I know that I can globally swap the Control and Command in Mac OS and this is not what I need. What I would like to do is keep both buttons as they are and only and make Ctrl+C, Ctrl+V, and Ctrl-X work as if they were pressed with the Command button. What is the easiest way to do this?

I've been using mac for years, but prefer to do software development on windows. I'm really used to is using the folowing shortcuts on windows very much:  <CTRL>  + INSERT: Copy <SHIFT> + INSERT: Paste <SHIFT> + DELETE: Cut   Of late, I've taken to doing even my development work on the Mac. However, as a matter of habit, I'm missing these shortcuts very much. Actually, I find these a lot more convenient than COMMAND + (C/V/X) combo.  Is there a way to reassign these three shortcuts at least?   I've look all over the internet and in the "Keyboards" system preferences but I did not find anything.  PS: If you're wondering where I find the INSERT keys on a mac book pro, I use a wireless keyboard.


I want to convert rotations given as quaternion from sensors to Unity. The sensors () axis are the following ones:    Unity is the following one:    I don't know how to map axis other than Z is up for the axis. Note that I don't really mind if I have a global rotation offset. I just want the sensors (they are multiple ones) relative orientation to be the same in Unity that in real life  Given  I think the following code should to the transformation:  Quaternion ConvertToUnity(Quaternion input) {     return new Quaternion(         -input.y,         -input.z,         -input.x,         input.w     ); }   Is that correct?

I have a quaternion from an IMU that id like to represent in unity. The issue is that the sensor uses a right handed coordinate system while unity uses a left handed coordinate system. In order to have the rotations of the IMU reflect in unity correctly, I would need to remap the axis. How can I do this by altering the quaternion components?  Specifically, I would need to map           sensor   unity forward  x        z up       z        y right    -y       x   I have seen multiple questions regarding this question especially this one.    However, it only explains a specific case where its a right hand to right hand remapping.  If possible, include an explanation without mathematics equations of how you would map any coordinate system to any other coordinate system.


Explain what programs (based around LaTeX) I need to download (Windows) in order to write up a mathematical document (must be able to do basic things like type mathematical symbols, insert equation labels, make changes to font colours and sizes etc.)  There are many variants of programs, which I am confused about. If possible, explain each one: LaTeX, MiKTeX, TexMaker, TeXworks, LyX etc.

Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see .


Let $X \sim Multinomial(n,p)$. The data takes the form $X=(X_1, \dots, X_k)$ where each $X_j$ is a count. Let $p=(p_1, \dots, p_k)$ where $p_j \geq 0$ and $\sum_{j=1}^{k}p_j =1$. The variance-covariance matrix of $X$ is: $$V(X) = \begin{pmatrix} np_1(1-p_1) & -np_1p_2 & \dots & -np_1 p_k \\ -np_1p_2 &  np_2(1-p_2) & \dots & -np_2p_k \\  \vdots & \vdots &  \vdots & \vdots \\ -np_1p_k & -np_2p_k &\dots &np_k(1-p_k) \end{pmatrix} $$ I understand the terms on the diagonal since $X_j \sim Binomial(n,p_j)$, but I'm stuck in proving the expressions of the terms outside the diagonal.

Problem 1.14 from .      For the multinomial distribution, show that   $$\operatorname{corr}(n_j,n_k)=\frac{-\pi_j\pi_k}{\sqrt{\pi_j(1-\pi_j)\pi_k(1-\pi_k)}}$$   Show that $\operatorname{corr}(n_1,n_2)=-1$ when $c=2$.   The multinomial density is $$p(n_1,n_2,\dots,n_{c-1})=\binom{n!}{n_1!,\dots,n_c!}\pi_1^{n_1}\dots\pi_c^{n_c}$$ Let $n_j=\sum_i y_{ij}$ where each $y_{ij}$ is Bernoulli with $E[y_{ij},y_{ik}]=0$, $E[y_{ij}]=\pi_j$ and $E[y_{ik}]=\pi_k$  Then $\sum_j n_j=n$, with dimension $(c-1)$ since $n_c=n-(n_1+n_2+,\dots,+n_{c-1})$. So each $n_j\sim Bin(n,\pi_j)$  $$\begin{cases}E[n_j]=n\pi_j\\ \operatorname{Var}(n_j)=\frac{\pi_j(1-\pi_j)}{n}\end{cases}$$ then  $$\operatorname{corr}(n_j,n_k)=\frac{-n\pi_j\pi_k}{\sqrt{n\pi_j(1-\pi-\pi_j)n\pi_k(1-\pi_k)}}=\frac{-\pi_j\pi_k}{\sqrt{\pi_j(1-\pi_j)\pi_k(1-\pi_k)}}.$$  Is that right? How I can show the second part?


I am sure I found this 3 times at . Someone marks my question as below:       This question may already have an answer here:      Why is return needed even after System.exit(0); 8 answers   I got about 7 answers on it and updated answers by answerers again and again. I have noticed that after an answer is edited, my question lost the above marking for duplicate. I think "..Ah they have remove the duplicate mark!". But after refreshing my browser, my question becomes as you see now. So, I describe it as a bug here.

I've come across a small issue which occurs when a question has been closed but the question itself or one of its answers are being edited.  Steps to reproduce:   Visit a closed question. (even closed years ago)   In a different tab or browser, edit the question or one of its answers. "an edit has been made to this post; click to load" message will appear above the edited post in the first tab/browser, click it. The .question-status div becomes hidden, which includes the closed notice below a question and, for a duplicate-closed question, the list of duplicates above the question body. This gives the appearance that the question is no longer closed (until you refresh).   Some screenshots:                I know it isn't common/important but it did confuse me when looking at a particularly bad question - I thought it had been reopened.   Is this an intentional feature? If so, what was the thinking behind it?    Another example  Before    After


I created a plane with a ground texture that has a displacement map to simulate the depth for the rocks and I made it slightly uneven with a cloud displacement modifier.   Now, I want to make this repeat and be larger but if I try to scale it up, everything increases in size when I want it to repeat.  I tried copying and pasting the plane and putting them next to each other but this is sloppy and I feel like it takes up too much resources.   Anyone have any insight on how to achieve what I'm going for? I appreciate it, thanks.  Shading Nodes   How my scene Looks   What I mean by stretching and growing

I just recently got into the nodes system, my knowledge on the subject is limited. I can't seem to find out how to tile textures using my current node setup, because it doesn't tile the them on its own. I know that I could be using a Vector Mapping node, but the way I'm modeling this requires that I texture each part of the building individually. If I use a Vector Mapping node, I'll have to manually adjust each individual part myself. The nodes I'm currently using  The problem that I'm having is that if I use the same nodes for a mesh with different dimensions they get stretched.  I want to avoid the need of using Vector Mapping nodes and just give it the ability to tile the texture so that it goes over a mesh of any size without stretching.


I suddenly got the File sync error (auth failed (AUTH_FAILED) message on Ubuntu 13.10. It worked flawlessly for several months. I tried all methods reported in        I can connect (so username and password are OK) but it doesn't sync.  It says  File Sync in progress" and "Getting information, please wait" and that is all. Later it says "File sync is disconnected" and still "Getting information, please wait  So, where is the problem ?

Recently I started getting a File sync error on all 3 of my PCs running Ubuntu One.  One is running Ubuntu, the other 2 are running Windows 8.  Looking at the list of clients on the web, none of them were there anymore.    I found this article:      On how to fix the issue for my Ubuntu PC and it worked perfectly.  Now I am looking for a similar fix for Windows but haven't found one yet.  I've tried un-installing Ubuntu One and re-installing it, but it must still be holding the keys somewhere because it never asked me to login again.    Does anyone know where I can clear these keys to get my files syncing on Windows again?


This might be a very stupid question but comes to mind when we encounter each and every topic of pure maths. Why we are studying this, what are the applications of this etc etc. The topics in the pure maths are abstract unlike applied mathematics. What will be the best answer satisfy a student of mathematics, to the question application of mathematics? Actually our mathematics teachers generally dont focus on applications in mathematics. Does this mean that mathematicians are more interested in the extension/generalization of previously known field or results rather than their applications?

I am trying to think/know about something, but I don't know if my base premise is plausible. Here we go.  Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because it has no practical utility, but I guess that according to the history of mathematics, the math that is useful today was once pure mathematics (I'm not so sure but I guess that when the calculus was invented, it hadn't a practical application).  Also, I guess that the development of pure mathematics is important because it allows us to think about non-intuitive objects before encountering some phenomena that is similar to these mathematical non-intuitive objects, with this in mind can you provide me historical examples of pure mathematics becoming "useful"?


I need help proving that if $\lim_n x_n = 0$ then $\lim_n \frac{x_1+x_2+...x_n}{n}=0$  I know $x_1+x_2+...+x_n = \sum x_n$ is a series that is a converges uniformly if and only if for every $\varepsilon>0$ there exists M.

I have this problem I'm working on. Hints are much appreciated (I don't want complete proof):  In a normed vector space, if $ x_n \longrightarrow x $ then  $ z_n = \frac{x_1 + \dots +x_n}{n} \longrightarrow x $   I've been trying adding and subtracting inside the norm... but I don't seem to get anywhere.  Thanks!


We know that Tom Riddle was obsessed with immortality and was planning about it ever since he was a little boy. If he had the time to meticulously plan for those Horcruxes, why did he not go in search for the three things that could guarantee his immortality and provide him with the power he had always desired?

Why did Voldemort never seek the Hallows before the events of the second wizard war?  It seems it would have been much easier for him to retrieve them.  James had the cloak, Regulus had the resurrection stone(not sure if I remember that correctly, I could be wrong), and Dumbledore had the elder wand.  It seems that it would have been much easier for Voldemort to get to the three seeing as the cloak was with Harry who's location was unknown and the stone was within the snitch Harry caught, which only he could open.  So, why did Voldemort wait to seek the Hallows?


I have to use the old version of Blast (not Blast+) to compare DNA sequences and I have to know the number of all hits. They are not given in the header and I have to know them for many many of blast outputs and its nearly impossible to count them (or to export them in excel). I think I probably have to write a 'Perl Script' and I did my best but I am not familiar with programming and it is not working. Furthermore I had a look on the internet and they are always comparing it to BIO Search. I have e code, which for me looks pretty good,but it also done a comparison with BIO Search, what I don't need/want.   use strict; use warnings; use Bio::SearchIO;   Usage information  die "Usage: $0 <BLAST-report-file> <number-of-top-hits> <output-file>\n", if (@ARGV != 3);  my ($infile,$numHits,$outfile) = @ARGV;     print "Parsing the BLAST result ...";     my $in = Bio::SearchIO->new(-format => 'blast', -file => $infile);     open (OUT,">$outfile") or die "Cannot open $outfile: $!";  # print the header info for tab-deliminated columns print OUT "query_name\tquery_length\taccession_number\tlength\tdescription\tE value\tbit score\tframe\tquery_start\t"; print OUT "query_end\thit_start\thit_end\tpositives\tidentical\n";  # extraction of information for each result recursively while ( my $result = $in->next_result ) {     # the name of the query sequence     print OUT $result->query_name . "\t";          # the length of the query sequence         print OUT $result->query_length;          # output "no hits found" if there is no hits         if ( $result->num_hits == 0 ) {       print OUT "\tNo hits found\n";          } else {       my $count = 0;                  # process each hit recursively         while (my $hit = $result->next_hit) {             print OUT "\t" if ($count > 0);                             # get the accession numbers of the hits        print OUT "\t" . $hit->accession . "\t";                         # get the lengths of the hit sequences                         print OUT $hit->length . "\t";                             # get the description of the hit sequences        print OUT $hit->description . "\t";                         # get the E value of the hit             print OUT $hit->significance . "\t";                             #get the bit score of the hit        print OUT $hit->bits . "\t";                          my $hspcount = 0;                          # process the top HSP for the top hit             while (my $hsp = $hit->next_hsp) {                             print OUT "\t\t\t\t\t\t\t", if ($hspcount > 0);                              # get the frame of the query sequence         print OUT $hsp->query->frame . "\t";                                 # get the start and the end of the query sequence in the alignment                 print OUT $hsp->start('query') . "\t" . $hsp->end('query'). "\t";                                 # get the start and the end of the hit sequence in the alignment                 print OUT $hsp->start('hit') . "\t" . $hsp->end('hit') . "\t";                                 # get the similarity value                 printf OUT "%.1f" , ($hsp->frac_conserved * 100);         print OUT "%\t";                                     # get the identity value         printf OUT "%.1f" , ($hsp->frac_identical * 100);                     print OUT "%\n";                                 $hspcount++;                             }        $count++;                          # flow control for the number of hits needed             last if ($count == $numHits);         }         } } close OUT; print " DONE!!!\n";   May someone help me, please. I need a program, which first tells me the header and then the number of hits. I am a little bit desperate and would be so happy if someone can help me. That would be so nice. Greetings Tina

I generated a series of local BLAST databases using makeblastdb of metagenomic data and am searching for the presence of a particular gene. While I can do the normal BLAST analysis looking at e-values, % identity, etc. I haven't been able to figure out how to determine how many times a given sequence exists in the database.  So: given a BLAST database of metagenomic data where a particular gene may exist multiple times, how do I determine the copy number of a given BLAST hit?  Thanks in advance.


We know that thin-film interference creates colors by constructive and destructive interference of different wavelengths.  One of the better images I refer to is this:  Though the example only traces one ray of light, a different ray striking at C can be seen to interfere with the first, so having just the original ray interfere with itself, completely neglecting the distance CD, is reasonable. The path length through the medium results in different phase shifts for different wavelengths, ultimately resulting in different interference for different colors. My question is, why don't we see this happen in thicker materials? I have a guess:  For thicker materials, variation in surface perfection results in a wide range of light paths (a small change in A results in large changes in B, which results in even larger changes in C), so everything averages out.  This effect is strengthened by dispersion. If this is the case, are there examples of thick materials constructed with sufficient precision to show interference?

I had always kind of wondered why we didn't see interference in things like windows -- we were taught that the condition is that the thickness of the film/slab/medium just has to be an integral number of wavelengths, $d=m\lambda$. My logic was, if visible light has wavelengths ~400-780nm, any window pane has got to be an integral number of wavelengths (or close to integral) for some of the wavelengths in the visible.  For example, if a window is, $6mm = 6\times10^6nm$ thick, then you should see interference for wavelengths (and some range around them) 200nm, 250nm, 300nm, 400nm, 500nm, 600nm... Because 6mm is an integral number of each of those.  Obviously that would be really annoying and isn't the case. I found  (warning: PDF) source that seems to explain it and I was wondering if what they're saying is sound. On the 10th page (p171 for them), it says that the reason we don't see this interference is that no window is that smooth, it has a variance in the thickness of at least several wavelengths, so the interference effect is effectively average out among all those thicknesses, which usually gets rid of it. They do the math and show that.  Is that the reason?  If so, that leads me to two questions: Could we, if we were really careful and used something like MBE, make a glass window with that sort of accuracy, and then see interference effects in the optical range? I know that quartz crystal monitors can easily give you nanometer accuracy for evaporators and sputterers, but they also have pretty limited growth rates.  My second question is, then, do we see interference effects in glass windows with electromagnetic radiation of a comparable wavelength, like microwaves?  Thanks!


Say, I'm given a filename like libasound.so.2. Is there a way to query the package manager to correlate the filename with its corresponding package?  I'm interested to get answers for any package manager, but my primary focus is on apt and yum.

On Debian systems (and derivatives):  $ dpkg --search /bin/ls coreutils: /bin/ls   That is, the file /bin/ls belongs to the Debian package named coreutils.  But this only works if the package is installed. What if it's not?


I'm using TeXnicCenter 2.0 with SumatraPDF and MiKTEX2.9 and try to use the inverse search. I set up the profile according to the instructions / different fora but I can’t manage to get it work then using  \input{./folder/file.tex}   In the *.synctex file the link   Input:75:C:\mainfolder\folder\file.tex    shows up correctly, however, somewhere in between the file. Now, I copied the link to the end of list of inputs at the top of the synctex-file, saved it and its working fine.   Does anybody has an idea, who I could this running (automatically;-)? Is that a known bug?  Thanks in advance for your time!

I've got a document that compiles without error or warnings (and looks about right) but for some segments of the document synctex doesn't seem to be working.  What could be wrong?  The document consists of one root .tex file which \inputs a bunch of others.  Synctex works for all these sub-documents - except for one.  In practice, this means I can Ctrl-Click in the viewer and find the appropriate spot both in parts of the text before and after this particular subdocument.  Conversely, I can Ctrl-Click in the editor and jump to the right spot in the view in all subdocuments but this one.  However, when I Ctrl-Click on a part of the output corresponding to this particular subdocument I get the following error popup: Cannot read file "E:/emn/uni/Thesis/doc": Access is denied. in the TeXworks viewer.  The path in this error message exists but is a directory: namely the one containing the tex files.   All filenames consist of only latin letters, numbers, and underscores and the extension .tex.  The problematic file is called G2MLVQ_9_Refinements.tex whereas a (working) file is called G2MLVQ_7_Implementation.tex I can't make a small example which fails - small examples don't fail; however the order of files seems to matter, so perhaps something in an earlier file is affecting synctex later on... (once I've isolated this, I'll update the question). Concerns MiKTeX 2.9 and the bundled TeXworks version 0.4.3 r.857.   I'm stumped: what could be going wrong?  Edit: user59152 tried to isolate the error:     It is virtually impossible to create a minimum working example (MWE) for this problem, so I have posted a . You can see the file names at the tops of the windows. The one being edited (Introduction.tex) comes BEFORE the file that can't be opened using inverse search (SourceAndSinkFreeContinuumRVtracking.tex). The screencapture movie confirms that \clearpage restores inverse search capability, but fouls up the layout of the document, so this problem appears to remain unsolved.  I'm using TeXworks version 0.4.4 r.1003 and MikTex 2.9.


Warning:   To avoid catastrophic data loss, readers should NOT run this, nor any variations on it!   I would like to understand what does this command do: sudo rm -rf/*

What does rm -rf do when used to remove files or directories?  How do the -r and -f options work together?


Does anybody know if it's possible to disable mouse wheel up-down events in gnome-terminal? I have a rather twitchy mouse wheel, and every time it twitches it does a history lookup in my terminal. But I still want to be able to middle-click paste.

Is there a way to disable scrolling through command history for the Xfce terminal? I don't wish to rely on palm rejection, I'd just like it disabled when I'm using the terminal. Specifically I'm talking about not cycling through previous commands at the prompt when scrolling with mouse/touchpad.


Prove that there does not exist a group $G$ with a group of automorphisms isomorphic to $\mathbb{Z}$ or $\mathbb{Z}/n\mathbb{Z}$ with odd $n \gt 2$.  I assumed the opposite, let there exist a group $G$ such that $\mathrm{Aut} (G) \cong \mathbb{Z}$ or $\mathrm{Aut} (G)  \cong  \mathbb{Z} / n \mathbb {Z}$. Since the subgroup of the cyclic group is also cyclic, $\mathrm{Inn}(G)$ is cyclic. $\operatorname{Inn} (G) \cong G / Z (G) $.  So $G$ is Abelian.  If $\mathrm{Aut}(G)$ has an element whose order is not equal to $2$, then we take the automorphism $p (x) = x^{-1}$. This is an automorphism of order $2$. There remains a case where the order of each automorphism is $2$. Help with this case.

I had this "almost bonus" question on the final in Group Theory recently: prove that there is no such group $G$ which would satisfy Aut$(G)\cong \mathbb{Z}_n$, where $n$ is an odd integer. I don't have much certainty if this proof is OK, and one's opinion would be appreciated.  Here's my attempt:     Suppose that there exists such a group $G$ that satisfies the above condition. Since $\mathbb{Z}_n$ is cyclic, Aut$(G)$ is also cyclic and $G$ is abelian, which implies that Inn$(G)\cong \{e\}$. Thus Aut$(G)=$Out$(G)$. (I don't think this fact is important here though). Now, since an automorphism sends a generator to a generator, and since each automorphism is completely determined by such mapping, |Aut($G$)| must be of factorial order. But an integer factorial is always even. However, $|\mathbb{Z}_n|$ is odd, which is a contradiction. Therefore, no such $G$ exists.   I'm afraid that my proof is not very nice, but at least a genuine attempt was made.


Is there a way to open multiple finder directories at the same time without necessarily opening two windows? I'm thinking something similar to opening multiple tabs in a mac terminal.

I often need to open many finder windows at the same time and my desktop becomes cluttered.   Is there any way to get tabs in Finder so one window can host multiple folders?


I have a small program that reads a json file that gives the weather, time, temp, wind, ect. I need to calculate the average tempature for 2009 through 2015. The years are in an array, and are in length, around 60k. I am trying to write a small loop that will first find the position of the first instance of the year 2009 and then the last instance of the year 2009. Then I can run my average temp loop through that, but I am running into an issue as seen below.  place will be the index of the array. However, no matter how I run my code, it always equals -1, rather than giving me the position of the index in the array. Both arguments in the if statements are strings.   So what am I doing wrong?   String twozerozeronine = "2009"; int place = -1; for (int a = 0; a < years.size(); a++){     if (years.get(a) == twozerozeronine){         place = 1;          break;     } } System.out.println(place);

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Prove that $\sqrt{\frac{a}{a+b}}+\sqrt{\frac{b}{b+c}}+\sqrt{\frac{c}{c+a}}\gt1$, where a, b, c >0. I tried, $\sqrt{\frac{a}{a+b}}+\sqrt{\frac{b}{b+c}}+\sqrt{\frac{c}{c+a}} = \frac{a}{\sqrt{a}\sqrt{a+b}}+\frac{b}{\sqrt{b}\sqrt{b+c}}+\frac{c}{\sqrt{c}\sqrt{c+a}} \ge \frac{(\sqrt{a}+\sqrt{b}+\sqrt{c})^2}{\sqrt{a}\sqrt{a+b}+\sqrt{b}\sqrt{b+c}+\sqrt{c}\sqrt{c+a}}$. Then $\sqrt{a}\sqrt{a+b} \le \sqrt{2}/2 (2a+(a+b))$. This only gave me $\sqrt{2}/2 + \sqrt{2}(\frac{ab+bc+ca}{a+b+c})$.

The link below is a MSE question discussing the maximum value of the expression  $$ \sqrt{\frac{2a}{a+b}} + \sqrt{\frac{2b}{b+c}} + \sqrt{\frac{2c}{c+a}} $$  which is $3$.   I thought about the minimum of the same expression over nonnegative reals.  My reasoning was as follows :  Using the fact that $\sqrt{X+Y+Z} \le \sqrt X + \sqrt Y + \sqrt Z$, and the fact $u + v \le u+v+w$ we can already assert that the expression to minimize is $\ge  \sqrt 2$  Now taking $a = 0$, $b\to 0^+$ and $c$ arbitrary we see that the expression can take values arbitrarily close to $\sqrt 2$. Thus $\sqrt 2 $ is the infimum. but It seems not to be a minimum while the continuous function we have must have a minimum on the compact sphere (homogenous expression). Is there anything wrong with this approach ? Then, What would the result be if we restrict ourselves to positive reals. Thanks.


I'd like to transfer 200gb of files between two Win10 laptops wirelessly. What would be the most time-saving option?

What is the most efficient way to transfer a large number/amount of data, such as 430-450 GB, from one Windows 10 laptop to another?  Could someone guide me visually using a short yet comprehensive tutorial? And which connector/cable should I use to transfer between two internal HDDs?  I think all the laptop specs are fairly standard and fairly inexpensive. The laptop internal HDD data interfaces are both SATA.


I'm making new theme with bootstrap, and having little trouble setting up content. Firstly content is set up like this:

         <?php the_content(); ?>

   The problem is I need two column layout, images that have width > height are col-sm-12 or 100%, and those that are width < height are col-sm-6 that is 50%. How can I add function like:  if ($w > $h) {     $class = "col-sm-12"; } else {     $class = "col-sm-6"; }   And also with adding those classes I have to nest columns so all images should be wrapped in .row div.   Any suggestions?  Edit  Images are from content editor, in posts, and solution above works but it gives me already set values like large=1024x1024, I want natural sizes of images. eg. If my image is 1920x1080 to return those values.

I'm making a custom function for my WordPress site.  function mediumFeaturedImage() {     if ( has_post_thumbnail() ) { ?>     <a href="<?php the_permalink(); ?>">         <?php the_post_thumbnail( 'medium' ); ?>          <?php } else { ?>                                     <img src="<?php echo get_template_directory_uri(); ?>/images/no-image.jpg" alt="No Image Given" width="220" height="145"/>     <?php } }   I set the medium size images to 220 x 145 in Settings > Media.  But if you look at the default 'no-image' code block here, I used hard-coded numerals as width="220" height="145". But I want to use this function into some other projects of mine. And I won't use the same settings for medium sized images always. It'll be different from site to site. And always I want my code to be dynamic. Therefore I want a code like this:  <img src="<?php echo get_template_directory_uri(); ?>/images/no-image.jpg" width="<?php $getimagesize('medium','width); ?>" height="<?php $getimagesize('medium','height); ?>"/>   It's not mandatory using a function like me. Is there a built-in code like this, that will grab the sizes I assigned in Media settings in WP-Admin, always?  Or, by using the  how can I grab the width and height of medium size image only, that assigned for medium sized images in Admin panel?  Possible?


So I have this bmx bike where the back tire's inner tube was leaking air and I'd have to inflate it every day or so. And I just got a new tube and it's having the same issue. Anyone got any ideas?

I ride my cruiser to the supermarket and back, using either a trailer or a basket over the front wheel for carrying groceries. The bike has developed a persistent slow leak on the front wheel, and I've replaced the tube without it helping. I can't see anything puncturing the tire, and the spokes aren't poking through the rim tape that I can see.   These are 26" wheels with low pressure (around 40 - 50 psi). What else can I look for that might be causing this?


I think I need to work with the determinant of an arbitrary matrix from this family but am not sure.

let $n\gt1$  be a fixed natural number, $S:=${$A $: $M_n (\mathbb{R})$ be all real matrix,define this meter for all $A=[a_{ij}]$ $B=[b_{ij}]$   $d(A,B)$:=max{|$a_{ij}-b_{ij}$|:i,j=1,2,2...,n} and $GL(n,\mathbb R)$ is set of all $n\times n$ non singular matrix how to prove that $GL(n,\mathbb R)$ is  not connected and open subset of $S$ ?  thanks in advance


Can I play Minecraft PE multiplayer without an Internet connection on either device? My brother and I have it on seperate devices, but we are not allowed to be on the Internet. Can we play via Bluetooth together? If so, how?

Me and my sibling want to play Minecraft together. Is there a way to use Bluetooth instead of WiFi to get connected? If so, how? We have MCPE version 15.0.


i want to show that $k[x,x^{-1}]$ (where $k$ is a field ) is a PID . i have some proof but seems too- straight forward to be correct take the natural homomorphism $\phi: K[x]\to S^{-1}K[x]$ where  $S=(x^1,x^2...)$ for we know that for every ideal of $S^{-1}K(x)$ Lets say $I$ , $\phi^{-1}(I)$ is an ideal of $K[x]$ Which is PID so $\phi^{-1}(I)=(f)$ for some $f$ on $K[x]$ then is holds that the ideal $I$ is generated by $(f/1)$ ? if yes we've shown that $k[x,x^{-1}]$ is a PID?

Disclaimer: this is a homework question. I'm looking for direction, not an answer.     Given a field $F$, show that $F[x,x^{-1}]$ is a principal ideal domain.   I'm unsure how to proceed. Would it be better to prove this directly? (ie, let $I$ be an ideal, show that $I = (f)$ for some $f \in F[x,x^{-1}]$). The proof that polynomials are a PID would involve (I imagine) division by remainder and use of degree, both of which don't seem to have obvious parallels for Laurent polynomials. Should I try and devise some parallels and mimic the proof for polynomials? Or is this overkill? (or just wrong?)  edit 1: I guess the approach I mentioned above amounts to showing that Laurent polynomials are a euclidean domain (we know that euclidean domain => principle ideal domain, so this would be sufficient) Are they a euclidean domain though? (it seems like this would have been the question if they were, instead of asking if they were a PID).  edit 2: I've spat this out, think most parts of it are correct, though it seems kind of ugly/cumbersome (but that might just be me trying to spell things out more than is needed):     Given a Laurent polynomial $f \in F[x,x^{-1}]$, define its "negative   degree" $\deg^-(f)$ to be the largest power of $x^{-1}$ that appears   in $f$.      Let $I$ be an ideal of $F[x,x^{-1}]$. Note that $\{x^{-\deg^-(f)}f \mid f \in I\} \subseteq F[x]$. Let $J$ be the   ideal in $F[x]$ generated by this set. $F[x]$ is a principal ideal   domain, so $J$ is a principal ideal and we have $J = (j)$ for some $j \in F[x]$.      We claim $I = (j)$ (now meaning an ideal of $F[x,x^{-1}]$).      Let $f \in I$. Then $x^{-\deg^-(f)}f \in J$, meaning $f = x^{\deg^-(f)}g$, where $g = x^{-\deg^-(f)}f$ is in $J$. Because $g \in J = (j)$, there exists $g' \in F[x]$ such that $g = g'j$, and thus $f = (x^{\deg^-(f)}g')j$ is a multiple of $j$, so $f \in (j)$.      Let $f \in (j)$. Then $f = gj$ for some $g \in F[x,x^{-1}]$. But note   that $j = x^{-\deg^-(f')}f'$ for some $f' \in I$, so $f = gx^{-\deg^-(f')}f'$, so $f$ is a multiple of an element of an ideal   $I$, so $f$ itself is in $I$.      This shows $I = (j)$. So an arbitrary ideal of $F[x,x^{-1}]$ is   principal, so $F[x,x^{-1}]$ is a principal ideal domain.   I kind of feel like I still don't "get" the proof (I more-or-less see how each part works with the others but I'm having trouble seeing the bigger picture), though this may be due to a poor handle on ideals in general.


I am making a banner for my company at about 8 x 4.5 feet. I'm wondering what I should scale the format down to and what resolution it would require for the company to be able to scale it and print it that big?

For wall-sized graphics and large banners (e.g. 3m × 5m), what is an acceptable PPI for print? As I understand it 300 ppi is the typical for 'small' artworks (esp. for clean text resolution). However, for small artworks, the audience usually engages at a much closer distance. Therefore, in the interests of keeping a bitmap file down to a reasonable size, can you get away with a much-reduced PPI for a large format/banner print?


Opening the ad on a new tab (Ctrl+Click) doesn't work. It simply appends a query string. Clicking on the ad shows the navbar in the gif area.

Today I came across an ad on this question on SO:  (I don't expect it to stay very long).   There was a community promotion ad on the right hand side of the site, I think for one of our English sites. It had a sentence that I only partially remember:     Idiom ... poor or even poorer   I found it interesting, so I clicked that ad. Which caused a new instance of SO to open within the ad space. Unfortunately I failed to take a screenshot. I've been refreshing the page like crazy, but can't get the ad to appear again.  Edit: I managed to get a new community add, for the photography site, and captured a screenshot:   Edit2: This bug still persists, I saw it today with an OOP add from CodeReview, and an area 51 add.


I have months old problem of missing "Save" button on the user account edit form. Which is annoying to the point that now I have to find the solution.   I don't usually use account edit form since there is only one user. I have updated many modules and different cores but problem always remained there. Right now I am running latest core which is 7.23. And all modules are updated. This is a multilingual website.    Since this problem has appeared I am unable to save any change in any user account. Please have a look on the image attached. Please help.  Thanks.

Here is what the bottom of my "leaflet" content type edit form (i.e. admin > structure > content types > leaflet > edit) looks like:   Here is what the bottom of my "testimony" content type edit form looks like:   Note that there are no save/delete buttons! Another of my content types has also now picked up this bug. This just happened. I have no idea why. I can't save changes! I tried flushing all caches and it didn't help. I'm an administrator and I have permissions for everything.  Why would this have happened and what can I do? Drupal 7.19.


I see the different definitions of $\mathcal{L}$ . First one is in the book :A First Journey through Logic it says the language consists two parts:logical symbols and non-logical symbols. the non-logical symbols consists three part: $\mathcal{C}^{\mathcal{L}}$,$\mathcal{F}_{n}^{\mathcal{L}}$,$\mathcal{R}_{n}^{\mathcal{L}}$,$n\in \mathbb{N^{*}}$, which each mean the set of constant symbol,the sequence of set of function,the sequence of set of relation. And the second one is in the book:Lectures on Inﬁnitary Model Theory the definition is:the second part just consist: a set of function symbols, relation symbols and constant symbols.  So, I want ask is the the sequence of set of function or the sequence of set of relation requires countable?

I've been reading about mathematical logic and computability theory, but I'm somewhat confused on one note: what exactly is a language? What does it mean when I am told "let $\langle 0, +, \leq \rangle$ be a language"? I looked this up everywhere I could, but haven't found a satisfactory/clear answer.


For each $n=1,2,{\dots}$ and $x\in(0,{\pi})$, prove that the series $$S_n(x)=\sum_{k=1}^{n} \frac{\sin(kx)}{k}>0$$

Show the following inequality for any $x\in [0, \pi]$ and $n\in \mathbb{N}^*$, $$ \sum_{1\le k\le n}\frac{\sin kx}{k}\ge 0. $$  I have this question a very long time ago from a book or magazine but I cannot solve it by myself and did not know how to solve it until today.   My try: for $n=1, 2, 3$, one can check this by hand.


I am finding problem in evaluating the flowing function using Rouché's theorem. I have looked out for examples but it lacks the explanation and steps to reach the required output. I need to determine the number of zeros of the function f(y) = y^5+14y+1 for 1 < |y| < 2 I have understood that i need to break it into 2 parts. If you could help me out. Thank you !

Find the number of zeroes (counting multiplicity) of $p(z)=z^6+z^3+10z^2+4z+3$ inside the annulus $1<|z|<2$. I think this can be solved using Rouché’s theorem. First consider $|z|\leq 1$ on the boundary $|z|=1$ and $|z^6+z^3|<|10z^2+4z+3|$ which can be shown using triangle inequalities, the left side is at most $2$ while right side is at least $3$. We could also consider $|z|\leq 1+ \epsilon$ and our proof still works. Thus $p(z)$ has 2 roots inside $|z|\leq 1$. Also for $|z|= 2$ we have $|z^6+z^3|>|10z^2+4z+3|$. Thus we have 6 zeroes of $p(z)$ inside $|z|<2$ and therefore 4 of them are in $1<|z|<2$. Is this correct? The only "tricky" part is ruling out that there are zeros on $|z|=1$.


I would like to know if I can just watch any one of the Planet of the Apes franchise movies and understand it, or do I have to watch all of them?  I'd be fine with either, but I want a clear, correct, and easy understanding and answer.

Basically, I ended somewhere on the reboot film made in 2001. I would like to get back to Planet of Apes series and watch it again.  With Star Wars franchise, there is famous order of how should one watch the series. Is there something similar with The Planet of Apes series?


Suppose that A is a $50 × 50$ matrix such that $A^3 = 0$. Show that the inverse of $I_{50} − A$ is $A^2 + A + I_{50}$.   I'm not even sure how to approach this problem. Any help on how to go about answering this question?  I'd like an explanation along with the solution, if possible. Thank you.

Possible Duplicate:          Given $A^{2012}=0$ prove that $A+I$ is invertible and find an expression for $(A+I)^{-1}$ in terms of $A$. ($I$ is the identity matrix).


Is it possible to allow users to leave comments to a document that lives in Sharepoint? I've seen document ratings, but is there a way to allow comments?

My users have requested the ability to start threaded conversations around documents in a document library.    This can be achieved with a third party add-in,  .   This is OK, but the products not really a 'prime time' component for serious production use.  I've seen the "Create Document Workspace" option, but it makes a copy of the document in another location.   I'm having a hard time believing that SharePoint, a collaborative platform by design, wouldn't have the ability to discuss and work on a document collaboratively?   Surely there is a way to allow users to discuss a document together?


After reading  in which it is clearly stated that     Gold is operations (security, science, engineering, etc.), Red is command.   Why is Kirk dressed in Gold?

In the original Star Trek engineers and security officers wore red shirts but in ST:TNG engineers and security officers wore yellow shirts and command officers wore red shirts.  Was it ever explained why there was a uniform color change?


I want to use Ubuntu 16.10 from my 8gb usb pen-drive. I've noticed that whenever I make any changes to it they all get reverted after shut down.  All the files I have downloaded, documents, etc, get automatically deleted.  Everything else is working completely fine except no changes are saved.

I have created a USB flash drive with the latest Ubuntu version, but it is not persistent. How can I make it persistent without repeating the whole process?


I have never come across this before and it's completely stumped me!  I am using some custom front end posting scripts in Wordpress, these work absolutely fine, everything is escaped correctly before the data is saved to the db etc, but I seem to be having an issue with the apostrophe (single quote) when entered on a Mac keyboard.  An example post using various chars is entered in the text area :   a post with other chars `~":;?/[]{}-_=+!£$%^&*()'   And this is what is saved in the db (and then displayed on the page when called) :   a post with other chars `~":;?/[]{}-_=+!£$%^&*()&#039;   This is how the data is being saved to the db for clarity :  esc_attr(strip_tags($_POST['postContent'])),   If I copy and paste an apostrophe from a webpage like this for example it saves just fine :   Ain’t that strange!   But that slanted apostrophe isn't available (as standard) on the Mac keyboard, the default is the single quote '  I have never come across this issue before.  Anybody got any suggestions or workarounds as I'm at my wits end!

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


I have some expressions which behave in a strange way:  "600x400".split('x').map(parseInt) "600x400".split('x').map(parseFloat)   And  "0,1,0,0,0,1".split(',').map(parseInt) "0,1,0,0,0,1".split(',').map(parseFloat)   Applying parseInt to the arrays of strings makes the second element NaN while parseFloat gives the right number.  Bug in JavaScript ?

From the :  [1,4,9].map(Math.sqrt)   will yield:  [1,2,3]   Why then does this:  ['1','2','3'].map(parseInt)   yield this:  [1, NaN, NaN]   I have tested in Firefox 3.0.1 and Chrome 0.3 and just as a disclaimer, I know this is not cross-browser functionality (no IE).  I found out that the following will accomplish the desired effect. However, it still doesn’t explain the errant behavior of parseInt.  ['1','2','3'].map(function(i){return +i;}) // returns [1,2,3]


I just finished recording an audio file for one of my podcasts.  And I'm debating whether I should delete the following sentence:      If you haven't already watched my first video, there's a link to it in the description below.     I am trying to suggest to viewers that they watch my videos in order, which I think the sentence does.  But I think this sentence is also ungrammatical and nonsensical.   Whether or not my viewers have watched my first video, a link to that video will be in the description.    I suppose I could change it to      If you haven't already watched my first video, please watch that first. You can find a link to it in the description below.     But changing audio files is such a pain.  Would it be ok to leave the sentence as is?

More and more often I read sentences such as the following:   If you're not familiar with Miami's “Golden Era”, this film captures it brilliantly.  If you're not aware of the basics, two teams of five players spawn on corners of a map.    If you're not familiar with it, Pinboard is a bookmarking service that lets you save URLs. If you're not aware of how to transfer funds from your Main wallet to your Australian wallet, this explains how: In case you're wondering, mBio wasn't fooled. In case you don't know Marco, he was one of Masahiko Kimura's first apprentices.   Are they correct?  Why? If they are not, then what is wrong, and how can they be best corrected?    P.S. By "correct" I mean do they follow  and ?  P.P.S. Although they're harder to find, I found more examples in the New York Times!  Publication in the NYT means these sentence structures are correct, right?   If you’re not familiar with this little tweak, it’s simple.  If you’re not familiar with your provider’s policy, New York’s Department of Financial Services publishes a helpful chart.  In case you're wondering, the rupiah is the national currency of Indonesia.


I am using the  and noticed that when you use \angle, the resulting symbol is not the same height as the text as it is for computer modern, as seen in the below picture.  What can I do the make the symbol the same height as the text, as seen below for CM?

How can I get something like in the figure, where G in the middle is larger than normal letters in math mode?


df tells me that the server uses 84% of the HDD it uses.  $ df -h Filesystem      Size  Used Avail Use% Mounted on /dev/xvda1       30G   24G  4.6G  84% / none            4.0K     0  4.0K   0% /sys/fs/cgroup udev            1.9G   12K  1.9G   1% /dev tmpfs           375M  216K  375M   1% /run none            5.0M     0  5.0M   0% /run/lock none            1.9G     0  1.9G   0% /run/shm none            100M     0  100M   0% /run/user   I am trying to search all the disk usage of every directory in the root but I cannot find the reported 24 GB of data:  $ sudo du -hs -x /* 9.6M    /bin 20M /boot 8.0K    /data 12K /dev 5.8M    /etc 1.9G    /home 0   /initrd.img 60M /lib 4.0K    /lib64 16K /lost+found 4.0K    /media 4.0K    /mnt 4.0K    /opt du: cannot access ‘/proc/17167/task/17167/fd/4’: No such file or directory du: cannot access ‘/proc/17167/task/17167/fdinfo/4’: No such file or directory du: cannot access ‘/proc/17167/fd/4’: No such file or directory du: cannot access ‘/proc/17167/fdinfo/4’: No such file or directory 0   /proc 24K /root 216K    /run 9.4M    /sbin 8.0K    /srv 0   /sys 1.7M    /tmp 1.1G    /usr 5.3G    /var 0   /vmlinuz   By adding the number above I get somewhere between 8 and 9 GB. Where are the rest up to 24 GB?

When I execute the command df -h /tmp it says disk utilization is 100%, but when it try du -sh /tmp it says disk utilization is 2%.  I want to know why these commands shows different output, how these two commands work and what is the solution to this problem.  Context: /tmp is installed on it own file system. I am using Ubuntu 12.04 server edition on my VPS account. Due to this problem utilization of /tmp 100% according to df some programs complain about free space in /tmp.


Can someone explain in what situations is RTOS used?  What are pros and cons of RTOS relative to simple MCU applications     with no OS?

I have written plenty of bare metal code for PIC and x86 processors.  Can someone tell me how and when should I need an operating system?  Conversely, what application or situation can be dealt with or without an operating system as well?


Good time of day. Can you help me please with this task? Consider a polynomial of degree $n$ with leading coefficient equal to 1. Prove that the maximum of its modulus in a circle of radius 1 not less than one. When it is equal to one? I tried to use Rouche's theorem. But it was unsuccessful. Thank you

Let $p(z)$ be a monic polynomial of degree $n$.   Prove that $\max\limits_{|z|=1}|p(z)|\geq 1$ and that equlity holds if and only if $p(z)=z^n$.  I first observed that $p^{(n)}(z)=n!$. Therefore by Cauchy's formula  $$n!=p^{(n)}(0)=\frac{n!}{2\pi i}\int\limits_{|z|=1}\frac{p(z)}{(z-0)^{n+1}}dz\implies 1\leq\frac{1}{2\pi}\int\limits_{|z|=1}|p(z)|dz\leq\max\limits_{|z|=1}|p(z)|$$  Now, clearly if $p(z)=z^n$ then $\max\limits_{|z|=1}|p(z)|= 1$, but what about the converse?


I have two variables. Sense of belonging and anxiety. I found a Pearson's correlation that was weak but significant. The significance was probably due to sample size (n=400). Then I conducted a t-test of high and low sense of belonging and anxiety. The t-test found a significant difference between the group of 0.6, had a medium effect size. I'm having trouble now though because I don't understand how one can say there is weak/no relationship and then the t test indicates there are significant differences between the groups. Can anyone help me 'get' why this happens/what it means?  I don't think there is a contradiction I just don't understand how to interpret the results.

I am looking at the probability of opting into a program based on a continuous variables $X_1$, $X_2$, $X_3$, etc.  When I divide the sample into people who opted in and did not opt in and do a t-test I find that the mean of all the $X$'s for those opting in is significantly different from the mean for those not opting in.  However, when I look at a correlation matrix for the $X$'s and opting in I find really low correlation coefficients -- from between $.04$ and $.13$.  But my t-tests are significant at the 95%+ confidence level.  How do I square these two results?


$ (X_n : n = 1, 2, ...) $ is a Markov chain with state space $(-1, 0, 1)$. Then which of the following is the correct answer?   $(sin(X_n) : n = 1, 2, ...$) is a Markov chain. $(cos(X_n) : n = 1, 2, ...$) is a Markov chain. $(|X_n| : n = 1, 2, ...$) is a Markov chain. $(X_n^2 : n = 1, 2, ...$) is a Markov chain. None of the above is correct.   Is it option 5 is the correct answer since option 1&2 are continuous, option 3&4 cannot be negative value, so that the state space cannot be -1?

The first question: $ (X_n : n = 1, 2, ...) $ is a Markov chain with state space $(-1, 0, 1)$.   $(sin(X_n) : n = 1, 2, ...$) is a Markov chain. $(cos(X_n) : n = 1, 2, ...$) is a Markov chain. $(|X_n| : n = 1, 2, ...$) is a Markov chain. $(X_n^2 : n = 1, 2, ...$) is a Markov chain. None of the above is correct.   Is it option 5 is the correct answer since option 1&2 are continuous, option 3&4 cannot be negative value, so that the state space cannot be -1?  The second question: Suppose we have three random variables $X_0, X_1$ and $X_2$ forming a Markov process with time domain $(0, 1, 2)$. Then, which of the following is correct.   $X_1,X_2,X_0$ also form a Markov process. $X_2,X_0,X_1$ also form a Markov process. $X_0,X_2,X_1$ also form a Markov process. $X_2,X_1,X_0$ also form a Markov process. None of the above is correct.   Is it option 4 is the correct answer since it is a one-step transition?


Let M be an infinite set and A be countable prove that there is a 1-1 correspondence between $A\cup M$ and M.   can anyone give me a hint?

I have $A$ as an infinite set and $S$ as a countably infinite set, (so that means there exists a one-to-one correspondence between $S$ and $\mathbb{N}$).  How do I show that there always exists a bijection between $A$ and $A\cup S$? Can it be done by showing that there is a bijection from $A$ to $S$ or from $A$ to itself? I am lost on this one.   Oh, and can it be possible that there is no bijection if it is between $S$ and $A\cup S$? What about a map that maps $\mathbb{N}\to \mathbb{N}\cup\mathbb{R}$?


I'd like to build an error handler which will make an empty file marked with the error_occur time.  The core idea is to use the result of date command as a parameter.  I did:  time_stamp=$(date) touch $time_stamp   But this turns out to create a series of empty file like 2014, Wed, 11:15:20.  How to convert time_stamp to a whole string here?

Or, an introductory guide to robust filename handling and other string passing in shell scripts.  I wrote a shell script which works well most of the time. But it chokes on some inputs (e.g. on some file names).  I encountered a problem such as the following:   I have a file name containing a space hello world, and it was treated as two separate files hello and world. I have an input line with two consecutive spaces and they shrank to one in the input. Leading and trailing whitespace disappears from input lines. Sometimes, when the input contains one of the characters \[*?, they are replaced by some text which is is actually the name of files. There is an apostrophe ' (or a double quote ") in the input and things got weird after that point. There is a backslash in the input (or: I am using Cygwin and some of my file names have Windows-style \ separators).   What is going on and how do I fix it?


Bike Description  Front suspension, knobby tires  Frame: Aluminum w/semi-integrated head tube, bi-oval down tube w/integrated gusset, rack & fender mounts, disc compatible dropouts, replaceable derailleur hanger  Front Suspension: Front suspension SR Suntour XCT w/coil spring and preload, 80mm travel Wheels: Formula alloy FM21 front hub, FM31 rear hub; Bontrager 550 36-hole rims w/brushed sidewalls  Shifters: Shimano EF51, 7 speed? Something like that.  Brakeset: Tektro linear pull brakes w/Shimano EF51 levers  19" frame- I believe.    My son is in his first triathlon end of May. He is 12, 5'2 and 31" inseam. So we gather he needs a Med bike 19"+(50cm) but going through growth spurts... We would love to get him a new/used road bike, however it is a big expense, and he just grew two inches this month (and summer is coming with more spurts on the way). I don't want to invest in a bike that will be too small for him in June, so finding a way to make this work.   So, we are looking at the temporary. We all have mountain bikes, and was recommended to us, that we switch out the suspension with light weight, rigid forks, and also switch out our wheels/tires. It is not a road bike, but will get us through till our son gets to a more interchangeable height.  What size, or type of fork is recommended? Is there a difference in size? We can afford alloy, or aluminum for both wheels and forks, and looking to spend about $200 for the temp. situation. And then tires, what is recommended. Are there additional things that are missing in the componentry that would be needed to pull this together? Not as in brakes or gears, just bear bones. We are not looking to build a bike, just have a go between solution while my son is growing.   Suggestions, appreciated!  Cheers  ( Yes I got the inseam right. You should see all of his high waders. He is leggy. Enough that the rest of him will be catching up soon.)

I just bought a new MTB and am planning to change my previous MTB into a Road Bike.   How do I do it? What kind of parts do I need to change or add or remove?  I am not looking to for a full conversion into specialised road bike. But like the answers are suggesting, I am looking for a bridge between commuter or road bike. My majors concerns to be met are:   Should be fast enough to compete with road racers over short distance Should be light as a road  Should be as close as possible in as cheap as possible.


From a 3rd party tool we got some text. I have to create an application which read the text and extract the text from a attribute.  BodyItems=[[Length=45, Text="Emphasis on subjective\, conscious experience "], [Length=47, StartIndex=45, Text="How you think\, feel\, perceive your social world"], [IndentationLevel=1, Length=38, StartIndex=92, Text="Chapter 12:  Personality and Cognition"], [IndentationLevel=1, Length=37, StartIndex=130, Text="Chapter 14:  Personality and the Self"], [IndentationLevel=1, Length=36, StartIndex=167, Text="Chapter 17:  Personality and Culture"]]   I need to create a regex which process the above line of text and list the text which are wrapped inside  Text="........"]. I tried to create a regex but it has only one match . Here is my regex  string strRegex = @"Text=\""[\w\W]*\""\]";   I want to create a regex which give the below output   Text="Emphasis on subjective\, conscious experience "] Text="How you think\, feel\, perceive your social world"] Text="Chapter 12:  Personality and Cognition"] Text="Chapter 14:  Personality and the Self"] Text="Chapter 17:  Personality and Culture"]

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?


Let $R$ be a region in $xy$-plane bounded by $y=x^2$ , $y=4x^2$, $xy=1$ and $xy=5$. Then find the value of the integral $\iint _R \frac{y^2}{x} dxdy$ I am not able to get any function of $x$ and $y$ in terms of $u$ and $v$ such that I can find limit of the integrals. Is there any other way to solve this?

Question: Let $R$ be the region in $xy$-plane bounded by the curves $y=x^2,y=4x^2,xy=1,xy=5$. Then find the value of line integral $\iint_R\frac{y^2}{x}dydx$.  I found it tough and time taking if I evaluate this integral from general method, is there any theorem which make it easy? Since the question is asked in competitive exam so I hope there must be an easy and fast way to solve it. Any help will be appreciable. Thanks in advance.


I know that there is some magic cast on his name later in the series, but has it always been like this? What's the origin of this title?

Pursuant to , it's plausible that the typical witch or wizard would use 'He-Who-Must-Not-Be-Named' (if they assume Taboo Spell is intact after death of Voldemort). But, why would the Aurors and those in the Ministry of Magic (who had first rate protection) also use it? Even Snape (the Half-Blood Prince) hesitated to say 'Voldemort', and he was under the protection of Dumbledore, Dumbledore being the only wizard Voldemort ever feared.  What was the point of the Death Eaters being scared to say 'Voldemort' when, ostensibly, Voldemort wasn't even alive? Yes, it's true that some believed Voldemort would return, but, at the time, it was just that -- a belief. Were people scared that the Death Eaters might give a list of all those who used Voldemort's name to Voldemort upon his return?


Similar as in this , I have a problems with small probabilities in likelihoods, but I believe the thread does not apply to me.  The likelihood is a product of probabilities. The log-likelihood is a sum of the log of probabilities. in R I use optim for optimization of a log-likelihood. It then happens that for 'bad' choices of the parameters the log-likelihood contribution (log probability) for some observation(s) is numerically identical to zero in R (but in fact is larger than zero by an infinitesimal small amount). So the sum of the log-likelihood contributions is negative infinity (due to few observations giving this contribution) indicating a bad fit but optimization is not possible anymore.   What is the standard way of dealing with this problem?

I currently have a likelihood function defined as the following:  $$  L=\prod_{i=1}^{N}\left[\prod_{s=1}^{S_i}L_{is}(y\space|\space \rho_A)\times\phi + \prod_{s=1}^{S_i}L_{is}(y\space|\space \rho_B)\times(1-\phi)\right] $$  Here, $y$ is an observation, $\rho_A$ and $\rho_B$ are defined to be a vector set of parameters, and $\phi$ is just a variable.   What makes this likelihood different than the usual likelihoods I have seen is that not only are there are $N$ observations, but each observation has sub-values up to $S_i$, for $i=1,...,N$.   My problem right now is that the $L_{is}(y\space|\space \rho_A)$ are small to begin with, with some values around $0.000000001$ or even $0$. Therefore, if I multiply many of these small values, I get an even smaller result that R or most other languages will just treat as zero. However, taking the logarithm of $L$ only converts the first product into a sum, which doesn't help at all.  I've also tried to take the exponential, and then the log of the product, but I still have values that go straight to zero. Would anyone know of a prudent transformation to use? I have tried to use the log-transform method where I find the maximum, then re-scale, as in here: . However, it appears that this would work for likelihood's with denominator's of zero. Thanks!


So I have to pause a process for a second and then Start the other one, So basically I have to pause and resume this processes.  Also I have to use a Stack. Have to Save the process as it's executing so I can resume it. Has to have an ID and show the Priority.  Anybody knows what I have to use?  using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; using System.Diagnostics; using System.Threading; using System.Runtime.InteropServices;  namespace Práctica_2 {     class Program     {              static void Main(string[] args)             {                  Process Contador = new Process();                 Process Datos = new Process();                 Process Google = new Process();                 Process Numero = new Process();                 Process Finalizar = new Process();                   try                 {                                         System.Diagnostics.Process.Start("C:\\Users\\M-00\\Desktop\\Práctica 2\\Datos\\Datos\\obj\\Debug\\Datos.exe");                     Datos.Start();                     Thread.Sleep(250);                 }                 catch (Exception e)                 {                     Console.WriteLine(e.Message);                 }                  try                 {                     System.Diagnostics.Process.Start("C:\\Users\\M-00\\Desktop\\Práctica 2\\Contador\\Contador\\obj\\Debug\\Contador.exe");                     Contador.Start();                     Datos.WaitForExit(250);                     Thread.Sleep(500);                 }                 catch (Exception e)                 {                     Console.WriteLine(e.Message);                 }                  try                 {                     System.Diagnostics.Process.Start("C:\\Users\\M-00\\Desktop\\Numeros\\Numeros\\obj\\Debug\\Numeros.exe");                     Numero.Start();                     Datos.WaitForExit(500);                     Thread.Sleep(750);                 }                 catch (Exception e)                 {                     Console.WriteLine(e.Message);                 }             }         }     }

How do I suspend a whole process (like the Process Explorer does when I click Suspend) in C#.  I'm starting the Process with Process.Start, and on a certain event, I want to suspend the process to be able to do some investigation on a "snapshot" of it.


Running Linux Mint 17.1 & MATE 1.8.1  When I open the terminal window with ctrl+T, I want it to switch the path automatically to ~/workspace. How do I do this?

When I open my non-login shell in Ubuntu, my present working directory is /home/user_name (my $HOME environment variable), but I want to change this such that when I start my terminal I am in some other directory.  I have read that when I start my terminal in Ubuntu a .bashrc file is sourced. So I added   export HOME=/home/user_name/Documents    to my .bashrc file. Now, when I open my terminal I am still in /home/user_name directory.  How can I change this?


I am getting a java.lang.NullPointerException error, and even though I checked mInternshipId and it is the same as I was expecting, it does not work.   This is my Firebase Content    This is my Internship Class  public class Internship {     private String internshipId;     private String internshipTitle;     private String internshipDesc;     private String internshipDate;     private String internshipImage;     private String internshipCreatorId;      public Internship() {      }      public Internship(String internshipId, String internshipTitle, String internshipDesc, String internshipDate, String internshipImage, String internshipCreatorId) {         this.internshipId = internshipId;         this.internshipTitle = internshipTitle;         this.internshipDesc = internshipDesc;         this.internshipDate = internshipDate;         this.internshipImage = internshipImage;         this.internshipCreatorId = internshipCreatorId;     }      public String getInternshipTitle() {         return internshipTitle;     }       public String getInternshipId() {         return internshipId;     }      public void setInternshipId(String internshipId) {         this.internshipId = internshipId;     }      public void setInternshipTitle(String internshipTitle) {         this.internshipTitle = internshipTitle;     }      public String getInternshipDesc() {         return internshipDesc;     }      public void setInternshipDesc(String internshipDesc) {         this.internshipDesc = internshipDesc;     }      public String getInternshipDate() {         return internshipDate;     }      public void setInternshipDate(String internshipDate) {         this.internshipDate = internshipDate;     }      public String getInternshipImage() {         return internshipImage;     }      public void setInternshipImage(String internshipImage) {         this.internshipImage = internshipImage;     }      public String getInternshipCreatorId() {         return internshipCreatorId;     }      public void setInternshipCreatorId(String internshipCreatorId) {         this.internshipCreatorId = internshipCreatorId;     } }   This is where I am using it. It shows that mInternship is not been initialized. Thank you everyone in advance for your time.  //Get The Internship ID     Intent intent = getIntent();     mInternshipId = intent.getStringExtra(INTERNSHIP_ID);      //Initialize the Database Reference     databaseReference = FirebaseDatabase.getInstance().getReference().child("Internships").child(mInternshipId);     databaseReference.addValueEventListener(new ValueEventListener() {         @Override         public void onDataChange(@NonNull DataSnapshot dataSnapshot) {              //Initialize Useful Variables             mInternship = dataSnapshot.getValue(Internship.class);             organizationId = mInternship.getInternshipCreatorId();             databaseReference = FirebaseDatabase.getInstance().getReference().child("Users").child("Organizations").child(organizationId);             databaseReference.addValueEventListener(new ValueEventListener() {                 @Override                 public void onDataChange(@NonNull DataSnapshot dataSnapshot) {                     internshipLocation = (String) dataSnapshot.child("location").getValue();                 }                  @Override                 public void onCancelled(@NonNull DatabaseError databaseError) {                 }             });         }          @Override         public void onCancelled(@NonNull DatabaseError databaseError) {         }     });

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I was trying to build animation to show How $\zeta(1/2+it)$ would look as $t$ changes. If the $\text{Re}(s)$ were greater than $1$, I could simply use the definition of the zeta function. $$\zeta(s)=\sum_{n=0}^\infty \frac{1}{n^s}$$ But as the above sum doesn't converge for $\text{Re}(s)\leq 1$, I'm in trouble. I don't know if I can use analytic continuation for it. So I'm asking if there is some trivial way to find $\zeta(1/2+it)$  for  $\text{Re}(s)\leq 1$.

I am told that when computing the zeroes one does not use the normal definition of the rieman zeta function but an altogether different one that obeys the same functional relation. What is this other function that they use explicitly given?  Also if I were to take one of these non trivial zeroes and plug it into the original definition would my answer tend towards zero as I evaluate the series?


I am currently writing my PhD thesis (genetics) and I encountered the following problem: The text contains a lot of gene names (italic) with mutations indicated as superscripts. So, rather than typing the whole command each time, I defined custom commands to make things easier. But the automatic italic correction does not work if it is wrapped up in an custom command (MWE below). Putting "\ " inside the command helps but messes things up, when making an enumeration.  Is there a workaround for this?  MWE:  \documentclass{article}  \newcommand{\test}{\textit{gene\textsuperscript{mutation}}}  \begin{document} Example where spacing problems with \test show up.  Putting \textit{gene\textsuperscript{mutation}} directly into the text works perfect. \end{document}

I have a definition:  \newcommand{\arnold}{Arnold Schwarzenegger}   When I refer to it by:  \arnold is a   it is rendered as:   Arnold Schwarzeneggeris a    In order to have a space in front of "is" I would need to write  \arnold\ is a   Is there some other shorter way?


Consider an imaginary cube of liquid as shown in the figure.    Why should all the forces on the cube be same? The cube can be stationary even if the forces on parallel, opposite vertical sides are equal and opposite in direction. The cube can be arbitrarily small or large.  Edit $-$  Based on the answer by Steeven, I just want to consider a similar hypothetical experiment of that sort. Imagine a container with rigid, smooth balls. If I apply pressure $P$ on all the sides of this container, will I get this much amount of increased pressure on the upper and lower sides? I think that more the spheres are small and more in number, the more pronounced the above-mentioned effect will be seen.(This is my guess)

I'd like answers both in the more intuitive side an on the more precise side.   Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a  triangular prism, yield different results. Will this fact, then, be dependent on the format of the molecules of the liquid ?  I've heard of the rotational symmetry of liquids. What is its precise statement ? Why is it true ?


Here is a question that has been nagging me for a few years: Which is the right usage:  "Didn't used to" or "didn't use to?"  Examples: We lived on the coast for years but we didn't use to go to the beach! We lived on the coast for years but we didn't USED TO go to the beach!  He didn't use to read stories as a child, but he grew up to be a writer. He didn't USED TO read stories as a child, but he grew up to be a writer.  Did you use to play video games in your youth? Did you USED TO play video games in your youth?  I have seen this question asked on many other websites, and there has been a great deal of debate, but it had generally been inconclusive.  I personally consider 'didn't USED TO' a wrong usage, but would like an expert opinion.

What is the negative form of "I used to be"? I often hear "I didn't used to be" but that sounds awfully wrong in my ears.


ECC multiplication over GF(p) is clearly one-way.  How about ECC over real number?  Is ECC division over real number also practically impossible?

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?


I am having trouble writing to a samba share from a linux client (a Windows client can read and write just fine). According to ls -la run from the linux client, I should have full permissions:  james@Q35-ICH9:~$ ls -la /mnt/ total 8 drwxr-xr-x  3 root  root  4096 Feb 25 09:38 . drwxr-xr-x 24 root  root  4096 Feb 25 04:39 .. drwxrwxrwx 61 james james    0 Feb 26 05:39 cloudshare  james@Q35-ICH9:~$ getfacl  /mnt/cloudshare/ getfacl: Removing leading '/' from absolute path names # file: mnt/cloudshare/ # owner: james # group: james user::rwx group::rwx other::rwx   but:  james@Q35-ICH9:~$ touch  /mnt/cloudshare/test touch: cannot touch '/mnt/cloudshare/test': Permission denied   But if I use sudo, I can touch:  james@Q35-ICH9:~$ sudo touch  /mnt/cloudshare/test   The user also has full access to the parent folder:  james@Q35-ICH9:~$ ls -la /mnt/ total 8 drwxrwxrwx  3 james james 4096 Feb 25 09:38 . drwxr-xr-x 24 root  root  4096 Feb 25 04:39 .. drwxrwxrwx 61 james james    0 Feb 26 07:42 cloudshare   I am confused as to why I need to be root to write to cloudshare even though 'james' should have full permissions (as far as I can see).

I have access to a cifs network drive. When I mount it under my OSX machine, I can read and write from and to it.   When I mount the drive in ubuntu, using:  sudo mount -t cifs -o username=${USER},password=${PASSWORD} //server-address/folder /mount/path/on/ubuntu   I am not able to write to the network drive, but I can read from it. I have checked the permissions and owner of the mount folder, they look like:  4.0K drwxr-xr-x  4 root root    0 Nov 12  2010 Mounted_folder   I cannot change the owner, because I get the error:  chown: changing ownership of `/Volumes/Mounted_folder': Not a directory   When I descend deeper into the network drive, and change the ownership there, I get the error that I have no permission to change the folder´s owner.  What should I do to activate my write permission?


I'm trying to get property values as an Array in order to use them to display some data in a PDF file. When I try something like this all properties values are equal null.  Product p = new Product("989-ST", "Magazine Vogue"); System.out.println(p.getData().length); for(String e : p.getData()){ System.out.print(e + " "); } //--Output:: 2 //--null     null   My Prdocut class is like:  Public class Product { private String sku; private String descripcion;   public Product() {  }  public Product(String sku, String descripcion) {     sku = this.sku;     descripcion = this.descripcion;  }  public String getDescripcion() {     return descripcion; } public void setDescripcion(String descripcion) {     this.descripcion = descripcion; } public String getSku() {     return sku; } public void setSku(String sku) {     this.sku = sku; }  public String[] getData() {     String[] data = { this.descripcion, this.sku };     return data; } }   Am I missing something? Because when I set the property values using setters I can get the expected values:  Product p = new Product(); p.setSku("989-ST"); p.setDescription("Magazine Vogue"); System.out.println(p.getData().length); for(String e : p.getData()){ System.out.print(e + " "); } //--Output:: 2 //--989-ST     Magazine Vogue


Let $(X,d)$ a metric space. Show that $d'(x,y)=\dfrac{d(x,y)}{1+d(x,y)}$ define a metric on $X$.  Hello, I have this problem. The triangular inequality is my difficulty. Indeed, we have that show that $d'(x,z)\le d'(x,y)+d'(y,z),\forall x,y,z\in X.$ Good, I do this...  $d'(x,z)=\dfrac{d(x,z)}{1+d(x,z)}\le \dfrac{d(x,y)+d(y,z)}{1+d(x,z)}=\dfrac{d(x,y)}{1+d(x,z)}+\dfrac{d(y,z)}{1+d(x,z)}.$  I don't understand how does with $d(x,z)$? Or if exists any form for bounded this expression.

Let $(X,d)$ be a metric space and for $x,y \in X$ define $$d_b(x,y) = \dfrac{d(x,y)}{1 + d(x,y)}$$ a) show that $d_b$ is a metric on $X$  Hint: consider the derivative of $f(t)$ = $\dfrac{t}{1+t}$  b) show that $ d$ and $ d_b $ are equivalent metrics. c) let $(X,d) $ be $(\mathbb{R}, |\cdot|)$ Show that there exists no $ M>0$ such that $ |x-y| $ $\leq$ $Md_b$ $(x,y)$ for all $ x,y$ $\in$ $\mathbb{R}$  I have calculated $f(t)$ and $f'(t)$ and from this I know $f(t)$ is an increasing function as $f'(t)$ is strictly positive. But I don't know where to go from here or how to do parts b) and c)


I would like to create two different title pages (one with the author information and the thanks notes and one without) by using the \maketitle command. Repeating the commands one after another wasn't successful.    Using the \titling package creates the same title, even though I enter an empty field for the author (i.e., \author{}) and insert no \thanks notes after the title.   Is there an elegant and an easy way to create two different title pages with different information? I would be glad, if someone can help me here.   Here is the code I tried running with the \titling package, which repeats the same titlepage:  \title{Title text\thanks{Thanks}}  \author{Author Name}  \date{D}  \begin{document}  \pagenumbering{roman}  \oneandhalfspacing  \begin{titlepage}  \maketitle   \date{}  \begin{abstract}  \spacing{2}  \thispagestyle{empty}  Some text for the abstract  \end{abstract}  \end{titlepage}  \begin{document}  \pagenumbering{roman}  \oneandhalfspacing  \begin{titlepage}  \maketitle  \date{}  \title{Title Text}  \author{}  \date{}  \begin{abstract}  \spacing{2}  \thispagestyle{empty}  \date{}  Some text for the abstract  \end{abstract}  \end{titlepage}  \newpage  \pagenumbering{arabic}  \spacing{2}  \section{Introduction}

I need to have two \maketitles in a document. The titling package handles this almost perfectly. The issue is that I use the \thanks command in the \title and in the \author, and then, in the second \maketitle, the text of the \thanks command is repeated twice. Does anyone know how I can get rid of the second occurrence of the text of the \thanks command? Thanks, Eilon  \documentclass[12pt]{article} \usepackage{titling} \begin{document}  \begin{titlepage} \title{First title\thanks{I thank my kids.}} \author{Author1\thanks{Affiliation of author1. } and Author2\thanks{Affiliation of author2.}} \maketitle \end{titlepage}  \begin{titlepage} \title{Second title} \maketitle \end{titlepage} \end{document}


I mean, yes Obi-wan says he will become extremely powerful, but really he doesn't. The only thing he does is give Luke some advice that could be given to him through the X-wing headset anyway. So how is that powerful,     and where was he when Han died?   So the question is, why would forceghosts ever be seen as powerful and why do they disappear after some time?

The default answer among most people to my previous  seems to be that Obi-Wan was referring to becoming a force ghost. Now whilst this seems pretty cool, you are now hindered into well Kyle Jones says it best     Force Immortality seems like a bust to me. Obi-Wan could get around the galaxy without a starship, true, but the fine print of the immortality contract restricted him to visiting only a few close friends. Seems like being alive with a good galactic cellphone plan would be an all-around better deal. And of course there were the women... – Kyle Jones    So what gives? Are you inherently more powerful as a force ghost?


The other day, I was hunting for a word to describe someone I know. The trait denoted by this word is the tendency to rapidly spot--as though unconsciously seeking out--double meanings, especially of the racier sort, in messages whose intent was probably innocuous.

I know there is a word for it — I heard it when I was young. What is the word to describe a person who catches the sexual overtones in a normal (non-sexual) conversation?  Here's one example I have (I said this and then laughed because it was my comment and went over my own head at the time):  I was considering a name for a mobile dog grooming business. I thought 'Doggie Style' was great. Of course, the room full of my husband's friends laughed at me, telling me I'd never get approved for a license with that name. What word would I use to describe them?


Some brokers offer fractional shares. So when i buy half share of stock (0.5) whose buy the rest half of share because in stock exchanges(e.g. nyse,nasdaq,bats) you can only exchange whole shares.

I've been trying to find out some more information about fractional shares, and how they work. I understand conceptually, you own x% of a share rather than x "full" shares, but I'm curious about how such a system is implemented.  As I understand it, in a "traditional" purchase of shares, the role of a broker is to act as an executor on your behalf, and does not hold any assets themselves. In the case of a fractional share, is this then not the case? For example, the broker holds the complete shares, and then just ensures that they keep an internal record of each partial owner in their system? So there would be no external record of partial ownership?  Thanks!


I would like to know how to type the symbol of  in LaTeX:    I tried to use , but it does not give me anything.

For example, I want to put a circle around \land, just like one can put a circle around + by writing \oplus. Is there a general method to do this?


A user posted this link in chat:  Well, almost; he linked to this: (don't mind the newline I've added for your comparison pleasure) http://www.newegg.com/Product/Product.aspx? Item=N82E16811119233&cm_re=Cooler_Master_haf_912-_-11-119-233-_-Product)  ...but as you can see above, Markdown looks at that couple of -_-s and decides that it's actually an attempt to make the link italic. Attempting to fix the link as such:  (again, ignore the whitespace). [http://www.newegg.com/Product/Product.aspx?  Item=N82E16811119233&cm_re=Cooler_Master_haf_912-_-11-119-233-_-Product]  (http://www.newegg.com/Product/Product.aspx?   Item=N82E16811119233&cm_re=Cooler_Master_haf_912-_-11-119-233-_-Product)  Results in [this message on chat][1], rendered so: (again, whitespace and HTML comment added for you):                                           http://www.newegg.com/Product/Product.aspx?        Item=N82E16811119233&amp;cm_re=Cooler_Ma&zwnj;&#8203;ster_haf_912--11-119-233--Produc   It just so happens that the link works anyway, even with the erroneous  and s injected in it. [1]:

So, this is the URL:  http://code.google.com/p/es-lab/wiki/Talks#Changes_to_ECMAScript,_Part_2:_Harmony_Highlights_-_proxies_and   When I insert the URL like so:  [Title](URL)   the last part of the URL changes from  Highlights_-_proxies_and   to   Highlights/i-_proxies_and   What's going on here?  Note: See my comment below for a live demonstration of the issue! Feel free to copy the URL and try it for yourself... (It seems that the URL is only altered if the []() notation appears within a comment, but not when it appears within a question/answer.)


Let $A$ be the unit circle in the $xy$ plane in $3$-dimensional real space and let $A_+$ be a semicircle. I have to compute the homology of $\mathbb{R}^3\setminus A_+$. I was thinking that $\mathbb{R}^3\setminus A_+$ is homotopically equivalent to $\mathbb{R}^3\setminus \{(1,0,0)\}$  which can than be proved to be homeomorphic to $S^2$. However, I have trouble finding a retraction $g:\mathbb{R}^3\setminus \{(1,0,0)\}\rightarrow \mathbb{R}^3\setminus A_+$  to construct the equivalence, since homotopy equivalence is not stable under subtractions, i.e. if $A,B\subset X$, $A$ homotopically equivalent to $B$ it does not follow that $X\setminus A$ homotopically equivalent to $X\setminus B$.

Here is a problem and my attempt at the solution. If my conclusion or the proof is incorrect I would appreciate a pointer in the right direction. Thanks in advance.  Let $S^1$ be the unit circle in the xy plane in $\mathbb{R^3}$ and let $E^1_+$ and $E^1_-$ be two of its semicircles. Find the homology groups (with integer coefficients) of a) $\mathbb{R^3}\setminus E^1_+$ and b) $\mathbb{R^3}\setminus \ S^1$.  Attempt of solution:   a) $H_n(\mathbb{R^3},S^1)\cong H_n(\mathbb{R^3}\setminus E^1_+, E^1_-)$, by excision. Then $H_n(\mathbb{R^3}\setminus E^1_+, E^1_-) \cong H_n(\mathbb{R^3}\setminus E^1_+, {pt})$, since $E^1_-$ is contractible. Then we know $H_n(\mathbb{R^3}\setminus E^1_+, {pt}) \cong \tilde{H_n}(\mathbb{R^3}\setminus E^1_+)\cong H_n(\mathbb{R^3}\setminus E^1_+)$ for $n>0$. So we get $H_n(\mathbb{R^3}\setminus E^1_+) \cong H_n(\mathbb{R^3},S^1)$. From the long exact sequence of relative homology we know that $H_n(\mathbb{R^3},S^1) \cong H_{n-1}(S^1)$, so $H_n(\mathbb{R^3}\setminus E^1_+)\cong \mathbb{Z}$ for $n=1,2$.  For $n=0$ we also get $\mathbb{Z}$ since $\mathbb{R^3}\setminus E^1_+$ is arcwise connected.  b) the same reasoning but starting with $H_n(\mathbb{R}^3,E^2_+)$, where $E^2_+$ is the upper hemisphere of $S^2$, gives $H_n(\mathbb{R}^3 \setminus S^1) \cong H_{n-1}(E^2_+)$, but  $E^2_+$ is contractible so $H_n(\mathbb{R}^3 \setminus S^1)\cong \mathbb{Z}$ for $n=1$ and for $n=0$ it is also $\mathbb{Z}$ since $\mathbb{R}^3 \setminus S^1$ is arcwise connected. For $n>1$, $H_n(\mathbb{R}^3 \setminus S^1)=0$.  EDIT @msteve pointed out that b) is wrong. Excision can't be used like in a) since $S^1$ isn't in the interior of $E^2_+$. So a different approach is needed here.


I understand the other districts can't, because during the dark wars the Capitol thinks those districts were the rebels (and yes, even Districts 1 and 2 had rebels). But would citizens of District 1 and 2, who the Capitol citizens or particularly Snow knows quite well, be not allowed to move to the Capitol and/or participate in Snow's rebel punishment known as "the Hunger Games"?

Reading  got me thinking about permitted citizenship.  Are citizens of other districts allowed to permanently move to, or become citizens of the Capitol?   My gut says, "No." The citizens of the other districts are being punished, so it makes little sense to allow them a true, legal escape from their punishments. Even victors are only given new homes in their own districts, keeping them there.


I would like to import JPG file into my document in LaTeX. The code below works but only for EPS files, but I need JPG. How can I fix it?  \documentclass{article} \usepackage{graphicx} \begin{document} \includegraphics{image} \end{document}

There several types of graphics files. In no particular order .jpeg .eps .pdf .png .tif .jif (and no doubt others). Some work with latex, dvips and some work with pdflatex. How am I supposed to know which?  Just to confuse matters, metapost produces .eps but I can use these with pdflatex as long as I put in a four line incantation.  Can anyone explain this?


What I'm trying to do is to construct a linear model in a form like  $$ Y = \beta_0X_0-\beta_1X_1+\beta_2X_2 + \beta_3 $$  where $\beta_0$, $\beta_1$ and $\beta_2$ are coefficient of predictors $X_0$, $X_1$ and \beta_2 respectively. And, They all are positive, which means my assumption of the model is that $X_1$ has negative effect towards the response $Y$. Perhaps, I misunderstand the concept of regression, but if anyone has an idea how to achieve this in R, please enlighten me. Or any other approach apart from regression model. Thanks in advance.

I'm working with some real world data and the regression models are yielding some counterintuitive results. Normally I trust the statistics but in reality some of these things can not be true. The main problem that I am seeing is that an increase in one variable is causing an increase in the response when, in fact in reality, they must be negatively correlated.  Is there a way to force a specific sign for each of the regression coefficients? Any R code to do this would be appreciated as well.  Thanks for any and all help!


I understand the fact that a static charge produces an electric field around it.  I accept the fact(without questioning) that a moving charge produces a magnetic field.  Question 1 : If a moving charge produces both electric and magnetic fields why can we not say that it produces an EMW?  Question 2 : How does an accelerated charge produce EMW?

How the electro-magnetic waves are produced by the accelerating charged particle? Graphical explanations are most welcomed. Is the explanation given by the below mentioned article correct regarding the movement of electromagnetic waves?


This is a question about the classical two envelopes paradox problem. The solution posted in  seems to be uniform across all the sources I've seen. The question is:  Suppose that there are two envelopes. One containing $\$m$ and the other containing $\$2m$. You don't know which envelope contains which. You pick one at random. You want to decide if you should switch to the other envelope under the following conditions (1) You are NOT allowed to open your envelope and see how much is inside. (2) You are allowed to open your envelope and see how much is inside.  The mathematical approach shows that for (1), you don't gain anything from switching because each envelope has an expected value of $\$1.5$. The mathematical approach shows that for (2), you gain  $\$0.25$ from switching to the other envelope. I don't understand the solution for (2). The logic is that when you peek into your envelope and you observe $\$x$, this means that the other envelope has $\$x / 2$ or $\$2x$ with equal probability. I'm not sure if I agree with this, as I think the solution for (2) should be the same as (1). I don't think you can say that the other envelope contains $\$x / 2$ or $\$2x$. Suppose that $x = \$m$. This would mean that if you claim the other envelope contains either $\$x / 2$ or $\$2x$, then that would mean the other envelope contains $\$m/2$ or $\$2m$, but we know that the other envelope contains only $\$m$ or $\$2m$ and there's no envelope with $\$m/2$. The analogous issue occurs if $x = \$2m$. Ultimately, I'm just not seeing how observing how much you have changes anything. Like if I were to simulate this with monte carlo or to do this in real life with two envelopes, I don't see how I'm going to, gain, on average by choosing the other envelope after I open my envelope and see what's inside, so that brings me back to the same situation as not observing what's inside my envelope in the first place. Could someone explain? What if we applied this same logic to a True/False test? Say there are 100 questions, and you know there are 50 false and 50 true answers. Say I initially picked True for all the answers. According to the above logic, I should switch all my answers to False? If that's the case, then I clearly don't gain anything from switching.

Suppose you're given two envelopes. Both envelopes have money in them, and you're told that one envelope has twice as much money as the other. Suppose you pick one of the envelopes. Should you switch to the other one?  Intuitively, you don't know anything about either envelope, so it'd be ridiculous to say that you should switch to the other envelope to maximize your expected money.   However, consider this argument. Let $x$ be the amount of money in the envelope you picked. If $y$ is the amount of money in the other envelope, then the expected value equals  $$E(y) = \frac{1}{2}\left(\frac{1}{2}x\right) + \frac{1}{2}\left(2x\right) = \frac{5}{4} x$$  But $5x/4 > x$, so you should switch!    The Wikipedia article says that $x$ stands for two different things, so this reasoning doesn't work. I say this is not a valid resolution.   Consider opening up the envelope that you pick, and finding $\$10$ inside. Then you can run the expected value calculation to get $$E(y) = \frac{1}{2} \cdot \$5+\frac{1}{2} \cdot \$20 = \$12.50$$  This means that if you open one of the envelopes and find $\$10$, you should switch to the other envelope. The $\$10$ doesn't stand for two different things, it literally just means $\$10$.   But you don't have to open up the envelope to run this calculation, you can just imagine what's inside, and run the calculation based on that. This is what "Let $x$ be the amount in the envelope" means. The problem with the argument is not that $x$ stands for two different things.   So what is the problem?    Previous questions on stack exchange have given the resolution that I just said I wasn't satisfied by, so please don't mark this as a duplicate. I want a different resolution, or a more satisfying explanation of why $x$ does stand for two different things.  Apparently there is still research being published about this problem - maybe it isn't so obvious?    I think there's something subtle wrong with the premise. Because there's no uniform probability distribution on $\mathbb{R}$, statements like "random real number" are not well-defined. Likewise, I think "one envelope has twice as much money as the other" assumes some probability distribution on $\mathbb{R}$, and perhaps our expected value calculation assumes that this distribution is uniform, which it cannot be ...


I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


I personally like the Beamer theme `Frankfurt', however for longer presentations with a lot of slides/sections I'm finding that the header space where the sections and the slide dots are listed is not large enough.  My preference would be that rather than listing all sections, the header space only showed the current section plus the navigation dots, either left-justified or centered.  Here is a MWE of what you get by default:  \documentclass[pdf]{beamer} \mode<presentation>{\usetheme{Frankfurt}}  \title{The title} \author{A name} \begin{document}  \begin{frame} \titlepage \end{frame}  \begin{frame} \tableofcontents \end{frame}  \section{Section 1} \subsection{} \begin{frame}{stuff} some stuff \end{frame}  \begin{frame}{stuff} some stuff \end{frame}  \section{Section 2} \subsection{} \begin{frame}{stuff} some stuff \end{frame}  \begin{frame}{stuff} some stuff \end{frame}  \end{document}   You can see in the MWE result that both section 1 and 2 are listed in the header for all slides.  I don't know the first thing about modifying beamer layouts - anyone have advice? thanks!

I am wondering whether we can use the subsection part of the beamer infolines outer theme headline (the right half) to show the miniframe bullets of the current section. Assuming the section has three frames, the headline would look like this  First frame of the section:         Section Title @oo        Frame title    Next frame of the section:         Section Title o@o        Frame title    and so on.  I guess this can be done by hacking around \dohead, but I couldn't figure out how to tweak things. Any help will be greatly appreciated.


I close the Skype app in my Android phone (samsung s3 mini)  If Skype is open on my pc and I receive a call it also starts automacically in my phone without my input!   How can I avoid such a strange behavior? Thank you

I'm using the newly released market version of Skype on my ADP1 running CyanogenMod 6.0.  I can't seem to quit the Skype program. There doesn't seem to be any mechanism for signing out of Skype once signed in. I can kill the task, but the next time anything triggers it it think it has the right to sign in and be online again, bar nothing. The task bar icon just takes you to the program, but the program doesn't seem to have any menus, doesn't respond the the back button etc.  Ideas?


Suppose that the second fundamental form of a surface patch $\sigma$ is zero everywhere.   How can we prove that $\sigma$ is an open subset of a plane?   The second fundamental form of a surface patch $\sigma$ is $$Ldu^2+2Mdudv+Ndv^2$$ where $L=\sigma_{uu}\cdot \textbf{N}, \ M=\sigma_{uv}\cdot \textbf{N}, \ N=\sigma_{vv}\cdot \textbf{N}$.   What does it mean that the second fundamental form of a surface patch $\sigma$ is zero everywhere? That $L=M=N=0$ ?   $$$$   EDIT:   We have that $\sigma_u\times\sigma_v$ is perpendicular to both $\sigma_u$ and $\sigma_v$.  So $N=\frac{\sigma_u\times \sigma_v}{\|\sigma_u\times\sigma_v\|}$ is perpendicular to both $\sigma_u$ and $\sigma_v$.  Therefore, $ \sigma_u \cdot N=0$ and $\sigma_v\cdot N=0$.   We also have that $$\sigma_{uu}\cdot N=0, \sigma_{uv}\cdot N=0, \sigma_{vv}\cdot N=0$$   So, $$( \sigma_u\cdot N)_u=0 \Rightarrow \sigma_{uu}\cdot N+\sigma_u \cdot N_u=0 \Rightarrow \sigma_u \cdot N_u=0$$  $$( \sigma_u\cdot N)_v=0 \Rightarrow \sigma_{uv}\cdot N+\sigma_u \cdot N_v=0 \Rightarrow \sigma_u \cdot N_v=0$$  $$( \sigma_v\cdot N)_u=0 \Rightarrow \sigma_{vu}\cdot N+\sigma_v \cdot N_u=0 \Rightarrow \sigma_v \cdot N_u=0$$  $$( \sigma_v\cdot N)_v=0 \Rightarrow \sigma_{vv}\cdot N+\sigma_v \cdot N_v=0 \Rightarrow \sigma_v \cdot N_v=0$$   So, $N_u$ and $N_v$ are perpendicular to $\sigma_u$ and $\sigma_v$.  We have that $N_u$ and $N_v$ are perpendicular to $N$. $N$ is perpendicular to the tangent plane. So, this implies that $N_u$ and $N_v$ lie in the tangent plane of the surface, which is spanned by $\sigma_u$ and $\sigma_v$.   We have that $N_u$ lies in the tangent plane that is spanned by $\sigma_u$ and $\sigma_v$, and that $\sigma_u\cdot N_u=0$ and $ \sigma_v\cdot N_u=0$, which means that $N_u$ is perpendicular to $\sigma_u$ and $\sigma_v$.  This can only hold when $N_u=0$.  Respectively, we get $N_v=0$.  Is this correct?   Since $N_u=N_v=0$, we conclude that $N$ is constant.   Since $N$ is perpendicular to the tangent plane, we have that $\sigma_u \cdot N=\sigma_v\cdot N=0$. So,   $(\sigma\cdot N)_u =\sigma_u\cdot N=0$   $(\sigma\cdot N)_v =\sigma_v\cdot N=0$   So, we have that $\sigma\cdot N=c$, where $c$ is a constant.   How co we conclude from here that $\sigma$ is an open subset of a plane?

This is my question:  Let P be a plane considered as a surface in 3-space. Show that its second fundamental form is zero. Conversely, show that if the second fundamental form of a surface is identically zero then the surface is a plane.  So far I have that the general equation of the plane is $$ax+by+cz+d=0.$$ Then $$M(u,v)=(u,v,\alpha u + \beta v + \gamma),$$ where $a,b,c,d,\alpha,\beta, \gamma$ are all constants and $c\not=0$. Then $M_u=(1,0,\alpha)$ and $M_v=(0,1,\beta)$. I know that $\vec{n} =\frac{M_u \times M_v}{|M_u \times M_v|}$ which gives $$ \vec{n}=\frac{(-\alpha,-\beta, 1)}{\sqrt{\alpha^2+\beta^2+1}}.$$ Hence, the unit norm is a constant. $$ M_{uu}=M_{uv}=M_{vv}=0$$ Hence $l=m=n=0$, so the second fundamental form is $$ ldu^2+mdudv+ndv^2=0.$$  Now I need to show the converse, but I don't know how. Please help :)