I was wondering whether there are any words in English that have three words spelt together like "eee" or "ooo". I'm not talking about abstract and meaningless words like "hmmm" or "zzz", but is there any other such word?
One of my friends argues that princessship is the only word which has 3 identical letter comes together (s) ,but I think there is no word such as princessship.  Can anyone tell me whether this is a real word, and if there are any more English words which have 3 letters consecutively?
I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up indicating the model without the significant variable is a worse fit. Should I remove the non-significant predictor or should I leave it in as it is a better model? Explicit formula for Bernoulli numbers by using only the recurrence relation It is not hard to show, by induction on $m\in\mathbb N$, that there exist a sequence $(B_n)_{n\geq0}$ of rational numbers such that  $$\sum_{k=1}^nk^m=\frac1{m+1}\sum_{k=0}^m\binom{m+1}kB_k\,n^{m+1-k},\ \style{font-family:inherit;}{\text{for all}}\ n\geq1\,.$$  These are the Bernoulli numbers of the second kind, that is, $B_1=+1/2$. A corollary of the proof (by induction) of the fact above is a recurrence formula for such numbers $B_n$, which are known as Bernoulli numbers:  $$\sum_{k=0}^{n-1}\binom nkB_k=0\,.\tag{$\ast$}$$  On the other hand, there are a number of explicit formulae for $B_n$, which are obtained using the equality $\frac x{e^x-1}=\sum_{n=0}^\infty B_n\,\frac{x^n}{n!}$; see  and . For example:  $$B_n=\sum_{k=0}^n\frac1{k+1}\sum_{r=0}^k(-1)^r\binom krr^n\,.\tag{$\ast\ast$}$$  Is there some clever way to manipulate the recurrence $(\ast)$ in order to obtain $(\ast\ast)$? jQuery/JavaScript to replace broken images I use a dual monitor.  The colors appear entirely different on the new monitor than they do on my laptop.  When you are selecting colors etc, to be included in a website design, it totally freaks me out.  Is there no software solution that finds how the settings of one of the monitor is and puts that to the second one?  Otherwise what all settings do I need to change manually on the second monitor to make it appear as it does on the laptop?  Thanks in advance. In Windows there is a straightforward "Format" option in a flash drive's right-click pop-up menu. Where's that in Ubuntu? Why do we care about eigenvalues of graphs?  Of course, any novel question in mathematics is interesting, but there is an entire discipline of mathematics devoted to studying these eigenvalues, so they must be important.  I always assumed that spectral graph theory extends graph theory by providing tools to prove things we couldn't otherwise, somewhat like how representation theory extends finite group theory.  But most results I see in spectral graph theory seem to concern eigenvalues  not as means to an end, but as objects of interest in their own right.  I also considered practical value as motivation, e.g. using a given set of eigenvalues to put bounds on essential properties of graphs, such as maximum vertex degree.  But I can't imagine a situation in which I would have access to a graph's eigenvalues before I would know much more elementary information like maximum vertex degree.  (EDIT: for example, dtldarek points out that $\lambda_2$ is related to diameter, but then why would we need $\lambda_2$ when we already have diameter?  Is this somehow conceptually beneficial?)     So, what is the meaning of graph spectra intuitively?  And for what practical purposes are they used?  Why is finding the eigenvalues of a graph's adjacency/Laplacian matrices more than just a novel problem? What metadata does a LibreOffice file contain and how to remove it? I am using LibreOffice on Linux. One way I know of viewing and removing metadata from a LibreOffice file is going to File -&gt; Properties -&gt; General, unchecking  “apply user data” and click reset. Then go to “Description” and “Custom” Properties and remove information from there, if exists.   Does it truly remove all the metadata or something is left and what is it and what other methods can I use to remove it?   Also, if I unzip a LibreOffice file, is contents.xml the only place where metadata may be found?  If I forgot to remove any metadata, is it possible that the username is transmitted? Two footnotes in a heading, only one is displayed at the end of the page I'm adding two footnotes to a section heading:  \documentclass{article} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lipsum}  \usepackage[stable]{footmisc}  \usepackage{titlesec}  \begin{document} \section{test \footnote{This is footnote no1.} \footnote{This is footnote no2.} } \lipsum[4] \end{document}   The heading will have both of the footnotes, but at the end of the page only the second is displayed. The problem appears to be \usepackage{titlesec}, because it works fine without it.    Stuff I specified in \usepackage{titlesec}:  \renewcommand\thesection{\arabic{section}}  \renewcommand\thesubsection{\arabic{subsection}}  \renewcommand\thesubsubsection{\arabic{subsubsection}}  \titleformat{\section}[block]{\Large\scshape\centering}{\thesection}{1em}{}  \titleformat{\subsection}[block]{\large\scshape}{\thesection.\thesubsection}{1em}{}  \titleformat{\subsubsection}[block]{\large\scshape}{\thesection.\thesubsection.\thesubsubsection}{1em}{}   Thanks in advance! Prove Uncountable set minus a countable set is uncountable Let B be a countable set, and let A be an uncountable set. Prove that A-B is uncountable The problem from Burton: show that the equation $n^2 + (n+1)^2 = m^3$ has no solution in the positive integers.  So far, I can see that gcd($n$,$n+1$)$=1$ and $m \equiv_4 1$ and $m=a^2 + b^2$ for some integers a,b. I'm guessing I need to reach a contradiction.  At this point, I am stuck. Any hints? This morning, I read Wikipedia's informal definition of a limit:     Informally, a function f assigns an output $f(x)$ to every input $x$. The   function has a limit $L$ at an input $p$ if $f(x)$ is "close" to $L$ whenever   $x$ is "close" to $p$. In other words, $f(x)$ becomes closer and closer to $L$   as $x$ moves closer and closer to $p$.   To me that sounds like something that might be better described as a 'target'.  If I take a simple function, say one that only multiplies the input by $2$; and if my limit is $10$ at an input $5$: then I've described something that seems to match the elements contained in Wikipedia's definition. I don't believe that that's right. To me it looks like an elementary-algebra problem ($2p = 10$). To make it more calculusy, I could graph the function's output when I use inputs other than $p$, but that really wouldn't give me anything but an illustration of the fact that one's answer moves farther from the right answer as it becomes more wrong (go figure).   So limits are important; what I've just described is trivial. I do not understand them. I know calculus is often used for solving real-world challenges, and that limits are an important element of calculus, so I assume there must be some simple real-world examples of what it is that limits describe.   What is a simple example of a limit in the real world?  Thank you  -Hal. Is ECC over real numbers possible? Many elliptic-curve cryptosystems today use GF(p) or GF(2^m). What if, say, we use big floating numbers with the classical point addition formulas - is a cryptosystem possible to build on that? SCP through multiple hosts describes how to SSH into a machine that can only be accessed through one or more hosts (that can also be SSH'd into).  Is there an equivalent way of using scp? That is, copy a file to my local machine from the far machine (assuming I have password or key access to all machines along the way)? I let him do it.   and     I allow him to do it.   Why does the latter require to?  What are the "rules" of using to with an infinitive? When is it necessary? Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$ $f(z)$ is a function such that $|f(z)| &gt; |z|$ for all $z\in\mathbb{C}$  How would you prove the function $\frac{1}{f(z)}$ is bounded. I think you have to use the $|f(z)|\leq M$ but I'm not sure. Question is about Ubuntu release process. Are migrations from n to n+1 releases expected?  Assuming we have server with installed Ubuntu 14.04 LTS. Will it be smoothly upgradable to Ubuntu 16.04 LTS via apt-get upgrade ?  Assumptions:   scope is software therefore we assume that given hardware is supported on both releases (upgrading from and to) that's why, always before upgrade you are asked to make backup to be able to revert in case of failure Proof involving absolute value and maximums Given the definition for any real numbers a and b, the max function is   $\max\{a, b\} =  \begin{cases}                                    a \text{ if } a \geq b \\                                    b \text{ if } a &lt; b \\   \end{cases} $  Lemma: for any two real numbers $a\text{ and }b, a \leq \max\{a,b\}$ and $ b \leq \max\{a,b\}$.  Prove that for real numbers, $a, b$, and $x$, if a $\leq x \leq$ b then $|x| \leq \max\{|a|,|b|\}$.  So far, I have  $x \geq 0$ or $x &lt; 0$ by the law of trichotomy  Case 1: $x\geq 0$  $|x| = x$ by the definition of absolute value  and I'm not sure where to go from there. Any hints? What is Quantization? Force pagebreak after every sentence/paragraph Is there a way to force a pagebreak after every sentence or paragraph?  This may seem like an odd thing to do, but for catching typos and just general editing I find it much easier to look at a sentence or paragraph in isolation so that I am not tempted to skip ahead.  Currently, I just zoom in so I can only see a few word at a time, but this is not a perfect solution.