$x'=x^2- \frac{2}{t^2}$  Hmm I have not idea how to do it... Maybe any smart substitution could work?
Solve differential equation:  $x'=x^2- \frac{2}{t^2}$  Maybe is it sth connected with homogeneous equation? I have no idea how to solve it.
$$\sum_{k=1}^{\infty} \frac{1}{k^{\ln k}}.$$  I have some problems with this sum, I have tried most of the common methods, such as the ratio/root test, integral test, etc. I do believe it looks like a problem easily solvable by a direct comparison with some p-series, however, I do not know how to formulate the inequality.   I did try using the common fact that $\ln(x) \ll x^p$ for large $x$ but that of course only bounds it from below with a convergent series saying nothing about ours. Also I tried rewriting the 'summand' as $e^{\ln(k^{\ln k})}=e^{\ln k \cdot \ln k}$ but this did not really yield anything.   Any answer or hint would be greatly appreciated. CSS Margin Collapsing So essentially does margin collapsing occur when you don't set any margin or padding or border to a given div element? How should spare change be exchanged? So I have about $50 in pennies, dimes and nickels.  What would you do with it?  I'm asking because I don't think spending hours rolling up the change and taking it to the bank is the best/most creative thing.  More info:  I took the change to the bank (not rolled up).  The banker asked me if I knew the exact amount... when all I had was a huge bag of change weighing like 30-40 pounds :-p  I said I didn't know the exact amount.  So the banker put all the change into a different bag, gave me a little receipt and said look for a deposit to your account in about a week.  Next time I'll just find a coinstar machine. I don't like waiting a week to have my change counted.  Also I'm sure the banker could fish out the quarters and no one would be the wiser :-) Including a relative path to a class file Reverse of number in PHP not showing correct output Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$ I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof? Shapefile projections not matching up in QGIS? To start off with, I'm very new to QGIS. I'm attempting to place a shapefile with locations for 3 substations on a map of Peniche, Portugal. The locations for the substations are given in latitude and longitude coordinates.   When I start off by importing the substation shapefile, I make sure that both the layer CRS and project CRS are set to EPSG:32629, which gives each substation point the correct coordinates, however the scale is at 1:1, which is not correct. As soon as I then add a raster map of the region or a shapefile of Portugal using the same CRS the position of the substations also becomes incorrect.   I'm sure there's a simple solution I'm not getting, but I've been trying for a while and have had no success. Here's a dropbox link to the files I noticed that after joining a table to a shapefile the headers of each fields in the table used for the join are changed by QGIS and they are attributed to a different name.  For instance, I had a shapefile with vegetation_codes and a table with vegetation_codes and veg_definition (these were the headers). After joining the table to the shapefile and also saving the shapefile and creating a new one, the vegetation_classes header was changed into vegetati_1.  Is there a way to keep the original headers?  I am using QGIS Dufour on Windows 7 and the table that I join to the shapefile is CSV (tried with dbf as well and the problem is the same). Let $y$ be a differentiable function on $\mathbb{R}$. If  $$\lim_{x\rightarrow \infty}(y(x)+y'(x))=0$$ Then how does one show that $$\lim_{x\rightarrow \infty}y(x)=0$$ I'd appreciate some help on this problem. Thanks a lot. The Windows 10 April 2018 Update includes a new feature called Timeline which tacks the activities and allows you to see what you have done earlier, sends it to Microsoft servers, so that you can resume work on a 2nd device, which is connected to the same Microsoft account when you press the Tasks View button in the taskbar:    How can I disable the Timeline because I don't want that my activity gets tracked? Prove Lipschitz function $f$ with constant $K$ is integrable on $[0, 1].$ We suppose that $f : [0, 1] \rightarrow \mathbb{R}$ is a Lipschitz function with constant $K$. We want to show that $f$ is integrable on $[0, 1].$  I've been trying to use the Darboux criterion of integrability by trying to show that, for $\epsilon &gt; 0$, $$S^*(f,P) - S_*(f, P) &lt; \epsilon,$$ where $S^*(f, P)$ and $S_*(f, P)$ are the Upper and Lower Riemann Sums, respectively.  This is what I have so far: $$\sum_{i=1}^n M_i (x_i - x_{i-1})- \sum_{i=1}^n m_i (x_i - x_{i-1}) = \sum_{i=1}^n (M_i - m_i) (x_i - x_{i-1})$$ $$\le \sum_{i=1}^n K (x_i - x_{i-1}).$$ because $|f(x) - f(u)| \le K|x-u| \le K |1|$, since $x\in [0, 1]$. Then, $$\sum_{i=1}^n K (x_i - x_{i-1}) = K.$$ However, this is only a single upper bound, not an arbitrary $\epsilon.$ Can I get some pointers about how to proceed? Thanks! Shorten title on each beamer slide In a beamer presentation the title is long but ok for the first slide. The problem is that when the title appears below on each slide it is very long and I would like to use here some sort of running or shorter title, how can this be done? Can someone help me figure out the big-O for the recurrence relation $T(n) = T(n^{1/2}) + 1$?  I didn't think the master theorem would work since it requires $T(n) = T(n/b)$... to have $b$ as a constant. I was wondering if anyone could shed some light on a method to approach this problem? (not looking for a solution) Get OS-level system information How can I make my local repository available for git-pull? Unicode filenames on Windows with Python & subprocess.Popen() Is (rest) mass quantized? I learned today in class that photons and light are quantized.  I also remember that electric charge is quantized as well.  I was thinking about these implications, and I was wondering if (rest) mass was similarly quantized.  That is, if we describe certain finite irreducible masses $x$, $y$, $z$, etc., then all masses are integer multiples of these irreducible masses.  Or do masses exist along a continuum, as charge and light were thought to exist on before the discovery of photons and electrons?  (I'm only referring to invariant/rest mass.) How to work out sqft/m of land coverage? I am currently self teaching myself on qgis whilst volenteering on a project on a river catchment and your help is hugely appreciated!  I need to be able to work out the percentage of land cover or sqft/m coverage. I have all the land uses on as a vector layer over my river catchment.   Many thanks and let me know what other info i need to give as a newbie! I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending. Implicit 'which is', 'which are' A new study has shown that millions of pieces of junk floating in  space could be a big hazard for satellites orbiting Earth.   Is there an implicit 'which are' in front of floating in space? Why is 'which are'  not written?