Did most people throughout the galaxy know of Luke Skywalker's role in destroying the first Death Star?  I would suspect the rebellion would keep his role a secret since they would not want the empire to target him.

Preface: I am aware that there are other threads that discuss the Jedi/Sith aspects of common knowledge in the Star Wars universe such as ,  and . My question is not about knowledge of the Jedi/Sith stuff as much as the “wars” of Star Wars itself. To me it seems as if the general population of the galaxy knows they are oppressed, but are not really aware there is an active war to end that oppression regardless of the “religious” aspect that seems to have started it all.    So the some of the trailers for the new film, Star Wars: The Force Awakens have a key scene where Han Solo states:     It’s true. All of it. The Dark Side. The Jedi. They’re real.   Okay, so I understand how the whole mystical concept of “The Force” might have been lost by the sands of time. But what about the rest of it? Objectively thinking of how the original trilogy was presented it seems everything was secretive or clandestine in many ways:   Star Wars: The mission to recover the Death Star plans from the Rebels was carried out by one Star Destroyer lead by Darth Vader. When the idea the plans were jettisoned to Tatooine in an escape pod, Stormtroopers are sent to the planet, but everything is somewhat secretive. Even the massacre of the Jawas was done in a way to make it seem as if Tusken Raiders (aka: Sand People) carried out the attack. The rest of the film follows the same notes including the attack on Yavin moon that contained the secret rebel base. The Empire Strikes Back: Again, Darth Vader is hunting down Rebels and they are hiding on an ice planet seemingly as far away from everything as possible. The trip to see Yoda on Dagobah was not shared by Luke with anyone, and when Han Solo heads to Bespin, it’s to seek refuge. And heck, even Lando Calrissian brags about how his operation in Cloud City is small enough to not attract the attention of the Empire. So everything that happens there is known only to the parties involved it seems. Return of the Jedi: The rescue of Han Solo from Tatooine is yet another clandestine operation carried out by a small group of friends trying to save the life of a fellow friend. When Jabba dies and his ships are destroyed, who cares and who knows what happened outside of that group? Jabba’s just a huge crime lord and his death would not mean much to other criminals let alone raise an eyebrow by others. Then the whole Death Star II operation on Endor is yet again, a secret operation.   And there we go. It seems that everything that transpires in the the original trilogy are all special operations and “need to know” operations at best carried out by two opposing sides who might be fighting for larger power, but it’s not like—for example—a World War II struggle it seems. It all seems like small scale operations in a lager conflict much like action films such as  or .  So in this context, what exactly did the “wars” in the Star Wars actually mean as far as awareness goes throughout the galaxy? My desire for “canon” extends into  the modern definition of Star Wars canon which means Disney canon as well; no fan-fiction or wild guesses please.  Again, it seems the new series of films will you touch on how “legendary” yet not real these events seem to contemporary residents in the Star Wars universe goes. But is there an canonical material that explicitly states something like, “The war against the Empire was important, yet not directly known by most inhabitants in the galaxy/universe of Star Wars.”  PS: FWIW, this all seems odd to me because to my knowledge—in the context of our own conflicts on Earth—even in pre-Internet/pre-modern communication times, wars and conflicts were known or conveyed in some way to even the most menial people in society. You talk to someone about the Crusades, the Civil War or even World War I nowadays people at least know that some kind of war happened even if they do not know any specifics of the conflict. But in the Star Wars universe, average citizens seem fairly clueless despite having apparently better technology and communication methods.


Does there exist a positive irrational number $\alpha,$ such that for any positive integer $n$ the number $\lfloor n\alpha  \rfloor$ is not a prime?

Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime? My try if $\alpha=\sqrt{17}$ then $\lfloor n\alpha \rfloor=4n$


Command \ifmmode misjudged in math environment of package amsmath. An mwe is like \documentclass{article} \usepackage{amsmath} \begin{document} \begin{gather}   \ifmmode123\else456\fi \end{gather} \end{document}  In math eqvironment, it should have produced 123 in gather environment. But the outcome is just the opposite. Similar cases appear in align, eqarray and so on. But in equation, it produces the right outcome. Is this a bug? Or how to fix it? Thansks for help!

I thought \ifmmode detected math mode, but clearly it does not: \documentclass{article} \usepackage{amsmath} \begin{document} \[     \ifmmode math \else not math \fi \] $\ifmmode math \else not math \fi$ \begin{align*}   \ifmmode math \else not math \fi \end{align*} \end{document}   How do I reliably detect math mode, including within align*?


Edit note:  This question with some good answers does not explain (or ask) why it is an adjective that's used as opposed to an adverb in this type of construction:        My Question:  Consider this sentence: "Garlic can be eaten raw or cooked".  In the dictionary, "raw" is an adjective only and is not an adverb. "Cooked" is also an adjective.  So, why can an adjective be placed after "eat" as in "Garlic can be eaten raw"?

In ‘catch me off guard’, is the ‘off guard’ an objective complement or adjective phrase that modifies ‘me’?      My Great Uncle Algie kept trying to catch me off guard and force some magic out of me — he pushed me off the end of Blackpool pier once, I nearly drowned — but nothing happened until I was eight.


I know this question has been asked a million times before, but I'm unable to find a solution to this specific issue.  I'm saving the word "Tečný" from my PHP 5.6 application to a MySQL 5.6 db, using PDO::prepare() and PDOStatement::execute();  The data being passed in is definitely correct. The DB connection is made using 'SET NAMES utf8'. and 'SET CHARACTER SET utf8'.   When the string reaches the db, it's saved as "Te?ný". However, when I save it manually with MySQL Workbench, it saves and retrieves correctly.  Am I missing something?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I'm seeking your help in understanding the difference between two different contrasts for dichotomous variables.  On this page:  under "Dichotomous Predictor Variables", there are two ways to code dichotomous predictors: using the contrast 0,1 or the contrast 1,-1. I kind of understand the distinction here (0,1 is dummy coding and 1,-1 adds to one group and subtracts from the other) but don't understand which to use in my regression.  For example, if I have two dichotomous predictors, gender (m/f) and athlete (y/n), I could use contrasts 0,1 on both or 1,-1 on both. What would be the interpretation of a main effect or an interaction effect when using the two different contrasts? Does it depend on whether my cells are of different sizes?


How to prove $\lim_{x\to\infty}\frac{x^{99}}{e^x}=0$?   I wasn't sure how to do this because both the top and the bottom limits independently turns out to be infinity!

In other words, how to prove:  For all real constants $a$ and $b$ such that $a > 1$, $$\lim_{n\to\infty}\frac{n^b}{a^n} = 0$$  I know the definition of limit but I feel that it's not enough to prove this theorem.


I need to draw the following game tree on tikz. It's a bayesian game. Sorry for the pic, I made it on Paint.   So basically there are 2 players G and T, N is the nature that gives a chance for each type of player. The action of G is continuous, that's why I put the curve line.    So, my main doubr is to put the continuous set of action for player G and to put the same set of information for players of the same type. As it can be seen in the following pic:     \documentclass[tikz,border=10pt,multi]{standalone} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usetikzlibrary{trees} \usetikzlibrary{calc} \tikzset{ % Two node styles for game trees: solid and hollow solid node/.style={circle,draw,inner sep=1.5,fill=black}, hollow node/.style={circle,draw,inner sep=1.5} } \begin{document} \begin{tikzpicture}[font=\footnotesize,edge from parent/.style={draw,thick}] % Two node styles: solid and hollow \tikzstyle{solid node}=[circle,draw,inner sep=1.2,fill=black]; \tikzstyle{hollow node}=[circle,draw,inner sep=1.2]; % Specify spacing for each level of the tree \tikzstyle{level 1}=[level distance=15mm,sibling distance=50mm] \tikzstyle{level 2}=[level distance=15mm,sibling distance=25mm] \tikzstyle{level 3}=[level distance=15mm,sibling distance=15mm] \tikzstyle{level 4}=[level distance=15mm,sibling distance=10mm] % The Tree \node(0)[hollow node]{} child{node[solid node]{} child{node[solid node]{} child{node[below]{$1,0$} edge from parent node[left]{$\gamma$} child{node[below]{$2,3$} edge from parent node[right]{$\tal$} edge from parent node[above left]{$P$} } %I need to put for options in the node child{node[solid node]{} edge from parent node[above right]{$N$} } edge from parent node[above left]{$\theta$} } child{node[solid node]{} child{node[solid node]{} child{node[below]{$1,0$} edge from parent node(m)[left]{$\gamma$} child{node[below]{$2,3$} edge from parent node(n)[right]{$\tal$} edge from parent node[above left]{$c$} } child{node[solid node]{} edge from parent node[above right]{$N$} } edge from parent node[above right]{$1-\theta$} } % information sets \drawloosely dotted,very thicktoout=-15,in=195; % movers \node[above,yshift=2]at(0){}; \foreach \x in {1,2} \node[above,yshift=2]at(0-\x){}; \node at($.5(m)+.5(n)$){1}; \end{tikzpicture} \end{document}   I tried using this code here:  \begin{tikzpicture} \tikzstyle{hollow node}=[circle,draw,inner sep=1.5] \tikzstyle{solid node}=[circle,draw,inner sep=1.5,fill=black] \tikzset{ red node/.style={circle,draw=red,fill=red,inner sep=1.2}, blue node/.style={rectangle,draw=blue,inner sep=2.5} } % Specify spacing for each level of the tree \tikzstyle{level 1}=[level distance=15mm,sibling distance=40mm] \tikzstyle{level 2}=[level distance=15mm,sibling distance=30mm] \tikzstyle{level 3}=[level distance=15mm,sibling distance=15mm] \tikzstyle{level 4}=[level distance=15mm,sibling distance=12mm]  \node[hollow node,label=above:{Natureza}]{} child{node(1)[solid node]{} child{node[solid node]{} edge from parent node[left]{$P$}} child{node[solid node]{} edge from parent node[right]{$N$}} edge from parent node[left,xshift=-3]{$\theta$} } child{node(2)[solid node]{} child{node[solid node]{} edge from parent node[left]{$P$}} child{node[solid node]{} edge from parent node[right]{$N$}} edge from parent node[right,xshift=3]{$1-\theta$} }; \node at ($(1)!.5!(2)$) {$Governo$}; \end{tikzpicture}   If anyone could help me, I would be glad.

I have been using TikZ to draw game-trees for my game-theory lectures (mostly using the automata package) but I could not figure out how to draw an arc across the edges the leave a given node. When we want to denote that a player has a continuum of actions available at a node, we usually draw an arc across the edge leaving such node. For example see the arc crossing the edges that leave the first node in this picture:     Any suggestions on how I could try to implement this in TikZ? Thanks!


How are competition questions designed? What techniques do designers employ to design math competition questions? How they know a problem can be solved by introductory methods?Some contest math questions involve the year of the contest as part of the question. I think designing a math problem is as important as knowing how to solve it.

The problems that appear in difficult math competitions such as the IMO or the Putnam exam are usually very difficult and require some ingenuity to solve. They also usually don't look like they can be solved by simply knowing more advanced theory and the such.  How do people typically come up with these problems? Do they arise naturally from advanced mathematics (the somewhat infamous 'grasshopper problem' from the 2009 IMO comes to mind - to my not exactly knowledgeable mind this problem looks like it popped out of basically nowhere)? What is the perspective that mathematicians take when seemingly "inventing" these problems with no theoretical motivation to them whatsoever?


please, I am dealing with this problem.  *Caused by: java.lang.NullPointerException     at main.PanelBatohu.<init>(PanelBatohu.java:19)     at main.Tajemny_ostrov_Adventura.start(Tajemny_ostrov_Adventura.java:79)*   and it refers to:  public PanelBatohu (Batoh batoh) {         this.batoh = batoh;         batoh.zaregistrujPozorovatele(this);         init();     }   and      **panelBatohu = new PanelBatohu(hra.getBatoh());     borderPane.setLeft(panelBatohu.getPanel());**   If I delete this last part, the program starts working, but with this part, it does not :(  Please, I do not know how to fix it, does anyone know?  Thank you in advance!  Best regards, John

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


I am a first year engineer student here in my country we have a first preparatory year so I was looking for a deep understanding book for trigonometry  Because I have always had a hard time with this hyperbolic and cosecant and inverse functions thing   So if any one could recommend a set of books in order to read to really understand and have a deep look at this subject would be great

I need to find a good book on trigonometry, I was using trigonometry demystified but I got sad when I read this line:     Now that you know how the circular functions are defined, you might wonder how the values are calculated. The answer: with an electronic calculator!   I know a book which seems to be really good: Loney's Plane Trigonometry, I'm just not sure if the book is up to date.


$\mathbf {The \ Problem \ is}:$ Does $-1$ have a square root in the ring $\frac{\mathbb R[x]}{\langle(x^2+1)^2\rangle}$ ? Justify your assertion .  $\mathbf {My \ approach} :$ Actually, the above quotient ring $R$ is obviously not an integral domain, and $\langle(x^2+1)^2\rangle \subset \langle(x^2+1)\rangle$ and we knnow $\frac{\mathbb R[x]}{\langle(x^2+1)\rangle} \cong \mathbb C$, but I can't get that what is meant by square root of $-1$ in $R$ ?  A little help is greatly appreciated.

Does there exist a square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$?  Now, any element in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$ is of the form $(a+ib)+e(c+id)$ where $i^2=-1$ and $e^2=0$. Now, setting $a=c=d=0$ and $b=1$, I think we would get a square of $-1$. Is this right? Any hints? Thanks beforehand.


I have only run across this word twice in my life and it was used to describe something that was deeply desired by a person, yet for them it was impossible to ever attain. Therefore, the word in question described what this thing was to them. For example:      "Given the problems with Dave's past, a healthy relationship with his dad is ___________. "

An example might be a car that is fast, luxurious, reliable, gets great gas mileage, and is very cheap. Clearly we'd all love to own such a car, but it doesn't exist, and probably never will. There's also some naiveté in assuming it would.  Is there a metaphor, idiom, or other phrase that connotes this?  "Gee, that sounds like a wonderful car, but unfortunately, it's a _____."    UPDATE:  With regard to the proposed dupe - that question has the same accepted answer, but it's not the same question. Two different questions can have the same answer. Please let me know if you disagree.


I am new to Independent Component Analysis (ICA) and have a rudimentary understanding of the method.    I understand that PCA finds vectors on which the projected data has maximum variance. ICA, on the other hand, finds vectors on which the projected data is statistically independent however, what those ICA is actually producing as a benefit when applied to a dataset ?  Let say that I want to apply FastICA to the iris dataset of scikit-learn. (maybe not the best example as it only have 4 features however I use it for illustration)  from sklearn import datasets from sklearn.preprocessing import Imputer imp = Imputer(missing_values='NaN', strategy='mean', axis=0) imp.fit(X) X = datasets.load_iris().data  ica = FastICA(n_components=2) X_trans = ica.fit_transform(X) print ica.components_ plt.scatter(X_trans[:, 0], X_trans[:, 1])     In this example I selected 2 components for ICA for visualization purpose however there should be a way to select the optimal number of components ? What does the plot is supposed to show me in this example ? What objet or property the vectors correspond to ?  How can this be used in practice?  I also find  and went through it however my question is a bit more specific. What ICA has to offer if applied on a dataset. In the example I gave, I use ICA. Why one would use ICA? What are the property of the vectors produced by ICA and in the example ?

In the absence of good a priori guesses about the number of components to request in Independent Components Analysis, I'm looking to automate a selection process.  I think that a reasonable criterion might be the number that minimizes the global evidence for correlation amongst the computed components. Here's pseudocode of this approach:   for each candidate number of components, n:     run ICA specifying n as requested number of components     for each pair (c1,c2) of resulting components:         compute a model, m1: lm(c1 ~ 1)         compute a model, m2: lm(c1 ~ c2)         compute log likelihood ratio ( AIC(m2)-AIC(m1) ) representing the relative likelihood of a correlation between c1 & c2     compute mean log likelihood ratio across pairs Choose the final number of components as that which minimizes the mean log likelihood of component relatedness   I figure this should automatically penalize candidates larger than the "true" number of components because ICAs resulting from such candidates should be forced to distribute information from single true components across multiple estimated components, increasing the average evidence of correlation across pairs of components.    Does this make sense? If so, is there a faster way of achieving an aggregate metric of relatedness across estimated components than the mean log likelihood approach suggested above (which can be rather slow computationally)? If this approach doesn't make sense, what might a good alternative procedure look like?


Currently, I am in India and I have to file my US Federal tax return by July 15, 2020. However, the postal service from India to USA has completely been blocked due to Covid-19. I am seriously puzzled about the situation. Please suggest any means to resolve it.

I am reading this from the IRS site:    … which says the following:     Where to File      If you are a U.S. citizen or resident alien (including a green card holder) and you live in a foreign country, mail your U.S. tax   return to:      Department of the Treasury   Internal Revenue Service Center   Austin, TX 73301-0215   USA   The above would seem to suggest that electronic submission is not possible in this case.  E.g. in the following scenario:  Consider someone who met the substantial presence test for the last year of their VISA (say 2019) and then moved back to their native country and needs to file the 2019 tax return (in the Spring of 2020). According to the above, it would seem that they need to physically mail the tax return and cannot submit electronically (either directly or through their accountant).  Am I reading this wrong or can one electronically submit both the federal and the state tax returns for the last year of their presence in the US, during the tax season of the Spring of the year that follows (when they've already left the States)?


I'm just wondering why this schottky diode have three pins?   I know two of the pins acts like rectifier but what does the a third pin do?  Source:

In case they have no use to the end users and have no function, why are they given as pins instead of being just closed? Some ICs have even 4-5 NC continuously (in accordance to their pin number).


Asus g53 laptop, Ubuntu 14.04, KDE 4.13.3  Fn+{f5f6} should change the screen brightness but only the animation appears with the panel (I can increase the values but the brightness does no change)   I have already tried to add this to grub  GRUB_CMDLINE_LINUX_DEFAULT="quiet splash pcie_aspm=force acpi_backlight=vendor"   Does not work. I tried this one too, I do not know what should happen after the first command but I just got back the console without anything seeming to happen:   I have also installed this    On GNOME and Unity this function works like a charm. Why not on KDE? Keyboard backlight is working on KDE.

I've installed Ubuntu 16.04 on my Asus X555LJ.  But I don't know how to install drivers or how to enable function keys to controls screen backlight brightness.


Which verb form is grammatically correct here? My intuition says 'satisfy' but a textbook I'm reading says otherwise (Core Syntax: A Minimalist Approach. If interested, a legal copy is available ).

I was surfing the internet the other day when I found this phrase: Instead your precious time and attention is wasted. To my ears, it sounds wrong. But I'm not a native English speaker, so I consulted with a number of them, and some of them said that it was "is" because the adjective modifies only the noun "time" and not "attention". Others said it "is" because that's just how it is. But I still believe it should be "are". Any help is appreciated.


Give an example of a non-abelian group G containing a proper normal subgroup N such that $G/N$ is abelian.  I KNOW THERE IS A QUESTION OF THE SAME NAME.   However, I need more involved assistance.  My professor suggested looking at the dihedral group $D_6$. I intend to find a homomorphism with a kernel that is the subgroup. The kernel of this homomorphism is a subgroup of G and is obviously normal.  However, why does this imply that $G/N$ is abelian, esp. since G itself is non-abelian?

I am wondering if my claim is correct, and how to formalize/write it? Thank you.     Give an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian.   So I am thinking of the dihedral group of triangle, with $3$ rotations and $2$ reflections. This is not abelian; but if I quotient $3$ rotations, the group has only two elements, which must be abelian.


Suppose G is a group and as per usual, the commutator is $[g,h] := ghg^{-1}h^{-1}$ for $g,h \in G$.  I need to show that the product of any number of commutators can be written in the following defined form:  $g_1 \cdot g_2 \cdot \dots \cdot g_n \cdot g_1^{-1} \cdot g_2^{-1} \cdot \dots \cdot g_n^{-1}$ where all $g_i \in G$ for $1 \geq i \geq n$  Every identity I know with commutators uses 2-3 elements (and their inverses), so I'm having trouble proving this since the starting point I'm at involves 4 elements that are not necessarily related. I figured the best thing to do would be to use induction but for the base case I have, for example, $[g_1,g_2][g_3,g_4]=(g_1g_2g_1^{-1}g_2^{-1})(g_3g_4g_3^{-1}g_4^{-1})$ and I can't seem to manipulate that in anyway.

I need help in folloving lemma.  Lemma: Any product of $k$ commutators is expressible in the form $a_1^{-1}a_2^{-1}...a_{2k}^{-1}a_1a_2...a_{2k}$  I guess author means that any product  $[x_1,y_1][x_2,y_2]...[x_k,y_k]$ can be expressible in that form $a_1^{-1}a_2^{-1}...a_{2k}^{-1}a_1a_2...a_{2k}$ where $[x_i,y_i]=x_i^{-1}y_i^{-1}x_iy_i$.  I tried to prove it by induction on $k$ but I failed.  If anyone can prove it,I would be thankful.


I have this div that has a width of 100% and a height of 90px. Inside the div I have a img that is 90px in height, but I let the width set itself. So how do I set the img withing the div, without knowing it's width?

How can I horizontally center a
 within another
 using CSS?

Foo foo


Due to cost-cutting measures I've been asked if I can migrate ArcPy code to a GDAL equivalent.  I'm fairly new to GIS, ArcPy, and GDAL.  Is there a website or guide which caters to providing equivalencies between ArcPy and GDAL?  I am not asking for any specific script examples tailored to geoprocessing shape files.  I'm looking for an overall guide.  Or something in that direction.

I would like to use a Python script that is not based on arcpy to do things like  query a shapefile by attributes, create new layer from selection, and calculate areas of a polygon and convert polygons to points.  Anyone have any code examples of using other Python modules or libraries? I am able to do this easily using arcpy but i wanted to explore other options.


I was going through Theorem 3.39 from Baby Rudin page no 69. I will restate the theorem,  Given the power series $\sum_{n\geq0}c_{n}z^{n}$, put $\alpha=\limsup_{n\rightarrow\infty}\sqrt[n]{|c_{n}|}$ and $R=\frac{1}{\alpha}$(If $\alpha=0$, $R=\infty$ and vice-versa). Then $\sum_{n\geq0}c_{n}z^{n}$ converges if $|z|<R$ and diverges if $|z|>R$.  In the proof of the theorem, the root test is applied to individual terms in the power series. I tried the same using ratio test and the expression of reciprocal of the radius of convergence becomes $\alpha = \limsup_{n\to\infty}\frac{|c_{n+1}|}{|c_{n}|}$. Then using the inequality $\limsup_{n\to\infty}\frac{|c_{n+1}|}{|c_{n}|}\geq\limsup_{n\rightarrow\infty}\sqrt[n]{|c_{n}|}$, if it is followed strictly, there will be two distinct radius of convergence(let $R_{1}$ and $R_{2}$) and this cannot be the case, since the series will converge and diverge in an annular region with radius $R_{1}$ and $R_{2}$, by ratio test and root test. So, the only possible scenario can be the two are equal, implying equality holds in that inequality, i.e. $\limsup_{n\to\infty}\frac{|c_{n+1}|}{|c_{n}|}=\limsup_{n\rightarrow\infty}\sqrt[n]{|c_{n}|}$. But this looks so absurd since it makes the inequality totally meaningless. I am unable to figure out where is the gap in my thinking. Any help will be appreciated.

Question: Give a sequence $(a_n)_{n=1}^\infty$ with $a_n>0$ such that root test works while ratio test does not work, that is,    $$\lim_{n\rightarrow\infty}(a_n)^{\frac{1}{n}} \text{ exists}$$   while    $$\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n} \text{ does not exist}.$$   My attempt:   Define a sequence $(a_n)_{n=1}^\infty$ such that      $$ a_n =  \begin{cases}        2^{n-1} & \text{if }n \text{ is odd,} \\    2^{n+1} & \text{if }n \text{ is even}.    \end{cases}  $$         Odd subsequence $(a_{n_j})_{j=1}^\infty$ implies that $\lim_{j\rightarrow\infty}(a_{n_j})^{\frac{1}{n_j}} = \lim_{j\rightarrow\infty} 2^{1-\frac{1}{n_j}} = 2 $ while even subsequence $(a_{n_k})_{k=1}^\infty$ implies that $\lim_{k\rightarrow\infty}(a_{n_k})^{\frac{1}{n_k}} = \lim_{k\rightarrow\infty} 2^{1+\frac{1}{n_k}} = 2.$     It follows that $\lim_{n\rightarrow\infty}(a_n)^{\frac{1}{n}} = 2,$ that is, root test works.      However, for odd subsequence $(a_{n_j})_{j=1}^\infty,$     $$\lim_{j\rightarrow\infty}\frac{a_{n_j+1}}{a_{n_j}} = \lim_{n\rightarrow\infty} \frac{2^{n_j+1}}{2^{n_j-1}} = \lim_{n\rightarrow\infty} 4 = 4.$$     For even subsequence $(a_{n_k})_{k=1}^\infty,$     $$\lim_{k\rightarrow\infty}\frac{a_{n_k+1}}{a_{n_k}} = \lim_{k\rightarrow\infty} \frac{2^{n_k-1}}{2^{n_k+1}} = \lim_{k\rightarrow\infty} \frac{1}{4} = \frac{1}{4}.$$     Therefore, $\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}$ does not exist, that is, ratio test does not work.  Does my example work?


If I have an RGB value of (0, 0, 0) I get pure black. Now, since CMY are the opposite colors of RGB - shouldn't (100, 100, 100, 0) in CMYK mean pure black? Why is this equivalent to #363639, which is not even a pure gray?

I'm having a rather annoying problem! I have RGB images made in Photoshop that I need to convert to CMYK.  When I save the file my black background is converted to a light grey! I tried deleting my background and adding a pure black background in my PSD file but even that comes out grey! There is no way to save black? The colors all look fine in Photoshop, it's just when I save them as TIFF/JPEG.  How can I prevent this?


I'm searching for a function $f\notin L^{\infty}(\Omega)$, but $f\in L^p(\Omega)$ for all $1\le p <\infty$. And it has to be $|\Omega |<\infty$. I tried $f(x)=\frac{1}{2\sqrt{x}}$ and $\Omega= (0,1)$ and something like that, but it is $f\notin L^p(\Omega)$ for all $1\le p <\infty$. Could you help me?

Let $X$ be the interval $[0,1]$ with Lebesgue measure. Is there a function $f\in L^p(X)$ for all $p\in[1,\infty)$ that is not $\in L^\infty(X)$? If so, what is an example?   Motivation: In a course on measure theory this fall, I've learned proofs that $L^p(X)\supset L^q(X)$ if $q>p$ and that if $f\in L^\infty(X)$, then $\|f\|_\infty = \lim \limits_{p\to\infty} \|f\|_p$.  This prompted me to wonder if $L^\infty(X) = \bigcap _p L^p(X)$. A classmate gave me a general theoretical reason to believe the contrary: $L^p(X)$ is a  for $1 \lt p \lt \infty$ but not for $p=1,\infty$; but intersections of reflexive spaces are reflexive. This logic seems sound to me; but it implies the containment $L^\infty(X) \subset \bigcap_p L^p(X)$ is strict.  If so, there must be a function that is $L^p$ for all $p$ but not a.e. bounded. What is it?


I'm having issues proving that a sequent is valid, without any premises given.   Prove $⊢ (p \to q) \lor (q \to r)$ by natural deduction. Prove $⊢ \forall x \forall y P(x, y) \to \exists y \forall x P(x, y)$ by natural deduction.   I don't know where to begin with, as I normally use my premises in the first place. What's the general approach when encountering a sequent like theses ones?

I tried to prove that $(p \to q) \lor (q \to p)$ is a tautology.  I used $p$ and $¬q$ as conditions. (Premises 1 and 5)  I managed to get to a solution, but I'm not sure if it's right.  Can you please check it?   Thank you!!!:)


The recent arrest of someone behind Silk Road is in the news today, he was arrested in a San Francisco public library.  A couple of background articles  and .  To what extent, if any, did staff and/or admins have in assisting law enforcement agencies in arresting this programmer?  Did they voluntarily cooperate, or was it a legal requirement to cooperate under US law?    An answer from some authority saying Stack Exchange is not able to discuss the issue with users is also acceptable to me.

Does Stack Exchange report on the numbers of requests and orders it receives from law enforcement agencies, as , , ,  and  do?


Often when I ask a question it gets closed, but I don't understand what makes it too broad or off-topic and people aren't explaining it in comments.  I'm getting frustrated; I want to contribute constructively but I've run into this enough that I've hit an automatic block and don't know how to fix it.  I've reached out several times to the people who closed my questions, and they all just re-directed me to the standard Stack Exchange help talking about how to write a good question. And it may be just me but after reading through it several times I think I'm already doing what it recommends.  Despite the times my posts have been flagged I had many posts that did well, got useful feedback, and got at least 40 upvotes. Yet I have been question banned on Stack Overflow because of low-quality questions that "don't help the community".  They provided a link to another Stack Exchange page showing what I can do to fix this, but it sounds like it will be a very long time before the ban will be lifted.  It appears obvious to me that this site isn't a bunch of bad people trying to be mean or trolling. I've found some really nice people here on Stack Exchange. But I'm having trouble understanding this ban I'm now under.  Now I'm not innocent; I have quickly run through and posted a question about the bash terminal in the Ubuntu community when the question wasn't strictly Ubuntu. But it seems like people are being harsh for no apparent reason.  I don't know, maybe I'm just not good at gathering information from the stack exchange tips, or maybe it is them, I don't know. But since the flaggers didn't help me, I would like to ask here in public before I can no longer ask questions here either. Am I missing something? Are there just that many harsh people on the stack exchange community? Are the Official Stack Exchange tips really unhelpful or am I missing something? I could really use your help.  I'm, not looking for , nor am I asking for anyone to reopen one of my closed questions without me making modifications first.

If you are reading this, you may have been affected by one of our post quality bans. If so, it is important that you  to understand what has happened and how to regain the permissions that you lost. While trying to ask a question, one could see:  We are no longer accepting questions from this account. See  to learn more.  Likewise, for answers:  We are no longer accepting answers from this account. See  to learn more.   Why am I getting this message? Are deleted posts taken into account too? Is a question/answer ban the same as a suspension? How do I avoid getting a question ban? How long do I have to wait before I can post again? What can I do to release the ban? How can I reactivate my account? Can I simply create a new account? I'll just ask somewhere else on the SE network, and they'll migrate my question to the correct site! Will a ban on one Stack Exchange site affect my standing on other sites in the network? Does this apply to meta sites too? My account is in good standing. Why am I still blocked?


I'm using Samsung S9 ( OneUI version 2.5, Android version 10 ). Is there any way to stop a particular app from accessing the vibration feature of the phone? Even if I turn on the silent mode and turn off the vibration for all notifications, certain apps keep on vibrating the phone even for minor actions. I find this really annoying and I want to block these apps from having access to the vibration feature. How to do this? In detail : I'm the kind of person who doesn't like the concept of vibration haptic feedback. I'm okay with my phone vibrating for essential notifications such as calls and texts when I'm in a meeting and my phone is in silent mode. However, I don't like the phone vibrating for silly things such as a key-press, or forwarding a video etc. It gives me a weird feeling and also vibration consumes the battery. Recently this problem became really annoying, as Youtube introduced segments in videos. Now, when I try to forward the video using the progress bar, the phone gives a really strong vibration, Which is annoying and consumes a lot of power. I looked in the settings of the Youtube app and there is no way to stop it from vibrating. Is there any way to block the youtube app from having access to the vibration motor?

I have a Moto G6 Play that vibrates like it is getting notifications but it's not. The vibration is inconsistent and seems random so I would like to know if there is a logcat or something I can run to log which app is calling the vibration so that I can shut it off? The same thing happens on my wife's phone, same model, and it does my head in. The device is running Android 9.


I have a aura:if expression that renders a inputNumber field after checkbox is clicked and certain other criteria matches.  Now, I want that inputNumber to be focused (and set certain attributes, like inputMode : numeric) after I click the checkbox.   The problem is that component.find("amount").getElement() returns null. There is a potential workaround to use setTimeout, but it's not elegant and breaks on iOS (Mobile Safari only pops keyboard if focus() event was received synchronously).  Code below.  Component:  <input   value="{! v.foo.Selected }"   name="{!v.foo.Key + v.index}"   type="checkbox"   id="{! v.foo.Key + v.index }"   onclick="{! c.selectfoo }"   data-value="{! v.foo.Name }"   data-key="{! v.foo.Key }"   aura:id="fooBox" /> <aura:if isTrue="{! and(v.foo.AmountRequired, v.foo.Selected) }"> <div class="slds-form-element__control">   <ui:inputNumber      class="slds-input"     format="$###,###,###"     placeholder="$"     aura:id="amount"      value="{! v.foo.SumAssured }"     keyup="{! c.moveFocus }"/> </div> </aura:if>   Controller:  selectBenefit: function(component, event, helper) {     var selected = component.get('v.Benefit.Selected');     component.set('v.Benefit.Selected', !selected); }   Renderer:  ({     rerender : function(component, helper){         this.superRerender();         var amount = component.find("amount");          console.log(amount);         console.log(amount.getElement()); //returns null          //below somewhat works         if (amount.isValid()){             window.setTimeout(                 $A.getCallback(function() {                     if (component.isValid() && amount.isValid()) {                         var input = amount.getElement();                         console.log(input);                         input.focus();                         input.setAttribute("pattern", "\\d*");                         input.setAttribute("inputmode", "numeric");                       }                 }), 200             );            }     } })   EDIT: Tried different approach and still got same race condition problem. After toggling 'slds-hide' class on an element, focus() doesn't execute, most likely because it's not visible yet:  $A.util.toggleClass(component.find("amountContainer"), "slds-hide");     if( component.get('v.Benefit.AmountRequired') && !selected ){         console.log(component.find("amount").getElement()) }

What are the actions that might destructively interfere with the lightning app's lifecycle? Is a breakpoint\debugger statement one of such?  For example there is a case that I happen to meet regularly after Winter 17 release (everything below is performed with Locker Service on, switching it off is not an option). Assume we have some component with an init event handler and "select" element:  ... <aura:handler name="init" value="{!this}" action="{!c.doInit}"/> <select aura:id="select-element" class="slds-select" onchange="{!c.handleSelect}"></select>   And here's an "init" handler:  doInit : function(component, event, helper) {     // do smth     debugger; // this can be a debugger statement or manually put browser's breakpoint }   If we happen to have an open console and we catch this breakpoint (immediately resuming it, or not) - in any time later there's no chance to get access to element:  ... component.find("select-element").getElement;   Same happens with div element's, maybe with others.  With absolutely same component's layout and js-controller\helper etc. but with browser's console closed (hence the breakpoint isn't caught) getElement function is there and some code that depends on it will execute successfully.  EDIT: the DOM element is there already (meaning if I use afterRender or some custom button to get a breakpoint far after the init() was executed), I can see it and interact with it - but the getElement function nevertheless is unreachable at that same moment.


running wc -w against latex files does not amswer question of actual words of content in article, book. Therefore, how to count them?

Often assignments (or even papers) have a word count limit. That is not a big deal when using Word, but I don't know how to do that using LaTeX. My solution has been so far to compile the document and then do a rough word count of my pdf file, sometimes even copying the contents of the pdf file and pasting in Word to get a mostly correct Word count.  Is there any tool (maybe even an online tool), package, script or software to do that directly from my .tex document and still get the right word count (i.e., ignore commands, equations, etc)?


From a unix admin standpoint what is the difference please between those terminologies : Service, Process, Thread, Task, Job, Daemon ?

How are these fundamentally different "things" on Windows? Aren't all running things Processes? It seems that every Application has an associated process that shuts it down if it is shut down. It looks like one process can manage more than one application instance. And Services, I'm not even sure what they are, exactly. Are they not processes themselves?


If a yo-yo's string is not attached to anything and the yo-yo is dropped, it is obvious it will fall at $g$.  In this scenario, Tension of string = 0.  If a yo-yo's string is attached to a cieling and it is dropped, what is $R$ (path of center of mass)?  Well, we know from experience that the yo-yo is going to fall at least, but is it going to fall at $g$?  We know it is rotating as well.  What would $T$ (tension of string) be?  Would $T$ = yo-yo's mass * gravity?  Assume that there is no friction.  A related question is: if there is a stick in space and a force is applied to the center of mass, and for another stick in space an equivalent force is applied to the edge of the stick, will both sticks' center of mass move the same?  Would the 2nd stick be rotating?

Suppose there is one rod and a force F is applied in two cases: Case 1: exactly at the middle on center of mass Case 2: at one end of rod   In which case would the center of mass of rod be accelerated more? Or would acceleration of its center of mass be the same in each case? I have worked towards this and found case 2 would impart a greater acceleration. I just want to check my answer and see if I am making a mistake here.(The question just came into my head and I don't have any source to check the answer from) $$My$$ $$solution:$$ In case 1 the rod would undergo a translational motion and C.O.M. would get an acceleration of $F/M$. In case 2 the rod would rotate about its other end and a torque would act which would be equal to $Fl$. Equating this to $I\alpha$ we get $\alpha$ = $3F/Ml$ and since C.O.M. is at $l/2$(rod is of uniform density) acceleration would be equal to $3F/2M$. Is my solution and thinking correct?


Whenever I log in to a server, log out later, and log in again, Minecraft keeps giving me a time out error for all servers.  I have tried restarting my computer, and I also tried restarting Minecraft. But it did not work.  The only solution I found that works is turning my Internet connection off, then turning my Internet connection back on, but I cannot do that all the time. Please give me another solution.

My friend had hosted a Minecraft server before and brought it back up today with my help. He and anyone in his LAN can connect. However we have had a few people try to connect, including me, and when we try to connect it gives the message:  Failed to connect to the server Connection timed out: connect  What does this exactly mean? How do we fix this?


I am generating a set of particles that follow a streamline and I would like the particles to change color according to their position along the line. The tricky part is that the streamline has a image texture shader and I would like the particles to be matching the texture.   Is there a simple way to do so?   Many thanks in advance!

I have a series of tubes that were inputted as VRMLs with varying colors. I have made a path out of them and have the sphere following the tubes. I want to link the color of the sphere to be the same as the tube while the sphere is traveling in time over the tubes. How can I link the colors? I also want the sphere to glow with the color of the tube.


FileZilla is spending way too much time copying files that are already there because the clocks on my systems vary too much.  I want to set them all to the Master Clock (like WWV)  According to the NIST page, the National Bureau of Standards suggests using time.nist.gov as the address that will reach a working system among all of the Stratum-1 and 2 servers available:      Obviously, Ubuntu is using time server pools, like Microsoft does, which are many hops away from the master clock source.  My question is in the title:  How do I set Ubuntu to use the primary time server time.nist.gov?

I would like to configure my Ubuntu 12.04 server to synchronize its clock with a specific NTP server. Where to set this up?


I have a Jailbroken iPhone5s Or well I had one. I couldn't install any apps or update any apps so I reset my Phone with reset all in settings It was stuck in the Recovery Screen just stuck. I then plugged it in with iTunes and done Update and Restore but then it was just stuck in that screen. I left it in there for about 6 hours and I can't seem to fix at all. Is there any way to fix this?

I recently received an iOS device and it was jailbroken. When I wanted to unjailbreak it, I used "Erase All Content and Settings." The loading screen came on and it has not changed. After rebooting the device, it is now stuck at the Apple logo. What should I do?


In ArcGIS Desktop we are able to create a file geodatabase and also a feature class.   Is this possible in QGIS?

I have spent around 2 days to find the way to open GDB (Esri geodatabase) in QGIS (or any other open source software) but still without success.  I have downloaded the newest OSGeo4W installer and tried the setup - express desktop install - all packages, as well as advanced install incl gdal-filegdb.  Can you describe a more detailed procedure, including installation and how to open .gdb in QGIS (OSGeo4W installation)?


My tags are follows: test.tex \documentclass{book} \usepackage[natbib,authordate,backend=biber]{biblatex-chicago}%  \addbibresource{test.bib}  \makeatletter \AtEveryBibitem{\global\undef\bbx@lasthash} \makeatother  \begin{document}  \citet{baker_tenenbaum_saxe06} and \citet{baker_saxe_tenenbaum09}  \printbibliography  \end{document}  test.bib @inproceedings{baker_tenenbaum_saxe06, Author = {C. L. Baker and J. Tenenbaum and R. Saxe}, Booktitle = {Advances in neural information processing systems}, Date-Added = {2014-01-30 12:16:28 +0100}, Date-Modified = {2014-02-01 00:11:49 +0100}, Publisher = {Cambridge, MA: MIT Press}, Title = {Bayesian models of human action understanding}, Volume = {18}, Year = {2006}}  @article{baker_saxe_tenenbaum09, Author = {C. L. Baker and J. Tenenbaum and R. Saxe}, Date-Added = {2014-01-30 12:11:35 +0100}, Date-Modified = {2014-02-05 23:44:19 +0100}, Journal = {Cognition}, Number = {3}, Pages = {329--349}, Title = {Action understanding as inverse planning}, Volume = {113}, Year = {2009}}   Above codes are working fine, is it possible to get the marked letters are in caps by auto? (It comes in uppercase if I change in .bib file) Please advise...

According to the 16th version of the Chicago Manual of Style, titles in the reference list are now supposed to be capitalized in title case style rather than sentence casing. Yet, as far as I understand, BibLaTeX-chicago (0.9.9b) does not seem to make any automatic changes to the capitalization of .bib-entries.   Is there any way (except for doing it manually for each entry, of course) to get BibLaTeX-chicago use title case capitalization for the entry field title in all entry-types (regardless of how the title is formatted in the .bib-field) ?   Here's a MEW:  \documentclass[12pt, a4paper]{article} \usepackage[authordate,strict,backend=biber, cmsdate=old]{biblatex-chicago} \begin{filecontents}{bibsample2.bib} @BOOK{Smith2003,  title = {This is the book title},  publisher = {Penguin},  year = {2003},  author = {Smith, James},  address = {London},     } @ARTICLE{Doe1970,  author = {Doe, John J.},  title = {this is the article title},  journal = {Great Journal},  year = {1970},  volume = {40},  pages = {207-234}, } \end{filecontents} \addbibresource{bibsample2.bib} \begin{document} \autocite{Smith2003} \autocite{Doe1970} \printbibliography \end{document}   So, what I'm looking for is for these titles to be spelled as   This is the Book Title  This is the Article Title  in the output.  I'm using the latest version of BibLaTeX (2.5), Biber (1.5) and BibLaTeX-chicago (0.9.9b).  Any pointers are greatly appreciated..


So I need to prove that T(n) is $O(n\text{log}(n))$, considering $c>0$ is a constant and using substitution method What I've tried so far: We need to prove that $T(n) \leq dn\text{log}(n), d\geq0$ Assuming that $T(\frac{n}{2}) \leq dn\text{ln}(\frac{n}{2})$, we have $T(n) \leq dn\text{ln}(\lfloor{\frac{n}{2}}\rfloor) + dn\text{ln}(\lceil{\frac{n}{2}}\rceil) + 1$ Removing the ceil and the floor, I'm guessing we don't want to equal both of them to $\frac{n}{2}$, so $T(n) \leq dn\text{ln}(\frac{n}{2}) + dn\text{ln}(\frac{n+1}{2}) + 1$ $T(n) \leq dn\text{ln}(n)-dn\text{ln}(2) + dn\text{ln}(n+1) - dn\text{ln}(2)+1$ $T(n) \leq dn\ln(n) + dn\ln(n+1) -2dn + 1$ And I have no idea how to continue this.

I'm learning algorithms by myself and am using the excellent  to do that. It has been quite a long time since I last studied math, so maybe the solution to my problem is trivial.  Exercise 4.3-5 asks to prove that $\Theta(n \lg n)$ is the solution to the "exact" recurrence for merge sort using the substitution method.  The recurrence is: $T(n) = T(\lceil n/2 \rceil) + T(\lfloor n/2 \rfloor) + \Theta(n)$  Here is how I started to tackle the problem:  I need to prove that the recurrence is $O(n \lg n)$ and $\Omega(n \lg n)$ to prove that it is $\Theta(n \lg n)$. Let's begin with $O(n \lg n)$.  Let's assume that the bound $T(m) \leq cn \lg n$ holds for all $c > 0$, $m > 0$, $m > n$; in particular for $m = n/2$, yielding:  $$ T(n/2) \leq cn/2 \lg(n/2) $$  Substituting into the recurrence yields:  $$\begin{aligned} T(n) &\leq c n/2 \lg(n/2) + c n/2 \lg(n/2) + \Theta(n) \\\\ &= cn \lg(n) - (cn - \Theta(n)) \end{aligned}$$  And then I'm blocked, I guess I have to remove $\Theta(n)$ with something like $kn$ but it does not seem very rigorous.


The page I'm talking about is the Accounts tab in the Network Profile, example . The primary sort key seems fairly clearly "reputation," descending. However, secondary sort keys don't seem obvious. What I would expect is that:  If two accounts have equal reputation, question count, answer count, the one with more badges (perhaps gold, silver, bronze in that order) would appear higher in the list. If two accounts have the same reputation and badge counts and answer count, the one with more questions should appear higher in the list. If two accounts have the same reputation and badge counts and question count, the one with more answers should appear higher in the list. If two accounts have the same reputation, badge counts, question and answer count, the one most recently visited should appear higher in the list. (?) If two accounts have the same reputation, badge counts, question and answer count, and visit recency, the older account should appear higher in the list. (?) If two accounts have the same reputation, badge counts, question and answer count, visit recency, and age, they should be in alphabetical order. (?)  Currently, "" seems to be the "actual" current state unless I'm missing a pattern. Why not add additional sort criteria to the list creation, to more easily sort by level of activity descending? Also, I'll make this one more of a feature request for additional sort levels than  which asks more about the current state of the art, so as to help distinguish the two.

How are accounts sorted if they have the same rep?    I don't see any logic.


i am trying to texbox over to button but my case first line texbox then next line in button  html:-
                                 <input type="text" id="surName" /><button id="add" class="hidden">Add</button>                                 Surname
   css:-  .custom-input #surnamediv #add{         vertical-align:middle;     }

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


Which of the following is considered correct? ". . . where I was at age five." or ". . . where I was at age 5."

The junction has a stop sign on each of the four entrances.   The junction has a stop sign on each of the 4 entrances.   The first is preferred, for some reason, by many English texts. Why? I haven't seen this phenomenon in other languages.


I just got a second hand Dell XPS 12 to use for web testing (I currently only use mac but are having a case where I must check how things looks in IE). It has Windows 10 on it. When I check with dell web site it was first delivered with 8.1 but was upgraded to Windows 10 while that was free.  Theres a million programs and files on the computer so I would like to re-install it using Windows 10.  If I understood correctly checking with MS the license should be coupled with that hardware (when upgraded to Win10) so I could just download the Win 10 ISO from MS and run an installation from that.  What do you think? Should I try to extract the license key first? And if so How? :) Or should I try to find a Dell recovery image instead? Any ideas and tips?  Thanks!  --  Here is what I did  I downloaded the Windows 10 iso from Microsoft and created a bootable USB drive with the provided tool. I booted the computer from that and when it asked for a serial I just clicked I don't have one and continued the installation.  When Windows was installed and I had put in my Wifi password it had activated itself with Microsoft. The license key is generated based on the motherboard for all (or many?) of the upgrades from Windows 8.

I have a Windows machine (laptop) that needs fixing. The current installation is really badly broken (e.g. the taskbar is unresponsive, but the Explorer windows work, booting takes literally half an hour) and when I try to access the settings app and click on the tile to access the reset settings it instantly crashes. The same happens in Safe Mode.  I have created a USB install medium using the tool offered by Windows on my own Windows desktop machine. I've ensured that both the laptop and the USB tool have the same version of Windows (Home, 64-bit, NL). When I want to reinstall Windows on the laptop with this stick I am asked to enter a serial number which I obviously don't have. I don't want to try and see if I can phone activate it, because if it fails the install is gone.  I need to reinstall this Windows machine from a USB stick. There are a few problems I can't find an immediate solution for on the .   If I use a tool such as  to extract the serial number, will this work? If the above does not work, how can I reinstall this Windows machine?


If $A$ and $B$ are two orthogonal matrices of rank $n$ and $Det(A)+Det(B)=0$,then prove or disprove that $Det(A+B)=0$.  My attempt: Since the two matrices are orthogonal the value of their determinants will either be $1$ or $-1$. But how to prove that $Det(A+B)=Det(A)+Det(B)$

I am trying to solve following problem.      Let $A, B \in \mathbb{R}^{n\times n}$ be an orthogonal matrices and $\det(A) = -\det(B)$. How can it be proven that $A+B$ is singular?   I could start with implication:  $\det(A)=-\det(B) \Rightarrow B$ is created from $A$ by swapping two lines or columns.   But I am not sure if this implication is correct.


I have made the leaf shape and want to bend with the reference image.     I have on the proportional editing on also. But the problem its not bending its moving from the place.        Later i have to extrude and offset.  Any suggestion and help. Thanks

I'd like to curve my object, but I'm considering two options.  The first one is to make the object up with lots of vertices, like a sphere can be. The second is to apply some kind of modifier curve to a straight mesh, as I've understood there is such a possibility.  Here's an awesome pen drawing of what I'd like to achieve:    and here's my current even more awesome result:    Rather non-awesomely, they don't quite match. So if someone would kindly point me to the correct method to achieving a nice-looking solution with relatively low polygons, I'd be much enlightened


I got an iPhone from a friend and he’s far away at the moment but the phone has a software issue. I wanted to wipe the phone and restore it to a “new” state, but I was told it’ll require an Apple ID.  Can I enter my current Apple ID, or do I need to contact my friend to provide his password?

I bought a used iPhone 4.  The previous owner re-set the phone, but did not remove the device from their iCloud.  It is asking me for their iCloud information when I try to set-up the phone.  I don't have contact with the previous owner anymore.  Is there a way to remove the device from their iCloud so I can use a new one?


Show that $\|.\|_{1/2}$ is not a norm. would anybody guide me that how can i prove or disprove?  thanks

please I tried to find counterexamples to see that $l^p$ is not norm with $p<1$ in the triangle inequality but I have problems with convergence when I choose some successions. Thanks.


The most common kind of deviation is the standard deviation.  $$ \text{Sd}(x) = \sqrt{\text{Mean}((x - \text{Mean}(x))^2)}$$  The standard deviation is very similar to the mean absolute deviance or  $$ \text{MAD}(x) = \text{Mean}(|x - \text{Mean}(x)|)$$  but is often simpler to calculate or obeys nice algebraic properties.  But there are a lot of other measures of variance. For example, there is the most common absolute deviance from the mean value:  $ \text{Mode}(|x - \text{Mean}(x)|)$.  It is not clear to me why I should prefer the standard deviation over other kinds of measures of dispersion. I suppose the simplest answer is that this measure of dispersion is the most highly studied and well known and using other methods of dispersion will confuse people you try to communicate with.  I guess I would have to use these kind of alternative measures for pathological distributions like the Cauchy distribution though.

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard?  The definition of standard deviation:  $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$   Can't we just take the absolute value instead and still be a good measurement?  $\sigma = E\left[|X - \mu|\right]$


I bought a Dell Inspiron 5491 with Windows 10 preinstalled and now I'd like to install linux on 2nd hard drive (SSD). When I run the Ubuntu with USB and select Try Ubuntu or Install Ubuntu the black screen appear with the blinking cursor on top left, after a second the cursor disappear and nothing else... I have to shutdown my laptop holding down the power button.  In the BIOS I have disable the "secure boot" and set the AHCI instead the RAID default settings because I read on some post that this could be a problem. But these settings, in my case, doesn't resolve anything.  Follow some specifications of DELL Inspiron 5491:   CPU : Intel i7 10510U  GPU : NVIDIA® GeForce® MX230 with 2GB GDDR5 graphics memory  RAM : 8GB, 8Gx1, DDR4, 2666MHz   Do you provide me a piece of advice or suggestions? Thank you for your time.

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


Am an Indian passport holder. About to tour Greece. Received the Schengen visa from Greek authorities. My flight is from Mumbai to Paris and connecting flight from Paris to Athens. At Paris,there is a change of terminals from 2C to 1. Will I have to go thru immigration? I do not wish to get stuck as Schengen issued is by Greece and it says valid for Schengen stages. It's a multiple entry, C Category 1 month visa. Is it a requirement that there should be first entry to the Schengen state that issued the visa?

In case, if I get a multiple-entry Schengen visa in one of the embassies in Ukraine, Kyiv - should my first trip be to the country which issued the visa?  Any there any requirements of this sort? Does this condition vary depending on embassy which issued the visa?  What are the possible consequences on not visiting that country first? Does it somehow depend on country where the embassy is (i.e. non-Schengen and not EU members)?


My mac terminal prompt is:   wbk-er-10-132-118-162:~ johnjara$   I did echo $PS1 and got \h:\W \u\$, which would be the hostname: the basename of $PWD, my username, respectively. My  computer name in System Preferences > Sharing is Copper's Macbook Pro.   So what is \h here for my Mac if not computer name? How do I change it?   Also, why my IP address would be there in hostname?

My computer name in System Preferences > Sharing is set to "archos", but is showing as "iphone" on Terminal. It just started doing this after I loaded Xcode for doing iPhone development: Last login: Mon Nov  7 14:46:55 on ttys001 iphone:~ travis$   Any ideas what could be causing this?


A particular professor is known for his arbitrary  grading policies. Each paper receives a grade  from the set {A, A-, B+, B, B-, C+}, with equal  probability, independently of other papers. How  many papers do you expect to hand in before you  receive each possible grade at least once?

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?


I am constantly using stackoverflow as a great resource to begin any search for questions/solutions I am looking for.  As there are more and more questions/answers with the best answer bubbling to the top, wouldn't it make sense to have a wiki page to take these answers and add them to one common wiki page for this certain tag/topic?  I think this would add a great deal of benefit to the stackoverflow site.  It would not only become a place to search for a specific tag/topic, but also a quick reference manual.  Being a wiki, this could constantly be updated as better answers/solutions are found.  Just a thought.

Create or allow for a community-wiki editable home page per tag. One where we could place essentially the tag-specific FAQ and other tag-specific links.


I am an Australian and arrived in the Schengen end of April 2015. I travelled as a tourist around the schengen for 90 days and within the 90 days obtained a Working Holiday Visa in Netherlands. My working holiday visa in Netherlands will expire the beginning of July 2016. My question is, can I travel within the schengen for another 90 days as a tourist ? If so, do I need to somehow reset my stay here by re-entering the schengen as a tourist? I.e. travel to the UK at the end of my visa and re-enter ?

I have searched the web a lot and could not find an answer that fits my situation. Here are two links that are quite contradictory:       My situation:  I've visited Portugal in December 2012 for 29 days on a Schengen visa valid from December 1st, 2012 to February 1st, 2013 for research purposes (I am a Ph.D. student). I want to visit Sweden from February 10th, 2013 to May 10th, 2013 (89 days). I have applied for a Schengen visa again (for research). How will the 90/180 rule work in my situation?


Does Gríma have a surname? Wormtongue was a nickname/epithet and not his actual name - but did he have a genuine one?

While all the Hobbits I can think of have a combination of first- and lastname (e.g., Bilbo Baggins, Peregrin Took, the Sackville-Baggins's,...), I can't think of any character* of another race that has a lastname:   Men seem to like to add a reference to their ancestors (e.g., Aragorn, Arathorn's son or Isildur's heir) Dwarves seem to like descriptive or honorary names (e.g., Thorin Oakenshield, Dain Ironfoot). They are not lastnames though, since they do not get passed on to descendants. Elves don't have a need for lastnames, since elvish names are unique. Some nevertheless seem to have an additive (e.g., Legolas Greenleaf). Likewise, I can't find any usage of lastnames among Ents, Eagles, Istari, Orcs, trolls,...   But why would a society that is quite rural and not a leader of modernization be the only one to use a modern naming system with first- and lastnames?  *Except for Tom Bombandil. But he is, well, "special".


Hello all,   As you can see from this , I was in the test branch by mistake and the folder shajhanshi is happened to be my main directory.  Which command I should use to exit from that? I tried few commands but none of them worked. I'm a newbie in using git commands. Thank you.

Ok, after seeing , I have decided to skip to the end and go with .  So what I need is a beginner's practical guide to Git.  "Beginner" being defined as someone who knows how to handle their compiler, understands to some level what a  is, and has touched source control without understanding it very well.  "Practical" being defined as this person doesn't want to get into great detail regarding what Git is doing in the background, and doesn't even care (or know) that it's distributed.  Your answers might hint at the possibilities, but try to aim for the beginner that wants to keep a 'main' repository on a 'server' which is backed up and secure, and treat their local repository as merely a 'client' resource.  So:  Installation/Setup    How do you set up Git?  Try to cover Linux, Windows, Mac, think 'client/server' mindset.         Working with the code          How do you handle binary files (visio docs, for instance, or compiler environments)? How do you merge files changed at the "same time"?    Tagging, branching, releases, baselines    How do you pull a particular 'release'?   How do you resolve conflicts and complete the merge? How do you merge parts of one branch into another branch?        Other   Describe and link to a good GUI, IDE plugin, etc. that makes Git a non-command line resource, but please list its limitations as well as its good.    - Cross platform, included with Git  - Cross platform history viewer, included with Git  - Mac OS X  - Mac OS X history viewer  - Cross platform, commercial, beta  - console GUI for Linux  - GUI for Windows, Linux  - package for Windows, includes friendly GUI  Any other common tasks a beginner should know?     How do I work effectively with a subversion repository set as my source control source?   Other Git beginner's references                 Delving into Git     (and )    I will go through the entries from time to time and 'tidy' them up so they have a consistent look/feel and it's easy to scan the list - feel free to follow a simple "header - brief explanation - list of instructions - gotchas and extra info" template.  I'll also link to the entries from the bullet list above so it's easy to find them later.


The command:  grep -rl "KORD" ./   searches a directory and returns a list of files containing "KORD" in the file contents (not the title).  Users-MacBook-Air:myPhotorec user$ grep -rl "KORD" ./ .//output_apikey.txt .//recup_dir.17/f13470392.txt .//recup_dir.49/f45361992.txt .//recup_dir.49/f45362424.txt .//recup_dir.53/f48768408.txt .//recup_dir.53/f49295480.txt   Is there a preferred command(xargs?) that augment the grep command to print the output file list to the console and copy each file to the a directory: ./ORD ?   I suspect that there is more than one way to 'skin a cat': I am looking forward to seeing more than one solution  JOHN1024's XARGS Solution  The duplicate label prevents posting this modified posting as answer:  Try:  grep -rl --null --include '*.txt' KORD . | xargs -0r cp -t /path/to/dest   Because this command uses NUL-separation, it is safe for all file names including those with difficult names that include blanks, tabs, or even newlines.  The above requires GNU cp.  For BSD/OSX, try:  grep -rl --null --include '*.txt' KORD . | xargs -0 sh -c 'cp "$@" /path/to/dest' sh   How it works:   grep options and arguments   -r tells grep to search recursively through the directory structure. (On FreeBSD, -r will follow symlinks into directories.  This is not true of  either OS/X or recent versions of GNU grep.) --include '*.txt' tells grep to only return files whose names match the glob *.txt (including hidden ones like .foo.txt or .txt). -l tells grep to only return the names of matching files, not the match itself. --null tells grep to use NUL characters to separate the file names. LINUX/UNIX tells grep to look only for files whose contents include the regex LINUX/UNIX . search in the current directory. You can omit it in recent versions of GNU grep, but then you'd need to pass a -- option terminator to cp to guard against file names that start with -.  xargs options and arguments   -0 tells xargs to expect NUL-separated input. -r tells xargs not to run the command unless at least one file was found.  (This option is not needed on either BSD or OSX and is not compatible with OSX's xargs.) cp -t /path/to/dest copies the directories to the target directory.  (-t requires GNU cp.)

I have a collection of files ( *.zip, *.txt, *.tar.gz, *.doc, ...etc ). These files  reside within a path. I want to find all the files ( *.txt), then copy, only, the text files that contain specific words ( e.g LINUX/UNIX).  I ran the following:  find . -name "*.txt" | grep 'LINUX/UNIX'   This command was able to find all the text files, then "grep" filtered the resultant text files by listing only the text files that contain 'LINUX/UNIX'.   How can I copy these final files (i.e. the text files that contain 'LINUX/UNIX') to a specific path of choice?  I tried to apply xargs  find . -name "*.txt" | grep 'LINUX/UNIX' | xargs cp <to a path>   But it didn't work


On Puzzling, I noticed first that there wasn't an option to protect my own questions. I brought this up in chat, and other high-rep users replied that it has disappeared for them too. Not sure if this is just Puzzling, or site wide, but I have just under 16k rep and have had the privilege a while. It's odd it just disappeared. . EDIT: It's all questions, including 24 hour old ones with new user answers.  that has no protect option for me.

I've found a trend that I'd like to discuss. There are users that have reached 15K+ reputation that are participating in a question and then protecting it so that low reputation users can't answer. This wouldn't be a problem if the question was attracting poor, low quality or spam answers from these low reputation users. However, in these cases, that's not what's happening.  The  privilege has the following guideline:     Questions should be protected when they are garnering lots of views and newbies are adding "me too!", "thanks!" and possibly even spam non-answers.   Some recent examples to consider:     This Q&A are by the same user. There are no deleted answers on the question. (14 views)   This Q&A are by the same user. There is a second answer that is not the highest of quality, but the user has 200+ reputation and wouldn't be affected by the protection anyway. (23 views)  This question was protected by the author of the only answer. There are no competing answers. (36 views)  This question was protected by the author of the only answer. There are no competing answers. (37 views)  This question was protected by the author of the only answer. There are no competing answers. (50 views)  This question was protected by the author of the only answer. There are no competing answers. (64 views)  This question was protected by the author of the question (not the answer). There is only one answer. (140 views)   Proposal  I'd like to propose a couple small changes to how a user can protect a question:  The question should not be able to be protected if all of the following are true   Has less a low number of views. We use 100 views to determine when . I think 100 would work here too. None of the posts have garnered low quality or spam flags None of the answers have a score less than 0 The user protecting the question is a participant   If any of those criteria are no longer true, then the participants should be able to protect it normally. I worked with  to spot check the flags on the above posts. There are not any low quality or spam flags.  This means that the final question in my example would be able to be protected by both participants.  If you haven't answered the question, you would be able to protect a question as normal. The idea is that the author of the question or answers can't protect if if the other three criteria are true  Motivation  The idea is to prevent locking out low reputation users from these questions. They are not gathering the types of answers mentioned in the  that require a post to be protected. Instead, it looks like a conflict of interest. The user protecting the post is one of the users that can benefit the most from preventing competing answers.


I have a BDD Mysql (utf8_general_ci) with a table TypeIntervention In the table I have ID =1 nomI = dépannage I use the sql : $nom ='depannage'; $sql = "select * from TypeIntervention WHERE nomI = '$nom' limit 1"; $con->set_charset("utf8"); $result = mysqli_query($con, $sql); if($result->num_rows > 0) {    while($row = $result->fetch_assoc()) {     echo "found";    } } else {     echo("Not found"); }     // on ferme la connexion mysqli_close($con);  The echo is "Found" but it must be "Not found" because "depannage" is not equal to "dépannage". If I change $nom for "Test" the request tell me not found. In this case It's OK but why "dépannage" seems to be equal to "depannage" ???? Thanks for your help

I have a MySQL table with utf8 general ci collation. In the table, I can see two entries:  abad abád  I am using a query that looks like this:  SELECT *  FROM `words` WHERE `word` = 'abád'   The query result gives both words:  abad abád  Is there a way to indicate that I only want MySQL to find the accented word? I want the query to only return    abád    I have also tried this query:  SELECT *  FROM `words` WHERE BINARY `word` = 'abád'   It gives me no results. Thank you for the help.


I am trying to use \officialeuro symbol redefined as a unit for siunitx package. LaTeX seems to interpret the unit as letter instead of a symbol \documentclass{book}  \usepackage{eurosym}  \usepackage{siunitx} \DeclareSIUnit{\euro}{\officialeuro}  \begin{document}          $\SI{110}{\kilo\euro}$      \end{document}

I need to make this equation in LateX but I get some errors when i try to do that.    Can you help me please??


The "duplicate answer" flag is currently showing like this:     Duplicate answers: 17872778 – Community♦ 5 hours ago   The link isn't being coded properly.

Oy!  links are broken, on Stack Overflow at least:        Nothing clickable here.  Markup: Duplicate answers: &lt;a href=&#39;/a/17872807&#39;&gt;17872807&lt;/a&gt;


How can I check the version of the installed Apparmor on a Linux system?

I would like to know how to get the version information of an installed program that doesn't have the      --version or -version   method implemented.


I am trying to prove this. We are told that $(X,\mathcal{X},\mu)$ is a measure space, and $\mu(X)=1$. We are also told that $f$ is a bounded, measurable function on $X$.   So how can I prove that \begin{eqnarray} \lim\limits_{p\rightarrow +\infty }||f||_{L^p}=||f||_{L^\infty}. \end{eqnarray} Any help please?

Could someone help me prove that given a finite measure space $(X, \mathcal{M}, \sigma)$ and a measurable function $f:X\to\mathbb{R}$ in $L^\infty$ and some $L^q$, $\displaystyle\lim_{p\to\infty}\|f\|_p=\|f\|_\infty$?    I don't know where to start.


I am having issues with objects overlapping.   If I create a red rectangle in Illustrator, then copy it, and paste it directly on top of itself and change it to white, I get a red outline, even though the object is supposed to cover the other object behind.   Why is that? It's driving me nuts, please someone help me out :)

I made a couple of vector shapes in AI and I get this strange thin border appearing around them. I can't get rid of it. Any suggestions?    Zoomed in:


I need to convert an milliseconds into Days, Hours, Minutes Second.  ex: 5 Days, 4 hours, 13 minutes, 1 second.  Thanks

I need to convert an arbitrary amount of milliseconds into Days, Hours, Minutes Second.  For example: 10 Days, 5 hours, 13 minutes, 1 second.


I'm trying to generate a code as string in my android application and save it to a text file. When you press a Share button, the code should be read from the text file and be copied to the clipboard.  I guess I'm not understanding something about acivity/context. Of course I read in the documentation about it, but I can't figure out the problem. Hope you guys could help me!  FileSystem.java  package com.niclasjaksch.shoppinglist;  import android.content.Context;  import androidx.appcompat.app.AppCompatActivity;  import java.io.File; import java.io.FileInputStream; import java.io.FileOutputStream; import java.io.IOException;  class FileSystem extends AppCompatActivity {      static String filename = "shoppinglist_code.txt";      void Create() {         try {             FileOutputStream fOut = openFileOutput(filename, Context.MODE_PRIVATE);             String str = Utility.randomString(10);             fOut.write(str.getBytes());             fOut.close();         } catch (IOException e) {             e.printStackTrace();         }     }     String Read() {         String result = "";         try {             FileInputStream fin = openFileInput(filename);             int c;             while( (c = fin.read()) != -1){                 result += c;             }             fin.close();         } catch (Exception e) {             System.out.println("An error occurred.");             e.printStackTrace();         }         return result;     }     void Clear() {         try {             File dir = getFilesDir();             File file = new File(dir, filename);             file.delete();         } catch (Exception e) {             System.out.println("An error occurred.");             e.printStackTrace();         }     }  }   Share.java  package com.niclasjaksch.shoppinglist;  import android.content.ClipData;  import androidx.appcompat.app.AppCompatActivity;  class Share extends AppCompatActivity {      android.content.ClipboardManager clipboardManager = null;     FileSystem fs = new FileSystem();      void Share() {         String code = fs.Read();         if(code == "" || code == null) {             fs.Create();             code = fs.Read();         }         ClipData clipData = ClipData.newPlainText("Source Text", code);         clipboardManager.setPrimaryClip(clipData);     } }   MainActivity.java      ...      Share share = new Share();      ...      @Override     public boolean onOptionsItemSelected(@NonNull MenuItem item) {         switch (item.getItemId()) {             case R.id.item_share:                 share.Share();                 return true;             default:                 return super.onOptionsItemSelected(item);         }     }   Getting a NullPointerException in this line:  FileOutputStream fOut = openFileOutput(filename, Context.MODE_PRIVATE);

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


I encountered a fun formula that says $$e^{a \frac{d}{dx}}f(x)=f(x+a).$$ Now, I remember reading somewhere that this can be "used to solve delay differential equations". Take the simplest case, where $$x'(t)=x(t-1).$$  If you apply that exponential to both sides,   $$e^{ \frac{d}{dx}}x'(t)=x(t)$$  then it does look kind of close to a Laplace transform before integrating, so I can see the potential. But then, how do you actually solve for a solution with this?

I am not sure whether this question is even well-posed. But today I learnt that $e^Df(x) = f(x+1)$ where $D$ is differential operator and  $$e^D \triangleq \sum_{i=0}^{\infty} \frac{D^i}{i!}.$$  (ref. )  So I was curious as to whether the differential equation  $$\frac{df(t)}{dt} = e^Df(t) = f(t+1)$$  has any solutions apart from $f = 0$?


Instead of seeing:     (username) has approved 297 edit suggestions and rejected 121 edit suggestions and improved 21 edit suggestions   Can that be rephrased to this?     (username) has approved 297, rejected 121, and improved 21 edit suggestions   Or perhaps something better? The duplicated edit suggestions seems wordy and superfluous and redundant.  would naturally remove the common bits between elements joined by the coördinating conjunction, so the current wording sounds somewhat un-Englishy.  What are your thoughts? Or is this a pointless suggestion?

I've noticed that the reviewer stats in the review queue contain awkward uses of :        has approved $count edit suggestions and rejected $count edit suggestions and improved $count edit suggestions    This has always irked me but I never bothered to complain about it publicly til now. The wording should be changed to       has approved $count edit suggestions, rejected $count edit suggestions and improved $count edit suggestions    Or one of the better suggestions from   The discussion about whether there should be a  in the sentence is a separate one entirely, but I think it's unnatural and unreadable to string the ands together like they are.


Feeble minded noob here. My issue is with trying to map images to a set of faces. Each one appears white, despite the image appearing in texture and material viewport shading.  I understand I need an Image which is attached to a texture and then to a material?    Thanks guys.

I'm having some trouble while trying to render a scene; what happens is, when I render it in Cycles, everything in the picture is orange instead of its material. When I render it in Blender Render nothing shows up at all except for the sky background.  Orange room in Cycles:   When rendered in Internal Render:


I read that Frey's curve is a semi-stable elliptic curve. What doe this mean ? I can find two dimensional representations of $y^2 = x^3 + ax + b$ in Wikipedia. What does $y^2 = x(x-a)(x+b)$ look like if $a$ and $b$ are solutions to $FLT$ ?

How can I transform the elliptic curve $E/\mathbb{C}$ of the form $$y^2=4(x-e_1)(x-e_2)(x-e_3)$$ with $e_1>e_2>e_3\in\mathbb{R}$ roots of $E$ into a Weierstrass-Form $y^2=x^3+ax+b$?


I have two files. I want to exclude anything that is in file 2 from file 1.   Example)  File #1 - List of 500 domain names  domain1 domain2 domain3 etc..   File #2 - Alexa's Top 1,000,000 domain names  domain1 domain2 domain3 etc..   I would think this would work.  cat file1 | grep -v -f file2 > results   This always results in "Killed" for anything over 10k+ in file2.   /var/log/messages shows it runs out of memory. The box has 12GB RAM.  Aug 25 02:21:18 V-RHEL-EM kernel: Out of memory: Kill process 13779 (grep) score 860 or sacrifice child Aug 25 02:21:18 V-RHEL-EM kernel: Killed process 13779 (grep), UID 0, total-vm:9377064kB, anon-rss:7400368kB, file-rss:0kB, shmem-rss:0kB   Is there a better way to do this?

file_A (~500MB, 1.6M lines) consists of all equal length search terms, 1 per line, not sorted.  file_B consists of all equal length text lines, 1 per line, not sorted  I've been able to run "grep -F -f file_A file_B >> output.txt" with any size file_B without problem on a box with 52GB ram. Problem is I'm now limited to 4GB ram and thus the size of file_A is now too large for this to run without exhausting available memory.  Short of manually chopping up file_A into smaller bites, is there any easy way to script this to grep for first 1000 lines of file_A, then when thats finished to automatically grep for lines 1001-2000, ect. until I've gone through all of file_A?


Let the Given Number be 'K'. I need to store a,b numbers inside K. After some modification I need to get both numbers.

is there some way to create unique number from 2 positive integer numbers? Result must be unique even for these pairs: 2 and 30, 1 and 15, 4 and 60. In general, if I take 2 random numbers result must be unique(or with very high probability unique)  Thanks a lot  EDIT: calculation is for computer program,so computational complexity is important


is there a tool in blender that works similiar to how the looping tool in 3ds max works in which it will calculate my loop to auto clean my geometry. or make a curve i've been using loop tool addon however it it doesn't clean existing geometry just curves. It would be helpful if the tool also does like in max moves the edges to the center between the two existing edges. the tool that i'm looking for is set flow. if there are other tools like this in blender or a good addon to add similiar functions that would be helpful i dont want to spend hrs cleaning geometry if it can be sped up.      so if the geometry is screwy like this i need to clikc the loop flow a few times to get this thats what i am looking for

Is there a way in blender or an addon that allows me to select a bunch of faces (or verts) and evenly distributes (or relaxes) them into quads clean quads.  Without screwing up the vert ID/order.  Edit: I would like to have the shapes of my quads to turn into perfect squares while maintaining the volume of the object and the vertex order.


When there is a  for tag wiki, I can only either Accept it or Reject it.  But what if there is only slight thing to improve which I want to suggest, so I don't want to either Accept it or Reject it or Skip it?  I can't see Improve Edit option which normally appear for regular posts.  Is this something to be implemented in the future? Or this works deliberately like that?

I've been approving or rejecting Tag Wiki Excerpt Edit Suggestions, but some of them are close and I'd like to just tweak them.  We can improve regular edit suggestions, how about giving us an Improve button for Tag Wiki Edit Suggestions.  Note: If I click on the tag wiki excerpt link, then it takes me to a Tag Wiki page with an edit pending link, but clicking on that just takes me back to the first page, where I can only approve/reject.


Let $\triangle ABC$ be a acute triangle. Prove that: $$(\frac{1}{cosA}-1)(\frac{1}{cosB}-1)(\frac{1}{cosC}-1) \ge 1 $$ My attempt: $$\Leftrightarrow (1-cosA)(1-cosB)(1-cosC)\ge cosA.cosB.cosC$$ $$\Leftrightarrow 1-2cosA.cosB.cosC + cosA.cosB + cosB.cosC+cosA.cosC \ge cosA+cosB+cosC $$ $$\Leftrightarrow cos^2A+cos^2B+cos^2C + cosA.cosB + cosB.cosC+cosA.cosC \ge cosA+cosB+cosC $$ $$ 0<cos A,cos B,cosC<1$$ $$cos^2A+cos^2B+cos^2C=1-2cosA.cosB.cosC\ge 3\sqrt[3]{cosA.cosB.cosC}$$ $$\Rightarrow cosA.cosB.cosC \le \frac{1}{8}$$ And I was stuck here. Could you help me ?

If $A,B,C$ are angles of a triangle, find the extreme value of $\cos A\cos B\cos C$.   I have tried using $A+B+C=\pi$, and applying all and any trig formulas, also AM-GM, but nothing  helps.  On this topic we learned also about Cauchy inequality, but I have no experience with it.  The answer according to Mathematica is when $A=B=C=60$.  Any ideas?


When I type the password to log in nothing happens, the only thing that happens is something similar to a refresh (I'm using Ubuntu 14.04 LTS).  When I type in a wrong password it says that it's wrong, while when I type in the correct one nothing happens at all.

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


my web application is run at IE 7.  Now is it possible to run this web application in Ubuntu desktop using IE 7?

I am developing one site which has chat feature in Rails. I am using Ubuntu 12.04 LTS. I need to check that the site is IE9 because the chat feature using socket io of HTML5. I want to know that how to install IE9 in Ubuntu. I have looked at Chrome and Firefox extensions but if any standalone is available then please give me suggestion.


I need to read the numeric value of one line in a text file  color=7   so var color will = 7

I need to do an  request in JavaScript. What's the best way to do that?  I need to do this in a Mac OS X dashcode widget.


I am using MiKTex 2.9. I would like to include the 'Abbreviations' page in my contents page, along with the roman numeral page number. However when I use the \section{section name}command it gives the title a section number. And when I use \section*{section name}, the title does not appear in the contents page. I have also tried the suggestion from  but I get an 'undefined control error'.   Can you please advise? I have attached my MWE.       \documentclass[a4paper,11pt]{article} \usepackage{color} \usepackage{graphicx, epstopdf} \usepackage{gensymb} \usepackage{times} \usepackage{adjustbox} \usepackage{tabulary} \usepackage{tabularx} \usepackage{booktabs,caption, makecell} \usepackage{pdflscape,afterpage,caption} \usepackage[british]{babel} \usepackage[backend=bibtex, citestyle=ieee, bibstyle=ieee]{biblatex} \usepackage[section]{placeins}%Allows you to permanently fix figures.   \begin{document} \pagenumbering{roman} \newpage \tableofcontents \newpage \section*{Abbreviations} \begin{table}[ht] \setlength\tabcolsep{60pt} \centering   \small  % your table     \hspace*{-18mm}% \begin{tabular}{cc} \toprule {Abbreviation}&{Explanation}\\ [0.5ex] \midrule Item1&Item1\\ Item1&Item1\\ Item1&Item1\\ Item1&Item1\\ Item1&Item1\\ Item1&Item1\\ Item1&Item1\\ Item1&Item1\\ \bottomrule  \end{tabular}%     \hspace*{-12mm}% \label{table:ETD Raman} \end{table} \newpage \pagenumbering{arabic} \section{Test 1} Video provides a powerful way to help you prove your point. When you click Online Video, you can paste in the embed code for the video you want to add. You can also type a keyword to search online for the video that best fits your document.  \end{document}   Thanks in advance!

I'm using the report document class for a thesis, and I need to add things like "Acknowledgements" and an "Introduction". I noticed that there is an \abstract command which would have been wonderful if applied similarly. How do I add these without messing up the chapters' numbering while being picked up by the ToC in proper order and page numbering?


Quote from    "...The wavefunction evolves smoothly in time while isolated from other systems."  However, by the studying, my feeling was that all we need was for the wavefunction to be piecewise continuous, where the function itself assure the probability density and momentum to be continuous.  I.e. Finite square well boundary condition: Suppose a particle in finite square well where the function was bounded(no Dirac Delta Condition).  The the function was cut into $\psi_1$ from $(-\infty,-a]$, $\psi_2$ from $[-a,a]$, and $\psi_3$ from $[a,\infty)$.  When looking at the boundary condition at point $a$, traditionally they write $\psi_2(a)=\psi_3(a)$ and $\psi_2^\prime (a)=\psi_3^\prime(a)$.   I felt like function $\psi_2(a)$ and $\psi_3(a)$ didn't actually carry the meaning at $a$. Instead, since they $\psi_2$ and $\psi_3$ was already the eigenfunciton, the true condition required here ought to be $(\psi_2(a))^*\psi_2(a)=(\psi_3(a))^*\psi_3(a)$ and $(\psi_2^\prime(a))^*\psi_2^\prime (a)=(\psi_3^\prime(a))^*\psi_3^\prime(a)$.  Another example of step well we given:     Thus quote from Billy, in that case:" ontinuity of probability density implies continuity of wavefunction."  My question were:   Do we still need function itself to be continuous once we obtain the probability density and momentum to be continuous? (Notice the latter case was a weaker condition and, once it was satisfied, all operators and operations could be implied onto the function.)  In the specific case of step well momentum and probability density to be continuous meant $\Psi$ and $\partial_x \Psi$ to be continuous (1D case). However, was that true in general? (ask for proof)

Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention anything.


Note: This is not a duplicate of . The accepted answer there gives some answer to my question here, but the question is not a duplicate...   I'm currently brushing up on some algebra with "Abstract Algebra" by Grillet, Second Edition.  We consider, for a unital Ring $R$ and a family of sets $(X_i)_{i\in I}$ the polynomial ring  $$ R[(X_i)_{i\in I}] $$  I don't think the details of this construction are too important here; suffice it to say that we are dealing with the free $R$-algebra over the free commutative monoid of all monomials $$ X^k=\Pi_{i\in I}\, X^{k_i}\,,\; k \in \mathbb{N}^I\,, k_i = 0\, \text{ for almost all } i $$ with multiplication $X^k X^l = X^{k+l}$.  The degree of a polynomial $0 \neq A \in R[(X_i)_{i\in I}]$ with coefficients $a_k$ is defined as $$ \max\left\{\sum_{i \in I} k_i;\, k\in I^\mathbb{N}\,,\, k_i = 0\, \text{ for almost all } i\, \land \, a_k \neq 0\right\} $$  I generally put quite a lot of trust into textbooks as carefully written as this one, but the following statement on page 127 seems wrong to me and I am stuck trying to prove it:     Proposition 6.4. For all $A, B \neq 0$ in $R[(X_i)_{i\in I}]$:   ...   (4)  if $R$ has no zero divisors, then $\deg(\,AB\,) = \deg A + \deg B$   What I have proven is $\deg(\,AB\,) \leq \deg A + \deg B$, which was part (3) of the proposition.  However, part (4) baffles me. I started out expecting this to be easy but got stuck; and now I'm really a little too exhausted because I couldn't let go and kept on thinking about how to prove this. I'm actually wondering if this is actually wrong and was just a copy-paste error from the corresponding page 121 for the univariate case, where we have the exact same statement, safe for there only being one variable. A counterexample is probably not that hard, but I'm really too tired right now, and then I actually already got sidetracked just brushing up on basics required for my bachelor's thesis with this already, in the first place.  Why I feel like this isn't right: For $k \in I^\mathbb{N}$ with finite support, the $k$-th coefficient of $AB$ is  $$ (AB)_k = \sum_{(m,\,n) \in (I^\mathbb{N})^2;\,m + n = k} a_m b_n $$  where the $a_i, b_i$ are the coefficients of $A$, respectively $B$. In the univariate case, the degree formula holds if $R$ has no zero divisors, because the leading coefficient of the product is the product of the leading coefficients. However, in the multivariate case, each coefficient can be a sum of products:  Picking indices $\nu\,,\, \mu$ with $\sum_i \nu_i = \deg A$ and $\sum_i \mu_i = \deg B$, I don't see how $R$ having no zero divisors would lead to the coefficient $$ (AB)_{\nu + \mu} = \sum_{(m,\,n) \in (I^\mathbb{N})^2;\,m + n = \nu + \mu} a_m b_n $$ being nonzero, although it seems obvious that $AB \neq 0$ if we look at the $i$-degree $$ \max\left\{k_i;\, k\in I^\mathbb{N}\,,\, k_j = 0\, \text{ for almost all } j\, \land \, a_k \neq 0\right\} $$ for some $i \in I$ (should I be wrong with this reasoning, please tell me), so that $R[(X_i)_{i\in I}]$ is a domain, if $R$ is.  I also failed to find anything about this on good old Google or here.  So, am I right in assuming this part of the proposition quoted above is wrong?  I'm all out of creative mojo, so if someone could just plug me an easy counterexample, I'd be very, very happy... if the statement is actually true, I'd appreciate some help in proving it.

Let $R$ be an integral domain and $f,g\in R[X_1,...,X_n]$ where $n>1$. What is an example of a pair $f,g$ such that $\deg(fg)<\deg(f)+\deg(g)$?   Moreover, I have proven that the units of $R[X_1,...,X_n]$ are just the units in $R$. (Proof is done inductively) Is it true?  EDIT    Even though the each term in the underlined summation is nonzero, isn't it possible that the summation is 0? Why is this impossible ?


I have a Dell Inspiron 14r (N4110) with an Intel Core i3 and 4gb of ram. It runs very smoothly, however gaming on this laptop is very limited. This is mostly because of integrated graphics but i have seen a computer with a Core i5, and very similar specs otherwise, run games that the N4110 cannot. This other computer has integrated graphics and 6gb of ram.  I am wondering whether upgrading ram or upgrading the processor make the most difference in performance. Which setup would get better performance, an i5 with 4gb of ram or an i3 with 8 gb of ram? (Both with integrated graphics)  Also, is there a certain point at which you have too much ram for the computer to ever possibly use? For instance is there really any difference in performance between 8 gb and 16 gb of ram?

I have an IBM X31 with 1GB of RAM and a 1.4GHz proccessor running Windows 7 Home premium. Which would be more worthwhile to upgrade, the RAM to 2GB or the processor to a max of maybe 2GHz? Thanx in advance =)


i was wondering this question. Here's the picture about that. It is that little black dot in the center. As far as i have learned it is just for displaying the center of mass. It often draws my attention and i need to hide it.

Is there a way to hide the selected object's origin in the 3D view? By default all unselected object's origins do not show, but even after deselecting everything with A A it still shows the active object's origin. I know the Only Render checkbox will hide all the origins, but in this case it hides too much.