This is trickier than it looks at first blush.  In Excel, columns have letter identifiers:    1st column is "A" 2nd is "B" ...  26th is "Z" 27th is "AA" 28th is "AB" ... "ZY" "ZZ" "AAA" ...   I am looking for the cleanest algorithm (i.e. the most readable) that can turn the column number into the column identifier.  I explicitely don't want a solution that works inside Excel. It needs to run standalone.  I have my solution, but am looking for other approaches.  Here are my (NUnit) test cases. They are correct, to the best of my knowledge.      [TestCase(1, "A")]     [TestCase(26, "Z")]     [TestCase(27, "AA")]     [TestCase(52, "AZ")]     [TestCase(53, "BA")]     [TestCase(702, "ZZ")]     [TestCase(703, "AAA")]     [TestCase(18278, "ZZZ")]     [TestCase(18279, "AAAA")]     [TestCase(475255, "AAAAA")]
How do you convert a numerical number to an Excel column name in C# without using automation getting the value directly from Excel.  Excel 2007 has a possible range of 1 to 16384, which is the number of columns that it supports. The resulting values should be in the form of excel column names, e.g. A, AA, AAA etc.
How long does Alchemist's Fire burn? Looked and looked, can't find the answer anywhere (maybe I'm blind):  How long does Alchemist's Fire burn for?  In the item description within , it says:     On a hit, the target takes 1d4 fire damage at the start of each of its turns. A creature can end this damage by using its action to make a DC 10 Dexterity check to extinguish the flames.   Yet no mention of the burn rate.  One round after a hit?  2?  A minute?  Continuous until extinguished? I want to extrude a curve in two directions.    Or join both curves into one, is it possible? I've tried copying it and then join segments, but I don't see Remove Doubles option while working with curves. Why do the planets' orbital distances fall on an exponential curve? Background: I was recently reading a book on the planets to my son and I noticed a pattern in the distributions of the planets.  The planets' distances roughly follow an exponential distribution.  Below is a plot of scaled, log orbital distances $$ \tilde{d_n} = \frac{\log(d_n/d_1)}{\log(d_2/d_1)} $$ with the line $an+b$:   Where $d_1$ corresponds to Mercury and so on. Ceres is included, Pluto is excluded.  By linear regression, $a = 0.90, b = -1.06$.  For the statistically minded, the data has a Pearson's correlation of 0.996.  Note that this is a well known phenomenon, see  and references.  The code used to generate the plot may be provided on request.  Question: What is the mechanism that leads to this distribution?  Aside: Is there a good introductory text on solar system formation for the mathematically inclined?  Update: This is also known as Titius–Bode law. Pre-generate Review audits to avoid the lag? For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous. This is from Apostol's Mathematical Analysis.  Let $f$ be a function defined in $[0, 1]$ such that for each real number $y$ either there is no value of $x \in [0, 1]$ such that $f(x) = y$ or there are exactly two such values of $x$. Prove that a) $f$ must be discontinuous on $[0, 1]$. b) $f$ has an infinite number of discontinuities in $[0, 1]$.  Long back I had tried to solve the problem. I reasoned for a) as follows: Suppose that $f$ is continuous and let $m, M$ be its minimum and maximum values on $[0, 1]$. Clearly if $m = M$ then $f$ is constant and clearly for every $x \in [0, 1]$ we have $f(x) = m = M$ which contradicts given property of $f$. So we must have $m &lt; M$. Clearly there are now four distinct points $a, b, c, d$ in $[0, 1]$ such that $f(a) = f(b) = m, f(c) = f(d) = M$. By checking possible linear orderings of $a, b, c, d$ I could find a find a value of $y \in (m, M)$ for which there exist more than 2 values of $x$ such that $f(x) = y$. However this approach looks very clumsy and I suspect much simpler and easier proof is possible. Part b) seemed bit complex and my only guess was that probably $f$ was discontinuous on each subinterval of $[0, 1]$ but I could not prove this claim (may be the claim is wrong!). Perhaps there is a simpler solution to this part of the problem. Apostol's also asks to provide an example of such a function. Any hints on the overall problem will be appreciated.  Update: After looking at Marc's answer, I think I have found a way to show that there are infinitely many discontinuities. Earlier the solution was a part of the question itself but it made the question look quite lengthy hence I moved it to a separate answer. Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true? I'm working through a problem regarding expected values in Markov chains, and at some point it says:     Recall from probability that if $X$ is a positive integer valued random variable, then $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X &gt; k)$.   I know that by definition $\mathbb{E}[X] = \sum_a a\mathbb{P}(X = a)$, but I can't see how the above equality follows from this, nor am I sure if this is how to approach the problem. Basically, I have a kindle fire that uses a form of the android OS and was wondering if there was a way I could run similar apps on my Ubuntu system. Specifically I'd like the news reader program "Pulse".  Anybody know if such an emulator or workaround exists? Can anyone help me out with this,    This is from a custom object " Quotation", The look up field " Main Driver" is a look up to Personal account object. The below fields are as well exists in the personal account. I need whatever value would be choosen in the main driver, automatically the below values will get pop up.  I amm trying to write a trigger for this, but just got stuck, Error showing as,      Error: Compile Error: Variable does not exist: Account.Age__c at line   7 column 17   How can i define the Account variable in the Quotation object trigger ?  trigger MainDriverRelatedFields on Quotation__c (before insert,before update) {      for(Quotation__c obj : Trigger.new){          if(obj.Main_Driver__c!=null) {              obj.AgeMainD__c=Account.Age__c;              obj.GenderMainD__c=Account.Contact_Individual_Gender__c;          }      }  } Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$ Let $(a_n)_{n=0}^{\infty}$  be a sequence of real numbers satisfying $\sum_{1}^{\infty} |a_n - a_{n-1}| &lt; \infty$   Which of the following conclusions must then be true?  The series $\sum a_nx^n$ converges   Nowhere on $ \mathbb{R}$ Everywhere on $  \mathbb{R}$ On some interval containing $(-1,1)$ Only on $(-1,1)$   What I have tried is Make an inequality with $|a -b| \leq |a| +|b|$ .. but i cant proceed further .. Any sort of help will be deeply appreciable . In single-blind peer-review, can you reveal your identity without the editor's consent? In my field (chemistry), review is always done in a single blind process, i.e. the author does not know who the referees were, but the referees do know who the authors are. In ten years, I have never seen a referee breaching this anonymity, e.g. by signing their review, unless they got prior approval by the editor (in order to continue discuss things further with the authors, once the manuscript was accepted for publication).  So, it seemed logical to assume that in single blind peer-review, the reviewer should not disclose his identity without the editor's consent. Yet, some people have told me ( and ; also IRL a friend from human sciences) that they have seen people sign their reviews, or write emails to them after the review but before the paper is published.  So, in single-blind peer-review, can you reveal your identity without the editor's consent? Does it depends on the customs of each field, or is there a hard rule? (in which case, the few anecdotes I heard were outliers) Removing files matching a numeric range regular expression I have a folder which has many files. Some of the data files are labelled 1, 2, 3, ..., 300  I want to remove these data files using the terminal. How do I do this?   I want to do something like   rm some-regular-expression-giving-numbers-from-0--300 How do I use jpnevulator to capture and log the serial traffic between an application and hardware serial port? OK, I've been googling for hours so I obviously have not been able to understand the answers to the various questions that have already been asked about this subject.  I am hoping that, by asking the question again in a more specific way, I will be able to get an answer I can understand.  I have some application running in linux that communicates with an external device attached to a serial port.  I want be able to capture and log the data sent in both directions between the application and the device, with timestamps at the beginning of each line in the file.  As a test case, I am using minicom as the application I want to monitor, connected via a null modem cable to another computer also running minicom.  I have already confirmed that, if I type characters on either of the computers, characters appear in the other computer's terminal.  So far, so good.  I then found this question:    In the answer to this question, the program jpnevulator is suggested.  However, when reviewing the man page, I could not figure out the right way to use jpnevulator to get what I want.  Here is what I tried to do:  First, I opened a terminal window and typed the following command:  $jpnevulator --tty=/dev/ttyS0 --pty --pass --read --ascii --timing-print --file=serial.log   I saw the output:     jpnevulator: slave pts device is /dev/pts/18  I then opened another terminal window and typed the following command:  minicom -D/dev/pts/18 -b115200   Minicom opened without complaint.  However, when I typed characters in either terminal (local and remote), nothing appeared in either terminal.  jpnevulator only logged the data written to /dev/pts/18.  My expectation is that jpnevulator :   reads data from /dev/pts/18 and "passes" this data on to /dev/ttyS0 while also writing this data to the specified file. reads data from /dev/ttyS0 and "passes" this data on to /dev/pts/18 while also writing this data to the specified file.   I am aware of the remark in the faq that says "Jpnevulator was never built to sit in between the kernel and your application. I'm sorry."  However the very same faq states in the second paragraph down: "Now with a little bit of luck some good news: A little while ago Eric Shattow suggested to use pseudo-terminal devices to sit in between the kernel and your application."  That is the approach I am trying to take but I am having no success.  What am I missing?  Thanks to all in advance.  Cheers, Allan  p.s. I was successfully able to capture the back and forth traffic using the socat method mentioned in the existing question I referenced but this method did not offer any way of timestamping the traffic.  I was hoping that jpnevulator would have provided this for me. What damage will powering down instead of shutting down do? What makes RSA secure by using prime numbers? I am just learning about the RSA algorithm. Looking at the first two steps:   Choose two distinct prime numbers $p$ and $q$. Compute $n = pq$.    I have some probably stupid questions:   Why do $p$ and $q$ have to be prime numbers? Why couldn't they be any integers or odd integers? Or does that break the whole algorithm? Because prime numbers are rare in comparison to regular integers, does restricting the algorithm to only prime numbers reduce security? It would seem easier to find the private key if an attacker knows it's only going to be some prime number? EDIT:  My question was poorly worded.   I wasn't asking about showing $\ln(1+x) &gt; \frac{2x}{2+x}$ for $x&gt;0$.   What I wanted to know is why the lower bound provided by $ \frac{2x}{2+x}$ was so tight for small positive values of $x$. This is addressed in robjohn's answer. I recently upgraded to 12.04 from 11.10 and since upgrading have been unable to log in to my user profile. The upgrade went okay and I can login to a guest session fine but whenever I try to login to my profile, after entering my password, I just return to the login screen.  I've changed my password in Root (passwd &lt;username&gt;) and can log in to tty1 with no issues, it's just in GUI I'm having problems.  I'm using a HP dv7 laptop, 32-bit Ubuntu install, Intel® Core™2 Duo CPU P7350 @ 2.00GHz × 2, Nvidia graphics.  Any help would be appreciated. Relating the union of the power set of a set to the set itself How to calculate hash value of a file in Java? I need to pass an ID and a password to a batch file at the time of running rather than hardcoding them into the file.  Here's what the command line looks like:  test.cmd admin P@55w0rd &gt; test-log.txt What are the requirements for a (beta) site logo?