Can a non-zero vector have zero image under every linear functional?

Let $X$ be an infinite-dimensional vector space, and let $x_0$ be an element of $X$ such that $f(x_0)=0$ for every linear functional $f$ defined on $X$. Then can we prove that $x_0$ is the zero vector in $X$? Or, is it possible to find a non-zero $x_0$ whose image under every linear functional is zero?   In the case of $X$ being finite-dimensional, we can prove that if $f(x_0)=0$ for every linear functional $f$ on $X$, then $x_0$ must be the zero vector. What is the situation in the infinite-dimensional case?


Google webmaster tools add HTTP and HTTPS?

I have a website which is only reachable under .... The http:// is 301 redirected to https:// and the https:// without www is 301 redirected to .... In Google Webmaster Tools I have added the website twice, one with www and one without www. Is it necessary to add the http:// as well?  Thanks for advice.


Some of the comments on the question  got me thinking. I've always assumed that after Newt's father got infected, all of the following happens off-screen:   He makes it back to the colony with an alien inside him. That alien "hatches" and kills a few people.   Some more people go back to the original ship looking for answers, and bring back more eggs to experiment on. Something goes wrong (probably due to the first alien), and more people get infected. At some stage the aliens go back to the ship and bring back a queen. Or perhaps the colonists do, but I always thought it was the alien.   User Beta has a different view. Beta says:     I assumed that the colonists in "Aliens" brought only a few parasites   (or one) from the derelict ship, one of them became a queen, and most   of the adults we saw were from her eggs   This seems perfectly valid to me, perhaps making more sense than my original assumptions.    Does anyone know for a fact where the queen came from?


I have bumped many times into entropy, but it has never been clear for me why we use this formula:  If $X$ is random variable then its entropy is:  $$H(X) = -\displaystyle\sum_{x} p(x)\log p(x).$$  Why are we using this formula? Where did this formula come from? I'm looking for the intuition. Is it because this function just happens to have some good analytical and practical properties? Is it just because it works? Where did Shannon get this from? Did he sit under a tree and entropy fell to his head like the apple did for Newton? How do you interpret this quantity in the real physical world?


I have a 2gb chromebook with 64-bit ubuntu 12.04 and it runs extremly slow and often crashes so how to I downgrade it to 32-bit or is their another solution?


Indicate an object's method through his pointer in C++

I'm currently learning OpenGL in C++.   I'm trying to read the keyboard inputs by setting glfwSetKeyCallback(this->window, ctrl->key_callback); Where this->windowis my GLFWwindow* window and ctrl->key_callback is a method of my custom object Controller.  I'm getting a compiler error with MSVC:     non-standard syntax; use '&' to create a pointer to member   How can I indicate the key_callback method trough that Controller* ctrl pointer?  Where the error pops out:  void Class1::set_callback(Controller* ctrl) {     glfwSetKeyCallback(this->window, ctrl->key_callback); }   Controller.h  #include "Class1.h" #include "GLFW/glfw3.h"  class Controller {     public:         Controller(Class1* c);         ~Controller();         void key_callback(GLFWwindow* glwindow, int key, int scancode, int action, int mods);      private:         Window* window; };   I'm calling set_callback in main.cpp  #include "Class1.h" #include "Controller.h"  int main() {     Class1* my_class = new Class1();     Controller* controller = new Controller(my_class);     my_class->set_callback(controller);     return 0; }   Please let me know if I didn't formulate my question/title right, I'm pretty confused with this syntax


suggests that the wizard can use:   Axes Daggers Maces Spears Swords   (Click on the Wizard icon, and all of those weapons are not disabled, meaning that the class can use them.)   explains weapons types, but it is not clear whether the Wizard can use only wands, or other weapons.  So do you know the exact list or weapons type that a class can use? Or can you find this information somethere?  My motivation to know is that the damage per second of those weapons can change quite a bit from one to the other, and the spell damage is based on that. For example, the level 1 wand () is only 3 DPS, whereas the level 1 spear () has a DPS of 7.2–8.4.


Flip Flop circuit - what is high in relation to?

I am reading about "flip flop" circuits (and I've bought one as an integrated circuit to mess with). When it says that when the SET goes high, then Q (output) will be high, what is "high" in relation to? Could I feed in -5v and call that low, while 0v is high? Or connect +5v and call that high and 0v low? Or are flip flops usually biased so that they expect a positive or negative voltage at their terminals?  The IC that I bought has the following terminals: SET, RESET, DATA, CLOCK, Q and Q(with bar over it).


How do I recover from accidentally removing dpkg?

By mistake I have removed dpkg from my pc (ubuntu 16.04). When I am running apt commands, it was showing error :  Could not exec dpkg! E: Sub-process /usr/bin/dpkg returned an error code (100)   Can anyone suggest me any solution to this. Thanks in advance !!!


Allow incoming remote desktop connection when connected to VPN

Environment: Windows 10, Cisco AnyConnect Client  I have a PC at home. I often connect to it when I am out of the home. However, I have to use a VPN client to get in touch of my servers. And the problem is as soon as I connect to the VPN, my home PC can't accept incoming remote desktop connection because of the network environment has changed.  For now, the only workaround I found is that by install Chrome Remote Desktop, I can use Chrome Remote Desktop to connect the home PC when I am not at home and I have to establish a VPN connection on the home PC.  I am wondering if there is a way to make a hole or some DMZ like config so that I can connect to my home PC through the Windows's built-in RDP service when the home PC is connecting to a VPN?  Thanks.


What is the simplest way to convert convert 5V DC to 100V DC, 0.2 Amps?

What will be the simplest way to convert convert 5V DC to 100V DC, for low power application ~0.2 Amps for a portable electrophoresis power supply?


If there is no absolute time, how can we say the Big Bang was 13.8 billion years ago?

The Big Bang is supposed to have happened 13.8 billion years ago.  Question: Given that there is no absolute time and different observers do not agree on the amount of time that has elapsed, how can we say that the Big Bang happened 13.8 billion years ago? Why wouldn't this kind of statement be ambiguous?  For example, say Alice stays on Earth for another billion years. She now measures the Big Bang at an (ostensible) 14.8 billion years ago. Meanwhile Bob goes zipping around the galaxy at 0.99c, and when he returns only 0.1 billion years of time has passed for him. His Big Bang is now 13.9 billion years ago. Both his and Alice's statements of the age of the universe are correct, making any statement about how many years ago the Big Bang happened ambiguous.  I feel like I'm forgetting something obvious here, but I can't place it. What am I missing?


Intuition behind logarithm change of base

I try to understand the actual intuition behind the logarithm properties and came across  that explains the multiplication and thereby also the division properties very nicely:     Suppose you have a table of powers of 2, which looks like this: (after revision)      $$\begin{array}{rrrrrrrrrr} 0&1&2&3&4&5&6&7&8&9&10\\ 1&2&4&8&16&32&64&128&256&512&1024 \end{array}$$      Each column says how many twos you have to multiply to get the number in that column.  For example, if you multiply 5 twos, you get $2\cdot2\cdot2\cdot2\cdot2=32$, which is the number in column 5.      Now suppose you want to multiply two numbers from the bottom row, say $16\cdot 64$.  Well, the $16$ is the product of 4 twos, and the $64$ is the product of 6 twos, so when you multiply them together you get a product of 10 twos, which is $1024$.   I found that very helpful to understand the actual proofs for this property.  I still struggle to get the idea behind the change of base rule. I'm familiar with the proof that goes like:  $$\log_a x = y \implies a^y = x$$ $$\log_b a^y = \log_b x$$ $$y \cdot \log_b a = \log_b x$$ $$y = \frac{\log_b x}{\log_b a}$$  But can somehow provide a explanation in the style of the quoted answer why this actually works?


Is the decay of nuclei also depending on the 'age' of nuclei or whether they are created or not?

Usually the decay is said to be randomly but the average period of decay of certain atoms are stable. So if you randomly take a bunch of the same atoms the average time before the decay will fe be 5 days.   But imagine that you could create a bunch of atoms at the same time by decaying uranium atoms. Imagine that you succeeded in creating at the same time a buch of polonium atoms. So they all have the same age. Is the time that those polonium atoms decays in lead also has the same variety of decay with a certain average time or are all polonium atoms decaying more or less at the same time?  Perhaps uranium is not a good example, but it is about the principle question.  To make a distinction of other questions: when atoms are created is there a difference is spreading decay time among those atoms or is the spread of decay time the same, although of course the average time would stay the same?


what is link baiting? What is the process?

I am not familiar with the term Link baitingwhat is it and how can I use it in seo.   Is it useful?   can anyone describe it for me?


Expected value of the conditional choice probability

I would like to compute the conditional choice probability which is defined as follows \begin{equation} p_k=Prob(f(m_k)+u_k>f(m_i)+u_i, \forall  i\neq k|m) \end{equation} where $u_i, i=1,...,N$ are independently and identically distributed normal variables with $u_i\sim N(0,\sigma_i^2)$ and $m_i, i=1,...,N$ are independently and identically distributed standard uniform random variables, $m_i\sim i.i.d. U[0,1]$.  In words, $p_k$ is the probability that out of $N$ options, the choice $k$ has the greatest value conditional on having a realization for the vector $m$. Because $u_i-u_k\sim N(0, \sigma_i^2+\sigma_k^2)$, $p_k$ can be rewritten as \begin{equation}p_k=\prod_{i\neq k}\Phi\left(\frac{f(m_k)-f(m_i)}{\sqrt{\sigma_i+\sigma_k}}|m\right) \end{equation} where $\Phi(\cdot)$ denotes the CDF of standard normal distribution. Next, I would like to find the expected value of $p_k$ by integrating out the possible values of $m$ as follows \begin{equation} E[p_k]=\int_{(0,1)^N}\prod_{i\neq k}\Phi\left(\frac{f(m_k)-f(m_i)}{\sqrt{\sigma_i+\sigma_k}}\right) d\mathbf m \end{equation} Is it possible to use the properties of the uniform and standard normal distributions to get a more compact solution for $E[p_k]?$


Tags field placeholder is cut-off on posting a new question:        Google Chrome on iOS 11.


Is there anything canon in the Terminator Universe that picks up where Terminator: The Sarah Connors Chronicles leaves off?

So, Terminator canon is pretty twisted, given all that time-travel stuff.  But in the canon that includes the T:SCC, does anything pick up where the show left off that is considered canon?


e.g. I didn't get to where I am now unless ... or I wouldn't have got where I am now ... Are these both correct? The first sentence I found in a EFL series New English File. I have never heard this used in HampshireUK nor have I ever used it myself.


Include badge rank in Badges table on data explorer

I've discovered that there's no way to differentiate between a bronze, silver, and gold tag badge. For example, take this query (run on SO):  SELECT * FROM Badges WHERE Name = 'javascript'   It returns:  Id      UserId  Name       Date           ------- ------- ---------- -------------  273683  16417   javascript 2009-04-01 18:40:06 378136  5445    javascript 2009-07-10 15:03:24 571563  18936   javascript 2009-12-04 01:47:14 664312  34397   javascript 2010-02-10 20:15:53 666137  187606  javascript 2010-02-11 02:05:05 759018  182668  javascript 2010-04-03 23:50:08 845349  96100   javascript 2010-06-02 15:01:59 847409  145190  javascript 2010-01-31 06:10:51 1032904 45433   javascript 2010-08-16 10:23:44 1037159 25330   javascript 2010-01-29 19:32:19 ...   How am I supposed to tell if it's a bronze, silver, or gold tag badge?  Therefore, I request that a.) a Rank column be added or b.) tag badge names be changed to javascript-bronze, javascript-silver, and javascript-gold.


Every time I ran an app a windows security alert pops up.  It doesn't matter which button to press, it will appear next time anyway.  I tried to disable all messages and even turn off windows firewall, but it doesn't help.


What is the story of "$n-1$" in the denominator of an estimated variance?

In the book "Numerical Recipes in C" there is said that      there is a long story about why the denominator of variance is $N-1$ instead of $N$. If you have never heard that story, you may consult any good statistics text.   What is that story? What book is the story written in?


How do I restart/reload Apache when it can't determine the domain name?

After installing  I tried to restart or reload Apache and I received the following message:  $ sudo /etc/init.d/apache2 reload  * Reloading web server config apache2 apache2: Could not reliably determine the server's fully qualified domain name, using 127.0.0.1 for ServerName


How do virtual photons exist without violating conservation of energy?

If virtual particles cancel out after being created from spacetime flunctuations because they come in matter-antimatter pairs, how do virtual photons cancel out, due to a photon being its own antiparticle?


When (if ever) is a frequentist approach substantively better than a Bayesian?

Background: I do not have an formal training in Bayesian statistics (though I am very interested in learning more), but I know enough--I think--to get the gist of why many feel as though they are preferable to Frequentist statistics. Even the undergraduates in the introductory statistics (in social sciences) class I am teaching find the Bayesian approach appealing--"Why are we interested in calculating the probability of the data, given the null? Why can't we just quantify the probability of the null hypothesis? Or the alternative hypothesis? And I've also read  like , which attest to the empirical benefits of Bayesian statistics as well. But then I came across this quote by Blasco (2001; emphasis added):     If the animal breeder is not interested in the philosophical problems associated with induction, but in tools to solve problems, both Bayesian and frequentist schools of inference are well established and it is not necessary to justify why one or the other school is preferred. Neither of them now has operational difficulties, with the exception of some complex cases...To choose one school or the other should be related to whether there are solutions in one school that the other does not offer, to how easily the problems are solved, and to how comfortable the scientist feels with the particular way of expression results.    The Question: The Blasco quote seems to suggest that there might be times when a Frequentist approach is actually preferable to a Bayesian one. And so I am curious: when would a frequentist approach be preferable over a Bayesian approach? I'm interested in answers that tackle the question both conceptually (i.e., when is knowing the probability of the data conditioned on the null hypothesis especially useful?) and empirically (i.e., under what conditions do Frequentist methods excel vs. Bayesian?).   It would also be preferable if answers were conveyed as accessibly as possible--it would be nice to take some responses back to my class to share with my students (though I understand some level of technicality is required).   Finally, despite being a regular user of Frequentist statistics, I am actually open to the possibility that Bayesian just wins across the board.


Intuition behind Caratheodory's definition for measurable sets?

I start saying that I know this question has been already proposed a thousand times on this forum BUT I couldn't find a direct answer so I try asking on my own.  What's the intuitive meaning of this definition of measurable set?  $\cdot$ Let $X$ be a set and $\lambda^*$ an outer measure. Then $X$ is said to be measurable if for each $B\in X \lambda^*(B)=\lambda^*(B\cap X) + \lambda^*(B\cap X^C)$  Or equivalently if  $\lambda_*(X)=\lambda^*(X)$.  I feel OK with the second definition because it looks kind of similar to the intuition in Riemann Jordan "measure", but why are the two equivalent?  Thanks.


Preventing infomation from being searched

How do you prevent other users from searching another users information in a list? I have a list called student database where users who gain access to site login and fill out form and update there files. How do I prevent others users from searching other users information in the search engine?


I'm checking for an empty jTable value, some of my jTable cells have no input but still not an empty string. How to check for empty strings in jTable?  I made 1 column and 4 rows. The first 2 rows have inputs. The last 2 rows have no input. The last two rows appears to have value, how can I check for an empty jTable value?  //Row 1 Value: James //Row 2 Value: Mark //Row 3 Value: <nothing> //Row 4 Value: <nothing>  int i = 0; while (i < jTable1.getRowCount()) {     if (jTable1.getValueAt(i, 0) != "") {         JOptionPane.showMessageDialog(null, "Is not empty");         i++;     } }  I was expecting to get only 2 message dialog. Thanks.


What are the cheapest licenses for Windows Server (current) which I can legally run

1) A Web server  2) A Server running MySQL  Please list any technical limitations, if you know them (e.g. max memory).  Thank you


Live USB for Ubuntu 13.10 does't recognize Windows 8 OS

I have created a Live USB for Ubuntu 13.10 64 bit using Universal-USB-Installer-1.9.4.4  I have restarted and booted from the USB; tried Ubuntu without installing. Everything works fine there including web browsing, videos, installing new software etc. So I decide to install Ubuntu as dual boot option to Windows 8.  When I tried installing, the options do not show the existing Windows 8 OS. It shows only the option to install Ubuntu as standalone OS. The step by step installation instructions available online mention that it should show option like "Install Ubuntu alongside Windows 8"  I have a Dell Inspiron 3521 with Windows 8; UEFI boot. I have 3 options for the boot menu: "UEFI Security boot On", "UEFI Security boot Off" and "Legacy boot".   Please advise how I can get to dual boot Windows 8 and Ubuntu. I know that USB setup is good as I am able to boot and try from it without installing. May be boot settings?  Thanks in Advance! ~KK


How to delay command blocks until player respawns?

I have a command block line set up so that it detects for a players death, then gives them weakness for 600 seconds. It applies weakness to soon before they get out of the respawn time. If there is not way to delay a command is there a way to detect a player respawn?


Principal axes, what are they and how to decide them?

I am reading a book about data mining and am currently in a chapter about Principal Component Analysis. But I am not sure from the explanation in the book what the principal axes are and how to find them.  If I have the feature vector $X = \{(-3,-1,-1),(0,-1,0),(-2,-1,2),(1,-1,3)\}$, how do I find the principal axes?  Thanks!


I'm creating a lib on vectors in typescript. My very first test failed:).  It's related to object equality in TypeScript/JavaScript but I can't find a way to make the test green. No object equality is mentioned in typescript's official doc .  Could someone please give me a hand ?  This is the source code.  class Vector {     x: number;     y: number;      constructor(x: number, y: number) {         this.x = x;         this.y = y;     }      add(that: Vector) {         return new Vector(this.x + that.x, this.y + that.y);     } }  export = Vector;   Then I have a unit test on this class as follows    var Vector = require("../lib/vector")   describe("vector", function () {   it("should add another vector", function () {     var v1 = new Vector(1, 1);     var v2 = new Vector(2, 3);     expect(v1.add(v2)).toEqual(new Vector(3, 4));   }); });   When executed obtains the following error  Failures:  1) vector should add another vector 1.1) Expected Vector({ x: 3, y: 4 }) to be Vector({ x: 3, y: 4 }).


If you open up XCode (or probably another IDE) and type in __ you can see a lot of variables which starts with __. (in the auto complete box).  Why did the developers add the _s in there?


Why does a force not do any work if it's perpendicular to the motion?

I have a book that says the Moon's orbit is [in this context assumed to be] circular. The Earth does no work on the moon. The gravitational force is perpendicular to the motion. Why is there no work done if support force is perpendicular to the motion?


What is the most easy way for a noob guy in coding to create interactive web-maps ? In GIS field I've worked with QGIS as open-source software, but keept my project on desktop. In my research I've found this combination for web maps-- Geoserver+Leaflet.  Right now I'm studying Geoserver's documentation. Any tutorials to recomend ?


Maximum gap between samples drawn without replacement from a discrete uniform distribution

This problem is related to my lab's research in robotic coverage:  Randomly draw $n$ numbers from the set $\{1,2,\ldots,m\}$ without replacement, and sort the numbers in ascending order.  $1\le n\le m$.   From this sorted list of numbers $\{a_{(1)},a_{(2)},…,a_{(n)}\}$, generate the difference between consecutive numbers and the boundaries: $g = \{a_{(1)},a_{(2)}−a_{(1)},\ldots,a_{(n)}−a_{(n-1)},m+1-a_{(n)}\}$. This gives $n+1$ gaps.  What is the distribution of the maximum gap?   $P(\max(g) = k) = P(k;m,n) = ? $  This can be framed using : $P(g_{(n+1)} = k) = P(k;m,n) = ? $  See , but this question asks the distribution of the maximum gap.  I'd be satisfied with the average value, $\mathbb{E}[g_{(n+1)}]$.  If $n=m$ all the gaps are size 1. If $n+1 = m$ there is one gap of size $2$, and $n+1$ possible locations. The maximum gap size is $m-n+1$, and this gap can be placed before or after any of the $n$  numbers, for a total of $n+1$ possible positions. The smallest maximum gap size is $\lceil\frac{m-n}{n+1}\rceil$. Define the probability of any given combination $T= {m \choose n}^{-1}$.    I've partially solved the probability mass function as $ P(g_{(n+1)} = k) = P(k;m,n) =  \begin{cases} 0     & k < \lceil\frac{m-n}{n+1}\rceil\\ 1     & k = \frac{m-n}{n+1} \\ 1     & k = 1 \text{ (occurs when $m=n$)} \\ T(n+1)& k = 2 \text{ (occurs when $m=n+1$)} \\ T(n+1)& k = \frac{m-(n-1)}{n}  \\ ?     &  \frac{m-(n-1)}{n} \le k \le m-n+1 \\ T(n+1)& k = m-n+1\\ 0     & k > m-n+1 \end{cases}  \tag{1} $  Current work (1):  The equation for the first gap, $a_{(1)}$ is straightforward: $$ P(a_{(1)} = k) = P(k;m,n) = \frac{1}{{m \choose n}} \sum_{k=1}^{m-n+1} {m-k-1 \choose n-1} $$ The expected value has a simple value: $\mathbb{E}[P(a_{(1)})] =  \frac{1}{ {m \choose n}} \sum_{k=1}^{m-n+1} {m-k-1 \choose n-1} k = \frac{m-n}{1+n}$. By symmetry, I expect all $n$ gaps to have this distribution. Perhaps the solution could be found by drawing from this distribution $n$ times.  Current work (2): it is easy to run Monte Carlo simulations.  simMaxGap[m_, n_] := Max[Differences[Sort[Join[RandomSample[Range[m], n], {0, m+1}]]]]; m = 1000; n = 1; trials = 100000; SmoothHistogram[Table[simMaxGap[m, n], {trials}], Filling -> Axis, Frame -> {True, True, False, False}, FrameLabel -> {"k (Max gap)", "Probability"}, PlotLabel -> StringForm["m=``,n=``,smooth histogram of maximum map for `` trials", m, n, trials]][![enter image description here][1]][1]


What can I do when my e-mails to professors go unanswered?

I have accepted as postdoc researcher in a Swedish university. Three professors in the university are correspondent for this position. I have to travel to Sweden within 2 weeks and start my new job. However, I should make sure about some issue before leaving my homeland. They all are so quick in answering. However, I sent them a short e-mail but did not receive any reply from 10 days ago. I don't  know what I should do. Does such a behavior mean "No"? Or am I annoying them because of my e-mail?


Why can I see a table in user_tables but can't find it in dba_tables?

I have created a table with the "create table as (select.....)" statement by the user called "X", which is a copy of another table, from a user called "Y".  When I list all the tables from dba_tables, owned by X, there isn't anything, but if I write "select tablespace_name, table_name from user_tables;" I can see the new tabble owned by me (the X user).


How can I set env variables so that KDE recognizes them?

I need to set some environment variables such as the XDG spec ones, before KDE starts in such a way that kwin and any apps run from KDE will inherit them. Where could I do this, and how?


In what order should I watch Monogatari series?

I am new to Monogatari series and it looks really confusing to get into it. Most of the people online suggest watching it in release order however there exist chronological order which i really don't know much about. Which is the correct order to watch Monogatari series?


how to setup ubuntu that fstab runs after network is connected?

right now   I have setup /etc/fstab like this:  //192.168.5.167/H /mnt/ssd cifs credentials=/root/.smbreds,noauto,x- systemd.automount 0 0   I want to set it up like first network should be connected and then fstab mount should get mounted.


If $X_1,\ldots,X_n\sim Uniform(0,1)$ and $Y=\max[X_1,\ldots,X_n]$, find $E(Y)$.   I don't really have any good starting point. I guess Y is a function of the X's and so I might be able to apply the theorem about the expectation of a function, but I don't know how to deal with this since max is a discrete function.  Can anybody help me please?


Is the function $f(x)= \begin{cases} 0, & \text{if}\ x\ \text{is rational} \\ x, & \text{otherwise} \end{cases}$, continuous?

Consider the function $$f(x)= \begin{cases}       0, & \text{if}\ x\ \text{is rational} \\       x, & \text{otherwise}     \end{cases}$$  My question is - Is the function continuous at zero? I understood that the function is not continuous at any other points in $\mathbb{R}$. But for zero I think it is continuous as for any sequence $\{x_n\}_{n\in \mathbb{N}}$ consisting of rational and irrationals that converges to zero, the function takes the value $0$ for rationals which obviously converges to $0$ and for irrationals the function is the identity function which also goes to $0$ as $x_n$ goes to zero. Am I correct?  Thanks!


Combining two different material in to one in node editor

I liked to combine two different materials in to one material in nodes, so that  I could create mountain like structures.  I try to use the noise as the base of the mountain structure, and add a different snow like material to the top of the hills where the normal height is high in the noise texture.  How do I combine two different material on top of each other, so that the height decides what material is used?


Can you help me to change window's appearance in Ubuntu 16.04 to be like this image?


Intuition behind the implicit function theorem.

Is there any intuition behind the implicit function theorem? Take $F(x,y)=0$ where $y=f(x)$. Then,  $$ \frac{dy}{dx}=-\frac{F_x}{F_y} $$  I see that the derivative is equal to the reciprocal of the partial derivatives, what is the intuition behind this?


Margin/Padding/Border (?) issue with HTML table

Having HTML code

   with CSS styles  * {     border: none;     margin: 0;     padding: 0; } table {     position: absolute;     left: 50%;     top: 50%;     width: 110px;     height: 92px;     margin-left: -55px;     margin-top: -46px; } img {     width: 110px;     height: 92px; }   accessible in ,  I would expect to have no margin, no padding and no border in the table content. However table height is not same as the image height. There are some extra pixels somewhere in td element.  What is a problem here? Is it style or html code?


Low gpa, but plenty of experience: Neuroscience grad school chances? How can I improve?

I am a Neurobiology, Physiology and Behavior (NPB) undergrad student at UC Davis. I am taking my last year and a half (with 5th year) of classes. I transferred to UC Davis from UC Santa Cruz for my junior year; I completed lower div bio, gen chem, ochem, physics, and calc at UCSC. These are my projected gpa breakdowns:  GPA: Overall gpa: 3.312 (upward trend) Overall major gpa: 3.200 (upward trend) UC Davis major gpa: 3.705 (upward trend)  I am retaking two D+'s, one NPB related the other is not. They were within two quarters and I had a family medical emergency, so I had a rough time. Other than that I have never gotten a D, and got one C- that was also during those bad quarters.  EXPERIENCE: (in process of/completed) 1 first author & 2 coauthor papers: I have worked in a cognitive neuroscience lab since summer after freshman year at UC Davis, total I will work there for 5 years upon completing my 5th year. I am the coauthor of a paper soon to be published, am in the process of creating an experiment I will be a first author on, and will be a coauthor of another paper my colleague and I are creating.  LETTERS OF REC: I will have strong letters of rec from both UCSC and UCD. I spent two days a week going to graduate student discussions regarding Alzheimer's at UCSC and was offered a lab position, so two professors there would be options for letters of rec. The doctor I work for at UCD will write me a letter of rec, and I transferred to UCD because of the lab position only, so I'm sure that would be a strong letter of rec.  I'm concerned, because my overall gpa is very low. It didn't click in my head that lower div classes mattered freshman and sophomore year. I am working to get all A's this year, but if I don't, my major gpa will be around a 3.149. I am committed to getting all A's though and made it possible to do so. Ultimate goal is PhD at a top school, but I think I need a master's first to bump my gpa up.  What do you all think? Anything else I can do besides work on grades? Thanks for your help!


I do not find any option to change my username. Please do add a feature to change the user name.


Symmetry of second derivative - Sufficiency of twice-differentiability

Symmetry of second derivative states that for $u=u(x,y)$ if $u_x,u_y$ exists and $u_{xy},u_{yx}$ exists and continuous then $u_{xy}=u_{yx}$.  I proved that statement using the mean value theorem.   While I was looking in Wikipedia there is a section called "Sufficiency of twice-differentiability", if $u(x,y):E^{\text{open set}}\subset \Bbb R^2\to \Bbb R$ and $u_x,u_y,u_{yx}$ exists everywhere and $u_{yx}$ is continuous at a point in $E$ then $u_{xy}$ exists at that point and equal to $u_{yx}$.  My question is, while I proved Symmetry of second derivative I had to assume the continuity of $u_{xy}$ and $u_{yx}$, so how can I prove that this is true without even assuming the existence of one of the second derivative? I'm sitting on this for a long time and I couldn't think on any starting point and would love help with this.


I want run a rule from trigger (Lead Assignment rule - default) when a new lead is created. I tried something but its not working. Don't know which one is correct way to do that. below you can find my code with bugs. I got something from this  but I don't want to do database operations. I just want to run my rule. Someone please help me.  trigger leadAssignment on Lead (after insert) {     for (Lead l : Trigger.new) {         if(l.My_Field__c != null && !l.My_Field__c.isEmpty())         {            Database.DMLOptions dmo = new Database.DMLOptions();            dmo.assignmentRuleHeader.useDefaultRule = true;            }     } }   isEmpty() not working any better way to do that? If this information is not enough just comment it I will update. Thanks in advance.


Upgrade from Ubuntu 12.10 to 13.04 "Failed to fetch cdrom://Ubuntu 12.10 _Quantal Quetzal"

I am not able to upgrade to the latest version 13.04. The error is:  Failed to download repository information Check your Internet connection. Details W:Failed to fetch cdrom://Ubuntu 12.10 _Quantal Quetzal_ - Release i386 (20121017.2)/dists/quantal/main/binary-i386/Packages   Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs, W:Failed to fetch cdrom://Ubuntu 12.10 _Quantal Quetzal_ - Release i386 (20121017.2)/dists/quantal/restricted/binary-i386/Packages Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs, E:Some index files failed to download. They have been ignored, or old ones used instead.


Cauchy's induction principle states that:     The set of  propositions  $p(1),...,p(n),...$ are all  valid if:           $p(2)$ is true.   $p(n)$ implies  $p(n-1)$ is true.   $p(n)$ implies $p(2n)$ is true.      How  to prove  Cauchy's induction principle? Can we use it to  prove what we  can prove with weak  and strong induction?  If yes how  to  prove using Cauchy's induction principle  $$ 1+2^1+2^2+...+2^n=2^{n+1}-1 $$


I am going from India to Japan. I have Japan visa. My flight is via Hong kong. Transit time is around 5 hours. Is it required to have Hong kong visa?


Is there a proper way to clean the iPhone screen?

Is there a particular proper way to clean the iPhone's glass, oleographic coated, screen in order to maintain its luster?


I have a PNG plot with a couple of black patches in it, and I'd like to refer to it in the \caption of the figure. According to the TikZ manual, I'd have to  \tikz \fill[black] (1ex,1ex) circle (1ex);   which works perfectly outside a \caption. Using this inside a \caption, though, leaves me with the compile error  ! Use of \use@pgflibrary doesn't match its definition. \pgfutil@ifnextchar ...1\def \pgfutil@reserved@a {                                               #2}\def \pgfutil@reserved@... l.375 ...blah blah.}  ?   The following produces the compile error  \documentclass{article} \usepackage{tikz}  \begin{document} \tikz \fill[orange] (1ex,1ex) circle (1ex); \begin{figure} \caption{\tikz \fill[orange] (1ex,1ex) circle (1ex);} \end{figure} \end{document}   Any hints here?


Masking footage over 3d objects in Blender 2.8+?

I don't get how to make a mask and use it properly. What I'd like know exactly is how to make a mask of a certain area of the footage, keep it tracked to the footage and make the mask layered in front of any 3d mesh.  Q: How do I create a proper mask to place any 3d object behind an element of my footage?


Installing Ubuntu from USB stick onto itself

My HP Proliant Microserver USB boot and run stick failed so I created a new Ubuntu 16.04 USB bootable stick on my mac as per my previous notes, e.g.:   hdiutil convert -format UDRW -o ubuntu-16.04-server-amd64.img ubuntu-16.04-server-amd64.iso diskutil list # shows disk3 diskutil unmountDisk /dev/disk3s1 dd if=ubuntu-16.04-server-amd64.img.dmg of=/dev/rdisk3 bs=10m  # Write to the first partition!!! diskutil eject /dev/disk3   I then installed the USB stick into the HP and booted which comes up into the install process where I followed all steps until partitioning where I selected Use entire disk. An error then pops up stating that a failure occurred writing the partition table probably because the disk is in use and suggesting a reboot. I then attempted a reboot, but the USB stick no longer boots.  I also tried the above with Ubuntu 18.04 (from ubuntu-18.04-live-server-amd64.iso), but when it reaches the file system setup it shows no disk to install to (it must install to itself). Hitting Cancel then reboots the system starting the install process all over again.  I know this worked in the past for 16.04, but cannot figure out what is going on - unless the USB sticks are a problem?  Any suggestions would be much appreciated. Note that Ubuntu must run from the original boot USB stick with full functionality, e.g. create users, network config, disk volumes, etc.


Expansion of space vs movement within space

I understand that some very distant objects (galaxies) are moving away from us at speeds exceeding the speed of light and that such expansion induced speed is not limited by the theory of relativity. However these objects may also be moving within space at speeds limited by relativity. How do we distinguish between these 2 components of speed, following different laws?


Formula symbols for mixed model using lme4

I often confuse symbols :, |, / and * in the R formulas, particularly when fitting mixed models with lme4. Can somebody explain clearly the differences between them?   Later edit by @amoeba (Jan 2018): this question had a long and extremely confusing R code. I cut it all out for the benefit of future readers. Please see edit history if interested.


How the first tree in gradient boosting classifier is constructed and the split criteria

I am aware how GB classifiers are constructed as regression trees and predictions are made, but not sure how the initial tree and node splitting for it is done.  Can someone please explain how the first tree in GBM  (classifier) is constructed, and how the node splitting criteria for the first tree is decided.  I am not sure, what we are predicting for the first tree (even assuming a constant is initialized, how gradient of loss are computed from the constant).  If mse is the node split criteria, what is it composed of (I mean, squared difference of what values??). Thank you.


C# Debugging functions that contain lambda expressions

I have a function with a lambda expression something like:  int maxOccurrences = ( from field in data select field ).Max( f => f.Occurrences )   P.S. I'm sure that there's a nicer / neater / more idiomatic version of the above statement, it might be nice to know what that might be, although its not important to the question!  If I modify anything else within the function whilst debugging say a Console.Write expression, the debugger states:     Modifying a 'method' which contains a lambda expression will prevent the debug session from continuing while Edit and Continue is enabled.   I was wondering why this might be the case?  I would have thought that the IL generated for the lamba function and the Console.Write statement would be separate and that the Debugger could alter and modify when necessary. Is there some fundamental concept that I'm missing concerning the lamda functionality?


How to model an entity type that can have different sets of attributes?

I’m having some trouble in recreating a database with a one-to-many (1:M) relationship between Users and Items. This is pretty straightforward, yes; however, each Item belongs to a certain Category (e.g., a Car, a Boat or a Plane), and each Category has a particular number of attributes, e.g.: Car structure: +----+--------------+--------------+ | PK | Attribute #1 | Attribute #2 | +----+--------------+--------------+  Boat structure: +----+--------------+--------------+--------------+ | PK | Attribute #1 | Attribute #2 | Attribute #3 | +----+--------------+--------------+--------------+  Plane structure: +----+--------------+--------------+--------------+--------------+ | PK | Attribute #1 | Attribute #2 | Attribute #3 | Attribute #4 | +----+--------------+--------------+--------------+--------------+  Because of this diversity in the number of attributes (columns), I initially thought it would be a good idea to create one separate table for each Category, so I would avoid several NULLs and thus making a better use of the indexing. Although it looked great at first, I couldn’t find a way to create the relationship between the Items and the Categories through the database because, at least in my modest experience as a database administrator, when creating Foreign Keys, I inform explicitly a database the table name and column. In the end, I would like a solid structure to store all data, while having all the means to list all attributes of all Items a User may have with one query. I could hardcode dynamic queries with the server-side language, but I feel this is wrong and not very optimal. Additional information These are my responses to MDCCL comments:  1. How many Item Categories of interest are there in your business context, three (i.e., Cars, Boats and Planes) or more?  In fact, it’s very simple: There are only five Categories in total.  2. Will the same Item always belong to the same User (that is, once a given Item has been “assigned” to a certain User it cannot be changed)?  No, they could change. In the fictional scenario of the question, it would be like User A sells Item #1 for User B, so the ownership must be reflected.  3. Are there attributes that are shared by some or all of the Categories?  Not shared but, from memory, I can tell that at least three attributes are present in all Categories.  4. Is there a chance that the cardinality of the relationship between User and Item is many-to-many (M:N) instead of one-to-many (1:M)? For example, in the case of following business rules: A User owns zero-one-or-many Items and An Item is owned by one-to-many Users  No, because Items would describe a physical object. Users will have a virtual copy of them, each one identified by a unique   5. Regarding your following response to one of the question comments:  “In the fictional scenario of the question, it would be like User A sells Item #1 for User B, so the ownership must be reflected.”  It seems that you are planning to keep track of the item ownership evolution, so to speak. In this way, which attributes would you like to store about such phenomenon? Only the modification of the attribute that indicates the specific User who is the Owner of a specific Item?  No, not really. The ownership may change, but I don’t need to keep track of the previous Owner.


I am writing a report using class article. Since I have already started with article, I want to know if there is any wait to have frontmater and mainmatter like in class book. I want my introduction section number to be 1 and all titles (and page numbers) before to be with roman numerals.  Thanks.


Apache accepting requests to other servers?

I'm having problems with apache server (CentOS VPS at Amazon). When apache starts, it starts to receive hundreds of requests, this is an example of the log:  173.208.216.165 - - [25/Jan/2015:18:23:11 +0000] "GET http://go.padstm.com/resources/img/iebt.png HTTP/1.0" 200 36023 "http://go.padstm.com/?id=173374&t=iframe&var=33110" "Mozilla/5.0 (Windows; U; Windows NT 6.1; ru; rv:1.9.2.3) Gecko/20100401 Firefox/4.0 (.NET CLR 3.5.30729)"   The path /resources/img/iebt.png is in my server, but not go.padstm.com. The strangest thing is that apache is accepting all the requests.  Other example: in this case, the entire resource is NOT in my server, but apache returns 200:  198.204.239.250 - - [25/Jan/2015:19:04:39 +0000] "GET http://fstads.com/show.php?z=26&pl=494&j=1&code=1422237874120 HTTP/1.0" 200 10819 "http://financezhen.com/?p=186#respond" "Mozilla/5.0 (Windows NT 6.1; Win64; x64; rv:2.2a1pre) Gecko/20110324 Firefox/4.2a1pre"   I don't know why these requests goes to my server, or why it returns 200...  Also, when apache starts and module prefork is enabled, it launches multiple httpd processes. If worker module is enabled, it launches multiple threads. Ok, but in both cases apache ends up consuming all the CPU and memory of the server, and there is not traffic directed to my server.  More info: ProxyRequests is Off. Also: I'm using ip-based vhosts:  NameVirtualHost xxx.xxx.xxx.xxx:80  <VirtualHost xxx.xxx.xxx.xxx:80>     ServerName mydomain.com     ServerAlias www.mydomain.com     DocumentRoot /var/www/html/w3prod     ServerAdmin admin@localhost     UseCanonicalName Off     CustomLog /var/log/httpd/w3prod.mydomain.com combined     ErrorLog /var/log/httpd/w3prod_error.mydomain.com </VirtualHost> <VirtualHost xxx.xxx.xxx.xxx:80>     ServerName picfarm.mydomain.com     ServerAlias www.picfarm.mydomain.com     DocumentRoot /var/www/html/picfarm     ServerAdmin admin@localhost     UseCanonicalName Off     CustomLog /var/log/httpd/picfarm.mydomain.com combined     ErrorLog /var/log/httpd/picfarm_error.mydomain.com </VirtualHost> <VirtualHost xxx.xxx.xxx.xxx:80>     ServerName test.mydomain.com     ServerAlias www.test.mydomain.com     DocumentRoot /var/www/html/engine-test     ServerAdmin admin@localhost     UseCanonicalName Off     CustomLog /var/log/httpd/test.mydomain.com combined     ErrorLog  /var/log/httpd/test_error.mydomain.com     ProxyRequests Off     ProxyPreserveHost On     <Proxy *>             Order deny,allow             Allow from all     </Proxy>     ProxyPass /bosh http://xxx.xxx.xxx.xxx:7070/http-bind/     ProxyPassReverse /bosh http://xxx.xxx.xxx.xxx:7070/http-bind/     ProxyPass / http://xxx.xxx.xxx.xxx:8080/     ProxyPassReverse / http://xxx.xxx.xxx.xxx:8080/ </VirtualHost>   Any help would be appreciated. Thanks!


Preventing applications from stealing focus in Windows 10

There is a  asking for a solution for windows 7. I have recently grew tired of newly launched applications to steal focus from my currently opened window. Is there a way how to prevent programs from stealing focus in Windows 10?  Thank you


Ubuntu is booting into terminal instead of GUI Interface

I recently upgraded my computer to Ubuntu 12.04 from 10.04 and it started messing up, as in, freezing up on certain programs and then randomly logging out and going to the log-in screen.  I've done all of the upgrades and it still wasn't working properly.  Now when I turn the computer on, instead of booting to the GUI Interface, it boots straight to the terminal.  Is there any command I can type to boot it properly?  And if so, what do I do to keep it booting properly?    I did some research and found that some people used the "startx" command, but it didn't work for me.  This is what it said:   "X: user not authorized to run the X server, aborting. X10:  fatal 10 error 11 (Resource temporarily unavailable) on X server ":0"       after 7 requests (7 known processed) with 0 events remaining."  Any help would be greatly appreciated!


Java - Pass by "Reference Value"? Retrieved Reference Value or Value?

If I have a class like the one below:  public class Foo() {     private RandomObject randomObject = new RandomObject();      public RandomObject GetRandromObject()     {         return randomObject;     } }   And in another class I do this:  public class Goo() {     private Foo fooObject = new Foo();      public Goo()     {         RandomObject ro = fooObject.GetRandomObject();          ro.ChangeNumberVariable(23);     } }   Will the fooObject have the randomObject NumberVariable changed to 23?  If not would I just have to have a method in Foo called SetRandomObject and just pass in ro? Would this be a good substitute for passing by reference in Java?  What if I just did this:  public class Goo() {     private Foo fooObject = new Foo();      public Goo()     {         fooObject.GetRandomObject().ChangeNumberVarialbe(23);     } }   Is it still not changing the NumberVariable?


How to get correct number after calculation? For instance, I want 2.2 - 1 equal to 1.2 and not 1.2000000000002. Wanna get exactly correct answer without rounding the number itself and without just simply changing the way of printing the number via print('%1.1f' % number).


Remote Desktop Session Black after Minimize

PROBLEM: When I minimize a remote desktop session and restore it, the remote desktop screen shows up black. This only happens when connecting to a particular computer.   DETAILS: If I start clicking around in the black area, portions of the screen will start redrawing and showing up correctly. For example, if I leave a window open in the remote session and click where that window is located on the remote computer, then that window--and only that window--will redraw, and sometimes a portion of that window won't redraw (usually the toolbar).  And to clarify--the window only has to be minimized momentarily, so it doesn't seem to be a timeout issue. Clicking or typing in the remote session still causes the remote computer to respond appropriately. Disconnecting from the session and reconnecting restores the whole screen image, as does clicking all over the place in the black image (causing each section to redraw).  CONFIGURATION: This problem only happens for me when connecting to a particular computer (a W2K Server box configured to allow remote administration) and only with certain client computers. I've tried 7 different client computers with various versions of Remote Desktop (the OSes were: Win2K, Server 2003, Server 2008, Windows 7 RC, 3 XP) and two of them exhibit the problem (one is one of the XP boxes and the other is Windows 7). Those same computers can RDP to other computers without problem.  RESOLUTION ATTEMPTS: I have tried the following:   Disable the LOCAL screen saver as mentioned on  Turned off bitmap caching in the client, as mentioned on many forums. Updated to version 6.1 of the remote desktop client Using mRemote (I doubted this would work since it uses MS's code for connecting to RDP servers) Turning off all video acceleration.   QUESTION: Any ideas on what is causing this?


MC 1.9: Chunk Loader for Redstone Circuits?

I have developed an automatic train system using minecarts and redstone circuits to let the minecarts travel between stations. It worked so far for lines in the near environment. But I noticed that it fails for longer distances, because the chunks are not loaded - therefore the minecart will stop and never come back, until the chunks were loaded by a passing player.    I am using a 1.9 Vanilla server, and I have full access to the server.  The Chunks don't need to be loaded when no player is on the server. But if there are players, the chunks containing the stations and the line should always be loaded when players are online.  How can I achieve this?  I am willing to install server mods, if necessary, but I only found a mod for MC 1.7. For some tutorials, I am confused about "Lazy Load chunks" and "entity chunks", and I do not know which type I need for my scenario. I also read that it might be possible using command block chains, but I do not know exactly how this works (and if it actually works for this scenario).    I do not understand why you think it is a duplicate. Once again, if the end station is set to a spawn point, then the whole track in the middle (the powered rail) won't work. So the linked question doesn't fit the problem situation.


Is there a general proof for this?  The portion of the tangent to any conic intercepted between the point of contact and the directrix subtends a right angle at the focus of the conic?  For parabola, it can be solved this way: the tangent at $P=(at^2, 2at)$ is $ty = x + at^2$. This meets the directrix at the point $Q=(-a,a(t^2 - 1)/t)$. Now, $\text{Slope of }SQ\times\text{Slope of }SP = -1$. Hence, $∠PSQ = 90°$. A similar way of writing the parametric coordinates and equating the product of slopes to $-1$ yields the desired result for other conics. But is there a geometric proof for any general conic?


Kibana cannot be accessed through port 5601 in browser

I cannot get to kibana through web UI. I'm set the necessary ports in firewall-cmd, I've configured kibana.yml and elasticsearch.yml. I'm not seeing any relevant errors, or at least don't know if they are if they are there. It just shows 'Site cannot be reached' for the appropriate port. Later on I would like to have put kibana on a subdomain kibana.domain.com, but I would first like to confirm that it's working without a subdomain. I can confirm that my domain and nginx are working Current versions: OS - Centos 8 Elasticsearch - 7.10.2 Kibana - I have no clue how to get the version through terminal (there aren't version conflicts to my knowledge so it shouldn't matter. It's 7.x) There is only one instance of kibana running on 5601 from what I can see. netstat -tulpn | grep LISTEN tcp        0      0 127.0.0.1:5601          0.0.0.0:*               LISTEN      290961/node tcp        0      0 0.0.0.0:111             0.0.0.0:*               LISTEN      1/systemd tcp        0      0 0.0.0.0:80              0.0.0.0:*               LISTEN      290425/nginx: maste tcp        0      0 0.0.0.0:22              0.0.0.0:*               LISTEN      4738/sshd tcp        0      0 0.0.0.0:443             0.0.0.0:*               LISTEN      290425/nginx: maste tcp6       0      0 :::111                  :::*                    LISTEN      1/systemd tcp6       0      0 :::80                   :::*                    LISTEN      290425/nginx: maste tcp6       0      0 127.0.0.1:9200          :::*                    LISTEN      287716/java tcp6       0      0 127.0.0.1:9300          :::*                    LISTEN      287716/java tcp6       0      0 :::22                   :::*                    LISTEN      4738/sshd tcp6       0      0 :::443                  :::*                    LISTEN      290425/nginx: maste  kibana.yml server.port: 5601 server.host: "127.0.0.1" elasticsearch.hosts: ["http://127.0.0.1:9200"]  elasticsearch.yml cluster.name: portfolio_es_cluster node.name: portfolio_es_node path.data: /var/lib/elasticsearch path.logs: /var/log/elasticsearch network.host: 127.0.0.1 http.port: 9200  Curl for kibana locally works curl -XGET http://localhost:5601/status -I HTTP/1.1 200 OK content-security-policy: script-src 'unsafe-eval' 'self'; worker-src blob: 'self'; style-src 'unsafe-inline' 'self' kbn-name: mykibananame kbn-license-sig: d9d95bb2e2230b29804216ff76 content-type: text/html; charset=utf-8 cache-control: private, no-cache, no-store, must-revalidate content-length: 121035 vary: accept-encoding accept-ranges: bytes Date: Mon, 18 Jan 2021 06:53:36 GMT Connection: keep-alive  firewall-cmd --list-all public (active)   target: default   icmp-block-inversion: no   interfaces: eth0 eth1   sources:   services: cockpit dhcpv6-client http https ssh   ports: 5601/tcp 9200/tcp   protocols:   masquerade: no   forward-ports:   source-ports:   icmp-blocks:   rich rules:


Is it possible to "lock", or protect, the spacing of a math formula displayed in-text, so that latex will not stretch and squeeze the formula?   I would not like to do this globally for all formulas, but I have one formula ($(-+++)$) that appears repeatedly. Is it possible force latex to always display it with the same spacing?  Update: I now realise that the problem in rendering $(-+++)$ was not due to stretching/squeezing in a paragraph, but due to the special role of + and - in latex formulas. The first - and + are presumably treated as delimiters between terms in a formula, and the latter two two are rendered differently with a shorter spacing. The solution $({-}{+}{+}{+})$ given by cgnieder solves this spacing problem, and gives equal spaces between all +:s and -:s. How to remove such spaces has been asked before: .


Does $G\cong G/H$ imply that $H$ is trivial?

Let $G$ be any group such that  $$G\cong G/H$$ where $H$ is a normal subgroup of $G$.  If $G$ is finite, then $H$ is the trivial subgroup $\{e\}$. Does the result still hold when $G$ is infinite ? In what kind of group could I search for a counterexample ?


Only after reading it carefully several times did I begin to make sense of the poem. Only after reading it carefully several times I began making sense of the poem.   I know that the first one is correct but I do not understand why.  Other than sounding strange, why is the second one incorrect?  Thank you very much!


Is there a way to tell Nautilus not to generate previews of PDF files?

I tend to download lots of articles as PDFs, and I find that when I browse a directory of these Nautilus takes 1 minute to load the directory. I assume that's because it's generating previews of their front pages. That feature is useless to me, alas.  I'd like to tell it not to do that.


My ex changed my authorization password. I am not at all tech savvy by any means and have no idea what to do

I have a toshiba satellite laptop that I purchased from a friend while in a relationship with my ex. during our breakup he changed my password and now I can't authorize any important changes that are needed for upgrades, deleting files etc. Unfortunately for me he is much more familiar with computers than I am and I'm not even sure if this is the only change or problem he created . I've tried many suggestions that I found online including deleting the keyring and related files with absolutely no success. Can someone please help me out.


Wallpaper not updating on startup/login screen

I have updated my wallpaper recently and now when I restart my computer or logout, my old wallpaper still shows (blurred, obviously) on the login screen. When I login, my new wallpaper is there. Is there a way to fix this?  Unfortunately this possible duplicate does not address my issue:  This is not after updating to Mojave OS. I have not updated to it. So I do not have a "Mojave.heic"


I can't figure this out, I'm trying to run winetricks and install prerequisites needed for running 32-bit Windows software, but I don't even know how to begin to do that. Every time I open winetricks it opens as 64-bit winetricks. I don't know what I'm doing.


im reading a arm based mcu board schematic and there is 100R resistor (R30) at external 25MHz oscillator source. What is the main reason of using serial resistor at clock line ?


How do i create a sed script to prompt the user to replace a number in a file?

I'm new in Unix, and I'm learning about sed command. I need to write a very small script for searching a number in a file and replacing it. I tried doing grep, and than deleting the specific phone number from a file, and then adding another one. But i was told that i can use sed in a script to replace. I know how to use the sed command on a command line for search, and replacing something. But how do i write a script, which lets the user search a number, and then let the user enter the number which they want to replace the old number with.   So far what i did was use grep to find a number, that works. but now I'm stuck at how can i let the user add in the new number, so the new number can replace the old one. I tried piping grep to sed, and vice versa. No luck so far. I sound redundant, :/ but I'm really frustrated. Any help will be appreciated :D.


How to grep a date lesser than a particular date in a file

I have a log file like Blah blah blah 2018-12-13.  Now I want to grep the log files with a date before 2018-05-01.  My intention is to filter the Log files lesser than 2018-05-01


$f:[0,1] \to [0,1]$ be a continuous function. Prove there exists a point p an element of $[0,1]$ such that $f(p)=p$  I have no idea how to do this but is it asking me for a proof if the intermediate value theorem?  i'm not entirely sure how the IVT would solve this because it doesn't specify $f(p)=p$.


Template files not working with child theme

This is the second week in a row that I'm having trouble trying to get a child theme working with Wordpress, despite having studied the  and following it word for word.  I'm developing with a local installation using XAMPP.  The parent theme I'm trying to use is called blocksy, and it's in the wp-content/themes directory. Within that directory, I created another directory  called industry-road, and in that created a style.css and functions.php.  This is the content of the style.css:  /*! Theme Name: Industry Road Author: My Name Version: 1.0.0 Template: blocksy Tags: blog, e-commerce, wide-blocks, block-styles, grid-layout, one-column, two-columns, three-columns, four-columns, right-sidebar, left-sidebar, translation-ready, custom-colors, custom-logo, custom-menu, featured-images, footer-widgets, full-width-template, theme-options, threaded-comments */   And this is the content of functions.php:  ?php add_action( 'wp_enqueue_scripts', 'my_theme_enqueue_styles' ); function my_theme_enqueue_styles() {      $parent_style = 'blocksy'; // This is 'twentyfifteen-style' for the Twenty Fifteen theme.      wp_enqueue_style( $parent_style, get_template_directory_uri() . '/style.css' );     wp_enqueue_style( 'industry-road',         get_stylesheet_directory_uri() . '/style.css',         array( $parent_style ),         wp_get_theme()->get('Version')     ); } ?>   When I activate the child theme the Wordpress Dashboard does show that it is a child theme of blocksy.   However, when I attempt to copy a file blocksy/inc/hero-section.php into industry-road/inc/hero-section.php (creating the necessary directory structure as I do) and change a line in it, nothing changes on my site.  When making the same change to the original hero-section file in the parent theme, however, the change takes effect immediately.   In other words, despite the fact that my child theme seems to be activated and working correctly, and despite the fact that the Codex says template files in the child theme should override their equivalent files in the parent theme, this isn't happening.   What exactly is going on here and how can I fix it?


Take infrared photo with digital camera?

With a film camera it is easy to take infrared photos, just get infrared film.  Is there any way to do this with a standard professional digital camera?  My understanding is that such cameras have a 700-1000nm filter to block infrared light. Can this filter be removed somehow?


Why is "A only if B" equivalent to "(not A) or B"?

I've encountered this recently and I just can't wrap my head around it. My book states that   $$A \rightarrow B \equiv \neg A \lor B$$  It's my understanding that $A \rightarrow B$ means that if $A$ is true, then $B$ is true.   But, $\neg A \lor B$ would allow for us to have that $\neg A$ is true and $B$ is true, which seems to be pretty much that exact opposite of $A \rightarrow B$, so how can these be equivalent?


I have a website with the domain as ‘domain.tld’. I have a product let’s call it as ‘Name A’. The product is used for purpose say ‘Purpose 1 software’. Now I need to optimise the SEO of the product page for both product name and product purpose. So I decided to add the 2 keywords (‘Purpose 1 software’, ‘Name A’) in the page url. But what will be the best way to gain high SEO rankings for the product page with both the keywords? Using them in URLs as below examples?   domain.tld/product/Purpose-1-software/name-a/    ? domain.tld/product/ Purpose-1-software /#name-a   ? Or is there any other way?   Note: In the URL, I need to give more priority to ‘purpose 1 software’ rather than ‘name A’ as I target new customers. Purpose 1 software is only one part of the software. Actually, Name A is the multipurpose software and I would like to target that software for many purposes in the SEO.  Please let me know the best way to include those 2 keywords in the URL.  Update:  I can make any changes for the url/permalink since i am using wordpress for hosting my site.


What is the link between foreach and IEnumerable?

The foreach statement repeats a group of embedded statements for each element in an array or an object collection that implements the System.Collections.IEnumerable or    System.Collections.Generic.IEnumerable<T> interface.     I understand that if we want to use foreach on an object collection, we need to implement IEnumerable on it.   I want to understand how does implementin IEnumerable enable the usage of 'foreach'?  The source code of IEnumerable seems to have only one function 'GetEnumerator', and obviously there is no implementation because IEnumerable is an interface - So how does the foreach keyword actually use IEnumerable interface for enumeration?  Edit: Also trying to understand it in this context:     IEnumerable<Int> myNumbers = new IEnumerable<Int>();    Which GetEnumerator() is called/used here?    Edit 2:  So the answer seems to be:     1: DuckTyping -- (thanks  @Alexei Levenkov. I accepted @horrorcat as an answer because I can accept only one :) )     2. I made an obvious mistake in trying to create a concrete instance of an interface (in the second part of my question) -- (thanks @Gary Vass)


I'm using the listings package to insert code into the document. My research led me towards the literate option of listings to control operator highlighting. I have one issue - the right round bracket won't accept the rule. Every other line in this snippet of code works as intended.   \documentclass[11pt, twoside]{book}  \usepackage{verbatim}               % For commenting out multy line commands %\usepackage[utf8]{inputenc} \usepackage{xcolor}   \usepackage{lipsum}                 % Dummy Text \usepackage{listings}               % Code Inclusion  \definecolor{codegray}{HTML}{A0A0A0} \definecolor{codegreen}{HTML}{00A000} \definecolor{codeblue}{HTML}{0000A0} \definecolor{codelightblue}{HTML}{0000FF} \definecolor{codepurple}{HTML}{F000F0} \definecolor{codered}{HTML}{FF003A}  %----------------- Code Formatting Options --------------- \lstset {  backgroundcolor=\color{white},   % choose the background color;     commentstyle=\color{codegray}, keywordstyle=\color{codeblue}, stringstyle=\color{codelightblue}, identifierstyle=\color{black}, literate=% *{0}{{{\color{codepurple}{0}}}}1  {1}{{{\color{codepurple}{1}}}}1  {2}{{{\color{codepurple}{2}}}}1  {3}{{{\color{codepurple}{3}}}}1  {4}{{{\color{codepurple}{4}}}}1  {5}{{{\color{codepurple}{5}}}}1  {6}{{{\color{codepurple}{6}}}}1  {7}{{{\color{codepurple}{7}}}}1  {8}{{{\color{codepurple}{8}}}}1  {9}{{{\color{codepurple}{9}}}}1  {[}{{{\color{codered}{[}}}}1  {]}{{{\color{codered}{]}}}}1     {(}{{{\color{codered}{(}}}}1  {)}{{{\color{codered}{)}}}}1    %problematic )  {=}{{{\color{codered}{=}}}}1      {+}{{{\color{codered}+}}}1    {-}{{{\color{codered}-}}}1  {*}{{{\color{codered}*}}}1  {>}{{{\color{codered}>}}}1  {<}{{{\color{codered}<}}}1  {|}{{{\color{codered}|}}}1  {&}{{{\color{codered}&}}}1  {!}{{{\color{codered}!}}}1  {:}{{{\color{codered}:}}}1  {;}{{{\color{codered};}}}1  {,}{{{\color{codered},}}}1  {\{}{{{\color{codered}\{}}}1      {\}}{{{\color{codered}\}}}}1,  %tag=[s]{()},                                  % you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument language=C,                      % the language of the code basicstyle=\linespread{.9}\ttfamily\footnotesize,        % the size of the fonts that are used for the code. Line spread should not be more than 1. numbers=left,                    % where to put the line-numbers; possible values are (none, left, right) numbersep=5pt,                   % how far the line-numbers are from the code stepnumber=1,                    % the step between two line-numbers. If it's 1, each line will be numbered showstringspaces=false,          % underline spaces within strings only tabsize=1,                       % sets default tabsize to 1 spaces breaklines=true,                 % sets automatic line breaking breakatwhitespace=false,         % sets if automatic breaks should only happen at whitespace numberstyle=\tiny\color{white},  % the style that is used for the line-numbers frame=l, framesep=4.5mm,                  % sets the thickness of the background framexleftmargin=0.5mm,          % sets the distance from the code fillcolor=\color{myDarkGray},          % sets the background colour rulecolor=\color{myDarkGray},          % sets the left border colour %aboveskip=5mm,                  % creates space abjove the code, but within the box %belowskip=10mm                  % creates space below the code, but within the box }  \begin{document}  \lstinputlisting{file.c}  \end{document}   The output:


How to assign unused special keys on keyboard to a macro?

I have an old "compaq internet keyboard" pictured below. Many of the top keys no longer work in windows 10 without the correct software, or do something completely unrelated (for example: eject opens vlc).  My interest is not to make these keys do what they are supposed to. My interest is to repurpose these keys to do something useful. For example, a couple buttons could open different applications, another one could be dedicated to showing task view, another 2 for copy/paste, etc. Is there any way to accomplish this?


Interpretation of "transition rate" in Fermi's golden rule

This is a question I asked myself a couple of years back, and which a student recently reminded me of. My off-the-cuff answer is wrong, and whilst I can make some hand-waving responses I'd like a canonical one!  In the derivation of Fermi's Golden Rule (#2 of course), one first calculates the quantity $P(t)\equiv P_{a\rightarrow b}(t)$ to lowest order in $t$. This is the probability that, if the system was in initial state $a$, and a measurement is made after a time $t$, the system is found to be in state $b$. One finds that, to lowest order in the perturbation and for $\left< a \mid b \right > = 0$, $$P(t) \propto \left( \frac{\sin(\omega t/2)}{\omega/2} \right)^2, \qquad \hbar\omega = E_b - E_a $$  Then one says $P(t) = \text{const.} \times t \times f_\omega(t)$ where as $t$ increases $f$ becomes very sharply peaked around $\omega=0$, with peak of height $t$ and width $1/t$, and with total area below the curve fixed at $2\pi$. In other words, $f_t(\omega)$ looks like $2\pi \delta(\omega)$ for large $t$.  Now suppose we consider the total probability $Q(t)$ of jumping to any one of a family of interesting states, e.g. emitting photons of arbitrary momenta. Accordingly, let us assume a continuum of states with density in energy given by $\rho(\omega)$. Then one deduces that $Q(t) \sim \text{const.} \times t \rho$, and defines a "transition rate" by $Q(t)/t$ which we note is independent of time.  The issue I have with this is the following: $Q(t)/t$ has the very specific meaning of "The chance that a jump $a \to F$ (for a family $F$ of interesting states) occurs after making a measurement a time $t$ from the system being in state $a$, divided by the time we wait to make this measurement." It is not immediately clear to me why this is a quantity in a physical/experimental context which is deserving of the name "transition rate". In particular, note that   $t$ must be large enough that the $\delta$ function approximation is reasonable, so the small-$t$ regime of the formula is not trustworthy; $t$ must be small enough that the perturbation expansion is reasonable (and also presumably so that the $\delta$ function approximation is not insanely sensitive to whether there is a genuine continuum of states or simply very finely spaced states) so the large-$t$ regime of the formula is not trustworthy. Therefore the physical setup in which one measures $P(t)/t$ events per unit time must use properties as if some measurement/decoherence occurs made in some intermediate range of $t$. What is the microscopic detail of this physical setup, and why is this intermediate range interesting? Edit: Also I would like to emphasize that the nature of $P(t),Q(t)$ is such that whenever one "makes a measurement", the "time since in initial state" is reset to 0. It seems that the "time between measurements" is in this intermediate range. (Of course, this isn't necessarily about measurements, but might be to do with decoherence times or similar too, I'm simply not sure.) People tell me that the Golden Rule is used in calculating lifetimes on occasion, so I would like to understand why this works!     Succinct question: In what sense is $Q(t)/t$ a transition rate?


'asked today' shown on question 'asked 18 hours ago'

While viewing a question that I asked yesterday, the asked day is showing as today as shown in the screenshot:    Day is shown as today, the question was asked 18 hours ago and my current time is 11.46 am. My timezone is UTC+5.30 (Chennai).


Give Tag synonyms their own review queue

As per Robert Harvey's suggestion , lets have a review queue for tag synonyms.  It should be filtered so that users will only be shown what they can vote on.  This should help all those languishing tag synonyms.


In Eclipse, under Windows -> Preference -> Java -> Code Style, you can define code templates for comments and code, and you can setup a code formatter.   I'm wondering if it is possible in Eclipse to have these setting take affect every time I save a source file.  Basically, instead of me highlighting everything and pressing Ctrl+Shift+F, I want Eclipse to be responsible for making sure my code is formatted properly.  Is this possible and how do you set it up?  Note On Using the Auto-Format:  It's probably best to choose "Format Edited Lines" as merging changes becomes very difficult when you reformat a whole file that is in source control already that was not formatted properly. Already did this to a co-worker.


I don't know how to install Skype on Ubuntu 16.04.1. It was all okay until I updated my Ubuntu and now I can't install Skype.


Hotel search site with "out of pocket" price

I'm looking for a hotel search site that does the following things:   List the price as "what you pay" including all fees, taxes, surcharges, etc. Has a map view Ideally allows to search for "free cancellation"   Background: All my favorite search sites seems to have degraded a lot over the last few years, e.g. hipmunk.com, booking.com, hotels.com. They used to list the actual out of pocket price but now it's getting much more expensive when you get to the payment page, which makes it really hard to compare prices and plan to a budget. That's partially driven by the idiotic "resort fee" that many hotels have started charging. I had extreme case on hotwire.com today: advertised rate $74/night, actual price to pay was $139. Almost double.   Also, since maybe 2015/2016 the difference between "free cancellation" and "prepaid" has gone way up from almost nothing to a substantial percentage of the rate.  That, again, makes it hard to search for a "free cancellation" rate, since only the pre-paid ones will show up in the comparison.  Any tip for a website or some other search mechanism that allows comparing "true cost" for "free cancellation" rates would be appreciated.  EDIT Clarifying the question, since there seems to be some confusion. Let's say I have $200, I can spend on a room tonight in Boston. I'd like to see of a list of hotels that I can afford. Currently it's easy enough to see a list of hotels and prices, but the list prices are substantially lower than the actual price and the difference or ratio isn't constant either. For example, for tonight on hipmunk.com   "Taj Boston": lists at $170 but costs $225   "Westin Copley" lists at $180 but costs only $205.   So I have to always click through to the payment page to get the actual price and it's cumbersome to find hotels that match my price target.


Windows Update fails working on windows 7 with Error Code 8024200D

It may seem at first that we have many answers to this question but I tried them all but the update still fails.  Note: Windows 7 does not stuck in checking for updates. However, it downloads them but fails to install them : (No duplicates were found for this question).  Some of posts I've used to solve the issue:  Those all steps I have done:     1.  Stop the Windows Update related Services.    net stop wuauserv  // Ok : mean operation succeeded   net stop bits    // Ok   2. I deleted all files in:  C:\Windows\SoftwareDistribution folder and delete all the files and folders inside.    3. Restart the Windows Update related Services. net start wuauserv  // ok   net start bits      // ok        4. I have tried **Windows Update Troubleshooter** (WindowsUpdateDiagnostic.diagcab) : It said that the problems were     > solved !         Another try, I have installed the last update of Windows Update Agent-7.6      6. Last but not least: I tried to install failed updates manually but installation failed and sometimes cause system failure to start (need revert changes).  7. I tried a clean boot : disabled all non microsoft and startup services. Still updates failed with the same error.  8. Finally, I tried both WSUS offline updater 10.9 and Windows update MiniTool. Both of them failed.   Without forgetting doing a full Virus/Malware analysis and removal :D    After doing all of those steps and restarted my laptop many times the problem is not solved so any other methods to try are welcome.  Below part of my WindowsUpdate.log (Updated):  2017-01-21  21:15:20:871    1124    e2c AU  >>##  RESUMED  ## AU: Search for updates [CallId = {47F56A40-D8E6-4382-A523-1C96F796DCB9}] 2017-01-21  21:15:20:871    1124    e2c AU    # 97 updates detected 2017-01-21  21:15:20:884    1124    e2c AU  ######### 2017-01-21  21:15:20:884    1124    e2c AU  ##  END  ##  AU: Search for updates [CallId = {47F56A40-D8E6-4382-A523-1C96F796DCB9}] 2017-01-21  21:15:20:884    1124    e2c AU  ############# 2017-01-21  21:15:20:885    1124    e2c AU  Successfully wrote event for AU health state:0 2017-01-21  21:15:20:901    1124    8d4 Report  REPORT EVENT: {EAE73EBD-E9E8-49B2-A8BF-AA599200389F}    2017-01-21 21:15:20:860-0000    1   147 101 {00000000-0000-0000-0000-000000000000}  0   0   AutomaticUpdates    Success Software Synchronization    Windows Update Client successfully detected 97 updates. 2017-01-21  21:15:20:911    1124    e2c AU  ############# 2017-01-21  21:15:20:911    1124    e2c AU  ## START ##  AU: Refresh featured updates info 2017-01-21  21:15:20:911    1124    e2c AU  ######### 2017-01-21  21:15:20:911    1124    e2c AU  No featured updates available. 2017-01-21  21:15:20:911    1124    e2c AU  ######### 2017-01-21  21:15:20:911    1124    e2c AU  ##  END  ##  AU: Refresh featured updates info 2017-01-21  21:15:20:911    1124    e2c AU  ############# 2017-01-21  21:15:20:911    1124    e2c AU  AU setting next detection timeout to 2017-01-22 18:30:12 2017-01-21  21:15:20:911    1124    e2c AU  Successfully wrote event for AU health state:0 2017-01-21  21:15:20:953    1124    e2c AU  Successfully wrote event for AU health state:0 2017-01-21  21:28:07:000    1124    cf4 AU  AU setting next sqm report timeout to 2017-01-22 21:28:07 2017-01-21  23:17:05:744    1124    174c    AU  Getting featured update notifications.  fIncludeDismissed = true 2017-01-21  23:17:05:745    1124    174c    AU  No featured updates available. 2017-01-21  23:17:05:846    1124    174c    AU  WARNING: Returning due to error from GetDownloadProgressUx, error = 0x8024000C 2017-01-21  23:17:05:846    1124    174c    AU  WARNING: GetInteractiveInstallProgress failed, error = 0x8024000C


Ubuntu 20.04.1 has been released one week ago but is not proposed as an upgrade by my Ubuntu 18.04

My system is currently running Ubuntu 18.04. Ubuntu 20.04.1 has been out one week ago, yet it is not proposed as an upgrade by the software manager:  A call to sudo do-release-upgrade -c returns Checking for a new Ubuntu release There is no development version of an LTS available. To upgrade to the latest non-LTS develoment release  set Prompt=normal in /etc/update-manager/release-upgrades.  Am I being impatient, or is something wrong here? (In case that is relevant, I was actually running 16.04, and wanted to switch to 20.04 once the first point release is out. Hopping to 18.04 is a necessary step in the process -- this one happened flawlessly).


Section anchors invisible in main body, but visible in table of contents?

I'm writing up my PhD thesis using the memior class.  This thesis starts off by using chapters and sections as one normally would.  Later on in the thesis though, I insert many pdfs into this document using pdfpages.  I want to treat each one of these pdfs as a separate section of a chapter, but I don't want the section titles to appear in the main text, because each time that happens, an ugly page is created between the pdfs which is empty except for the section name.  I need to be able to but a \label in each of these sections so I can refer to them, and I also want the table of contents to list them with the appropriate section number and correctly link to them.  This is similar to a couple of other questions, but in those cases it seems the problem can be solved by simply using \addcontentsline{toc}{chapter}{#1} and \phantomsection.  In my case though, that solution prevents the sections from receiving numbers in the table of contents, and prevents \label from assigning each section a unique section number within a chapter.


Why do we assign values to divergent series?  For example, the series $1+2+3+4... = -1/12$.  I understand the proof for this, but I feel like it uses false math, and I recall reading that you can't do arithmetic/algebra with series that aren't absolutely convergent.  Obviously this series diverges, but why do we say it equals -1/12?  Thanks!


Calculating amount of cubes that fit in a sphere

I know that the problem of finding out how many spheres can fit in a cube is a commonly asked and well documented one, but I am struggling to find anything on the inverse of the problem, namely:     How many cubes of a certain Length x Width x Height fit in a sphere of a certain radius?   As in the spheres-in-a cube problem I am sure it depends on the stacking method but I was wondering if there might also be an optimum as given by the .  I would also then like to expand the analogy to the amount of spheres that can fit in a cylinder of certain diameter and length.  Any insight into the problem will be appreciated, thanks!


Selecting LiDAR return point type in LiDAR dataset with ArcPy?

I am trying to create a Digital Earth Model (DEM) using ArcPy under ArcGIS Pro 2, but I am running into some problems.   I can generate a DEM within ArcGIS Pro by selecting only the ground points under LAS files in the LAS dataset properties, but when I try to run the same code within ArcPy, it generates a DEM using all the points.   Any ideas how you select the return point type in ArcPy?   Here is the code that I have used.  arcpy.conversion.LasDatasetToRaster(lasd, "Test_arcpy_dem", "ELEVATION", "BINNING AVERAGE LINEAR", "FLOAT", "CELLSIZE", 10, 1)   As I said, this generates two different outputs, depending if I am in ArcGIS Pro or not.


Will an Ubuntu upgrade restore my rights privileges?

I couldn't log in to my system because of a certain command I ran,  I was able to access my system shell and saw the option for upgrade. Will the upgrade restore my rights privileges so that I can log in to my system again?  Please your help is highly  appreciated.


publishing a conference paper in a journal

some years ago (2007) I have published a  paper in a conference as a poster paper. Now I want to send it to a journal and change the affiliation, or maybe some minor changes. I didn't see any policy about a previous published paper in a conference, however there is a policy as the following:     The submission has not been previously published, nor is it before   another journal for consideration (or an explanation has been provided   in Comments to the Editor).   Could I send my paper to this journal?   Is it a normal thing to first publish a paper in  a conference and then trying to send it to a journal?


How would some of the top deck archetypes handle discard decks?

In the past, I asked , one that's designed to just empty your hand as fast as possible with cards like Hymn to Tourach and many others. I have also read  on playing around targeted discard.  However, at this point my friend has rebuilt his deck to a very high degree of efficiency. I often lose one of my opening lands to Hymn, and any creatures I get out are killed by targeted kill spells or board wipe like Drown in Sorrow. I never have a chance to play higher cost creatures because my hand gets emptied by discard spells. Lately I've been playing white weenie / equipment with some very good cards like Mother of Runes, Swords to Plowshares, Aegis of the Gods, Jitte, Stoneforge Mystic, and more, but ultimately all my creatures get killed by board clear and my hand is emptied. He will sometimes clear the board 3-4 times before I get killed by a combination of Black Vise, Quest for the Nihil Stone, and Guiltfeeder.  Again, I know discard decks aren't exactly one of the main Legacy archetypes. But I'm looking at decks like Miracles, Jund, D&T, OmniTell, Merfolk, and others, and to be frank, probably because I'm inexperienced with tournaments, I can't see how they would respond to this strategy. (Okay, I see how D&T stops it fairly easily, but not the others.)  How would some of the major Legacy archetypes respond to a discard deck?


Sending email with phpmailer from my domain goes to spam

I'm trying to send emails using phpmailer but every mail that i sended, finish in the spam folder.  This is the code  require("phpmailer/class.phpmailer.php"); // or wherever you put phpmail.class  $username="xxx"; $password="yyy";  $mail = new PHPMailer; $mail->isMail(); $mail->IsHTML(true); $mail->SMTPDebug = 4; $mail->setFrom('news@lexvirtual.cl', 'Lexvirtual'); $mail->addAddress("roasdf@gmail.com", "hola"); $mail->Subject = 'Nueva postulación lexvirtual.cl'; $mail->AddEmbeddedImage('../assets/img/common/lexvirtual_logo.png', 'logoimg', '../assets/img/common/lexvirtual_logo.png');  $body = file_get_contents('email_templates/register.php');  $body = str_replace('%username%', $username, $body); $body = str_replace('%password%', $password, $body); $message = $body; $mail->msgHTML($message);  if ($mail->send()) { echo "email enviado"; } else { echo "email no enviado"; }   I'm sending the email from my domain that is lexvirtual (the same domain that i'm using to send the email (news@lexvirtual.cl)).  Now i'm using a template using html but when i send a email using only text, still send the email to spam. I tried reading other questions about this problem,but still can't fix the issue.  Someone can help me please?


What does $\mathbb{R} \setminus S$ mean?

What does $\mathbb{R}\setminus S$ mean? I am not getting it what it actually means. I have found it manywhere in real-analysis like in the definition of boundary points of a set. Can anyone tell me what it means really?


Attributing contributions to academic work that occur in Stack Exchange

Sometimes we may ask questions on stack exchange or online forums wherein the response is helpful or even essential to a piece of work that gets published in an academic journal. If this occurs, how should credit be given to those involved in the exchange? Should they all be included as authors? Should a link to the forum be included as a reference in the paper?  Once something is in a stack exchange or forum, it's "published". Perhaps in the future, the current peer review model will transform into people writing blogs and posting in forums and databases. But for now, how might this issue be dealt with while forums, blogs, etc coexist with journals?


Whenever I am trying to update using  sudo apt-get update I am facing the following errors:  W: Failed to fetch http://in.archive.ubuntu.com/ubuntu/dists/trusty-updates/InRelease  Unable to find expected entry 'main/binary-1386/Packages' in Release file (Wrong sources.list entry or malformed file)  W: Failed to fetch http://ppa.launchpad.net/mc3man/mpv-tests/ubuntu/dists/trusty/InRelease  Unable to find expected entry 'main/binary-1386/Packages' in Release file (Wrong sources.list entry or malformed file)   How to fix this error?


A question on differentiability at a point

Is a continuous function differentiable at $x=c$ if the limit of its derivative has a value at that point? That is, if $$\lim_{x \rightarrow c} f'(x) = L = \lim_{x \rightarrow c^+} f'(x) =\lim_{x \rightarrow c^-} f'(x)$$ Intuitively, the slopes of the tangents approach the same value and since the function is continuous a jump-discontinuity isn't possible so it appears the slope at the point should be $L$ too. However, I cannot seem to locate such a theorem, so I suspect my intuition is wrong. Is it?


Bibliography exasperation: References in numerical order, as they appear in document

I have been searching around online trying to figure out why my references appear to be numbered in a seemingly random order. I have read probably 20 different webpages in total, including many questions on this site and I cannot fix the problem.  However so far I have learned that biblatex and bibtex are not the same thing? My guess is there are loads of different "bibliography executables/programs/compilers" (?) [I have no idea what you actually call something like biblatex] and I think this has been one source of confusion.  The most simple thing to do is give you my main tex file:  \documentclass[11pt, twoside]{report} \usepackage[a4paper,width=150mm,top=25mm,bottom=25mm,bindingoffset=6mm]{geometry}  \usepackage{fancyhdr} \pagestyle{fancy} \fancyhead{} \fancyhead[LO,RE]{\rightmark} \fancyfoot{} \fancyfoot[LE,RO]{\myname} \fancyfoot[CE,CO]{\thepage}  \usepackage{amsmath} \usepackage{physics} \usepackage{graphicx} \usepackage{siunitx} \sisetup{range-phrase=-,range-units=single} \usepackage[font=small,labelfont=bf]{caption}   \usepackage{longtable}   \usepackage{mymacros}  \extrafloats{100}  \pagenumbering{roman}  \usepackage[backend=bibtex,style=numeric]{biblatex} \addbibresource{references.bib}  \begin{document}      \input{title.tex}      \tableofcontents     \listoffigures     \listoftables      \clearpage     \pagenumbering{arabic}      \chapter{Chapter 1...}     \input{chapters/chapter1.tex}      \input{chapters/theory.tex}      \clearpage     \section{Conclusion}      \chapter{Appendix}     \input{chapters/appendix.tex}      \printbibliography  \end{document}   I compile this with texstudio, and the first reference number is [8]. The next is [12]. I want the order to be [1], [2], etc.  I can provide the references.bib file, but essentially it looks like this (here are a few examples)  % normal/inverted heirachy image @article{Artusa:2014wnl,     author         = "Artusa, D. R. and others",     title          = "{Exploring the Neutrinoless Double Beta Decay in the     Inverted Neutrino Hierarchy with Bolometric Detectors}",     collaboration  = "CUORE",     journal        = "Eur. Phys. J.",     volume         = "C74",     year           = "2014",     pages          = "3096",     doi            = "10.1140/epjc/s10052-014-3096-8",     eprint         = "1404.4469",     archivePrefix  = "arXiv",     primaryClass   = "nucl-ex",     SLACcitation   = "%%CITATION = ARXIV:1404.4469;%%" }  % KATRIN paper @article{1703.05272,     Author = {J. Behrens and P. C. -O. Ranitzsch and M. Beck and A. Beglarian and M. Erhard and S. Groh and V. Hannen and M. Kraus and H. -W. Ortjohann and O. Rest and K. Schlösser and T. Thümmler and K. Valerius and K. Wierman and J. F. Wilkerson and D. Winzen and M. Zacher and C. Weinheimer},     Title = {A pulsed, mono-energetic and angular-selective UV photo-electron source for the commissioning of the KATRIN experiment},     Year = {2017},     Eprint = {1703.05272},     Eprinttype = {arXiv},     Doi = {10.1140/epjc/s10052-017-4972-9}, }   I can't think of anything else which would be useful. I hope it is a simple mistake that I have made because this has been confusing me all morning and I have not been able to resolve the issue.  Here is a screenshot to demonstrate the issue...


I was wondering if it was possible to find functions $f$ such that $$ f'(x)=f(x+1) $$ for all $x \in \mathbb{R}$. The only thing i've found so far is that it implies $$ f^{\left(n\right)}\left(x\right)=f\left(x+n\right) $$ is there any way to solve this ?


Perspective Redux (why objects seem smaller as the distance increases)

Last time I brought  up, the best answer featured an image that looked something like this:    The argument here is that as the distance increases between the eye and the object, the angle gets smaller. It's not even a physical phenomenon: it's a geometrical phenomenon.  Fine. Let's look at this from a different angle, no pun intended.  The diameter of the human eye lens is roughly 10 mm. According to the above logic, an object whose size is smaller than that (say a raindrop) should NEVER decrease in size while the distance increases, and should remain visible no matter how far away it is (Pluto's orbit and beyond):    What am I missing?


How is energy acquired from ATP (i.e. What is the energy-releasing equation involving ATP plus water)?  I Would be grateful for the answer.


Which one is better in the following sentence? I think I can use both.    [Even though/Even if] we wear fashionable clothes, we can't be truly beautiful without good manners.


If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid?  I infer that the $r^{-2}$ term in the Electric field comes as a result of solid angle in 3 dimensions. Would this be valid in higher dimensions? The flux would depend on the spatial dimensions. Because in the verification of Gauss law the $\frac{da}{r^2}$ terms is written as solid angle. Does this mean for Electric field varying in some other way, we would be talking about the solid angle of that dimension? Even if it were true for higher dimensions, which it might be, does it hold for fractional powers of $r$?


Aperture priority on Canon EOS 55 shows underexposured

I must be misunderstanding something here. I'm consistently reading an underexposure when I use aperture priority mode.  So here I'm in manual mode, f2.5, 1/20s and the camera says the exposure is fine.    And then if I set the camera to aperture priority mode with the same aperture of f2.5, it's opting for a 1/125s shutter speed and thus is showing as underexposed.    Even setting the exposure compensation doesn't change it from showing as underexposed. I've experienced the same problem in bright sunlight where I had to set the shutter speed to 1/750s to get an OK exposure on manual.  In response to the comments I'm including a picture of the exposure compensation setting when on aperture priority mode    Can anyone advise me what the problem might be? This is quite a different beast to my DSLR so I'm feeling a bit lost.


Is a continuous real-valued function with an almost everywhere continuous derivative necessarily differentiable on $\mathbb{R}$?

Setting:  Let $a\in \mathbb{R}$, and let $f$ be a function which is continuous on $\mathbb{R}$, differentiable on $(\infty,a)\cup (a,\infty)$, and has the property that $\lim_{x\to a^{-}}f'(x) = \lim_{x\to a^{+}}f'(x) = L$ for some $L\in\mathbb{R}$.  Question:  Does it automatically follow that $f$ is differentiable at $a\in \mathbb{R}$?  My intuition wants to say yes since we are placing such strong conditions on $f$, and if I were going to try to prove this I would pursue the following logic:  Argument:  \begin{align*} f'(a) &= \lim_{h\to 0}\frac{f(a+h) - f(a)}{h}\\ &= \lim_{h\to 0}\left[\lim_{x\to a^{-}}\frac{f(x+h) - f(x)}{h}\right]\text{using continuity of} f \text{at }a\\ &= \color{red}{\lim_{x\to a^{-}}\left[\lim_{h\to 0}\frac{f(x+h) - f(x)}{h}\right]}\\ &= \lim_{x\to a^{-}}f'(x)\\ &= L \end{align*}  or using essentially the same argument from the other side.....  \begin{align*} f'(a) &= \lim_{h\to 0}\frac{f(a+h) - f(a)}{h}\\ &= \lim_{h\to 0}\left[\lim_{x\to a^{+}}\frac{f(x+h) - f(x)}{h}\right]\text{using continuity of} f \text{at }a\\ &= \color{blue}{\lim_{x\to a^{+}}\left[\lim_{h\to 0}\frac{f(x+h) - f(x)}{h}\right]}\\ &= \lim_{x\to a^{+}}f'(x)\\ &= L \end{align*}  But the steps that I've outlined in red and blue correspond to geniune gaps in my argument.  We cannot always interchange such limits without caution, but perhaps due to the strong assumptions on $f$ we can in this case.  Is there an example of a function $f$ (of course, satisfying the conditions give above) for which this logic fails?  If not, how can I fix my argument?


ChaCha20 - How confidentiality is lost if reusing nonce?

I read that (key, nonce) pair should be used only once for encryption of a message. My question is how confidentiality can be lost if two peers using a shared key use same (key, nonce) pair to encrypt their own messages (messages of peers would be different).


Going out to bulk buy tomorrow and stock up on a few things Butter being one of many. How long can butter be stored in the refrigerator? We want to maximize our stock but not waste anything.


When I run  import numpy as np  # Create small random numbers a = np.random.rand(10)  # Check whether their sum and their flipped sum is the same print(np.sum(a) == np.sum(a)) print(np.sum(np.flipud(a)) == np.sum(a))   the first statement is always true, whereas the second statement sometimes returns false, depending on the random numbers, and I have no idea why. I see this in both, Python 2.7 and Python 3.6. Interestingly, if I apply flipud twice like so:  print(np.sum(np.flipud(np.flipud(a))) == np.sum(a))   I always get True.  Edit: Some useful info on a related issue .


How would I negate single digits in a binary number?

Let's say I have a binary number like: 0101010101. Now I want to negate only the 1st 5th and 8th digit to change it to 1101110001. Is there an algorithm to do this? If so, how does it work?


I would like a better understanding of the famous birthday paradox.  "What is the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday?"  I understood the first part, where the probability reaches 100% when the number of people reaches 367 by the pigeonhole principle. But I am not understanding the explanation beyond that. How do they say that the probability is 99.9% with 70 people and 50% with 23 people? And how do you further generalize the answer? And why is it a "paradox"?


How to redirect page on Jquery validation success

I am using jquery for validation set some rules.  If validation success I want to redirect to another page. How can I do it?  // validate contact form on keyup and submit $("#contactForm").validate({     //set the rules for the field names     rules: {         name: {             required: true,             minlength: 2         },         email: {             required: true,             email: 4         },      },     //set messages to appear inline     messages: {         name: "Please enter your name",         password: "Please enter your email"     }  });