I have almost finished reading the basics of Bosonic String Theory from Becker, Becker and Schwartz as well as Tong's notes. What is the best book to start reading about Superstring theory (something which is slightly easier than Polchinski). I am confused among these options:  String Theory in a nutshell by E. Kiritsis String Theory and M theory by Becker, Becker and Schwartz. Green, Schwartz and Witten volume 1 Superstring Theory by E. Kiritsis Something else
I am in the last year of MSc. and would like to read string theory. I have the Zwiebach Book, but along with it what other advanced book can be followed, which can be a complimentary to Zwiebach. I would like a more mathematically rigorous book or lecture notes along with Zwiebach.   Specifically, mention whether the book discusses string theory   Rigorously? Intuitively?   What's the scope of the book? Does it cover the advanced materials, e.g. Matrix string theory, F-theory, string field theory, etc. Maybe even String Phenomenology?
I've recently searched how I could get the application's directory in Java. I've finally found the answer but I've needed surprisingly long because searching for such a generic term isn't easy. I think it would be a good idea to compile a list of how to achieve this in multiple languages.  Feel free to up/downvote if you (don't) like the idea and please contribute if you like it.  Clarification:  There's a fine distinction between the directory that contains the executable file and the current working directory (given by pwd under Unix). I was originally interested in the former but feel free to post methods for determining the latter as well (clarifying which one you mean). Include the "People Reached" and "Helpful Flags (count)" data in SEDE Proving that a list of perfect square numbers is complete Well, I have a number  $n$ that is given by:  $$n=1+12x^2\left(1+x\right)\tag1$$  I want to find $x\in\mathbb{Z}$ such that $n$ is a perfect square.  I found the following solutions:  $$\left(x,n\right)=\left\{\left(-1,1^2\right),\left(0,1^2\right),\left(1,5^2\right),\left(4,31^2\right),\left(6,55^2\right)\right\}\tag2$$     Is there a way to prove that this a complete set of solutions? So I mean that the solutions given in formula $(2)$ are the only ones?     My work:   We know that: $$ 1 + 12x^2 \left(1+x \right) \ge 0   \space \Longleftrightarrow \space   x \ge -\frac{1+2^{-2/3}+2^{2/3}}{3}   \approx -1.07245 \tag3 $$ So we know that for $x&lt;-1$ there are definitely no solutions. The conditions $a^2b^2=b^2a^2$ and $a^3b^3=b^3a^3$ make the group $G$ abelian? I want to enable GPU rendering, but there is no option in User Preferences > System:    Why is this? How can I get cycles to render using my GPU? Plot 4D data with color as 4th dimension How does Meta Stack Exchange work? Meta Stack Exchange seems to have different rules and user behavior than the "regular" Stack Exchange sites.  How is it different?    Individual questions answered below:                Related The Find Familiar spell states, in part:  As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons.  The question arising from this is:  Is this pocket dimension different for every familiar in the world? Thus being a personal pocket dimension? If this is true, then it should be able to store items given by its master for safe keeping away from anyone else, as long as these are items that a familiar could carry with it. Can the familiar bring small items with it into the pocket dimension for safe keeping? Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable. Turning a cipher into a hashing function The Degree of Zero Polynomial. I wonder why the degree of the zero polynomial is $-\infty$ ?  I heard that, it is $-\infty$ to make the formula $\deg(fg)=\deg(f)+\deg(g)$ hold when one of these polynomials is zero. However, if that was the only reason we could have said that it is $\infty$ instead. "export PS1=" for customizing shell prompt Where does pp (PAR) unpack add (-a) files? How do I post text so that it is formatted as code?  What do I need to do so that my code shows up properly &mdash; not escaped or removed &mdash; when posted? And how to get the correct syntax highlighting?     For more information, see "" in the . Can we calculate the standard error of prediction just based on simple linear regression output? The standard error of prediction in simple linear regression is $\hat\sigma\sqrt{1/n+(x_j-\bar{x})^2/\Sigma{(x_i-\bar{x})^2}}$.  My question is to calculate the standard error of prediction for $pop=1029$ just based on the following regression output. I can get all except $\bar{x}$. And I also know how to calculate the approximate standard error of prediction based on the standard errors of intercept and coefficient of $pop$, ignoring their correlation. Why does water pouring from a glass sometimes travel down the side of the glass? If you have a glass of water, say, three quarters full and you pour it at an angle of say, $45^{\circ}$ with respect to the the table, the water comes out of the glass and goes directly down towards the floor.  However, when the glass is more full, or even three quarters full and the 'angle of pouring' is far less with respect the table, when the water comes out of the glass, rather than going straight down it kind of stays stuck to the glass and travels down the outside of it.  Why does this happen? (I'm sure many of you have observed it yourself by accident and ended up making a mess). Function is Continuous When Restricted to Closed Sets Which Cover the Space Suppose that $\{A_i\}$ is a finite collection of closed sets in $X$ such that $X = \bigcup A_i$, and $f : X \to Y$ restricted to each $A_i$ is continuous. Then $f$ is continuous.   Okay. The base case ($n=2$) is just the pasting lemma. I am having a little trouble with the inductive case, specifically with what the hypothesis is and how to deal with continuity with respect to subspaces. I believe the inductive hypothesis is to assume that any function over a topological space that is the union of $n-1$ closed sets such that the function restricted to each of these $n-1$ closed set is continuous must be continuous over the whole space. Then I assume I have a topological space $X = \bigcup_{i=1}^n A_i$, where each $A_i$ is closed, and a function $f : X \to Y$ such that $f|_{A_i}$ is continuous for each $i$. Thus $X = \bigcup_{i=1}^{n-1} A_i \cup A_n$, where $C = \bigcup_{i=1}^{n-1} A_i$ is closed since it is a finite union of closed sets. If I can show $f|_C$ is continuous, then I simply apply the pasting lemma to finish the problem. Give $C$ the subspace topology, and notice that each $A_i$ is closed in $C$. Thus we have a topological space $C$ that is the union of $n-1$ closed. But do I still have continuity $f$ restricted to $A_i$ since I am no longer considering them subspaces of $X$ but of $C$? When one says $f|_{A_i}$ is continuous, is one saying that $f$ is continuous when restricted to $A_i$ and $A_i$ is given the subspace topology?  EDIT:  I think I figured out the lemma I need. Claim: Let $A$ and $C$ be subspaces of $X$ such that $A \subseteq C$. Topologize $C$ with subspace topology with respect to $X$. Then the subspace topology on $A$ as a subspace of $X$ (call it $\tau_X$) is the same as the subspace topology of $A$ as a subspace of $C$ (call it $\tau_C$).   Proof: Let $U$ be open in $X$. Then $A \cap U$ is some open set in $A$ as a subspace of $X$. Since $C$ is a subspace of $X$, $C \cap U$ is open in $C$ as a subspace of $X$. Then $A \cap (C \cap U) = (A \cap C) \cap U = A \cap U$ is open in $A$ as a subspace of $C$, thereby proving $\tau_X \subseteq \tau_C$. Now let $O$ be some open set in $C$ as a subspace of $X$. Then $A \cap O$ is some open subset of $A$ as a subspace of $C$. But $O = C \cap U$ for some open set in $X$. Therefore $A \cap O = A \cap (C \cap U)= A \cap U$, which is also open in $A$ as a subspace of $X$. Hence $\tau_C \subseteq \tau_X$  Kind of obvious. But it was hard to spot the need for this lemma when I was considering subspace of subspaces and continuous functions, etc. Am I right in thinking this is the lemma I need? On the usage of "the" article with acronyms and initialisms I've read  and  I know that  1. The article is often used with initials that are pronounced letter by letter (initialisms).  2. The article is often NOT used with initials that are pronounced as a word (acronyms).  I used 'often' because I'm not sure about possible exceptions.  In my field of study (Operations Research), initials are frequently used to represent optimization problems (e.g., the TSP). I discussed this point with my university supervisor who makes comments on my reports (English is not his native language). He responded that:  "What I learned from [...] was that whenever we use (specific) acronyms, we don't use 'the' when they are within a sentence, and we use 'the' when a sentence starts with them. For instance,  (i) The HCP is an NP-Complete problem.  (ii) We developed a new algorithm to solve HCP."  HCP stands for the Hamiltonian Cycle Problem. It is really confusing me because I do not know when to use and when not to use the article. For example, on , the author Jane Watson writes:     Use a definite article with an initialism if the spelled out term begins with “the” but is not covered in the initialism.   which implies that I should use the article with "HCP". What do you think? How to get the ASCII value of a character How do I get the  value of a character as an int in ? How do you make the shapefile a Read-only so the client can not make any edits using 10.2.2 ArcGIS.  It is not within a geodatabase, just a stand alone shapefile.  I am using Windows 8