I've been reading up on why the value of 0^0 is controversial (see ) and I wondered: is it possible for $i^i$ to have a value? I plugged it into a TI-83 calculator and it returned 0.2078795764 (!) How is this possible and why is the result a real number not a complex number?  Update I realize how to use Euler's Identity of $e^{i\theta} = \cos(\theta) + i\sin(\theta)$ and I understand the oldest answer's value of $\theta = \pi/2$ to solve for $i^i$, but doesn't this mean I can pick any odd multiple of $\pi/2$ (such as $3\pi/2, 5\pi/2$, etc.) as a value of $\theta$? Does that mean that $i^i$ is somehow "periodic" like the cosine curve is?
What is the value of $1^i$? $\,$
How do I programmatically obtain the version in JBoss AS 5.1? Get complete stats of process started/terminated during login of user account When I login, I notice many process quickly start and terminate in task manager. But it happens very fast and I cannot save details about them (like process name, command line, CPU usage,..)  How can I collect stats about them so I can view them later I am working on a website for a client, and even though the site ranks extremely well for various different keywords (which is good), if I search for the site's name the homepage does not appear even on the second page on Google. I have to add the .com so it will appear.  But, for big brands like Best Buy, Nike and millions of others it is enough to just search for the brand itself and the first or second suggestion on Google is the brand's homepage.  How can I raise my brand's authority in Google so it will appear in Google on the first page when some searches for it?  I have tried changing the breadcrumbs so instead of "HOME" it is now the brandname, linked to the homepage. I thought that it will help with internal linking if the anchor text is the brand's name instead of the word "HOME".  Any ideas please? In Java, for a string x, what is the runtime cost of s.length()? Is it O(1) or O(n)? I've been told that code such as:  for (int i = 0; i &lt; x.length(); i++) {     // blah }   is actually O(n^2) because of the repeated calls to x.length(). Instead I should use:  int l = x.length(); for (int i = 0; i &lt; l; i++) {     // blah }   Is this true? Is string length stored as a private integer attribute of the String class? Or does String.length() really walk the whole string just to determine its length? Work the Spring There's a book that I read several years ago that I'd like to find.  However, I cannot remember enough about it to find it myself.  Neither the title nor author remain in my mind, nor any keyword or phrase that's unique enough for the Grand Google to nail for me.  Hence my desperate plea here.  In the book, there is an interstellar civilization composed of several power blocks.  The entire civilization did not fill the galaxy, but it did span several stellar systems.  Maybe 10s or 100s.  I seem to remember that one of the civilizations was a decentralized group referred to as the Brotherhood and they seemed to have been keen on preserving old learning and political ideals.  A derelict alien spacecraft from outside all of this had been discovered and at least two of the power blocks sent ships to recover it.  I don't recall if they knew at the time about the power the alien ship had, but they must have had some clue since there was some urgency in capturing this ship.  One of the ships sent to capture the Alien craft was commanded by somebody who was rather shaken up, to say the least.  He had had some big trauma in his past (like... the last ship he captained was annihilated with all hands.) so he was kinda bummed out about things and wasn't really putting his heart into getting this done.  He was assisted by the ship's AI who had a lot of soul-to-soul chats with the captain, and at one point almost relieved him of command because he was just not getting the job done.  I think the ship's name was Boaz.  These were the "good guys".  There was at least one other ship sent from the "bad guys."  The alien craft had some remarkable powers.  The interior volume was apparently infinite and the operators could see and manipulate anything in the universe.  There might have been some example given where all the rats somewhere were found and disposed of.  Whoever had control was tempted by the ole absolute power corrupts absolutely problem, but nobody but nobody could stop them because of their power.  They could eat and multiply within the ship and become real bad-asses.  But alas... (or hurray, depending upon which side you're one) everything fails eventually, and whoever controlled the ship would eventually succumb to some horrible end.  Whereupon the ship became derelict again until some other lucky race found it and repeated the cycle.  The ship had an AI that was real interested in taking the power for itself, but there was some mechanical, spring-loaded, mechanism outside of its control that needed to be worked in order to execute power.  The AI apparently never figured out how to "work the spring" and this made him crazy angry.  The ending is equally foggy for me.  I'm pretty sure the good guys got the ship.  They agonized over what to do with it.  Apparently it was indestructable and nobody wanted to taste the temptation of all that power.  In the end they dumped it on the surface of a neutron star.  There it sat forever more, probably with the crazy AI really pissed off about being there.  If you've read this book, you'll recognize it immediately from these clues.  I'm looking forward to finding out the name of this book.  Thanks! How to align two images side by side if one label has more lines I have two same sized images and want them side by side with a caption under them.  My code looks like this:   \begin{figure}[H] \centering \begin{minipage}{.5\textwidth}   \centering     \includegraphics[width=\textwidth]{3}     \caption{label1}   \label{fig:test1} \end{minipage}% \begin{minipage}{.5\textwidth}   \centering     \includegraphics[width=\textwidth]{4}     \caption{label2}   \label{fig:test2} \end{minipage} \end{figure}   which works fine until one of the labels has 2 lines, than it looks like this:    and I woud like to prevent it to look something like this:    How can it be done?  Thanks Is there an exception to the prohibition against ending a sentence with “ ’s ” at work here? The ’s can be used as a contraction representing a weak, unstressed word that is not pronounced.  It allegedly cannot occur in sentence final position.        She is not ready, but he is.   She’s not ready, but he is.   She’s not ready, but *he’s.      The last one is not grammatical there.  Similarly, here the last one is not grammatical:        He has not started yet, but she has.   He’s not started yet, but she has.   He’s not started yet, but *she’s.       claims this is because you cannot end a sentence with a weak form.  It backs up its point with reasonably scholarly documentation.  However, this does not seem to be invariably true.        Shall we go to the movies?  Yes, let us go.   Shall we go to the movies?  Yes, let’s go.   Shall we go to the movies?  Yes, let’s.      Unlike the third example in the first two sets, here in this case the third example is indeed grammatical, despite ending with a weak form.  Is this an exception to the rule, or is there another rule at work here? How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$? If $a_1,\dots,a_n$ are all unequal positive quantities, then prove that: $$\prod_{i=1}^n a_i^{a_i} &gt; \left(\frac{\sum_{i=1}^n a_i}{n}\right)^{\sum_{i=1}^n a_i}$$ No other conditions are given. I tried to solve it using logarithms, but I could not understand how can I prove $${a_1\log a_1}+{a_2 \log a_2}+\dots+{a_n\log a_n} &gt; {(a_1+\dots +a_n)}  \left(\log(a+\dots+a_n)-\log(n)\right)$$ And please tell me, is there any standard method to solve this kind of problems? One definition of an  is:     An abbreviation formed by (usually initial) letters taken from a word or series of words, that is itself pronounced as a word, such as RAM, radar, or scuba; sometimes contrasted with initialism.   An  is:     A term formed from the initial letter or letters of several words or parts of words, but which is itself pronounced letter by letter.   If I pronounce an initialism, as a word, and not just as letters, does that 'make' it an acronym? Why does the following code in C work?  const char* str = NULL; str = "test"; str = "test2";   Since str is a pointer to a constant character, why are we allowed to assign it different string literals?  Further, how can we protect str from being modified?  It seems like this could be a problem if, for example, we later assigned str to a longer string which ended up writing over another portion of memory.  I should add that in my test, I printed out the memory address of str before and after each of my assignments and it never changed.  So, although str is a pointer to a const char, the memory is actually being modified.  I wondered if perhaps this is a legacy issue with C? I am using the document class article. Once I place a part in the document, all subsequent sections belong to the part automatically. How can I reset a section such that it does not belong to a part?  The following sample demonstrates what I want to achieve:  \section{Introduction}  \part{Part 1} \section{Section 1 belonging to part 1} \section{Section 2 belonging to part 1}  \part{Part 2} \section{Section 1 belonging to part 2} \section{Section 2 belonging to part 2}  % should not belong to Part 2 \section{Conclusion} Bernoulli numbers, taylor series expansion of tan x I found the following formula here: .  Taylor series of $\tan x$:  $$\tan x = \sum_{n\,=\,1}^\infty \frac {(-1)^{n-1}2^{2n} (2^{2n}-1) B_{2n}} {(2n)!} x^{2n - 1} $$.  I do not understand what the Bernoulli number means in this formula. My problems are the following ones:  I do not know anything about Bernoulli numbers. I do not know how to expand the Bernoulli number in the formula you see further up. What expansion will be the final result? How did you arrive there? Why did you arrive there? How did you know that you should use the specific Bernoulli-related terms that you used in your answer? What is the purpose of the Bernoulli number in this formula?  A great deal of thanks. Anyone on the Android Jelly Bean OS and not able to buy Apps/Books through wallet? I have just bought the Samsung GalaxyNote 800 and am facing this issue.   The error is (RPC:S-7:AEC-0).   What is the solution? Why is the last digit of $n^5$ equal to the last digit of $n$? Is there a word for someone who has others do all their work for them? In a way like a slave master. More though like say someone who had robots do all their work and they were never themselves productive and had no drive. If you've read R.U.R. you'll understand the question better. I'm looking for a word with more definition than just lazy.  Update 1: It think I may actually go with drone if anything. I think that definition fits what I'm looking for the best. I also liked the definition of the British term layabout that one person mentioned, but I will probably use drone. Thanks for all the help and sorry if I was confusing or unclear.  Update 2: I needed this word for use in an essay I was writing which I have now handed in. Thanks for the help guys. No more suggestions needed. I have a set of predictors in a linear regression, as well as three control variables. The issue here is that one of my variables of interest is only statistically significant if the control variables are included in the final model. However, the control variables themselves are not statistically significant.  Here is how the multicollinearity of all my variables look like (including control variables):   &gt; vif(lm(return ~ EQ + EFF + SIZE + MOM + MSCR + UMP, data = as.data.frame(port.df)))        EQ      EFF     SIZE      MOM     MSCR      UMP   3.687171 3.481672 2.781901 1.064312 1.438596 1.003408   &gt; vif(lm(return ~ EQ + MOM + MSCR, data = as.data.frame(port.df)))        EQ      MOM     MSCR   1.359992 1.048142 1.412658    My variables of interest are EQ, MOM and MSCR, and the control variables are EFF, SIZE and UMP. EQ is only significant if the three control var are included, and becomes insignificant when they are not:   Here are the coefficients (1rst row) and t-stats (2nd row) when control variables are included (notice that EQ is statistically significant)         intercept           EQ          EFF        SIZE         MOM       MSCR          UMP [1,] 0.005206246 -0.006310531 0.0001229055 0.004125551 0.007738259 0.00473377 5.838596e-06 [2,] 1.866628909 -1.746583234 0.0388823612 1.178460997 2.145062820 2.08131100 1.994863e-01  Now, here is the result of the regression when the control variables are excluded (notice that EQ is NOT statistically significant anymore)         intercept           EQ         MOM       MSCR [1,] 0.007313402 -0.002111833 0.007128606 0.00668364 [2,] 2.652662996 -0.595391117 2.036985378 2.80177366    The problem is that when I include my control variables, all my variables of interest are significant, but my control variables are not.  Which variables should I include in my final model? How should I structure my final model then, given the fact that the model will be used for forecasting?  Thank you, I'm using TeXLive 2014. Here's a MWE:  \documentclass{article} \usepackage{tkz-fct}         % Must appear before {thmtools}  \usepackage{thmtools} \declaretheorem{theorem}  \begin{document}   \begin{tikzpicture}     \tkzInit  % No need to even plot anything!   \end{tikzpicture}    \begin{theorem}[A Silly Theorem]     Let $a = 1$. Then $a &gt; 0$.   \end{theorem} \end{document}   The error message is:  ! Extra \endcsname. \kv@processor@default ...fincsname\@xa \endcsname                                                   \csname iftrue\endcsname \... l.12   \begin{theorem}[A Silly Theorem]   If the optional theorem name is removed, all is well. Adding \protect{} doesn't help.  Any idea how to remove this conflict?  Thanks! Citation: refer to author or paper? What is the British English way of referring to a source in-text.  Is it plural because there are two authors, like this:         X and Y (2011) describe ...   Or is it singular because you are referring to a singular source, like this:     X and Y (2011) describes...   So what I am asking is whether you refer to the source or to the authors? I will like to know some of the android emulators that work really well with Ubuntu 11.10 and above. I want to try 'whatsapp' on Ubuntu through an android emulator. Thanks in advance Clusering based on categorical variables? I am working on a project and currently experimenting cluster analysis. The dataset is mainly categorical variables and discrete numbers. Please pardon my poor programming skills as I am not very familiar with MathJax, but I will try to summarize the data set in words in the following three examples.   imagine column 1 is participants names of course, from column2 - 5, each column's value range from 1 (least important) - 5 (most important). so in this case, column 2-8 only have discrete data.  column 6 for example, since this is a multiple choice question. row 1 chose "nice" as an answer, however, row 2 chose "poor". In this case, we have one column that contains multiple categorical answers. for column 7-9, this is another type of multiple choice questions. However this time, each column represents only one answer. column 7 only allows string values "true", column 8 only allows string "somewhat". So in this case, we have multiple columns that represent multiple answers of the same question.    Any ideas how to solve this? Thankful to any input!   A2       A3       A4       A5       A6       A7         A8         A9 1        4        5        4        nice     true       somewhate  false 2        4        3        1        poor     true                  false 1        5        2        1        nice                somewhate     3        2        1        5        nice     true                  false