What is the mathematical term for an operation that is self reversing?  For example:   Multiplying by -1 1/x   In general:  f(f(x)) = x
I can think of several examples of functions such that twice application of the function is equivalent to no application of it.   Additive inverse Multiplicative inverse Fourier transform Complex conjugation Any group built up from $\mathbb{Z}_2$, applying (one of) the $\mathbb{Z}_2$ parts' operation.   "Idempotent" came to mind, but that's wrong. It means $f(f(x)) = f(x)$, not $f(f(x))=x$.  What is the word for this "flip-flop" property?
URL line breaks with biblatex How do I allow long URLs to have line breaks at any point. This is in the bibliography not the main text. I am trying to save space so don't want extra spaces to be added to make it only break at slashes, for example, as it does by default.  I am using biblatex+biber. Force a program to run *without* administrator privileges or UAC? Is there any way that I can force a program that normally requires administrator privileges (via UAC) to run without them? (ie: no UAC prompt and no system-wide access.)  Added: Without modifying the executable itself.    In spite of James's answer, I have found a few ways that it can almost be done:   By modifying the executable I can remove the trustInfo entry from the manifest (or the manifest entirely, so I can use an external one), allowing the program to start without UAC. Unfortunately this modifies the executable, so it exits shortly after due to an internal checksum test. By using Process Explorer I can launch it as a Limited User. However this seems to limit it significantly more than I would like (it runs like Protected Mode IE and so can access significantly less than what my standard un-elevated user can). What is EFI in partition scheme? Recently I changed my partition scheme from MBR to GPT, and during after conversion I saw a another partition named EFI ... I don't have a good idea what does it do or its purpose ... but I think it's use for backup's.  So my question here is can you explain/tell me about EFI and it purpose? An infinite Penney's game. Context: I need to solve one variation of the . Problem: Two players ($A$ and $B$) throw a coin until one of the victory sequences appears. For player $A$ the victory sequence is $HTT$, for player $B$ the victory sequence is $TTH$. What is the probability that $A$ wins and what is the expected number of throws given that $A$ won? My attempt: Intuitively, it seems that player $B$ is more likely to win. Basically, I reliase that we can use the Markov-Chains, but my idea is only draw a binary tree and consider the sequences on the n-th step. My another idea was to calculate the expected number of throws to get, say, $HH$ that would be equal to $r_{HH}$: $$r_{HH} =  \frac{1}{4}E(number|HH) + \frac{1}{4}E(number|HH)+ \frac{1}{4}E(number|TT)+ \frac{1}{4}E(number|TH) = \frac{1}{4}(9 + \frac{5}{2} r_{HH})$$  And get $r_{HH}$. My issues: I don't really understand how to join these ideas to get a proper solution. A spaceship crew stuck in a damaged spaceship that's losing power Is it OK to reduce the charging current for a Li-ion 18650 battery? I am using NCR18650 batteries with the tp4056 charging module.  When I connect the charger at 2.8&nbsp;V (fully discharged), the tp4056 IC is getting hot at a 1&nbsp;A charge current. Is it OK to reduce this charge current by changing the charge current selecting resistor? So the tp4056 IC heat would be reduced, wouldn't it?  For my application I don't need a quick charge. With a low current, charging time will be increased, but it does not matter for my application.  Will reducing the charge current affect the battery's lifetime? Or will it damage the battery?  I am trying to reduce the heat of the tp4056 IC by reducing the charging current, maybe from 1&nbsp;A to 500&nbsp;mA or less. The 18650 battery never heats for a 1&nbsp;A charge current. How to get a list of current open windows/process with Java? Does any one know how do I get the current open windows or process of a local machine using Java?    What I'm trying to do is: list the current open task, windows or process open, like in  Windows Taskmanager, but using a multi-platform approach - using only Java if it's possible. Question mark for sentence which starts with a question but doesn't end with one I'm basically looking at sentences which start with a question, and end with an explanation to it. But there may be more instances of a similar structure. Sample sentence :      Can you book a room in advance, because otherwise we'd be in trouble   Should this sentence end with a period or a question mark?  PS: I read the apparently similar question  but the sentence structure there is different from what I'm looking for.  Edit: I just discovered that this question is a duplicate. A resolved question already  exists:   But i do like the explanations here better. Is there a term for this word play where a song intentionally avoids completing a rhyme? Take this for example:  In this , at 1:04 to 1:10, the person goes on rapping with a rhyming word at the end of each line, but he pauses before the end of the last word and, being humans, we predict the next word (due to the hint from the rhyme) that he is going to say but he avoids it intentionally. Is there a word or phrase for this word play?     ...and the beat still knocks when I sort my socks   I'm five foot eleven of sex   from the tip of my head to my gorgeous...   knees    Not the best example I could find but I think it sums up my point quite well. Mutable or immutable class? Take as an example the well-known . In the original paper, the regression model was used to model the amount people were willing to pay for improved air quality.  But the 'people' whose behaviour was being modelled was never specified. Presumably, it was not limited to 'residents of Greater Boston'. Only implausibly would it be 'humans anywhere on the planet'. Nor, 'all US residents'.   So what inference are we invited by the authors to draw about the scope they intend for their theory? Perhaps 'all residents of large US metro areas'. But - what about other First World metro areas? The first two sections of the Boston paper scrupulously avoid any reference which might suggest that they had a particular 'population' to which their 'sample' was to apply.  There is also the dimension of time - the data came from the 70s, whereas the theory is has no time limitations spelt out.  Plus - going back to first principles - how could the Boston data be treated as a sample of a population including, say, the Chicago metro area when no data from the Chicago area was considered?   Besides, lots of the covariates in the Boston regression weren't samples at all, but totals - so, for example, the proportion of blacks was supplied from census stats.  My question: how can we conceive the Boston data as supporting the geographically unlimited propositions in the paper? Is there a mathematical way of showing equivalence or approximation of the Boston data analysis to other cities? Or is it just assumed as a matter of common sense - such that the paper's authors would be amazed to think anyone could have any doubts on the matter? Find $\sum_{n=1}^\infty \frac{n^3}{n!}$. Why would I vote for an increase in the number of authorized shares? Is "89.9%" singular or plural? Confused About Trigonometric Substitution What are the applications of the ## preprocessor operator and gotchas to consider? As mentioned in many of my previous questions, I'm working through K&amp;R, and am currently into the preprocessor. One of the more interesting things &mdash; something I never knew before from any of my prior attempts to learn C &mdash; is the ## preprocessor operator. According to K&amp;R:     The preprocessor operator ##   provides a way to concatenate actual   arguments during macro expansion. If a   parameter in the replacement text is   adjacent to a ##, the parameter is   replaced by the actual argument, the   ## and surrounding white space are   removed, and the result is re-scanned.   For example, the macro paste   concatenates its two arguments:      #define  paste(front, back)  front ## back      so paste(name, 1) creates the token   name1.   How and why would someone use this in the real world? What are practical examples of its use, and are there gotchas to consider? For example, you're doing a research for a car to purchase. You get a list of cars with engine number, city where a car was assembled, and a color. What's missing is make, model and price. How are "related" questions selected? Derived template-class access to base-class member-data Physical Explanation for "Kolmogorov -5/3 spectrum" in Fluid Mechanics According to Kolmogorov, the energy spectrum function of a turbulent fluid is given as,  $E(k)=C\epsilon^{\frac{2}{3}}k^{\frac{-5}{3}}$  where $\epsilon$ is the energy flux and $k=\frac{2\pi}{r}$ where $r$ is the length scale.   The normal explanation I see in most physics texts and articles is that the -5/3 exponent is found purely through dimensional analysis. Obviously dimensional analysis is very useful, but often times there is a more physical explanation as well. Does anyone have any insights?