A bit of a random one here... I've got a basic table that I'm using for temporary data inserts - and for that reason, I don't need or want a unique ID - however, I'm seeing odd behaviour! (or it feels odd to me at least) If I insert data into the table, and then immediately run a select statement on the same table (no ordering going on) - the new row ends up in the middle of the results - how / why ? This isn't a problem for me - I don't particularly care how it orders the data for this particular table (and I'm aware we could add a unique column, PK etc, autoinc identifier etc to handle this situation) - but it's just something I've never seen before - I'm convinced that on the hundreds of occasions I've done this previously, new data always ends up at the bottom of the list! - Am I going mad? is this normal? is there a way to always insert data to the end ? Thanks Chris

Recently I was explaining to colleagues the importance of having a column by which to sort data in a database table if it is necessary to do so, for example for chronologically-ordered data. This proved somewhat difficult because they could simply re-run their query seemingly endlessly and it would always return the same set of rows in the same order.  I have noticed this before and all I could really do is insist that they trust me and not simply assume that a database table will behave like a traditional CSV or Excel file.  For example, executing the (PostgreSQL) query  create table mytable (     id INTEGER PRIMARY KEY,     data TEXT ); INSERT INTO mytable VALUES     (0, 'a'),     (1, 'b'),     (2, 'c'),     (3, 'd'),     (4, 'e'),     (5, 'f'),     (6, 'g'),     (7, 'h'),     (8, 'i'),     (9, 'j');   will create a table with a clear conceptual order. Selecting that same data in the simplest way would be:  SELECT * FROM mytable;   Always gives me the following results:   id | data  ----+------   0 | a   1 | b   2 | c   3 | d   4 | e   5 | f   6 | g   7 | h   8 | i   9 | j (10 rows)   I can do this over and over again and it will always return to me the same data in the same order. However I know that this implicit order can be broken, I have seen it before, particularly in large datasets, where some random value will get apparently thrown up into the "wrong" place when selected. But it has occurred to me that I don't know how this happens or how to reproduce it. I find it difficult to get results on Google because the search query tends to just return general help on sorting result sets.  So, my questions are essentially these:   How can I demonstrably and concretely prove that the return order of rows from a query without an ORDER BY statement is not reliable, preferably by causing and showing a breakdown of the implicit order even when the table in question is not updated or edited? Does it make any difference at all if the data is only inserted once en masse and then never updated again?   I would prefer a postgres-based answer since that is the one I am most familiar with but I'm more interested in the theory itself.


I would like to know how to calculate the area of the vector layer (red in the photo) under each polygon (white square in the photo). The red layer has the area (km2) in its attributes. But what I want to know is how much (area) of the pink layer is within the square grid. Both my layers are in meters already.

I am new to QGIS - I want to estimate the area of the reef under a polygon grid. My shapefiles are already in meters, however I am having a hard time calculating the area under the grid layer. Attached are the photos. I want to calculate the total area of the bold black polygons (reefs) under each grid square (image 2). How much reef is inside each square, for example, grid1: 25 sq.km, grid 1 sq.km, etc. Each reef polygon has its corresponding area in the layer attribute table.    ADDITIONAL PHOTO: RED IS THE REEF  THE ATTRIBUTES OF THE REEF LAYER


I'll admit, I know nothing about Blender. Hadn't even heard the name until last week. A client of mine is looking to replace a 2010 Mac Pro with something more recent.  I told them that I'd do some research to determine where the 'sweet spot' in price/performance was on Apple's current Mac Pro offerings.  So, my question is. How much of blender work is CPU-related, and how much is GPU related? Where do you think the best price/performance ratio lies?  Should I prioritize spending on the CPU, the GPU or look for a balance?  The six-core/D500 GPU is my current plan, but I'm willing to be persuaded.

The rendering time on my laptop is starting to become absurd in order to get a decent looking scene. I am looking at building a pc that is well suited for blender. What components are the most important? Most of my projects are rendered using cycles, so a Nvidia graphics card is a must plus lots of ram. But I want some more information, like what cpu (Amd?)? What graphics cards would you recommend? If you have the time could you list a couple different builds such as premium, budget, ect.?  I know that there are other ways of lowering the rendering time (i.e. better poly management), but I have been looking to build my own rig for a while.   Thanks Guys!


I read the book series a long time ago. Hopefully the bits I remember, listed below, are enough to go on.   From memory there are three or four books in the series and I read them in the mid 2000's, in English, and they were pitched at a youth/young adult level though not afraid to tackle some serious issues (fairly sure there is a main character death at some point) The main character was a girl in her teens (name potentially beginning with an 'A' and maybe tied to the name of one of the books and/or the series?) and she had red hair She was human and living in modern times and ended up mixed up in a bunch of conflict in multiple other worlds or dimensions (I think the first time she got dragged into it she had been exploring out the back of her house and there were portals or gateways under the hill) and developed various powers/magic through the books and obviously ended up having to save the world  She ends up having had previous lives and during the series she gets access to the memories from the previous lives  May have been some form of time travel included There were a number of other races in the novels who inhabited the other worlds, and there was elemental magic around There was a floating mountain at some point I think, and dragons

I read this book in the early-ish 2000s (in English) and all I can remember are some oddly specific details.  The protagonist was a girl with red hair who somehow meets up with her companions from her previous life (which she doesn't remember). I'm pretty sure all of them were mythical creatures or something similar;  one of them was a troll. Towards the end of the book, the girl has to step into something magic that gives her back her memories and also makes her hair darker red; I think they described it as auburn.  I also vaguely remember time travel being a part of the story; she ends up changing her own decision by placing a button next to a door and I think that stops her friends from getting killed. There might have been a scene where she unscrews a hook from the ceiling because it got screwed in the wrong way.  From what I can remember, the cover was the girl riding on the back of the troll, which actually looked kind of like a gorilla. I think the title started with a R; it might have been the main character's name.


I want to add a shortcut to a file in another directory (where it isn't located). How do I do that? I see no option to do so after right clicking the respective file.

I am installing p4v in /opt, but /usr/bin is on my path.  Is it possible to create a soft or symbolic link for p4v from /opt to /usr/bin, so I can just type "p4v" since /usr/bin is in my path?


Let $\{f_n\}$ be a sequence of real-valued functions on $[0,1]$ and let $M$ be a real number such that:  (i) for each $n,$ $f_n$ is continuous; (ii) for each $x\in[0,1]$ and for each $n,$  $f_n(x)\leq f_{n+1}(x)\leq M.$  Prove that $\{f_n\}$ converges pointwise on $[0,1]$ to a function $f$ which is lower semicontinuous.  (that is for all $\{x_n\}\subset [0,1]$ and for all $x\in [0,1],$ $x_n\to x\implies \liminf\limits_{n\to\infty}f(x_n)\leq f(x).$  Please, can anyone help me out with this?

Suppose $F$ is a nondecreasing and right continuous function, and the sequence $\{x_n\}_{n\geq1}$ converges to $x$. Then $\liminf\limits_{n\to\infty}F(x_n)\leq F(x)$.    How can I prove this?


I have this situation on my hd:    I would increase the space of sda10 with the double unallocated space. There is a way to do that?

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I am trying to get the table name from the dbset property.  When a change is made I get the name of the class  Type myType = entry.Entity.GetType().BaseType; string name = myType.Name;   This gives me a string with the name of the class. In this example Employee.    public virtual DbSet<Employee> Employees { get; set; }   I'm trying to get the name of the table by sending the class to the following method.  public static string GetTableName<T>(this DbContext context) where T : class {     ObjectContext objectContext = ((IObjectContextAdapter)context).ObjectContext;      return objectContext.GetTableName<T>(); }  public static string GetTableName<T>(this ObjectContext context) where T : class {     string sql = context.CreateObjectSet<T>().ToTraceString();     Regex regex = new Regex("FROM (?<table>.*) AS");     Match match = regex.Match(sql);      string table = match.Groups["table"].Value;     return table; }   The problem is, these methods expect a class name and not a string.  How can I convert the string to a class name, or modify the method to accept the string.

What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod<T>() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod<T>()?         GenericMethod<myType>(); // This doesn't work          // What changes to call StaticMethod<T>()?         Sample.StaticMethod<myType>(); // This also doesn't work     }      public void GenericMethod<T>()     {         // ...     }      public static void StaticMethod<T>()     {         //...     } }


I'd like to add a link to the glossary in my main text.  See the \nameref{XXX} on page \ref{XXX}.   So far I couldn't find out the name of the label of the glossary. There should be one, since the link in my TOC works. How can I find out the name of the label?

I'm using the glossaries package. I created a custom glossary called foo with the title, "My Foo Glossary Title":  \newglossary[fgg]{foo}{fgs}{fgo}{My Foo Glossary}   Ideally, I'd like to make a reference to this glossary in my text using \nameref or \autoref, such that it looks like "...please see My Foo Glossary." via something resembling the following code:  ...please see \nameref{foo}.   This doesn't work....  I understand that I needed to add a label to the glossary in order to reference it (isn't it already labelled somehow -- it has to have a label if it is on the Table of Contents page, right?). I redefined the \glossarypreamble macro as follows:  \renewcommand*{\glossarypreamble}{% \label{\currentglossary}% }   Then I was able to link to it as follows:  ...please see \autoref{foo}.   Trouble is, this produces the text "Appendix A.3" rather than "My Foo Glossary". How can I get the link to display the text equivalent to \glossarytoctitle?  Thanks in advance!


There have been a few questions asked here about why you can't define static methods within interfaces, but none of them address a basic inconsistency: why can you define static fields and static inner types within an interface, but not static methods?  Static inner types perhaps aren't a fair comparison, since that's just syntactic sugar that generates a new class, but why fields but not methods?  An argument against static methods within interfaces is that it breaks the virtual table resolution strategy used by the JVM, but shouldn't that apply equally to static fields, i.e. the compiler can just inline it?  Consistency is what I desire, and Java should have either supported no statics of any form within an interface, or it should be consistent and allow them.

EDIT: As of Java 8, static methods are now allowed in interfaces.  Here's the example:  public interface IXMLizable<T> {   static T newInstanceFromXML(Element e);   Element toXMLElement(); }   Of course this won't work.  But why not?  One of the possible issues would be, what happens when you call:  IXMLizable.newInstanceFromXML(e);   In this case, I think it should just call an empty method (i.e. {}).  All subclasses would be forced to implement the static method, so they'd all be fine when calling the static method.  So why isn't this possible?  EDIT: I guess I'm looking for answer that's deeper than "because that's the way Java is".   Is there a particular technological reason why static methods can't be overwritten? That is, why did the designers of Java decide to make instance methods overrideable but not static methods?  EDIT: The problem with my design is I'm trying to use interfaces to enforce a coding convention.  That is, the goal of the interface is twofold:   I want the IXMLizable interface to allow me to convert classes that implement it to XML elements (using polymorphism, works fine). If someone wants to make a new instance of a class that implements the IXMLizable interface, they will always know that there will be a newInstanceFromXML(Element e) static constructor.   Is there any other way to ensure this, other than just putting a comment in the interface?


How/Why  Do Koi have a lifespan of hundreds of years? Do humans have a lifespan of decades? Do dogs have such a short lifespan?  Within these questions I pose further questions.  How does size relate to lifespan. Elephants?  If dogs were to evolve independent of humans (at this point) would they rule the world?

Why does evolution not make life longer for humans or any other species?  Wouldn't evolution favour a long life?


Can we say that $\frac{\sin x}{x}$ is defined at $x=0$? When is a function defined within its domain?

On plotting graph for $\frac{\sin x}{x}$ using Wolfram|Alpha and Google, got that :   also, I can get the value of $\lim_{x\rightarrow 0} \frac{\sin x}{x} = 1$ using squeeze theorem and as illustrated on sources such as .   But I'm not able to understand how the function is defined at $x=0$ and its value came out to be $1$ at that point. As promised in the plot for the function.  Using limits I got the idea about the behavior of the function in the neighborhood of that point but not its value exactly at $x=0$.


On a Riemannian manifold  $(M,g)$, there always exists local orthonormal frame $\{E_i\}$ with respect to the metric $g$. But there does not necessarily exist orthonormal coordinate frame $\{ \frac{\partial}{\partial x^i} \}$ in a small neighborhood around a point $p$, where $\{x^i:U \rightarrow \mathbb{R}$ } are coordinate maps.  My question is the follow:  instead of local orthonormal coordinate frame, is it possible to find local orthogonal coordinate frame?  i.e. with respect to some coordinate system, the metric g can be written locally as $$g= g_{ii} {dx^{i}}dx^i$$  For surface, I know this is true because of something stronger, the existence of isothermal coordinate. I wonder whether this is possible for higher dimension.

This is probably a very naive question, but so far I could not find an answer:  Let $(M,g)$ be a Riemannian manifold. Can we always find "orthogonal coordinates" locally?  More precisely, I am asking if for every $p \in M$ there exists a neighbourhood $U$ and a diffeomorphism $\phi:\mathbb{R}^n \to U$, such that $g_{ij}=g(d\phi(e_i),d\phi(e_j))=0$ for $i \neq j$.  Clarification: Note that I want $g_{ij}=0$ on all $U$, not just at $p$. Also, I allow $g_{ii} \neq g_{jj}$ for $i \neq j$ (the special case where $g_{ii}$ is independent of $i$ is called isothermal coordinates-and corresponds to conformal flatness of $U$).  Of course, this is  weaker than requiring $M$ to be conformally flat, since a (linear) map which maps an orthogonal basis to an orthogonal basis does not need to be conformal.


Suppose $T$ is minimal sufficient statistics for a family of distribution. If $T = H(U)$ where $U$ has the same dimension as that of $T$, then does it imply that $U$ is also minimal sufficient?  I think the answer to this question should be NO. I will give one example for this... Consider for a single observation $X$ for the family $\{f_0(x), f_0(x) \;| \;x\in \mathbb{R}\}$ where $f_0(x) = \frac{1}{\sqrt{2\pi}}\exp(-\frac{x^2}2)$ and $f_1(x) = \frac{1}{\pi(1+x^2)}$ Then, we know that $\frac{f_1(x)}{f_0(x)} = \frac{\pi(1+x^2)\exp(-x^2/2)}{\sqrt{2\pi}} = T(x)$ is minimal sufficient for this family. Let $U = x^2$, then clearly $T$ is a function of $U$, however, $U$ is not a function of $T$. Hence, $U$ has the same dimension as $T$, but not minimal sufficent

I came cross an interesting  saying  If the dimension of a sufficient statistic $T(X)$ is the same as that of the parameter space, then $T(X)$ is minimal sufficient.  Is this is true? I examined some examples e.g. full-rank exponential families, curved exponential families e.g. $N(\theta, \theta^2)$, and some uniform distributions, e.g. $U(-\theta,\theta)$, $U(0,\theta)$, $U(\theta,\theta+a)$ and found their sufficient statistic has the same dimension with the parameter space and indeed they are minimal sufficient. Is this quoted statement correct? Can you please provide a reference of a proof, or a counter example?


I am trying a couple of regex´s to try to extract a txt from a file. I try  with no sucess lets say I have this string: This is _localizer["my test 1."]' (here I want 'my test 1.') or This is _localizer["my test 2."] And this is _localizer["my test 3."]' (here I want 'my test 2.' and 'my test 3.') In other others, the regex need to understand the begin anchor (_localizer[") and the end anchor ("]) and need to know that sometime there are multiple 'localizer' in the same line. In the txt I want to extract sometimes will have / or \ and others characters that may will make regex fail. What I am trying to do: Regex r = new Regex(@"_localizer[(.+?)]");                 var matches = r.Matches(txt)                                 .Select(xx=> xx.Value)                                 .Distinct();  cheers

I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps?


I am trying to write a script that will delete all comments and everything in between inside C files in my current directory. I've been using sed, and this is what I have so far:   sed -i '/ * [^()] */d' *.c  This works when the comments are on the same line as an asterisk or backslash.   However it doesn't work when there is a commented line without a slash or asterisk.   I know sed goes line by line, I just don't know how to tell it to keep deleting until it sees a */.

I did tried sed and awk, but its not working as the character involves / which is already there in command as delimiter. Please let me know how can I achieve this. Below is a sample Example. We want to remove the commented sections, i.e /*.....*/ /*This is to print the output data*/ proc print data=sashelp.cars; run; /*Creating dataset*/ data abc; set xyz; run;


This questions might be simple to most of you but while reading about Shapiro Wilk test to test the normality assumption for one-way ANOVA, I got confused. Can somebody tell me which is the correct procedure, do we perform Shapiro-Wilk for each treatment level (so for example if I have treatments A, B, and C, then we can have 3 shapiro-Wilk test results) or  is it tested for the entire treatment (meaning, performing Shapiro-Wilk once)?

It is a general and maybe basic question, but it will help me to avoid a mistake. To test the dependence of continuous variable on nominal with parametric test (t-test, ANOVA), "the data has to be normally distributed" (distribution have to be not much violated from normal).   But I don't clearly understand: I have to test the normality of the continuous data together (whole sample) or the normality of data in every single group?   And if my groups have small sizes (n=4-6), and therefore I fail to reject null, does this indicate a permission to use parametric methods?  Can anyone provide me a link to some good examples of statistical (biomedical) hypothesis testing with R (google did not helped)?


Everytime when I try to install Ubuntu 14.04 there is a message saying there are serious errors while checking for drive /. It also says some files are not ready yet or no present.  I have tried Ubuntu 13 and that doesn't work too but Ubuntu 12 works. What can I do?

I have just set up my new system by creating three partitions on a whole hard disk (/boot, /home, swap and /). I saw  article and now I am getting those errors and the system provide me with some options: (I to ignore, S to skip mounting or M for manual recovery).   I am forced to choose skip mounting because I don't know what manual recovery is. Despite the error I get I think that the system boots okay because I can use the system but this error is very annoying.


I've got a few macros that perform floating point lookups and calculations for me and I'm interesting in plotting their results. They're the kind of calculation which requires if/else, so they can't be easily written as a simple math formula for \addplot.  I've been able to plot the results using a \foreach, but only by having a separate \addplot for each point in the series:  \foreach \x in {1,...,100}{   \edef\temp{\noexpand \addplot coordinates{ (\x,\myMacro{\x}) }; }   \temp }   Granted, I'm sure that I could force it to look like one data series, but that seems like a very inelegant solution. Is it possible to define a data series where y values are provided by a LaTeX macro?  Something like  \addplot{    \coordinates{      foreach \x in {1,...,100){        (\x,\myMacro{\x})      }    } };   or  \addplot[variableICanPassToMacro=\x, domain=1:100] ({\x},{\myMacro{\x}});   ?

I've got a few macros that perform floating point lookups and calculations for me and I'm interesting in plotting their results. They're the kind of calculation which requires if/else, so they can't be easily written as a simple math formula for \addplot.  Thanks to a previous question (), I now know to use \pgfmathdeclarefunction, but after trying it I've found that addplot seems to prepend a "0Y" or "1Y" to values before passing them as function arguments. My external macros aren't prepared to handle this extra text, and I'm not sure why it's there.   In the course of testing things out, I've also found that calling a function defined with pgfmathdeclarefunction can also change the positioning of the graph...  \documentclass{article}  \usepackage{xparse}  \usepackage{pgfplots} \pgfplotsset{compat=1.10}  \begin{document}  % Example of a macro which does math outside of pgf     \ExplSyntaxOn     \DeclareExpandableDocumentCommand \doubleMacro { m }%      {%       \fp_eval:n { #1*2 }%Math performed by a package other than pgfplots      }%     \ExplSyntaxOff    %Demo: macro does work in regular text \doubleMacro{1.1}.  % Defining custom pgf functions for plotting      \pgfmathdeclarefunction{mathDoubleMacro}{1}{%         \pgfmathparse{\doubleMacro{#1}} %Calls macro which performs math done by another package     }      \pgfmathdeclarefunction{mathDoublePgf}{1}{%         \pgfmathparse{#1*2} %Uses pgf to do the same thing as an external macro could     }  %Generic plot with function given directly to \addplot \begin{center} \begin{tikzpicture}     \begin{axis}         \addplot[domain=0:1] {2*x};     \end{axis} \end{tikzpicture} \end{center}  %Plot using first macro: complains about 'Unknown fp word Y.' \begin{center} \begin{tikzpicture}     \begin{axis}         %\addplot[domain=0:1] {mathDoubleMacro(x)};%Commented out because it gives problems     \end{axis} \end{tikzpicture} \end{center}  %Plot using second macro: works, but graph is displaced to the right of the expected position \begin{center} \begin{tikzpicture}     \begin{axis}         \addplot[domain=0:1] {mathDoublePgf(x)};     \end{axis} \end{tikzpicture} \end{center}  \end{document}   If I define mathDoubleMacro as calling a non-existent macro, then the errors show which x-values which the addplot is trying to evaluate y at:    0Y0.0e0  1Y4.1666e-2 1Y8.3332e-2 ...  1Y9.9998401e-1   What are these nY's all about, and why does \addplot[domain=0:1] {mathDoublePgf(x)} give a graph with different positioning?


I know this is an old question and there are several answers for this using eigenvalues and matrix factorization but they have not taught in my matrix analysis course yet. Therefore, my question would be a different proof for the following:  $$\text{rank}(p)=\text{trace}(p)$$  where $p$ is an $n \times n$ matrix. The only thing that we are allowed to use is $p^2=p$ and the fact that $\text{trace}(AB)=\text{trace}(BA)=$ where $A,B$ are conformable matrices.  Please notice what I have asked before answering the question.

If $A $ is  an  $n \times n$  matrix  over $\mathbb C$ such that $A^2=A$ then is it true  that  $\operatorname{trace} A = \operatorname{rank} A$?


I want to create a file which contains some commands (suppose 4 commands) such that when I click on that file, the commands will executed in terminal. Is it possible ? I am using Ubuntu 14.04 LTS. Thanks in advance !

Let me start by saying that I'm very new to Ubuntu in general, so I realize this may be a basic question. I'm using xubuntu 14.04. I recently got a wireless usb working by following the steps .  The instructions say that anytime the kernel updates, I must recompile by entering the following into the terminal:  cd ~/mt7601/src make clean make sudo make install sudo modprobe mt7601Usta   I'd like to know if there's anyway to create an icon on my desktop that I can just double click that will have the effect of entering the above commands into the terminal?


There is the enumerateWithBlock method of NSArray, but I need to enumerate in a reverse order, is there a block for doing that, or do I have to use for loop instead, not even the fast loop, but the traditional for (int i = array.count - 1 ; i >= 0 ; i--) one?  Thanks!

I need to reverse my NSArray.  As an example:  [1,2,3,4,5] must become: [5,4,3,2,1]  What is the best way to achieve this?


The Lagrangian of a massless particle in a Freedman-Robertson metric has to be invariant under reparametrization of the world-line. Unfortunately the Euler-Lagrange equations give a non linear relation for the time parameter and the free one, which strongly depends on the factor scale: if I choose the free parameter for the world-line, I also define the factor scale and this is physically inconsistent. I have postulated the simplest Lagrangian, a Lagrange parameter times the constraint: what is the origin of this inconsistency?

How is it possible to define the energy for a massless particle in a Freedman-Robertson-Walker metric if the Lagrangian is not invariant under time-translation?  I have postulated the simplest Lagrangian for a massless particle (a Lagrange multiplier times the constraint) and it is obviously not time-invariant. Not only: if I work since at the beginning using the proper time as a evolution parameter, the dynamics in the Lagrange parameter and the spatial components is physically inconsistent, giving meaningless results like a scale factor equal to the Lagrange multiplier. Is there something wrong in my assumption for the Lagrangian?


\documentclass[14pt]{memoir} \usepackage{lmodern} \usepackage{amsfonts} \usepackage{amstext} \usepackage{amsmath} \usepackage{amsmath} \usepackage{mathrsfs} \usepackage{amsthm} \usepackage{mathtools}  \begin{document} $$P:=\prod_{\sigma\in \textnormal{Gal}(L/K)}\big(X-\sigma(b)\big)\in A[X],$$ \end{document}

This question led to a new package:      While writing down my Combinatorics exercises I found that the binomial coefficient's delimiters weren't displayed as indicated inside the amsmath documentation.  By subsequent trials and errors I was able to reduce the volume of my document to this simpler and fully compilable MWE:  \documentclass[11pt]{article} % \usepackage{amsmath} % \makeatletter % \usepackage{lmodern} \usepackage{lipsum} % \makeatother % \begin{document} % \lipsum[1] \begin{equation} 2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2} \end{equation} \lipsum[1] % \end{document}   Which gives (using TeXworks 0.44 on MikTeX 2.9.4521 updated 09/10/13) this un-expected result:        While the amsmath doc shows that with the loaded packages inside the MWE the result would actually be like this:        From here we can see that the delimiters on the first example are a little bit stretched vertically as they surpass the arguments inside the binom. coeff.  The more strange event is that when I comment the line \usepackage{lmodern} the result on delimiter's shape in my example looks exactly as the amsmath doc:  \documentclass[11pt]{article} % \usepackage{amsmath} % \makeatletter % %\usepackage{lmodern} \usepackage{lipsum} % \makeatother % \begin{document} % \lipsum[1] \begin{equation} 2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2} \end{equation} \lipsum[1] % \end{document}   Output:        From here I deduce that the problem lies inside lmodern, but I'd like to keep using this package and fix this wierd "issue" with the math mode. Is there some clue that I've missed or this is in fact an update-process bug infecting amsmath's delimiter control?


I am trying to call my methods within main but after entering my dollars and cents, the values don't change when I print them  import java.text.DecimalFormat; import java.util.Scanner;  public class ChangeMachine {   public static void main(String[] args) {  System.out.println("Change is good");  int dollars = 0; int cents = 0; int toonie = dollars/2; int loonie  = dollars%2; int quarter = cents/25; int dime = (cents%25)/10; int nickel = ((cents%25)%10)/5;      ChangeMachine.getAmountFromUser(dollars, cents);     ChangeMachine.calculateCoins(dollars, cents);     ChangeMachine.displayInvoice(dollars, cents, toonie, loonie, quarter, dime, nickel);  }   Method to input the dollars and cents Here I'm able to enter the amount but it won't appear when I try to display it  public static void getAmountFromUser(int dollars, int cents) {  Scanner input = new Scanner(System.in);      System.out.print("How many dollars? ");     dollars = input.nextInt();      System.out.print("How many cents? ");     cents = input.nextInt();     System.out.println();      input.close();  }   Method to calculate coins  public static void calculateCoins (int dollars, int cents){ DecimalFormat df = new DecimalFormat("#0.00"); double amount = dollars + cents/100.0; System.out.println("$"+df.format(amount)+" requires:");  //-----Bonus----- dollars=dollars+(cents+2)/100; cents=(cents+2)%100; //---------------  }   Method to display coins needed  public static void displayInvoice (int dollars, int cents, int toonie, int    loonie, int quarter, int dime, int nickel){   System.out.println(toonie+" Toonies"); System.out.println(loonie+" Loonies"); System.out.println(quarter+" Quarters"); System.out.println(dime+" Dimes"); System.out.println(nickel+" Nickels");  }  }

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


Fifth edition D&D's experience progression is linear for the first few levels, then takes on an approximately parabolic relationship as shown in the graph on the lower left. However, the amount of experience required to gain a level (i.e. the change in experience between levels) does not follow the approximately linear relationship implied by a parabola, as shown in the graph on the right. At several levels, the amount of experience required to gain a level is the same as what was required to gain the previous level (e.g. level 13 requires 20,000 xp over level 12, and level 14 requires 20,000 xp over level 13). In fact, levels 12, 13 and 14 all require less experience to gain than level 11.                 My question in two parts:   Is there a record of game design philosophy explaining the uneven advancement requirements? Does any such game design philosophy imply that an even and strictly increasing progression of xp requisites from level to level would create specific problem? (E.g. is it actually important that the xp requirement at level 11 be a big bump over the requirements for the succeeding three levels? Is it important that several levels have the same xp  requirements as the previous level? Do important things break or work less well otherwise? (Assuming that such an "otherwise" would preserve the same near-parabolic increase in total xp.)   Note: All xp data are based on the 5th edition D&D Player's Hand Book.

At every level from 1st to 11th, the experience needed to reach the next level (from the current level) increases every level. However, this pattern gets broken for most of the later levels:   Going from 10th to 11th takes 21,000xp (= 85k - 64k), but 11th to 12th takes only 15,000xp! (= 100k - 85k). Both 13th and 14th level only take extra 20k experience each, i.e. the amount needed doesn't increase between those two levels. Levels 16 and 17 similarly only need 30k experience each, and 18 and 19 only need 40k experience each.   Why does the last half of the experience chart have some of these levels maintain the same experience costs, and even briefly decrease the experience cost for 12th level?


I am asking this because I saw a dictionary produced from two different sources, in which one number is a float, and the same number is a string.  data = {'name': 'jack', 'confidence': '0.95'}  The 'confidence' is a float in once case, and a str in another case. Why is that?   conf = data.get('confidence')

How do I see the type of a variable whether it is unsigned 32 bit, signed 16 bit, etc.?  How do I view it?


In how many ways can a group of 100 coins be made up from 50,20,10,5,2 or 1 coin(s) respectively?  An alternative way of phrasing this would be how many ways can a group of 100 coins be made from choosing coins of value 50,20,10,5,2,1? I have tried the problem, and I've realised it is quite difficult to keep track of the arrangements checked (I know the answer is around 4000 though). Can this be solved without a computer?

I was trying to solve a problem similar to the "how many ways are there to make change for a dollar" problem.  I ran across a  that said I could use a generating function similar to the one quoted below:     The answer to our problem (293) is the   coefficient of $x^{100}$ in the reciprocal   of the following:      $(1-x)(1-x^5)(1-x^{10})(1-x^{25})(1-x^{50})(1-x^{100})$   But I must be missing something, as I can't figure out how they get from that to $293$. Any help on this would be appreciated.


I have a sum symbol with a quite long index underneath. This produces too much space between the following signs.  \begin{equation}  \sum_{X\leq-VaR_\alpha(X)}{P(X)\cdot x}  \end{equation}   I would like to see the index to reach under the P(X)x but in a very specific way: The X in the index should be left-aligned with the \sum symbol and any overlap of the index on the right of the symbol should displace the operand.  Is there any way to do this? I don't want to use a two lines index.

I would like to know if it is possible to force the equation to be closer to the operation sum? When there are a lot of subscript under the sum operator, it tends to pouch the equation to the right, and this is not very aesthetic.  \sum_{n\in N_{-i}}\sum_{\substack{j \in N_{-i} \\ j \neq n}}v_j


Prove that if $R$ is a non-commutative ring with $1$ and if $a,b \in R$ and if  $ab =1 $ but $ba \neq 1$ then $R$ is infinite  I'm not sure about this one.  I noticed that $ba$ is an idempotent, and thus $(1-ba)$ is idenmpotent... So far I have 5 elements wooh! Only need $\infty$ more! Haha but seriously i'm pretty confused, insight appreciated!

Let $A$ be a ring and $a\in A$ an element that has a right-inverse but does not have a left-inverse. Show that $a$ has infinitely many right-inverses.


How to display custom error message, when i do not fill the required input fields it will show custom error message.I don't want this standard message(Error: You must enter a value). please give me some ideas

I have always been curious what are the exact differences between all of the messaging options Visualforce provides, such as apex:message, apex:messages, apex:pageMessage, and apex:pageMessages. The description the Salesforce documentation at times can be rather cryptic.  <apex:message>      A message for a specific component, such as a warning or   error. If an  or  component is not   included in a page, most warning and error messages are only shown in   the debug log. -      <apex:messages>      All messages that were generated for all components on the current   page. If an  or  component is not   included in a page, most warning and error messages are only shown in   the debug log. -      <apex:pageMessage>      This component should be used for presenting custom messages in the   page using the Salesforce pattern for errors, warnings and other types   of messages for a given severity. See also the pageMessages component. -      <apex:pageMessages>      This component displays all messages that were generated for all   components on the current page, presented using the Salesforce   styling. -     So, most of that sounds relatively similar. What are the differences and what are the use cases for each?


I know that the command for colored items is like this: /give @s diamond_sword{display:{Name:"{\"text\":\"fang\",\"color\":\"black\"}"}}  and for unbreakable enchanted tools, it is this (from what I remember): /give @s emerald{Unbreakable:1,Enchantments:[{id:sharpness,lvl:1000},{id:knockback,lvl:1000}]}  Is there a way I can combine the two?

I'm trying to create an item that can break certain blocks, but also has a colored name in 1.13.2   Here's the command I'm using.  /give iAugust minecraft:shears{display:{Name:"[{\"text\":\"Arcane Shears\",\"color\":\"aqua\",\"italic\":false,\"bold\":false}]CanDestroy:[minecraft:iron_bars]"}}   But it only has a colored name, and it can't break specific blocks.


I am currently conducting a quantitative experimental research wherein 2 groups will be my participants. The research aims to determine whether or not Code-Switching is an effective tool to achieve academic proficiency within the students.  Controlled Group - Will receive no treatment and will be simply taught in pure english; with respect to the given Medium of Instruction on such subject  Experimental Group - Will be taught in means of Code-Switching(shifting from one lang. to another)   I will be conducting a pre-test before the lecture (around 1-2 weeks) and a post-test will also be conducted after such lecture to measure which of the two groups understood the lesson better.   I've been searching for tests and I've found the following:  -two sample t-test -log linear analysis -Aspin-Welch Unequal-Variance test   Please help me in finding the best test to use to get accurate and reliable results.

Imagine the following common design:   100 participants are randomly allocated to either a treatment or a control group the dependent variable is numeric and measured pre- and post- treatment   Three obvious options for analysing such data are:   Test the group by time interaction effect in mixed ANOVA Do an ANCOVA with condition as the IV and the pre- measure as the covariate and post measure as the DV Do a t-test with condition as the IV and pre-post change scores as the DV   Question:    What is the best way to analyse such data?  Are there reasons to prefer one approach over another?


In the following sentence:     Furthermore, the tools require intensity data provided by an external software which, along with possible file conversion, increases the total execution time.   Should increase(s) be singular or plural?

Is a subject singular or plural with a modifying prepositional phrase that has plural objects?  Would it be "has" or "have" in this case:     The earthquake, along with its subsequent aftershocks, has/have created an atmosphere of panic among the city's residents.


I know how to color a cell of a table in one color, as shown here: . However, what I want is to have multiple colors in one cell.   Here is a mockup of what I hope is possible (sorry it's so big, I don't know how to make it smaller):   As a secondary question, it would also be lovely if I were able to programmatically condition the colors on the contents of the cell. So in my example above, all "a"s in the table would have a background of yellow, all "b"s brown, and so on. I have seen this:  but I think the implementation would be different with multiple colors in one cell.

I have been successfully using xcolor and its \cellcolor command for a while, and produced beautiful results with it. However, I would like to create some more advanced background effects: color the cell with two colors:    The example above is produced using , but this approach falls apart for a number of reasons:    Tikz's matrix command is not nearly as powerful as ordinary tabulars with the array package and others. I have some numeric data that I am happily aligning on the decimal point using dcolumn - I have no idea how I would do this is in a tikz matrix. I would like to emulate booktabs behaviour, but I just can't get it working.  suggests a workaround, but it doesn't work. The coloring falls apart if the width of the columns is not predefined:   and it all falls apart.  I have had a look through other questions;  and  manage to create one-colored bars dynamically;  combines tabularx and tikz in a promising approach, but I did not manage to adapt this to my purpose;  draws lines and manages to stick to a tabular environment - maybe a good starting point?   So ideally I would like to stick to a tabular environment, and be able to specify the cells' background content freely (for the point of this question I would be happy with a solution that gives me the diagonally separated effect as in the top left corner of the two examples), with a command such as \twocolor{blue}{purple}.


This is just a remake of the question : it is almost six years old so I thought maybe there are some news.  As explained in that question, I want the cursor in Emacs just stay at the location in the text while I scroll (so it becomes invisible if I scroll more than one window height below or above).  I've got an impression from that question that Emacs fans hate this idea, so let me explain that I really, really need it. Here is why: I am running  in Emacs. While it is computing something, occasionally I want to return back to contemplate what has been already computed. The cursor follows me, and if at that moment GAP produces output, it will go where the cursor currently is, producing big mess sometimes.  It means that I do not necessarily want to make cursor stay where it was. It would be also OK to force GAP placing output where the cursor was before Emacs moved it away. But I suspect that would be much more difficult to do. If not, please tell me how to do it.

Is there a way to stop Emacs from automatically moving my text-cursor position (aka, point) while I'm scrolling? I keep losing my location and marks with this annoying behavior.  I tested the following suggestion, with no success:  (setq scroll-preserve-screen-position t scroll-conservatively 0)   (I'm running Emacs 24.2 on Ubuntu and on OS X.)


Professor McGonagall was born in 1935 according to the official timeline. Yet, she appears to be teaching in Hogwarts in 1927, and long before that taught Newt and Leta.

Spoilers Ahead. If you haven't watched Fantastic Beasts: The Crimes of Grindelwald yet, please do not read further.  According to  and many other such fan pages, Minerva McGonagall, Harry's Transfiguration teacher was born in 1935 (although Pottermore , and no year). Now, in The Crimes of Grindelwald, we see a "Professor McGonagall" when the Aurors come to question Dumbledore about the whereabouts of Newt Scamander, which must have happened at least in the late 1920s if not exactly in 1927, if we follow the timeline shown in Fantastic Beasts. The same professor is also seen in a flashback which may have happened around ten years before this incident, when Dumbledore is teaching Newt and Leta's class. This would have happened in the 1910s then?  I even conjectured that maybe this is a different McGonagall teaching at the time Newt was a student, but the credits show Minerva McGonagall! If she was born in 1935 and these events occurred in 1927 or so (and earlier in the flashback), she wouldn't even have been born yet. How come she is fully grown and teaching in 1927? Was this some Minerva McGonagall senior? An ancestor to our beloved Transfiguration teacher and headmistress?


this is my first post here but it seems like a helpful place. I got a used 2010 MacBook pro last weekend, and have had a hell of a time trying to transfer data from my older MBP via Migration Assistant and Firewire. On the first attempt, I left the two computers running overnight, and my roommate unplugged the power adapter from the old one so that it died before the transfer finished.   I finally got around to trying again last night, and this hasn't gone well either. I created a new user account, went to Migration Assistant, and chose to overwrite the botched user account that had been mostly transferred from my old computer. I got to 47 minutes left, and accidentally unplugged the firewire cable! Needless to say, very frustrated with myself. I plugged it back in and waited for the drive to show back up on the desktop, but it's now been stuck on 47 minutes for a couple of hours. What should I do? Do I really have to start over completely yet again? Any help would be greatly appreciated.

I was using the  to transfer data from my old MacBook Pro to my new Mac.  I didn't anticipate issues using Wi-Fi, but the transfer of 250 GB of data using wasn't going to end within a day of starting, so I interrupted it and I intend on starting over using a wired network (or ) to speed the transfer.  However, now it says my HD on the new one has 60 GB occupied and I dont know where this exists. My created account has no documents/apps/etc.  I want to delete this and start fresh if the software won't clean up an aborted transfer reliably.  What is the best way to start over?


More than half of my hard disk space is occupied by "other" storage, how can I find and delete those files? some of it is probably garbage left from deleted or unused software.

Every few days I get notices on my MacBook that it's running or run out of hard drive space. Curiously, restarting the computer will enable me to recover gigabytes of space (this past time, it was able to recover about 2.2GB). However, I can't identify anything in my personal activity that consumed that space.  It's possible that it's a rogue iTunes podcast or a huge software update that my Mac is automatically downloading - would either of these reclaim the space upon a restart?  One possibility that I can think of is that FileVault has some sort of disk leak, allocating but not freeing files. Does this make sense? Is there a tool that I can run to determine where this space is going? Assuming it is FileVault, should I try to disable it? What's the best way to turn of FileVault on a nearly full computer?


There should be a notification when a moderator reviews or looks at a post which you've flagged.  The notification could show the status (helpful, declined, disputed, or something else) of your flag.  Edit  The reason for doing this is so that you would be able to see when a post which you have flagged has received moderator attention, at which point you could go back to the post. This would be good, for instance, if:   you flagged a post for migration to another site; after migration occurs, you could answer the question, since  that only unanswered questions should get migrated you flagged a post for removal of spam or otherwise nonconstructive content, and the content removal has to be carried out in batches

Long story short: since custom flag responses are messages to users like any other (answer, comment, suggested edit, chat message etc.), users should be notified about them!!    A problem I have with flagging, as it currently functions, is that flaggers are not notified about custom responses to flags, when they are given. I really don't care if I don't find out about every last flag of mine, whether it was marked "helpful" or not, but if a moderator went to the effort of typing out a custom response to my flag, explaining why it was or was not helpful, I'd like to see that response. The logical place for this response would be in the messages inbox (the red number thingy in the top left corner), where other responses to user actions (like answers, comments, edits, and chat messages) go.  This may also help to alleviate  of users not realizing that their flags go somewhere -- while I agree with her that "We shouldn't send notifications for [all] flag responses; that would be way too noisy for a lot of people," I think that in the event of a custom response, the flagger should be notified (because some mod thought that this information was relevant to the flagger), and it would not be too noisy because (in my experience1) most flags do not receive a custom response. This could provide one way that flaggers can be made aware of their flagging history.2    1 I don't know who can see this, but  on Mi Yodeya, to date, is 55 flags total (49 helpful), and only one custom response (....that I didn't see for a while, till I checked my flagging history for a different reason).  2 While I don't think that this will replace Monica's suggestion entirely, it would certainly help it a little.    To give credit where credit is due, while I came up with this idea myself, I did notice that someone else had posted about a similar idea earlier in a .  Edit: Just spotted  from the related questions along the side of the page; note that while that proposal is similar to this one, it was about sending all declined flags to the inbox, while I suggested that only the ones with custom responses should make it to the inbox.


I want to access 14.04 via remote desktop from xp. I installed vnc4server on my 14.04 system following this . Now what to do afterwards? Do I need to install some thing on xp? vnc client for xp? Maybe I can follow . All I need is to access the 14.04 desktop from xp. So if there is a solution, please just tell me:    what I need to install on 14.04, and  what I need to install on xp.

When using Terminal Server Client, it is possible to access the Windows desktop (remote desktop), from an Ubuntu PC.   Is the reverse possible?  What is the Windows XP application used to connect to an Ubuntu desktop?   Is the default mstsc application sufficient? If yes, what are the required settings on Ubuntu and Windows?  I want to view the desktop, not just an SSH terminal access.


Can't understand how to fix that error, it's unreal to me (can't find where's void in my code):  java.lang.NullPointerException: null     at survival.MainClass.onEnable(MainClass.java:16) ~[?:?]     at org.bukkit.plugin.java.JavaPlugin.setEnabled(JavaPlugin.java:264) ~[spigot.jar:git-Spigot-dcd1643-e60fc34]     at org.bukkit.plugin.java.JavaPluginLoader.enablePlugin(JavaPluginLoader.java:337) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at org.bukkit.plugin.SimplePluginManager.enablePlugin(SimplePluginManager.java:403) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at org.bukkit.craftbukkit.v1_12_R1.CraftServer.enablePlugin(CraftServer.java:381) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at org.bukkit.craftbukkit.v1_12_R1.CraftServer.enablePlugins(CraftServer.java:330) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at net.minecraft.server.v1_12_R1.MinecraftServer.t(MinecraftServer.java:422) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at net.minecraft.server.v1_12_R1.MinecraftServer.l(MinecraftServer.java:383) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at net.minecraft.server.v1_12_R1.MinecraftServer.a(MinecraftServer.java:338) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at net.minecraft.server.v1_12_R1.DedicatedServer.init(DedicatedServer.java:272) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at net.minecraft.server.v1_12_R1.MinecraftServer.run(MinecraftServer.java:545) [spigot.jar:git-Spigot-dcd1643-e60fc34]     at java.lang.Thread.run(Unknown Source) [?:1.8.0_161]   16 line is:  getCommand(commands.cmd3).setExecutor(commands);   Commands class:  public class Commands extends CommandExecute implements CommandExecutor, Listener {  public String cmd1 = "fly"; public String cmd2 = "feed"; public String cmd3 = "heal";  @Override public boolean onCommand(CommandSender sender, Command cmd, String label, String[] args) {     if (sender instanceof Player) {         if (cmd.getName().equalsIgnoreCase(cmd3)) {             Player p = (Player) sender;             if (p.getHealth() < 20) {                 p.setHealth(20);                 p.sendMessage(ChatColor.GOLD + "Healed succesfuly!");                 return true;             } else {                 p.sendMessage(ChatColor.RED + "You are already healed!");                 return true;             }          }         return false;     } else {         sender.sendMessage("Only for Players!");         return true;     }    }  }   MainClass:  public class MainClass extends JavaPlugin implements Listener{ private Commands commands = new Commands();  public void onEnable() {     getServer().getPluginManager().registerEvents(new MainHandler(), this);     getCommand(commands.cmd1).setExecutor(commands);     getCommand(commands.cmd2).setExecutor(commands);     getCommand(commands.cmd3).setExecutor(commands);   } }   Have cmd1 and cmd2 before that and they're working fine, problem with only cmd3 command.  in plugin.yml:  name: Survival main: survival.MainClass version: 1.1 commands:   fly:     description: Toggle flight mode     usage: /fly   feed:     description: Feeds player     usage: /feed   heal:     description: Heals player     usage: /heal   Tried all answers on stackoverflow, but nothing helped me

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?


the sequences $(x_n)_{n\geq 1}$ and $(y_n)_{n\geq 1}$ are given by:  $$\begin{align} x_1&=a \\ y_1&=b \\ x_{n+1}&= \sqrt{x_ny_n}\\  y_{n+1}&=\frac{x_n+y_n}{2} \end{align}$$  Prove that both sequences have equal limit $\lim_{n\to\infty} x_n = \lim_{n\to\infty} y_n$.  I cant use AM-GM because i dont know if that x(n) or y(n) are positive

(Arithmetic–Geometric Mean).   (a) Explain why $\sqrt{xy}≤ (x+y)/2$ for any two positive real numbers x and y. (The geometric mean is always less than the arithmetic mean.)   (b) Now let $0≤x_1 ≤y_1$ and define $x_{n+1} = \sqrt{x_{n}y_{n}}$ and $y_{n+1} = (x_{n} + y_{n})/2$ . Show $\lim x_n$ and $\lim y_n$ both exist and are equal.  My attempt:  (a) I know that I can show this by using $(\sqrt{x} -\sqrt{y})^2 \geq0$ but I dont know how to illustrate, let alone explain it.  (b) I know that $x_{n+1} \leq y_{n+1}$ for all $n \in \mathbb{N}$. But now I need to know how to show that they are equal.


Can anybody show me how $\lim \limits_{h \to 0} \dfrac{e^{h} - 1}{h} = 1$?

I was wondering how we could use the limit definition   $$ \lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$$  to find the derivative of $e^x$, I get to a point where I do not know how to simplify the indeterminate $\frac{0}{0}$. Below is what I have already done  $$\begin{align} &\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\ &\lim_{h \rightarrow 0} \frac{e^{x+h}-e^x}{h} \\ &\lim_{h \rightarrow 0} \frac{e^x (e^h-1)}{h} \\ &e^x \cdot \lim_{h \rightarrow 0} \frac{e^h-1}{h} \end{align}$$  Where can I go from here? Because, the $\lim$ portion reduces to indeterminate when $0$ is subbed into $h$.


I have an older app I need to access, which will not get past the initial installation screen with the message, "software is not supported on a 64-bit operating system. Please install on a 32-bit machine." (I am using W10 Pro x64.)  Is there any hack I can do to see if I can at least get the installer to complete? I could put a Win XP VM on my PC, but I would rather not have to do that.

I've got a Windows 10 Computer (home edition), which has 4GB of Ram and an i5 processor. I need to run an old 32 bit accounting programme. The vendor said it won't release a 64 bit version (although a 64bit version exists, it's missing key features from the older version).  The programme installs fine, but when I click on the programme icon, it says the programme won't work on a 64 bit system.   What options do I have?    I've done a fair bit of research, but it seems to run up dead ends.   1) WoW64     Apparently, this is supposed to let you run 32 bits on 64 bit Windows. However, I am not sure how to install it. I think it's for web servers only. However,  says it can work on Windows 7, but doesn't explain how to set it up (or if it will work on Windows 10).  2) XP mode     A 32bit Windows XP emulator. However, it seems to be for Windows 7 only. Also according to this , you need Windows Professional.   3) Virtual Box Machine    Let's you emulate Windows. Seems overkill for my purposes. Plus I would need to buy a 32 bit Windows license. I think it would run slowly with 4GB of Ram.  4) Partition drive into 32bit and 64 bit versions Apparently, you can use the free tool  to split the drive into two and then install separate 32bit and 64 bit versions.   Again, seems overkill and it looks like I would need buy a 32 bit Windows 10 license.   Are these my only options?     Images  Installation    First run (From the error message I guess it's a 16-bit program)   Clicking on programme


I am a Filipino and traveling to the USA on a K-1 visa with a stop in Narita.  My layover is 3 hours, do I need a short stay transit visa?

I will be transferring between two international flights at Tokyo Narita airport. I'm scheduled to depart the same day I arrive. I am planning to stay within the airport during the layover. Does anyone know if I will require a transit visa at Narita?


I am new to latex and find a bit hard to customize beamer template. Can you please explain how to add more than two sections(like the ones in the example Proportional argument systems and Argumentation systems on set constraint logic) and make it displayable.  Reference post to this question -   Thanks in advance.

I am preparing slides for my zeroth review (Project) using LaTeX. Now, I am very much appealed by this theme: . The theme's link is given here: . But, It is not available. I got the base theme Copenhagen but now I need to customize it to the colors and gradients applied in the theme. How do I do that? Here is my MWE:  \documentclass[12pt]{beamer} \usetheme{Copenhagen} \title{The title of the paper} \author{Subham Soni \and Sakthivel \and Syed Rabbani} \date{\today} \begin{document} \begin{frame} \titlepage \end{frame} \begin{frame}{Agenda} \tableofcontents \end{frame} \end{document}


I would ask this on stackoverflow but I wanted a more theoretical answer. I understand that vectors have magnitude and direction whereas points are just coordinates.  In computing and especially in data science we use vectors to represent objects with multiple attributes. But as I mentioned vectors have magnitude and directions and it seems to me that in order to describe the attributes or properties of an object it would be better if we used points.  Why do use vectors then?

I've been wondering for some time now about the difference between a point and a vector. In high school, it was very important to distinguish them from each other, and we used the notation $(x,y,z)$ for points and $[x,y,z]$ for vectors. We always had to translate the point $P=(a,b,c)$ to the vector $\overrightarrow{OP} =[a,b,c]$ before we started calculating with them.   Now, after I started at the university, people don't seem to care anymore. My professors either say that they're the same, or that they're almost the same, and the books I have seem to share that view. The book I use for my calculus course (Colley's Vector Calculus) says, among other things, the following:     [...] we adopt the point of view that a vector field assigns to each point $\textbf{x}$ in X a vector $\textbf{F}(\textbf{x})$ in $\mathbb{R}^n$, represented by an arrow whose tail is at the point $\textbf{x}$.   So it seems like a point is also a vector.  My question is this: Do mathematicians distinguish between points and vectors, and if they do, in what circumstances?


I just install MacTex and trying to compile my tex file with TeXShop:     Can't find required tool.      /usr/texbin/pdflatex does not exist. TeXShop is  a front end for TeX,   but you also need a TeX distribution. Perhaps such a distribution was   not installed or was removed during a system upgrade. If so, go to    and follow the instructions to (re)install   MacTeX. A less likely possibility is that a tool path is incorrectly   configured in TeXShop preferences. This can happen if you are using   the macports or fink distributions.   I found  similar but I got pdftex not found after typing  which pdftex.  Also, I try to find something like FixMacTeX2013.pkg of /Applications/TeX/ directory according to  and get a Setup-2015.pkg. Nothing happens after installation.  What could I fix it?     OS X EI Capitan 10.11.3

After having updated to Mac OS X El Capitan (10.11), I'm no more able to compile using either TexMaker or TexShop. This is the message I get from TexShop  "/usr/texbin/pdflatex does not exist. TeXShop is  a front end for TeX, but you also need a TeX distribution. Perhaps such a distribution was not installed or was removed during a system upgrade. If so, go to  and follow the instructions to (re)install MacTeX. A less likely possibility is that a tool path is incorrectly configured in TeXShop preferences. This can happen if you are using the macports or fink distributions."  I tried to change the path in Preferences-Engine, as many suggested. Yet, it doesn't work either. Any help?


I want to create sewer pipes where a player can walk inside on a 3D game. Then I'm trying to make them by multiple cylinders like this.  Now I have two problems. First, I don't know how to cut A's edge.  The other is how to cut B's side  faces.  I tried to do that by boolean modifier, but it didn't work. So will anyone tell me how to do that? Thanks.

How can I join these two meshes in a proper way? I know I can Ctrl J to join them, but how can I do so without having overlapping faces?


I am trying to show that $s_{n+1} = \frac{1}{2} \left(s_n + \frac{3}{s_n}\right)$ is a monotonic decreasing sequence for $n \ge 2$. Currently, my approach using induction is stuck because of the $\mathbf{s_n}$ term appearing in the denominator.   What I have so far:  Calculating a few terms: $s_1 = 1$, $s_2 = 2$, $s_3 = \frac{7}{4} < s_2$. For this to be monotonic decreasing, we have to show $s_{k+2} < s_{k+1}$.   For the base case, we assume for $k$ we have $s_{k+1} < s_k.$  The inductive step: to show $s_{k+2} < s_{k+1}$, i.e. to show $$\color{grey}{s_{k+2} = }\frac{1}{2} \left(s_{k+1} + \frac{3}{s_{k+1}}\right) < \frac{1}{2} \left(s_{k} + \frac{3}{s_{k}}\right) \color{grey}{= {s_{k+1}}_.}$$  In order to show $\dfrac{1}{2} \left(s_{k+1} + \frac{3}{s_{k+1}}\right) < \dfrac{1}{2} \left(s_{k} + \frac{3}{s_{k}}\right)$, I am stuck:  Given, $s_{k+1} < s_k$, I cannot then say $s_{k+1} + \mathbf{\frac{3}{s_{k+1}}} < s_k + \mathbf{\frac{3}{s_{k}}}$, because the $s_k, s_{k+1}$ terms which appears in the denominator may reverse the inequality. Any pointers on how to proceed further?  Disclaimer: I am revising real analysis on my own from the Kenneth Ross book, this is not strictly homework.

Suppose that $S_0$ and A are positive numbers, let $$S_{n+1} = \frac{1}{2}\left(S_n +\frac{A}{S_n}\right)$$ with $n \geq 0 $.      (a)Show that $S_{n+1} \geq \sqrt{A} $ if $n \geq 0$       (b)Show that $S_{n+1} \leq S_n $ , if $n \geq 1$      (c) Show that $s= \lim\limits_{n \rightarrow \infty} S_n$ exists      (d) find s   (a) Show that $S_{n+1} \geq \sqrt{A} $ if $n \geq 0$  Given $$P_n:  S_{n+1} = \frac{1}{2}\left(S_n +\frac{A}{S_n}\right) \geq \sqrt{A}$$  $$P_0: S_{1} = \frac{1}{2}\left(S_0 +\frac{A}{S_0}\right) \geq \sqrt{A}  $$  We assume that $P_n$ is true  $$P_{n+1}: S_{n+2}= \frac{1}{2}\left(S_{n+1} +\frac{A}{S_{n+1}}\right)$$ by assumption $$S_{n+2}= \frac{1}{2}\left(S_{n+1}\left(1 +\frac{A}{(S_{n+1})^2}\right)\right) \geq \frac{1}{2}\left(\sqrt{A}\left(1 +\frac{A}{(\sqrt{A})^2}\right)\right)$$ $$ S_{n+2}= \frac{1}{2}\left(S_{n+1} +\frac{A}{S_{n+1}}\right) \geq \sqrt{A}  $$  It follows that $S_{n+1} \geq \sqrt{A} $    (b) Show that $S_{n+1} \leq S_n $ , if $n \geq 1$  $$S_{n+1} \leq S_n$$ $$\frac{1}{2}\left(S_n +\frac{A}{S_n}\right) \leq S_n $$ Dividing by $S_n$ $$\frac{1}{2}\left(1 +\frac{A}{S_n^2}\right) \leq 1 $$ $$\frac{A}{2S_n^2} \leq \frac{1}{2}$$ $$A \leq S_n^2$$ $$S_n \geq \sqrt{A}$$ As  $S_{n+1} \leq S_n$ yields a true statement, it follows $S_{n+1} \leq S_n$ is true.    (c) Show that $s= \lim\limits_{n \rightarrow \infty} S_n$ exists  Since $S_{n+1} \leq S_n$, the sequence is non-increasing,   using the non-increasing theorem stating that      if $\{S_n\}$ is non-increasing then $$\lim\limits_{n \rightarrow > \infty} S_n = \inf\{S_n\} $$     (d) find s    Is the argumentation in (a) and (b) appropriate? Also, I have to admit I m getting less confident in my argumentation (c) and (d). How to proceed in (c) and (d)?  Much appreciated for your input or help.


I have run boot repairs twice and installed bionic beaver twice and still can't get the system to boot up.  I have generated the following url so someone can PLEASE give me a hand.   I installed and used Ubuntu 16.04 no issues I couldn't research and fix on my own but this bionic beaver is a POS.  No more upgrading for me.  I don't know enough.  Please help, I need a computer. Oh, there is no other OS on my laptop.

My computer doesn't boot. I format my Toshiba laptop with a bootable USB drive. I make this , and when i restart the computer after the installation, my computer does not boot. Then i run boot-repair and finishes with this . I reboot ant nothing happens. I review some questions before, but could't find anything yet. Can someone help me please?


If we move in the universe with about 1500 km/s (earth with 30 km/s + sun with 230 km/s in the milky way + milky way....) why there is no Doppler effect on my WiFi when i change the position in the direction and opposite direction of earth direction of travel? And also does the signal arrives faster or respectively slower with 1500 km/s when i change the position in the direction and opposite direction of earth direction of travel?

The title says it all.  If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right?  So my son posed me an interesting question today: since light travels as fast as anything can go, what if I shined light when moving in a car?  How should I answer his question?


I want to solidify my understanding of the "coding to interface" concept. As I understand it, one creates interfaces to delineate expected functionality, and then implements these "contracts" in concrete classes. To use the interface one can simply call the methods on an instance of the concrete class.  The obvious benefit is knowing of the functionality provided by the concrete class, irrespective of its specific implementation.   Based on the above:    Are there any fallacies in my understanding of "coding to interfaces"? Are there any benefits of coding to interfaces that I missed?   Thanks.

I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible?


I have a disk with a Ubuntu 20.04 partition and a 18.04 partition. If I update the 18.04 one to 20.04 I will have problems in grub?

I've been programming for about a year and I'm very new to Ubuntu. I'm currently working on a project with a mentor who suggested partitioning part of my drive with a fresh Ubuntu install. I've never done anything like this and most of the guides I've seen are for dual-booting Ubuntu and Windows/MacOS.  I'm currently running Ubuntu 16.04 on my laptop. I was wondering If I could keep my current setup and also partition part of my drive with a fresh install of Ubuntu 16.04?


Is there an equivalent Linux/Ubuntu procedure to the screen mirroring procedure described in this  for a Samsung Smart TV with Windows10?

I would like to show the screen of my Ubuntu laptop on a Samsung TV.  The TV has a menu entry called "mirror screen".  But up to now I found no way to get it working.  I need a wireless way to us the TV as monitor.  Any hints?  Exact hardware version: Samsung SmartTV UE55J6250   If it is not possible via software am willing to buy some hardware.


I'm looking for a special profile with a combination of two forms.  So that I can best manage the rounding/bevel of the junction of these two forms.  Is it possible and how can I get this result (see attached image)

How would one curve specific edges while leaving others alone? I'm trying to model this (circled) object, But can't figure out how to bevel side edges and leave the front-edge flat.     Tried using the bevel modifier in combination with edge creases but that apparently has no effect, not sure what else to do, as I am still very new to modeling/blender.


I have the following shell script: /var/local/myapp/bin/import  #!/bin/bash  # Move to base directory cd $(dirname $0) cd ..  # Execute and bail if one of them fails cake compile cake tms:fetch cake tms:fetch:clean cake tms:split cake tms:injest:main cake tms:injest:schedules   I'm trying to run it from cron. All users have access to cake. However, when I run this script with cron, I get the following error (on every cake line):  /var/local/myapp/bin/import: line 13: cake: command not found   Here's my crontab   * * * * * /var/local/myapp/bin/import   Also, I can't figure out an easy way to redirect the stdout of bin/import to a file when run from cron. Adding > /var/local/myapp/import.log to the end of the cron statement just truncates import.log - the only way I can do it is to add exec &> import.log to bin/import itself, which isn't what I want to do at all, because when I run it by hand I want to see the output on the screen.   Everything works perfectly when I just type /var/local/myapp/bin/import from my terminal.

This is a  about using cron & crontab.   You have been directed here because the community is fairly sure that the answer to your question can be found below. If your question is not answered below then the answers will help you gather information that will help the community help you. This information should be edited into your original question.  The answer for 'Why is my crontab not working, and how can I troubleshoot it?' can be seen below.  This addresses the cron system with the crontab highlighted.


From some lecture notes, it is also claimed that invertible elements in $Z/p^{3}Z$ is cyclic multiplicative group. How to show this?

I'm supposed to show that if $p$ is an odd prime (so its not $2$) that the multiplicative group $(\mathbb{Z}/p^{a}\mathbb{Z})^*$ is cyclic. It seems very hard to do for any $a$, so I'm thinking about using induction on a to make things easy. That being said, I don't really like group theory. How do I show the base case is cyclic and proceed?  Thanks everyone!


Despite many things we improved, in the recent years many projects failed.  Where to place "in the recent years" correctly?

Do we write in the recent years or in recent years? For example,  In the recent years, the influence of blablabla on blablabla has grown rapidly. In recent years, the influence of blablabla on blablabla has grown rapidly.  As far as I know, both are correct. But which one sounds more natural (more correct from a native speaker's point of view) or does it not matter?


I have created a program to convert amount in words. Its working fine up to 99999 amount values. Can't convert the other numbers and its not allowing cents. Can anyone help me to solve this issue? Below is my code:      private void button1_Click(object sender, EventArgs e)     {         string[] Ones = { "One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten", "Eleven", "Twelve", "Thirteen", "Fourteen", "Fifteen", "Sixteen", "Seventeen", "Eighteen", "Nineteen" };         string[] Tens = { "Ten", "Twenty", "Thirty", "Fourty", "Fifty", "Sixty", "Seventy", "Eighty", "Ninety" };         string[] oo = { "Hundred", "Two Hundred", "Three Hundred", "Four Hundred", "Five Hundred", "Six Hundred", "Seven Hundred", "Eight Hundred", "Nine Hundred" };         string[] Hundreds = { "one hundred thousand ", "two hundred thousand ", "three hundred ", "Four hundred", "Five hundred", "Six hundred", "Seven hundred", "Eight hundred", "Nine Hundred" };           int no = int.Parse(textBox3.Text);         string strWords = "";         if (no > 99999 && no < 1000000)         {             int i = no / 100000;             strWords = strWords + oo[i - 1] + "";             no = no % 100000;         }          if (no > 99999 && no < 1000000)         {             int i = no / 100000;             strWords = strWords + Hundreds[i - 1] + "";             no = no % 100000;         }          if (no > 9999 && no < 100000)         {             int i = no / 10000;             strWords = strWords + Tens[i - 1] + " ";             no = no % 10000;         }          if (no > 999 && no < 10000)         {             int i = no / 1000;             strWords = strWords + Ones[i - 1] + " Thousand ";             no = no % 1000;         }           if (no > 99 && no < 1000)         {             int i = no / 100;             strWords = strWords + Ones[i - 1] + " Hundred ";             no = no % 100;         }          if (no > 19 && no < 100)         {             int i = no / 10;             strWords = strWords + Tens[i - 1] + " ";             no = no % 10;         }          if (no > 0 && no < 20)         {             strWords = strWords + Ones[no - 1];         }          textBox4.Text = strWords + " only";      }

Is there an efficient method of converting an integer into the written numbers, for example:  string Written = IntegerToWritten(21);   would return "Twenty One".  Is there any way of doing this that doesn't involve a massive look-up table?


I want to use proof by induction to verify  $$\sum_{j=n}^{2n-1} (2j+1) = 3n^2.$$  First I assume that the expression is valid for some number k,  $S(k) = 2k + 1 $  Then k + 1 so that,  $S(k+1) = s(k) + a(k+1) = 3k^2 + (2(k+1)+1) = 3k^2 + 2k +3 $  However, if I try to insert j = k + 1 into the sum-formula $ 3n^2 $ it equals $3(k+1)^2= 3k^2 + 6k +3 $. Which is not the same. What am I doing wrong?

So I have the general summation formula that I was to prove using mathemathical induction on a Calculus level.  For all $n = {1,2,3,...}$ we have:  $$\sum_{j=n}^{2n-1} (2j + 1) = 3n^2$$  In the answer, the one completing the proof gets this, on the $n=k+1$:  $$\sum_{j=(k+1)}^{2(k+1)-1} (2j + 1) = \sum_{j=k}^{2k-1} (2j + 1) - (2k+1) + (4k+1) + (4k+3)$$  $$= 3k^2 + 6k + 3 = 3(k+1)^2$$  Can anyone explain how on earth this was done? When I tried, I was unable to factorize - I tried by adding the $(2(k+1)+1)$ to the $S_n$ formula and thereby confirm it, but I couldn't do it...


I have installed and deleted the package several times with Miktek. I am writing in TexMaker editor for Windows. Also it does not work for WinEdt. The code is.  \documentclass[article] \usepackage{expl3} \begin{document} 111 \end{document}   The complete error reads  ! Missing = inserted for \ifnum. to be read again  l.283 } I was expecting to see `<', `=', or `>'. Didn't. ) ! Missing = inserted for \ifnum. to be read again   Thanks in advance

I'm trying to get siunitx working. For some reason I keep getting this error:  ! Missing = inserted for \ifnum. <to be read again>                     - l.3 \begin           {document}^^M   I have tried a minimal document to make sure it is not some kind of compatibility issue. And I get that same error in the most minimal document possible.  I'm using pdfLaTeX to compile, and have tried both from TeXWorks and from bash. I'm using TeXLive, if that matters. I have also tried reinstalling siunitx, l3packages, and l3kernel. There was an issue with l3kernel before this, due to an apparently old version. But all three packages are now up to date. I've also reinstalled expl3 while trying to debug the original issue.  My minimal document is:  \documentclass{article} \usepackage{siunitx} \begin{document} \end{document}   The output I get is:  This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex) restricted \write18 enabled. entering extended mode (./untitled-2.tex LaTeX2e <2016/02/01> Babel <3.9q> and hyphenation patterns for 81 language(s) loaded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo)) (/home/<name>/texmf/tex/latex/siunitx/siunitx.sty (/home/<name>/texmf/tex/latex/l3kernel/expl3.sty (/home/<name>/texmf/tex/latex/l3kernel/expl3-code.tex) (/home/<name>/texmf/tex/latex/l3kernel/l3pdfmode.def)) (/home/<name>/texmf/tex/latex/l3packages/xparse/xparse.sty) (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty (/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty)) (/usr/share/texlive/texmf-dist/tex/latex/tools/array.sty) (/home/<name>/texmf/tex/latex/l3packages/l3keys2e/l3keys2e.sty) (/usr/share/texlive/texmf-dist/tex/latex/beamer/translator/translator.sty (/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/share/texlive/texmf-dist/tex/latex/beamer/translator/translator-language- mappings.tex))) ! Missing = inserted for \ifnum. <to be read again>                    - l.3 \begin          {document}^^M ?   Does anyone have any idea what might be going wrong here?


My input data   x =  [[ 1.] [ 2.] [ 3.] [ 4.] [ 5.] [ 6.] [ 7.] [ 8.] [ 9.] [10.]]  y =  [[ 2.45151081]  [ 3.85549532]  [ 6.98435572]  [ 7.11091693]  [ 5.91860089]  [ 7.33033817]  [ 8.77851672]  [ 9.77186197]  [ 9.87780907]  [11.52364423]]   ... is actually approximating the function y = -1/10 * X**2 + 2*x  Using:  from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression   I am trying to understand how SKLearn takes the following to approximate the function above...  polynomial_features = PolynomialFeatures(degree=odr_polynomial) x_poly = polynomial_features.fit_transform(x)     model = LinearRegression() model.fit(x_poly, y)   if I print(x_poly) I get  [[   1.    1.    1.    1.]  [   1.    2.    4.    8.]  [   1.    3.    9.   27.]  [   1.    4.   16.   64.]  [   1.    5.   25.  125.]  [   1.    6.   36.  216.]  [   1.    7.   49.  343.]  [   1.    8.   64.  512.]  [   1.    9.   81.  729.]  [   1.   10.  100. 1000.]]   it looks like this function has iterated x and generated  i**0 , i**1  , i**2  ,  i**3  (based on me asking for 3rd order polynomial)   I don't know the proper name for this but I'd describe it as "the base bits of the polynomial without the coefficients". I'm an amature coder. To the best of my ability to read the code of sklearn.linear_model.LinearRegression it uses scipy.linalg.lstsq under the hood and that function calls this the "design matrix"  Reading scipy.linalg.lstsq code is where I get lost. I understand how LEast Squares works but I can't understand how least squares is being applied to the 'design matrix" to derive the coefficients.  If I run the code with odr_polynomial = 3 I get:  coefficients: [[ 0.  3.05733751   -0.44144351   0.02535316]] y-intercept: [-0.12880603]   If I run the code with odr_polynomial = 2 (because the underlying function we're trying to approximate is 2nd order) I get:  coefficients: [[ 0.  1.12796227   -0.02311642]] y-intercept: [2.04649483]   Although I have asked this question in the context of using SKLearn and Scipy, I think this is also something that could be done with paper & pen. I really want to understand how the coefficients are being derived from the "design matrix".  I'd be grateful for any advice or insight you can share.

I usually hear about "ordinary least squares".  Is that the most widely used algorithm used for linear regression?  Are there reasons to use a different one?


Just to add a little bit of context to the question, I am using an Arduino Uno and a breadboard.  I have a 5V power source running to the positive (longer) lead of an LED (rated at about 2v and 20mA). I then have a 150 Ohm resistor connecting to the negative (shorter) lead of the LED. The resistor is then connected to ground.  I am using a breadboard, so whenever I remove the resistor and connect it from the power source to the positive (longer) lead of the LED, I still see the same amount of resistance.  In other words, with no resistor, the LED is at X brightness. However, with a resistor attached to either lead of the LED, there is the same amount of resistance (thus, the LED is dimmer, at X÷resistance brightness.)  Based on my very limited knowledge of electronics, I would've assumed that you would have to connect the resistor to the power source, and then to the positive lead of the LED, so that the voltage and current would drop before they got to the LED. This seems to be false, based on my little "experiment" here.  Why is this the case?

Please be kind, I am an electronics nub.  This is in reference to getting an LED to emit photons.  From what I read (Getting Started in Electronics - Forrest Mims III and Make: Electronics) electrons flow from the more negative side to the more positive side.  In an example experiment (involving a primary dry cell, a SPDT switch, a resistor and an LED) it states that the resistor MUST be connected to the anode of the LED.  In my mind, if the electrons flow from negative to positive, wouldn't the electron flow run through the LED before the resistor; thereby making the resistor pointless?


Hello this is expanding upon a question that was previously asked on stack exchange that I linked below. From what I understand of Black Holes is that overtime Hawking Radiation results in the Black Hole shrinking. This being do to virtual particle pairs. The point I find confusing, and I may be misunderstanding it, but the black shrinks due to negative energy of the particle it absorbs when the other particle escapes but it does not matter whether or not it was the matter of the antimatter that was absorbed. Is the Black Hole losing mass if it absorbs only the normal matter half of a virtual particle and the antimatter half escapes?

I was reading Brian Greene's "Hidden Reality" and came to the part about Hawking Radiation. Quantum jitters that occur near the event horizon of a black hole, which create both positive-energy particles and negative-energy particles, produce the so-called Hawking radiation. However, I do not understand why only the negative-energy particles are being absorbed into the black hole, while the positive-energy particles shoot outward. Shouldn't there be 50/50 chance that each type of particle is being absorbed by the black hole? Also, the book mentions that a negative-energy particle would appear to an observer inside the black hole as positive. Why?


I have seen this operation before but cant seem to recall the name or corresponding theory. This operation changes inner product $<a,b> = a^T b$ to $a^T R b$, where $R$ is some matrix. What does this do intuitively and what is the name?

To find out how something is called is the one thing I don't know how to use Google for.  If I have a vector $v$ and a symmetric matrix $H$, then the operation $v^T H v$ gives me some sort of projection of the matrix $H$ on the vector $v$. For example if $H$ is the Hessian, the operation gives me the second derivative in the direction of $v$.  What is the name of this operation?


My host OS is Gentoo, guest OS - Fedora. I have a web server on Fedora on port 8686 and it works perfectly on guest OS, but I can't access it on my host OS. I tried to use bridged network (then I got 2 different IPs to my guest and host machines from router) and NAT (then I forward port 8686). Nothing helped, but SSH works nicely when using both NAT and bridge (even if using the same port). How to solve this issue?

I have a VM webserver setup and I have installed and started Apache.  The VM has a bridged network interface and can be pinged from the host using 192.168.0.2.  However, if I type that same IP address into the browser on the host machine, I was expecting to see the default apache page generated on the VM, but instead, I get can't connect to 192.168.0.2 in the host machines browser.  I've clearly missed something out.  Anyone know what I have missed or done wrong?  Output from VM netstat -tnlp  tcp     0     0 0.0.0.0:22        0.0.0.0:*     LISTEN     950/sshd tcp     0     0 127.0.0.1:25      0.0.0.0:*     LISTEN    1026/master tcp     0     0 :::22                  :::*     LISTEN     904/sshd tcp     0     0 ::1:25                 :::*     LISTEN     980/master   Rough drawing of what I'm thinking the network activity/connectivity would look like.


$ \dfrac{2\sin x}{\cos 3x}  +  \dfrac{2\sin 3x}{\cos 9x}  + \dfrac{2\sin 9x}{\cos 27x} = \tan 27 x- \tan x$.  I did not get even to start with which formula. I tried using multiple angle identities but did not find any suitable place to use those. So please help.

The question asks to prove that -  $$\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x}  = \frac 12 (\tan 27x - \tan x) $$  I tried combining the first two or the last two fractions on the L.H.S to allow me to use the double angle formula and get $\sin 6x$ or $\sin 18x$ but that did not help at all.   I'm pretty sure that if I express everything in terms of $x$, the answer will ultimately appear but I'm also certain that there must be another simpler way.


I formatted the unallocated space to fat32 (don't know if that was right). Now I want to extend my dev/sda5 for more memory as I'm currently getting warnings about my low memory space. Above My /dev/sda5 is New Partition #1 with 19.53 gigs and below it is the linux-swap. I can take memory from the linux swap as well as I have quite a bit of RAM.  I read that I'm meant to boot off USB and run GParted, unswap the linux-swap and then delete it. Unmount the sda5 and after that, resize the /dev/sda5 to take up some of that hard drive space and then turn on swap afterwards. Is this right? Double checking because I already messed it up once.    Thank so much! Reading from here:

Previously, I have installed Windows 7 on my 320 GB laptop with three partitions 173, 84 and 63 GB each. The 63 GB partition was where the Windows was installed. The rest were for file containers.  Now I changed my OS to Ubuntu 12.04 LTS. I installed Ubuntu by replacing the entire Windows 7 on the 63 GB partition. The rest of the partitions remain as an NTFS Windows partition and I can still access them both (the 173 and 84 GB partitions).  Now I want to change the two partitions of Windows into an Ubuntu format partitions plus most importantly, I want to extend the 63 GB partition to more than a 100 GB because at the moment I am running out of disk space. Whenever I try to install any application, especially using wine, it always complains for a shortage of disk space.  How do I do the extending activity before I entirely format my laptop again and lose all the important files on my partitions?


I'm considering to apply for a PhD. My situation is roughly this:    GPA in my BSc is about 2/4. GPA in my MSc will be about 3.6/4   I have two peer-reviewed conference papers with proceedings and two peer-reviewed journal publications. I'm a first author in two of them. I could probably have two good recommendation letters. Third would be related to teaching, not research.  Would I have any chance to get admitted to top universities? I feel that the BSc GPA is a problem. And I'm now in a small university no one has never heard of. On the other hand, my MSc grades are good, and as different from my BSc grades as "night and day." Will schools likely give more weight to my MSc or BSc grades?

Suppose you do bad in undergraduate school in say computer science. But you do very well in a masters program in computer science. If you want to apply to a PhD program in computer science, will the masters degree grades offset the undergraduate degree grades?


I am developing backup script on linux (using bash linux [.sh]), and I need create a dialog (with command dialog) with progress bar to show to client status of the commands.  For example, I want a dialog box like:  Title: Installing required commands.  Dialog text:  We are installing required commands for Backup system. Installing sshpass command... (progress bar go here)  The same I want apply for the next commands:  sudo apt-get install sshpass #(used for example) sudo apt-get install rsync sudo mkdir sudo rsync -aAXv   Here example for I want make:   I using ubuntu desktop 16.04 LTS x64.

How can I create an progress bar with bash?  This is my script:   #!/bin/bash  pass='number1 number12 number13 number14 number15 number16'  chk='number14'  for i in $pass ; do  if [ "$i" == "$chk" ]; then  echo ' Found ^_^'  else  echo 'loading 50%'  fi  done   I want to replace echo 'loading 50%' with anything to create an progress bar.


I am confused by the notation in a homework problem. I think it relates to Cantor Diagonalisation but want  to know I am working with a power set first. Does this notation describe a power set?  {0,1}^A  Thank you.

I am not very well versed on set theory or syntax, but I thought I knew the basics.  However, in a book about databases I am reading now, the author uses $2^x$ to signify "a set of $x$."  For example, $2^{\text{dogs}}$ is a set of $\text {dogs}$, etc.    The author never really explained this or why he does it, I just picked up the meaning from context.    I am not sure why the exponent operator is used, nor am I sure what the number $2$ has to do with it.  The sets being represented are NOT powers of $2$ (in size)... they come in all sizes.  Is this a valid notation?  I have not seen it anywhere before...


I have laptop with dual boot(windows 8.1 pro + Ubuntu 16.04 LTS). when windows turned on after Ubuntu being in use, its time will change which become prior to the current time by 2 hours. For example: if the current time is 4:30 PM it became 2:30 PM and it is synchronized with the internet time. So why this happens? and how to fix that?

My current time in Windows7 is set to UTC +8 (Kuala Lumper). For some reason, the time is always 8 hours ahead. Curiously though, my applications seem to be using the 'right time' that is it is not 8 hours ahead. For example, the local time now is 12pm, windows time is reporting 8pm. If I send an email to myself via outlook, the time shown is 12pm. So only the windows time is off kilter.  I can fix this by syncing the time with the Internet Time Servers but it jumps back to the wrong time every few hours.  I have been having this problem since I dual booted my win7 with linux ubuntu if it helps.


I'm looking for some help trying to solve the geometry / camera positioning for a show clip. After many days of testing and tweaking I still can't get a matching result and I just don't understand why.  The tracking itself seems pretty stable, but the actual location and orientation of the camera does not match at all.  Target is to place a pretty big bed (width: ~1m, length: ~2m, height: ~2.5m) into the room.  In addition to some other randomly distributed markers, there are 4 markers on the ground, which mark exactly the middle of the outer posts of the bed. The distance from left to right is exactly 1980mm and the distance from front to back is exactly 974mm.    Technical Information:   Camera: Sony Alpha 7 III (35.6mm, 3:2 ratio, Full Frame Sensor) Lens: 28mm (Sony SEL28F20) Footage: 4K (16:9, 3840x2160), 25 FPS (PAL)   I tried:   Using other lenses: 24mm (Sony SEL24F14GM), 50mm (Sony SEL50F18F) Manually match camera position and orientation Using existing geometry as additional markers Using automatically generated markers ("detect features") Using less markers Let the solver automatically calculate the focal length, K1 & K2 Solving orientation via "Wall" - the result didn't make sense at all Solving orientation via "Floor" - the result was at least somewhere around where it should be The functions "Set X-Axis" and "Set Y-Axis" result in swapping the matching orientations by invalidating the respective other axis Manually played around with the lens distortion values (K1 & K2)   The by far best result I got was by manually placing the camera, but after around 5-6 hours of incrementally adjusting its position and orientation, I still didn't get a 100% match:    I uploaded my current blender project file and the associated video footage via  , if someone may want to have a look on his/her own.  Sometimes, after trying to solve the problem, blender got completely confused (just like me) and didn't allow to use any tracks to set the orientation ("Three tracks with bundles are needed to orient the floor"; solving the camera motion over and over again didn't fix it, so I threw away the whole solution and started over).   I would be very pleased about support in solving the problem.  Thank you.

sorry for my English, I write from Italy. I'll try to explain my problem. I'm tracking a footage with a solver error 0.2973. When I try to set the floor, the orientation of the camera is wrong (see screenshot).  So I tried to manually orient the camera, but even if well oriented respect to the xyz axes, geometry is incorrect as you can see from the screenshots below (the selected marker appears to be on the same plane but it is lower).  The video was recorded by a roof of a house so much higher than the road. It seems that Blender is not able to recognize this height and set the floor in a wrong point of view. Can someone help me solve this problem? Thank you


I need to upload a file through "browse" button , but when I chose a file , it seems as "fakepath" . My test faces an issue. How can I deal with it?

This is a canonical question, intended to provide a comprehensive answer to many related questions  During the course of a Webdriver test, I want to upload files. However, this opens a native file picker, which Webdriver doesn't seem to support interacting with. How do I interact with it?


I sent my manuscript to a journal which they accepted for publication without peer review. They asked for a 1000 euro service fee. I requested a withdrawal instead,  to which they replied asking whether I was interested in free publication to their other journal as part of their 'social responsibility policy'. My question is: does this sound like a predatory journal? Will they be able to snatch my work? (First time researcher here).

What are the best strategies for assessing if a journal is a "vanity" or "predatory" journal that should be avoided (both for publishing in and reviewing for)? For example, how would one go about determining if a journal/publisher belongs on ?


How can I start a project in rails 3.2 instead of 4.0?  I am unable to find a way to change it from the beginning.   I am using Nitrous.io to develop and it defaults to 4.0

I have two versions of rails (2.1.0 and 2.2.2) installed in my computer.  When I create a  new application, is it possible to specify that I want to use the older (2.1.0) version?