Why does an odd number price look smaller than an even number price?
Is there any advantage in marketing my product for £99.99 instead of £100?
Windows equivalent of the Linux command 'touch'? I had a tin of golden syrup for a long time - longer than I care to admit. When I opened it up yesterday (to sweeten up some mulled wine), it was granular (a bit like honey can be), and black around the edges.   Is this 'bad', or just different?   Is the blackness the result of some chemical reaction with the tin?  And in general, does it eventually go off, or does it last indefinitely? To be specific, I was trying this code:  package hello;  public class Hello {      Clock clock = new Clock();      public static void main(String args[]) {         clock.sayTime();     } }   But it gave the error      Cannot access non-static field in static method main   So I changed the declaration of clock to this:  static Clock clock = new Clock();   And it worked. What does it mean to put that keyword before the declaration? What exactly will it do and/or restrict in terms of what can be done to that object? BasicTeX - how to identify packages that need to be added after an upgrade I'm using the BasicTeX distribution on OS X and recently upgrade from the 2011 to the 2012 distribution. This forces me to add the packages that I had added over time to the BasixTeX 2011 installation by pulling them from the online repository with tlmgr. Is there a good way to list these packages that are not part of BasicTeX but are part of the complete TeXLive? What exactly is the point of memoryview in Python What temperature should I set my water heater to? I need to do create a file with a filename such as :&gt;?, is this possible somehow? Windows stops it. Extended Euclidean algorithm I have programmed the extended euclidean algorithm. Is this a good approach?  def ext_ggT(a, b):     x,y, u,v = 0,1, 1,0     while a != 0:         q, r = b//a, b%a         m, n = x-u*q, y-v*q         b,a, x,y, u,v = a,r, u,v, m,n     gcd = b     return gcd, x, y What are these  error below ?  Package natbib Warning: Citation `Krishna2014' on page 16 undefined on input li ne 502.  [16 &lt;./figure/aks smr.png&gt;] [17] [18] ! Undefined control sequence. l.560 \Bibliography                    {figure/bib} How do we compare the size of numbers that are around the size of Graham's number or larger? When numbers get as large as Graham's number, or somewhere around the point where we can't write them as numerical values, how do we compare them?  For example:  $$G&gt;S^{S^{S^{\dots}}}$$  Where $G$ is Graham's number and $S^{S^{S^{\dots}}}$ is $S$ raised to itself $S$ times and $S$ is Skewes number.  It appears obvious (I think) that Graham's number is indeed larger, but how does one go about proving that if both numbers are "so large" that they become hard to compare?  More generally, how do we compare numbers of this general size?  As a much harder problem than the above, imagine a function $G(x,y)$ where $G(64,3)=$ Graham's number.  The function $G(x,y)$ is as follows:  $$G(x,y)=y\uparrow^{(G(x-1,y))}y$$  Where $G(0,y)$ is given.  I ask to compare $G(60,S)$ and $G(64,3)$ How to set render engine in blender? What effect does the Barr body have, in relation to female Turner syndrome? Why do persons with  have  developmental abnormalities, when normal XX-females do not, even though they only have 1 active X chromosome? From what I know, one X-chromosome is inactivated into a Barr body in normal XX-females, but these obviously don't show the symptoms of Turner syndrome. What function does the inactive chromosome have? Why does a relay have a minimum applicable load? I am trying to find relays for my application and I read  which looks fine but specifies     Minimum applicable load: 10mV 10µA   In my circuit, it is expected that the relay closes but no voltage and current is applied. You can think of it as 2 relays in series where one is open and one is closed, so there is no current. This sounds like something I'd do since I was at school.  Why would a relay require a minimum voltage and current on the load side? Is it allowed to operate that relay under my conditions or not? What could possibly break in a relay if I don't respect this requirement? What does "minimum applicable load" mean? When and how do I need to consider this value? Tighten rope without turnbuckles? I have two 4-ft x 4" x 4" wood posts, and each post has a screw eye. There's 12 feet of distance between each post.  How can I tighten a piece of 1/2" diameter rope that goes through each screw eye and it's stretched tightly without having to buy turnbuckles?  There has to be a knot just for this. I've been testing PCA via SVD to decompose a simple time series data matrix, $X$.  I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each column represents $x_1$ and $x_2$.  The mean signal, $\hat{x}$, is defined as the mean along the row axis (average of $x_1$ and $x_2$ along each timepoint).  I normalize each column of $X$ by subtracting its mean and dividing by the standard deviation.  When I use [U S V] = svd(Xz) in matlab, regardless of how the variables are distributed (whether they are correlated or uncorrelated), one of the columns of the right singular matrix, V, always points in the same direction (to a multiplicative constant) as the mean vector $(1/2, 1/2)$.  But when add an additional third time series, this is never the case (where the mean vector is $(1/3, 1/3, 1/3)$.  Because I normalize the standard deviation for each vector, it does make sense that the direction of most variance given by PCA would be the diagonal 45 degree line.  But if both variables $x_1$ and $x_2$ are independent gaussians, couldn't the PCA direction be any direction since the distribution is radially symmetric?  MATLAB Code:  s = RandStream('mcg16807', 'Seed', 0); RandStream.setDefaultStream(s);  G = zeros(1000,2); G(:,1) = 40*randn(1000,1)-100; G(:,2) = tan(G(:,1)) + randn(1000,1); X = G - repmat(mean(G),[size(G,1), 1]); Xz = X./repmat(std(G),[size(G,1), 1]); [U S V] = svd(Xz); G_mean = mean(Xz,2); corrcoef(G_mean, U(:,1)) corrcoef(G_mean, U(:,2)) how to represent geography or zip code in machine learning model or recommender system? I am building a model and I think that geographic location is likely to be very good at predicting my target variable.  I have the zip code of each of my users. I am not entirely sure about the best way to include zip code as a predictor feature in my model though.  Although zip code is a number, it doesn't mean anything if the number goes up or down.   I could binarize all 30,000 zip codes and then include them as features or new columns (e.g., {user_1: {61822: 1, 62118: 0, 62444: 0, etc.}}.  However, this seems like it would add a ton of features to my model.   Any thoughts on the best way to handle this situation? Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$ If I add a comment but navigate (by mistake) to another page, I lose my unfinished comment (ok, depends on browser etc). On the other hand, when formulating a question, and I click on a link by mistake, I'm asked if I really want to leave.  It would be nice to have this warning for comments as well. Composition of a harmonic function with a holomorphic function is still harmonic If $f$ is a harmonic function in a domain $D \subset \mathbb{C}$, and $g$ is a conformal mapping of a domain $D_0$ onto $D$, is $f \circ g$ harmonic in $D_0$?   I noticed this question while reading several pdf of lecture notes, and I'm having trouble figuring it out. Can anyone help?  Thank you so much! I want to write batch or something, that will write output of top into a file on login.  I did top &gt;&gt; output-file, but it contains some strange character!  Can somebody give a simple tutorial about how to write batch file in Linux?