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When writing letter to an academic professor (not necessarily from student to professor), what is the appropriate way to address his/her title?  I have seen in letters using  Dear Prof. X even when the addressee is not a full professor  Dear Dr. X though, knowing that the addressee is a full professor  Dear Mr/Mrs X though, knowing that s/he has an academic title Does the series $\sum_{n=1}^{\infty}|x|^\sqrt n$ converge pointwise? If it then what would be the sum? Brasero says it won't burn the CD because the file is too big, what's going on? Is there a way to mount a disk directly to a specific folder? Multiple WHERE clause in Linq What should I do when flagging if I don't see the destination site in the list? Sometimes I want to flag a question on Stack Overflow because it belongs to  or , but I don't see those sites on the list provided when you click on:  It doesn't belong here > off topic  I usually see: Why do we need in RSA the modulus to be product of 2 primes? What if I accidentally run command "chmod -R" on system directories (/, /etc, ...) I accidently ran  sudo chmod 755 -R /   instead of  sudo chmod 755 -R ./   I stopped it after few seconds, but now there is some problems such as  sudo: must be setuid root   How can I revert permissions back? How to make child collide How to query More than 50000 records from sObject i need to count total number of records in an sObject which can have around one million records. Will the code below work ? If no, how can this be done ? I dont need to use this in a vf page.   I will be using this COUNT() SOQL Query in a batch class which is scheduled to run at specific time.  AggregateResult results = database.query('SELECT COUNT(id) result FROM someSObject');     System.debug('No of ids are: '+results.get('result')); I've read  about how some publishers (e.g., Springer) allows authors to submit to arXiv before journal submission, but they make authors wait for a year after acceptance to submit to arXiv.   My question is: Is it okay to submit to arXiv during the time when the paper is under consideration by the journal, for example after it has been "revised and resubmitted" but before final decision? Then what is the probability that out of $n$ men $A_1,A_2,....,A_n$ each aged $x$ years,$A_1$ will die and will be the first to die Let $p$ be the probability that a man aged $x$ years will die in a year time.Then what is the probability that out of $n$ men $A_1,A_2,....,A_n$ each aged $x$ years,$A_1$ will die and will be the first to die?  The probability that a man aged $x$ years will die in a year time$=p$  The probability that a man aged $x$ years will not die in a year time$=1-p$  But from here on,i got stuck.Some hints and suggestions are welcome. Can you have a class in a struct? If Z is a square integrable random variable such that $E[Z]&gt;0$, then prove that  $$P(Z\geq k) \geq \frac{(E(Z)-k)^2}{E(Z^2)} \forall k \in [0,E(Z)]. $$  This is a homework question and I don't even understand why the inequality is reversed comparing to Markov/Chebychev inequality. Should Cauchy-Schwartz inequality be used? If yes, then how to begin? Thanks a ton! Why are properties lost in the Cayley–Dickson construction? A challenge on the parabola Good Night ... Here I am editing the question and explaining the purpose of the same ... Mathematics course, and I love this science, I am very curious, and these days, studying a book of calculus found in (book from the library of the University) a sheet full of challenges, to share with a colleague, he gave me this challenge, which he also failed to respond ... I tried, I tried, I used the formulas of quadratic equation, and I've been trying since Friday (here in Brazil is Sunday at 22:33), and could not, and I ask your help, and please believe me, I struggled, tried to make substitutions, tried both, and I'm confused ... I must find the values of $ a, b $ and $ c $?  Consider a parabola whose roots, other are $x'$ and $x''$, and such that $x'=-x''$ where $x'&gt; 0$. Let $$A = (x', 0)$$ $$B = (x'', 0)$$ and $V$ the vertex of the parabola. Suppose that the equation of this parabola is $$y = ax^2 +bx+ c$$. Calculate the value of the discriminant $$\Delta=b^2-4ac$$, so that the triangle is equilateral AVB. How to simulate slow internet connections on the mac What's a good software solution to slow down internet connections on the mac for testing and simulations?  My primary need is when testing code in the iPhone / iOS simulator, so slowing down the connection for specific applications or processes would be great. System of congruences with variable I am looking over , and I came across a solution containing this:  Problem Bernardo chooses a three-digit positive integer $N$ and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer $S$. For example, if $N = 749$, Bernardo writes the numbers $10,\!444$ and $3,\!245$, and LeRoy obtains the sum $S = 13,\!689$. For how many choices of $N$ are the two rightmost digits of $S$, in order, the same as those of $2N$? $\textbf{(A)}\ 5 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D)}\ 20 \qquad\textbf{(E)}\ 25$ Solution 1 First, we can examine the units digits of the number base 5 and base 6 and eliminate some possibilities. Say that $N \equiv a \pmod{6}$ also that $N \equiv b \pmod{5}$ Substituting these equations into the question and setting the units digits of $2N$ and $S$ equal to each other, it can be seen that $b &lt; 5$ (because otherwise $a$ and $b$ will have different parities), and thus $a=b$. $N \equiv a \pmod{6}$, $N \equiv  a \pmod{5}$, $\implies N=a \pmod{30}$, $0 \le a \le 4$ Therefore, $N$ can be written as $30x+y$ and $2N$ can be written as $60x+2y$ Just keep in mind that $y$ can be one of five choices: $0, 1, 2, 3,$ or $4$, ; Also, we have already found which digits of $y$ will add up into the units digits of $2N$. Now, examine the tens digit, $x$ by using $\mod{25}$ and $\mod{36}$ to find the tens digit (units digits can be disregarded because $y=0,1,2,3,4$ will always work) Then we take $N=30x+y$ $\mod{25}$ and $\mod{36}$ to find the last two digits in the base $5$ and $6$ representation.[N \equiv 30x \pmod{36}][N \equiv 30x \equiv 5x \pmod{25}]Both of those must add up to[2N\equiv60x \pmod{100}] $N\equiv{30x\mod{36}}\\N\equiv{30x}\equiv{5x\mod{25}}$ Both of these must add up to $2N\equiv{60x\mod{100}}$ [...]  I'm not really sure which modular arithmetic rule to apply in the final three congruences, or where to start. How would I go about understand this? How many elements of order $k$ are in $S_n$? shell scripts are still working without #!(sha-bang line) I am new to shell scripts and many books have written that use #!(sha-bang) line in starting of the script to invoke the interpreter .And this will invoke a new shell for script and do the interpretation line by line.But one of my basic script is still running without the magic line.  so my questions are:   from where did my basic script get the interpreter. how did the script manages to locate the interpreter.   now let me tell you about my basic script it just contains the following line:  echo "basic script without the magic lines"