I have problem with something on my website. I am not entirely sure what is causing problems anymore.  Database collation: utf8_bin Table charset: utf8  Example of row in table:  ID Name KeyID  5  Ajša 3312  <?php header('Content-Type: text/html; charset=utf-8'); ...connection to server...  $sql = "select * from osebe where id=5;"; $result = $conn->query($sql);  if ($result->num_rows > 0) { while($row = $result->fetch_assoc()) {     echo "id: " . $row["ID"]. " - Name: " . $row["Name"]. " " . " - Key: ".$row["KeyID"]. "<br>"; } } else {     echo "0 results"; } $conn->close(); ?>   Output: id: Aj�a - Name: Aj�a - Key: 3312  Files have utf8 encoding as well, so i dont know what to do anymore.

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


$ su - Password:  # echo $PATH /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin # exit logout $ su Password:  # echo $PATH /usr/local/bin:/usr/bin:/bin:/usr/local/games:/usr/games   I have no idea why /bin and /sbin are not added to $PATH, if I do the plain su. This used to be the case. How can I fix this? I did notice that:  -rw-r--r-- 1 root root 0 Jan  8  2018 /etc/environment   But otherwise my system seems normal.  EDIT: I forgot the obligatory uname -a  Linux rpi3 4.17.0-1-arm64 #1 SMP Debian 4.17.8-1 (2018-07-20) aarch64 GNU/Linux   EDIT2:  $ cat /etc/issue Debian GNU/Linux buster/sid \n \l   all of the packages are from the "testing" repo, since "stable" ones don't work very well on aarch64.

On my fedora VM, when running with my user account I have /usr/local/bin in my path:  [justin@justin-fedora12 ~]$ env | grep PATH  PATH=/usr/kerberos/sbin:/usr/kerberos/bin:/usr/local/bin:/usr/bin:/bin:/usr/local/sbin:/usr/sbin:/sbin:/home/justin/bin   And likewise when running su:  [justin@justin-fedora12 ~]$ su - Password:  [root@justin-fedora12 justin]# env | grep PATH PATH=/usr/kerberos/sbin:/usr/kerberos/bin:/usr/local/bin:/usr/bin:/bin:/usr/local/sbin:/usr/sbin:/sbin:/home/justin/bin   However, when running via sudo, this directory is not in the path:  [root@justin-fedora12 justin]# exit [justin@justin-fedora12 ~]$ sudo bash [root@justin-fedora12 ~]# env | grep PATH PATH=/usr/kerberos/sbin:/usr/kerberos/bin:/sbin:/bin:/usr/sbin:/usr/bin   Why would the path be different when running via sudo?


I use the following code to send an email from my Gmail account. But the following error is occurred. Unable to connect to the remote server what's wrong with my code?         string from = "xxxx@gmail.com";         string to = TxtTo.Text;         string cc = "yyyy@gmail.com";         string subject = TxtSubject.Text;         string body = EdtContext.Content;         MailMessage EMail = new MailMessage();         MailAddress Sender = new MailAddress(from);         EMail.From = Sender;         EMail.To.Add(to);         EMail.CC.Add(cc);         EMail.Body = body;         EMail.IsBodyHtml = true;         EMail.Subject = subject;         EMail.BodyEncoding = Encoding.UTF8;         SmtpClient Local = new SmtpClient("smtp.gmail.com");//--- smtp          Local.Port = 465;          Local.EnableSsl = true;          Local.UseDefaultCredentials = false;                    Local.Credentials = new System.Net.NetworkCredential("xxxx@gmail.com", "*****");//------ email user and pass in sobhan mail         Local.Send(EMail);  *************** **Port 587 solved problem**

Instead of relying on my host to send an email, I was thinking of sending the email messages using my Gmail account. The emails are personalized emails to the bands I play on my show.   Is it possible to do it?


What is the probability that a random $\{0,1\}$, $n \times n$ matrix is invertible? Assume the 0 and 1 are each present in an entry with probability $\frac{1}{2}$. Is there an explicit formula as a function of $n$?  Does it tend to 1 as $n$ grows large? I'm sure this is all known...  Thanks!

Given a random square matrix of size $n\times n$ in the field $\mathbb F_2$, what is the probability that its determinant is $1$? (This is also the probability that the matrix is non-singular, since $\mathbb F_2$ only has the elements $0$ and $1$.)


I am from Pakistan and applied for tourist visa to the Netherlands for just 15 days.The objection is that I do not have strong ties with my country. How can I satisfy the embassy and get visa?  Reasons are that I have not strong ties with home country and chances of illegal immigration.

My husband is in Switzerland for 6 months with L permit.  I applied for visitor visa.  I submitted all documents with his entrance visa in which date of his coming back to India was not mentioned but later on after submission of visa documents to VFS office, I submitted his L-permit through mail.  But my visa got rejected stating " your intention to leave the territory of the member state before the expiry of visa could not be ascertained".  I also got confused on the answer of extension of my husbands visa permit during answering to the embassy council.  I have only 7 days left to reapply for visa.  I don't know what should I do?  Will I able to get visa again within 7 working  days??


I want to create a kbordermatrix with an underbrace and some text below. I tried it with  \documentclass{scrartcl} \usepackage{kbordermatrix} \begin{document} \[ \underbrace{ \kbordermatrix{  & 1 & 2  \\ 1 & a & b \\ 2 & c & d  }}_{test} \] \end{document}   which gave me this output:    As you can see the underbrace also goes below the rowlabels since they are treated as an extra column. Is there a way of using an underbrace which is only below the actual matrix?

How to put underbraces, inside the parenthesis of a matrix, to name both sides of the blocks?  \documentclass[a4paper,12pt]{article} \usepackage{amsmath} \usepackage{array} \begin{document} . . . \[ \left ( \begin{array}{rrr|rrr} 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right ) \] \end{document}   I'm compiling the code in my university server, where I can't install new packages.


Question: In what sense is "the kernel of a group homomorphism a universal"?  Do we here mean that a group homomorphism is a universal arrow in some comma category? If so, what comma category?  Attempt: If we let $K$ be a normal subgroup of $G$ and $i: K \rightarrow G$ being the inclusion homomorphism, then for any other normal subgroup $T$ of $K$ with $k : T \rightarrow K$ being another inclusion homomorphism and likewise with $j : T \rightarrow G$, then we have that $j = i \circ k$.  Now let $C$ be the category of the subgroups of $G$ with inclusion homomorphisms as morphisms. Let $S: C \rightarrow C$ be the identity functor on $C$.  Then do we not here have that $(K, i)$ is a universal arrow in $(C \downarrow G)$? And if so, is this the sense in which "the kernel of a group homomorphism is a universal"?  EDIT: Answers in another thread on this site have confused me in the sense that they don't discuss explicitly about universal arrows and comma categories.

I'm reading Mac Lane's "Categories for the Working Mathematician". I found the following sentence in page 59 of it:     Similarly, the kernel of a homomorphism (in $\mathbf{Ab}$, $\mathbf{Grp}$, $\mathbf{Rng}$, $R$-$\mathbf{Mod}$, . . .) is a universal, more exactly, a universal for a suitable contravariant functor.   I know how to express a quotient by a universal property in a category. But I really have trouble understanding how to express the kernel of a homomorphism as having a universal property.


Suppose I have called a function as, const data = await someFunction()  I want to calculate execution time of this function. For this I tried as, let startTime = Date.now(); const data = await someFunction() let endTime = Date.now();  And I calculated difference between endTime-startTime and the result I get i think is in millisecond and converted it to second. I would like second opinion on this whether this is one of the option to calculate or is there some more better method which can give me execution time in second.

I need to get execution time in milliseconds.  I originally asked this question back in 2008. The accepted answer then was to use  However, we can all agree now  that using the standard  API is more appropriate. I am therefore changing the accepted answer to this one.


Counterspell requires the following:     [a reaction], which you take when you see a creature within 60 feet of you casting a spell   The Flameskull's spellcasting block reads the following:     [The Flameskull] requires no somatic or material components to cast its spells.   If the Flameskull requires no visible components, can its spells be counterspelled?

Counterspell   1 reaction, which you take when you see a creature within 60 feet of you casting a spell.   Can I Counterspell a creature that completely eliminates component requirement?     Subtle Spell   When you cast a spell, you can spend 1 sorcery point to cast it without any somatic or verbal components.   If the spell is subtle then can I see it’s being cast in order to counterspell it?


I want to do a statistical test to test the following business assumptions: 1. Higher duration is associated with a lower score 2. However, Hypothesis (1) may or may not be true for all Survey reasons  What I am thinking of is to do a regression with interaction terms: score = duration + reason + duration * reason  My questions: 1. Is it possible to do a categorical * continuous variable interaction? Most resources I saw online only shows instances where the categorical variable is binary. I have a multi-group categorical variable. 2. Is there a graphical way of showing this?

I have a continuous outcome variable. I understand that if I have a binary predictor, and a continuous predictor, and an interaction, then the model looks like this:  $y_{i} = \beta_{0} + \beta_{1}x_{1} + \beta_{2}x_{2} + \beta_{3}x_{1}x_{2} + \varepsilon_{i}$  However, I'm thinking of making the binary predictor a categorical one instead, with three categories.    What will the model equation look like once I make that change? I understand that I'll need to have two dummy variables, but I can't conceptualize what the interaction will look like under that circumstance.  Does it make any difference whether I use 0,1 to code the binary predictor, or some other values like 1,2? This question also applies to the model with the categorical predictor, since in that case I'll have to decide how to code the dummy variables.  Prior to the interaction term being in my model I was encouraged to center the continuous predictor. Is centering (still) a good idea now that I have this interaction term?


I want to install absynth 5 on my computer. I found this code, here it is.   #!/bin/bash # Date : (2013-02-01) # Last revision : (2013-02-01) # Distribution used to test : Kubuntu 12.04 LTS # Author : DJYoshaBYD # Licence : GPLv3 # PlayOnLinux: 4.1.9  # CHANGELOG # [SuperPlumus] (2013-06-17 19-35) #   Update gettext message   [ "$PLAYONLINUX" = "" ] && exit 0 source "$PLAYONLINUX/lib/sources"  PREFIX="Absynth5" WINEVERSION="1.3.0" TITLE="Absynth 5" EDITOR="Native Instruments" GAME_URL="http://www.native-instruments.com" AUTHOR="DJYoshaBYD"  #Initialization POL_GetSetupImages "http://files.playonlinux.com/resources/setups/$PREFIX/top.jpg" "http://files.playonlinux.com/resources/setups/$PREFIX/left.jpg" "$TITLE" POL_SetupWindow_Init  POL_Debug_Init  # Presentation POL_SetupWindow_presentation "$TITLE" "$EDITOR" "$GAME_URL" "$AUTHOR" "$PREFIX"  # Create Prefix POL_SetupWindow_browse "$(eval_gettext 'Please select the setup file to run')" "$TITLE" POL_System_SetArch "x86" POL_Wine_SelectPrefix "$PREFIX" POL_Wine_PrefixCreate "$WINEVERSION"  #Dependencies  # Configuration Set_OS "winxp" Set_SoundDriver "alsa"  # Installation POL_Wine_WaitBefore "$TITLE" GC_DONT_GC=1 POL_Wine "$APP_ANSWER" POL_Wine_WaitExit "$TITLE"  # Create Shortcuts POL_Shortcut "Absynth\ 5.exe" "$TITLE"  POL_SetupWindow_message "$(eval_gettext 'NOTICE: For low-latency audio, look into WineASIO.')" "$TITLE"  POL_SetupWindow_Close exit 0   But I think it is supposed to go somewhere other than the Terminal because in the terminal after typing #!/bin/bash I still get a $ sign. Thank you in advance for all of your help.

Whenever I open a .sh file, it opens it in gedit instead of the terminal. I can't find any option similar to Right Click → Open With → Other Application... → Terminal.  How do I open this file in the terminal?


Suppose $A \ne \emptyset$ is bounded below. Let $-A$ denote the set of all $-x$ for $x$ in $A$. Prove that $-A \ne \emptyset$ that $-A$ is bounded above, and that $-\sup(-A)$ is the greatest lower bound of $A$.  I have absolute no clue, what I thought was:  Let $B = \inf A$  We assume $-A = \emptyset$ then we recognize that $A = x \in $R  If elements of $-A = -($elements of A) then we reach a contradiction because $-x$ exists as $A \ne \emptyset$.   I really cant prove anything else. This problem has me stumped. Anything is appreciated.

Let $A$ be a nonempty subset of real numbers which is bounded below. Let $-A$ be the set of of all numbers $-x$, where $x$ is in $A$. Prove that $\inf A = -\sup(-A)$   So far this is what I have  Let $\alpha=\inf(A)$, which allows us to say that $\alpha \leq x$ for all $x \in A$. Therefore, we know that $-\alpha \geq -x$ for all $x \in -A$. Therefore we know that $-\alpha$ is an upper bound of $-A$. $\ \ \ \ $  Now let $b$ be the upper bound of $-A$. There exists $b \geq-x \implies-b \leq x$ for all $x \in A$. Hence, \begin{align} -b & \leq \alpha\\ -\alpha & \leq b\\ -\alpha & = - \inf(A) = \sup (-A) \end{align}  By multiplying $-1$ on both sides, we get that $\inf(A) = -\sup (-A)$  Is my proof correct?


I would like my pc to power on automatically every day at a specific time. I know how to do this in BIOS. The problem is that when the pc is booted, it requires a password to log in on windows. The question is: How do I get my pc to login with my password automatically?  Thanks.  Clarification: What I want is to keep my account locked with a password. I don't want to disable my password in order to login automatically. The automation that I want, is to have a password, but inserted and log in automatically when my pc boots up automatically through rtc boot from bios.  Clarification 2: I don't want to disable my password universally. What I want is to still have my password active and inserted automatically when my pc boots automatically through rtc from bios. When I boot it up myself, I want it to ask me for the password.

It's tedious to type my password every time I start my Windows 10 VM, especially since you can't paste a password into the box. I want to set up automatic login.  Following the instructions  I tried to disable the "Users must enter a user name and password" option in netplwiz. But the option isn't there! It should be above the "users for this computer" list. Is there a setting I need to change to allow me to change the setting?


I have a pandas Series:  freq_features = num_occurrences/num_nodes print(type(freq_features)) print(freq_features)  <class 'pandas.core.series.Series'> PAT    0.386667 NUR    0.360000 MED    0.146667 ADM    0.106667   I round each value to 2 decimal places:  freq_features_rounded = freq_features.round(2) print type(freq_features_rounded) print freq_features_rounded  <class 'pandas.core.series.Series'> PAT    0.39 NUR    0.36 MED    0.15 ADM    0.11 dtype: float64   But when I use the to_dict() command, I get the non-rounded values (except for the ADM key):  freq_features_dict = freq_features_rounded.to_dict() print freq_features_dict {'NUR': 0.35999999999999999, 'ADM': 0.11, 'PAT': 0.39000000000000001, 'MED': 0.14999999999999999}   Why is this happening, and how can I get my rounded values into the dict() object as values?

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


The program is supposed to calculate your TDEE after taking in your gender, BMR, and activity level but it can't calculate it if the activity level won't go through and I feel like it's something to do with my if-statements but I really don't know how.   The value types of gender and level used to be char but my teacher told me to change it to String but it still didn't work.  import java.util.Scanner; public class TDEE_2 {     public static void main(String [ ] args)     {         Scanner in = new Scanner(System.in);         double activityFactor = 0.0;          System.out.println("Please enter your name: ");         String firstName = in.next();         String lastName = in.nextLine();         String name = firstName + lastName;          System.out.println("Please enter your BMR: ");         double bmr = in.nextDouble();          System.out.println("Please enter your gender (M/F): ");         String gender = in.next();          System.out.println("Select Your Activity Level");         System.out.println("[A] Resting (Sleeping, Reclining)");         System.out.println("[B] Sedentary (Minimal Movement)");         System.out.println("[C] Light (Sitting, Stading)");         System.out.println("[D] Moderate (Light Manual Labor, Dacing, Riding Bike)");         System.out.println("[E] Very Active (Team Sports, Hard Manual Labor)\n");          System.out.println("Enter the letter corresponding to your activity level: ");         String level = in.next();          if(gender == "M" && level == "A")             activityFactor = 1.0;         else if(gender == "M" && level == "B")             activityFactor = 1.3;         else if(gender == "M" && level == "C")             activityFactor = 1.6;         else if(gender == "M" && level == "D")             activityFactor = 1.7;         else if(gender == "M" && level == "E")             activityFactor = 2.1;         else if(gender == "M" && level == "F")             activityFactor = 2.4;         else if(gender == "F" && level == "A")             activityFactor = 1.0;         else if(gender == "F" && level == "B")             activityFactor = 1.3;         else if(gender == "F" && level == "C")             activityFactor = 1.5;         else if(gender == "F" && level == "D")             activityFactor = 1.6;         else if(gender == "F" && level == "E")             activityFactor = 1.9;         else if(gender == "F" && level == "F")             activityFactor = 2.2;         else             System.out.println("Sorry, you entered an invalid letter.");           double tdee = bmr * activityFactor;         System.out.println("Your results:");         System.out.println("Name: " + name + "\t\t Gender: " + gender);         System.out.println("BMR: " + bmr + " calories \t\t Activity Factor: " + activityFactor);         System.out.print("TDEE: " + tdee + " calories");     }        }   When I run it, Activity level and TDEE appear empty but they're supposed to have values.  I am new to java and don't know what to do sorry

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


For this equation I know the first step is to write $x^2-x=0 \pmod{ 111 5111}$ and then we know that we can write $111 5111=1051 \cdot 1061$ (product of prime numbers) so we have to solve the following:   Find $x\:$ s.t.   $1051 | x(x-1)$ ^ $1061 | x(x-1)$  What is the fastest way to solve this last step without a calculator?

I need the idempotent elements of $Z_{900}$ $2^2\cdot 3^2\cdot 5^2=900$ Of course there's $$0 \pmod 4 \\ 0 \pmod 9 \\ 0 \pmod {25} \\ $$ and $$ 1 \pmod 4 \\ 1 \pmod 9 \\ 1 \pmod {25} \\ $$ I found the answers by making a C++ program to test all numbers, but I don't know how to quick solve on paper. This is the output of the program $(0, 0, 0) \rightarrow 0 \\ (1, 1, 1) \rightarrow 1 \\ (0, 0, 1) \rightarrow 576 \\ (0, 1, 0) \rightarrow 100 \\ (1, 0, 0) \rightarrow 225 \\ (1, 1, 0) \rightarrow 325 \\ (0, 1, 1) \rightarrow 676 \\ (1, 0, 1) \rightarrow 801 \\$


System.out.printf(currForm.format(monthPay) + "        ");  I am trying to figure out how to format this code so that it aligns with the header which is outside this output. image of what the code appears as:  Basically the user controls the all the inputs, so I am trying to do my best to accommodate 3 and 4 digit monthly payment amounts and their spacing. As you can see, the column allignment gets progressively more misaligned from the header as we get into the more right columns. I also did use "\t" but a difference between the 3 and 4 digit monthly payments makes major alignment issues. Thanks!

Is there some easy way to pad Strings in Java?  Seems like something that should be in some StringUtil-like API, but I can't find anything that does this.


A way to think about gravitational fields is that they spawn as a consequence of mass literally bending time and space.  Is there an analog of this concerning charges and the electric field intensity?

After reading many questions, like   and , I wonder:   Is it possible to consider the other fundamental forces too, the electroweak interaction and the strong interaction or ultimately the unification of these, to be fictitious forces like gravity in the framework of general relativity?   If we want a final unification of all fundamental forces, hasn't this feature of gravity to become a feature of the other forces as well?


Using multiple branch/developers strategy for developing features causes some issues with built-in Drupal configuration management.   Our scenario is the following:   Create new feature and export config using drush Commit changes and configuration into git Move to another branch and start working in another feature Export config using drush (also exports config from the features added in the previous branch) Cannot move easily between branches as some content types are missing   What is the best way to use feature branches in a multiple developer team without creating this overhead?

I wonder if somebody found a solution for the following issue related to Drupal 8 development with Git branches:   You work on a new feature in a local feature branch for that you activate a contributed module or you write a custom module. This maybe delivers an own entity type and therefore creates a table after installing Meanwhile you need to fix a bug -> you change to a newly created bugfix branch which starts from the current dev branch After checking out the bugfix branch you import the current configurations to have the current active configuration of the branch -> the module you installed in feature branch is not activated anymore, the files of this module do not exist in the current bugfix branch You do your bugfixing and merge ths bugfix branch into develop branch. you change to your feature branch. To bring your local Drupal project to the status of this branch again you will import the configurations again   And here it comes to an exception: the table already exists in your database. When doing a drush cim it stops every following processing and you need to restart drush cim to import any further configurations.  Who does work with different feature branches and found a solution during development process to deal with this kind of situation?


I'm considering building a new Windows-based work PC.   Some of my work requires vast amounts of storage. Currently I'm serving that need by using a number of external USB drives.  Given that I never need those external drives anywhere else, for the new machine, I'd prefer a solution where those drives are fixed inside the PC, next to the SSD that will contain the system partition and the most essential work data.  However, because I live off the grid (and because HDDs can get loud!) I would like the storage hard disks to strictly remain turned off (ideally even when starting up!) until I need them - just like I would plug in a USB hard drive when I need it.  From what I've gathered, this is not possible using Windows' built-in energy saving features itself: its "power saving" features will affect either all hard disks at once, or none.  Is there a software, BIOS, or hardware solution that helps achieve this goal?

Obviously there are power management settings which Windows uses to determine when to power a hard drive off, and when to power it back on again. Powered down I assume doesn't mean absolute zero power, but it does mean the disk stops spinning.  I have a second hard drive which is a tad noisy. In fact, having invested in a new case, CPU cooler, power supply and fan-speed controller, it's now the noisiest component left in my computer. And I've kinda run out of money.  But... I don't need a second hard drive all the time.  So - is there a quick-and-easy way to make Windows unmount all partitions from a particular internal hard drive and power that drive down on demand, and then make it power the drive back up and re-mount the partitions when I'm going to need it?  Kinda the internal software-controlled equivalent of unplugging/reconnecting an external USB hard drive.  I dual boot, so I really need the answer for both Windows XP and Windows 7.


Please help me to fix this issue:  Error: File "/media/woeusb_source_1544544327_15932/sources/install.wim" in source image has exceed the FAT32 Filesystem 4GiB Single File Size Limitation and cannot be installed. You must specify a different --target-filesystem. Refer: https://github.com/slacka/WoeUSB/wiki/Limitations#fat32-filesystem-4gib-single-file-size-limitation for more info. Unmounting and removing "/media/woeusb_source_1544544327_15932"... You may now safely detach the target device   I also formatted the pendrive in NTFS and the error persists.

I tried to create a Windows 10 USB boot medium with WoeUSB. I formatted a USB drive with an NTFS partition, but WoeUSB complains with:  Installation failed! Exit code: 256 Log: WoeUSB v@@WOEUSB_VERSION@@ ============================== Mounting source filesystem... Error: File "/media/woeusb_source_1543626298_6098/sources/install.wim" in source image has exceed the FAT32 Filesystem 4GiB Single File Size Limitation and cannot be installed.  You must specify a different --target-filesystem. Refer: https://github.com/slacka/WoeUSB/wiki/Limitations#fat32-filesystem-4gib-single-file-size-limitation for more info. Unmounting and removing "/media/woeusb_source_1543626298_6098"... You may now safely detach the target device   I've also tried to start WoeUSB via command line, did not work.  sudo woeusb --partition Win10_1809Oct_English_x64.iso /dev/sdb   My iso is located in:     home/sawyer/Downloads/Win10_1809Oct_English_x64.iso  Thanks in advance! I've been trying to get windows installed for three nights now, so any help towards that goal is greatly appreciated.


It seems to me that when you scale a numeric variable you should do it separately in train and test set.   For example, if you have a numeric variable X. Normalized X is : ( X - m(X) ) / s(X).  When you have train and test sets, m(X) and s(X) should be calculated on each population. If not some information ( contained in global m and s ) pass from train to test set through globally normalized variables.  Is it correct to think so? Thanks for your answer.

A common good practice in Machine Learning is to do feature normalization or data standardization of the predictor variables, that's it, center the data substracting the mean and normalize it dividing by the variance (or standard deviation too). For self containment and to my understanding we do this to achieve two main things:   Avoid extra small model weights for the purpose of numerical stability. Ensure quick convergence of optimization algorithms like e.g. Conjugate Gradient so that the large magnitude of one predictor dimension w.r.t. the others doesn't lead to slow convergence.   We usually split the data into training, validation and testing sets. In the literature we usually see that to do feature normalization they take the mean and variance (or standard deviation) over the whole set of predictor variables. The big flaw I see here is that if you do that, you are in fact introducing future information into the training predictor variables namely the future information contained in the mean and variance.  Therefore, I do feature normalization over the training data and save the mean and variance. Then I apply feature normalization to the predictor variables of the validation and test data sets using the training mean and variances. Are there any fundamental flaws with this? can anyone recommend a better alternative?


I am still confused with the classifications of such nouns as area, spot, compound (which refers to a type of area), and area itself. Are they abstract or concrete nouns?

The words that express the tangible and visible things of our experience, such as sand or sea, are all nouns, as are those expressing intangibles such as love or idealism.  Also, some nouns, like field or grain, can be imagined both as tangible and intangible.  People, generally, refer to these nouns with the terms concrete (tangible) and abstract (intangible).  That being said, my question is, is there an English dictionary that—as well as identifying a word as a noun—additionally identifies the noun as either “abstract” or “concrete”? Are there any other resources that do this?


By theorems, I mean the ones you can find in an undergraduate course of mathematics, not the ones you can find in a textbook of automated proofs.  I mean by "proved by a computer" that an existing theorem was fully automatically proved by a computer().  I exclude verifications of existing theorems by a computer.  This is .

The  states:     Despite these theoretical limits, in practice, theorem provers can solve many hard problems...   However it is not clear whether these 'hard problems' are new. Do computer-generated proofs contribute anything to 'human-generated' mathematics?  I am aware of the four-color theorem but as mentioned on the Wikipedia page, perhaps it is more an example of proof-verification than automated reasoning. But maybe this is still the best example?


I start recording my screen for two hours by clicking cmd+shift+5, after that I stopped the recording, and immediately a popped up video appear with an option to share recorded video, I click the share button and choose telegram and I clicked done, my video doesn't shared to telegram neither saved on default saving location, i.e. desktop. I googled it but no solution work with me even  Any solution will save my day, what I recorded very important to me.

I recorded a movie (File > New Movie Recording) using Quicktime Player and when I stopped I accidentally clicked "Don't Save" instead of "Save".  Is that recorded content still on the hard drive somewhere, maybe in a temp or cache folder or something in a hidden directory?  I'd like to recover it.  Thanks.


I was just reading  and saw this under "Do":     Get your passports stamped at the tourist information centre. This is an excellent souvenir as they stick a visa tax stamp and then an official ink stamp over the top, €5   First my question was if this is legit because of course there are no border controls inside EU and I have heard many places, including this site, that only border stamps and other official docs can go in a passport.  Looking through  I assume it's talking about this:    Looks official.  Then I came across  but that is about EU citizens and I am not one. That question implies it is possible but I want to be clear. My question now is is it okay for a non EU person to ask for an official government stamp in the passport even when rules do not require passport stamping? If yes then where can you usually go to ask for that? Train stations?

It is known that passport stamps are a kind of collection for many people. But, inside European Union, we -EU citizens- are allowed to travel without passport, just with our national ID card (if we have in our countries).  Is there any way to get passport stamps like non-EU citizens? You can identify yourself with the passport of course, but they don't stamp it.


I'am trying to use the Python API to make a lot of different and randomized trees with the MTree add-on. But I'am struggling with an error telling me that the context is incorrect. RuntimeError: Operator bpy.ops.node.add_node.poll() failed, context is incorrect I've tried to use the bpy.context.active_node but that doesn't seem to exist even though it's in the . For now my code looks like this: import bpy bpy.ops.node.new_node_tree(type="mtree_node_tree", name="Tree1") bpy.context.area.add_node(type="MtreeParameters", use_transform=True)  But it gives out an error which I listed before at the 3rd line. The code should just put a node into the node tree, but it probably doesn't know where to. So does anyone know how to make the node tree the context?

I have been trying to write my first addon for Blender over the last couple of days. One error I came across quite often is the context is incorrect error for an operation of bpy.ops.  I learned that one can ask the poll function of an operator if the context is correct, but this does not tell why the context is correct/incorrect. What would be the best way to figure that out? Only way I could think of is to look into the code of the poll function. If that is the best way, what is the fastest way to find the appropriate piece of code?


if [[ 6 > 50 ]]; then     echo "true" fi  $ bash script.sh I'm missing something very obvious here. Why is 6 greater than 50 ?? ** EDIT ** I'm also try to solve for if [[ 6.5 > 50 ]]; then     echo "true" fi

Using echo "20+5" literally produces the text "20+5".  What command can I use to get the numeric sum, 25 in this case?  Also, what's the easiest way to do it just using bash for floating point? For example, echo $((3224/3807.0)) prints 0 :(.  I am looking for answers using either the basic command shell ('command line') itself or through using languages that are available from the command line.


I have the expression xy+xy'z+x'yz'. I have tried a number of ways to simplify it. What approach will ensure that this expression is reduced to its simplest form?

As stated in the title, I'm trying to simplify the following expression: $xy + xy'z + x'yz'$ I've only gotten as far as step 3:  $xy + xy'z + x'yz'$  $=x(y+y’z) + x’(yz’)$  $=x(y+y’z)+x(y’+z)$  But I don't know where to go from this step, I'm not sure if I'm allowe to rewrite y'z as y+z' (I'm not even sure if that would help)


"this code works for string id less than 20 but grater than 1000 it returns -1. " "---MySpinner.setSelection(adapter.getPosition(new CustomSpinnerList(String.valueOf(id), name)));// Sample    id="1254",name="Aaaaa aaa" ---------------------------------------------------------  private void setADivisions(int divisional_id) {     DatabaseHelper myDb= new DatabaseHelper(this);     ArrayList<CustomSpinnerList> MyArrList = new ArrayList<>();     Spinner MySpinner = (Spinner)findViewById (R.id.spinnerDivision);     List<SysDivisionTable>   MyList=myDb.get_all(Integer.valueOf(divisional_id));         int id=0;         String name="";         myDb.closeDB();         for(SysDivisionTable MyTable:MyList) {             if(MyTable.Get_col_A_division_id()==current_Adiv_id) {                  id=MyTable.Get_col_A_division_id();//="1245"                 name=MyTable.Get_col_A_division_name();="Aaaaa aaa"             }             MyArrList.add(new CustomSpinnerList(String.valueOf(MyTable.Get_col_A_division_id()), MyTable.Get_col_A_division_name()));         }      ArrayAdapter<CustomSpinnerList> adapter = new ArrayAdapter<CustomSpinnerList>(this, android.R.layout.simple_spinner_dropdown_item, MyArrList);     Log.d("D01", "adapter.String.valueOf(id) "+ String.valueOf(id)+ " *** "+name);     Log.d("D02", "adapter.getPosition"+ adapter.getPosition(new CustomSpinnerList(String.valueOf(id), name)));      MySpinner.setAdapter(adapter);     MySpinner.setSelection(adapter.getPosition(new CustomSpinnerList(String.valueOf(id), name)));// Sample    id="1254",name="Aaaaa aaa" }        public class CustomSpinnerList {         private String id;          private String name;          public CustomSpinnerList(String id, String name) {             this.id = id;             this.name = name;         }         public String getId() {             return id;         }         public void setId(String id) {             this.id = id;         }         public String getName() {             return name;         }         public void setName(String name) {             this.name = name;         }         @Override         public String toString() {             return name;         }         @Override         public boolean equals(Object obj) {             if(obj instanceof CustomSpinnerList){                 CustomSpinnerList c = (CustomSpinnerList)obj;                 if(c.getName().equals(name) && c.getId()==id ) return true;             }             return false;         }     }

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


I am not able to recover my files as I have accidentally deleted the files. Is there any application which will help me to recover the files.

Are there any tools, methods, incantations to recover recently deleted files on Ubuntu?  If it makes any difference, I want to recover a  2.x database file. But would be better to have a method/tool that works on any kind of file.


Show that for any prime numbers p, q, r , one has  the sum of p^2 and q^2 is not equal to r^2  How do i go about doing this question? Do I use mathematical induction or is there any other way to go about doing it? if i use mathematical induction, how do i set the induction statement? because there are three variables p,q and r. Stuck here and hope to get some help. thank you :)

Not sure how to start. Prove by induction? Please help!


I'm new to Blender and Cycles Render and I was setting up a basic test to produce a smooth polished bronze surface.  My understanding is that the Rendered 3D View from the Camera should match the Single Image output however I simply cannot get any objects, lights or planes to render - merely a flat world colour.  The Viewport:   Rendered Result:  I've tried various suggestions from other similar queeries (Ensuring I'm in Global View, ensure all objects are Visible to Render, Assign Each Object to a layer) and I can't quite get my head around what's not happening. Apologies if this is an obvious or stupid question as I am new to both Blender and 3D Modelling as a whole.  The Blender File:

I made a scene where a grenade bounces in and rolls across the floor, except the issue is when I render it the location changes slightly. I am running blender 2.78 with supported features only. I have turned all modifiers off and restarted blender. The problem still persists. Can anyone help me out? Note: I made the animation by baking a physics simulation to key frames. The room was also made by archimesh. (I have tried disabling archimesh in the user preferences but it didn't change anything) In the viewport it looks like this:  In the render it looks like this:  Notice in the bottom right that the grenade has not changed locations. To my eye it looks like the grenade is in the same place, but the floor has changed locations. But either way, I do not know why this is happening. Thanks!


i have xubuntu 14.04 LTS and i wan't to ask one question.I'am tried many pages ,but nowherewas this.Please help me i wan't to make my Xubuntu look like normal ubuntu(i have old laptop and the normal ubuntu is laging) and one thing is missing ,the overlay scrollbar please help me.

It looks like Ubuntu 11.04 will come with  by default. I do like them, but I don't like the current mix of scrollbar types as many applications don't yet use those overlay scrollbars.  Is there a way to disable overlay scrollbars (without removing the overlay-scrollbar package)?


Which prepositions are correct?       I am {on/at/in} the railway station.   I am {on/at/in} square.

I am really confused.  Which preposition is correct?     She is in/at the park.   They are in/at the park.   I am in/at the park.   Should I use in or at in these sentences?


I have a CSV file with many address and I need to find the coordinates. I think to import the CSV into  hoping that it find those points, then I would like to export a KMZ to import it in QGIS?  Am I wrong in this thought? If this is the only way to solve it, how can I find info to create this CSV file?  I imported the file into mymaps and I can see the points on the map. Then I exported it in KML/KMZ.  When I go to layer/add layer, QGIS import only a table (with the orginal info from CSV file) not a point shape file.  In the picture below you can see information from my imported addresses KMZ (this is not a geometry point shape file) and a correct test create into mymaps.  I have to add that into mymaps app the dataset looks identical.

I have a CSV with an address field (no lat/long), so I went to Google My Maps, imported the csv and geocoded of the records.  Now I export the layer as KML and added the KML to QGIS and Google Earth Pro, but in non of them I can see the markers. In fact in QGIS, the KML layer is added as datatable (no geometry).  What's happening? How can I export a geometry layer from google My Maps?


Many videos on YouTube while discussing black holes mention that it's born out of a heavy star when it collapses into a single point and that infinitely curves spacetime around it.   When all the mass is getting confined to one point isn't it violating the uncertainty principle?

If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?


This seems to be a common problem, I read all the post here but can't fix the error   This is BibTeX, Version 0.99d (MiKTeX 2.9.6350 64-bit) The top-level auxiliary file: revision6.aux I found no \citation commands---while reading file revision6.aux I found no \bibdata command---while reading file revision6.aux I found no \bibstyle command---while reading file revision6.aux (There were 3 error messages)  Process exited with error(s)   My code is super simple, just usepackage with backend and style for biblatex. Then I cited with the key generated by JabRef  \documentclass[11pt]{article}  \usepackage[letterpaper, margin=1in]{geometry} % page settings \usepackage{floatrow} \floatsetup[table]{capposition=top}  \usepackage{authblk} \usepackage{amsmath} \usepackage[ruled]{algorithm2e} \usepackage{sectsty} \allsectionsfont{\normalsize}  \usepackage{graphicx} \graphicspath{ {./figures/} } \usepackage[labelfont=bf]{caption}  \setlength{\parindent}{7mm}  \usepackage[backend=biber,style=numeric]{biblatex}  \addbibresource{ABCbib.bib} \title{ABC} \begin{document} \maketitle  \section{Introduction}     proteins \cite{Zhang2013}  \printbibliography \end{document}   The bib file looks like  @Article{Zhang2013,   author        = {Yaoyang Zhang and Bryan R. Fonslow and Bing Shan and Moon-Chang Baek and John R. Yates},   title         = {Protein Analysis by Shotgun/Bottom-up Proteomics},   journal       = {Chemical Reviews},   year          = {2013},   volume        = {113},   number        = {4},   pages         = {2343--2394},   month         = {apr},   doi           = {10.1021/cr3003533},   publisher     = {American Chemical Society ({ACS})}, }   EDIT: Then I tried both latex (or PdfLaTeX) -> Biber -> latex (or PdfLaTeX) -> latex (or PdfLaTeX) and got the error with warning Citation Zhang2013 on Page 1 undefined. May someone please guide me here? The configure is already changed to biber.exe and I input biber % for using as user command. But the error remains and ask me to rerun biber.

Running the minimal example  \documentclass{article} \usepackage{filecontents} \begin{filecontents*}{\jobname.bib} @ARTICLE{example,   author  = {Other, Anthony Norman},   title   = {Some things I did},   year    = {2014},   journal = {J.~Irrep. Res.},   volume  = {1},   number  = {1},   pages   = {1-10} } \end{filecontents*} \usepackage[backend=biber]{biblatex} \addbibresource{\jobname.bib} \begin{document} Hello\cite{example}. \printbibliography \end{document}   I get the warning There were undefined references.  I have read  and know that I need to run:   LaTeX Biber LaTeX   However, my editor is only set up to run BibTeX. How do I go about setting up my editor/IDE to be able to run Biber, and how do I run the LaTeX/Biber/LaTeX cycle?  Answers (sorted alphabetically by editor name)                    Answer guidelines   Each answer should be for one editor. If the editor is cross-platform, if possible give a single answer with notes covering the minor platform variations. Please edit the question to include new answers in the 'link list' Each answer should be 'stand alone', i.e. don't say 'It's almost the same as editor Y but ...' for the editor part Instructions for 'build tools' such as arara or latexmk are welcome but should explain how to set up the editor in question as not all editors allow simple addition of arbitrary tools


Today I went through my desktop stations running Linux Mint 17.3 Cinnamon and did a file system check of root partitions with Ext4 file systems as follows:  # fsck.ext4 -fn /dev/sdb2   The problem is that on all of the computers I see something similar to this one:  e2fsck 1.42.9 (4-Feb-2014) Warning!  /dev/sdb2 is mounted. Warning: skipping journal recovery because doing a read-only filesystem check. Pass 1: Checking inodes, blocks, and sizes Deleted inode 524292 has zero dtime.  Fix? no  Inodes that were part of a corrupted orphan linked list found.  Fix? no  Inode 524293 was part of the orphaned inode list.  IGNORED. Inode 524294 was part of the orphaned inode list.  IGNORED. Inode 524299 was part of the orphaned inode list.  IGNORED. Inode 524300 was part of the orphaned inode list.  IGNORED. Inode 524301 was part of the orphaned inode list.  IGNORED. Inode 524302 was part of the orphaned inode list.  IGNORED. Inode 524310 was part of the orphaned inode list.  IGNORED. Inode 524321 was part of the orphaned inode list.  IGNORED. Inode 524322 was part of the orphaned inode list.  IGNORED. Inode 524325 was part of the orphaned inode list.  IGNORED. Inode 2492565 was part of the orphaned inode list.  IGNORED. Inode 2622677 was part of the orphaned inode list.  IGNORED. Inode 2622678 was part of the orphaned inode list.  IGNORED. Inode 2883748 was part of the orphaned inode list.  IGNORED. Inode 2884069 was part of the orphaned inode list.  IGNORED. Inode 2885175 was part of the orphaned inode list.  IGNORED. Pass 2: Checking directory structure Entry 'Default_keyring.keyring' in /home/vlastimil/.local/share/keyrings (2495478) has deleted/unused inode 2498649.  Clear? no  Pass 3: Checking directory connectivity Pass 4: Checking reference counts Unattached inode 2491790 Connect to /lost+found? no  Pass 5: Checking group summary information Block bitmap differences:  -(34281--34303) -11650577 -(11650579--11650580) -11650591 -(11650594--11650595) -(13270059--13270073) -(13272582--13272583) -(20542474--20542475) +(26022912--26023347) -(26029568--26030003) Fix? no  Free blocks count wrong (14476802, counted=14476694). Fix? no  Inode bitmap differences:  -(524292--524294) -(524299--524302) -524310 -(524321--524322) -524325 +2491790 -2492565 -2498649 -(2622677--2622678) -2883748 -2884069 -2885175 Fix? no  Free inodes count wrong (7371936, counted=7371916). Fix? no   /dev/sdb2: ********** WARNING: Filesystem still has errors **********  /dev/sdb2: 443232/7815168 files (0.1% non-contiguous), 16757502/31234304 blocks   What I have tried:  # touch /forcefsck   This results in a 2-3 seconds lasting check on startup. Obviously not repairing anything.  That is most probably because my root file system is somehow clean.  # fsck.ext4 -n /dev/sdb2  e2fsck 1.42.9 (4-Feb-2014) Warning!  /dev/sdb2 is mounted. Warning: skipping journal recovery because doing a read-only filesystem check. /dev/sdb2: clean, 443232/7815168 files, 16757502/31234304 blocks   As I can't find almost anything for file system check on boot other than sudo touch /forcefsck, I tried these steps:   echo u > /proc/sysrq-trigger umount /dev/sdb2 fsck -fy /dev/sdb2   This did show up that it had it repaired, to make sure I ran the fsck again without errors. BUT, they are back once I reboot. I am confused right now. Please don't instruct like "create a flash drive and boot from it and ...". I want a solution on reboot or before reboot without booting from some flash drives. Thank you.

Yesterday, one of our computers dropped to grub shell or honestly, I am unsure what shell it was when we turned on the machine.  It showed that it can't mount the root filesystem or something in this sense, because of inconsistencies.  I ran, I believe:  fsck -fy /dev/sda2   Rebooted and the problem was gone.  Here comes the question part:  I already have in her root's crontab:   @reboot /home/ruzena/Development/bash/fs-check.sh    while the script contains:  #!/bin/bash touch /forcefsck   Thinking about it, I don't know, why I created script file for such a short command, but anyways...  Further, in the file:  /etc/default/rcS   I have defined:   FSCKFIX=yes    So I don't get it. How could the situation even arise?    What should I do to force the root filesystem check (and optionally a fix) at boot?  Or are these two things the maximum, that I can do?  OS: Linux Mint 18.x Cinnamon 64-bit.  fstab:  cat /etc/fstab | grep ext4   shows:   UUID=a121371e-eb12-43a0-a5ae-11af58ad09f4    /    ext4    errors=remount-ro    0    1    grub:   fsck.mode=force    was already added to the grub configuration.


Water in my electric kettle makes the most noise sixty to ninety seconds before the water comes to a full boil. I have been fooled many times by the noisy kettle, only to discover that the water was not yet hot enough for tea. The kettle is only at a full boil after the noise has subsided.    I have noticed the same phenomenon with many other kettles, including conventional kettles on kitchen ranges; it is not a peculiarity of this electric kettle.  Why does the boiling become quieter as the water reaches full boil?

It always seemed to me that the noise from electric kettles follows a pattern: It starts low, then increases, and decreases again before the water starts to boil.  To verify this, I performed a little experiment: I recorded the kettle using my cellphone at sampling frequency $44.1\ \mathrm{kHz}$. I used $1.2$ liters of water at room temperature (well, it's just normal tap water, I didn't actually perform a temperature measurement). I turned the kettle on at $t=0$, and it took $6$ minutes until the kettle switched itself off. Attached are the graph of the recording, a spectrogram (log scale) and an image of the kettle:        (Due to the high sampling frequency, this graph shows mainly the envelope of the audio, but this is what I'm interested in. you can notice on the graph the sound of the initial and final "clicks" of the switch).  Looking at the graph, the pattern is indeed very visible. The amplitude increases at a steady rate from $t=30\ \mathrm s$ to $t=90\ \mathrm s$, then it increases at a bigger rate and flattens at around $t=130\ \mathrm s$, it starts to decrease at $t=210\ \mathrm s$, and at $t=290\ \mathrm s$ (which is when it seemed to me that the water started to boil) increases again to a flat value until the end.  What may be the reason for this pattern?  (If needed, I can provide more info about the experimental setup and more data visualizations)    EDIT$1$: Apparently . But I still wonder about the various phases in the boiling process, which are not mentioned in the other question.


I'm trying to match this output from ansible ping module output:  srv1 | SUCCESS => {     "changed": false,     "ping": "pong" } srv2 | SUCCESS => {     "changed": false,     "ping": "pong" }   as well as this output from ansible setup module output:  srv1 | SUCCESS => { "ansible_facts": {     "ansible_all_ipv4_addresses": [         "192.168.50.100"     ],     "ansible_all_ipv6_addresses": [         "fe80::a00:27ff:fead:7504"     ],     "ansible_apparmor": {         "status": "disabled"     },     "ansible_architecture": "x86_64", ...a lot of lines } srv2 | SUCCESS => { "ansible_facts": {     "ansible_all_ipv4_addresses": [         "192.168.51.101"     ],     "ansible_all_ipv6_addresses": [         "fe80::a00:27ff:fe98:b137"     ],     "ansible_apparmor": {         "status": "disabled"     },     "ansible_architecture": "x86_64", ...a lot of lines }   I'd like to put everything between { .. } for specific host into matched variable, so later I can it using yaml.load.  I tried:  regex = r'(\w+)\s\|\s(\w+)\s=>\s(\{\n\s+"\w+":\s\w+,\n\s+"\w+":\s"\w+"\n\})' o = re.findall(regex,output,re.MULTILINE) for host in o:     yml = yaml.load(host[2])   This works for first output, but not for second. So I tried to generalize it:  regex = r'(\w+)\s\|\s(\w+)\s=>\s(\{.*\})' o = re.findall(regex,output,re.DOTALL) for host in o:     yml = yaml.load(host[2])   But this will match everything between starting { and last }.  What am I doing wrong?  Thanx for help

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


I want my equation and align environments to center with respect to nested indents, but they only seem to center with respect to the full page width.  Here is some example code:  \documentclass[12pt]{amsart} \usepackage{geometry, amsthm} \geometry{letterpaper, margin=1in}  \begin{document}  \begin{enumerate}     \item First level     \begin{enumerate}         \item Second Level         \begin{enumerate}             \item Third level\\             \begin{center}                 $x<y$ % Centered inside nested items             \end{center}             \begin{equation*}                 x < y % Centered in whole page             \end{equation*}         \end{enumerate}     \end{enumerate} \end{enumerate}   \end{document}   This is the resulting document:    Placing the equation/align inside a center doesn't work.  How do I get the align and equation environments to center with respect to nested indents?

I have equations inside an environment which has a larger left-margin than the main text (analogous to an enumerate/itemize environment, implemented with the changepage package's adjustwidth environment). Just as equations in enumerate/itemize behave, the equations are centered with respect to the entire text, rather than just the width of the container environment. I want the latter behavior.  I'm trying to accomplish this by wrapping all display-math in minipages. Namely, I'm modifying the mathdisplay environment in amsmath.sty as follows:  \makeatletter \let\oldmd\mathdisplay \def\mathdisplay#1{%   \newline   \begin{minipage}{\textwidth-\@totalleftmargin}%     \oldmd{#1}% } \let\oldendmd\endmathdisplay \def\endmathdisplay#1{%   \oldendmd{#1}%   \end{minipage} } \makeatother   This is almost working, but there are some issues with spacing which I don't understand how to fix. Here's how the the normal \[ ... \] and numbered \begin{equation} ... \end{equation} look with the above modification:      My main confusion is why the numbered version is behaving so differently from the unnumbered. But all in all I want to fix this so that the spacing above and below is even as it usually is. Any help is appreciated, thanks.  Edit: Here's a compilable example:  \documentclass{amsart}  \usepackage{lipsum} \usepackage{calc} \usepackage{changepage}  \makeatletter \let\oldmd\mathdisplay \def\mathdisplay#1{%   \newline   \begin{minipage}{\textwidth-\@totalleftmargin}%     \oldmd{#1}% } \let\oldendmd\endmathdisplay \def\endmathdisplay#1{%   \oldendmd{#1}%   \end{minipage} } \makeatother  \setlength{\parindent}{0pt}  \begin{document}  \lipsum[1]  \begin{adjustwidth}{20pt}{} \lipsum[2] \[ x \mapsto \hom(-,x) \]  \lipsum[3] \begin{equation}   y \mapsto \hom(y,-) \end{equation} \lipsum[4] \end{adjustwidth}  \lipsum[5]  \end{document}


The classification of finite simple group is a theorem describing all possible finite simple groups. The importance of simple groups is that they are, in a way, "irreducible" - they cannot be quotiented by any of their subgroup. They also come up in the composition series of a group, and hence it is sometimes said that every finite group is "made up" of finite simple groups. However, . I was therefore wondering whether some kind of classification of all finite groups is possible, which would give us means of constructing all groups? I know this is a rather vague question, but to give everyone some idea, here is the classification of finite abelian groups in the spirit of what I want:  Definition: Call a finite abelian group $G$ irreducible if it's not isomorphic to a direct product of two nontrivial groups.  Classification of finite irreducible groups: The finite irreducible groups are precisely the cyclic groups of prime power order.  Classification of finite abelian groups: Every finite abelian group can be written (uniquely) as a direct product of irreducible groups.  Long time ago I had a  that every finite group can be written as a direct product of simple groups, and together with CFSG this would provide a dream classification of all finite groups, but sadly this isn't true. Replacing this with a semidirect products doesn't give us a true statement either, and at this point I am out of ideas.  I realize that there might not be such a classification, and the difficulty in describing a groups of a given order (like $p^k$ with $p$ prime) only supports this. Nevertheless there still might be hope for a partial classification, like we have for simple groups or abelian groups, or maybe there is some description which is rather computationally infeasible.

I know a bit about simple groups. A finite Abelian group is a (direct) product of finite cyclic groups. The simple finite Abelian groups are exactly $\mathbb{Z}_p$ for $p$ a prime. And so, I understand how all finite Abelian groups are made up of finite simple groups.  But, from what I understand, all finite groups are in some way made up of (finite) simple groups.   My question is: how does that work? What does it (more precisely) mean that a finite group is made up of simple groups?  Edit: Thanks to Stefan for directing me to questions that have basically already have the answer. I have done a bit more of research on this and I think I can narrow my question a bit. I would like to understand how simple groups are the building blocks of all finite groups. That is, I would like to understand how, given a finite group $G$, one can find (or show there exists) simple groups $G_1, \dots, G_n$ such that $G$ is [insert something] of $G_1,\dots G_n$. From , I understand now that it somehow has to do with composition series and Jordan-Holder's Theorem. I think I understand the definition of a short exact sequence. From that same question:     Then $G$ is built from some uniquely determined (Jordan-Hölder) simple groups $H_i$ by taking extensions of these groups.   I still don't get how this group $G$ is determined by the simple groups.  I guess I am looking for more details basically putting together how one starts with a finite group $G$, "finds" simple groups $G_1, \dots G_n$ and then says that $G$ is isomorphic to something in terms of the simple groups.


basically says that range must behave exactly as this implementation (for positive step):  def range(start, stop, step):   x = start   while True:     if x >= stop: return     yield x     x += step   It also says that its arguments must be integers. Why is that? Isn't that definition also perfectly valid if step is a float?  In my case, I am esp. needing a range function which accepts a float type as its step argument. Is there any in Python or do I need to implement my own?    More specific: How would I translate this C code directly to Python in a nice way (i.e. not just doing it via a while-loop manually):  for(float x = 0; x < 10; x += 0.5f) { /* ... */ }

Is there a way to step between 0 and 1 by 0.1?   I thought I could do it like the following, but it failed:  for i in range(0, 1, 0.1):     print i   Instead, it says that the step argument cannot be zero, which I did not expect.


I'm curious. In the movie Avatar, how can machines fire the weapons and cause explosion? Clearly, Oxygen is required to cause Fire/Flames.  How is this possible in Pandora?

It was observed again and again in the movie Avatar that humans could not breathe the air present in Pandora. So it can be assumed Oxygen was not present in Pandora. But again the human fires which erupted in the Hometree bombing, wouldn't be sustained if there was no Oxygen at all. So what were the components present in the air of Pandora?  On the other hand if there was Oxygen, why could not the humans breathe there? So was the atmosphere in Pandora Oxygen filled or Oxygen free?


Can someone, please, tell me what to do to fix this error?

I'm trying to install Lubuntu on my laptop (sorta old 2005). [Laptop stats: Intel® Celeron® CPU 410 @ 1.46 GHz 1.47GHz, 448 MB of RAM]  I press Install and this message appears:   This kernel requires an x86-64 CPU, but only detected an i686 CPU.  Unable to boot - please use a kernel appropriate for your CPU.   What can I do to install Lubuntu on my computer?


How to print values in console (like System.out.println() in java) using scriplet in javascript while a function is called ? if i used System.out.println("test") in scriplet the values is getting printed while a jsp form is loading but i want it to print only when a java script is called.

Im running a ASP.NET Site where I have problems to find some JavaScript Errors just with manual testing.  Is there a possibility to catch all JavaScript Errors on the Clientside and log them on the Server i.e. in the EventLog (via Webservice or something like that)?


I tried this:  for(i = 0; i < 5; i++){     for(j = i + 1; j < 5; j++){         break(2);     }     alert(1); }   only to get:     SyntaxError: missing ; before statement   So, how would I break a nested loop in JavaScript?

What's the best way to break from nested loops in Javascript?  //Write the links to the page. for (var x = 0; x < Args.length; x++) {    for (var Heading in Navigation.Headings)    {       for (var Item in Navigation.Headings[Heading])       {          if (Args[x] == Navigation.Headings[Heading][Item].Name)          {             document.write(""                 + Navigation.Headings[Heading][Item].Name + " : ");             break; // <---HERE, I need to break out of two loops.          }       }    } }


Hi Is Google Cloud Mumbai (Asia-South1) facing issues due to COVID situation in Mumbai ? I am unable to create a new Compute Instance or start my old instance in all of the zones in Asia-South1 Mumbai region for over a month now in Zone A,B or C. I keep getting "Not Enough Resources available in this Zone". I am trying to create a 8GB RAM - 4 VCPU on E2 Platform instance with Cent OS 7 & 20GB SSD Disk space. I have waited for almost one month now and still no resolution of this issue. If this doesn't resolve soon it will cause a huge problem for my company from our clients. Kindly help please !

This is a  about a temporary shortage of available resources in Google Cloud services.   I'm a Brazilian user of Google Cloud's Compute Engine for a while and I managed to use it fine for quite some months. Unfortunately, in the last one month or so, I've been facing difficulties starting my instances (around 9 AM) due to the problem "the zone does not have enough resources available to fulfill the request".    At the start, it happened once or twice and then I was able to start my instance. But now it's almost impossible to start it even after dozens of attempts! Following the message's suggestion, I tried to create other instances in southamerica-east1-a nd c (mine was in b) only to find out the same problem happening there. The impression I get from this is that Google has saturated their physical capacities in South America and are doing nothing to increase it.  So what can I do about it? I can't move my server to the USA or something because it's ping sensitive (stock market applications) and, as someone still using the free trial period, I certainly won't start paying for GC if Google may handle me a product I can't use and will take weeks or months to fix.


Imagine that we could weigh antimatter on a scale. Would it have a negative or positive weight. EDIT: I see a similar question, but it dates from 2014. It mentions some experiments to be carried out. Any conclusive stuff?

I know that the gravitational interaction of antimatter is expected to be the same as normal matter.  But my question is, has it ever been experimentally validated?  I think it would not be a trivial experiment, because electromagnetic effects have to be eliminated, so neutral particles would be needed. Maybe diamagnetically trapped antihidrogen atoms could be examined as to which direction they fall?


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 just updated to macOS Mojave, and immediately noticed a couple of things:   My custom login screen wallpaper is gone. When you click on a user's name in the login screen, it switches to their personal background (their usual wallpaper for the first space on the primary monitor).   I assumed it had just overwritten my cached image file. But when I went to replace it, nothing happened. It turns out that com.apple.desktop.admin.png is gone entirely!    Right after taking that screenshot, I decided to poke into Desktop Pictures and found my personal login screen background, which looks promising. It contains one other folder, which  probably  (edit: confirmed) contains the login screen background of my administrator account.


Is there a list of packages that are installed on a fresh install?  I know, there is the other question  But that doesn't show, what will be the output of  dpkg --get-selections | grep -v deinstall | cut -f 1   right after a fresh install of Ubuntu desktop?  I would like to compare the resulting remaining list with the packages I have installed at the moment, so I can find out, what changed on the system since install.

I am developing an offline installer for all versions of Ubuntu, and I need Ubuntu's default installed packages list. Is there a way to get this information from any server (web server)? Any script to fetch any Ubuntu version's default installed packages list.  I will give the Ubuntu version, and the script will fetch the packages list.  Note: I need at least a server address. I can write a script for this.


Consider the following function: $f(x_1, \dots, x_n) = p_1 \log x_1 + \dots + p_n\log x_n$ subject to the constraint that $\sum_i p_i = \sum_i x_i = 1$. It is also known that $p_i \in [0,1]$ and $x_i \in [0,1]$.  I need to prove formally that the function has global maximum when $\frac{p_1}{x_1} = \dots = \frac{p_n}{x_n}$, i.e, $x_i = p_i$ gives the global maximum.  I can prove this formally for two variables by using the standard first and second derivative test (eliminate one of the variables). I can also verify empirically that $x_i = p_i$ is the global maximum of this function when $n > 2$ but want to prove this formally.   Is there a suitable technique for multivariate functions that I can use?

Okay, this is my another try on the question  which I unfortunately mis-stated and actually asked for a problem different than the one I have to solve. I wish to show that given the constraints $0 < a_i, b_j < 1$ and $\sum_{i=1}^{n} a_i = \sum_{i=1}^{n} b_i = 1$ we have the following inequality: $$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$$ The problem arose when I was trying to compute some topological pressures and $a_i, b_j$ are actually measures of some sets, but this inequality (if, hopefully, true) is purely algebraic. Can anyone provide some suggestions?


This  on increased frequency of urination in biology displays in the biology main page as shown below.    As clearly seen, the post says modified by Good Gravy. However on opening the post, I could find no modification by Good Gravy. The revision history of the question shows nothing.   What was modified? How was it done? Is that a bug?

.       The  has no sign of the user sharth The  also does not have any sign of related activity   I would like to know why the user's name is associated with the question. At least why their display name shows up as having modified the question timeline activity.  Possible reason that I can think of is that, .  Is this the reason?  Is there a way (for normal users), to look for such details, other than looking at the user activity and the question's revision history.


The following Python code:  def foo():     t = []     for i in range(1, 3):         def bar():             return i * i         t.append(bar)     return t  for f in foo():     print(f())   Outputs: 4 4. Why isn't the first call output 1? I thought the closure bar() could save the current value of i.    BTW, the almost equivalent Lua code:  function foo()     local t = {}     for i = 1, 2 do         local bar = function() return i * i end         table.insert(t, bar)     end     return t end  for _, f in ipairs(foo()) do     print(f()) end   Outputs 1 4 as what I expected.

While I was investigating a problem I had with lexical closures in Javascript code, I came along this problem in Python:  flist = []  for i in xrange(3):     def func(x): return x * i     flist.append(func)  for f in flist:     print f(2)   Note that this example mindfully avoids lambda. It prints "4 4 4", which is surprising. I'd expect "0 2 4".   This equivalent Perl code does it right:  my @flist = ();  foreach my $i (0 .. 2) {     push(@flist, sub {$i * $_[0]}); }  foreach my $f (@flist) {     print $f->(2), "\n"; }   "0 2 4" is printed.  Can you please explain the difference ?    Update:   The problem is not with i being global. This displays the same behavior:  flist = []  def outer():     for i in xrange(3):         def inner(x): return x * i         flist.append(inner)  outer() #~ print i   # commented because it causes an error  for f in flist:     print f(2)   As the commented line shows, i is unknown at that point. Still, it prints "4 4 4".


I recently installed Ubuntu along with Windows 10. It is working perfectly till today. But I updated my Ubuntu 16.04 form Software Updater and restarted my system.  After restarting I am getting following Error while opening other disk drives (named 136 GB Volume).    Please notice that I am able to access these drives(NTFS partitioned) before updating the system but now it is showing error.  Now I am having access to Computer drive only (that is EXT4).  Please help me to solve this issue. As I am new to Ubuntu.  Thanks!

Whenever I boot Ubuntu, I get a message that it cannot mount my windows partition, and I can choose to either wait, skip or manually mount.  When I try to enter my Windows partition through Nautilus I get a message saying that this partition is hibernated and that I need to enter the file system and properly close it, something I have done with no problem so I don't know why this happens.    Here's my partition table, if any more data is needed please let me know.     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048    20000767     9999360   83  Linux /dev/sda2        20002814   478001151   228999169    5  Extended /dev/sda3   *   478001152   622532607    72265728    7  HPFS/NTFS/exFAT /dev/sda4       622532608   625141759     1304576   82  Linux swap / Solaris /dev/sda5        20002816   478001151   228999168   83  Linux


My cleric and wizard were both stuck in glue in recent combat, and a third PC was down. Instead of rolling to free themselves, they opted to fight from where they were. Once the combat was "over", i.e. all beasts were felled, did they need to still roll "in turn" to free themselves and heal the dying PC or could they have "rolled free" on their own and healed him?  I am a new DM and my Husband is an old school D&D person - not that familiar with 5e but knows the old rules well. we disagreed on this, and I'm curious what you all think. Thanks!    In reading , the writer states combat continues until all things "combat related" are dealt with, which would mean turns continue in order, including saves from glue trap and death saves. If this is correct, then I suppose my question is answered, but I would like someone to clarify. I do not find anything in the PH discussion of combat that specifies when it ends.

Imagine that a PC gets reduced to 0 hit points during a battle. The battle continues for a couple more rounds and they roll their death saves, one success and one failure (not sure if this part of the question is relevant).  Then the rest of the party defeats the last enemy and battle is over. Now what?    Does the downed PC keep rolling death saves until they strike 3 one way or the other? Does everyone else repeatedly roll for Medicine to stabalise the dying PC? Or (as we've been ruling it) they are just assumed to become stabilised because combat is over (I'm fairly certain this probably isn't RAW or RAI though).   I've looked through the PHB and I've only managed to find descriptions of being stabilised during combat, not after it.  Ideally I'd like a rule quoted (or a tweet or something) to point to where such a thing is outlined in the rules, if it is written anywhere.


I have wrote a java programme to download a file from FTP server. I need to check are there any corruptions after download the file. so i decided to check md5 of the file before and after download.  I need to know how can i generate the md5 hash of this file, before it downloading ?

I am looking to use Java to get the MD5 checksum of a file.  I was really surprised but I haven't been able to find anything that shows how to get the MD5 checksum of a file.  How is it done?


What is the purpose of the Using block in C#? How is it different from a local variable?

User  answered the wonderful  question by mentioning the using keyword. Can you elaborate on that? What are the uses of using?


I am learning statistics mainly from a book : Elements de statistique, from three author of the Brussels University. 5th Edition  On the PCA chapter, however, I need to read from other sources, especially to understand how to describe what the axis represents from individual and variable analysis. I then read the whole courses that can be found everywhere over the Internet. And I have a trouble.  My book wrotes :      La droite qui ajuste le mieux le nuage N* des individus est celle autour de laquelle l'inertie de N* est minimale.   (The line that adjusts the best the cloud N* of individuals is the one around which the inertia of N* is minimal).   And the problem is : almost all other sources I can read are searching for the maximal inertia to find the best axes. I can't figure my book could be wrong (on it's 5th edition such a bug would had been found), so what is it trying to explain to me ? And why do I find the contrary elsewhere ?

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors & eigenvalues? What was the need for these concepts? How would you explain these to a layman?


How do I work out the distance Venus travels in one orbit mathematically? I know the parametric equations for its ellipse but I need to work out the total distance travelled in its orbital period.

I want to determine the length of an arc from the ellipse in the picture below:    How can I determine the length of $d$?


There is currently a user doing a large number of retags, and has currently suggested over 100 tag edits in the last few hours (about one every 30-45 seconds).  I appreciate enthusiasm, and correctly tagging things, but isn't this going a bit overboard?    Assuming the edits are all valid, is it really such a good idea to allow this?  For one thing, it's annoying to have a stream of questions all bumped up to the top of the Active queue for over an hour, and the Suggested Edit queue has been sitting at 40+ items for the same time period, but is it really hurting anything either?

I'm throwing this feature request out in response to the following two questions.       The current system for suggested edits seems to work perfectly fine in all cases but one: when a user (or group of users) decides to search for possible typos and edit posts en masse. I entirely agree with .        I do not believe it is possible to fix all the issues that might exist in the posts this way.   If you don't have edit privileges, you're causing work for users. Now, nobody minds this, unless you're not fixing all the issues in a   post and it's clear there's no thought going into the process at all.   Editing bumps things to the SO home page. Again, nobody minds and this is by design, but if you're fixing one tiny issue, is that a   reason to bump 100 questions to the home page? I'd say if you're   fixing all the issues with a post - including flagging what should be   flagged, closing what should be closed etc - great. If you're not,   you're bumping a whole lot of stuff...      There are a few more issues to consider, as well.   Even though a single user can (theoretically) suggest an unlimited number of edits, reviewers are limited in the number of edits that they can accept or reject per day. Most behavior on the Stack Exchange network is rate-limited: why shouldn't suggested edits be, as well? A single user's suggested edits can take up a disproportionate amount of the reviewers' time.   I therefore propose placing a limit on the rate of each user's suggested edits. There are a number of ways we could do this.   Limit the number of suggested edits per user per day—to approximately 100? This is a high enough threshold for any reasonable number of daily edits, and besides, after 100 suggested edits get approved there's no rep in it for the editor anyway. Limit the number of suggested edits per user per hour. Limit the number of outstanding (unreviewed) edits per user at any given time.   I personally like the last solution because it would encourage people to spend more time on each suggested edit and it would optimize for the valuable resource that is being spent on each suggested edit: reviewers' time.


When setting   sql_mode=""  in  /etc/mysql/my.cnf  server leaves this variable in it default value:    mysql> show variables like 'sql_mode';  +-------------------+------------------------------------------------------------------------+  | Variable_name | Value                                                                                | +-------------------+------------------------------------------------------------------------+  | sql_mode         | STRICT_TRANS_TABLES,NO_ENGINE_SUBSTITUTION  | +-------------------+------------------------------------------------------------------------+   However, if i set it manually in mysql shell:   set global sql_mode="";   server sets it as desired - to empty value. Till next server restart, when server sets this variable to default value again.  Tried in single and double quotes - no matter. No errors in error log. No other default configuration files of mysql loaded What's wrong?  Why?

After upgrading MySQL from 5.5 to 5.6, some our app face to problem and need set sql_mode to blank to solve this issue. I added sql_mode = '' to my.cnf but there was no effect on the mysql setting.  How do I keep the sql_mode blank ?


when I open Ubuntu Software Updater, and click the "Upgrade..." button, the window closes and no further events take place.

I am currently using Ubuntu 10.04. I know there is a 10.10 release, but can I upgrade directly to 11.04? Could you walk me through the steps please?


Yesterday I got sucked into a bingewatch of Computerphile's and Numberphile's videos on youtube. In particular I ended up watching some on Ackermann's function. While I knew already this function (and the effect it can have on mathematicians if ), I did not know that it was designed to be computable only through recursion (or, at least, that is what  claims).  The thing is that in a  is shown that you can the results can be computed through exponentiation, and  says that it is really easy to write doen the result using Knuth's up-arrow notation.  So here's lie my problem: [stretching for a moment the imagination and assuming that all integers are representable into a computer, avoiding the risk of overflows, that are outside the scope of this question] if it can be represented through Knuth's up-arrow notation, can't a program that does not use recursion be written to compute the value?  Is it any different for the original Ackermann's function? (the one that Wikipedia says it has 3 arguments instead of 2)

I am reading the wikipedia page on ackermann's function,   And I am having trouble understanding WHY ackermann's function is an example of a function which is not primitive recursive.  I understand that the ackermann function terminates, and thus is a total function. So why is it not primitive recursive? The only information that i can find on the wikipedia page is      [Ackermann's function] grows faster than any primitive recursive function and is therefore   not primitive recursive   Which isn't a good example of why it is not primitive recursive.  Could anyone explain to me how exactly ackermann's function is NOT primitive recursive please?


User Groups:  user 1 creates users 2,3,4.  user 2 creates users 5,6,7.  user 6 creates users 8,9,10,...etc  finally, user 1 can manage all users. and 6 can manage 8,9,10.  I am planned to store like this,  user - created_by  2   -        1  3    -      1  4    -      1  5    -      2      is this correct way of store data in MySQL database? anybody can help me to improve this database structure. Thank you.

Assume you have a flat table that stores an ordered tree hierarchy:  Id   Name         ParentId   Order  1   'Node 1'            0      10  2   'Node 1.1'          1      10  3   'Node 2'            0      20  4   'Node 1.1.1'        2      10  5   'Node 2.1'          3      10  6   'Node 1.2'          1      20   Here's a diagram, where we have [id] Name.  Root node 0 is fictional.                          [0] ROOT                           /    \                [1] Node 1          [3] Node 2               /       \                   \     [2] Node 1.1     [6] Node 1.2      [5] Node 2.1           /            [4] Node 1.1.1   What minimalistic approach would you use to output that to HTML (or text, for that matter) as a correctly ordered, correctly indented tree?   Assume further you only have basic data structures (arrays and hashmaps), no fancy objects with parent/children references, no ORM, no framework, just your two hands. The table is represented as a result set, which can be accessed randomly.   Pseudo code or plain English is okay, this is purely a conceptional question.  Bonus question: Is there a fundamentally better way to store a tree structure like this in a RDBMS?    EDITS AND ADDITIONS  To answer one commenter's ('s) question: A root node is not necessary, because it is never going to be displayed anyway. ParentId = 0 is the convention to express "these are top level". The Order column defines how nodes with the same parent are going to be sorted.  The "result set" I spoke of can be pictured as an array of hashmaps (to stay in that terminology). For my example was meant to be already there. Some answers go the extra mile and construct it first, but thats okay.  The tree can be arbitrarily deep. Each node can have N children. I did not exactly have a "millions of entries" tree in mind, though.  Don't mistake my choice of node naming ('Node 1.1.1') for something to rely on. The nodes could equally well be called 'Frank' or 'Bob', no naming structure is implied, this was merely to make it readable.  I have posted my own solution so you guys can pull it to pieces.


Find the number of bijective function  $g(n):\mathbb{N}\to \mathbb{N}$ such that it's satisfies $\sum_{n=1}^{\infty} \frac{g(n)}{n^2}<\infty$   I think  there is no such bijective function exists , suppose $g(n)=n$ then $\frac{g(n)}{n^2}=\frac{n}{n^2}=\frac{1}{n}$ , but $\sum_{n=1}^{\infty}\frac{1}{n} $ is  diverges . Now again $\sum_{n=1}^{\infty}\frac{1}{n} $ is converges if we omit the term $n$ whose last entries is $9$. But then don't understand how to construct such bijective function .(source:: )  This question is came in TIFR GS-2021 .

Let $f:\mathbb{N^*}\to\mathbb{N^*}$ an injective function. Show that the following infinite series $$\sum_{i=1}^{\infty}\frac{f(n)}{n^2}$$ is divergent. I am supposed to deal with this using the rearrangement inequality. But I don't know how!Could some explain this to me step by step? I really want to understand...


I want to know how to prove this inequality by mathematical induction: $a_k's$ are nonnegative numbers. Prove that$$a_1a_2\cdots a_n\leq \left(\frac{a_1+a_2+\cdots+a_n}{n}\right)^n.$$ In the inductive step, I tried using the inequality $ab\leq \frac{k}{k+1}a^\frac{k+1}{k}+\frac{1}{k+1}b^{k+1}$ but I got over estimate of what I was looking for.  Is there a better way of proving this by induction?

The arithmetic - geometric mean inequality states that $$\frac{x_1+ \ldots + x_n}{n} \geq \sqrt[n]{x_1 \cdots x_n}$$ I'm looking for some original proofs of this inequality. I can find the usual proofs on the internet but I was wondering if someone knew a proof that is unexpected in some way. e.g. can you link the theorem to some famous theorem, can you find a non-trivial geometric proof (I can find some of those), proofs that use theory that doesn't link to this inequality at first sight (e.g. differential equations …)?  Induction, backward induction, use of Jensen inequality, swapping terms, use of Lagrange multiplier, proof using thermodynamics (yeah, I know, it's rather some physical argument that this theorem might be true, not really a proof), convexity, … are some of the proofs I know.


I have 2 bash scripts: tmp/a.sh #!/bin/bash cd frontend yarn install yarn build  docker-compose build docker-compose up -d  b.sh #!/bin/bash ./tmp/a.sh  I want to launch a.sh from b.sh but when ls runs, it prints directory of b.sh(parent process). How do I preserve its path when a.sh runs?

How do I get the path of the directory in which a  script is located, inside that script? I want to use a Bash script as a launcher for another application. I want to change the working directory to the one where the Bash script is located, so I can operate on the files in that directory, like so: $ ./application


As you can see, the image is overhanging the edge of the box. This is also easy to see in editing and creating:    Here you can see that the dotted lines are blocked by the image going over it.

A   B   C   D   E   F             I don't even know. It just seemed weird.  Yes, I understand I could just avoid doing something like that. But the problem already exists with a single level.   Consider having 2 images in a post. Both exceed the maximum width of a post. One is nested in a list. Key to this issue is that my original images were much larger. They were automatically resized.  Image    List      I think it looks weird.


I'm playing Clash of Clans on my device. I had linked it to my Gmail account in the beginning. Because of storage issues, I disabled my Google Play. But I proceeded with the game.  Now when I try signing in using my Gmail account, it asks whether to replace the existing present village with the one that had been saved before disabling Google Play. Is there a way to load my existing village into it? Or is there a way to load my existing village to a new Gmail account on the same device?

I downloaded Clash of Clans to my iPad (iOS 7) this past weekend and started playing.    Of course, after a couple of hours I realized I made some newbie mistakes that are fatal to my future success.  I wanted to restart, but it seems the only way to do so is to reset the device which I really would like to avoid.  After some Googling I tried the option of logging out of Game Center and logging in with a different Apple ID.  But, sadly, CoC re-launched back into the existing game.  Is there any way I can start over? Or at least start a new game under a different account on the same device?


The obvious solution of Lattitude & Longitude doesn't work because it generates points more densely near the poles, and the other thing I came up with (Pick a random point in the unit cube, if it's in the unit sphere map it to the surface, and restart if it's outside) doesn't always find a point within a fixed number of tries.

How do I generate $1000$ points $\left(x, y, z\right)$ and make sure they land on a sphere whose center is $\left(0, 0, 0\right)$ and its diameter is $20$ ?.  Simply, how do I manipulate a point's coordinates so that the point lies on the sphere's "surface" ?.


How can I instruct python to generate an output file which keeps the color formatting specified in the main script?  I am working on the WRDS Cloud and I am using a shell file to execute a python script. The Cloud returns an output file which I can download and open like it is a txt file. However, this does not keep the color formatting that I specified in my original code.   I have tried to use different formatting packages in my python script but the result is always the same: the color is not displayed in the output file. I would really need to see the color because I use it to highlight some particular messages that represent warnings or errors. Therefore, I assume the only way around this is to instruct my python script to generate a different type of output, but I cannot figure out how.  my python script looks like this:  from colorama import * init() print(Fore.MAGENTA + 'Warning: The query failed' + Fore.RESET)   the output file looks like this (with no magenta color):  Warning: The query failed

How can I output colored text to the terminal in Python?


I've been told to use AddGeometryColumn to properly add a column with correct/preferred SRID. however I wonder if it's possible to fix/change the current column instead of adding a new? If there's no other way but to use this function should I remove the previous column?  Thanks a ton.

While importing my shapefile data to PostGIS, I did not select the proper Projection.  How do I now change the SRID of the data, without transforming the Coordinates?


In what scenario do we need to implement Singleton Class in javascript as below  var Singleton = (function () {     var instance;      function createInstance() {         var object = new Object("I am the instance");         return object;     }      return {         getInstance: function () {             if (!instance) {                 instance = createInstance();             }             return instance;         }     }; })();  function run() {      var instance1 = Singleton.getInstance();     var instance2 = Singleton.getInstance();      alert("Same instance? " + (instance1 === instance2));   }

The glorified global variable - becomes a gloried global class. Some say breaking object-oriented design.  Give me scenarios, other than the good old logger where it makes sense to use the singleton.


I was asked to define a non-perfect square. Now obviously, the first definition that comes to mind is a square that has a root that is not an integer. However, in the examples, 0.25 was considered a perfect square. And the square itself + its root were both not integers.  Is it that all non-perfect squares have irrational roots, e.g. $\sqrt{2}$?

It is well known that $\sqrt{2}$ is irrational, and by modifying the proof (replacing 'even' with 'divisible by $3$'), one can prove that $\sqrt{3}$ is irrational, as well.  On the other hand, clearly $\sqrt{n^2} = n$ for any positive integer $n$.  It seems that any positive integer has a square root that is either an integer or irrational number.        How do we prove that if $a \in  \mathbb N$, then $\sqrt a$ is an integer or an irrational number?      I also notice that I can modify the proof that $\sqrt{2}$ is irrational to prove that $\sqrt[3]{2}, \sqrt[4]{2}, \cdots$ are all irrational.  This suggests we can extend the previous result to other radicals.        Can we extend 1? That is, can we show that for any $a, b \in \mathbb{N}$, $a^{1/b}$ is either an integer or irrational?


I've found a lot of examples on how to use precompiled headers for MSVC, but I can't seem to find any examples using clang. From this SO post I can see the clang commands but I'm wondering how they translate into cmake:   to create pre-compiled header include all the headers you don't change > > into Query.h and use: clang -cc1 Query.h -emit-pch -o Query.h.pch to use the pre-compiled header type: clang -cc1 -include-pch Query.h.pch Query.cpp -shared -o libquery.so; Query.cpp needs to include Query.h  Edit: Using clang 6 and cmake 3.11.2

I have seen a few (old) posts on the 'net about hacking together some support for pre-compiled headers in CMake. They all seem a bit all-over the place and everyone has their own way of doing it. What is the best way of doing it currently?


THEE Apple, THEE Engine, THEE Imbecile, THEE Orange, THEE uncle and THA...for all [most] words beginning with consonants

I've been told that when "the" is proceeded by a vowel sound, like "apple" or "hour", it's pronounced as "thee" and not as "thu".  But after listening to a couple of songs, I noticed that sometimes this "rule" is not followed. Take for example the two Katy Perry's songs, "Roar" and "The one that got away". In the first she sings "I got thee eye of thu tiger", but in the second she sings "Thu one that got away".  I don't know if it was sang this way to better suit the song melody (I understand nothing about those techniques), but I got confused. What's the correct pronunciation?  Thanks in advance.


Does anyone know the add_action() hook to use immediately after a user is successfully authenticated.  Hook Test based on @mmm's answer  I ran this test from my mu-plugins.php file:  function check_for_superAdmin() {     if ( is_super_admin() ) { echo 'I\'m a Super Admin !'; exit; } } add_action( 'wp_login', 'check_for_superAdmin' );   the check_for_superAdmin() function works but the is_super_admin() function does not. I may need to pass a parameter in there. Checking....

I am writing a plugin that fetches some extended user info from a remote service and I need it to execute its function each time a user logs in.  Is there a hook that gets fired after login that I can add an action to?


Is it possible to get a secure random number generator from a secure hash function this way  First choose a natural number $n$ as seed, then if we are looking to generate random numbers from $0$ to $F$ (in hex), the first in the sequence is the last digit in the hash of $n$, the second in the sequence is the last digit in the hash of $n+1$, and so on. Does this  make a secure PRNG.

I was just looking at some , specifically at Hash_DRBG. I read briefly through the algorithm, and even though it is not overly complex, it still seems unnecessary to me. I asked myself how I would implement a (cryptographically secure) PRNG on top of a Hash algorithm (SHA256 or SHA512), what came up is:  Idea one:    Obviously this can only provide half the "strength" of the hash  Initialization: state = hash(seed); Iteration: output = first_half_of(state); state = hash(state); Reseeding: state = hash(state || new_seed)   Idea Two:  Maybe with a separate counter  Initialization: state = hash(seed); Iteration: output = hash(state); ++state; Reseeding: state = hash(state || new_seed)   Now, these two "schemes" seem safe to me, I'm a complete crypto noob though. The point is that I don't think that I'm the first one to think of these very basic PRNGs, and I'd like to understand the reason for NIST not to choose something similar in their recommendations. Do these PRNGs have some (obvious?) weaknesses? (If not, is there something known about after how many iterations they should be reseeded?)


It's easy to use prime factorization to show:     If $m\mid n^2$ then $\gcd(m,n^2/m)\mid n$.    Can anybody find some other proof - perhaps a simple reduction of some sort? Maybe solving $m^2x + n^2y=mn$, for example?  I suppose the result would follow if you could prove that $\gcd(m^2,n^2)=\gcd(m,n)^2$, since $\gcd(m,n)^2\mid mn$ since $\gcd(m,n)\mid m$ and $\gcd(m,n)\mid n$. That result doesn't even need $m\mid n^2$.

How to prove $\gcd(a^2, b^2) = (\gcd(a, b))^2$?  My attempt:  Let $\gcd(a, b) = d$.  Then $d|a$ and $d|b$ then $d^2|a^2$ and $d^2|b^2$. i.e $d^2$ divides $a^2 ~~\&~~ b^2$.


Given any really large number $x$, such as the busy beaver number $x=BB(BB(99))$, can we construct a proposition such that we know it has a proof or a disproof, but we also know the shortest such proof or disproof is longer then $x$ symbols?

Given any positive integer $n$, is there a way to quickly construct a statement $S$, such that the shortest proof of $S$, if it exists, must have length at least $n$?  And such that one out of $S$ or not $S$, is provable.    And question 2: If S, then a proof of S must have length atleast n. If not S, then a proof of not S must have length atleast n.  Edit:  I had in mind that the number of symbols in S be of the same order as the number of symbols required to specify n.