What is the digital sum of $(99...9)^3$ ? There are 12 nines in the expression. My attempt I have tried to write it as $(10^{12}-1)^3$ and tried to compute the digital sum of expanded expansion. But it is getting complicated and i am loosing track. Can any one help?

Someone had posted a question on this site as to what would be sum of digits of $999999999999^3$ (twelve $9s$ ) equal to?   I did some computation and found the pattern that sum of digits of  $9^3 = 18$,  $99^3 = 36$,  $999^3 = 54$ and so on. So, I had replied that sum of digits of  $999999999999^3 = 12 \cdot 18 = 216$.  Can anybody help me prove this, that sum of digits of  $(\underbrace{999\dots9}_{n\text{ times}})^3 = 18n.$


I want to have a header div on the top (which i can fill with other crap), and a footer div on the bottom. In the middle there should be a div with variable height to fill the whole screen.  Here is my code:

Header

This should be variable in height

Footer

   If you execute this, you will see that the yellow line is never filled and it has the same height as both the header and the footer. You can also see that the whole website has a brown background.  Can you help me with that?

I am working on a web application where I want the content to fill the height of the entire screen.  The page has a header, which contains a logo, and account information. This could be an arbitrary height. I want the content div to fill the rest of the page to the bottom.  I have a header div and a content div. At the moment I am using a table for the layout like so:  CSS and HTML    #page {     height: 100%; width: 100% }  #tdcontent {     height: 100%; }  #content {     overflow: auto; /* or overflow: hidden; */ }

...

...

     The entire height of the page is filled, and no scrolling is required.  For anything inside the content div, setting top: 0; will put it right underneath the header. Sometimes the content will be a real table, with its height set to 100%. Putting header inside content will not allow this to work.  Is there a way to achieve the same effect without using the table?  Update:  Elements inside the content div will have heights set to percentages as well. So something at 100% inside the div will fill it to the bottom. As will two elements at 50%.  Update 2:  For instance, if the header takes up 20% of the screen's height, a table specified at 50% inside #content would take up 40% of the screen space. So far, wrapping the entire thing in a table is the only thing that works.


Mr. Dursley arrived in the Grunnings parking lot. We use "at" for a specific place. So why "in" used in this sentence?

When do we use "at" and "in" with "arrive" talking about place, not time?


A chest of drawers has 3 drawers. Each drawer has 2 boxes. The boxes of one drawer contain a silver coin in each respectively, the boxes of another a gold coin in each box, and the boxes of the third drawer a gold and a silver coin, respectively. A drawer is selected at random and a box from the drawer is selected at random and opened. The coin is found to be silver. What is the probability that the coin in the other box is gold?  I got 0.5.

Possible Duplicate:          This is the Bertrand's Box Paradox I read about on Wikipedia:     Assume there is three boxes:       a box containing two gold coins,       a box with two silver coins       and a box with one of each.       After choosing a box at random and withdrawing one coin at random,       if that happens to be a gold coin,       the probability is actually 66% instead of 50%.      And the problem is equivalent to asking the question       "What is the probability that I will pick a box with two coins of the same color?".   No matter how hard I try, I just couldn't comprehend this..   How is the possibility of picking a gold coin the same as the probability of picking a box with two coins of the same color?  Does this imply there is a 66% chance of picking a gold coin and a 66% chance of picking a sliver coin?   If so, can we just say there is 50% chance of picking either one of them since both stand a 66% chance....?! and suddenly everything makes no sense..  [UPDATES] It is actually the probability of the remaining coin to be gold is 66% but not the probability of obtaining the gold coin is 66%.. I've misread it....   And everything makes sense now :D !


I have a Business Class Schengen visa type C, single entry, to Austria. The issuing country is also Austria. I have a few days free in between my meeting dates. I want to travel to other nearby EU countries for one-night stays in each.  Can I do this with the visa I have? If yes, then do I just book a plane ticket and travel. Or do I need some documents for that?  I got only a single-entry visa with a period of stay of 20 days.  I'm traveling first to Austria; then I booked a flight to Paris, France. Is that possible or should I travel only by train or road, since my visa is only single-entry? Can I fly to other Schengen countries with a single-entry visa?  As I have to get back to Austria after my second meeting, can I come back to Austria on a single-entry visa?

I am visiting a friend in Switzerland for ten days. I have already got visitor's visa for the same on my Indian passport. Particulars mentioned on my visa are:  1. 'Etats Schengen' , 2. Single entry 3. Dates of visit. & 4. Type of visa : C.  I understand that having already got ‘Etats Schengen' visa, I can travel to all Schengen countries.  I am also planning to visit Paris for a day during my stay in Switzerland. However, I never mentioned this in my visa application. I am planning to take a train from Geneva to Paris and book a hotel in Paris for one night. Can I possibly plan my Paris trip this way as I have Schengen visa, or I am not allowed to travel out of Switzerland as I never mentioned this in my visa application?   Also what does Single entry on my Schengen visa means: does it mean that I can enter and leave Switzerland only once or it means that I can enter and leave the Schengen region only once.


I've wrote a script to go to a Windows folder on my desktop. Here it is:  #!/bin/bash cd /mnt/c/users/username/desktop/testes/.../.../mydir   then chmod +x scriptname.  but when I call it (./scriptnameENTER), it does nothing and remains in my home directory.  I've tried sudo ./myscriptname also...

I just want to write a script which changes my directory.  I put the below commands in the file /home/alex/pathABC  #!/bin/sh cd /home/alex/Documents/A/B/C echo HelloWorld   I did   chmod +x pathABC   In the Terminal, while in /home/alex, I ran ./pathABC, but the output is just HelloWorld and the current directory is not changed.  So what is wrong?


I have a long layover in Heathrow, like 6 hours, and I have a Priority Pass card to access several lounges on terminals 1 and 3. But I will be arriving to T5, and leaving from there as well. Is there any way to change terminals so I can relax at some lounge?

We will be flying into and out of Terminal 5 at Heathrow. Now, my wife has taken fancy to a certain duty-free store located at Terminal 3. Assuming we factor in enough time before boarding our outbound flight from Terminal 5, are we allowed to enter Heathrow from Terminal 3, shop and then shuttle over to Terminal 5?


I got a query that joined some tables together, some have identical names, for example id is twice in the result, and when I try to echo the id, it displays the wrong one.   How can I solve that?  My query:  $content = " SELECT ct.*       , fe.*       , cn.*   FROM web_content ct   JOIN web_fieldsandfilters_elements fe      ON fe.item_id = ct.id   JOIN web_fieldsandfilters_connections cn      ON cn.element_id = fe.id  WHERE ct.alias = '".$conn->real_escape_string($_GET['alias'])."'     AND ct.state = 1   ORDER      BY ct.ordering ";   I would like to be able to just display it like this:   echo $contentcr[0]['id_ct'];   I want to still retrieve everything from web_content (which I named ct) but also name the id row differently. How can I do that?

I have two tables in my database:  NEWS table with columns:   id - the news id  user - the user id of the author)   USERS table with columns:   id - the user id   I want to execute this SQL:   SELECT * FROM news JOIN users ON news.user = user.id    When I get the results in PHP I would like to get associative array and get column names by $row['column-name']. How do I get the news ID and the user ID, having the same column name?


I have a new Late 2013 rMBP and a Mid 2011 iMac. I want to use the iMac in Target Display Mode so I can operate it as a second monitor for the laptop.  I have two questions:   I can easily turn on TDM on the iMac using ⌘ Cmd+F2, but cannot turn it off the same way. I have to unplug the Thunderbolt cable. Anyone know why? I only have one Apple keyboard and mouse, and both are bluetooth wireless. Right now they are paired to the iMac. I will instead pair them to the laptop so I can use them on that, but I need a keyboard that can toggle TDM on the iMac. I tried using a Dell keyboard (which in my experience, Apple treats the ⊞ Win as the ⌘ Cmd key) and using ⊞ Win+F2, but it doesn't toggle it. Is there any hope to use a non-Apple keyboard to toggle TDM on the iMac?

Here's my setup:  MacBook --> Thunderbolt Display --> iMac 27"  The MacBook is the primary computer I want to use;  the iMac is the (external) display.  This all works just fine.  The problem is, when I disconnect and then reconnect the MacBook, I have to manually put the iMac in Target Display Mode using the keyboard.  This means I need to keep a keyboard attached to the iMac, and it clutters up my desk!  Is there any way to switch the iMac into TDM without using the keyboard?  Maybe by logging in remotely?  I found a few similar questions, but... no answers!      Anyone?


** > Hey buddies I have a file having names of 200 countries.I want to print names of countries from 50th line to 80th line .How can  i do so in bash?? **


if I cast  on my opponent's creature that has a tap to sacrifice creature after he uses it's ability, does the activated ability happen?  My friends and I had a game where one of them used a tap ability to sacrifice this creature to deal 2 damage and I played .  In response does my creature die or his ability not go off since the sacrifice was not a part of the cost?

Player A taps  targeting Player B; its "deals 1 damage to target player" ability is placed on the stack.  Player B gets priority and responds with , targeting Goblin Fireslinger.  Both players pass priority. Snap resolves, and Goblin Fireslinger is returned to its owner's hand.  Does Player B still take 1 damage from Goblin Fireslinger's activated ability?  I know that if the creature had been killed/sent to the graveyard, the ability would still resolve, but I was told recently that because a player's hand is a private zone it couldn't. If anyone could confirm or deny this for me, it would be most appreciated.


Suppose that $$\sum_{n=0}^{\infty} a_n^{2}x^{n}$$ converges exactly on [-6,6]. Find the largest set on which you can guarantee that $$\sum_{n=0}^{\infty} a_nx^{n}$$ converges, and prove your answer.   I think the largest set is $(-\sqrt{6},\sqrt{6})$. I am not sure how to prove this answer.

There was a book problem I recently solved going like this:  $\sum_{n=0}^\infty a_n^2x^n$ converges on $[-6,6]$  What is the largest interval $\sum_{n=0}^\infty a_nx^n$ is guaranteed to converge on?    I already understand this:  $\limsup_{n\rightarrow\infty}|a_n^2|^{1/n}=1/6$  $\Rightarrow\limsup_{n\rightarrow\infty}|a_n|^{1/n}=1/\sqrt6$  $\Rightarrow$Radius of Convergence is $(-\sqrt6,\sqrt6)$ for $\sum_{n=0}^\infty a_nx^n$    What I was wondering however, is what are examples of what the values for $a_n$ could be where the endpoints dont converge for the series, but the series with $a_n^2$ converges on [-6,6]?


The purpose of the command should be replacing any IP in file myfile.txt with the local IP of the server automatically  i tried to use this command:  sed -i -e 's/[0-9]\{1,3\}\.[0-9]\{1,3\}\.[0-9]\{1,3\}\.[0-9]\{1,3\}/'"$(/sbin/ip -o -4 addr list eth0 | awk '{print $4}' | cut -d/ -f1)/g" myfile.txt   but got this error   sed: -e expression #1, char 71: unterminated `s' command

The purpose of the command should be replacing any IP in file myfile.txt with the local ip of the server automatically  example:  sed -i -e 's/[0-9]\{1,3\}\.[0-9]\{1,3\}\.[0-9]\{1,3\}\.[0-9]\{1,3\}/LOCALIP/g' myfile.txt   i want to know if it possible to use command for getting local ip address inside sed   basically i want to replace LOCALIP in my example with this command   /sbin/ip -o -4 addr list eth0 | awk '{print $4}' | cut -d/ -f1


Ok maybe not everyone but in "Resolution" the Doctor has to explain who the Daleks are despite the fact they have invaded Earth many times over the years, certainly anyone in the UK should be aware of them surely!

In "The Woman Who Fell to Earth (S11 E1)" the Doctor is found on a train after an alien appearance. When she suggests that the creature that fell through the roof of the train (not her) was an alien, Graham says "Don't be daft, there's no such thing as aliens."   However, at this point, there have been several major alien events on Earth, and by this point I thought aliens were common knowledge (though not many people know much about them). As I recall, just last season alien pyramids were landing on Earth.  On the other hand, it's possible that one of the various reboots or time messes changed on Earth changed the situation.  Given the events of the previous season, why would this man be skeptical of the existence of aliens?


I'm trying to make this simple smoke sim, but I just can't figure out what is going on. Instead of my rendered smoke looking smooth, it takes up this weird pixely effect. It feels like I have tried to change every setting from Domain resolution, high resolution, applying scale etc and nothing works. I'm rendering in Eevee (I tried cycles and get the same problem though). Also in Blender 2.81

I'm trying to make this simple smoke sim, but I just can't figure out what is going on. It feels like I have tried to change every setting from Domain resolution, high resolution, applying scale etc and nothing works. I'm rendering in Eevee (I tried cycles and get the same problem though). Also in Blender 2.81.


The scatter plot shows two data series (x,y) the are placed somehow around a tilted ellipse. This is in fact the way I have drawn this example plot. Which statistics of the data sets are the most suitable to estimate back the geometrical parameters of the underlying ellipse? The objective is to have an ellipse that deviates the least from the points (perhaps considering distances in direction normal to the ellipse?). Such parameters could be the location of the centre, the lengths of the major and minor axes and, interestingly, the tilt with respect to the x axis.  There are many mathematical representations for an  -- using any that is amenable to a statistical interpretation would do.

Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)?  Background: Using R Momocs library function  which returns confidence ellipse coordinates. Would be nice to abstract those points into a formula.  You can see my ellipse points in the image below;    Any suggestions much appreciated, Thanks


I used to be able to look at the Top Challenger Players (), and click on them, but I got into Ranked and it doesn't work anymore).  How do I watch a specific player's game?

I'm looking to see some full game replays in League of Legends (that are not my friends' game)  Those "Featured games" in the starter slider are always in progress, and what I'm looking for is to get in a random game that is still on the character select screen. (or at least still in the 3 minutes buffer)  Is there any way to do this?


Find all $n$ such that   $3^{2n+1}+2^{n+2}$ is divisible by $7$  Prove that your answer is correct   So I am not allowed to use mods,  as is a calculus question, I have tried by induction but can't get to prove that it works for $k+1$, by multiplying the equation by powers of $2$ and $3$.   Thank you for your help

Expanding the equation out gives  $(3^{2n}\times3)+(2^n\times2^2) \equiv 0\pmod{7}$   Is this correct? I'm a little hazy on my index laws.  Not sure if this is what I need to do? Am I on the right track?


I want to extend the root partition, which is /dev/sda4 in my case.  But the unallocated space I want to apply (/dev/sda5) is to the left of /dev/sda4.  How can I add the unallocated 19.53GB of storage space to /dev/sda4 and extend my root partition?

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


So I'm trying to achieve an animation in BI where there is a string that is attached at both ends to 2 separate objects. But I can't find anything that lets me take my string and attach it to them. The string is an elongated cylinder that has had a lot of loop cuts in the middle. Help please?

I am trying to rig a rope so that it spans between two objects. Technically it is a fuel line, regardless I am trying to get it to work with the soft-body physics, primarily because A, it will be affected by gravity, and B, the engine rotates in relation to the body of the vehicle.       As you can see, I have two bones that I want this fuel line (red line) to span between. I have been trying to use a bezier curve with soft-body enabled, but it only connects to one bone and flops around on the floor like a fish at the other end.(Why does it flop around if no forces are acting on it?)  Thank you for any assistance.


First of all this question is similar to  one but the difference is that I have an unknown quantity of parents. Is is possible and if so how would I get all parents of a child when I only know the Id of any child? I have a table like: +----+------------+----------+--------+ | Id |    name    | position | parent | +----+------------+----------+--------+ |  1 |        top |        1 |   NULL | |  2 |     middle |        1 |      1 | |  3 | bottom_1_1 |        1 |      2 | |  4 | bottom_1_2 |        2 |      2 | |  5 |   middle_2 |        2 |      1 | |  6 | bottom_2_1 |        1 |      5 | |  7 | bottom_2_2 |        2 |      5 |  Which would correspond to something like this visually: top  Ͱ middle     Ͱ bottom_1_1     Ͱ bottom_1_2  Ͱ middle_2      Ͱ bottom_2_1     Ͱ bottom_2_2  Unfortunately my knowledge of MySQL is not advanced enough to show some kind of foreach join method to give you as an example as I would only be able to go up 1 in the tree like: SELECT * FROM table WHERE Id in (7, (SELECT parent FROM table WHERE Id = 7))  This would return: +----+------------+----------+--------+ | Id |    name    | position | parent | +----+------------+----------+--------+ |  5 |   middle_2 |        2 |      1 | |  7 | bottom_2_1 |        2 |      5 |  But I would need something like the example below as the first entry of the above example still has a parent +----+------------+----------+--------+ | Id |    name    | position | parent | +----+------------+----------+--------+ |  1 |        top |        1 |   NULL | |  5 |   middle_2 |        2 |      1 | |  7 | bottom_2_1 |        2 |      5 |

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.


I want to make a detailed timeline of life events in a similar fashion of the attached photo, can someone share code?

I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization.


Last night I was trying to sell cards and level up when steam crashed. I could not get to the store or anything, and when it crashes it says,"Error Code: -118  Unable to connect to server. Server may be offline or you may not be connected to the internet." Now it lets me go to the store but when I try to go to my profile it just refreshes the store. How do you fix it?

Above is a screenshot of the error I am getting in my Steam application. It says:     "Unable to connect to server. Server may be offline or you may not be connected to the internet."   I have a connection to the internet and it's working properly, I have no clue what might be the cause of this problem but I can visit the site when I use the "cache" option instead as below;    Any idea what might be the fix for this?


We have trained two different neural networks for MNIST dataset. Here are the losses and accuracies obtained by these networks for the training data:  net0: loss: 20780.8291187 net1: loss: 209.928699374 net0: TRAIN ACCURACY     0.985890040888 net1: TRAIN ACCURACY     0.835298627336   The used loss function is the cross-entropy. We expect higher accuracies for lower losses, but here, the loss for net1 is about 100 times lower than net0 but its accuracy is lower. What is the reason?

Figure below shows the accuracy using different alpha values in L2 regularisation. As long as alpha is small in the range of $10^{-12}$ to $10^{-2}$ the accuracy remain the same. I do undarstand when alpha value is $10^{1}$ or greater it will increase the weights to a point where they do not fit the data optimal and then, resulting in under-fitting. What is the reason why the accuracy remain the same by smaller alpha values? The formula is: $$w^{2}=w^{1}-\alpha*w^{1}$$  where $w^{1}$ and $w^{2}$ are respectively the recent and the regularised weight parameters, $\alpha$ is the regularisation parameter specifying the amount of regularisation.


Let $G$ be a graph with $n$ vertices and $e$ edges such that $e>\binom{n-1}{2}$. Then $G$ must be connected. As usual, hints would be greatly appreciated. If it where$\binom{n}{2}$ then wouldn't everything be adjacent to itself? I'll try to answer the question myself at the end if I'm able to.

I'm trying to pick up a little graph theory out of Bondy and Murty's Graph Theory as suggested .  Problem 1.1.12 has given me a little hitch.     Let $G$ be a simple graph of order $n$ and size $m$. (So there are $n$ vertices and $m$ edges). If $m>\binom{n-1}{2}$, then $G$ is connected.   I'm following a hint in an appendix which says if $G$ is not connected, we can partition the vertices into parts $(X,Y)$ such that no edge joins a vertex in $X$ to a vertex in $Y$. What is the largest number of edges in $G$ if $|X|=r$ and $|Y|=n-r$?  I suppose the graphs on $X$ and $Y$ are then complete graphs, for a total of $\binom{r}{2}+\binom{n-r}{2}$ edges. Simplifying, this is $\frac{2r^2+n^2-2rn-n}{2}$, so I'm trying to show $$ \frac{2r^2+n^2-2rn-n}{2}\leq\frac{(n-1)(n-2)}{2} $$ to get the contrapositive.   The above is equivalent, if my algebra is correct, to showing $r\geq\frac{n-1}{n-r}$ for any $0\lt r\lt n$. This seems reasonable, but I can't quite show it. How would I do so?  Thanks.  I'd also be happy to see a solution that doesn't necessarily make use of the hint.


I have a function that looks something like  foo(object& obj) {  }   inside this function I need to call another function like this:  foo(object& obj) {     bar(pointer to obj); }   the bar function takes a pointer to the object as an argument. Could some help I can do convert from non pointer to pointer?

I know references are syntactic sugar, so code is easier to read and write. But what is the difference between a pointer variable and a reference variable?


Our home is 2700sqft 1 story. We have a swimming pool with a variable speed pump which barely runs and is on the lowest setting.  I also have a 40x60 workshop that has 100 amps coming off the house. I am only in the shop once or twice a week for probably no more than an hour each. We have radiant barrier in the attic. This month since it's been cooler we have barely used the electric heat and only turned the AC on maybe 3 times.   Our Kwh usage for the past year has been 5400kwhs up to 7898kwhs.   Our neighbor has almost the same size house and shop but he works in his shop daily for 6-10 hours each day. He doesn't use over 2000kwh per month.   My wife just told me about our $700 and up to $1300 electric bills.  This is ridiculous.  Thanks in advance for any info.

This might be subjective, I don't know. However, it's a serious problem for me. My electrical bill is outrageous. It's three times as large as my next-door neighbor, and four or five times the size of my neighbor's across the street. It's worse in the summer (I live in central TX), but I've had the air conditioner inspected, and while the house is right at the maximum capacity for our unit, the unit should still be able to take care of the load. That also doesn't explain why our winter bills are larger than the comparables.  What I would like to do is check the amount of current drawn by each running appliance and calculate where all my money is going. I just don't know how to go about doing this.


I am using QGIS Desktop 2.8.5 on a windows machine and I am using the composer tool to create images with a scalebar and legend. The following is a screenshot of the my working environment:     The image above appears exactly how I would like.  Now, when I export as a PDF, the resulting image is:    And when I export as an image (tiff, jpg, png), the resulting image is similar (my reputation is <10 so I cannot upload a third image).  In both cases, the exported image is distorted from the original. I've tried to export the image several times and the amount of distortion varies each time. I have also tried to use a different computer (also Windows with 2.8.5) and I get the same results.   Why is this happening and how can I remedy it?

I'm having trouble with the OpenLayers Plugin of Qgis and the map composer:  If I create an OSM-background layer and if I want to export this, the OSM-Layer looks perfectly all right in the normal qgis program window. But in the map composer and after export the layer has shifted relatively to my other shape layers (EPSG:32633 - WGS 84 / UTM zone 33N).  The second thing is that the output resolution of the exported osm-layer is very, very poor.   A really bad way of getting around this whole trouble would be to increase the screen resolution and make a screenshot of the map composition window of qgis. But I don't think this would be very professional. It also would cause a lot of pain :)   I'm using Qgis 1.8.0-Lisboa under Linux. The openlayers plugin is version 0.92.


I am using HP Compaq 6735b laptop and it comes with a ATI Mobility Radeon HD 3200 Graphics card. I have recently installed 12.04 on it.   Can someone tell me how will I know if the Graphics card is working or not?

I am planning on doing a fresh install of Ubuntu and want to know what is the correct way to install ATI Catalyst Video Driver?      There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience an index of each below:


How can I get list of users that a folders is shared to programatically?  I need a class or a method to do this, Is there any library or API for this?  I have a shared folder like \\faridb\TestSharedFolder an I want to get list of users (also in domain) that this folder is shared to.  The shared folder is on my own machine.   How can I get this list?

Is there a way through the .net framework to determine if a folder is shared or not?  Neither Diretory, DirectoryInfo or FileAttributes seem to have any corresponding field.  One thing I forgot to mention was that I want to be checking for network shares.  But I'll investigate the WMI stuff.


Let $X$ and $Y$ be two measurable spaces. I want to construct a function $f : X\times Y \to \mathbb{R}$ such that $f(x,\cdot) : Y \to \mathbb{R}$ is measurable for all $x \in X$ and $f(·,y) : X \to \mathbb{R}$ is measurable for all $y \in Y$, yet $f$ is not measurable in the product space. How can I construct such a function?

Some fellow classmates are preparing for a qualifying exam on real analysis, and asked me for help on the following question:  Let $ \ f:[0,1]^2\longrightarrow\mathbb{R}$ be such that: (i) $\ f(x,\cdot)$ is measurable for each fixed $x\in[0,1]$; (ii) $\ f(\cdot,y)$ is continuous for each fixed $y\in[0,1]$. Show that $\ f$ is measurable.  If we only assume that $\ f(\cdot,y)$ is measurable for each $y\in[0,1]$, rather than continuous, can we still conclude that $f$ is measurable?  I was able to come up with the following simple proof (at least I hope it is a proof) of the first statement using some standard arguments:  Proof. $ \ $ Define a sequence of functions $\{f_n:[0,1]^2\longrightarrow\mathbb{R}\}_{n\geq 1}$ by: $$ f_n(x,y)=f\bigg(\frac{i}{n},y\bigg), \qquad \text{for } x\in\bigg[\frac{i}{n},\frac{i+1}{n}\bigg], \ i=1,\cdots,n $$ Moreover, since $ \ f(\cdot,y)$ is continuous at $x=\tfrac{i}{n}$ for each $y$, for each $\epsilon>0$ there is a $\delta_y>0$ so that $$ \bigg| \ x-\frac{i}{n}\bigg|<\delta_y \qquad\Rightarrow\qquad \bigg| \ f(x,y)-f\bigg(\frac{i}{n},y\bigg)\bigg|<\epsilon; $$ therefore, for any $n>\tfrac{1}{\delta_y}$ and any fixed $(x,y)\in[0,1]^2$ with $x\in\big[\tfrac{i}{n},\tfrac{i+1}{n}\big]$, we have $$ \bigg| \ x-\frac{i}{n}\bigg|\leq \frac{1}{n}<\delta_y $$ and so $$ | \ f_n(x,y)-f(x,y)|=\bigg| \ f\bigg(\frac{i}{n},y\bigg)-f(x,y)\bigg|<\epsilon. \tag{$\ast$} $$ In other words, $ \ f_n\longrightarrow f$ pointwise.  Furthermore, we clearly have that $$ A_n:=\{(x,y)\in[0,1]^2 \ | \ f_n(x,y)>\alpha\} \qquad\qquad\qquad $$ $$ \qquad\qquad \ =\bigcup_{i=1}^{n-1}\bigg(\bigg[\frac{i}{n},\frac{i+1}{n}\bigg)\times \bigg\{y\in[0,1] \ \bigg| \ \ f\bigg(\frac{i}{n},y\bigg)>\alpha \bigg\}\bigg). $$ Since $ \ f\big(\tfrac{i}{n},\cdot\big)$ is measurable for each $i=1,\cdots,n$, the latter expression is a union of measurable sets.  This means that $ \ A_n$ is measurable, and therefore $ \ f_n$ is measurable for each $n\geq 1$.  Finally, as the limit of measurable functions is measurable, we conclude that $ \ f$ is measurable. $\hspace{6.25in}\square$  I'm fairly certain that the above proof is correct (anyone care to confirm?); however, that still leaves the following:  Question:  If $ \ f$ is merely measurable in each variable separately, is it measurable?  The proof I gave above uses the continuity assumption in $(\ast)$, so obviously the same proof will not work in this case, but I cannot come up with any counterexamples.  Any suggestions?


According to Karl Popper's falsification criterion only a falsifiable theory is said to be a scientific theory. If this is true, is Economics falsifiable and hence considered scientific?

In class, I made the argument that economics is not science, because it cannot undertake repeatable experiments. Someone rebutted: this would mean that I am ignore an emerging body of work, some by prominent Nobel Prize winners, that is transforming economics into a field firmly grounded in fact.   How would you justify whether economics is scientific or not?


Does anyone know if English has a regulator as Spanish does? We have "Real Academia Española" (Royal Spanish Academy) it seems English doesn't have one (). Even Klingon has one (he he).

For some languages, there are academies that decide topics such as grammar and spelling of things, for example, for the Spanish language, there are 22 academies in 22 different countries, all making decisions on spanish grammar in their country. I would like to know if there is something that serves the same purpose for the English language.


I am trying to read in an input from a user and I know my method needs a char* but is there anyway to make the input of cin able to be used by that char? (look at the comment at char* x.)  string y; cout << "Enter your file: "; cin >> y;  char * x = //here is where the string needs to go. If I type in the actual address it works, but I need it to work when the user just cin's the address//  string line,character_line; ifstream myfile; myfile.open (x); while(getline(myfile,line)) {     if (line[0] != '0' && line[0] != '1')     {         character_line = line;     }  }

How can I convert an std::string to a char* or a const char*?


I'm trying to get passed activation on my iPhone 7+ but my home button isn't working and I don't have an apple computer to get passed it, is there another way I can do it, possibly including a Chromebook or iPad air 3rd generation

My iPhone 5s had recently been cleaned of all files and data, including iCloud so I need to activate it. It prompts me to press the home button to activate but the home button on my iPhone doesn't work. Is there a way I can activate this phone without pressing the home button?


How to write the straight bar with subscript as I have attached in the picture?

How do I insert the line "|" after the equation in LaTeX (see image below)? I'm using LyX so if you can point me to the symbol of that line is also OK.    I don't know if this line has a proper name so the title of this question may be very vague. If you could provide me a name, I'll edit this question's title.


#include<stdio.h>  int main(void) {     int i=(1,2,3,4);     printf("%d",i);     return 0; }   When I'm given an online technical mock test I came to this question. Firstly I think there is an compilation error in line int i=(1,2,3,4); but I was wrong. I don't know why the output of this question is 4.

How does the comma operator work in C++?  For instance, if I do:  a = b, c;     Does a end up equaling b or c?   (Yes, I know this is easy to test - just documenting on here for someone to find the answer quickly.)  Update:  This question has exposed a nuance when using the comma operator.  Just to document this:  a = b, c;    // a is set to the value of b!  a = (b, c);  // a is set to the value of c!   This question was actually inspired by a typo in code.  What was intended to be  a = b; c = d;   Turned into  a = b,    //  <-  Note comma typo! c = d;


Since the ring was only able to be controlled by Sauron, why would he be afraid of someone else wielding it? Everyone, even the most powerful beings, admitted they couldn't use it. Yes, this question is more about Sauron's reaction. Another question said that Sauron was terribly afraid and I just didn't get the feeling that he was. But if he was why was he?

The temptation of the One Ring, we quickly learn, is always tied up with power: each character's fantasies of possessing it seem to be about what they would do with great power. Even Sam, as I recall, imagines the power to create great huge sweeping gardens. Boromir wants the power to save Gondor, etc.  But does the One Ring actually convey power to anyone but Sauron? It actually seems to diminish its bearers: Bilbo feels "thin" and "stretched", Sméagol becomes the wretched Gollum, Frodo is never quite the same even after it is destroyed. None of them seem more "powerful," even in the abstract way that magic-users in Tolkien operate. No mention is made, that I can recall, of a Ringbearer having greater stature or authority, or of people naturally following them or obeying their commands, while they possess the Ring.  The accepted answer to  implies that a being as powerful as Gandalf could dominate the Ring and break Sauron's hold over it, but even then Tolkien says that "It would have been the master in the end", and his descriptions of a Ringbearing Gandalf sound pretty much like Gandalf is using his own powers, not terribly augmented by the Ring:     [Gandalf] would have remained 'righteous', but self-righteous. He would have continued to rule and order things for 'good', and the benefit of his subjects according to his wisdom (which was and would have remained great).   Now that sounds out of character for a being as humble as Gandalf, but it doesn't actually sound like something he would have been unable to do before. It's a twisted motive, but not really an enhanced power.  Pretty much everyone in Middle-earth agrees that the One Ring will corrupt you, but they all seem to agree that it DOES convey great power even so. Why? Do we ever see any actual, "positive" effects from possessing the One Ring?


I am studying for a complex qual and I am having a little difficulty with the following problem.  Any help that you could give me would be awesome.  Thank you.  Let $f(z) = \sum_{n=0}^\infty a_nz^n$ be the Taylor series around $0$ of a function which is analytic in $\mathbb{C}$ \ ${z_0},$ $z_0\neq 0$ and has only a simple pole at $z_0$. Prove that $lim_{n\rightarrow \infty} a_n/a_{n+1} = z_0.$

This is my first question in mathSE, hope that it is suitable here!  I'm currently self-studying complex analysis using the book by Stein & Shakarchi, and this is one of the exercises (p.67, Q14) that I have no idea where to start.     Suppose $f$ is holomorphic in an open set $\Omega$ that contains the closed unit disc, except for a pole at $z_0$ on the unit circle. Show that if $f$ has the power series expansion $\sum_{n=0}^\infty a_n z^n$ in the open unit disc, then      $\displaystyle \lim_{n \to \infty} \frac{a_n}{a_{n+1}} = z_0$.   If the limit is taking on $|\frac{a_n}{a_{n+1}}|$ and assume the limit exists, by the radius of convergence we know that the answer is $1$. But what can we say about the limit of the coefficient ratio, which is a pure complex number? I've tried to expand the limit directly by definition, with no luck. And I couldn't see how we can apply any of the standard theorems in complex analysis.  I hope to get some initial directions about how we can start thinking on the problem, rather than a full answer. Thank you for the help!


I'd like to replace gedit, and use Sublime Text 3 as my default text editor for all text files on my Ubuntu system. Can you let me know how do I go about making this change?

I started using Sublime Text 2 a week or so ago and I loved it so much I've spent $60 on it and now want to use it for everything.  Gedit currently has ownership of most of the text file associations. I'd essentially like to replace any association to gedit with sublime-text-2.  Any tips available on bulk association changing? Desktop-neutral methods are preferred.


The problem with circuit is that it may give same ADC value even when the voltage of battery drops.....so please give me suggestions on that...thanks in advance.

Processor: PIC18F66K22 Compiler:  C18 (XC8 is fine also)   I've just made (and succesfully tested) code to measure the voltage on AN4 analog pin.  Now I want to try something else, not quite sure if it's theoretically possible.  My test-board has a PIC processor, with VDD,AVVD connected to a supply (ranging from 0(if the battery is empty/disconnected) to 4,2(full battery).  Can I use ADC to measure the VDD(-in) of my board?  Why not?:   It's not an ANx pin, not sure how to make the ADC measure it? (Channel?) If the voltage on VDD(-in) drops, will my ADC reference voltage also drop? (So when my PIC only gets 3,3V the ADC will still say it's 100% (as the max Voltage on the chip, also the reference is 3,3V).   Why/what do you ask?:   Can I just measure Channel 30 (VDDCORE)? Could I set my Vref to Vdd and measure a precision voltage reference with the A/D converter. (Not sure how) Or I could add a wire from VDD-in to an ANx pin? Will Internal VREF+ (4.096V) stay 4+V when the VDD-in is around 3,4V? Is there some kind of transformator that makes it so? Internal VREF+ (4.096V) is a bit lower than the max of the battery (4,2V), does this mean I can damage the ADC? Or just that the result will be max when the battery is full. (4,2V out of 4,096V)     Please mind that my knowledge of Electronics is "low". I've learnt way more about the software part in my education, but I'd like to know more about (Embedded) Electronics as it's a crucial part in Embedded Engineering. (It's sad how my school doesn't see this.)


I wonder if there is a way to break a line when it is too long with a curly bracket crossing the margin. Thanks.  \documentclass[12pt]{article} \begin{document} blablabla blablabla blablabla blablabla blablabla  blablabla blablabla blablabla. Here comes a long form, and it is extremely long. $\{1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10\}$.    \end{document}

In answering another question ,  suggested two excellent ways to allow line breaks in inline math mode after ,. One way was to use the \allowbreak command after the comma, and the other way was to globally redefine , so that line breaks are allowed.  I used the second approach, and was really fond of it, until I noted that the command \cite{} no longer works as expected: If I cited more than one reference, it showed [?] instead of the correct citation. Here's an example:  \documentclass{article}  %----------Redefining `,` ------------------% \makeatletter \def\old@comma{,} \catcode`\,=13 \def,{%   \ifmmode%     \old@comma\discretionary{}{}{}%   \else%     \old@comma%   \fi% } \makeatother %-------------------------------------------%  \begin{document}  \cite{A,B}  \begin{thebibliography}{A} \bibitem{A} ABC \bibitem{B} DEF \end{thebibliography}  \end{document}   What is wrong with redefining ,? How to correct it?


If I have the handle of a window, say hWnd, I can get the handle to its font type, say hFont, like this:  HFONT hFont = SendMessage(hWnd, WM_GETFONT, NULL, NULL);   After this point, how do I obtain a  structure (which contains many features of the font), from this  handle?  My purpose is not to create a font from scratch by calling . I want to read font properties into a LOGFONT structure, then arbitrarily modify it, and finally update the font by calling the  function and passing the modified LOGFONT object to it.  How do I do this?

I using the Win32 API and C/C++. I have a HFONT and want to use it to create a new HFONT. The new font should use the exact same font metrics except that it should be bold. Something like:  HFONT CreateBoldFont(HFONT hFont) {     LOGFONT lf;     GetLogicalFont(hFont, &lf);     lf.lfWeight = FW_BOLD;     return CreateFontIndirect(&lf); }   The "GetLogicalFont" is the missing API (as far as I can tell anyway). Is there some other way to do it? Preferrably something that works on Windows Mobile 5+.


MWE:  \documentclass[]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.12} \usetikzlibrary{plotmarks} \begin{document} \begin{tikzpicture} \begin{axis}   \addplot[mark=*] coordinates   {(0,0)};   \node[blue] at (0,0) {\pgfuseplotmark{*}}; \end{axis} \end{tikzpicture} \begin{tikzpicture} \begin{axis}   \addplot[mark=pentagon*] coordinates {(0,0)}; \node[red] at (0,0) {\pgfuseplotmark{pentagon*}}; \end{axis} \end{tikzpicture} \end{document}     As you can see in the first picture both markers are at the same position, but not in the second. What do I have to do to get the same positioning of the marker in the node as the one which is plotted with \addplot?  Update: Version numbers from log file:  Package: pgfplots 2015/05/02 v1.12.1 Data Visualization (1.12.1) Package: pgf 2013/12/18 v3.0.0 (rcs-revision 1.14) File: pgflibraryplotmarks.code.tex 2013/07/20 v3.0.0 (rcs-revision 1.13)   Other questions (this is more or less a duplicate):      (see most importantly this one!)

Using the suggestions from , I decided to use \pgfuseplotmark to make marks in my diagram.  However, there is some strange white space inserted to the left of the pgfmarks.  What should I do to remove it?  Here's an MWE:  \documentclass{article}  \usepackage{tikz} \usetikzlibrary{plotmarks}  \begin{document}  \begin{tikzpicture}   \node[draw] at (0,0) {!};   \node[draw] at (2,0) {\pgfuseplotmark{diamond*}}; \end{tikzpicture}  \end{document}


Looking for some help. Here's my qq plot. I already deleted the most extreme outliers, but some remain. Also, what about the distributional assumption?

I am working with a small dataset (21 observations) and have the following normal QQ plot in R:     Seeing that the plot does not support normality, what could I infer about the underlying distribution? It seems to me that a distribution more skewed to the right would be a better fit, is that right? Also, what other conclusions can we draw from the data?


How can I share my windows pc files to Ubuntu 16.04 LTS pc using network sharing?

I have a desktop (Ubuntu 13.04 & Win 7 Home Premium) and a Laptop (Ubuntu 12.04), both having WiFi adapters. I also have a WiFi router connected to internet which both my computers can access.  I want to share files between my desktop and my laptop using WiFi (similar to Homegroup on Windows 7 but without using Ethernet cables).  How do I set-up that?  I want to share files using both OSs, if anyone have have information about sharing files with any of the OS please answer!


This is essentially Exercise 1.3.1 from Durrett's probability theory textbook. In fact strict equality is true, but the other direction of inclusion is so trivial  that I decided to de-emphasise it in the question.   The biggest problem for me is that $\sigma(\mathcal A)$ looks quite intractable, and I need a more explicit representation. I'd like to guess that every set in $\sigma(\mathcal A)$ can be written as the output of countably many $A_n\in \mathcal A$ under countably often union, intersection and complements. But I lack the proof, or even the rigorous formulation of such an idea. Instead of attempting to characterise $\sigma(\mathcal A)$ which might be too large to, is there any smarter way to solve the problem?

For some collection of sets $A$, let $\sigma(A)$ denote the $\sigma$-algebra generated by $A$.  Let $C$ be some collection of subsets of a set $Y$, and let $f$ be a function from some set $X$ to $Y$. I want to prove:  $$f^{-1}(\sigma(C))=\sigma(f^{-1}(C))$$  I could prove that  $$\sigma(f^{-1}(C)) \subset f^{-1}(\sigma(C))$$  since complements and unions are 'preserved' by function inverse. But how do I go the other way?   EDIT: One way to go the other way would be to argue that any set in $\sigma(C)$ must be built by repeatedly applying the complement, union and intersection operations to elements of $C$ and all these operations are preserved when taking the inverse. The problem I am facing with the approach is formalizing the word "repeatedly".  [not-homework]


We are developing a library for our company's other teams. I'd like to design an Authentication interface, if the user of our library implement that interface in their project, then we will use their implementation (probably through reflection) to do the authentication. If there is no implementation then we will ignore this part.  The reason we do like this vs. providing method to register their auth class is we don't expose these kind of high level function to the project team. They will mostly work on the business logic part.

Some time ago, I came across a piece of code, that used some piece of standard Java functionality to locate the classes that implemented a given interface. I know the functions were hidden in some non-logical place, but they could be used for other classes as the package name implied. Back then I did not need it, so I forgot about it, but now I do, and I can't seem to find the functions again. Where can these functions be found?  Edit: I'm not looking for any IDE functions or anything, but rather something that can be executed within the Java application.


I have the following graph, where I want to label the edges. Is there a way I can integrate this in to the draw command?  { \begin{figure} \begin{center} \begin{tikzpicture}[every node/.style={circle, draw, scale=.8, fill=gray!50}, scale=1.0, rotate = 180, xscale = -1]  \node (1) at ( 2.55, 3.0) {1}; \node (2) at ( 3.87, 0.92) {2}; \node (3) at ( 6.85, 0.92) {3}; \node (4) at ( 8.17, 3.0) {4}; \node (5) at ( 6.85, 5.0) {5}; \node (6) at ( 3.87, 5.0) {6}; \node (7) at ( 10.2, 3.0) {7}; \node (8) at ( 12.2, 3.0) {8};  \draw (2) -- (1); \draw (3) -- (2); \draw (4) -- (3); \draw (7) -- (4); \draw (8) -- (7); \draw (6) -- (1); \draw (5) -- (6); \draw (4) -- (5);  \end{tikzpicture} \caption{Weight 2} \label{fig:wt2} \end{center} \end{figure} }

Is there some package to draw nice RDF graphs, such as the one below (taken from )?  Can such a graph (with the same style) be produced in TikZ?


I have a very small sample of code that uses a try:except block and I'm a bit confused as to why it returns hi as not being defined:  def myFunction():     try:         pass     except:         hi = "bunk"     print(hi)  hi = "blah" myFunction()   I would have expected it'll remain as "blah" unless it fell in the exception, in which case it'll turn into "bunk". When debugging, the IDE returns "blah" as the value of hi, but throws an exception when it tries to print it.  It appears as though hi becomes a local variable within the function, so once it gets to the print statement, it fails with an error that it's not defined as the try statement didn't define it.  Is that what is happening?  I realize that if it's not defined, it'll throw the UnboundLocalError, but the following works fine:  def myFunction(): ##    try: ##        pass ##    except: ##        hi = "bunk"     print(hi)  hi = "blah" myFunction()

The following code works as expected in both Python 2.5 and 3.0:  a, b, c = (1, 2, 3)  print(a, b, c)  def test():     print(a)     print(b)     print(c)    # (A)     #c+=1       # (B) test()   However, when I uncomment line (B), I get an UnboundLocalError: 'c' not assigned at line (A). The values of a and b are printed correctly. This has me completely baffled for two reasons:   Why is there a runtime error thrown at line (A) because of a later statement on line (B)? Why are variables a and b printed as expected, while c raises an error?   The only explanation I can come up with is that a local variable c is created by the assignment c+=1, which takes precedent over the "global" variable c even before the local variable is created. Of course, it doesn't make sense for a variable to "steal" scope before it exists.  Could someone please explain this behavior?


I need to understand how can we change module weight.   Do we really change that value for custom module. What are the default values? If we change weight value what will be effect on Drupal bootstrap process?

I am looking for solution how to change particular module's weight in D7. I know that it is possible to do in config tables in database, but I don't know how. Another solution that I found in Drupal.org is to use hooks - but I need more detail explanation or some guidance where I could get some tutorials about that.   The thing that I need to do is to make some priorities of some particular modules higher for it to load faster than other modules as otherwise they will not work. One of the examples is video streaming using Lightbox2 popup watching that on Safari browser on OS X - it's not loading until you change the priority of Lightbox module.


1) Is a pasta topped with actual calamari and prawns not a "calamari  and prawns pasta" ? 2) Prawn is a noun and the plural is prawns right? 3) Whats the reason behind the "prawn cocktail" use? 4) Can I say that a plate contains five prawns? Thx

Sorry for the title, it is not very evident and intuitive but I really do not how to tell it better...  Well, you know, several times, or better, many times, we use this form:  If I want to say:      "development of special weapons was   the first point in Hitler's   program..."   I will say this (a better form):      "special weapon development was..."   OK...  is it      "special weapon development"   or      "special weapons development" (note   the plural...)   what's the grammar rule in order to understand how to use this very used form?


I am attempting to extrude a logo that has been imported from an SVG file. The SVG file was made in Adobe Illustrator. I deleted many extraneous layers (at this point, curves) upon import to have just a few main layers.  However, I then desired to extrude this, either through a solidify modifier, or the extrude option in the curves panel. Whichever I try, the result is the same: even if the thickness is 0.1, the shape will go off into infinity for the extrusion.   It appears that the vertices are fine and there are no duplicate/overlapping ones (but please check me), and so I have no idea what could be causing this! This is the first time I've ever tried importing an SVG like this to use, so any pointers are welcomed!  showing extrusion off to infinity with settings    File:   Thanks, Nathan

I am sure this has been discussed quite a few times, but I found a tutorial recently doing the exact same thing as I did, but in my case my logo is messing up!  Here is the link to the workflow:   This is what it looks like after adding the solidify modifier:   I already recalced the normals of my spline, but besides that it messes up my spline shape, it had no effect.  Any suggestions on how to fix it?


This is something that I have struggled with for years. If I create a shape layer with rounded edges - for example with a 10px radius - if I resize the overall shape then the corner radius grows with it as well.  What I want to do is keep the radius of the edges whilst resizing the overall size.  The only way I can do this is by manually selecting the points on 2 corners and dragging one side of the shape layer. This is a bit of a pain though, and isn't the most efficient way of doing things  Is there an easy way to do this?

This question is about Photoshop CS6. Hopefully the feature was added in this version. Before posting I looked up Google and  and  but didn't find an answer for CS6.  So the question is: Is there a feature within CS6 or a script that allows to resize a vector element with rounded corners without using the Direct Selection Tool (white arrow tool) and not changing the border radius? What would be great would be something like simply using the transform tool or something like a grid resize tool.


When I multiply 100*4.6 or 100*4.9, the code produces 459.99999999999994 and 490.00000000000006, respectively. It only does this for these specific numbers. When I multiply 100*4.7, for example, it correctly produces the number 470.   I tried parseFloat() on a whim and it did not help (nor did I expect it to). I do not want to use Math.round or .toFixed() because, in my full code, I randomly generate the number that gets multiplied by 100, so sometimes it should have a decimal. (For example, if the code generates 100 * 3.652, the answer should be 365.2, so I do not want to simply round as a band-aid solution.)  Why is this multiplication error happening for these specific numbers?  Javascript:  var Product = 100* 4.6; $(".Product").html(Product);  var Product2 = 100* 4.7; $(".Product2").html(Product2);  var Product3 = 100* 4.9; $(".Product3").html(Product3);   HTML:

    JSFiddle:

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


Let $H$ be a subgroup of $G$. Let $K = \{x \in G: xax^{-1} \text { iff } a \in H\}.$ Prove $H$ is a subgroup of $K$.    Suppose $a \in H.$ Then $aaa^{-1} = a \in H.$ So, $a \in K.$ Thus, $H \subseteq K.$ Since $H$ is a group, $H$ s a subgroup of $K$. Would that work?

Closure under multiplication:  $\to$  Let $a, x, y \in H.$  Since $H$ is closed under inverses and multiplication, $xax^{-1} \in H$ and $yay^{-1} \in H.$ Since $H$ is closed under multiplication, $xyax^{-1}y^{-1} \in H.$   $\leftarrow$  Suppose $xyax^{-1}y^{-1} \in H$, then $a \in H$ since $H$ is closed under multiplication. So, $xy \in K.$  Closure under inverses:  Since $H$ is closed under multiplication and inverses, if $a \in H,$ then $x^{-1}ax \in H.$ If $x^{-1}ax \in H,$ then $a \in H$ because $H$ is a group. So, $x^{-1} \in K.$  Identity:  Suppose $a \in H.$ Then $a = eae^{-1} \in H.$ So, $e \in H.$  I'd like to see how I can fix/improve this proof.


On Gnome Ubuntu 16.04, my battery icon is mostly useless. The visual gauge is always far behind the true level, which I display as percentage, next to the gauge. For instance, I'm now at 11% but the icon shows something that would be above 50%. Only when I'm below 10% it shows a low red gauge.    Is there a fix or will I just remove it and live with the % ?

By default GNOME (and hence Ubuntu 17.10 and later releases) doesn't show battery percentage in the notification area of the Panel. There are  (for example , ,  etc.) which do the job.   Is there a way to attain the goal without using any extension?


I've read the CIS benchmark for Apache several times, but there are some points in it that I don't understand, as it was based on another distribution I use (Ubuntu 20.04). Some sites say to set apache user (www-data) as owner of /var/www/html, others say to use my user as owner of folder. On Ubuntu 20.04, the Apache user is www-data, and my Linux login user is examplemanager. But every file I create I use sudo to have permission to create. ls -l /var/www drwxr-xr-x 2 root root 4096 Jun  4 18:50 html  ls -l /var drwxr-xr-x  3 root root   4096 May 27 17:13 www  Which user should I set as the owner of /var/www/html and subfolders/files (root, www-data or examplemanager)? Since inside /var/www/html there will be a folder for each domain, eg:  /var/www/html/api.example.com /var/www/html/dash.example.com

This is a  about File Permissions on a Linux web server.   I have a Linux web server running Apache2 that hosts several websites. Each website has its own folder in /var/www/.  /var/www/contoso.com/ /var/www/contoso.net/ /var/www/fabrikam.com/   The base directory /var/www/ is owned by root:root. Apache is running as www-data:www-data. The Fabrikam website is maintained by two developers, Alice and Bob. Both Contoso websites are maintained by one developer, Eve. All websites allow users to upload images. If a website is compromised, the impact should be as limited as possible.  I want to know the best way to set up permissions so that Apache can serve the content, the website is secure from attacks, and the developers can still make changes. One of the websites is structured like this:  /var/www/fabrikam.com     /cache     /modules     /styles     /uploads     /index.php   How should the permissions be set on these directories and files? I read somewhere that you should never use 777 permissions on a website, but I don't understand what problems that could cause. During busy periods, the website automatically caches some pages and stores the results in the cache folder. All of the content submitted by website visitors is saved to the uploads folder.


I am new to blender and I accidentally added loads of toolbars. I need to open properties tabs to add skies and stuff, but I don't know how to do it and there are so many toolbars.

I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation.


There is this one thing called hero forge, and it looks really cool,  but... it really expencive for what im looking for, I also tryed Warhammer but that was expencive and the minis where not what I was looking for, I also tryed just the plane D&D characters they where cheap but not what i was looking for, so I was wondering if anyone new a good cheap place I can find my minis... (I am suplying for mor ethen myself) (about 5 people)

I'm looking to build a collection of fantasy miniatures, preferably pewter - but I don't want to buy them one at a time from my local hobby store... Much too expensive, and they don't often carry anything I'm interested in buying, which makes it a long term venture as well. So I'm looking for ideas on how to obtain many miniatures at once, preferably for cheap. D&D Miniatures aren't a good source for me as they're collectibles, and the prices on those are also prohibitive.  By the way - they don't have to be pewter, that's just my preference. =)


Here is the scenario I am trying to model.  I have a population of people who are susceptible to developing a disease. I observe each person for a different amount of time, summing to a total of 3000 person-years of observation.  During the observation period, I record 50 cases of this disease. The point estimate would then be 16.6 events per 1000 person-years.  How could I best quantify the uncertainty surrounding this estimate? Would these techniques still work for very few cases, or no cases at all? Implementation in R or Python would be appreciated.

for example, 30 events during 10000 person-years, the cumulative incidence rate is 3 per 1000 person-years, how to calculate its 95% CI?


This image appears on a LG TV screen saver. Does anyone know where in the world is this?  cheers

Can someone please tell me where this picture was taken?


This question stems from the exercise 2.50 of Griffith's Introduction to Electrodynamics, which I am rereading.  In the problem, he asks to find the charge density of a volume when the electric field is   $\textbf{E}(x,y,z) = ax\space \hat{x}$  And to find a possible explanation as to why the electric field would point in that particular direction.  We can easily show that electric field corresponds to a uniform charge density, but it is not simple to explain why, then, a uniform charge density would give rise to such an electric field.   If we want to answer why the field is oriented along the x axis instead of any other, we can argue that knowing the divergence and rotational of a field is not sufficient to determine it uniquely, and thus, a uniform charge density definitely could give rise to, say, $\textbf{E}(x,y,z) = ay\space \hat{y}$. This ambiguity would be lifted by the appropriate boundary conditions, which is trivial, in a way.  What I cannot grasp at all is how, if we consider a non-zero infinite distribution, these results even make sense. Due to rotational and translational symmetry, an infinite uniform charge density should give rise to no electric field. However, if we calculate the divergence of a null field, we get $\nabla \cdot\textbf{E}(x,y,z) = 0$ instead, which would require $\rho = 0$, in contradiction with our initial assumption.  I have tried to use Gauss's law to analyse the problem, but I reach a similar nonesensical answer: Consider a sphere in this infinite charge distribution, as well a spherical shell that touches the surface of the sphere and has infinite thickness (you can also consider an infinite number of shells with finite thickness that fill the whole space). From Gauss's law, the electric field the shell creates in the surface of the sphere is zero, while the electric field created by the sphere is proportional to its charge. Thus, the electric field in the surface of the sphere is radial and non-zero, in contradiction once again with symmetry arguments.  What is going on here?

Let us assume the universe filled with positive charge. About a particular point, all the positive charged particles will be symmetrical. Now consider a sphere of radius $r < \infty$ and apply Gauss law. According to Gauss law the electric flux through the sphere will be some finite value as it contains some positive charge. But by symmetry the electric field through the sphere and hence electric flux will be zero. This is a contradiction.


I'm having trouble formatting this SD card. The write protect switch is off, of course. I tried using the built-in card reader on my MacBook Air and then a USB one. It won't even format on my Windows machine. It's hard to believe the card is bad as it was working just fine about a month ago when I last used it and I barely wrote data to it in its lifetime.  It doesn't mount automatically, nor does it show up in the Disk Utility GUI. However, diskutil on the command line sees it just fine.    When I try to format it through diskutil with the following command:  sudo diskutil eraseDisk FAT32 NIKON MBRFormat /dev/disk3   It does not work and I get the following error message:    I'm just perplexed as it has been in a case and like I said above, I've barely used it. It's hard to believe it died while not being in a computer, but it wouldn't be the strangest thing I've experienced in my life on the computer.  It would be much appreciated if someone can help me revive the card, if possible.

I have a macbook pro running Snow Leopard.  I have Tuxera NTFS drivers.    I have a microSD card, in an adapter, in the slot.  The "lock" slider is in the "unlocked" position.  'Get Info' tells me the drive is formatted to FAT16.  The permissions panel tells me that I can only read.  Disk utility tells me it's not writable.  (It does this for the volume and also for the higher level Apple SD Card Reader Media)  What do I need to do to change permissions to turn this card writable?


I am new in PHP.  I use two ways to escaping string:  method 1. by using replace  function htmlreplace($str, $useBR = false) {     $str2 = $str;     $str2 = preg_replace ( "/</", "&lt;", $str2 );     $str2 = preg_replace ( "/>/", "&gt;", $str2 );     $str2 = preg_replace ( "/(\r\n|\n|\r)/", $useBR ? "<br />" : " ", $str2 );     $str2 = preg_replace ( "/&/", "&amp;", $str2 );     $str2 = preg_replace ( "/\'/", "&#39;", $str2 );     return preg_replace ( "/\"/", "&#34;", $str2 ); } $string='some string needs to insert into mysql'; stripslashes(htmlreplace($string));   method 2. After connecting to MySQL  function sanitizeString($var, $DBconnection) {     $var = strip_tags ( $var );     $var = htmlentities ( $var );     $var = stripslashes ( $var );     return $DBconnection->real_escape_string ( $var ); } $string='some string needs to insert into mysql'; trim ( sanitizeString ($string) );   From    shows these characters need to escape  NUL,  BS,  TAB,  LF,  CR,  SUB,  %,  ',  \,  _,  all other non-alphanumeric characters with ASCII values less than 256  From   shows addslashes() function will escape these characters: single quote ('), double quote ("), backslash () and NUL (the NULL byte)  As far as I know, escaping is for prevent SQL injection.  So I am curious about how many characters need to be escaped? what are they? Are they all ?  As for SQL injection prevent, thanks to Slico, Marc B, and bub help.  Thanks!

If user input is inserted without modification into an SQL query, then the application becomes vulnerable to , like in the following example:  $unsafe_variable = $_POST['user_input'];   mysql_query("INSERT INTO `table` (`column`) VALUES ('$unsafe_variable')");   That's because the user can input something like value'); DROP TABLE table;--, and the query becomes:  INSERT INTO `table` (`column`) VALUES('value'); DROP TABLE table;--')   What can be done to prevent this from happening?


Student coder here. I am trying to complete a project that asks me to install  a package called "libncurses5-dev" and run a program through Ubuntu.  It worked the first day, thankfully. However, on the second day I wanted  to set my default directory to my homework folder so that I could skip the  cd /mnt/c/Users/... step and just go straight to where my programs are. I  tried to follow a tutorial online but I believe I made a typo or something  because afterwards my Ubuntu kept crashing! I could not open it for long  enough to fix it, the error was something along the lines of "directory does  not exist." So, I uninstalled and reinstalled Ubuntu. I redid the process of  installing all the packages I needed for coding on WSL. However, when I need  to run my program, it keeps saying that I am missing a package. When I try  to install that package, it says the package does not exist. Please see the  attached files, which show what the project is supposed to look like and  what it looks like now. I looked at image 2 again and it shows that I made a typo in the library name, but after trying it again I get the same error  anyways. Thanks in advance for the help.

Simple enough question: is there some shell command (or GUI method) I can use that, given the path to a file on my system, tells me what package put it there? Assuming the file did in fact come from a package, that is.  Bonus question: what if it's a file that isn't installed on my system? Is there, say, a website that will let me look up a file and see what packages, if any, provide it?


I am from Australia and planning to visit Canada and U.S this year. I got my ESTA approval but not sure about coming to U.S. twice in a month. I will be visiting NY from Toronto and then back to Toronto and then Vancouver. From there I am planning a trip to LV & LA. Will there be an issue as my second visit will be in a couple of weeks time again to U.S.  Any help please as I am not sure about this, thanks.

Can I visit the US twice within a 90 day period under the Visa Waiver Programme? 2nd time is only to transfer (change terminal, not airside).


I have restarted my computer after an update, then I have noticed that the wifi signal was very weak. I have decided to download this package https://github.com/lwfinger/rtlwifi_new and reinstall the wifi driver but I have the following error: modprobe: ERROR: could not insert 'rtl8723be': Exec format error  I run the following in the package downloaded:   make sudo make install modinfo -p rtl8723be   I have following result :   swenc:Set to 1 for software crypto (default 0)  (bool) ips:Set to 0 to not use link power save (default 1)  (bool) swlps:Set to 1 to use SW control power save (default 0)  (bool) fwlps:Set to 1 to use FW control power save (default 1)  (bool) msi:Set to 1 to use MSI interrupts mode (default 0)  (bool) debug:Set debug level (0-5) (default 0) (int) disable_watchdog:Set to 1 to disable the watchdog (default 0)  (bool) ant_sel:Set to 1 or 2 to force antenna number (default 0)  (int)   .  sudo modprobe -r rtl8723be  sudo modprobe rtl8723be ant_sel=1   I have following result :  modprobe: ERROR: could not insert 'rtl8723be': Exec format error   I have tried to restart the adapter with the following command:  sudo service networking restart   I'm using ubuntu 17.04 | 4.10.0-33-generic

I have dual booted my Windows 8 laptop with Ubuntu 14.04. The wifi driver is Realtek rtl8723be. It didn't use to work but I updated the kernel to 3.18 and reinstalled the driver and that seemed to solve the problem for a few hours. Then it would be connected for around 30 minutes and then the connection would stop, even though the icon on the system tray would still indicate it's connected. The only thing that works is restarting the computer but then, again, after 30 minutes the connection stops.


has updated the firefox version two weeks ago. Now when I do apt-get install firefox-esr the 68 version is installed.   How can I install the previous version, which was 52 (if I'm not mistaken)? apt-get install firefox-esr-52 does not seem to do the trick.

I have installed Ubuntu 14.04, which already has Firefox v31. I want to install an older version of Firefox. How can i do it?


We have a pcb with an Atmega (MCU) on it, that most of the time is in sleep mode, consuming 50-100 uA .  When it wakes up, and only then , we need to take a sample of the battery voltage to send to the server .  I was considering few options and wonder which is the "right" if we dont want to loose current .   Voltage will be 3.6-4.2V when its full via 3.6V regulator .   connecting the battery with serial resistor(>50k ?? ) directly to the ADC. take 2  large resistors(100k?) and create voltage divider of the battery voltage , and connect the point between them to the ADC . connecting the battery directly to the ADC ?   --- should we measure after or before the regulator ??  A 100k resistor will leak about 50uA of current which is no that good ,because the Atmega itself should be the only and main consumer on sleep with 50-100uA .

What I am working with: I am running my self-made Arduino board (in the sense that I use the Arduino bootloader and code editor) at 3.3V, and powered from a Lithium ion battery, which is USB-charged by a corresponding Microchip charger IC.  What I am trying to achieve: I want to measure battery capacity once every minute or so. I have an LCD attached, so the idea is that the overall setup lets me know how the battery is doing at a given moment. The datasheet of the battery has a voltage versus discharge-level curve, and so by measuring the voltage of the battery, I can estimate the remaining capacity (very roughly but enough for me!).  What I did:   (EDIT: Resistor values updated and P-MOSFET switch added based on @stevenvh and @Jonny's suggestions).  I connected a voltage divider from the battery V_plus, with the larger "portion" going to an analog-read-pin (i.e., ADC) on the Arduino/Atmega chip. The divider is 33 KOhm-to-10 KOhm, thus allowing measurement up to 4.1 Volts maximum of the Li-ion battery from my 3.3V level microcontroller. Also, using one of the I/O pins connected to an n-channel MOSFET, I can switch the current through the divider only when I need the measurement. Here is a rough schematic (updated for a 2nd time based on suggestions of @stevenvh and @Nick):     My question:   How is my current setup? My only constraints are: (1) I would like to make a rough measurement of the battery capacity based on the voltage reading, as described above. (2) I would like to prevent the voltage divider from interfering with my charging IC's reading of battery presence (in my original setup, the divider sometimes caused the IC to misread presence even when the battery was absent).


as time goes on slowing with increase in mass. how can black hole ever form in finite time. is infinite time has different meaning for different observer. if so would the event of universe dying be different for different observer?

I've heard that, from the perspective of an external observer, something falling into a black hole will eventually look "frozen": light waves will move to the infrared and further into lower frequencies.  But what about that unfortunate individual falling into such a black hole? What will he/she see when looking back at our universe?   For instance, I wonder, will it be the ultimate end of the Universe? Can someone who just crossed events horizon of the black hole still receive messages from our side?


In Belgium fries are super popular. They taste really amazing and are very different than the common American french fry. My question is, what is the secret to replicate a Belgian style french fry. They have a perfectly crispy golden shell, about 1inch wide, 1/3 inch thick, soft on the inside and totally different than your average American style french fry.

How do Belgian fries differ from the French fries we are accustomed to eat in the US and Canada in such places as McDonald's, Wendy's, Burger King and so on? Is it the variety of potato, the preparation involved or something totally different? What oil do they use in Belgium?   I remember having them while I was visiting family in Belgium. The fries were somewhat crispy and thicker than over here.


In the early 2010s, I recall reading a trilogy of novels about 2 kids who have to keep earth's timeline from changing. In order to do this, they stayed on a loop of one day in a city (I think San Fransisco?) and if their surroundings changed in any small way, they'd know something happened in the past and messed with the timeline.  They also had some sort of bodyguard clone thing that was a man in the first book, was somehow made into a woman in the second, and both versions joined them in the last.  The only specifics I can remember about each book is that the first involves the First World War, the second involves dinosaurs. I have a vague recollection of Prince John in the third book, but nothing beyond that.  I was young when I read it, so I assume it's not very highbrow literature, just a YA fiction series or something like that.  Anyone remember this series?

This was a book where several kids who died in several historical disasters were given a choice by an old man about if they wanted to die in that disaster or come with him and be sort-of "time police", the only catch is that they would be locked into that role. There was a boy who was on the Titanic, a girl who was on one of the 9/11 planes, and I think one or two more. They are taken to this secret hideout which is in New York during a time loop of 9/11. When they are there, every day is the same day, September 11th 2001, and the reason for this is because it keeps them away from prying eyes. The current timeline, not the time loop, is in the future, where time travel technology is invented, and the old man and the kids serve to stop anyone from misusing time travel. In the current time, the future, a group of heavily armed Neo-Nazis raid a museum, maybe the natural history museum?, to abscond with the first time machine, which is on display, so they can go back and have the Nazis win World War 2. The Neo-Nazis succeed in their goal and go to Hitler's bunker in the Winter and show him all of their future technology. This book was part of the series, and the second book concerned dinosaurs.


I've encountered several proofs that $A = \mathbb{Z}[\frac{1 +i\sqrt{19}}{2}]$ is indeed a PID that is not euclidean. I'm quite confused with this one, which seems to be nonetheless using similar arguments. We consider that $A$ is euclidean, therefore it features a euclidean function $\nu$. Let $x \neq 0$ non-unit such that $\nu(x)$ is minimal, and let $\bar{y} \neq 0$ an element of the quotient space $A/(x)$. By definition of $x$, it is clear that if $y = qx + r$, then $r$ must be invertible, so $r = 1$ or $r = -1$ (because $\nu(r) < \nu(x)$).   From that we deduce that either $A \simeq \mathbb{F}_2$ or $A \simeq \mathbb{F}_3$. I'm not totally confident with this first fact. Indeed, it seems the only possible remainder (i.e. elements of $A/(x)$) are $0, 1, -1$. Either everyone of them is possible, and $A \simeq \mathbb{F}_3$, or only two of them occur ($0$ and $1$ for instance) and $A \simeq \mathbb{F}_2$. But when I tried writing actual proofs, I ended up proving the hypothesis (that $A$ is euclidian) is false.  (1) If $A  \simeq \mathbb{F}_2$, then $\bar{y}$ is a root of $T^2 + T + 1 \in A[T]$.  (2) If $A \simeq \mathbb{F}_3$ then $\bar{y}$ is a root of $T^2 - T - 1 \in A[T]$.  Both statements are allegedly contradictory, which seems wrong to me. ($\bar{y} \neq 0$, then $\bar{y} = 1 \in \mathbb{F}_2$, and clearly (1) is not satisfied.)

Let $\alpha = \frac{1+\sqrt{-19}}{2}$. Let $A = \mathbb Z[\alpha]$. Let's assume that we know that its invertibles are $\{1,-1\}$. During an exercise we proved that:     Lemma: If $(D,g)$ is a Euclidean domain such that its invertibles are $\{1,-1\}$, and $x$ is an element of minimal degree among the elements that are not invertible, then $D/(x)$ is isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.   Now the exercise asks:     Prove that $A$ is not a Euclidean Domain.   Everything hints to an argument by contradiction: let $(A, d)$ be a ED and $x$ an element of minimal degree among the non invertibles we'd like to show that $A/(x)$ is not isomorphic to $\mathbb Z/2\mathbb Z$ or $\mathbb Z/3\mathbb Z$.  How do we do that? My problem is that, since I don't know what this degree function looks like, I don't know how to choose this $x$!  I know that the elements of $A/(x)$ are of the form $a+(x)$, with $a$ of degree less than $x$ or zero. By minimality of $x$ this means that $a\in \{0, 1, -1\}$. Now I'm lost: how do we derive a contradiction from this?


Please let me know when to use GET method and when POST in REST API. As Post is supposed to be more secure, so can we use in case of getting the data from the database in REST API or it just can be used in case of adding new record in the database. Thanks for your views.

From what I can gather, there are three categories:   Never use GET and use POST Never use POST and use GET It doesn't matter which one you use.   Am I correct in assuming those three cases? If so, what are some examples from each case?


I have been struggling for a while to find any resources on how to remove this strange question mark square symbol: �  Standard str_replace and preg_match don't work. Can anybody assist in this? Settings the charset header('Content-Type: text/html; charset=utf-8') doest not work either. Nor does:ini_set("default_charset", 'utf-8');  I should mention I am using curl to request the data from a webpage.  Thanks

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.


Just wanted to check because I have multiple Schengen Visa and during the application I applied France as I will be spending more days in Paris and that is my point of entry. However the ticket I've booked going to Paris is through Czech Airlines and I have 12 hours layover at Prague-Vaclav airport. I want to check if I can go out from the airport and have a quick tour at Prague City Center?

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


We are in the year $2021$, why not finding all groups of order $2021$? First, note that $2021=43 \cdot 47$, its decomposition in primes (useful to keep in mind). Then, applying the Euler's totient function: $\varphi(2021)=42 \cdot 46$, so $2021$ and $\varphi(2021)$ are coprime. Thus, $2021$ is a . We can conclude that there is only one group of order $2021$, up to isomorphism, $\mathbb{Z}_{2021}$. I want to find out other proofs that any group of order $2021$ is cyclic, besides this simple observation. Any ideas are welcome, but I'm more interested in proofs that do not use powerful theorems like Sylow, with internal direct product (as in ). I need something that can be understood by a high school student (he only knows the basics), if possible. I was thinking of another approach: it is enough to prove that any group of order $2021$ is abelian, then, using the formula for the number of abelian finite groups (), we get: $a(2021)=p(1)^2=1$, so this group must be cyclic. We reach the same result if we notice that $2021$ is , but again, we discuss only the abelian case. P.S. Do not understand me wrong, I know about Sylow theorems, but I just can't explain in this manner to a boy that has just learned about groups.

Let $G$ be a group of order $pq$, $p>q$  and $p$, $q$ are primes. Then prove that  If $q\mid p-1$ then there exists a non abelian group of order $pq$. Any two non-abelian groups of order $pq$ are isomorphic.   I have proved that if $q\not\mid p-1$ then $G$ is cylic . But how to prove this one I have no idea. Any kind of hint is very much welcome. This problem is in Herstein book, page 75.


The relation $R$ is defined for all positive integers such that $(a,b) R (c,d) \longleftrightarrow a+d=b+c$. Show that $R$ is an equivalence relation.

Suppose $A$ is the set composed of all ordered pairs of positive integers. Let $R$ be the relation defined on $A$ where $(a,b) R (c,d)$ means that $a + d = b + c$.  (a) Prove that $R$ is an equivalence relation.  Here is what I have so far. Is this correct?  Reflexive: $a \sim a$ $\implies$ $a+b=a+b$; $(a,b) R (c,d)$  Symmetric: if $a \sim b$ then $b \sim a$ $\implies$ if $a+d=b+c$ then $c+b=d+a$  Transitive: if $a \sim b$ and $b \sim c$ then $a \sim c$ $\implies$ if $a+d=b+c$ and $c+f=d+e$ then $a+d=d+e$  (b) Find $[(1,1)]$.  I'm not sure how to approach this.


I have included the code from my JavaScript file and the header.html which gets loaded into index.html with the help of

. I have all my "script src" before the closing body tag in index.html. When I try to press the button I receive the following error:  Uncaught TypeError: Cannot read property 'addEventListener' of null  I am aware that this has something to do with the way I am loading my html files. Is there a way I could solve this issue? I am trying to keep the code redundancy more or less low and copying the whole header into every html file is not an option.   /* -- Loading assets -- */  $(document).ready(function() {   $("#header").load("assets/header.html");   $("#footer").load("assets/footer.html"); });  /* -- Mobile hamburger menu --*/  const hamburger = document.getElementById('hamburger'); const navList = document.getElementById('nav-list');  hamburger.addEventListener('click', () => {   navList.classList.toggle('show'); }); /* Seperate header.html file that gets loaded into index.html */
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    <button class="hamburger" id="hamburger">        </button>

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I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


I started learning Java and have small problem. I have classes Point and abc:  static class Point     {         int x;         int y;         Point(int x, int y)         {             this.x = x;             this.y = y;         }     }  static class abc     {         abc()          {             Scanner s = new Scanner(System.in);             Point[] p = new Point[2];             for (int i = 0; i < 2; ++i) {                 p[i].x = s.nextInt();                 p[i].y = s.nextInt();             }         }     }   But initialization in class abc doesn't work. When I try to write first number it gives:     Exception in thread "main" java.lang.NullPointerException      at main$abc.<init>(main.java:91)      at main.main(main.java:99)   What should I do to make it work?

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


When I go to  page I can't find the  account. What makes this site more special than the others? Why doesn't it appear in the list of accounts?

I think I'm having the same issue as reported in this question:    When I log into SEDE with the same OpenID account I use for SE, a different user comes up ("James Wiseman" on Stack Exchange and "adsense" in Data Explorer).  Is there anything I can do personally to rectify this, or must I rely on the admins?


I'm trying to add basic materials to a low-poly model, and was curious if there was any way to cut in edges in a circle from a single point, so I could apply materials to faces like seen in my reference image to the right. I could go through with the knife and make cuts by hand, but that seems tricky and time consuming for likely sloppy results. Any tips on how to achieve the texture pictured would be greatly appreciated.  The OP wrote in a comment:  I'm looking for a way to add edges without changing the mesh, just so I can apply materials to faces to color.

I'm attempting to model BB-8 from The Force Awakens, but I'm struggling to create the base shell of his body. He's essentially a sphere with 6 equally spaced circles cut out of its surface. The remaining shape is then cut into 8 segments, like here:    If I could even create one of the segments I could then duplicate it.  Any help is appreciated!


Is there a way to filter the "hot questions" displayed in the Stack Exchange menu?    I have a profile on Stack Overflow and that's pretty much it. Therefore the list as it is now is pretty useless because it just adds noise - I'm not coming to Stack Overflow to discuss terrorists and the like ;-)

I was going to make a filter for the "" by excluding some sites from it.  I noticed  which talks about "negative filtering" but does not explain how one can do it or if it is possible.  There does not seem to be a way to do this, though.  On the filter page, my only options are:  So how can I do "All sites except [list]"? It would also be nice if this could include similar functionality with the meta checkbox.  Something like "All main & meta sites except..."


I am trying to submit a form that I dynamically created.  I am using the .submit, but it is not working.  Here is my code  var $message = $('.message');    $message.submit(function(e){     console.log("Test"); });   $(document.body).on('click','.button', function(e) {      console.log($(this).val());     var $input = '';     $input = $('
Chat with '+$(this).val()+'
');     $input.append('

');     $input.append('<form class="message">');     $input.append('<input size = "35" class="messages">');     $input.append("
<input type='submit' class='send_message' value = 'Send' />");     $input.append('</form>');      $input.appendTo($("#contentWrap"));  });   The code for document.body created the form.  However, when I click the submit button nothing happens.  I also tried   $('#contentWrap').on("submit", ".message", function(e){             console.log("Test") });   $(parent).on(event, child, function) is what most of the posts I read say to do.  However, I must be doing something else wrong.  Here is the fill front end code in js fiddle


When voting for the Community Choice Flash Sale, I got this notification.     Once you reach Steam Level 5, you'll get a card every 3rd time you vote for the Community's Choice Flash Sale and you'll be granted the cards for your previous votes.   Can someone explain what these "cards" are and what it means by "you'll be granted the cards for your previous votes."?

Is it purely a 'gotta-have-them-all' mindset, or do they actually serve some purpose?  I notice that you are able to sell them on a community market. For a test I listed one, and someone bought it for 50p. Not exactly a huge amount, but I don't understand why someone would spend real money on them.  Am I missing something?   Are they redeemable for games or money off vouchers or something 'tangible' that I'm missing?


I am learning motion tracking. The CG object and my camera footage can be seen together. But when I render it, only the monkey shows up.  Is there something wrong with my compositor?

First time I've used cycles rendering engine.  I'm using a movie clip as the background in short animation. Selected RBGA under Property Tab, and Transparent under Film Tab.  It looks good and individual frames in OpenGL active viewport render, and looks fine.  When I try to get it to spit out PNG files of the finished animation the objects render out fine, except no movie clip background as Blender Render engine did when using Paper Sky setting.  Operator error, or am I trying to do something Cycles won't do?  Haven't found an answer in my searches so far.  Can anyone point me in the right direction please.   Addition:  I think I found my problem after a couple more hours of research.  Post should read "operator ignorance" instead of operator error.  Too tired to try the solution tonight, everything looks better in the morning. Thanks anyway.  Sorry, I just saw your posts.  Really tired.  Much appreciation.


I was wondering if anyone knows how to set the color of the text that shows up in the shell. I noticed the 'ls' uses a couple different colors when printing out information to the screen (on my Linux box), was wondering if I could take advantage of that in Python.

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


Im pretty new to c# comming from Obj-C and I have a class that has an Instanitializer function that takes some arguments and one of them is the main class Program. Now what Im trying to achieve is to pass this from Program to my new class object.  class Program {     static void Main(string[] args) {         Group grp = new Group(this, ...); // Error: Keyword 'this' is not valid in a static property, static method, or static field initializer          } }  class Group {     public Group(Program prog, some arguments...) {         // Stuff     } }   In Obj-C I couldve done this with self but here its not working and it doesnt seem to work to call a public function from a static method. Thanks beforehand.

I'm trying to use the this keyword in a static method, but the compiler won't allow me to use it.  Why not?


I was wondering if I can play Windows Games on Ubuntu through software so I can play games like Wildstar (MMO), Steam/Origin Games etc.  Personally I don't want to use Windows, I've always disliked it but to play the latest games you need it so I've always felt "forced" so to speak.  Thank you in advance  Dean

Can .exe and .msi files (Windows software) be installed in Ubuntu?


if $x > 0$, show that  $$f(x)=\int_0^\infty \frac{\cos(xt)}{1+t^2} \, dt= \frac{\pi}{2}e^{-x}$$  The problem appears in the book , under the chapter derivative and integral of Laplace transformation. So I tried to apply the equation   $$\int_0^\infty \frac {f(t)} t \, dt = \int_0^\infty F(p)\,dp,$$  where $F(p) = L[f(x)](p)$, the Laplace transformation of $f(t)$. However, I failed to manipulate the expression to apply this equality.  I need your help. Please not be misled by my approach, it might be totally wrong.

Let $x \in \mathbb R$  Find a closed form of $\int_0^\infty\dfrac{\cos(xt)}{1+t^2}dt$ .   Let me give some context: this is an exercise from an improper integrals course for undergraduates. My teacher was not able to give a valid solution without  resorting to Fourier series.   He actually wanted to prove first that the function is a solution of the ODE $$ y-y'' =0$$ without succeeding in proving it.   Anyway the result sould be $\dfrac{\pi}{2}e^{-x}$  Thanks for any help on this subject.


Rey grew up in an environment that was desert like. For her entire life prior to the movie, she was used to a warm environment (at least daytime).    It's clearly snowing, but she is wearing the same outfit she routinely wore on a planet that was described by Star Wars wiki with a climate of "." We don't know how cold the base was, but it's snowing, so clearly colder.  While I might not be a Jedi-in-training, when I go to an environment that is significantly colder it affects me physically. And I live in a climate which has seasons - not having grown in a desert for 20 years.  Shouldn't Rey have been somehow physically affected by this? Or at least.. been really cold?  Inspired by

In Star Wars: The Force Awakens, Rey can be seen wearing the same outfit wherever she goes. She wears it on a desert planet:   On an ice planet:   On a jungle planet:    Why is this? Shouldn't different environments require different clothes?  Why does Rey wear the same outfit in different environments?