. On the other hand, take Frankel's Geometry of Physics. Now, this is a nice book but it is very difficult for me to follow it because 1) Lack of proofs and 2)the notation does not agree with other math texts that I'm accustomed to. Of course, there are commonalities but enough is different that I find it really annoying to try to translate between the two...  Addendum (2):  For the benefit of future readers, In addition to suggestions below, I have found another text that also closely-aligns with the criteria I stated above. It is, Spacetime: Foundations of General Relativity and Differential Geometry by Marcus Kriele. The author begins by discussing affine geometry, analysis on manifolds, multilinear algebra and other underpinnings and leads into general relativity at roughly the midpoint of the text. The notation is also fairly consistent with the books on differential geometry I mentioned above.


In one of the labs for learning Linux system administrator I have to do :   Now change the value by modifying /etc/sysctl.conf and force the system to activate this setting file without a reboot. Check that this worked properly.   here is what i must do:     Add the following line to /etc/sysctl.conf:  net.ipv4.icmp_echo_ignore_all=1       and then do:  $ sysctl -p    how to do this and with which text editor?

I can't seem to edit and save config files in the root system (eg: /etc/dhcp/dhcpd.config); it just says "permission denied" or the save option is blocked in the text editor.  I'm pretty sure I'm a root user, but how do I make sure? If I am a root user, how do I fix this?


I am an Indian citizen having a valid multiple entry Schengen visa and want to travel from Delhi to Mexico via Amsterdam. I will stay in Mexico for 3 days & will head towards Paris. Do I need a Mexican visa or only a Schengen visa?

I have a valid Schengen visa in my Vietnamese passport. Can I use a Schengen Visa (Tourism) to visit Mexico ?


EDITED: I got a script running with a cronjob every day at 1 am: 0 1 * * * /bin/bash /home/performanceRatio.sh  It also appears in the cron.log: Feb  2 01:00:01 inf-education-67 CRON[108963]: (root) CMD (bash performanceRatio.sh) Feb  2 01:00:01 inf-education-67 CRON[108962]: (CRON) info (No MTA installed, discarding output)  Expected behavior is to update a mysql database. Changes appear if it's run manually. Using Ubuntu 20.04 My script looks like: #!/bin/bash PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin  python3 get_weather_data_crn.py && python3 pv.py  * * * * * env > /tmp/env.output shows: HOME=/root LOGNAME=root PATH=/usr/bin:/bin LANG=de_DE.UTF-8 SHELL=/bin/sh PWD=/root

Often, crontab scripts are not executed on schedule or as expected. There are numerous reasons for that:   wrong crontab notation permissions problem environment variables   This community wiki aims to aggregate the top reasons for crontab scripts not being executed as expected. Write each reason in a separate answer.  Please include one reason per answer - details about why it's not executed - and fix(es) for that one reason.  Please write only cron-specific issues, e.g. commands that execute as expected from the shell but execute erroneously by cron.


I have a requirement where I need to update an existing Contact in Salesforce from a Visualforce page on display of a Force.com site.  How can this be achieved, since there is no update permission on Standard objects.  Whatever I had tried is as below :   public without Sharing class ContactEditExt {  public PageReference CANCEL() {     return null; }  public Contact con; public Id recordId; public ContactEditExt() { recordId = apexPages.currentPage().getParameters().get('id'); System.debug('>>>>>>>recordId'+recordId); }  public Contact getcon() {     con = [Select Id, firstname, lastname, Account.name ,email, Double_OptIn__c, Double_OptIn_Time__c, Receive_Communication__c from Contact where Id =:recordID];         return con; } public pageReference saveStatusChange(){     if(con.Receive_Communication__c == true){         con.Double_OptIn__c = true;         con.Double_OptIn_Time__c = date.today();     } try{     update con; } catch(exception e){     System.debug('update Contact :'+e); } return null; }   }  Visualforce Page:       <apex:page sidebar="false" controller="ContactEditExt">  <apex:form >   <apex:sectionHeader title="Edit Contact for" subtitle=""/>    <apex:pageBlock >      <apex:pageBlockButtons >        <apex:commandButton value="Submit" action="{!saveStatusChange}"/>        <apex:commandButton value="Cancel" action="{!CANCEL}"/>      </apex:pageBlockButtons>        <apex:pageBlockSection Title="Update my Records" columns="1" >          <apex:inputText value="{!con.email}"/>          <apex:inputText value="{!con.Account.name}" label="Company"/>          <apex:inputText value="{!con.firstname}"/>          <apex:inputText value="{!con.lastname}"/>          <apex:inputCheckbox value="{!con.Receive_Communication__c}" label="I would like to receive communications from the Roundtable on Sustainable Biomaterials"/>         </apex:pageBlockSection>      </apex:pageBlock>  </apex:form> </apex:page>   Thanks in advance!

I have a client who wants external users to submit data via a Sites VF page and update Opportunity records.  Of course the Sites profile doesn't have permissions to update standard objects.  Also, the client does not want to purchase portal licenses for these external users.  I am considering two workarounds and am wondering if they are possible:  1 -- Write some Apex webservices and call them from the Sites page Visualforce controller.  Is it even possible to call your own webservices from a controller?  I presume the webservices would be running in system context?   2 -- Have the Sites page create a custom object record instead, and then write a trigger to update the opp record using the custom object.  Will the trigger be running in the system context and be able to update the opp?  Thanks David


I have been trying to render an animation of a spaceship, but no matter what I do it comes up like this:    But I see this in the camera:    I was wondering if anybody could help, thanks in advance.

I have a model of a building with a sidewalk around it.  Both show up when I switch to rendering mode in both Blender Render and Cycles Render mode.  But:  when I hit F12 for a final proper render, the building shows up -- but the sidewalk doesn't.    I've checked the normals and I thought the normals seemed pointed in the right direction.  I've set the Clipping on the Camera to a high number.  I removed all the materials from the sidewalk and added a new material-- the problem persists.  I've exported the blend as an FBX file and the Sidewalk shows up fine in Unity.  Just in final renders, it doesn't show up.    Here is a blend file: .  I tried to destroy everything unrelated to the issue and label things in a clear way.    Thanks.


I got this as a result (I can provide more information about the data itself if you would like it). I was curious about how one should interpret this chart that was created in R. I understand it has to do with the importance of variables in the model that was created, but what else can be derived from this chart?

I'm having some difficulty understanding how to interpret variable importance output from the Random Forest package. Mean decrease in accuracy is usually described as "the decrease in model accuracy from permuting the values in each feature".   Is this a statement about the feature as a whole or about specific values within the feature? In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the feature) in question from the model?   Say we have the following model:  require(randomForest) data(iris) set.seed(1) dat <- iris dat$Species <- factor(ifelse(dat$Species=='virginica','virginica','other')) model.rf <- randomForest(Species~., dat, ntree=25, importance=TRUE, nodesize=5) model.rf varImpPlot(model.rf)     Call:  randomForest(formula = Species ~ ., data = dat, ntree = 25,  proximity = TRUE, importance = TRUE, nodesize = 5)  Type of random forest: classification Number of trees: 25 No. of variables tried at each split: 2          OOB estimate of  error rate: 3.33% Confusion matrix:           other virginica class.error other        97         3        0.03 virginica     2        48        0.04     In this model, the OOB rate is rather low (around 5%). Yet, the Mean Decrease in Accuracy for the predictor (Petal.Length) with the highest value in this measure is only around 8.   Does this mean that removing Petal.Length from the model would only result in an additional misclassification of 8 or so observations on average?   How could the Mean Decrease in Accuracy for Petal.Length be so low, given that it's the highest in this measure, and thus the other variables have even lower values on this measure?


When trying to install Ubuntu the live mode seems to work fine but I go to install it and it freezes when I click install. I tried to install Linux Mint earlier today and it kept saying 'Computer has zero bytes of storage' and just freezing even when I delete all the partitions on my drive (I've also tried to format the partitions myself but I still seem too get the same problems). I just gave up and tried to install Ubuntu instead and it just seems to freeze when I try to install it. I'm not sure what's causing these problems. I tested a Windows recovery drive I have to see if it would get these errors when trying to re-install Windows but it didn't get any errors I'm quite new to Linux and would really like to use Ubuntu/Linux Mint as my operating system but I'm lost on whats causing these errors. Thank you

Okay, I apologize if there are similar threads... but I've scoured the internet and never have I run across a helpful answer. So I'll ask here...   I have an old laptop, an Acer Aspire 5515... It was running Vista and was taking 5-10 seconds to just do anything, even as simple as opening a folder. So I decided to install a windows-user-friendly version of Linux - something I've wanted to try for a long time. I ended up settling on Kubuntu because I read somewhere that it's medium-light weight, and good for people used to running windows, after all, I can always replace it with something different later on.   I went to the ubuntu site itself and downloaded  "kubuntu-16.04.1-desktop-am64"  Then the problems started flowing in. Some of it user error I admit... first the CD I got wasn't big enough, then I forgot you can't copy past an iso file, then I couldn't get the Acer to boot from cd drive  Eventually, I fixed these... I burnt the iso image right, used a larger DVD, and changed the bios to boot from the cd. I went to try to just 'try' Kubuntu but that just wasn't working very well, so I just went and tried to go ahead and replace the OS. I knew it would kill everything on the Vista, but I already transferred the files I wanted to keep and the computer was unusable as it was, so I figured why not.   I went through with trying to do the installation, and the first time got to about 80% when I got the Errno 5 Input/Output Error  Alright then... it said something about heat so I placed the computer on a low running box fan as a make shift computer fan (It was getting hot anyway), and I tried again. Made it to about the mid-60s and got the same error.   This time, I went and I double checked the iso... it's indeed the most recent one on the Ubuntu site, and then I used winMd5sum, which says the checksum is correct. I then got another disk and downloaded imgBurn and burnt a new disk at the lowest possible speed (tried for 1x, but it did 2x).   Tried again and it still pulled the same error around the same spot.  So this time at the bootup screen I pressed shift and chose Check for Defects, it returned with Errors found in 1 file  The memtest86 says no errors.  So I'm assuming that means there's a problem with the CD/iso? The check sum was supposedly correct and it was burnt on the lowest possible burn with trusted software. Also, the cd drive works just fine and the disk itself is brand new without a scuff on it.  I'm pretty stumped what to do. I'm going to try to find a cheap flash drive at the dollar store or something to try to boot from USB, but if there is any troubleshooting I could do to get this to work without having to spend money I can't really afford, that'd be really helpful.   As it stands I have a nearly 10-year-old computer with no OS whatsoever on it because the windows section is all deleted, but the Ubuntu section is not fully installed.


I have an iMac Pro. No camera shows in the system report under Camera, just under USB. My microphone is also not working. I tried resetting the NVRAM but it didn't solve the problem.    What should I do to fix it?

Does anybody have any alternative solutions? Seems like my computer no longer detect my built-in camera. I can't detect it in any application.  So far I have tried:   terminal killAll commands -> doesn't do anything and I get a 'No matching processes were found' message Restart both SMC and PRAM camera in safe mode also does not work webcam on Secondary account does not work   I am at the end of my wits here.


I've just started learning about various algorithms, and I'm attempting to write a program that tests the speed between the algorithms and outputs the time it takes each of them to run to the screen. As I've set it up, each algorithm is a subclass of a RunnableAlgorithm abstract class that creates new arrays of the same parameters for each iteration of the algorithm.   However, with each iteration of the algorithm, it seems to run faster! This is a snippet of the output - I've tried it several times, and it consistently will get faster the more times I run it.   SelectionSort warmup .. 45695528 ns SelectionSort: 996415 ns SelectionSort: 1044200 ns SelectionSort: 1260648 ns SelectionSort: 774839 ns SelectionSort: 738320 ns SelectionSort: 337446 ns   It has a "warmup" method called in the superclass ctor that (from my understanding) should load all of the used classes.   Warmup calls all the classes that are later called, which includes DecimalFormat, Random, System (for System.nanoTime() and System.out), along with running the algorithm several times.    SelectionSort s = new SelectionSort();    for (int i = 0; i < 6; i++) {      s.setTime();      s.algorithmAverage();      s.printTime();  }   setTime() sets a variable such that:   beginTime = System.nanoTime();    and printTime() is:   System.out.println(this.getClass().getName() + ": " + new     DecimalFormat(DECIMAL).format( System.nanoTime() - beginTime)     + " ns");   and algorithmAverage() runs the algorithm 10 times, which is what is being timed. Can anyone help me understand why it speeds up? Is the JVM optimizing the code to run because it's called so often? Is there a better, more consistent way for me to test the algorithms speeds other than System.nanoTime() which seems to be fairly unreliable?   Thank you in advanced!

What does a JIT compiler specifically do as opposed to a non-JIT compiler? Can someone give a succinct and easy to understand description?


I was under the impression that      char word[5] = "hello";   is the same as       char *word = "hello";    because arrays always decay into a pointer?

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


is my system strong enough to run most animations. Seem to be having problems rendering Intel 3.2 GHz 4GB RAM with nvidia 610

What are the system requirements for working with complex geometry in Blender? Things like RAM, GPU, CPU etc.?


package main;  public class Main {     double radius;     public Main(double newRadius) {         radius = newRadius;     }       public static void main (String [] args) {         Main x = new Main(1);         Main y = new Main(2);         Main temp;         // try to swap first time         temp = x;         x = y;         y = temp;         System.out.println(x.radius + " " +  y.radius);         x = new Main(1);         y = new Main(2);        // try to swap second time         swap(x, y);        System.out.println(x.radius + " " + y.radius);     }     public static void swap(Main x, Main y) {         Main temp = x;         x = y;         y = temp;     }  }   Why the first time worked, but the second time didn't? The first one did the swap, but the second one didn't. I'm passing the reference to the function. Why this doesn't work?

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


The  advertises "internal clock speeds exceeding 450 MHz," but the default clock pin is connected to a 100MHz oscillator. Is it possible to configure the Basys 3 to use a 450MHz clock?

So before this I only worked with simple 8 bit Atmel MCUs and I realized on my development board schematics it has only a 12Mhz crystal, yet the MCU operates at  up to 100MHz. (I think the default is 80MHz. I only made it higher once for fun. It's just a simple line in the code.)  How does it do that? Why does an Atmega328, for example, run at the used crystal speed?


In the Riemann sphere model, people extend the complex plane with a point at infinity: $\mathbb {C} \cup \{\infty \}$ and claim this expression: $\frac{1}{0}=\infty$. I'm confused with what is this $\infty$. Is it a member of $\{\aleph_n\}$ numbers? When we study infinities, we usually discuss cardinality. Does this $\infty$ corresponds to something's cardinality?

For example, can we say: $\infty=\lim\limits_{n\rightarrow\infty} n < \aleph_0$?  These are two different types of structures. The limit being like the length, extension, or just generic magnitude and the other being cardinality of a set. Can we compare magnitude to cardinality?  Intuitively, we can reach $\aleph_0$ by counting the natural numbers on the number line and in the process will be approaching $\infty$. Which leads me to believe $\infty\leq\aleph_0$. But I can't see why it should be a strict inequality. I feel like they should be of equal magnitude.  I saw on a recent comment that $2^\infty=\infty$, but are those infinities really the same? It seems not to me. Of course we (usually) have that  $2^{\aleph_0}=\aleph_1$ where ${\aleph_0}$ and $\aleph_1$ are clearly two very distinct infinities, countable vs uncountable at least. Maybe one might argue that as far as the concept of magnitude is concerned, all infinities are "equal".


I generally try to print all images for clients and require that they purchase a print prior to the release of any "small sized file" for holiday cards, web-use, but a faux-pas in my new (app-based) contract has a client requesting an image she didn't "buy" for the above listed use.    I need to create a size that will work well for a holiday card and web, but not for reproducing to a print. What should my LR output be to achieve this, assuming the card would be no larger than a 5x7?   Is there a formula that one can use to determine this on varied sizes? ,Say, 8x10 looks good, but at 11x14, pixelation occurs?  5 x 7 looks good, 8x10 does not?   I've posted in FB forums, however, the response was, "Trust that your client won't print large!" Um, right.  This is the key image in the group and the only one that she selected yet didn't buy in 11 x 14.

What size images do I need for common print sizes, such as wallet size, 8x10, and 16x20?  Is there a general formula?  How could that size change if, for example, a 16x20 was printed on canvas rather than photopaper?


I have an argument with the conclusion: 'The sky is blue and it is not the case that the sky is blue'.  Without knowing the premises of this argument, am I right in saying this argument is invalid since the this conclusion is necessarily false?

I've recently been trying to introduce myself to formal logic, and I've hit a stumbling point:  In the text I'm reading, a valid argument is defined as "an argument in which it is impossible for the premises to be true and at the same time the conclusion false."  The text then later prompts me to declare whether it's possible for an argument to be valid with a contradiction for a conclusion. The answer key then claims that yes, it is in fact possible, but offers no further explanation. I'm also supposed to create an example.  I just can't wrap my head around this one.  Here's the example I've worked up, is this a valid argument?   If grass is green then it is raining.  If water is wet then it is not raining.  Therefore: It is raining and not raining.   My head hurts.


//setImageBitmap gives nullPointerException  public class MainActivity extends ActionBarActivity {  @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     try {         BitmapFactory.Options bitmapOptions = new BitmapFactory.Options();         bitmapOptions.inSampleSize = 2;         Bitmap imageBitmap = BitmapFactory.decodeResource(getResources(), R.drawable.img, bitmapOptions);         //imageView for referencig imageView of layout file         ImageView imageView=(ImageView)findViewById(R.id.imageView1);              imageView.setImageBitmap(imageBitmap);         //setImageBitmap gives nullPointerException     }catch (Exception e){          e.printStackTrace();     }      //setContentView(imageView);      setContentView(R.layout.activity_main);  } }

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?


When do we use a collection of uncountable nouns? Which form of the verb should we use? Singular or plural? E.g.:  "Water and milk is/are essential." "Courage and bravery is/are slightly different."

What form of to be would be right to use in this case?     Why drug abuse in general and cannabis consumption in particular is/are dangerous for your health.


I am constructing a FrequencyBag that will take something like an Integer, String or Character, and it will take the data and pair it with its frequency.  For example:   FrequencyBag<Integer> fb = new FrequencyBag<Integer>();    fb.add(cat);   fb.add(dog);   fb.add(horse);   fb.add(cat);   fb.add(cat);   will look like   (cat,3) ---> (dog,1) ---> (horse, 1)   My method getMaxFreq() has no problem getting the max frequency (which is 3 for the example above)  when the bag contains elements, but when I try to return the value 0 for an empty null FrequencyBag() I get this error.  "Exception in thread "main" java.lang.NullPointerException" "FrequencyBag$Node.access$1(FrequencyBag.java:8)"  Here is my method below:      public int getMaxFreq() {      Node<T> currentNode = firstNode;     Node<T> nextNode = firstNode.next;      int compareVal = nextNode.freq;     int maxVal = currentNode.freq;      if (currentNode == null) {         maxVal = 0;         return maxVal;     }      while (nextNode.next != null) {          if (maxVal < compareVal) {             maxVal = compareVal;         }          else {             // Do nothing         }          currentNode = currentNode.next;         nextNode = nextNode.next;     }      if (nextNode.next == null) {         if (maxVal < nextNode.freq) {             maxVal = nextNode.freq;         } else {             // Do nothing         }          return maxVal;     }      return maxVal;  }     Instead of getting a null pointer error, I want to do this when I create an empty bag and call my getMaxFreq() method:   FrequencyBag<Integer> emptyBag = new FrequencyBag<Integer>();   System.out.println("Output: " + emptyBag.getMaxFreq());   Output: 0


Let $X,Y \sim$ Uniform$(0,1)$ be independent. Find the PDF for $X/Y$.  Let $Z=X/Y$. We want to find $F_z(z)=P(Z \leq z)=P(X/Y \leq z)$. We can make $Y$ super small with fixed $X$, and conversely we can make $X$ really small with fixed $Y$. Thus it appears to me that we have $0<z<\infty$.  I am struggling to find the subgraph of the unit square. We know that $X \leq Yz$. If $z = 1$, then we have a simple diagonal through the unit square. Increasing the value of $z$ shrinks what $Y$ can be since $X$ must be between $0$ and $1$. So we should see these lines fan out below the diagonal of the square as $z$ increases. Conversely, if $z$ approaches $0$, then we we limit the range of $X$, and so these lines fan out above the diagonal. What I am having trouble with is putting this all together and calculating the integral itself.

Suppose $x_1, x_2$ are IDD random variables uniformly distributed on the interval $(0,1)$.  What is the pdf of the quotient $x_2 / x_1$?


I was using Win10 for a while and now I want to install Ubuntu\Linux Mint as a second OS. But no matter what I do, I can't get into GRUB2 menu, each time it boots straight into Windows.  I'm using ASUS Rampage IV Extreme motherboard.  I made a separate partition for Linux install, on the same SSD as Windows (Samsung EVO 1TB).  I'm installing using "Something else", creating "/" and "/home" partitions. Then I tried choosing either HDD's root or Windows EFI partition to install bootloader to - no luck with either option.  I tried running boot-repair from LiveCD, and it just broke Windows boot. I reverted it back.  So, right now I have Windows 10 and I can boot into it. I have Linux Mint Sonya installed on separate partition, but I can't boot into it, and I can't get into GRUB menu. There's only Windows Boot Manager available in BIOS, or SSD root, none of those options gets me into GRUB.  I have Fast boot turned off in windows, and there's no secure boot in BIOS.  How can I make this work?  I am thinking about installing Ubuntu instead of Mint, and I suppose there's no difference in boot process between Ubuntu 16.X and Mint, so I hope it's ok to ask this question here.

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


Am trying to draw a simple rectangle and there seems to be minor issue with two of the endpoints (f and d in the following). I tried line cap=rect as suggested by  but that did not seem to work.  The resulting image:    \documentclass{standalone} \setlength\PreviewBorder{5pt}%  \usepackage{tikz}  \newcommand*{\Width}{2.0} \newcommand*{\Height}{3.0} \newcommand*{\Depth}{1.0}  \begin{document} \begin{tikzpicture}%     \coordinate (A) at ( 0,       0,     \Depth);%     \coordinate (B) at (\Height,  0,     \Depth);%     \coordinate (C) at (\Height,  0,      0);%     \coordinate (D) at (\Height, \Width,  0);%     \coordinate (E) at ( 0,      \Width,  0);%     \coordinate (F) at ( 0,      \Width, \Depth);%     \coordinate (G) at (\Height, \Width, \Depth);%     \coordinate (H) at ( 0,       0,      0);%     %     \draw [blue, ultra thick,line cap=rect]%         (A) -- (B) -- (C) -- (D) -- (E) -- (F) -- cycle;%     \draw [blue, ultra thick,line cap=rect]%         (B) -- (G) -- (F) -- (E) -- (D) -- (G) -- cycle;%      \path (D)  [right] node {$d$};% Problem Point 1     \path (F)  [left ] node {$f$};% Problem Point 2 \end{tikzpicture}% \end{document}   This problem about  seems related, but I do not understand how to adapt that to my problem.


I had a lot of important data in WDmypassport external HD but I made this HD bootable (using media creation tool) without knowing that it can wipe off my data backup. I am new to this and I admit this was a big blunder. Can I get the complete data back, organized like before. Is there any way? There are a lot of recovery tools but they all give data unorganized, which can be a big loss in my case. Any help would be appreciated.

What steps can I take to try to recover lost or inaccessible data from any storage device?  Answers:   This applies to any computer storage device, e.g. internal/external hard drives, USB sticks, flash memory. The most important thing is to STOP using it, any type of I/O can ruin your chances of a recovery.     We have separate questions covering common problems with USB flash drives in greater detail:


I have been working in LaTeX for a while, and during the typing I noticed that many places I skipped pressing the Shift key to make the first letter of a sentence capital. After checking here and there on internet, I found that LaTeX doesn't have any option to do that automatically and there are some macros etc which can do, but I want to know if there is any simple way to do it. Especially when you have a report of hundreds of pages and finding each one is a bit hard to manually update to a capital letter.  MS Word does it automatically.

I'm writing a report together with another person, and he often neglects to use a capital letter at the start of each sentence. Is it possible to get LaTeX to correct this automatically instead of doing so by hand?


I have four div blocks and I want to Centre the Horizontally, they keep stacking under each other.. any ideas how I can do this.

1. name of the company

2. name of the company

3. name of the company

4. name of the company

How can I horizontally center a
 within another
 using CSS?

Foo foo


Hello can I get help with this question?  Compute the distance between the point $R(1, 1, 1)$ and the line $$ \begin{bmatrix}         0 \\         -1 \\         1 \\         \end{bmatrix} + t \begin{bmatrix}         1 \\         -2 \\         2 \\         \end{bmatrix} $$  For what I visualized:

I have calculated the parametric form of my line as: $X = (2,2,0) + t(1,2,2)$ and have been given a point $Q = (1,-1,-1)$, how would I calculate the distance from $Q$ to the line?


I'm using biblatex for my report and I've run into a small problem. When I have multiple authors in my .bib file my bibliography displays the initials of the authors (after the first) in the wrong order and I get an unwanted 'and'. So what I get:  1. Klinkrad, H. and J. Doe, 2006. Space Debris: Models and Risk Analysis. Berlin: Springer.   What I want is:   1. Klinkrad, H., Doe, J. 2006. Space Debris: Models and Risk Analysis. Berlin: Springer.   I've included a MWE and my sources.bib code:  \documentclass[a4paper,10pt]{report} \usepackage[bibstyle=authoryear, citestyle=authoryear,sorting=none,backend=biber,natbib,dashed=false]{biblatex} \addbibresource{sources.bib} \NewBibliographyString{available} \usepackage[english]{babel} \DefineBibliographyStrings{english}{available = {available at},} \DefineBibliographyStrings{english}{urlseen = {[Accessed},} \DeclareFieldFormat{url}{\bibstring{available}\addcolon\space\textless\url{#1}\textgreater} \DeclareFieldFormat{urldate}{\space\bibstring{urlseen}\space#1]}  \defbibenvironment{bibliography} {\enumerate{} {\setlength{\leftmargin}{\bibhang}% \setlength{\itemindent}{-\leftmargin}% \setlength{\itemsep}{\bibitemsep}% \setlength{\parsep}{\bibparsep}}} {\endenumerate} {\item} \usepackage{xpatch} \xpatchbibmacro{date+extrayear}{%   \printtext[parens]% }{%   \setunit{\addcomma\space}%   \printtext% }{}{}  \begin{document} \nocite{*}  \printbibliography \end{document}   And my sources.bib code:  @Book{space_debris_klinkrad,   Title                    = {Space Debris: Models and Risk Analysis},   Author                   = {Klinkrad, H. and Doe, J.},   Publisher                = {Springer},   Address                  = {Berlin},   Year                     = {2006}, }   I think it is a simple change in the definition of the Author field. However, I've not been able to find the solution anywhere.  Thanks!

With biblatex and verbose-trad2 style, I would like to reverse the order of the last name and the first name for inline references.  The default behavior is:     John DOE, Title, place : publisher, year   for inline references (in my case, in a footnote with footcite command) and:     DOE, John, Title, place : publisher, year   in the bibliography at the end of the document.  I would like to have both inline and final references in the following format (similar to the bibiography style).      DOE, John, Title, place : publisher, year   P-S : There are some close questions (like ) but only about the final bibliography (and no inline references). \DeclareNameAlias{sortname}{last-first} works only for the ending references (not inline ones).


If someone with not much mathematics in his luggage asks me: What is so special about $\pi$? then off course I have an answer. Even if $i$ would be the subject (I allready see him gazing at my mysterious smile). But when I am asked about $e$ then I grow silent (or try to change the subject). Please help me out of this. Give me a nice characterization of $e$.    Edit:  I am informed now that this question is somehow a duplicate of . I agree with that judgment. Sorry for that. Next time I will first have a closer look at the questions that have allready been asked. Thank you also. I find very nice answers  and advice everyone interested to have a look.

Potentially related-questions, shown before posting, didn't have anything like this, so I apologize in advance if this is a duplicate.    I know there are many ways of calculating (or should I say "ending up at") the constant e.  How would you explain e concisely?  It's a rather beautiful number, but when friends have asked me "what is e?" I'm usually at a loss for words -- I always figured the math explains it, but I would really like to know how others conceptualize it, especially in common-language (say, "English").     related but not the same:


One of my tasks is to proof that something is correct or incorrect using induction. Since I am from Germany and don't know the right word in English I do my best to give all necessary info. We are talking about "words" and amounts of words which are in so called alphabets.     Let $\Sigma \overset{\Delta} = \{a, b\}$ and $S_1 \overset{\Delta} = \{a^n \mid n \in \Bbb N\}$. Prove using induction that $$\forall w \in \Sigma^* . w \in S_1 \to \big( w = \lambda \lor (\forall \ 1 \le i \le |w| . (w)_i = a) \big) .$$   How to prove that? Any help is upvoted, thank you.

I am having trouble to understand the way of using a induction for the following example:     Let $\Sigma \overset{\Delta} = \{a, b\}$ and $S_1 \overset{\Delta} = \{a^n \mid n \in \Bbb N\}$. Prove using induction that $$\forall w \in \Sigma^* . w \in S_1 \to \big( w = \lambda \lor (\forall \ 1 \le i \le |w| . (w)_i = a) \big) .$$   How to do that? Any help is upvoted.


What makes be an intransitive verb? How do we know that the analysis of It is me as transitive by tradtional grammars is incorrect? And how does this analysis apply to other verbs, like hurt for example below:    How to tell if hurt in It hurt me is a copula? It can be replaced by other to be linking verbs (Is, was etc.) Even though (Is, was) are stative verbs while hurt is more of a dynamic/action verb.     The following verbs are true linking verbs: any form of the verb be [am,is, are, was, were, has been, are being, might have been, etc.],become, and seem. These true linking verbs are always linking verbs.      **Then you have a list of verbs with multiple personalities: appear, feel,grow, look, prove, remain, smell, sound, taste, and turn. Sometimes these verbs are linking verbs; sometimes they are action verbs.      How do you tell when they are action verbs and when they are linking verbs?      If you can substitute am, is, or are    and the sentence still sounds logical, you have a linking verb on your hands.**      If, after the substitution, the sentence makes no sense, you are dealing with an action verb instead.       Source:    Normally action verbs have direct objects, but nearly all verbs can be used as transitve and intransitive, e.g. the verb drive: compare "He drives fast" and "He drives the car fast". The first is a predicative compliment but what about the second one? And in, "It was given to her" - is her a compliment or an object? (Even though her is normally associated with the object pronoun, consider: It was her)   Furthermore can the verb "hurt" be a reporting verb relating the feelings of the subject rather than an action verb like (I feel hurt) or (I am hurt) in "It hurt me"? If it is seen as an action verb, me is an object, while the other interpretation is that there is no object and hurt is being used intransitively. If it is the latter, what differentiates "It hurt me" and "It is I/me" grammatically as predicative compliments?

It was ... salted the earth around your flower deck.    I wrote the second form "It was me". I have chosen the most "appropriate" answer to this question as somebody who is learning English.  This decision was made on a phonetic basis so it's for sure I made a mistake.   Surely you have a rational explanation to this exercise, maybe a grammar rule, or is it an English expression?


I am trying to install PCAP-core-1.8.2/ () on CentOS release 6.2 and I keep getting the error when I run:       perl Makefile.PL  Can't locate File/ShareDir/Install.pm in @INC (@INC contains: /usr/local/lib64/perl5 /usr/local/share/perl5 /usr/lib64/perl5/vendor_perl /usr/share/perl5/vendor_perl /usr/lib64/perl5 /usr/share/perl5 .) at Makefile.PL line 24.   Line 24 is this:  use File::ShareDir::Install;   I see it can't find File/ShareDir/Install.pm so when I try and find this perl module:  locate Install.pm  I get this:  /usr/share/perl5/ExtUtils/Install.pm   and in my .bashrc file I added this directory - but I am not sure what is going wrong either in the PERL5LIB PATH or elsewhere? Any suggestions would be gratefully received.

I get this error:  Can't locate Foo.pm in @INC  Is there an easier way to install it than downloading, untarring, making, etc?


I need to create alphanumeric unique IDs of length 7 or 10. Similar to the shorter version of Git commit IDs (7a471b2).  I tried UUID, but the generated unique ID is longer than I need.  Is there a built-in method / code snippet in Java that can help here?

I'm looking to create a simple short-lived reservation system, and I'd like to generate confirmation numbers that are   unique random-looking alphanumeric short-ish, at least much shorter than 32 character-long strings returned by sha1   I'm only looking to have ~500 reservations, so I don't imagine high likelyhood of collissions.  One idea I had is generate an sha1 hash based on a date-time stamp and username, then truncating it to its first 10 characters.  Would something like that be reliably unique enough for the purposes of processing ~500 reservations?


There are too many negative markings on my questions on Stack Overflow. So I want to migrate my account to another new account. I want all my information to migrate except the questions.  Is it possible?

If you are reading this, you may have been affected by one of our post quality bans. If so, it is important that you  to understand what has happened and how to regain the permissions that you lost. While trying to ask a question, one could see:  We are no longer accepting questions from this account. See  to learn more.  Likewise, for answers:  We are no longer accepting answers from this account. See  to learn more.   Why am I getting this message? Are deleted posts taken into account too? Is a question/answer ban the same as a suspension? How do I avoid getting a question ban? How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account? Can I simply create a new account? I'll just ask somewhere else on the SE network, and they'll migrate my question to the correct site! Will a ban on one Stack Exchange site affect my standing on other sites in the network? Does this apply to meta sites too? My account is in good standing. Why am I still blocked?


My daughter is starting school in the US (we stay in Thailand) and my wife and I would like to accompany her back. There is a much better deal if we buy round trip tickets, but flying back would only be my wife and myself (contenting through China) . What will happen if my daughter doesn't use her ticket to return with us?

Say I want to book a flight from Fort Lauderdale to Chicago.  Say the airline also flies to St. Louis from Fort Launderdale but has a connecting flight through Chicago.  If I book that flights from FLL->ORD->STL and just get off in Chicago, what possible problems can I run into, assuming I didn't check any bags and only have carry on?  This scenario exist for Southwest, but I wanted this be more of a general question that would apply to all airlines.


I am new to this field of SEO.  My site is intended to target local customers only.  I want to generate quality backlinks for my site. Is there any tools to generate quality backlinks. Or blog sites to improve count of backlinks.  I am trying to improve my page ranking .  Any Other SEO tips also would be highly appreciated!  Thanks in Advance

What are the best ways to improve a site's position in the Google search results?