Problems in solving Number Theory problems (specifically Congruences)

I am very new to Number Theory, I understood the basic concepts and theorems but what I am struggling at is that I am not able to apply them on questions, and basically I am not able to process the problem in 'number theory' theorems rather I am thinking from an absolute manner. I have solved around 15-20 divisibility problems of Number Theory and I still have no idea how you deal with congruences in a real problem, for example: Prove that for positive integer $ n$ we have $169| 3^{3n+3}-26n-27$. My approach to this problem was by simplifying the expression as much as I can but it involved congruences, which didn't even strike me. Even when I am reading congruence questions' answers, I am not able to simply understand Now I have a number of questions:  first, does it take time to develop that 'intuition' while solving problems? second, can elementary number theory be mastered through sheer practice? third, is there a good resource to study and practice congruences?


$\sqrt{2+\sqrt{2+\sqrt{2+\dots}}}$   $\dots\sqrt{2+\sqrt{2+\sqrt{2}}}$  Why they are different?


I'm looking for a word that refers to someone subservient in an overly attentive or annoying way.


How to select areas from a target layer which do not intersect source layer?

I have two different layers, one is county boundary and another one is soil map.   My question is I would like to select only those areas which are outside the county boundary.   Using "Select by location" I can select every polygon located inside the county boundary but it is not what I need, I need only the unselected polygons.   What should I do?   I am using Arcmap 10.


Errors when calling functinos of template class [C++]

In the main.cpp I called the functions of VLA's object. If I put the code of VLA class into VLA.cpp and VLA.h, then I would get the problem upon when compiling, whatever using Clion, Terminal, Xcode... But I put all the code in main.cpp then it would be OK. I wonder just because I use template <typename T>? If I don't use template everything would be OK.


Lots of training data in cross validation -> overfitting?

So I've read conflicting information and am confused. I read that more relevant training data will decrease the variance of a model. However, I read about how in k-fold cross validation, if k is very large, and you train on k-1 of the folds, and test on 1 fold, then the variance will likely be really high, since the training size is huge. Which one of these is true?


Maximizing a linear function over an ellipsoid

Let $A \in \mathbb{R}^{n\times n}$ be a positive definite matrix, $x \in \mathbb{R}^n$ and $c \in \mathbb{R} \setminus \{0\}$. I got to determine the maximum  $$\max\{c^Ty:y\in \mathcal{E} (A,x)\}$$  where $\mathcal{E} (A,x)$ is an ellipsoid defined by $A$ and $x$.   How can I determine this maximum? Can anyone give me a hint?


Why is the period of rotation the same for two stars orbiting the same centre?

In a binary star system, two stars $A$ and $B$ follow circular orbits, of radius $R$ and $r$ respectively, centred on their common centre of mass $O$. The mass of star $A$ is $M$, and that of star $B$ is $m$. I am having trouble with the following problem:  Explain why the period of rotation of star $A$ is equal to the period of rotation of star $B$.   By using Kepler's Third Law, we know that $$r^3\propto T^2.$$ In this question, however, we want to show that they are the same. How should I approach this question? I only notice that the two stars are always on the straight line joining them and the centre $O$.


I found this questions from past year maths competition in my country, I've tried any possible way to find it, but it is just way too hard.  if $x, y$ are non-zero numbers satisfying $x^2 + xy + y^2 = 0$, find the value of $$\left(\frac{x}{x+y} \right)^{2007} + \left(\frac{y}{x+y} \right)^{2007}$$ (A). $2$ (B). $1$ (C). $0$ (D). $-1$ (E). $-2$  expanding it would give us $$ \frac { x^{2007} + y^{2007}} {(x+y)^{2007}}$$ how do I calculate this? Very appreciate for all of those who had helped me


Is there a way to book a two-way flight where the return flight is more than a year after departure?

I'd like to fly from Israel to Australia and to have the possibility of returning more than a year after the outgoing flight. So far the flight conditions I have checked only allow up to a year difference between the outgoing and the return flight, and even if I change the date of the return flight, I can only do this to a date which is up to a year after the outgoing flight.  Is there a way to do this without paying for two one-way flights?    The reason is that one-way flights tend to be around the same price as two-way flights and I will end up paying much more if I book two one-way flights.


Does the existence of graviton contradict gravity being spacetime curvature?

Is gravity a property-curvature of space-time it's self as descriped in GR?  Or the notion of 'graviton' is necessary in order  to embed the 'classical GR theory' to the quantum's mechanics 'world' because it is considered more fundamental?  Or they can be both valid as well, because there's no such contradiction?


Using the find utility within a simple function in .bashrc does not work. Why?

I'm using the latest arch kernel 5.7.12-arch1-1, the latest bash version 5.0.017-1 and the latest coreutils-8.32-1 which the find utility is a part of. I have the following code in my .bashrc to make easy work of finding files on the system. But I can't quite get it working. At the bash command prompt the following all produce the correct output, listing the correct files I wish to locate find . -iname '*driving*licence*part*' find . -iname '*driving*licence' find . -iname '*driving*' So why does f driving licence part f driving licence f driving using the below function not? Each if statement is parsing for the number of variables provided. function f () {            # find files            # update the files location database       sudo updatedb       if [ -n "$1" ] && [ -n "$2" ] && [ -n "$3" ]; then        find . -iname '*$1*$2*$3*'     fi      if [ -n "$1" ] && [ -n "$2" ]; then        find . -iname '*$1*$2*'     fi      if [ -n "$1" ]; then        find . -iname '*$1*'     fi   }


My Minecraft looks like this its supposed to be black and red carpet how do i  fix this i tried F4 and Fn but it just turns my computer screen off i also tried the 3d settings but it was already off,Restarting also isnt working.This is on 1.12.2 and its everywhere on my singleplayer and on my multi


I recieved a postdoc offer but I still have another postdoc interview. Should I accept or cancel?

This month, I have number of postdocs interviews planned. I just passed the first one and I did really good, the PI just send me an informal email telling me that I did really good and I should expect a decision tomorrow (I just got interviewed the day before). So, I'm expecting good news. Here's the issue, I still have an interview by the end of the month that I am looking for, and another one at a another university 4 weeks from now. For this last interview, I really like the research project they're working on and my strong skills are the essential skills they're looking for. So, I'm confident about this last interview. I don't want to decide anything until I pass these 3 interviews, but the committee in the first interview is moving way too quickly for me. So, I don't know what to do. On the scenario where I received an offer from the first interview tomorrow or early next week. Should I cancel the interviews that I am actually looking for? Is it acceptable to accept the offer and still have the other interviews? (You know where I'm going with this)


Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is   $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$  where $0\leq x\leq L $ and $L$ is length of the box.  So for $n>1$, probability density & hence probability of finding location of the electron at certain $x$ is $0$. The electron moves from left to right & right to left between the walls of the well. So Mathematics says that electron can not be found at certain $x$ node locations within the box; which is very strange. But is there any experimental evidence for this? While crossing these special $x$ node locations, as if electron disappears from the box. This is very absurd.  My question is: Is this a just mathematical result (without any reality) or a physical reality/actuality?


We have a  tag, which has no description. What types of questions is this tag meant to be used for?


Is Rational number under multiplication group?

A binary operation $*$ is defined on $\mathbb{Q}$ such that $a*b=ab$.  So, it is just simple multiplication.   I found out that this is a group with identity $=1$ and inverse is reciprocal of element "$a$" in $G$.  But, my answer key says that this is not a group because axiom 3 (inverse) fails.  I can't see why it is not a group.  Is my answer key wrong or am I wrong?


Semi positive definite matrix is always positive definite matrix

Can we say that a semi-positive definite matrix is always a positive definite matrix but not vice versa? If No, kindly explain.


Do I need an ESTA for a connecting flight to Mexico?

I'm flying to Mexico and I have a connecting flight over Philadelphia (e.g. Munich -> Philadelphia -> Cancun).  My stop in USA is about 4 hours, and I am not planning to leave the airport during that time.  Do I need an ESTA or visa?


I don't know how I've done this but I've created somehow a folder named "-p". Now I'm trying to delete it but my buntu is thinking I'm passing -p as a paremeter.  What can I do?  Ubuntu Server 15.


Uncountable sets of Hausdorff dimension zero

Let $A \subset \mathbb{R}$ be a countable set.  It is easy to see that $A$ has Hausdorff dimension $\dim_H(A) = 0$.  Do there exist uncountable sets $A \subset \mathbb{R}$ with $\dim_H(A) = 0$?


I have like 50000 records that meet my condition for batch processing. My batch process begins at say 10:01 AM and ends at 10:10 AM. I set my batch size to be 200.  Can someone tell me what would happen  a) If an user creates a record at 10:03 AM that meet my condition...will this record be also be processed or not ?  b) Will the records which are getting processed during Batch 1 are technically locked till that particular batch is processed completely ?  c) What will be the behaviour if a record in Batch N does not meet my condition anymore but that particular batch has already been started to process ?  d) Is it possible to create a parallel processing of sorts such that Salesforce (instead of running one batch at a time) it will start processing parallely with multiple batches ?  I searched online and I could find manual/instructions with respect to how to run batch apex but I am not able to get clarity with respect to these specific cases.


I have about 10million values that I need to put in some type of look up table, so I was wondering which would be more efficient a list or dict?  I know you can do something like this for both:  if something in dict_of_stuff:     pass   and  if something in list_of_stuff:     pass   My thought is the dict will be faster and more efficient.  Thanks for your help.  EDIT 1  Little more info on what I'm trying to do.  .  I'm making a look up table to see if a value calculated has all ready been calculated.   EDIT 2  Efficiency for look up.  EDIT 3  There are no values assosiated with the value...so would a set be better?


$\left\{e\right\}$ Closed Implies $T_0$ and Regular Topological Group

Let $G$ be a topological group with identity $e$ such that $\left\{e\right\}$ is closed. Then $G$ is $T_0$ and regular.   $G$ is trivially $T_0$.  Let $C\subset G$ be closed and $C\not\ni g\in G$. For every $h\in C$, I was able to find an open neighborhood $U_h\not\ni g$ of $h$. I am stuck trying to find an open neighborhood $U$ of $g$ disjoint from $\bigcup_{h\in C}U_h$.


I just (December 12, 2018) downloaded the training manual and data. I'm trying to get started but I cant find the first part to download the OpenStreetMap part.  "In the Vector menu dropdown, select OpenStreetMap -> Download Data. You can then manually enter the co-ordinates of the region you wish to use, or you can use an existing layer to set the co-ordinates."  I see the Vector menu on the top ribbon, but the dropdown does not have the right option. I cruised around but didn't see a way to add it.


How to change default draw color for all styles in tikzpicture?

Assume I have a tikzpicture with different draw objects such as lines, circles, rectangle, shapes etc.  When I do not specify a color the default draw color is black.  My question is: how can I change the default draw color (black) for all objects in TiKZ picture (scope) to something else. So it should not change outside tikz picture.  This allow me to quickly (visually) test replacing default black with something else.  Tx


Any solutions to Veritasium's hydrodynamic levitation?

So this Youtube video has been around for a while now  . Also this  may be related.  I just wanted to know if there is any standard hydrodynamic terms to explain it. Derek clearly states it is not about Bernoulli principle, as in this case the ball rotation is important.  Has any recent paper/videos discussed what happens if you do the same experiment with hydrophobic spheres? Can it be predicted with laminar flow theories or does it need turbulence?  Too many questions have been posed, but not so many responses on the internet yet.  Edit: I said Derek stated "it wasn't Coandă effect", yet what he says is that it is not "just Bernoulli's principle". Coandă effect is the typical hairdryer ping-pong ball levitation which is explained by Bernoulli's principle.   Edit2: rephrasing.  Additional comment: There seems to be two explanations "water adhere to the sphere and is ejected conserving horizontal momentum" and "Magnus effect" (ME). The later is not so obvious to me as the system is in equilibrium and there are two fluids, water and air, (does ME means air pushes the ball horizontally?).   Edit3: DESCRIPTION To avoid rot links and people that do not want to see the video, I'll try to explain the phenomena. You have a sphere and a water jet. The water jet is vertical (opposite to gravity), and touches the sphere almost tangentially. The ball not only rotates due to the water jet but also stays at constant height from the ground. The angular velocity can be defined in the direction of the cross product between the position of the contact point between the jet and the sphere (origin in the center of the sphere) and the direction of the jet. Some water drops fly away at the top of the sphere away from the jet.  Edit4: New question, would this phenomenon occur if there was no air?


I am trying to install Java 8 on Ubuntu. Due to restrictions on download at my work place, I cannot install using apt-get. Hence, I downloaded the archive from Oracle's website, named jdk-8u25-linux-x64.gz. However, when I extracted it, there was only a file inside it, named jdk-8u25-linux-x64. How to install using that file?


equirectangular rendering for Blender Internal?

Can such frames/videos be rendered in Blender Internal as well? If not, how indirectly?  EDIT: The below solution is great as long as you can write your own Python script and only render solid objects. When you need things like particles/hair, it won't work as those won't be reflected.


I accidentally got pregnant, is there a way to become unpregnant?

I am already at the population cap for my vault - 200 dwellers - but while I was switching dwellers around rooms, I left two very charismatic dwellers in their living quarters together for too long, and now one of them is pregnant.  Since I'm at the population cap, what happens? Presumably my dweller will remain permanently pregnant now?


How to prevent remote users from shutting down/rebooting the Windows?

Is it there any way to prevent remote users from shutting down/rebooting the Windows.  follows these steps:  Unfortunately, I cannot disable remote access to my computer. Is there a way to prevent this?


Let $a$ and $b$ be positive integers such that $ab + 1$ divides $a^2 + b^2$. Show that $(a^2 + b^2)/(ab + 1)$ is a perfect square.

Hi I have been working on this problem for a while and don't understand the solution given.  Here is the solution:  Suppose that $(a^2 + b^2)/(ab + 1) = k$ and we assume that there exists one or more solution to the given condition where k is not a perfect square. For a given value of k, let (A,B) be the solution to this equation that minimizes the value of A+B and WLOG, lets say that $A \ge B$. Let's look at the universe of solutions for (x,B).   $(a^2 + b^2)/(ab+1) = k$  $x^2 + B^2 = k(xB+1)$  $x^2 - kB(x) + (B^2 - k) = 0$   One root of the above equation is clearly A, and by vieta's formulas, the sum of the roots is $kb$ and the product of the roots is $b^2 - k$. Thus, the other root can be written as $c = (kb - A) = (b^2 - k)/A$. The left side of the equality means that the other root is an integer. Additionally, we know that this new root cannot be 0 because $b^2 = k$, and we assumed that k is not a perfect square. If $c < 0$, then $c^2 - kb(c) + (b^2 - k) \ge c^2 + k - b^2 - k > 0$.  The above inequality contradicts the fact that c has to be the root of the equation. Since we know that $A \ge B$, $c = (B^2 - k)/A < B^2/A < B < A$, thus implies that $c + B < A + B$.  Which contradicts the minimality of (A, B)  I don't get how they came to the left side of the equality means that the other root is an integer. I also don't get how they came to if $c < 0$, then $c^2 - kb(c) + (b^2 - k) \ge c^2 + k - b^2 - k > 0$. Why add the extra k's to $c^2 + k - b^2 - k$? And how does that inequality contradict c being a root?   Thanks!


Maximum Possible Elo Rating (in closed group)

I'm trying to determine if there is a theoretical maximum  rating one player could attain in a closed group of $N$ players (assuming for simplicity that they all start with some rating $c$, such that the total Elo of the system is always $Nc$), and if there is a maximum what that maximum is in terms of $N$ and $c$ (or even if it can be lower bounded in those terms). I believe it's easiest and potentially useful to think of the $N=2$ case first, and see whether there is a maximum difference in rating between two players which could be obtained through their playing successive games. Elo Background In an Elo system, each game scores such that the winner receives 1 point and the loser 0 points, with both players receiving 0.5 points for draws, and the change to a player's Elo rating is based on the difference between their actual score and their expected score, where expected score is calculated as a function of the involved players' relative Elo ratings. More precisely, given Elo ratings $R_A$ and $R_B$, the expected scores in a match between players $A$ and $B$ are given from: \begin{align} &E_A = \frac{1}{1+10^{(R_B-R_A)/400}} \in (0,1)\\  &E_B = \frac{1}{1+10^{(R_A-R_B)/400}} = 1- E_A \end{align} and, given that player $A$'s actual score is $S_A$, Elo ratings are updated (for some positive constant $k$) as: \begin{align} R_A' &= R_A + k(S_A-E_A) \\ R_B' &= R_B -k(S_A-E_A) \end{align} where generally $k=16$. Original Problem Assuming player $A$ wins the game with player $B$, we can express the rating difference after $A$'s victory $d' = R_A' -R_B'$ as a function of their initial rating difference $d = R_A - R_B$: \begin{align} d' &= R_A' -R_B' \\  &= R_A -R_B + 2k(1-E_A) \\ &= d + 2k(E_B) \\ &= d + \frac{2k}{1+10^{d/400}} \end{align} We could then express the difference in rating between players $A$, $B$ after $A$'s winning $n$ games with a recurrence relation: \begin{align} &d_0 = R_A - R_B \\ &d_n = d_{n-1} + \frac{2k}{1+10^{d_{n-1}/400}} \end{align} If $\lim_{n\to \infty}d_n=\infty$ for arbitrary $d_0$ then that would of course imply the maximum Elo score in any group of players is $\infty$. This seems unlikely given that the change between terms of this sequence approaches 0 as $n\to\infty$ (the winner starts to win essentially no Elo as the number of games goes to infinity), though I'm not sure if the Elo change actually approaches 0 fast enough for the series to be convergent. If the series does converge, however, it seems that if we could determine $\lim_{n\to \infty}d_n$ for particular $d_0$, then  we could use it iteratively to calculate the maximum possible Elo in a group of $N$ players with initial ratings $c$ through first calculating how much Elo some given player $A$ is able to pull off another player $B$ (by dividing the limiting term $d_\infty$  with $d_0=c-c=0$ by 2 and adding that amount to player $A$'s rating while subtracting it from $B$'s), and then repeating this for all pairs of players $A$, $B_i$. You could then continue to iteratively maximize among the remaining players $B_i$ into some player $B_j$, and extract from $B_j$ into $A$, but I'm not sure if this iterative process for increasing $A$'s rating would approach any particular limit in terms of $N$ and $c$. I also don't know how one would calculate $\lim_{n\to \infty}d_n$, so I'd would appreciate any help there or a nudge in a better direction if that is very nontrivial/if anyone sees an alternative way to a closed form solution for the maximum Elo rating given arbitrary $N$ and $c$.


Am I able to store games downloaded from PSN onto an external hard drive

I have an 80GB PS3 from 2009, and the hard drive is almost full. I recently got a PS4 as well, so I signed up to Playstation Plus but could not download and install any of the free games on my PS3 because there was no room on the HDD. I have an external HDD that is formatted to FAT32 that I can watch TV shows and Movies on through my PS3, but can I move my downloaded games onto the external HDD and install and play them from there. I also have other games that had to be installed, like GTA 5 and the Assassin's Creed heritage collection which take up heaps of room too.


Itemize without any type of bullets. Why?

I am trying to elaborate a list with bullets.  But, when I do it, the PDF file is with no bullets at all!  Why?  \RequirePackage{flashmovie} \documentclass[12pt]{beamer} \setbeamertemplate{footline} {   \leavevmode%   \hbox{%       \insertframenumber{} / \inserttotalframenumber\hspace*{2ex}     }   \vskip0pt% } \usepackage[backend=biber]{biblatex} \addbibresource{Presentacion.bib} \usepackage{tikz} \usepackage{ragged2e}  \usepackage{animate} \usepackage{gensymb} \usepackage{tabularx} \usepackage{amsmath,amsfonts, amssymb} \usepackage{cancel} \usepackage{mathtools} \usepackage[version=4]{mhchem} \usepackage{rotating} \usepackage[all]{xy} \usepackage{pdflscape} \usepackage{multirow} \usepackage{gensymb} \usepackage{chemfig} \usepackage{multicol} \usepackage[spanish]{babel} \usepackage{expl3} \usepackage{l3regex} \usepackage{enumitem} \usepackage{stackengine} \usecolortheme{seahorse} \usetheme{Goettingen}  \begin{document} \justify \begin{frame}   \titlepage \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   %%%%%%%%%%%%%%%%% \section{Balance} \subsection{reacciones} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{reacciones} %\begin{frame}{}[plain] \justify Las reacciones  \begin{itemize}     \item ds \end{itemize}  \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document}


How to use Greek letters (in a presentation)

I would like to include the following line from Wikipedia in a presentation:     στεγανός steganós ‚bedeckt‘ und γράφειν gráphein ‚schreiben‘   But I am unable to convince pdflatex to include the greek letters. I have already tried to use (from: )  \usepackage[german,greek]{babel} \usepackage[utf8]{inputenc} ... \latintext ... \textgreek{στεγανός} steganós ‚bedeckt‘   which printed the Latin text just fine, but the Greek text was not set at all. I would like to avoid using  $\sigma\tau\epsilon...$   if possible. I should also mention that I would like to achieve this with TeX Live-only packages.


If a character falls from a great height and has a skill or item that may save them if used early enough, how does one determine where in the fall the item is used? Depending on the reason for the fall, there may of course be some DC to avoid falling in the first place (usually a Reflex check against the DC of the trap that's opening up beneath you) but what I'd like to know is what happens once it's decided that the character is definitely going to fall.  For example, say I have some kind of teleportation effect that can get me back on solid ground, but the rules say that it doesn't affect my momentum, so if I'm falling at speed I'll still hit the ground hard when I emerge wherever I teleport to. So, this will only save me if I can do it fast enough - for D&D3.5e that's basically before I've fallen ten feet (or twenty if I can make a DC 15 Jump or Tumble check to negate damage from the first ten). How do we determine if I manage that? Can we assume I make it if the activation of the effect is fast enough? Is there another check? My instinct is that it'd be another Reflex check, but I'm not sure what the DC would be.


What justifies probability in the case of a onetime experiment?

If I have an "experiment", the results of which can be classified clearly into "outcomes" (like rolling a die), then I can make a concrete and verifiable empirical claim that "if you repeat this experiment many times, the frequency of this outcome will tend towards this number". This is what I mean when I say that the probability of something is such and such a number.  But then what is the meaning of the phrase "there is a 25% chance of rain tomorrow"? If I repeat the experiment of it being tomorrow many many times... what? It just doesn't make any sense, the definition of probability given above just doesn't apply.  To take an even more concrete example, let's say someone presents you a box containing one million black balls and one white. You get to take out one ball (and only one). If it's white, they give you a thousand dollars. Otherwise, you give them a thousand dollars. They're very stubborn and won't let you refuse to play unless you can give a satisfying philosophical explanation as to why you don't want to. What could you say?  Is there a name for this "paradox"? Is there a solution to it?


Tiny lifeforms on planetoid that live at accelerated time rate

A book I once owned and read back in late-80's or early-90's that I have not been able to identify title & author for:  It was a SF story concerning tiny native lifeforms, living on either a planetoid or possibly a dead/neutron star, that evolve at a seemingly accelerated time rate. Most of their story is told in the few days of observation (from orbit) by a human expedition to the planet, during which time-frame the race below progresses from stone-age tech level to being more advanced than the human observers, and eventually flying up to meet the humans in small advanced craft powered by micro-singularities... one of which accidentally 'disintegrates' the tip of a human scientist's nose in the process.


Angular velocity: $\omega = vr$ or $\omega = v/r$?

Which one is the formula of angular velocity? Is it $\omega= vr$? If not then why does the source below use $mvr=nh/2\pi$, where $mvr$ is angular momentum and $vr$ is angular velocity? Again $\omega=v/r$ shows radian per second. I saw $\omega= vr$ in one book and $\omega= v/r$ in another!


Distribution of Ratio of Exponential and Gamma random variable

A recent question () asked about the distribution of the ratio of two random variables, and the answer accepted there was a reference to Wikipedia which (in simplified and restated form) claims that if $X$ is a Gamma random variable with parameters $(n, 1)$ and $Y$ is an exponential random variable with parameter $1$, then $Y/X$ is a Pareto random variable with parameters $(1, n)$.  Presumably $X$ and $Y$ need to be independent for this result to hold.  But, Wikipedia's page on Pareto random variables doesn't seem to include a statement as to what $(1, n)$ means, though based on what it does says, a reasonable interpretation is that the Pareto random variable takes on values in $(1,\infty)$ and its complementary CDF decays away as $z^{-n}$.  My question is:  what is the intuitive explanation for the ratio $Y/X$ to have value $1$ or more?  It would seem that all positive values should occur, and indeed the event  $\{Y < X\}$ should have large probability since the Gamma random variable has larger mean than the exponential random variable.  I did work out the complementary CDF of $Y/X$ and got $(1+z)^{-n}$ for $z > 0$ which is not quite what Wikipedia claims.  Added Note:  Thanks to Sasha and Didier Piau for confirming my calculation that for $z > 0$,  $P\{Y/X > z\} = (1+z)^{-n}$ which of course implies that  $$P\{Y/X + 1 > z\} = P\{Y/X > z-1\} = (1 + z - 1)^{-n} = z^{-n}~ \text{for}~ z > 1$$ and thus it is $Y/X + 1$ which is a Pareto random variable, not $Y/X$ as claimed by Wikipedia.  This leads to a simple answer to  a  posed by S Huntsman:  Are there any (pairs) of simple distributions that give rise to a power law ratio?     If $W$ and $X$ are the $(n+1)$-th and $n$-th arrival times in a (homogeneous) Poisson process, then $W/X$ is a Pareto $(1,n)$ random variable:  $P\{W/X > a\} = a^{-n}$ for $a > 1$.   I suspect that this result is quite well known in the theory  of Poisson processes but I don't have a reference for it.


Why can't I see matcaps having pressed F12? I have them in the 3D View but the render shows just the "basic" material.


There was this question on one of the whiteboards at my company, and I found it intriguing. Maybe it's a dumb thing to ask. Maybe there is a simple answer that I couldn't see. Anyway, here it is:   Does there exist a non-trivial, monotonically increasing function such that $f'(x) = f(f(x))$ (in $\mathbb{R}$)?   I checked a bunch of functions, from elementary to special (gamma, digamma, zeta, Riemann, Lambert ...) and none seems to work (not surprisingly). I managed to convince myself that a function expressible as a power series would not work, regardless of convergence issues, because the derivative lowers the degree of polynomials, when the composition raises it. The Dirac delta or some sort of generalized function looked promising for a while, but the Dirac delta is not monotonically increasing anyway, and I'm not very familiar with generalized functions. I tried to use the Fourier transform on both sides, but it seems the Fourier transform is difficult for f(f(x)) (at least for me). I thought about somehow seeing "taking the derivative" as a differential operator, finding its (infinite) matrix in some basis (which one?), do the same thing to the RHS and show that the 2 matrices could not be identified (reducing the problem to a linear algebra problem) - that didn't work. Nothing on the geometric front either. I thought about trying to prove that there is no such function by deducing a contradiction, but didn't manage that. My hunch is that no such function exists, based on the completely invalid and semi-meaningless idea that differentiation pulls f in one direction, and composition in the other. Any idea?


setter method return self not work, it's a bug?

I want to iterate an array of strings, and assign each of them to a fresh instance of class User, and I expect that I will got an array of User objects:  class User   def name=(name)     @name = name     self   end end  original_array = ["aaa", "bbb", "bbb"] result = original_array.collect { |str| User.new.name = str }   but the result is an array of strings!  puts result.inspect            # => ["aaa", "bbb", "bbb"] puts result === original_array # => true   I have no idea of where I went wrong?


Electric field and potential in a point inside conductor for a particular case

Lets say we have an irregularly shaped conductor with a random cavity inside it and a charge +q outside the conductor. Now I have to find the potential inside the conductor due to induced charges on conductor and +q outside the conductor. Now from the property of conductors with cavity, the field due to outer surface charges and outer charges is 0 inside the conductor. Since there will be a field outside the conductor due to +q and induced charge in outersurface, we cant say that line integral of field due to these two till the surface is not 0 and hence potential is not 0. Due to which potential due to these two is also not zero inside the conductor. Am I right?


I was solving practice problems for my upcoming midterm and however I got stuck with this question type.  It is asking me to find all roots and then sketch it.  $(1+i\sqrt{3})^{1/2}$  How do we proceed?


So I'm considering updating to Yosemite, but I have a 2011, low end MBP, and Im a bit afraid that its going to be slow. If I do upgrade, is there anyway that I can revert back to mavericks? I've seen a bunch of things online, but that was only for the developer previews, which rely on the Mavericks installer still being on the app store, which I don't think it is.  Thanks.


I would like to know whether this is correct:  He uses a car instead of a bus. What does he use a car instead of?


Why were there no Interdictor-class Star Destroyers included in the taskforce hunting the rebels at the Battle of Hoth?

In the , the Imperial forces attempted to blockade any escaping rebel ships.    Clearly the idea of  at least some of the rebel ships wasn't completely off the table.  Yet notably absent from the taskforce was any representation of the .    Interdictors are designed specifically for capturing enemy vessels, employing gravity well projectors to prevent enemy ships from escaping into hyperspace.   They seemed to be a fairly common tool in the Imperial arsenal, at least by the time of  rise, and the Wookieepedia article indicates that Darth Vader used an Interdictor-class vessel as his command ship shortly after the Battle of Yavin.  If one had been present, the Ion cannon defense would not have helped the Rebels escape, and while the Millenium Falcon would likely still have managed to escape, an Interdictor-class ship would have seemed a very useful tool for Vader to have around.  Is there any canon explanation given as to why there was no Interdictor-class Star Destroyer present at Hoth?


Get free space of "C:" drive using batch file

I want to write a batch file which gives me free space left in C drive.


What is security testing? Please suggest how can I start. Any tools or any methods?

I want to learn security testing. To be candid I have just heard this term and never tried it. Is it beneficial for the product if security testing is done? How can I start? Do organizations value security testing and would it be another asset if added to my skill set?


Show $xy=yx$ for all $x\in H$ and $y\in K$

Given $H$ and $K$ are normal subgroups in $G$ such that $H \bigcap K=${$1_G$}  SHOW: $xy = yx$ for all $x \in H$ and $y \in K$  This is what I have so far:  $x \in H$ and $y \in K$  $\therefore g_{1}xg_{1}^{-1}=x$   and $g_{2}yg_{2}^{-1}=y$    for $g_{1}, g_{2} \in G$  $\therefore xy=g_{1}xg_{1}^{-1}g_{2}yg_{2}^{-1}$  $=g_{2}yg_{2}^{-1}g_{1}xg_{1}^{-1}$  $=yx$  is this correct?


How to write notation of "set of real numbers" in LaTex?

How to write this maths symbol below:    I search in , but it said \R and $\R$  but is not working.


What is it for? How do I use it? How is it different from the regular Command Prompt? Is there anything I should know before starting to use it? Any awesome things you can do with it that a super user should know about?


Using request_uri instead of Query string affects SEO

Out of curiosity only. If I used (see below)  https://www.example.com/index.php?blog/game/free-mmorg-review  will it affect SEO rankings? The above url clearly give a simple hierarchy of the web. So I was curious if I can use this.  I found some website using query string like (see below)  https://www.example.com/index.php?q=blog&category=game&id=free-mmorg-review  and it might generate duplicate if category and id swap the position. Just curious. I know it is pretty to use. (see below)  https://www.example.com/blog/game/free-mmorg-review   But will it be okay if I use this  https://www.example.com/index.php?blog/game/free-mmorg-review  or  https://www.example.com/?blog/game/free-mmorg-review  I found this simple server that serves php but it does not come with apache mod_rewrite so it's like running a php server directly and I can use (below) to produce somehow pretty url.  https://www.example.com/?blog/game/free-mmorg-review  Of course I will add some proper validation to make sure that /index.php?blog or /?blog will be the present.  I did some research about this but all I see is using a query string not like this. Is there a drawback using this http://www.example.com/index.php?blog/game/article_title


Why is a vector space with weak topology a topological vector space?

Proposition:Let X be a given vector space and Γ be the set of linear functional on X.Let X endowed with a weak topology with respect to Γ.Then X is a topological vector space.  What I need to show is (x,y)∈X×X→x+y is continuous and (α,x)∈C×X→αx is continuous.However,generally a weak topology assure only the continuity of each linear functions on X.So I don’t know how to show the proposition.Please give me a hint or answer.


How is the air pushed by the fan?  At first, the fan moved and the air did not move, then the air pressure increased.  The air pressure increases and the air starts to move.  Is my understanding correct?


How do I make Endermen spawn more frequently?

I'm playing vanilla Minecraft, and am getting ready to head to the end.  I need Eyes of Ender (and hence Ender Pearls), and in my main hunting grounds (a large desert area) as little as one Enderman may spawn per night.  Is there any way to "promote" Enderman spawning so I can get pearls more quickly?


Prove: The integer p-1 is a quadratic residue of an odd prime p if and only if p congruent 1 ( mod4).  That’s right?!


How to get current directory of main python file?

I am using argparse in a python file "hello.py"  I am executing this file using   python hello.py -infile "ex1.txt" -op1 "2"  ....   How to get which directory "hello.py" file is located? I know that os.path.dirname() can be used for infile, but how to know the same thing "hello.py"?


I received a task to find out whether the following series converges:  $$\sum_{x=1}^\infty\sin(x)$$  On first look it seems simple, but as I keep thinking about it, there's not a single lemma or criterion that I can use to tackle the problem.  D'alembert ? Doesn't work: The following is meaningless IMHO: $\lim\limits_{x \to \infty}{}\frac{\sin(x+1)}{\sin(x)}$  That series isn't monotonic... you can't understand the rules for when will a member of the series be negative or positive.  All I know is that $\sin(x)$ is blocked between (-1) and 1. Though it's easy to see that $ \sum\limits_{x=1}^\infty\lvert\sin(x) \rvert$ diverges.    May I use  for $\pi$ in order to construct  2 subseries:   One that shows that $\sin(x)$ converges to the limit 1 Another one that shows that $\sin(x)$ converges to the limit 0   And we know that a series can't converge to 2 different numbers, hence it diverges?


"Nobody want to go there," or "nobody wants to go there"?

In English, the number 0 is treated as plural. It is then:   0 seconds 1 second    1.2 seconds   2 seconds     Shouldn't it be "nobody want to go there," instead of "nobody wants to go there"?  I also saw in TOEFL that "any __" should be used with a singular.  But I see it very common that it is a plural also.  Why is that?  (updated: example, "we don't have any apples any more" vs "If you get any apple, please let me know.")


I need any app or any website by the help of that i can easily download the mp3 or video songs or movie from Youtube.com

Looking for a app for ubuntu 14.04  I need a app to download the songs and video from  youtube.com.  Is there any way to get the sign of download on youtube while watching any favourite songs or videoes?  In my friends computer the download option comes on youtube while watching any movie or song on youtube.com,  he was using Windows7. But I am using Ubuntu 14.04 LTS.  By clicking on download, he was able to download that songs from youtube directly?  I need a best app or website in Ubuntu to download the songs from youtube.com


I have many files in folder1 and I would like to move them to folder2. There are a small number of files already in folder2 (a hundred compared to several thousand in folder1) and I would like to move all files from folder1 to folder2 except when there is a file name conflict. (At that point I'll examine the remaining files individually and skip/modify/replace as needed.)  Is there a good way to do this? I'm on Windows 10 but I can use bash via MinGW if it's more convenient.  This is like  except that it involves thousands of files instead of a single file.


I was reading the new changes with Ubuntu 17.04 and one caught my eye which was moving from the typical swap partition model to a new swap file model for new installs.   Are there benefits for using this as opposed to a swap partition, maybe related to or in terms of performance, space saving, more in line with today's hardware like SSD and NVMe or something else?  Another related question is how can I migrate from a swap partition to a swap file? I'm guessing using dd but want to confirm since I did not know about the swap file scheme until now.  And lastly, will hibernation be an issue with swap files?  Of course these questions might be related to cases where the user has a lot of RAM and the swap is rarely used (I'm guessing). So just to confirm that this information will help me and others with the same doubts.


What happens if we try to integrate a function like $\frac{1}{z}$ over the circle radius one centered at one, since the function is holomorphic in the interior, but at the point on the contour $z=0$, the function does not exist.  What about the general case of a function being holomorphic on a circular domain and we take the contour integral on the boundary. How do we do it?


About Abstract Class constructor in Java

I have question about if I could call a constructor in another constructor in abstract class. For example,  public abstract class Sth{   protected Sth(){}   protected Sth(int number){}   protected Sth(String word){     int number = 0;     this(number);   }   It seems that Java does not allow me to do this. I wondered if there is any way we could let this happen? Thanks  -----------------------------------------------Explanation---------------------------------------------------------------------- The goal I want to do is to call the second constructor specifically. I got error with must calling the first constructor in Java. So I wondered if we can just skip first constructor without remove any code here. Sorry for the confusion.


Single Column Appendix in twocolumn article

My article uses the twocolumn parameter of the article document class. However I want to list my images as a multipage appendix at the end of the document (in a new page) but I want a single column appendix so that I can center my figures properly.   I have tried to use the minipage environment inside \twocolumn [  ] but it does not seem to work. Take a look at the code:  %document body, packages etc. \newpage  \section*{Appendix} \begin{center} \begin{minipage}[c]{\textwidth}  \begin{figure}     \includegraphics[width=\columnwidth]{curve1}   \caption{An arbitrary initial poinset $\mathbb{S}^2$.}     \label{curve1} \end{figure} %figure curve 1    \end{minipage}   \end{center} \end{document}   For instance, the figure does not appear to be rendered and the error which is returned by the compiler is:  Not in outer par mode


How can I download Mavericks from Yosemite?

Does anyone know how to download Mavericks from Yosemite?  I'm trying to get the image to put on a different computer but it won't let me download it from the App Store.  I click "download" and it says "OS X 10.10 is already installed on this computer.  Are you sure you want to download OS X 10.9?".  I click "OK" and it does absolutely nothing.  [edit]  Solution for anyone looking for it:   Same thing works here.   Open App Store Modify /System/Library/CoreServices/SystemVersion.plist and set 10.10 to 10.8 Start Download Revert modifications


A world position pass is a pass used for composting other elements into the scene after the initial render. In a world position pass the R, G, B values correspond to the X, Y, Z axis (or X, Z, Y). A world position pass could look something like this. (Image form another 3d app)    Is there a way to render out corresponding world space coordinates of each pixel?


I want to combine a multiple row and a column table in LaTeX format yet I'm not able to do.  Here is what I want in latex template.    Can anyone help me with this? Thank you.


How does one choose which articles to cite for a very broad sentence?

For example, take the sentence: "Gaussians are widely used in mathematics & statistics". At this point there probably tens of thousands of papers that use Gaussian functions in some way (that's not even counting the papers in other fields like the social sciences that make use of Gaussians). It's impractical to cite them all. The sentence still calls for at least some citations though. How does one choose which papers to cite?


Why does parseInt() in map() only work for first item in an array?

Output from Node.js repl:  > ["1", "2"].map(i => parseInt(i)); // correct [ 1, 2 ] > ["1", "2"].map(i => i); // correct [ '1', '2' ] > ["1", "2"].map(parseInt); // what is causing the NaN? [ 1, NaN ]   Should not the last result be [1, 2]?  Version:  $ node --version v6.9.1


What are all the homomorphisms between the rings $\mathbb{Z}_{18}$ and $\mathbb{Z}_{15}$?

Any homomorphism $φ$ between the rings $\mathbb{Z}_{18}$ and $\mathbb{Z}_{15}$ is completely defined by $φ(1)$. So from  $$0 = φ(0) = φ(18) = φ(18 \cdot 1) = 18 \cdot φ(1) = 15 \cdot φ(1) + 3 \cdot φ(1) = 3 \cdot φ(1)$$  we get that $φ(1)$ is either $5$ or $10$. But how can I prove or disprove that these two are valid homomorphisms?


Combine multiple rows from other table into 1 column in mysql


As a general case, Where can I find scripts/screenplays/transcripts of movies and TV shows?


ConcurrentModification Exception while Iterating

I have looked at other questions that deal with similar problems, but it seems that this particular case is rather unique.  The code below is supposed to go through a list of Events and put them in a map if their times overlap.  // identify events that occur at the same time List<Event> remainingEvents = new LinkedList<>(); remainingEvents = Event.getAllEvents();  for (Event event1 : Event.getAllEvents()) {     for (Event event2 : remainingEvents) {          // check if it is the same event         if (event1 == event2)             continue;          // check whether they overlap         if (event1.overlapsWith(event2)) {             simultEvents.put(event1, event2);         }     }      // event1 is now exhausted     remainingEvents.remove(event1); }   Notice that I am modifying the remainingEvents list after the iteration is complete, not during. Therefore, I do  not understand why I am getting a ConccurentModificationException.   Elipse also tells me that the error occurs on this line:   for (Event event1 : Event.getAllEvents()) {   which makes no sense since I am not modifying anything relating to it.  Note that this is not a duplicate because I am not modifying the list until I am done Iterating with it (unlike other questions), and the error occurs on a line that has nothing to do with the removal


I've been active in SO for about 3 months and i was wondering why sometimes SO show those top 5% this month and others top 2% this quarter.      My questions are:   How SO decide to show monthly, quarterly, etc. Which one is better to show? (if there is any) Are this rank links showed to every user with enough rep? If so, how much rep is "enough"?


I'd like to move my .bash_profile to Dropbox to have my custom Terminal functions available on all my Macs. Is this possible and are there possible implications?  For example I have a command for doing a git add and commit in one go:  function gax() {     git add .     git commit -m "$1" }   I've been unable to find any information about this.


sudo startx and not able to log in anymore

I did sudo startx then lost the left side bar and wasn't able to do anything. Therfore I shut down my computer, started it and discovered I wasn't able to log to my session anymore... Have anyone an idea of what's going on and how to cope with?


How to show that for sequence $x_1=2$, and $x_{n+1}=\frac12\big(x_n+\frac2{x_n}\big)$; for all $n$, $(x_n)^2>2$?

How to show that for sequence $x_1=2$, and $x_{n+1}=\frac12\big(x_n+\frac2{x_n}\big)$; for all $n$, $(x_n)^2>2$ ?   I tried using induction: let  $(x_k)^2>2$, so $(x_{k+1})^2=\frac14\big(x_k^2+\frac4{x_k^2}+4\big)>\frac32+\frac1{x_k^2}$. I can't go further!


I know a lot of female programmers, and I know there are a good number of them out there.  But I don't recall ever having one of my questions answered by, nor have I ever answered a question by a female programmer here at Stack Overflow.  Now I mostly deal in the Delphi tag, and that may make a difference. But I've got the feeling there is something about the programming social network that Stack Overflow is, along with its form of mini-competition (via reputation) that turns most ladies off.  When I go down the first few pages of top users by rep, there is nary a lady to be found.  Go over to Quantcast and . Go down to the Demographics, and you'll see that a full 20% of the visits are by females. So they are here, lurking and using the wonderful info that Stack Overflow provides.  Then why aren't there more of them participating, both with questions and answers?  What can Stack Overflow do to persuade female programmers to participate more?    So after a dozen downvotes offset by a dozen upvotes, and accusations by many that I am a bigot, the bottom line seems to be that Stack Overflow appeals to males more than females.  This is my observation and I believe a proper analysis would support the hypotheses that a much higher percentage of male programmers use Stack Overflow than the percentage of female programmers.    Assuming that is the case, then Stack Overflow is geared more towards the male psyche than the female. If so, I again ask, what can they do about that?      This question was asked in StackOverflow Meta on November 20, 2009. It was made Community Wiki. It was asked in a constructive manner and should be considered an appropriate question for Meta.   Yet it was closed over two years after it was asked as "not constructive" after more than 40 upvotes and 10 favorites and 16 answers.   Now it resides here on Meta StackExchange, still closed. I just shake my head.


Automatic Saving for Highly Rated but Closed or Deleted Questions?

We all come through Google to questions like "Which is better Matlab or OpenCV?" or "What are the best resources for learning ?"  These questions tend to be closed, sometimes marked for deletion, be primary opinion based, have hundreds of upvotes, and be really useful.  It would be good if these were always available, perhaps though automatic migration to another StackExchange instead of deletion.  While the knowledge is not in the StackOverflow form, it is knowledge none the less.  Is there any consistent attempt to save this knowledge?


I need your help. My postfix is sending spam mails. I checked my main.cf and it should be fine. In the following a snippet of my mail.log Jan  3 22:35:41 mail postfix/pickup[104179]: 866352963F01: uid=33 from=<web424794656434@mydomain.net> Jan  3 22:35:41 mail postfix/cleanup[104027]: 866352963F01: message-id=<06760aed1118c62b0c4fb17967316e92@www.mydomain.net> Jan  3 22:35:41 mail opendkim[3895]: 866352963F01: DKIM-Signature field added (s=key1, d=mydomain.net) Jan  3 22:35:41 mail postfix/qmgr[27451]: 866352963F01: from=<web424794656434@mydomain.net>, size=6867, nrcpt=1 (queue active)   Any clue what happen? Thanks in advance!


Changes to $PATH won't save after closing the terminal session

I downloaded the latest version of Scala and saved it to /opt folder. Then I tried to add /opt/scala-2.11.2/bin to the PATH in order to have easier access to commands like scala and scalac. After executing the command :  export PATH=$PATH:/opt/scala-2.11.2/bin/   and then :  echo $PATH   I see the path in there. At that time I can also use the commands scala and scalac.   Then if I close the terminal and restart  , the path /opt/scala-2.11.2/bin/ is not in echo $PATH anymore. And thus I can not execute the commands . What is my problem ?


Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+...+a_n)^2 $

I recently encountered the following problem: If $\sum a_n^2 $ converges and $\alpha_n= \frac{a_1+...+a_n}{n}$ then show that:  $$4\sum_{n \ge 1} a_n^2 \ge \sum_{n \ge 1} \alpha_n^2$$  I had an approach which i did not manage to utilize, so i am asking if anyone has an idea if it can be used or not:   We note that the right hand side will be maximized if $a_i$ are all of the same sign. Without Loss of Generality, suppose that $a_i \ge 0$. If we use (1.), another way to maximize the right hand side would be if $a_i \ge a_{j}$ for all $i>j$. Let us also suppose that this is true.   And i stop there, i tried many approaches but nothing seemed to work. I thank you in advance for any hint and/or a complete solution.  Supplementary question: Can we construct a similar problem for integrals (instead of series)?


I got Solstice for a comment on the 22nd?

I just got the Solstice Winterbash hat here on Meta Stack Exchange. Checking my activity, I have not posted or commented yesterday (the 21st). I do, however, have an upvoted comment today. That comment was posted on the 22nd in UTC.  I'm happy to have gotten Solstice here, but it wasn't really deserved. Is this a bug, or is Stack Exchange being generous?


How do you say "which each" or "who each"?

I speak in Persian, sometimes as I translate a sentence from my native language to English, I doubt if its structure is correct.  I want to say (for example)  "I have some children who each have a responsibility".  "There are some objects which each does something"..  Are they grammatical sentences? what should I say instead?


Two years ago, when I was a super beginner to logic, my logic teacher, who is famous in our Country, told me that $1+1=2$ is not a tautology, but a logical truth. However, after reading some truly rigorous logic books(not mathematical logic books yet), I think that $1+1=2$ is neither a tautology, nor a logical truth; my teacher was wrong.  What I think is that $1+1=2$ is followed by the axioms of natural numbers or real numbers. It may be transfered to a predicate logic sentence like $f(a,a)=b$, so it is not automatically true under every model. Instead, $1+1=2$ is a logical consequence of the axioms of numbers, only the models that satifies the axioms of numbers will satisfy $1+1=2$. Am I right? Or is there somewhere I should revise?


I installed Ubuntu on a disk partition just two days ago and everything work like a charm. The only problem I'm having is with the screen temperature color. In Windows I use f.lux and I set the color temperature as red as possible (3500K) all-day-long. I want to do the same in Ubuntu but I faced many issues:   f.lux doesn't change the color at all Redshift changes the temperature for a couple of seconds, then it suddenly goes back to the normal color GNOME Night Light has the same problem of Redshift: the change is not permanent although I set the color temperature to be 3500K from 5AM to 3AM   Is anyone having the same problem? How can I fix it?    System info:   Ubuntu 18.04.1 LTS GNOME 3.28.2 External monitor HP 24" 60,00 Hz


I'd like to combine the split and miniframes themes of beamer. For example, I would have the miniframes appear in the right half of the title bar (where the subsections appear). If there are any subsections, I'd have the miniframes below or next to the subsection title. This is a sample document.  \documentclass[compress,aspectratio=43]{beamer}  \useoutertheme{miniframes} \useoutertheme{split} %\setbeamertemplate{headline}[miniframes theme] \usecolortheme{whale}  \begin{document}  \section{First Section} \frame{} \frame{} \frame{}  \section{Second Section}  \subsection{sub1} \frame{} \frame{} \frame{}  \subsection{sub2} \frame{} \frame{} \frame{}  \end{document}   I won't ask if it's possible, because everything is possible with TeX, but rather whether someone can help me :)  To show what I mean, these are the headlines with miniframes:    These are with split:    And I want something like this mockup:


Who is doing the normalization of wave function in the time evolution of wave function?

In the Schrödinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations simultaneously. Why not? I know it does not yield, but I am always baffled, who is doing the normalization of the wave function? Observers, the system, the measuring process, God?


Why is log-of-sum-of-exponentials $f(x)=\log\left(\sum_{i=1}^n e^ {x_i}\right)$ a convex function for $x \in\mathbb R^n$?

How to prove $f(x)=\log\left(\displaystyle\sum_{i=1}^n e^{x_i}\right)$ is a convex function?  EDIT1: for above function $f(x)$, following inequalities hold:  $$\max\{x_1,x_2,\ldots,x_n\}\leqslant f(x)\leqslant\max\{x_1,x_2,\ldots,x_n\}+\log n$$  and I have tried proving its convexity via definition of a convex function with above inequalities, but that didn't work.  EDIT2: I have posted my answers below.


How do I find the Logistic Distribution for a Logit Regression in R

As far as I am aware, R gives the output of a logit model, of the form: glm.logit=glm(model,binomial(),Data.df)  as the log-odds ratio. I would like to obtain the distributional function $\frac{exp(\beta'x_i)}{1+exp(\beta'x_i)}$ from my model


A word meaning someone who can speak well to influence people

I am looking for an adjective/noun for someone who is able to speak/ makes speeches very well and uses words effectively to influence/impress people.


How to keep a unique data for all the classes/instances using it?

Many had explained the use of static in Python but one point seems not got emphasized. In several other major languages static also means a static datum is a unique(only) copy in the scope. I am coding some astronomical objects that use large VSOP87 data sets. However all the class/derived class or the instances of classes will use only a particular set of the data. In C++/Java/C# using static for those data can easily fulfill the purpose. For instance in C++/C#/Java, the code will almost looks like below:  public class Earth { ..... static earthVSOP87XYZ[][] = {.....}; // in a very large size }   All the Earth's instances share the only copy of earthVSOP87XYZ and the data are well encapsulated. Is there any way in Python 3 to achieve the same result?


How to make text in a cell in lightning-datatable clickable ? Not entire column

I have requirement to make text in a cell in a column clickable based on condition in lightning-datatable For example:  N/A should be plain text but next one should be clickable with just label S-00001000


How to make a multi emitter BJT transistor?

Im trying to create the 74XX series IC's from scratch, using just transistors, resistors and diodes. I intend to chain them together and create some logic systems. Right now i'm trying to create a basic NAND gate but i can't find any transistors with at least two emitters. Why? Can i just take two transistors and solder together first the bases and then the collectors? Or maybe create it from diodes?  What i want to know is where can i obtain such a transistor or how to make one. I know how it works and where its used.  Here is an image of a NAND TTL gate:


Cause of centripetal acceleration in a ring

Suppose a ring is rotating in space with an angular velocity $\omega .$ Then each element of the ring is having an acceleration of $m\omega^2 r$ ($r$ is the radius of the ring) but what force is causing this acceleration in each element? The acceleration is inward so the force should also be inward but there is nothing to provide this force . The neighbouring elements can only provide a tangential force on a particular element, this force will not have any component along the radius so this can not be the reason for the centripetal acceleration. So how are the elements accelerating and moving with a constant angular velocity ?


Why is the covariant derivative of the stress-energy-momentum tensor zero?

I have read somewhere that the covariant derivative of the stress-energy-momentum tensor is zero and this is one of the key features in formulating the field equations. Is there a proof for this assumption? Could you explain?


"He gritted his teeth."   I can't tell if gritted is correct because both gritted and grit don't sound right to me in this sentence.  The dictionary says that both grit and gritted are the past tense. (Nowhere does it say 'grot' btw)  In the grit vs gritted they're asking which one is correct when they both technically are and the answers for it aren't useful to me, plus I am asking how it fits in t h i s sentence because I know grit can fit into other sentences, but I wasn't sure if it would fit in mine.


Third grade spiral in TikZ - dimension too large

I'm trying to draw a smooth third grade spiral (r^3 = a^3\cdot \varphi) over $60\times 60$mm grid and I'm getting the "Dimension too large"-error if I set $a > 320$ but I need to fill the grid area completely:  \begin{tikzpicture}[x=1mm, y=1mm]      \draw[step=1, line width=0.1mm, opacity=0.3] (-30, -30) grid (30, 30);      \draw [domain=0:50, variable=\t, samples=1000]          plot ({\t r}:{pow(320*\t, 1/3)}); \end{tikzpicture}     Is there any way to avoid this error?


PHP have string 200 characters long and then cut off at last white space

I am working on this piece of code that will take my string and make it 200 characters long and then after that remove the last white space so my string will look like this 'This is my' instead of 'This is my stri'  This is what I got thus far:  $description = substr($value['description'], 0, 200);   and now I want it to remove the last white space in the string. After googleing it, all I found was the php trim function, but nothing about removing the last one, just all..  any tips?


Confusion with how partial fractions work

I have trouble with the logic behind Partial Fractions, which I will elaborate about here. I have two problems with it.  Firstly, why, if I have a polynomial like  $$f(x)= \frac{3}{(x+4)^2(x+3)}$$  That when I decompose it I get something like:  $$\frac{3}{(x+4)^2(x+3)} = \frac{A}{x+4} + \frac{B}{(x+4)^2} + \frac{C}{x+3}$$  But why do I have an $x+4$ and a $(x+4)^2$ when there's only a $(x+4)^2$ and $x+3$ in the denominator? It seems like there is a lack of equivalence here, like we are breaking a conservation law here.  For instance, if it were like  $$\frac{3}{(x+3)(3x+4)}$$  We would have, more intuitively in my opinion:  $$\frac{3}{(x+3)(3x+4)} = \frac{A}{x+3} + \frac{B}{3x+4}$$  Which makes me feel like the logical proceed of the above example, and applying it to the first would be this:  $$\frac{3}{(x+4)^2(x+3)} = \frac{A}{(x+4)^2} + \frac{B}{x+3}$$  Okay, secondly:  Why, when we're dealing with a term of the form $(x^2 + C)$ where $C$ is some constant, its partial fraction decomposition is of the form $Ax + B$ in the numerator, like in the following example:  $$\frac{4}{(x-4)^2(x^2+3)} = \frac{A}{x-4} + \frac{B}{(x-4)^2} + \frac{Cx + D}{x^2+3}$$  I'm not sure what clues one in to doing that?


this are the similar post that i post on    i got this wire-face problem     and i think the problem solved  it is a camera clipping for sure.  thank you coco knight, mr  Zak, rick riggs.  thank you all of you guys.  thank you


$(S_0+\ldots + S_n)_{n\geq 0}$ not a Markov chain

Assume that $Y_0,\ldots , Y_n$ are independent random variables with the following identical distribution: $Y_i=1$ with propability $p$ and $Y_i=0$ with propability $1-p$. Also set $S_0=0$ and $S_n=Y_0+\ldots + Y_n$.  It's quite trivial that $(Y_n)_{n\geq 0}$ is a Markov chain, and I managed to show that $(X_n)=(S_n)_{n\geq 0}$ is also a Markov chain, by showing that  $\mathbb{P}(X_{n+1}=i_{n+1}\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(X_{n+1}-X_n=i_{n+1}-X_n\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(Y_{n+1}=i_{n+1}-X_n\,|\,X_0=i_0,\ldots,X_n=i_n)=\mathbb{P}(Y_{n+1}=i_{n+1}-i_n)=\mathbb{P}(Y_{n+1}+i_n=i_{n+1})=\mathbb{P}(X_{n+1}=i_{n+1}\,|\,X_n=i_n)$  However I am now running into the problem that I have to find whether or not $(X_n)=(S_0+\ldots + S_n)_{n\geq 0}$ is a Markov chain. I suspect that it isn't, but i'm having trouble finding a counterexample. I also need to find if $(X_n)=(S_n, S_0+\ldots+S_n)$ is a Markov chain, but I think this actually might be one, since $X_n$ gives "more information" (so to speak) to $X_(n+1)$. Again, having trouble actually proving that.  I appreciate any help, tips etc you can give me.


Use first argument as second argument with modifications

In bash I am considering the log: atop_20210228 Is there a way to: mv atop_20210228 $FIRSTARGUMENT.bkup So that I would be moving atop_20210228 but just appending .bkup to the end?


Let be $(x_n)$ a sequence defined by $x_1=1$ and $x_{n+1}=\frac{1}{2}(x_n+\frac{2}{x_n})$.  $(x_n)$ is increasing or decreasing? I do not know if $(x_n)$ is bounded. I would like to know if $(x_n)$ is convergent. Any suggestions?


I had seen many answers to install MySQL. I had tried everything. It shows: There's no MySQL already installed Unable to locate package MySQL-server For synaptic, there's no keyword found Unable to connect to 172.17.0.1:3128 if I try update.  Am sick of all the errors.  Can anyone guide me from the beginning to install MySQL ?? Please asap since it's urgent ! :) Thanks in advance !


Unmet dependencies for packages required to compile FFmpeg

I tried following the instructions from "How to compile FFmpeg for Ubuntu" at . These are: sudo apt-get update -qq && sudo apt-get -y install \   autoconf \   automake \   build-essential \   cmake \   git-core \   libass-dev \   libfreetype6-dev \   libgnutls28-dev \   libsdl2-dev \   libtool \   libva-dev \   libvdpau-dev \   libvorbis-dev \   libxcb1-dev \   libxcb-shm0-dev \   libxcb-xfixes0-dev \   pkg-config \   texinfo \   wget \   yasm \   zlib1g-dev  However, I get: The following packages have unmet dependencies.  libsdl2-dev : Depends: libsdl2-2.0-0 (= 2.0.8+dfsg1-1ubuntu1.18.04.4) but 2.0.9+dfsg1-1ubuntu1 is to be installed E: Unable to correct problems, you have held broken packages.


Use of GCD Distributive Law in proof of Euclid's Lemma

Suppose that c|ab and (b, c) = 1. Then c|a  Proof (ab, ac) =|a|(b, c) = |a|. But by hypothesis, one has c|ab, which implies that c|(ab, ac). We thus conclude that c|a. And the proof is complete.  I am sure it is very simple but I cant seem to understand the stage c|ab implies that c|(ab,ac). I would appreciate if someone could show me this.


In a flat space, where special relativity works, a travelling body can only return to the same point if we apply some kind of acceleration to the body.  So twin paradox is not a paradox because a travelling body that returns to the same point where it starts is not an inertial reference.  But then we have general relativity, that states that mass (energy) curves space-time. So when a photon changes its trajectory passing nearby sun, it's actually moving in a straight line, but in a curved space-time.  Now we can create a new version of twin paradox, where the spaceship that carries one of the twins uses the curvature of some astronomical body (like Jupiter, sun or a black hole) to return to the same point?  In that case which twin will be older?  How to solve the paradox in this context?


Ubuntu 15.04, Asus Flipbook TP500LN No Internet and touchpad did use NDISwrapper

So I installed Ubunutu 15.04 on my Asus Flipbook TP500LN, but I don't have acces to wi-fi (ethernet does work). Now I read about Ndiswrapper, I installed the program and used it to install my wi-fi driver, which I got from the official Asus website. It all went pretty well, but even though it says that the driver is installed and there is a yes I still don't have acces to wi-fi.  I also tried checking additional drivers, but the wi-fi driver doesn't show up.  How can I fix this?  Thanks in advance for all the replies  P.s. My touchpad also doesn't work, but I'm more concerned with the wi-fi not working  Edit: After using sudo ndisgtk I get Gtk-Message: GtkDialog mapped without transient parent. This is discouraged.  Edit2: thanks for the comments Ron here is what it says:   00:00.0 Host bridge: Intel Corporation Haswell-ULT DRAM Controller (rev 0b) 00:02.0 VGA compatible controller: Intel Corporation Haswell-ULT Integrated Graphics Controller (rev 0b) 00:03.0 Audio device: Intel Corporation Haswell-ULT HD Audio Controller (rev 0b) 00:14.0 USB controller: Intel Corporation 8 Series USB xHCI HC (rev 04) 00:16.0 Communication controller: Intel Corporation 8 Series HECI #0 (rev 04) 00:1b.0 Audio device: Intel Corporation 8 Series HD Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation 8 Series PCI Express Root Port 1 (rev e4) 00:1c.2 PCI bridge: Intel Corporation 8 Series PCI Express Root Port 3 (rev e4) 00:1c.3 PCI bridge: Intel Corporation 8 Series PCI Express Root Port 4 (rev e4) 00:1c.4 PCI bridge: Intel Corporation 8 Series PCI Express Root Port 5 (rev e4) 00:1d.0 USB controller: Intel Corporation 8 Series USB EHCI #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation 8 Series LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation 8 Series SATA Controller 1 [AHCI mode] (rev 04) 00:1f.3 SMBus: Intel Corporation 8 Series SMBus Controller (rev 04) 02:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. Device 5287 (rev 01) 02:00.1 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 12) 03:00.0 Network controller: MEDIATEK Corp. MT7630e 802.11bgn Wireless Network Adapter 04:00.0 3D controller: NVIDIA Corporation GM108M [GeForce 840M] (rev a2)


Area under and slope of the motion graphs

I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph. I'm confused that area is a 2 dimensional concept and it may indicate distance or displacement, which are 1 dimensional quantities.


how to use salt to sign a message and how is it effective?

I've had an assignment to sign a file using hash and salt, so I read about salt and I got why it's important when it comes to password, but not to sign messages.   How do I sign something using salt? The only way I could think of is that I add the salt to the message then hash both and then send the hash along with the salt (encrypted of course)… but it makes no sense to me. Even if what I said earlier is how it's done, it's not useful at all. How and why would I use salt to sign a message ?


Converting Personal geodatabase to GML format using ArcGIS Desktop?

I am working on ArcGIS 10.3.   Does anyone know how to convert a personal geodatabase into a GML format?


Infinitesimal transformations and Poisson brackets

I want to understand how bracket operations in general are related to symmetry and infinitesimal transformations (in hindsight of quantumfieldtheory), so I calculated an example with a particle that is moving on a circle with a generic potential. (I used simple polar coordinates in two dimensions)  $H(r,p_{r})= \frac{p^{2}_{r}}{2m}+V(r)$  $H(\phi, p_{\phi})=\frac{p^{2}_{\phi}}{2mr^{2}}+V(\phi)$  Now I know that if you take the Poisson bracket with the Hamiltonian you just get the infinitesimal transformation in time right? So  $\{r,H(r,p_{r})\}= \frac{p_{r}}{m}$  $\{\phi,H(\phi,p_{\phi})\}= \frac{p_{\phi}}{mr^{2}}$  But what if I want to do an infinitesimal transformation of the $r$ or the $\phi$ coordinates? I know that the generator of translations is just the momentum, and that the generator of rotations is angular momentum. How would I do that with the Poisson bracket in this case? And for example when I do an infinitesimal transformation with the radius $r$, what does that mean? Is it that the radius is infinitesimally transformed, or is it more like a global translation where the whole system is somehow translated? Similarly with the angle $\phi$, is it that the angle is locally changed, or is it that the "whole" system is rotated?


Finding the value of $\alpha^2\beta+\beta^2\gamma+\gamma^2\alpha$

If $\alpha,\beta,\gamma$ are the roots of the cubic polynomial $px^3+qx^2+rx+s$, then how can I find the value of $\alpha^2\beta+\beta^2\gamma+\gamma^2\alpha$ in terms of p,q,r and s?  My attempt: Using Vieta's formulas, $$\alpha+\beta+\gamma=\frac{-q}{p}$$ $$\alpha\beta+\beta\gamma+\gamma\alpha=\frac{r}{p}$$ $$\alpha\beta\gamma=\frac{-s}{p}$$ I first thought that this would help. We can find $\alpha\beta\gamma$ by Vieta's formula but the expression inside this bracket could not be possibly found. $$\alpha^2\beta+\beta^2\gamma+\gamma^2\alpha=\alpha\beta\gamma\left(\frac{\alpha}{\gamma}+\frac{\beta}{\alpha}+\frac{\gamma}{\beta}\right)$$ Then, I found $$\alpha^2+\beta^2+\gamma^2=(\alpha+\beta+\gamma)^2-2(\alpha\beta+\beta\gamma+\gamma\alpha)=\frac{q^2-2rp}{p^2}$$ But here all $\alpha^2$, $\beta^2$ and $\gamma^2$ are all multiplied with different factors, so possibility of taking a common factor is ruled out. Then, I thought to take an example. By chance, I could get a pattern. For example, take the polynomial $x^3-1$. The roots of this polynomial are $1,\omega,\omega^2$. Then, in this case the expression evaluates to $1^2\cdot \omega+\omega^2\cdot 1+\omega^4\cdot 1=\omega-1$. The expression in this case gives a complex result, so possibly couldn't be expressed in terms of $p,q,r,s$. Any hint is appreciated.


Generating correlated uniform random variable with R

I am trying to generate Correlated Uniform Random Variables with given mean, standard and correlation structure. I have looked through various posts in this topic including this() and seems to can't get through.   Here is how I am proceeding.  set.seed(12) corr_raw=matrix(0.7, nrow = 4,ncol=4) # Correlations diag(corr_raw)=c(1,1,1,1) colnames(corr_raw)<-c("A","B","C","D") rownames(corr_raw)<-colnames(corr_raw)  Cov=(std_dev%*%t(std_dev))*corr_raw # covariance matrix  #mean and standard deviation  mu<-c(1,3,2,4) std_dev<-0.4*mu #assumed std_dev = 0.4*mean  #Cholesky Decomposition matrix L L<-chol(Cov, pivot =T) Z<-matrix(nrow = 0,ncol=10000)  for (i in colnames(Cov))   {   #stddev(Unif)=(B-A)/sqrt(12)=1; and mean(Unif)=(B+A)/2=0; A=-sqrt(3) and B=+sqrt(3)   Z<- rbind(Z,runif(10000,-1.732,1.732))   } x=mu+L%*%Z  #transform to get the desired mean and variance corr<-cor(t(x)) #find correlation of the generated random variable x   However, the corr(x) and corr_raw does not match. What am I doing wrong ?


Ctrl+Shift+U is a combined shortcut in Eclipse. But when I press it, it shows up a u, just like input with an underline. I guess this shortcut has been declared by Ubuntu, so I can't use it. I used to solve this problem by typing Caps Lock first. Is there any better method?


Is the force in Coulomb's law a vector field?

In the definition of the electric field we have a vector field and a force. The vector field $\mathbf{E}(\mathbf{r})$ is a function of $\mathbf{r}$.   What about the force, is it a vector $\mathbf{F}$ (not a function of $\mathbf{r}$) or a vector field $\mathbf{F}(\mathbf{r})$?  The definition is $\mathbf{F}=q\mathbf{E}(\mathbf{r})$, but if we write it explicit, shouldn't it be $\mathbf{F}(\mathbf{r})=q\mathbf{E}(\mathbf{r})$?  I thinking if we have $$ \mathbf{F}=\frac{q}{4\pi\epsilon_0}\sum_{i=1}^N q_i\frac{\mathbf{r}-\mathbf{r}_i}{\vert\mathbf{r}-\mathbf{r}_i\lvert^3} $$ is it the same as  $$ \mathbf{F}(\mathbf{r})=\frac{q}{4\pi\epsilon_0}\sum_{i=1}^N q_i\frac{\mathbf{r}-\mathbf{r}_i}{\vert\mathbf{r}-\mathbf{r}_i\lvert^3} \quad ? $$ Then $$ \frac{\mathbf{F}(\mathbf{r})}{q}= \underbrace{\frac{1}{4\pi\epsilon_0}\sum_{i=1}^N q_i\frac{\mathbf{r}-\mathbf{r}_i}{\vert\mathbf{r}-\mathbf{r}_i\lvert^3}}_{\mathbf{E}(\mathbf{r})}=\mathbf{E}(\mathbf{r}) $$ So $$ \mathbf{F}(\mathbf{r})=q\mathbf{E}(\mathbf{r}) $$ Is this correct or I'm talking rubbish?


I am trying to replace images that are not found, or that have width or height 1px. I managed to do this in PHP with this:  $imgName = $resultList->IMAGE1; // ex http://www.domain.com/image.png   if (@file_get_contents($imgName) && $imgName !== 'h') {     // detects the image size (NOT based on width and height attributes) $imgNamearray = getimagesize($imgName);  $size = $imgNamearray[3];     if ($size == 'width="1" height="1"') {       $imgName = $base_path . 'uploads/no-img.jpg';     }   } else {     $imgName = $base_path . 'uploads/no-img.jpg';   }   I tried this code in jQuery:   $('body').append('

'); $('#init').hide();  $('#myimg').bind("load",function(){     alert(this.height) })   which can be found in a fiddle here  but I am a noob in jQuery, please help me this. It's much appreciated.


Powering 12V device from 5/9/12V powerbank

I recently bought the Litionite Falcon powerbank that has one of its outs designed for 5/9/12V. The 12V is at 1.5A which I thought would be enough for my 12V/0.8A camera. However, connecting the camera to the charger with a USB to 0.7mm jack doesn't work. Indeed, I can measure only some 5.3V coming through the USB cable which explains why the camera doesn't recognise the power.   How do I get the 12V from the powerbank to charge my camera? Do I need a special USB cable? Do I need one with a step up? Or is it enough to wire the USB differently?


invalid use of incomplete type 'class ...' STL vector

I have some questions with the definition of a class inheriting STL vector. This class is suppost to publicly inherit from std::vector, but I keep getting the following error from the compiter. I am almost certainly that it is due to faulty including of <vector>, yet I don't know how to fix it.  In file included from useMVector.cpp [Error] invalid use of incomplete type 'class MVector<T, size>' In file included from MVector.cpp      from useMVector.cpp [Error] declaration of 'class MVector<T, size>' recipe for target 'useMVector.o' failed   The relevant code is listed here:    useMVector.cpp:    #include <stdlib.h> #include "MVector.cpp"  using namespace std;  int main() {     return 0; }   MVector.h:  #ifndef _MVECTOR_ #define _MVECTOR_  #include <iostream> #include <stdlib.h> #include <vector>  using namespace std;  template<class T, int size> class MVector : public std::vector<T> {     public:         // constructer:         MVector();         // operator=, copy constructor and destructor from std::vector         // iterator from std::vector          // methodes:          // addition with vector         template<class T2>         MVector<T, size> operator+(const MVector<T2,size>& y);         ... };  #endif // _MVECTOR_   MVector.cpp  #include "MVector.h"  template<class T, int size> MVector<T, size>::MVector() : std::vector<T>::vector(size, 0) {};  template<class T2, class T, int size> MVector<T,size> MVector<T,size>::operator+(const MVector<T2,size>& y) {  }


can you model a square in an equation ?  like a circle for example $r^2 = x^2 + y^2$  and lets say we have a square with: centered at $(3,3)$  $2 \leq x \leq 4$ and $2 \leq y\leq 4$  can we somehow make an equation for that square ?


Is every endomorphism of the quaternion ring surjective?

Is the quaternion ring an EAS Division ring?  An EAS Division ring is a ring $D$ such that each endomorphism of $D$ is surjective.  I know that $\mathbb{R}$ and $\mathbb{Q}$ are EAS Division rings.


I am tasked to find the integral part of $\sqrt{2018+\sqrt{2018+\sqrt{...+2018}}}$, where the number of $2018$ is $2018$.  My attempt:  I came up with an upper bound, which was $\sqrt{2018+\sqrt{2018+\sqrt{2018+...}}}$, where there were infinite number of $2018$.  I let this be $a$, and then I have $a^2=2018+a$, giving me $45.4249374...$.  My problem here is that I have no idea what to set as a lower bound.  Can anyone give me a hint to solve this?  Alternatively, another approach could also be provided if it is more efficient.


I want to add the following code in my  section of the front page using a Drupal 8 sub theme of Bartik.   Can anybody help how to do it? What is the best way to do it in this new twig version of theme? Where is page.tpl?  <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js"></script> <script type="text/javascript" src="stepcarousel.js"></script>


How to calculate $\lim\limits_{n \to \infty} nx^{n+1}$ where $x\in(-1,1)$

How do I calculate $\lim\limits_{n \to \infty} nx^{n+1}$ where $x\in(-1,1)$?  Intuitive I think it's 0. I tried L'Hôpital's but it seems too complicated and I'm sure there's a simpler solution.


I've got an laptop with a intel chip, and I'd like to setup dual monitors in Xfce.  How do I do this?


Inline tag edits don't show my edit until the page is refreshed

I often use the  on Stack Overflow. However, the "Edited [time] ago" box below doesn't appear until after the page is refreshed. This is different than the behavior if I use the edit link; doing this will show "edited [time] ago" immediately. Is this  or a ?


Installing Ubuntu alongside pre-installed Windows 8

I am currently trying to install Ubuntu on my new laptop that came with Windows 8 pre-installed. Here's what I have done:  - created bootable flash drive with Ubuntu installer  - created a partition (ext4) using half of my total hard drive space (around 225 GB) The problem I encounter is that Ubuntu is not detecting any OS, which in this case would be my Windows 8. I think I may be able to just manually choose my newly created partition, but I am still hesitant to proceed because of this. I'm not sure exactly what I should do. I want to install it permanently anyway, but I was under the impression that there would be an option for "Try Ubuntu" and I only see "Install Ubuntu", and I don't want it to somehow mess up my current OS, as I want to be able to boot into either one. I noticed that people had said in other places to disable quickboot in the BIOS, and I haven't figured out how to do this. I disabled Fast Startup, but I am pretty sure that isn't the same thing.    I went ahead and installed, and it seems to be working fine. I was wondering though, I only created the root abd swap partitions, and I noticed that it was suggested there be 3, root, home and swap, with home being the disk for most if the memory. should i format the partition, create the home partition and then reinstall?


Using For Loops To Initialize And Add JTextFields and JLabels to JPanel Using Arrays Causes Error

I'm trying to make a program that takes input from the user for how many students they have in their class and their names/grades and calculate average and letter grades. I'm trying to get better with For Loops and Arrays and this is what I chose to do. The only problem is when the init() method is called to make the window. The class is extending JFrame  import java.util.Scanner;  import javax.swing.JButton; import javax.swing.JFrame; import javax.swing.JLabel; import javax.swing.JPanel; import javax.swing.JTextField;  @SuppressWarnings("serial") public class GradesGUI_2 extends JFrame {  static Scanner s = new Scanner(System.in); static int num;  public static void main(String[] args) {      System.out.println("How many students are in your class?");     num = s.nextInt();      GradesGUI_2 window = new GradesGUI_2("Title");     window.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);  }  //-------------------------------------------------  static JPanel p; JTextField[] name = new JTextField[num], grade = new JTextField[num]; JLabel[] nlabel = new JLabel[num], glabel = new JLabel[num]; int height = 50;  //-------------------------------------------------  GradesGUI_2(String title) {     super(title);     this.init();     this.setVisible(true);     this.setLocationRelativeTo(null); }  //-------------------------------------------------  void init() {     //Create JLabel/JTextField     for(int i = 0; i < num; i++) {         nlabel[i] = new JLabel("Name " + i);         glabel[i] = new JLabel("Grade " + i);         name[i] = new JTextField(10);         grade[i] = new JTextField(1);          height += 25;     }      for(int i = 0; i < num; i++) {         p.add(nlabel[i]);         p.add(glabel[i]);         p.add(name[i]);         p.add(grade[i]);     }        this.setSize(350, height);     this.add(p); }   }  What the console displays:  How many students are in your class? 7 Exception in thread "main" java.lang.NullPointerException     at GradesGUI_2.init(GradesGUI_2.java:59)     at GradesGUI_2.<init>(GradesGUI_2.java:40)     at GradesGUI_2.main(GradesGUI_2.java:20)   The error happens when the components are added to the panel. Please answer. Thank you!


Is it self-plagiarism to copy & paste from my own published paper to my grant application?

If I copy & paste sentences from my own published paper to my grant application, will it be considered self-plagiarism? Is it forbidden? The grant application is not published anywhere; this is an internal submission for the  grant agency.


Are System.IO.Compression.GZipStream or System.IO.Compression.Deflate compatible with zlib compression?


How to create a list of objects inside a for loop in Python without inherit attribute values

The code below creates a list of objects that contains a list as attribute and a method to append items to this list but this appending is not working like I expected.  What I expected: Each list MyList inside of each object MyObj to have only 3 elements.    How it is working: The list MyList inside of MyObj[0] has 3 elements The list MyList inside of MyObj[1] has 6 elements The list MyList inside of MyObj[2] has 9 elements  It seems to me the object MyObj[i] appends the MyList of prevous object MyObj[i-1]. How the code should be like to make each list MyList of each MyObj[i] have only the 3 elements inserted by the method add_to_list?  Python code:  class MyClass:     MyList = []      def add_to_list(self):          for item in range(3):             self.MyList.append("Item " + str(item))   MyObj = []  for i in range(3):     MyObj.append(MyClass())     MyObj[i].add_to_list()      print("Object " + str(i))     print(MyObj[i].MyList)


Indicate number of items in meta review queues when displayed from main review page

When viewing the review page on main, each queue has a number next to it indicating how many items remain. At the end of the list of queues is a link to the meta review page, but this gives no indication of whether there are any meta items to review:    Since many sites have very few reviews in the meta queue, clicking through to find out if there are meta reviews usually gives a negative result, giving an incentive to stop checking. If there was a number, simply showing the total number of meta reviews (the sum of the individual meta review queues), then on those occasions when a meta review appears, it would be picked up more quickly as no one would need to check the meta review page to notice it.


How to display the most popular posts of all the blogs in a mu setup?

When you visit wordpress.com, they have a list of the most popular posts right on the front page. I was wondering if there was a way to do the same thing on my multisite installation. Is it possible, and if it is, how would I go about doing it (plugin? theme?)?


I am quite new in Ubuntu. I wanted to install a .msi file (SkypeMeetingsApp.msi)and read that you can do this using Wine, so I've installed it. I have put the file on the Desktop, opened the terminal and have written  cd Desktop   Then :  msiexec /i SkypeMeetingsApp.msi   But it says:  0009:err:mscoree:LoadLibraryShim error reading registry key for installroot 0009:err:mscoree:LoadLibraryShim error reading registry key for installroot 0009:err:mscoree:LoadLibraryShim error reading registry key for installroot 0009:err:mscoree:LoadLibraryShim error reading registry key for installroot   What can I do? it says the same thing with this command :  wine start SkypeMeetingsApp.msi


Efficient way to check local Wordpress php files and Database for malicious code?

First of all, I am not a WP superuser. Recently a friend of mine got hacked, by hacked I mean he didn't update his WP for a long time and got malicious code injected which sent spam, so his hoster blocked him. He only has the infected files, which were already checked and cleaned by a developer...by hand. Now I should setup a new server running his code. But I would like to let a tool check the code of the theme at least and DB. I will setup a fresh installation and re-install the plugins, to make sure that these are free of bad code. So what I have is only the hand-cleaned code, so I don't know what injection we had before, so I can't search for the same pattern or anything.  I found some tools, which check the WP-Website for bad code, like sucuri - sitecheck, but this is not an option for me. I would like to check the code locally. What do you guys recommend me to do?


I am using code::blocks 12.11 (gcc) on a 32 bit OS. I have the following structure:  struct node  { int a; float b; char d; struct node* c; } s1;   now individually,  sizeof(int);    sizeof(float);    sizeof(char);   gives output 4 4 1 bytes respectively. so i calculate size of structure as 13 bytes. But the following  sizeof(s1); or sizeof(struct node);   gives output 16bytes.  I am unable to figure out why this is so. Please help me out here. Thanks.


null object reference - confused with Objects in Java

I'm confused with the objects and constructor in Java. I query from a SQLiteDatabase but I couldn't get the correct object/answer. I know my codes look messy and I need to clean it up but I don't know where to start...  public static class QObject {          public String word;         public String definition;          public QObject(String word, String definition) {             this.word = word;             this.definition = definition;         }          public QObject getAnswer(String message) {              QObject quizObject = null;             String query = "select * from " + TABLE_NAME + " where " + COL_WORD + " = '" + message + "'";              Cursor cursor = this.getDbConnection().rawQuery(query, null);                 if(cursor.moveToFirst()) {                     do {                         String myword = cursor.getString(cursor.getColumnIndexOrThrow(COL_WORD));                         String mydefinition = cursor.getString(cursor.getColumnIndexOrThrow(COL_DEFINITION));                         quizObject = new QObject(word, definition);                     } while (cursor.moveToNext());                 }                 cursor.close();                 return quizObject;         }          private SQLiteDatabase getDbConnection() {             return dbHelper.getReadableDatabase();         }     } }      public void searchName(View view) {         String word = null;         String definition = null;         DatabaseTable db = new DatabaseTable(this);          DatabaseBackend dbBackend = new DatabaseBackend(MainActivity.this);         DatabaseObject dbo = new DatabaseObject(this);         DatabaseB.QObject quizobject = new DatabaseB.QObject(word, definition);         DatabaseB.QObject allQuizQuestions = quizobject.getAnswer(message);          String answer = allQuizQuestions.definition;          TextView textView = findViewById(R.id.textView2);         textView.setText(answer);      }   The error message is null object reference:  Caused by: java.lang.reflect.InvocationTargetException at java.lang.reflect.Method.invoke(Native Method) at android.support.v7.app.AppCompatViewInflater$DeclaredOnClickListener.onClick(AppCompatViewInflater.java:288) ... Caused by: java.lang.NullPointerException: Attempt to read from field 'java.lang.String com.justkitting.orion.databasetest.MainActivity$DatabaseB$QObject.definition' on a null object reference at com.justkitting.orion.databasetest.MainActivity.searchName(MainActivity.java:139) at java.lang.reflect.Method.invoke(Native Method) ...   Many many thanks.


I am still new to this, so I apologise if I don't make a lot of sense!   I am using QGIS 2.4.0 Chugiak.  I am working on a project set to the GDA94/MGA Zone 50 coordinate system with 'on the fly transformation' enabled. I have added a shapefile that was created in ArcGis and set the coordinate system to the same as the projects (GDA94/MGA Zone 50). However, the shapefile is projecting at a much larger scale and A LOT further away than it should be. I have tried changing the coordinate system of the shapefile and reprojecting the shapefile, but haven't had any luck.  Any chance someone may be able to help?


Rigify widgets generating in wrong position and won't rotate

I am having issues with the rig i generated through rigify. When I hit "generate rig" a rig is created with the "palm" widget turned vertical instead of horizontal. I also cannot rotate any of the widgets in pose mode. The widget highlighted in blue will not move or rotate. The same thing happens with other blue and green widgets in the rig.  The file is located here:  Any help would be greatly appreciated!


Can a Linux user belong to more than one group?  If it is allowed, then one use may access files from two groups, that would be quite nice!  If not, is there any alternative way to have this function?  This issue is not the same as  or


A friend of mine sent me a sum of some 300 EUR (from Iceland to Croatia) but mistakenly used the IBAN of my bank and not my bank account. He included my full name and bank's SWIFT code.    What is the procedure now? Will the money be returned to his bank?  If so, how long will it take?  If anyone had any similar situations like this, please help me with any info.   Cheers.


I'm trying to fit an exponential model using nls, but I don't know how to select the starting values for the parameters. I know this question has been answered multiple times, but I spent some days surfing on forums and I couldn't find the solution for my particular case.  they showed the very same problem, but the solution of liniarizing the data taking logs doesn't work wor me, because the fit of the transformed data is not linear. I would really appreciate a piece of advice here.  Here an example of my kind of data:  mes1 <- data.frame(CO2=c(354.68, 362.43, 374.12, 380.45, 385.92, 394.19, 400.2, 405.85, 407.81, 410.71, 414.77), time=c(1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101))  CO2i <- mes1$CO2[1] Timei <- mes1$time[1] exp_eq <- function(time,B,CO2i,a,Timei){B + (CO2i- B)^(-a*(Timei-time))}   I know other kind of equations might work better, but I must use this one since is the reference in the field. The only thing I need is estimate the initial values for a and B  m <- nls(CO2 ~ exp_eq(time,B,CO2i,a,Timei)), data = mes1, start = list(B = 1, a = 1))   Many thanks in advance for your support.


Huge confusion with Fermions and Bosons and how they relate to total spin of atom

I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, and each fermion has a 1/2 spin. Since there are an even number of fermions, the total spin value is an integer. This spin number is the "intrinsic" spin number that cannot be changed, but its orientation "up" or "down" can be changed.  For atomic Hydrogen, it is a Boson because it has integer spin, however it also has a single electron. I read on physics forums, , that the spin of atom comes from the electrons and not its nucleus. I also read on here, , that the spin of atomic Hydrogen is 1/2! The answer says atomic Hydrogen has spin 1/2 because it ignores the nuclear spin.  This is one thing that is confusing me. Shouldn't atomic Hydrogen have an integer spin because of the nuclear component? So does atomic Hydrogen have spin and is affected by a magnetic field? Nuclear spins are affected by magnetic fields, but they aren't as affected as electrons according to the discussion on physics forums.  Why do we ignore nuclear spin sometimes? Also, can someone help me out here with all the possibilities?  Is there a Boson with an half integer spin value? (Surely, there must not be) However atomic Hydrogen is one of those cases! (It seems...) (Why don't we cancel out the nuclear spin with the electron spin?)  Say we have another atom that is a Boson, It has unpaired electrons in different orbitals, so what determines whether or not electrons fill in orbitals as spin up or down? Does spin down nuclear spin cancel out a electron up spin?


Prove that $$\sum_{d\mid n}(-1)^{n/d}\varphi(d)=\begin{cases}-n&2\nmid n\\0&2\mid n\end{cases}$$  I have came across the above question.  I have done the following:   $n$ is odd then so is $n/d$ which would result $(-1)^{n/d}$ $=-1$   I am assuming you would have to use Gauss:   $$\sum_{d/n} φ(d) = n$$  $===>$ $$\sum_{d/n} (-1)^{n/d}φ(d) = -\sum_{d/n}φ(d)=-n$$   $n$ is even then $n=2^{a}m$, where we can say $m$ is odd.   I am not sure what else to do from here. Any help would be appreciated.


Professor cc to other professors when I ask about the PhD student vacancy. Should I answer as a group or to individuals?

I wrote an email to Prof. X to ask about a PhD student vacancy and talk about a topic in one of his papers. He refused to accept me because of his retirement and replied with a warming email. In that, he cc-ed two others that he thought might be interested in me, Prof. Y and Prof. Z. Prof. Y refused because his area is somewhat distinct to mine; Prof. Z hasn't answered yet. I haven't responded to anyone yet. I also want to ask Prof. X's opinion about Prof. T's work, who is actually the one that I want to follow.  How should I respond to this? My feeling is that if Prof. X cc-ed others, this means that he wants to create a group discussion. As a group, everyone should have the right to hear each other voices. Should I reply to the group with a generic "thank you" email?  But if I do that, then I have to send another private emails to Prof. X and Prof. Z. I just worry that this will make me looks sneaky because I don't have the courage to discuss this in public.   What should I do?