Show UISearchDisplayTableView when search string is empty
UISearchDisplayController - how to preload searchResultTableView
java.lang.StringIndexOutOfBoundsException: String index out of range I'm looking for a formula to calculate the sum of $(a+b+c+d+...)^n$ but with coefficients equal to 1. For example in $(a+b+c)^2$. I want the sum of $a^2 + b^2 + c^2 + ab + bc + ca$. And for $(a+b+c+d)^3$, I want the sum of $a^3 + b^3 + c^3 + a^2b + a^2c + b^2a + b^2c + c^2a + c^2b + abc$. Similarly, I want the sum of expansion of $(a+b+c+d+e+....)^n$ with coefficient equal to 1. I tried to find the pattern by expanding the $(a+b+c)^2$. And I found that its formula is $a^2 + b^2 + c^2$ + $\frac{((a+b+c)^2 - a^2-b^2-c^2)}{2}$. This works for the power of 2. But fails on other powers. Any help will be really appreciated. I have made a fancy title page using titleformat and tikz, but I now face the following problem. The \chaptertitlename command returns \chaptername or \appendixname. I would like to spread the letters of the text returned by \chaptertitlename to a given length.  For example I would like to be able to call: \mycommand{\chaptertitlename}{3cm} in order to space the letters of \chaptertitlename on a total length of 3cm. How to do that ?  EDIT: This example illustrates a nearly working thing:  \documentclass[11pt]{article} \usepackage{fontspec} \newcommand{\spreadletters}[2]{\makebox[#2][s]{#1}}  \begin{document} \spreadletters{m y w o r d}{3cm} \end{document}   How to convert myword to m y w o r d ?  EDIT 2: Can someone explain me why the first work and not the second one (and how to make it work) ?  \documentclass[11pt]{book} \usepackage{fontspec} \usepackage{seqsplit} \usepackage[explicit]{titlesec}  \newcommand{\spreadletters}[2]{\makebox[#2][s]{\seqsplit{#1}}}  \begin{document} \chapter{First} \spreadletters{myword}{10cm} \linebreak % This is working \spreadletters{\chaptertitlename}{10cm} % This is not working \end{document} Adding Edge Loops Around Airplane Window I would like to add an edge loop around each one of these windows and are not 100% sure on the best way to do it even after watching some videos.  If someone could point me in the right direction that would be great. Thanks. YA coming-of-age fantasy series, protagonist keeps pigs I lost a series books during a move and I'm thinking I might like to get them for my son.  They are about a teenage orphan who lives with a (sort of) wizard who's primarily known for his prize pig. There is a "bad guy" but he doesn't do much - he starts off the action in one by scaring the pig, and the boy has to chase after it. He goes on several such adventures, notably one to "find his true nature" that ends with him staring into a pool.  I suppose it could be the early books of , but I'm pretty sure I read them in the 1980s, not 90s, and title seems wrong. And unlike the Wiki description, in the series I'm thinking of, there's no real magic to speak of - its "out there" but does not seem to be part of the action that I recall. Time taken to hit a pattern of heads and tails in a series of coin-tosses Inspired by Peter Donnelly's talk at , in which he discusses how long it would take for a certain pattern to appear in a series of coin tosses, I created the following script in R. Given two patterns 'hth' and 'htt', it calculates how long it takes (i.e. how many coin tosses) on average before you hit one of these patterns.  coin &lt;- c('h','t')  hit &lt;- function(seq) {     miss &lt;- TRUE     fail &lt;- 3     trp  &lt;- sample(coin,3,replace=T)     while (miss) {         if (all(seq == trp)) {             miss &lt;- FALSE         }         else {             trp &lt;- c(trp[2],trp[3],sample(coin,1,T))             fail &lt;- fail + 1         }     }     return(fail) }  n &lt;- 5000 trials &lt;- data.frame("hth"=rep(NA,n),"htt"=rep(NA,n))  hth &lt;- c('h','t','h') htt &lt;- c('h','t','t')  set.seed(4321) for (i in 1:n) {     trials[i,] &lt;- c(hit(hth),hit(htt))     } summary(trials)   The summary statistics are as follows,        hth             htt          Min.   : 3.00   Min.   : 3.000    1st Qu.: 4.00   1st Qu.: 5.000    Median : 8.00   Median : 7.000    Mean   :10.08   Mean   : 8.014    3rd Qu.:13.00   3rd Qu.:10.000    Max.   :70.00   Max.   :42.000    In the talk it is explained that the average number of coin tosses would be different for the two patterns; as can be seen from my simulation. Despite watching the talk a few times I'm still not quite getting why this would be the case. I understand that 'hth' overlaps itself and intuitively I would think that you would hit 'hth' sooner than 'htt', but this is not the case. I would really appreciate it if someone could explain this to me. A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$? I did not know what to search to see if this existed elsewhere. But, I could not find it. Here's the question:  Does there exist a continuously differentiable function, $f: [0,1] \rightarrow [0, \infty)$, such that the following hold? (i) $f(0) = 0$ (ii) $f'(x) \le c f(x)$ for all $x$ ($c$ is a fixed constant) (iii) $f \not\equiv 0$  This was a fun problem someone asked me a long time ago. I have always been convinced there is no such function, but I cannot prove it. I have mainly tried using the mean value theorem (in multiple forms), and re-wording the problem in terms of the integral of a continuous function to no avail. I spent some time trying to use (ii), the definition of derivative, and squeeze theorem, but no luck. After much time trying to prove non-existence, I spent a little time trying to find such a function... also with no luck. This problems ability to avoid being solved has since taken away the original fun and replaced it with a twinge of annoyance. Let $a_n$ be a sequence such that $\forall n\in \mathbb n: 0&lt;a\le a_n\le b &lt;\infty.$      Prove:          $\displaystyle\limsup_{n\to\infty}\frac 1 {a_n}=\frac 1 {\displaystyle\liminf_{n\to\infty}a_n}$   $\displaystyle\limsup_{n\to\infty}a_n\cdot \limsup_{n\to\infty}\frac 1 {a_n} \ge 1$ and there's an equality iff $a_n$ is converging.       Suppose there are two subsequences: $a_{n_l}, \ a_{n_k}$ such that $\lim a_{n_k} = k, \ \lim a_{n_l}=l$ and suppose $l\le k$, so $\lim \frac 1 {a_{n_k}}=\frac 1 k , \ \lim \frac 1 {a_{n_l}}=\frac 1 l$ so clearly: $\frac 1 k\le \frac 1 l\le l\le k$ so it's easy to see once the largest limit (supermum) is 'inverted' it has to become the smallest limit (infimum).   I realize this doesn't show equality, I don't know how to do the other way and I'm not even sure if what I did is good. If $a_n$ converges, suppose to $L$ as its limit then we have: $L\cdot \frac 1 L=1$.  If it does not converge then $a_n$ may tend to infinity or won't have a limit. From 1 we can change it to $\displaystyle\limsup_{n\to\infty}a_n\cdot \frac 1 {\displaystyle\liminf_{n\to\infty}a_n} \ge 1$ and from BW, every sequence has a converging subsequence, and since for converging subsequences: $\liminf a_n\le \limsup a_n$ we have $\frac {\limsup a_n} {\liminf a_n}=\limsup a_n\cdot \limsup\frac 1 {a_n} \ge 1$.   This should probably be in absolute value since one of those subsequnce limits can be negative, but it isn't in absolute value in the question. Increasing spacing between section number and title in the table of contents I'm using the simple ordinary \tableofcontents command to produce a table of contents, and I find that the resulting spacing between the section number and the section title is too small:    Can someone tell me how to fix this, please. My documentclass is memoir, if that matters. This option, which was present in the "Mouse and Touchpad" settings panel in previous versions, is for some reason absent in 16.04 LTS. Does anyone know why this is, and/or how to fix it? Thanks. Recover scaling factor in TikZ Does it exist some tikz register (let say \zoomfactor) that provides the curent scale factor. For example can I do something like :   \begin{tikzpicture}[scale=2]     \begin{scope}[scale=1.5]         \draw (0,0) circle (\zoomfactor);     \end{scope} \end{tikzpicture}   and to obtain circle of size 3=2*1.5 ? Overlapping matches in Regex I can't seem to find an answer to this problem, and I'm wondering if one exists. Simplified example:  Consider a string "nnnn", where I want to find all matches of "nn" - but also those that overlap with each other. So the regex would provide the following 3 matches:   nnnn nnnn nnnn   I realize this is not exactly what regexes are meant for, but walking the string and parsing this manually seems like an awful lot of code, considering that in reality the matches would have to be done using a pattern, not a literal string. Agreement in "[Singular Noun] Is/Are [Plural Noun]"? Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$? In my textbook on elementary number theory from a class last year, as well as elsewhere through my academic experience and even posts here, I often see the greatest common divisor notated as $(a,b)$ (where this represents the greatest common divisor of $a,b$).  My question is, why is such an unusual notation used? I say it's unusual (if not a bit absurd), for a couple of reasons:   It is unintuitive. It does not grant the reader an immediate knowledge of what it means. In particular, I can easily see it being misinterpreted as an ordered pair of points, and not as a function (which it basically is and I touch on in a second) or representing a single value. Good notation would be immediately understood, no? One should not struggle with parsing through the context or meaning. A clearer notation is often used, and just three letters away. You could certainly think of $(a,b)$ as an ordered pair, if we consider it a function. I often see the alternate $gcd(a,b)$: a function, which takes in two inputs ($a$ and $b$), and outputs their greatest common divisor (or factor, if you prefer). Merely adding the three letters makes the notation clearer by clarifying it is  a function, and using a relatively well-accepted acronym. (Or, at least, I often hear it abbreviated "g.c.d." in school.)   I've mulled this over for a while and I can't think of much without borrowing inspiration from other "unusual" notations. For example:   Common understanding in context: consider the $\log(x)$ function. Depending on context, without a base stated as seen here, it can be presumed to mean whatever is most "appropriate." It could be base $e$ (common in mathematics), base $10$ (common in engineering), or base $2$ (common in computer science). The ambiguity is essentially resolved by context in other words - personally, not a fan of that (I like the explicit stating of bases for full clarity), but if such a motivation holds elsewhere, it might stand to reason that $(a,b)$ could just be taken as a shorthand and "understood" in the context of number theory to simply be the greatest common divisor. That it is in fact used despite $gcd(a,b)$ being clearer and somewhat common also does seem to suggest this playing a role. Perhaps it just started that way and it kept being used. For example,  (based on a ) regarding how logarithms, roots, and exponentiation can be unintuitive from a notation perspective, and proposes an alternative, easier to understand notation. I haven't been in middle school in nearly a decade, but guessing from discussions online, that obviously hasn't really picked up too much. In that sense, perhaps it's like that for $(a,b)$: like we still notate exponentiation, etc., the same way today despite how counterintuitive it is (at least for students), perhaps it just "stuck" and proliferated?   I wasn't able to easily find any reason why online, and it bugs me a bit, so I ask:     Why do we so unintuitively notate the greatest common divisor of two numbers $a,b$ as $(a,b)$?   I of course recognize that this is somewhat moot in light of how easily it's made clear - as established above, all I have to do is append the front of the parenthetical by $gcd$ or $gcf$ to make it way better. And of course, people do that. But I'm more curious in where this ambiguous former notation arose and, in light of a better notation, why it is still used today. Before I start, YES, I have done my own research - I know how annoying a repeat question is. Yet each answer is so specific to others...  When I tried the beta 2.8 64 bit, it says "Blender requires a driver with at least OpenGL 3.3 support. The program will now close."    The question: I know that it is true that 2.8 requires OpenGL 3.3. But does my PC not have it, doesn't support it, or do I have it and blender won't detect it? I'm not sure what info to include or what to look for, so here's my PC's specs:  Windows 10 (64 bit) Core -        Intel Core i5-2400 CPU @ 3.10GHz RAM -         8GB (7.89GB usable) System type - 64-bit Operating System, x64-based processor  Thanks!  EDIT: Graphics properties: I remember after Stargate: Universe was cancelled, that I read, somewhere on the web, either part of an interview or an article by one of the producers about what they were planning if there had been a third season.  (He said they weren't sure whether they'd set it soon after the ending of the second season, or later, or were going to do something else.)  He also wrote that, while he felt okay discussing that, he did not feel like he could reveal how the story about the superstructure the Destiny had found would turn out.  He said that was something the other two producers had worked out and he didn't want to reveal it and would leave it up to them to reveal it if they wanted to.  Was this ever revealed?  Did the other producers ever discuss or reveal anything about what was going to happen with that storyline?    Addition: I'm referring to the superstructure that is the message found in the background radiation throughout the universe, not anything from the planet builders or other easily seen physical structures. You can post a link to an android market application by useing a link that looks like:     market://search?q=pname:package    While browsing the market, is it possible to find an app's package name? Or is there a convenient way to get or share a link to a market app? Is there any way to post a link to a market app that normal (non-android) browsers can make use of? Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $. So we obviously we want $ x^{2} + y^{2} + 1 \equiv 0 ~ (\text{mod} ~ p) $.  I haven’t learned much about quadratic congruences, so I don’t really know how to go forward. I suppose you can write it as $ x^{2} \equiv -1 - y^{2} ~ (\text{mod} ~ p) $, but again, I’m not sure where to go. I know about the Legendre symbol and quadratic residues, which I know are involved in this question, but I don’t know how to apply what I know. :( In column B I have contact number. I want to add a country code to all of them.  For example, if the number is 123456, I want it to become 88123456.    Each number is in 1 row, and there are about a thousand of them, so I want an automatic way to do this that allows me to add the country code to each of them without a space. I think my MacBook Pro battery was replaced by Apple's service team. How do I check that? I handed my MacBook Pro (15" Touch bar) to the service centre in order to have the keyboard replaced. Now, when I check the battery cycle count, it shows "1". Before it was at "82".   Also, I'm getting a battery life of only 4.5 - 5 hours now.   Is there a way to find if my battery was replaced or not?