Using built in GPS in windows 8 with precise location?
Get specific GPS location somehow on windows 8
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? Regular expression: match start or whitespace Can a regular expression match whitespace or the start of a string?  I'm trying to replace currency the abbreviation GBP with a £ symbol. I could just match anything starting GBP, but I'd like to be a bit more conservative, and look for certain delimiters around it.  &gt;&gt;&gt; import re &gt;&gt;&gt; text = u'GBP 5 Off when you spend GBP75.00'  &gt;&gt;&gt; re.sub(ur'GBP([\W\d])', ur'£\g&lt;1&gt;', text) # matches GBP with any prefix u'\xa3 5 Off when you spend \xa375.00'  &gt;&gt;&gt; re.sub(ur'^GBP([\W\d])', ur'£\g&lt;1&gt;', text) # matches at start only u'\xa3 5 Off when you spend GBP75.00'  &gt;&gt;&gt; re.sub(ur'(\W)GBP([\W\d])', ur'\g&lt;1&gt;£\g&lt;2&gt;', text) # matches whitespace prefix only u'GBP 5 Off when you spend \xa375.00'   Can I do both of the latter examples at the same time? Lets say I have a loop in Bash:  for foo in `some-command` do    do-something $foo done   do-something is cpu bound and I have a nice shiny 4 core processor. I'd like to be able to run up to 4 do-something's at once.  The naive approach seems to be:  for foo in `some-command` do    do-something $foo &amp; done   This will run all do-somethings at once, but there are a couple downsides, mainly that do-something may also have some significant I/O which performing all at once might slow down a bit. The other problem is that this code block returns immediately, so no way to do other work when all the do-somethings are finished.  How would you write this loop so there are always X do-somethings running at once? Are there any disadvantages to unusual RAM amounts for virtual machines? This is going to seem like a silly question, but many many years ago I somehow got it into my head, perhaps from reading an article or speaking to people 'in the know' that a computer should not be run with 'odd' amounts of ram, such as 3,  5, 7 etc...    Is there any truth in this whatsoever?  I have a vmware environment with many servers in it.  I want to go through and alter the amounts of ram to reduce the overall ram usage and in many cases I want to give a server 3gb of ram as opposed to 4 or 2. How to respond to "How much funding will you bring?" as an interview question for a faculty job? Limit of a function with powers (L'Hopital doesnt work) I have a little problem with limit of this function:  $\lim_{x \to \infty} x^2(2017^{\frac{1}{x}} - 2017^{\frac{1}{x+1}})$  I have tried de L'Hopital rule twice, but it doesn't work. Now I have no idea how to do it. I am flying from the US to Edinburgh, UK. My layover is at Heathrow. Will I need to go through customs and check bags again at Heathrow before I take the next flight? Render not showing UV texture I have added a texture to a cube in the UV editor and it shows up fine in textured view  But when I render it there is no texture  What have I done wrong? For $a\ge 0$ let's define $$I(a)=\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right)dx.$$ Find explicit formula for $I(a)$.   My attempt: Let  $$\begin{align*} f_n(x) &amp;= \frac{\ln\left(1-2 \left(a+\frac{1}{n}\right)\cos x+\left(a+\frac{1}{n}\right)^2\right)-\ln\left(1-2a\cos x+a^2\right)}{\frac{1}{n}}\\ &amp;=\frac{\ln\left(\displaystyle\frac{1-2 \left(a+\frac{1}{n}\right)\cos x+\left(a+\frac{1}{n}\right)^2}{1-2a\cos x+a^2}\right)}{\frac{1}{n}}\\ &amp;=\frac{\ln\left(1+\dfrac{1}{n}\left(\displaystyle\frac{2a-2\cos x+\frac{1}{n}}{1-2a\cos x+a^2}\right)\right)}{\frac{1}{n}}. \end{align*}$$ Now it is easy to see that $f_n(x) \to \frac{2a-2\cos x}{1-2a\cos x+a^2}$ as $n \to \infty$. $|f_n(x)|\le \frac{2a+2}{(1-a)^2}$ RHS is integrable so $\lim_{n\to\infty}\int_0^\pi f_n(x)dx = \int_0^\pi \frac{2a-2\cos x}{1-2a\cos x+a^2} dx=I'(a)$. But  $$\int_0^\pi \frac{2a-2\cos x}{1-2a\cos x+a^2}=\int_0^\pi\left(1-\frac{(1-a)^2}{1-2a\cos x+a^2}\right)dx.$$ Consider $$\int_0^\pi\frac{dx}{1-2a\cos x+a^2}=\int_0^\infty\frac{\frac{dy}{1+t^2}}{1-2a\frac{1-t^2}{1+t^2}+a^2}=\int_0^\infty\frac{dt}{1+t^2-2a(1-t^2)+a^2(1+t^2)}=\int_0^\infty\frac{dt}{(1-a)^2+\left((1+a)t\right)^2}\stackrel{(*)}{=}\frac{1}{(1-a)^2}\int_0^\infty\frac{dt}{1+\left(\frac{1+a}{1-a}t\right)^2}=\frac{1}{(1-a)(1+a)}\int_0^\infty\frac{du}{1+u^2}=\frac{1}{(1-a)(1+a)}\frac{\pi}{2}.$$ So $$I'(a)=\frac{\pi}{2}\left(2-\frac{1-a}{1+a}\right)\Rightarrow I(a)=\frac{\pi}{2}\left(3a-2\ln\left(a+1\right)\right).$$  It looks too easy, is there any crucial lack?  $(*)$ — we have to check $a=1$ here by hand and actually consider $[0,1), (1,\infty)$ but result on these two intervals may differ only by constant - it may be important but in my opinion not crucial for this proof. XeTeX: What happened to \mathcal and \mathscr? Recently I switched from pdflatex to xelatex to be able to use OpenType fonts. I like to use variables highlighted using \mathcal for specific variables, while I used to use \mathscr-typeset variables for matrices. But when I compile with XeLaTeX they look exaclty the same.  Old code  \documentclass{standalone} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        New code  \documentclass{standalone} \usepackage{unicode-math} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Broken code  I tried to get back the glyphs from mathrsfs, but it failed this way.  \documentclass{standalone} \usepackage{unicode-math} \usepackage{mathrsfs} \begin{document} $\mathcal{C} = \mathscr{C}$ \end{document}   Output        Question: How can I get back the behaviour? In principle I'd like to have the old \mathcal letters from the pdflatex-version of Computer/Latin Modern.    Alternate solutions (Addendum 2016/05/11) How do I show that there exists variational/action principle for a given classical system? We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following:      If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always exists an action functional $A$, where    $$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$    such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?    I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all. Why did Obi-Wan allow Leia to get adopted by such a high profile figure? I know that Leia is a princess because she was adopted by the Queen of Alderaan, but why would Obi-Wan allow this? Wasn't the original plan of Obi-Wan and Yoda to hide the Skywalkers from Palpatine? Luke was placed into a very low-profile position, being the child of two farmers on a backwater planet. However, Leia occupies a very important political position.  Is there any reason why Obi-Wan would do this if he was trying to hide her? This question is about cosmology and general relativity. I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read that the universe is infinite.   Does it have infinite mass or is it dishomogeneous?  How can the universe transition from being finite near the big bang and infinite 14 billion years later? Or would an infinite universe not necessarily have a big bang at all? How can I get back to Blender's default theme? I am trying to classify using randomForest classification in GEE . However, I always get the error User memory limit exceeded, so I assume the number  of the feature are too large. Nevertheless, I saw many developers can classify even bigger dataset, so I am wondering if there is a better option there? The code can be accessed via  var fire= ee.FeatureCollection('users/spatola/recovery_rf_1712').map(function(feature){     var num = ee.Number.parse(feature.get('CLC_311'));     return feature.set('CLC_311', num);   }) var indices= ['EVI_mean','Dnbr','NBR2_mean','NBR2_min','NBR2_max','EVI_min','EVI_max']; var fire1=  fire.filter(ee.Filter.notNull(indices)); var fire2= fire1.select('Class_R','Dnbr','EVI_max','NBR2_max','imageId') var bands= ['NBR2_max', 'EVI_max']; var classProperty= 'Class_R'; var random= fire2.randomColumn('random'); var split_train= 0.8; var split_test= 0.2; var trainPartition= random.filter(ee.Filter.lt('random',split_train)); var testPartition= random.filter(ee.Filter.gte('random',split_test));  var RFtrained_c= ee.Classifier.smileRandomForest({  numberOfTrees: 100,  minLeafPopulation:2,  seed: 123,  }) .setOutputMode('CLASSIFICATION') .train({     features: trainPartition,     inputProperties: bands,     classProperty: classProperty,     }) print(RFtrained_c); var dict =  RFtrained_c.explain(); var test = testPartition.classify(RFtrained_c) print(test.first()) I'm trying to figure out how to use "not only... but also" properly. Basically, my goal is to combine two clauses by using "not only".  For negations, I've figured out two styles that both sound correct:   He knew that if he fractures his finger, not only would he not be able to compete in the water polo tournament, he would not be able to take the SAT on Monday, either. He knew that if he fractures his finger, neither would he be able to compete in the water polo tournament, nor would he be able to take the SAT on Monday.   However, I don't know how to form a sentence that does not include a negation while using "not only". Here are a few possibilities that I've considered:   Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was also given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, but he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was given a full scholarship. Thanks to his remarkable performance on the SAT, not only was he accepted into Harvard, he was also given a full scholarship.   In those four possibilities, I'm varying the usage of "but" and "also" in the last clause.  What is the proper usage of "not only"? Ignore .DS_Store and Icon files in a folder with Cocoa NSFIleManager How to combine two QUERY results into one column I have the following QUERY  =query(XX!A2:A;" select A where A&gt;'50' ")   and  =query(YY!A2:A;" select A where A&gt;'50' ")   how do I combine these two data sources so I don't have to have two separate columns they process data to?   best would be if the 1st row from XX is followed by the 1st row of YY, 2nd row followed by 2nd row... and so on If the above option is not easily possible, it is OK for one query to be followed by the second one (if I expect correctly that the start of the second will be moved with newly added data into the first one) Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous I am looking for a real valued function of real variable that is $n$-differentiable, but whose $n$th derivative is not continuous.  This is my function:  $f_n(x) = x^{n+1} \cdot \sin{\frac{1}{x}}$, if $x \neq 0$ and 0, if $x=0$. $n\in \{0,1,2,\ldots\}$ For example, if $n=0$, $f_0$ it's continuous and non diferentiable in $0$. I would like to create a minecraft server for me and and my boyfriend to play on.  How do I set it up? Do I need any additional software? Do you have some links to walkthroughs or tutorials?  I have tried to set this up a few times but have failed every time.