nautilus not opening showing the following error when I tried to open through terminal
Nautilus doesn't launch on Ubuntu
Let $G$ be a non-empty finite set with an associative binary operation so that cancellation law holds, i.e. $ab=ac$ or $ba=ca$ implies $b=c$, for any choices of $a,b,c$ in $G$. Assume that there is an identity element $e$ in $G$. Show that $G$ is a group.  Proof: To show $G$ is a group, conditions must hold. Suppose that $ab=ac$, then $b=eb=(a^{-1}a)b =a^{-1}(ab)=a^{-1}(ac) =(a^{-1}a)c=ec=c$. So left cancellation holds in $G$.  2) Suppose $ba=ca$, then $b=be=b(aa^{-1}) =(ba)a^{-1}=(ca)a^{-1} =c(aa^{-1})=ce=c$. So right cancellation holds in $G$.  3) If $a$ exists in $G$ then $aa^{-1}=a^{-1}a=e$, where $a$ is an inverse of $a^{-1}$. Since inverses are unique, $(a^{-1})^{-1}=a$.  4) Let $x$ be the inverse of $ab$. Then $(ab)x=e$. By associativity we have $a(bx)=aa^{-1}$. Through left cancellation we have  $bx=a^{-1}bx=ea^{-1}=b(b^{-1}a^{-1})$ and $x=b^{-1}a^{-1}$.  Thus $(ab)^{-1}=b^{-1}a^{-1}$. So all conditions hold, $G$ is a group.  Is this proof correct? I know to show $G$ is a group these conditions have to be met. This is all I have to show right? How to fairly select a random number for a game without trusting a third party? To find:  $$\int \sqrt{1+\sin(x)} dx$$  What I  tried:  I put $\tan(\frac{x}{2}) = t$, using which I got it to:  $$I = 2\int \dfrac{1+t}{(1+t^2)^{\frac{3}{2}}}dt$$  Now I am badly stuck. There seems no way to approach this one. Please give a hint. Also, can we initially to some manipulations on the original integral to make it easy? Thank you. How can std::make_heap be implemented while making at most 3N comparisons? Ward model implementation: specular component too weak I'm trying to implement the Ward shading model, the anisotropic, computationally efficient version:       This is how I made it:    float alphaX=0.5, alphaY=0.5; // asinotropic roughness float minFloat= 1.e-6;   vec4 Ward(vec3 L, vec3 N, vec3 V) {     vec3 H= normalize(L+V);     float NdotL= max(dot(N,L),0.0);     float NdotV= max(dot(N,V),0.0);      vec3 e= vec3(1.0,0.0,0.0);     vec3 T= normalize(cross(N,e));     vec3 B= normalize(cross(N,T));     float HdotT= max(dot(H,T),0.0);     float HdotB= max(dot(H,B),0.0);     float HdotN= max(dot(H,N),0.0);      float beta= -2.0 * ( pow(HdotN/alphaX, 2.0) + pow(HdotB/alphaY,2.0) ) / (1.0 + HdotN);     float den= max(minFloat, 4.0 * pi * alphaX * alphaY * sqrt(NdotL * NdotV) );     vec4 specular= Ps * 1.0/den * exp(beta);     return (Pd + specular) * NdotL; }   But I get a result similar to a lambertian surface or Oren-Nayar model, where the specular component is absent: What is the best way to dump entire objects to a log in C#? So for viewing a current object's state at runtime, I really like what the Visual Studio Immediate window gives me.  Just doing a simple  ? objectname   Will give me a nicely formatted 'dump' of the object.    Is there an easy way to do this in code, so I can do something similar when logging? I just finished a test as part of a job interview, and one question stumped me, even using Google for reference. I'd like to see what the StackOverflow crew can do with it:  The memset_16aligned function requires a 16-byte aligned pointer passed to it, or it will crash. a) How would you allocate 1024 bytes of memory, and align it to a 16 byte boundary? b) Free the memory after the memset_16aligned has executed.  {        void *mem;    void *ptr;     // answer a) here     memset_16aligned(ptr, 0, 1024);     // answer b) here     } Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$ Can any one give a generalization of the following properties in a single proof? I have checked the results, which I have given below by trial and error method. I am looking for a general proof, which will cover the all my results below:   Every third Fibonacci number is even. 3 divides every 4th Fibonacci number. 5 divides every 5th Fibonacci number. 4 divides every 6th Fibonacci number. 13 divides every 7th Fibonacci number. 7 divides every 8th Fibonacci number. 17 divides every 9th Fibonacci number. 11 divides every 10th Fibonacci number. 6, 9, 12 and 16 divides every 12th Fibonacci number. 29 divides every 14th Fibonacci number. 10 and 61 divides every 15th Fibonacci number. 15 divides every 20th Fibonacci number. A question of Euclidean domain I need a counsel about my websites' domain.  Let's say I have just bought two domains: xyz.com and xyzphotography.com.  As we can see, the first one is shorter but way less meaningful than the second one. The second one contains a photography keyword but it's longer.  I have only one website which is my photography portfolio. Can you advise me how to set those domains to make it all as SEO-friendly as possible? Which one should be the main one, does the rest should work on their own or have some kind of SEO-friendly redirect to the main domain? Plain integer partitions of $n$ using $r$ parts Division of number $n$ on parts $a_1,...,a_r$ where $a_1 \le ... \le a_r$ we call a plain if $a_1 = 1$ and $a_i - a_{i-1} \le 1$ for $2 \le i \le r$. Find enumerator (generating function) for plain divisions.  my try  The hint was to use bijection between plain divisions and some commonly know enumerator. I tried to use enumerator of divisions on different parts: $$ (1+x)(1+x^2)...(1+x^r)$$ where number of plain divisions is  $$[x^n](1+x)(1+x^2)...(1+x^r) $$ let function  $$f(n,r) = [x^n](1+x)(1+x^2)...(1+x^r) $$  For some first divisions it works. For example: $$f(4,3) = 1 $$ $$f(6,3) = 1 $$ $$f(11,5) = 2$$ But when I tried to find bijection, I failed. I found that this function isn't correct because $f(15,6) = 4$ but should be equal to $3$ because: $$15 = 1,1, 2, 3, 4, 4 \\ 15 = 1, 2, 2, 3, 3, 4\\ 15 = 1, 2, 3, 3, 3, 3 $$. There I stucked. What are review tests (audits) and how do they work? I recently received this rather amusing message while reviewing a user's first post:  Congratulations! This was only a test, designed to make sure you were paying attention. This post has already been removed, but thanks for taking time to leave feedback for the author.   What is the purpose of this test? How does the audit work? What happens if I fail? Why was the system expecting me to negatively review a good post, or positively review a bad post? A review is obviously an audit. Should I report it? Do review audits count toward the Reviewer badge? Do robo-reviewers dream of electric sheep? Sophomore's dream: $\int_0^{1} x^{-x} \; dx = \sum_{n=1}^\infty n^{-n}$ Bibliographies from multiple .bib files I would like to use multiple .bib files for my article, such as file1.bib, file2.bib. However, I would like my references not to be separated (such as &quot;Primary sources&quot;, &quot;Secondary sources&quot;, etc.). These bibliographies just need to be merged into one. One way to do this is to copy-paste these .bib files into one .bib file, and this would solve the problem. However, I would like to keep it split into several .bib files, by topic (file1.bib contains articles on topic1, file2.bib contains articles on topic2, and so on). I tried to do \bibliographystyle{alpha}  \bibliography{file1} \bibliography{file2}  but this just gives me the same bibliography twice! Repeating "to" and "will" in enumerations of verbs Should I use the second "will" in constructions like this one: "it will definitely help you and will make the text more readable"  And should I write "to" before every infinitive in enumeration, or only before the first one, e.g. "it helps to develop and test" or "it helps to develop and to test"? Could this example be influenced by the fact that "help" can go with to-invinitive and bare infinitive, and with other verbs the rule would be different? How do I dynamically create the variable name in a PHP loop? I would like to replace the usual \hat in maths with a larger one, but I do not want it to stretch. The size I want is "the smallest \widehat" (as in $\widehat{.}$). Is there a way to put that one above a wide character like M ($\widehat{M}$ would stretch and give be an even wider hat).  I guess I have a lack of understanding for the mechanism behind accents that extend, so feel free to explain. Examples  I've recently found examples of using pairs of enclosing braces {}, with nothing in between the opening and closing braces, as arguments to commands and even to their options:  cat foo | xargs -I{} echo {}  find . -size 0 -exec rm -i {} \;  No Documentation  My problem is that I cannot find a documentation in the  that describes the usage of {} in such context as in the examples above.  I do not think it is a , because a dollar sign must precede the enclosing braces in a parameter expansion as in ${}.  It cannot be a  either, because it takes the form of {x..y[..incr]}, where x and y are not optional.  It also cannot be a  either, because {} is used as arguments.  Questions   What does a pair of enclosing braces {} even mean, in general, as an argument to any command that accepts it? Where can I find a documentation that describes the usage of {} as arguments? The "Spell Storing" ability of the Shield Guardian says:     To do so, the wearer must cast the spell on the guardian.  The spell has no effect but is stored within the guardian.   This seems to indicate you cannot cast, for instance, Fire Shield on the Guardian, because that has a range of Self.  This seems different than what is intended, as the wording for a ring of spell storing is:     This ring stores spells cast into it, holding them until the attuned   wearer uses them....Any creature can cast a spell of 1st through 5th   level into the ring by touching the ring as the spell is cast.  The spell has no effect, other than to be stored in the   ring.   The use of the word "into," which does not seem to indicate any range, versus the use of the word "on," which seems to mean the guardian is a target of the spell.    Which is the correct interpretation, grammatically, versus what is the RAI? When I tried to run , I got the below screen:    The captcha is missing!  I tried in other browsers too.    Update:  From @Oded's comments, I changed to HTTP and it was working perfectly.  Out of curiosity I would like to know why the captcha isn't working when accessing Data Explorer over HTTPS.