After upgrading to 17.10 I noticed that my installation is using my onboard Intel graphics as VGA adapter instead of my Nvidia 940M.  I already installed the additional drivers from the software & updates, but this had no effect.  Output of lspci -k | grep -EA2 'VGA|3D'  00:02.0 VGA compatible controller: Intel Corporation HD Graphics 530 (rev 06)     Subsystem: CLEVO/KAPOK Computer HD Graphics 530     Kernel driver in use: i915 -- 01:00.0 3D controller: NVIDIA Corporation GM108M [GeForce 940M] (rev a2)     Subsystem: CLEVO/KAPOK Computer GM108M [GeForce 940M]     Kernel modules: nvidiafb, nouveau   And after running gpu-manager  last_boot_file: /var/lib/ubuntu-drivers-common/last_gfx_boot new_boot_file: /var/lib/ubuntu-drivers-common/last_gfx_boot can't access /run/u-d-c-nvidia-was-loaded file /etc/modprobe.d is not a file can't access /run/u-d-c-fglrx-was-loaded file /etc/modprobe.d is not a file /etc/modprobe.d is not a file /etc/modprobe.d is not a file can't access /opt/amdgpu-pro/bin/amdgpu-pro-px /etc/modprobe.d is not a file Looking for fglrx modules in /lib/modules/4.13.0-16-lowlatency/updates/dkms Error: can't open /lib/modules/4.13.0-16-lowlatency/updates/dkms Looking for nvidia modules in /lib/modules/4.13.0-16-lowlatency/updates/dkms Error: can't open /lib/modules/4.13.0-16-lowlatency/updates/dkms Looking for amdgpu modules in /lib/modules/4.13.0-16-lowlatency/updates/dkms Error: can't open /lib/modules/4.13.0-16-lowlatency/updates/dkms Is nvidia loaded? no Was nvidia unloaded? no Is nvidia blacklisted? no Is fglrx loaded? no Was fglrx unloaded? no Is fglrx blacklisted? no Is intel loaded? yes Is radeon loaded? no Is radeon blacklisted? no Is amdgpu loaded? no Is amdgpu blacklisted? no Is amdgpu versioned? no Is amdgpu pro stack? no Is nouveau loaded? no Is nouveau blacklisted? yes Is fglrx kernel module available? no Is nvidia kernel module available? no Is amdgpu kernel module available? no Vendor/Device Id: 8086:191b BusID "PCI:0@0:2:0" Is boot vga? yes Vendor/Device Id: 10de:1347 BusID "PCI:1@0:0:0" Is boot vga? no Error: can't access /sys/bus/pci/devices/0000:01:00.0/driver The device is not bound to any driver. Skipping... Skipping "/dev/dri/card0", driven by "i915" Skipping "/dev/dri/card0", driven by "i915" Skipping "/dev/dri/card0", driven by "i915" Found "/dev/dri/card0", driven by "i915" output 0:     card0-eDP-1 Number of connected outputs for /dev/dri/card0: 1 Does it require offloading? yes last cards number = 1 Has amd? no Has intel? yes Has nvidia? no How many cards? 1 Has the system changed? No main_arch_path x86_64-linux-gnu, other_arch_path i386-linux-gnu update-alternatives: error: no alternatives for x86_64-linux-gnu_gfxcore_conf Current alternative: /usr/lib/x86_64-linux-gnu/mesa/ld.so.conf Current core alternative: (null) Current egl alternative: /usr/lib/x86_64-linux-gnu/mesa-egl/ld.so.conf Is nvidia enabled? no Is nvidia egl enabled? no Is fglrx enabled? no Is mesa enabled? yes Is mesa egl enabled? yes Is pxpress enabled? no Is prime enabled? no Is prime egl enabled? no Is nvidia available? yes Is nvidia egl available? no Is fglrx available? no Is fglrx-core available? no Is mesa available? yes Is mesa egl available? yes Is pxpress available? no Is prime available? yes Is prime egl available? no Single card detected Nothing to do No change - nothing to do   How can I set my Nvidia card to be my main display adapter?  Thanks in advance

This is my first post in this forum. I am new to Linux, just installed Ubuntu 11.10 on my Sony Vaio VGN-Z12 with two graphic cards Intel and NVidia Geforce 9300 GS.  After the installation the lightdm works on Intel card but with very law display quality. I installed Nvidia driver from the official website as well as this PPA.  sudo apt-add-repository ppa:ubuntu-x-swat/x-updates sudo apt-get update sudo apt-get install nvidia-current       Once I installed the driver and run nvidia-xconfig which creates xorg.conf file, the xserver will not start with error "no screen". If I delete the xorg.conf file then I am able to start the xserver normally but with intel display (bad quality)


I'm learning vue.js now on laracasts.com and there jeffrey way shows 2 way to display data on web page.  One is to display data from Laravel foreach and second is to display data with vue.js. I have one question: is there any difference by performance to display data with Laravel or display data with vue.js?

For the following pretty straightforward task: query a list of products from a DB and present it on a webpage, consider 2 setups:  Setup1: PHP script queries. All content is built on the server and the entire page is served back to the client.  Setup2: Static HTML "page skeleton" requesting content using AJAX. Received content is parsed on the client side using Javascript and rendered using innerHTML or similar.  Of course the second setup only makes sense when you have pages, categories and tags for the client user to choose from.  I need to compare these two, at least by means of:   time it will take content to be served user experience (setup1 is delivered as a whole, setup2 is delivered in "two parts") scalability - how do the setups compare when I have 100,000 queries daily   Any thoughts on the issue will be much appreciated.


This is a very unspecific and maybe stupid question, so I apologize for that. We recently had an exam that I failed, because I had pretty much no time to practice before that. Now I got to learn all that stuff that I should've known, yet there was one exercise where I have no clue how one would get a result.     Calculate $$\lim_{n \to \infty}\sqrt{n} \cdot (\sqrt{n+1} - \sqrt{n}).$$   The solution appears to be $\frac{1}{2}$, however I have exactly no clue on how to get to that.  If someone could throw a keyword at me, that would lead me on my path, it could already be very helpful.

I was trying to do this limit $$\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$$  and I cant, I will be pleased if someone give me a hint to do it.


I am attempting to use the Grouping Analysis tool in the Spatial Statistics (in ArcGIS 10.2)  to group state high schools (points) together based on enrollment and location.  Is there a way to make each cluster the same size?  I am able to set how many groups I want, but I cannot seem to make each the same size.

One of my tasks for work is to divide parcels into groups. These groups will be used by agents to talk to property owners. The goal is to make the agent's job easy by grouping parcels that are near each other together, as well as divide the parcels into equal numbers so that the work is distributed evenly. The number of agents can fluctuate from a couple to 10+.  Currently I perform this task manually, but would like to automate the process if at all possible. I've explored various ArcGIS tools, but none seem to suit my need. I tried a script (in python) that makes use of near_analysis and selecting of polygons, but it's rather random and takes forever to accomplish a semi-correct result that then takes me longer to fix than if I just did everything manually from the start.  Is there a reliable method to automate this task?  Results example (hopefully without the division we see in yellow):


As per Einstein space is flexible it means it can be curved with mass but I am not able to visualize the relationship between space and time (space-time continuum). According to Newton Apple falls because earth pulls the apple towards it and it is easy to visualize but As per Einstein Apple remains at that place but time passes so it appears to be falling(how can I visualize the same)?

They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a force of gravity.  That makes perfect sense for planetary orbits, but a lot less sense for the expression of gravity that we are the most familiar with in our day-to-day lives: "what goes up must come down."  Imagine that I hold a ball in my hand, several feet off the ground, with my fingers curled around it, and my hand is above the ball.  Then I open my fingers, releasing my grip on it, being very careful to not impart any momentum to the ball from my hand as I do so.  An object at rest remains at rest unless acted upon by an outside force.  If the ball is not moving (relative to my inertial reference frame), it has no path to travel that's any different from the Earth's path through space.  It should remain at rest, hanging there in the air.  And yet it falls, demonstrating that an outside force (gravity) did indeed act upon it.  How does curved space explain this?


Now I created RD Web Access (RDWA) in windows server 2008 R2 everything is work well.  I need your help, I have a problem    Customer A use user A in PC A ( user created in windows server 2008 r2) login in RDWA ex: . and run programs Customer A go to another pc (PC B) also login by use User A access webpage . and run programs. Now programs in PC A is disconnect and Programs is continue show in PC B. I want if user A login first another user using the same user can’t login or have a notification “ Another user of your computer is currently using this connection.  This user must disconnect before you can log on.”    Important: I already found notification in source of rd web C:\Windows\Web\RDWeb\Pages\en-US\login.aspx.  please focus   bWorkspaceDisconnected = false but it’s not work if I login one user in the same time ??? how make it work for my section   ****I will explain for you. User A: Login in PC A at 9:22 AM and now he's using. Another people use user A login in PC B in 9:25 AM. I want the people login in time 9:25 Am can't login because user A already login ( 9:22 AM) and now he using** People login after exist user login before will not login for useing. That's my hope please help me. Thank you so much**

Quick question: I have a situation where I need to let multiple people on different PCs log into one server 2008 machine as administrator simultaneously over remote desktop. I have the CALs for it, it's just not set up correctly. When one user tries to log in, it boots the other out. What I need is to present to them a different session, just each as logged in as admin. Sorry for the slightly rambling post, I'm new here. Thanks!


Please help, I cannot for the life of me figure out why my output file is created, but there is nothing written to it. I read on a similar question that I had to close the output file as the information is buffered and only outputs when the file is closed. I had already done that before reading that post, other than that I cannot find any other post that helps me with this  import java.util.Scanner; import java.io.File; import java.io.FileNotFoundException; import java.util.Formatter; import java.util.Arrays; public class MyFile {  public static void main(String[] args) {     try {         // creating a File instance to reference text file in Java         File inputFile = new File("C:\\input.txt");          //creating a Scanner instance to read File in Java         Scanner scanfile = new Scanner(inputFile);          //creating a file to output results of program to         Formatter outputfile = new Formatter("C:\\output.txt");          //read each line of file using the Scanner instance "scanfile"         while (scanfile.hasNextLine()) {             String line = scanfile.nextLine();              //splitting String "line" into 2 parts at the ":"             String[] parts = line.split(":");             String part1 = parts[0];             String part2 = parts[1];              //splitting part2 into an array of integers at ","             String[] lineNumString = part2.split(",");             int[] lineNums = new int[lineNumString.length];             for (int i = 0; i < lineNumString.length; i++ ) {                 lineNums[i] = Integer.parseInt(lineNumString[i]);             }              /*now that we have the line split into an operator (min, max or avg) and an array of numbers             we can identify the operator with an if and else if statements, then manipulate the integer array according              to the operator*/              //Outputting max value if operator is max             if (part1 == "max") {                 String outputText = "The Max of " + Arrays.toString(lineNums) + " is " + maxOfArray(lineNums) + ". \r\n";                 outputfile.format("%s", outputText);              }              //Outputting min value if operator is min                else if (part1 == "min") {                 String outputText = "The Min of " + Arrays.toString(lineNums) + " is " + minOfArray(lineNums) + ". \r\n";                 outputfile.format("%s", outputText);             }              //Outputting avg value if operator is avg             else if (part1 == "avg") {                 String outputText = "The Min of " + Arrays.toString(lineNums) + " is " + avgOfArray(lineNums) + ". \r\n";                 outputfile.format("%s", outputText);              }          }         scanfile.close();         outputfile.close();     }      // print out error messages for input file not found or for being unable to create or write to an output file.     catch (FileNotFoundException e) {         System.out.println("Error.");     }    } // method for determining the max value in an array of integers public static int maxOfArray(int[] inputArray) {     int maxValue = inputArray[0];     for (int i = 1; i < inputArray.length; i++) {         if (inputArray[i] > maxValue) {             maxValue = inputArray[i];         }      }     return maxValue; }  // method for determining the min value in an array of integers public static int minOfArray(int[] inputArray) {     int minValue = inputArray[0];     for (int i = 1; i < inputArray.length; i++) {         if (inputArray[i] < minValue) {             minValue = inputArray[i];         }      }     return minValue; }  //method for determining avg value of an array of integers public static int avgOfArray(int[] inputArray) {     int sum = 0;      for (int i : inputArray) {         sum += i;     }     int average = sum / inputArray.length;     return average; }   }

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


What would $2^{3^4}$ equate to? I can think of two rules that may apply:  $a^{b^c} = a^{(b^c)}$ (Making $2^{3^4} = 2^{81}\approx2.417\cdot10^{24}$) or  $a^{b^c} = (a^b)^c = a^{bc}$ (Making $2^{3^4} = 2^{12} = 4096$)  Which of these is true?

Does math have an incorrect notation / syntax? I don't mean writing misaligned notation (google), but when you take something like a number to powers to powers to powers, $${{2^2}^2}^3$$ (I was told this is incorrect notation by a teacher). Is it really incorrect, or does it just need to be simplified with parentheses? Do people write maths like this?  a radical expression with the root being a radical expression? $$\sqrt[\sqrt{2^3}]{2}$$


I am trying find the number of onto group homomorphisms from $U(20)$ onto $U(15)$ where $U(n):=\{1\leq r\leq n: (r, n)=1\}$.   Here is what I tried.  Since $U(20)\cong \mathbb Z_4\times \mathbb Z_2\cong U(15)$, it follows that only we need to find the number of onto group homomorphisms from $\mathbb Z_2\times \mathbb Z_4$ onto $\mathbb Z_2\times \mathbb Z_4$. Let $f$ be one such onto group homomorphism. Then by first isomorphism theorem we must have $$\frac{\mathbb Z_2\times \mathbb Z_4}{\ker f}\cong \mathbb Z_2\times \mathbb Z_4.$$  This tells that $|\ker f|=1$ and hence $f$ is an isomorphisms.   NOW ?  How many isomorphisms are there from $\mathbb Z_2\times \mathbb Z_4$ to $\mathbb Z_2\times \mathbb Z_4$: is it a valid question ? If so, what should I reply ?  Can someone show me what I am doing wrong please ?

Well, I was trying find out the number of group homomorphisms from $U(20)$ onto $U(15)$ which I reduce to the problem of finding the number of automorphisms for $\mathbb Z_2\times \mathbb Z_4$. But don't know how shall I proceed.   Any help will be appreciated.


I am trying to remove   libnvidia-compute-440_440.36-0ubuntu0~0.18.04.1_amd64.deb  root@miki:/var/cache/apt/archives# sudo dpkg --remove libnvidia-compute-440_440.36-0ubuntu0~0.18.04.1_amd64.deb   It does not work  dpkg: error: --remove needs a valid package name but 'libnvidia-compute-440_440.36-0ubuntu0~0.18.04.1_amd64.deb' is not: illegal package name in specifier 'libnvidia-compute-440_440.36-0ubuntu0~0.18.04.1_amd64.deb': character '~' not allowed (only letters, digits and characters '-+._')   What are the alternatives?

Suppose I download a .deb package from a website and install it. (I assume that when I double click the .deb file, the package is installed through a GUI that interfaces with dpkg right?)  How can I uninstall it?


Running echo "Hello world!" in bash:  # echo "Hello world!" -bash: !": event not found   Why does bash complain "!": event not found"? No !, everything is OK:    # echo "Hello world" Hello world   Update: My bash version:    # bash --version GNU bash, version 4.2.46(1)-release (x86_64-redhat-linux-gnu)

I tried to create a script by echo'ing the contents into a file, instead of opening it with a editor  echo -e "#!/bin/bash \n /usr/bin/command args"  > .scripts/command   The output:     bash: !/bin/bash: event not found   I've isolated this strange behavior to the .  $ echo ! !    $ echo "!" bash: !: event not found  $ echo \#! #!  $ echo \#!/bin/bash bash: !/bin/bash: event not found    Why is bang causing this?   What are these "events" that bash refers to?     How do I get past this problem and print "#!/bin/bash" to the screen or my file?


In our textbook, it's written that light rays will follow the minimum or maximum distance after being reflected from the plane surface and thus the path will be fixed.  At somewhere, I read that light would follow all possible ways. But in this case, the probability of those unlikely paths gets cancelled. Maybe, it could be the selection of nature of Quantum Mechanics says something different but still I don't know. If we consider point '$A$' as the source of light, then at a point '$O$' (not mentioned in the following figure), light drops on the mirror and then is reflected towards point '$B$'. Then we can possibly notify the whole path as $AOB$ = $s$  Now Fermat's principle is saying that '$s$' would be the maximum or minimum for the light's trajectory showing the equation $$ \frac {ds}{dx} = 0$$ It seems a bit confusing to me because all I knew is that light follows the way it takes least time to travel. So, what's the logic behind the longest way? Can we lead any conclusion anyhow with the term $ \frac {ds}{dx} = 0$ for defining it?

This is a thought experiment where I have made a "C" shaped hole inside diamond. The refractive index $(\mu)$ of diamond is 2.45. Say we shine a laser from top of the "C" as shown. My calculations show that light reaching A can reach B in the least possible time if gone through the "C". but I'm pretty sure the perpendicular laser beam travels undeflected and straight down. Though I don't have experimental evidence, I see something wrong either with my intuition or with the theory. It would be great if someone could clarify. *       'a' in the diagram is the thickness of the cutout and all comparable distances can be taken 'a'.


I put my Japanese made Snow Peak cast iron pots in the oven and they cam out full of black flakes. Even after i washed pots and water was running clear, paper towel was completely black after i dried my pans.  Any idea how to fix this problem? Is it safe to use pots now?

I bought a brand new Lodge 12" cast iron pan, washed it in soap and warm water and dried it with a paper towel thoroughly. Then I applied a thin layer of canola oil with a paper towel (paper towel was clean - not black after this application) and then heated the empty pan on my electric stove for 15-20 minutes. The oil on the pan smoked a bit, some parts of the pan turned slightly ashy (grey). Mostly everything looked OK.   After I turned it off and cooled the pan, I now take a clean paper towel and rub the surface and I see black flakes! What is this? Is this the oil broken down? Can I cook in the pan or wash it with soap to eliminate the black flakes? Once washed and dried should I rub canola oil again? This is my first experience with cast iron. Any pointers will help.


Is it bad to use 'str.length()' in a for loop or any kind of loop? Does this make O(n^2) complexity? If it is bad, we can assign it to a variable and use the variable instead, right?

I've been told that code such as:  for (int i = 0; i < x.length(); i++) {     // blah }   is actually O(n^2) because of the repeated calls to x.length(). Instead I should use:  int l = x.length(); for (int i = 0; i < l; i++) {     // blah }   Is this true? Is string length stored as a private integer attribute of the String class? Or does String.length() really walk the whole string just to determine its length?


Hi this is actually a pretty simple question but not sure if there’s a simple answer.   But is it possible for a webpage to trigger a key press on a machine. Like hitting the A key or maybe the shift?

Is it possible to simulate key press events programmatically in JavaScript?


I need technical support with my donut (Blenderguru tutorial). My sprinkles suddenly appear on my donut bun? I have managed to make a renderling. But after I opened and closed the program, it looks like this. What happened?? I hope someone can help me?

I am a beginner to Blender and watching .  At 8:46 is when my problem occurs, because my sprinkles are appearing beneath the icing.


In this algorithm I need to create points inside every polygon. The easy solution I was thought was using the centroid. With some help of the community we reach in this algorithm  from qgis.PyQt.QtGui import * from qgis.PyQt.QtCore import * import processing   source_layer = iface.addVectorLayer("folder/Polygon.shp", "Setor", "ogr") crs = source_layer.crs().toWkt()  # Define additional attributes already on the layer level centroid_layer = QgsVectorLayer('Point?field=cd_geocodi:string&crs=' + crs, 'MyPoint' , 'memory')  centroid_layer.startEditing() # Loop over all features points = 50 p = 1 while p <= points: #reading every feature and getting those centroid and one attribute     for source_feature in source_layer.getFeatures():         geometry = source_feature.geometry()         centroid = geometry.centroid()         name = source_feature.attribute("CD_GEOCODI") # select the attribute          # Create the new feature with the fields of the memory layer         # And set geometry and attribute before adding it to the target layer         centroid_feature = QgsFeature(centroid_layer.fields())         centroid_feature.setGeometry(centroid)         centroid_feature['cd_geocodi'] = name         centroid_layer.addFeature(centroid_feature)     p += 1 centroid_layer.commitChanges()  # Add the layer to the registry QgsMapLayerRegistry.instance().addMapLayer(centroid_layer)   #https://docs.qgis.org/2.8/en/docs/user_manual/processing_algs/qgis/vector_analysis_tools/countpointsinpolygonweighted.html  #counting points inside polygons  Result = "folder/output.shp" processing.runalg("qgis:countpointsinpolygon", source_layer, centroid_layer, 'NUMPOINTS', Result) iface.addVectorLayer(Result, 'result', 'ogr')   But depending on how unusual is the polygon the centroid is calculated in other polygon, like below:    I found answers like  who makes me think about create a for inside another for, to use some similar logic to filter the polygon area and insert a random point inside. I had try to adapt these algorithms, but I did not make it. Probably because my skills are limited.  Can someone help me?

Is it possible (without writing Python code - sorry I'm not a developer) to create a point layer from a polygon layer but ensure the point is within the polygon? The ftools centroid tool is cool but some centroids are created outside the polygon (i.e. irregular polygon). In ArcGIS there is a "Feature to Point" tool similar to the ftools 'polygon centroids' tool but has a checkbox to force the point to be within the polygon.


alter table enquiry alter  column RejectReson int default 0   I want alter the column data type with default value zero,but it is not happening.

How can I add a column with a default value to an existing table in  / ?


I tried to capture the screen of my desktop in Ubuntu but when I try to do it in these two ways the drop down menus do not appear in the capture only the windows appear and the desktop menus do not capture them.  The first photo I took as an example of someone else I can not capture the screen this way      Why is this happening to me?

Whenever I try to take a screen-shot (in my Ubuntu 12.04 box ) with the global menu, context menu for any window/file, it doesn't work. I don't seem to be able to take snapshots with menu dropped down. How do I get this fixed?  PS. The problem is in both Unity and Gnome3 environments.


Is there a possibility to do this? All queries and actions performed in any database need to be logged, because of in house compliance.   I need information (and/or source) if we need MS SQL 2017 Standard or Enterprise in order to ensure that the DB Admin's activities (run, modify, etc queries...) are logged and not only the activities performed by non-admin users.

Is there a way to log all Microsoft SQL Server queries executed on a certain server, with their respective durations?  I'd like to be able to analyze all queries will a tool like what  does for PostgreSQL. While we're at it: do you know of any such tools?


EDIT: I do not think this is a copy of an existing question.  The references of my 2 declared string point at the same memory location, so why is my == (reference comparison) giving false?  It is not a character by character comparison.   I am writing test files to get a better understanding of Java String references and comparisons.  I expected the 3rd line of my code to be :     Should be true: true   Why is it not?     public class testr {      public static void main(String[] args) {         // TODO Auto-generated method stub          String s = "s";         String t = "s";           System.out.println("String s hashcode: " + s.hashCode());         System.out.println("String t hashcode: " + t.hashCode());         System.out.println("Should be true: " + s==t);      }  }   Output:  String s hashcode: 115 String t hashcode: 115 false

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


I know that the opposite is possible  i.e. using 2 DAC's to get a higher quality output, but is it possible with ADC's?

Suppose I have a pair of 12-bit ADC's, I can imagine that they can be cascaded to get <= 24-bit output.  I can think of simply using one for the positive range and the other for the negative range, though there probably will be some distortion in the cross-over region. (suppose we can ignore are a few error bits or, perhaps, place a 3rd ADC to measure the value around 0 volts).  Another option I had been thinking of is using a single hi-speed ADC and switching the reference voltages to get a higher resolution at lower speed. Also there should be a way of getting a real-valued result with using one fixed-ref ADC and then switching the aref's of the secondary converter to get more precise value in between.  Any comments and suggestions are welcome.  I am presuming that a quad 8-bit (or dual 12-bit) chip is less expensive then a single 24-bit chip.


Task: find all natural numbers $n$ which give us $5^{2n+1}2^{n+2}+3^{n+2}2^{2n+1}$ divisible by $19$. What I have done so far: $5^{2n+1}2^{n+2}+3^{n+2}2^{2n+1} = 25^n\cdot 5\cdot2^n\cdot2^2+3^n\cdot3^2\cdot4^n\cdot2 = 20\cdot25^n\cdot2^n + 18\cdot3^n\cdot4^n$. That's it. I've read about the rule of divisibility by $19$. First of all, it did not help much and secondly, I think it's impossible to memorize all the divisibility rules for such a variety of numbers up to $19$ and even greater. Isn't there a more general principle for these tasks? Thanks in advance!

Prove that the expression    $$5^{2n+1} * 2^{n+2} + 3^{n+2} * 2^{2n+1}$$   is divisible by $19$.   I'll skip the basis step (as I have done last time) but I can conclude that it's only divisible by 19 for integers n ≥ 0 (or whole numbers).  II.  Assume that  $$5^{2k+1} * 2^{k+2} + 3^{k+2} * 2^{2k+1}$$ is divisible by 19. Then, $$5^{2k+3} * 2^{k+3} + 3^{k+3} * 2^{2k+3}$$ is divisible by 19.   Now this is where I get lost, I try to "dismember" the expression to get  $$5^{2k}* 5^3 * 2^k * 2^3 + 3^k * 3^3 * 2^{2k} * 2^3$$  I also try to get it similar to to the assumption to make use of the said assumption yielding $$5^{2k}* 5 * 5^2 * 2^k * 2^2 * 2 + 3^k * 3^2 * 3 * 2^{2k} * 2 * 2^2$$ $$5^{2k+1} * 5^2 * 2^{k+2} * 2 + 3^{k+2} * 3 * 2^{2k+1} * 2^2$$ $$5^{2k+1} * 25 * 2^{k+2} * 2 + 3^{k+2} * 3 * 2^{2k+1} * 2^2$$ $$50 * 5^{2k+1} * 2^{k+2} + 12 * 3^{k+2} * 2^{2k+1}$$ And this is where I get lost.. : (  Am I missing out something? Had I done it wrong? The number 19 is prime which makes it hard to handle for me. Thanks!  EDIT : After some pondering, I answered it this way : $$50 * 5^{2k+1} * 2^{k+2} + 12 * 3^{k+2} * 2^{2k+1}$$ I realized that 50 can be written as 38 + 12 (and 38 is a multiple of 19) Hence, $$ 38 + 12 * 5^{2k+1} * 2^{k+2} + 12 * 3^{k+2} * 2^{2k+1} $$ Factoring out 12, I get : $$ 38 + 12(5^{2k+1} * 2^{k+2} + 3^{k+2} * 2^{2k+1}) $$ 38 is divisible by 19 and the long expression is divisible by 19 (per the assumption) and qed. Is this correct ?


My other Stack Exchange account Find Me In The Woods was linked to a google account of mine that was accidentally deleted. I need to recover the account. I know my old google account email and password. Can anyone help me get back in to my old account?

How do I log in if my OpenID is not available, or maybe even no longer exists? Can I restore my lost account, or do I need to start over?  See also:


In Finder > Select a folder > Right click, we get a popup with an option to create a new folder:    Is there a way to add menu item New Textfile for adding a new text file?

In Windows, one can create a new file using Right Click -> Add New -> Type of File. Is there an analogous action in Lion?  I just want to create a new blank file on my Desktop.


Let's say I implement an algorithm that shuffles a deck by simply swapping any 2 cards. How many times do I need to swap in order to have an even number of chances for any order.  Assume the following pseudocode:  for n=0: n<num_iterations:   r1 = random(52)   r2 = random(52)   swap(card[r1],card[r2])   Assume that the random() function returns a value between 0 and 51 inclusively, with perfectly normal distribution. What value should num_iterations be in order to have the deck with even probabilities across all permutations?  Does it make a difference if r1 and r2 are possibly identical any number of times?  To be clear, the question is not about the algorithm in particular or how to improve it. It is about how to calculate the value num_iterations, such that any bias is statistically insignificant. I understand this is not a good algorithm but if num_iterations where n² say, I'm sure any bias would statistically vanish, but there is likely a lower value than n². What is it? How can it be calculated?

This is a follow-up to a Stackoverflow .  There are established algorithms (such as the ) that one should use to shuffle an array, rather than relying on "naive" ad-hoc implementations.   I am now interested in proving (or disproving) that my naive algorithm is broken (as in: does not generate all possible permutations with equal probability).  Here is the algorithm:     Loop a couple of times (length of array should do), and in every iteration, get two random array indexes and swap the two elements there.   Obviously, this needs more random numbers than KFY (twice as much), but aside from that does it work properly? And what would be the appropriate number of iterations (is "length of array" enough)?


Well, as the trace is present upon an underage Wizard before he comes of age, hence the Ministry being able to detect underage magic immediately whenever the underage Wizard does it, I still don't quite understand the following situations.  (Is it traceable by location or by person?)  When Dobby did the Hover Charm (Year 2), the Ministry couldn't differentiate whether it was indeed Dobby or Harry Potter who performed it. Suggesting the Ministry detect some kind of magic at a particular address they have on record as being resident to an underage wizard?  However, when Arthur Weasley visited Harry Potter at Privet Drive (Year 4), he did a lot of magic, including magically dodging the teacups Mr. Dursley was throwing as him, and as well as performing an anti-Engorgment charm to return Dudley's tongue to a normal size. So how come did the Ministry differentiate who actually performed magic?  Moreover, at The Burrow, what happens if an underage Harry or Ron performs magic? Can't simply the elders say they performed magic instead?  Update: After reading two answers below I'm still confused. If magic is location based, Tonks, Madeye and Dumbledore all do a lot of magic at Privet Drive and Harry is never caught. Additionally, can't Harry do magic at The Burrow and Mrs. Weasley simply say she did it instead. Whereas if Magic is person based, obviously it isn't because they could differentiate that Dobby performed the magic and not Harry.

In the first book Hermione mentions that she has tried a few spells, before ever arriving at Hogwarts, Sorcerer's Stone, Ch 6:     I've tried a few spells just for practice and it's all worked for me.   Clearly she didn't get into trouble for that. In the second book after Dobby performs a Hover Charm Harry receives a letter from the Ministry of Magic, in Ch 2:     We have received intelligence that a Hover Charm was used at your place of       residence this evening at twelve minutes past nine.      As you know, underage wizards are not permitted to perform spells outside school,       and further spellwork on your part may lead to expulsion from said school (Decree for       the Reasonable Restriction of Underage Socery, 1875, Paragraph C).        We would also ask you to remember that any magical activity that risks notice by        members of the non-magical community (Muggles) is a serious offense under section 13       of the International Confederation of Warlocks' Statute of Secrecy.   In the fifth book (Order of the Phoenix) Ch 2 Harry receives a letter after saving Dudley from the Dementors:     We have received intelligence that you performed the Patronus Charm at twenty-       three minutes past nine this evening in a Muggle-inhabited area in the presence of a        Muggle.      The severity of this breach of the Decree for the Reasonable Restriction of        Underage Sorcery has resulted in your expulsion from Hogwarts School of Witchcraft        and Wizardry. Ministry representatives will be calling at your place of residence        shortly to destroy your wand.      As you have already received an official warning for a previous offense under        section 13 of the International Confederation of Wizards' Statute of Secrecy, we        regret to inform you that your presence is required at a disciplinary hearing at        the Ministry of Magic at 9 A.M. on August 12th.   Students appear to use magic outside of Hogwarts, without getting in trouble, except for Harry Potter. In the movies the violations are even worse, with Hermione repairing Harry's glasses, Harry casting Lumos Maxima repeatedly in his bedroom.   What is the level of severity (or complexity) of spell which will generate the notice of the Ministry of Magic?


I designed a logo with a CMYK of C:60, M:0 ,Y:50, K:0. On my PC (Windows 8) it appears teal, which is the color that the client wanted. When I sent it to her, it appeared like a very bright lime green, and the same happened  at the printer. I don't know if this problem is from my Adobe suit or my PC colors. I checked the color on Illustrator CS5, Photoshop CS5, PDF, and when I open it as a .jpeg file as well, it's teal everywhere. And I made sure that the document is set to CMYK as well as the colors.  When I checked the values online, they appeared like the bright lime green my clients mentioned.  How can I resolve this because I'm having the same problem now with a different design. I have a bright maroon for a background of a poster, but on other devices it seems closer to black. Please help!

I designed a mockup on my LG monitor. When I view the same design on another monitor that I own, the colors seem drastically different. I reset both of the monitors to their factory defaults, but still the issue persists. I'm wondering if some of my clients might dislike my designs because of this. What should I do?  How can I make sure that what I design is what my client sees?  Even worse still, I've realized that my laptop is showing different colors too.


I've been using a Western Digital elements 2TB external USB 3.0 drive for half a year now, and it always worked fine, until yesterday. I don't know why, but it just stopped working, instead of spinning up, the drive would just make some buzzing noise. I recognized this as the head stuck on the platter so I opened the drive to confirm. I moved the head back to its resting position, and closed the drive.  Now I can hear the motor spin up as it normally would, but the drive still doesn't get detected on my computer. Instead, it makes clicking noises about twice a second .  I think this might be the head continously switching on and off the platter. Any ideas how to fix this? Could it be caused by a defect circuit board?

I dont know whether I can ask this question here or not. Please consider this if it not a proper place.  Here is my problem, I was using Windows XP previously and I changed it with Windows 8. After installation of Windows 8 when I booted it up, I found my HDD behavior changed. Sometimes it is running and sometimes it is not.  My system specification is :  Intel Motherboard (945 Express Chipset) Processor (Core 2 duo) RAM (2 GB) HDD(500 GB)   When I open my HDD for getting the cause of problem (I open that casing and check head  and disk). I did not find any hardware visible problem. Just it is stop rotating, before it can boot OS.  Can someone help me to fix this problem or recover data in this case.  NOTE : Warranty period expired, and I have my 5 projects in that and some important documents.


Here is my current thought; Let $f = df', g = dg'$ for some polynomials $f',g'$ by division theorem $f = gq + r$ for some polynomial $r,q$. We have $r = f - gq = df' - dg'q = d(f'-dg')$; hence, $d$ divides $r$; similarly, $d'$ divides $r$. So theree are polynomial $a,b$ such that $r = da = d'b$. My plan is to show that $r=gcd(f,g)$ as well, so I have degree($r$) = degree($da$) = degree($d'b$) = degree($d$) = degree($d'$) implies that $a,b$ just constant.  I  can write $d = \frac{b}{a}d'$ But I'm stuck at how to prove $r=gcd(f,g)$ Any Ideas ?

The book I am reading mentioned that the greatest common divisor of $a_1, \cdots a_n$ in an integral domain $R$, whenever it exists, is unique up to arbitrary invertible factors. What does "up to arbitrary invertible factors" mean?  Definition: Let $a_1, \cdots, a_n$ be nonzero elements of the ring $R$. An element $d \in R$ is a greates comon divisor of $a_1, \cdots a_n$ if it possesses the properties:   $d \vert a_i$, for $i=1, c\dots n$ $c \vert a_i$, for $i=1, \cdots n$ implies $c \vert d$.


For $-\pi<a<+\pi$ the integral $$\int_{-\infty}^{+\infty} e^{i\lambda x}\frac{\sinh (ax)}{\sinh(\pi x)}dx$$ is expected to return $$\frac{\sin(a)}{\cos(a) + \cosh(\lambda)}$$ but I am getting $$\frac{\sin(a)}{e^{\lambda}+\cos(a)}$$ by considering a rectangular contour. Please help.

Using a rectangular contour in the complex plane, bypassing the poles at $z=0$ and $z=i$, i got $$\int_{-\infty}^{+\infty}\frac{\sinh(ax)e^{ikx}}{\sinh(\pi x)}dx - e^{-k}\int_{-\infty}^{+\infty}\frac{\sinh[a(x+i)]e^{ikx}}{\sinh(\pi x)}dx = \sin(a)e^{-k}$$  and now?


I was trying to filled a Uk APPLICATION on the 6th December,2018,When i was filling my Uk application form online,i discovered i made a mistake and there is no means to correct mistake after payment stage,so i decided to cancel the application and fill a form for refund and after completed the refund form, i got a message that it will be refunded in the next 28 days.so i filled another application and made another payment, but up till now i did not receive the refund for the application that i cancel in my card .Please what can i do?

I applied online for a visa application to the UK. I'm from Sri Lanka. Yesterday I cancelled the appointment, I changed my mind. I will not go to the visa appointment. Now my question is how I get my refund?


I have a list of links here:   That I would liked all downloaded. Would anyone know how this would go?

How can I download all pages from a website?  Any platform is fine.


I am starting to do product photography but I dont know whether I should keep the uv filter on my lens or not.

Are there any real downsides to using a UV filter?  I know that a poor quality UV filter can effect image quality ... but, assuming I use a good quality UV filter, will that actually be an issue? Is there any other reason not to use one?


The exponent of prime number of 3 in 100! is 48. It means 100! is divisible by $3^48$ $$E_3(100!) = \left\lfloor\frac{100}3\right\rfloor + \left\lfloor\frac{100}{3^2}\right\rfloor + \left\lfloor\frac{100}{3^3}\right\rfloor + \left\lfloor\frac{100}{3^4}\right\rfloor  = 33+11+3+1 = 48$$ What is the derivation/math behind the above logic?

How does one find the highest power of a prime $p$ that divides $N!$ and other related products?  Related question: How many zeros are there at the end of $N!$?    This is being done to reduce abstract duplicates. See   and  for more details.


I'm thinking about replacing my actual OS (Windows 7 Home Premium 64 bit) with the latest version of Ubuntu, but i'm totally new with this "switching OS" thing. What steps should i follow to correctly replace Windows with Ubuntu? I'm using a Samsung laptop, model 305V5A S02.

My laptop is filled with viruses and Windows XP is just becoming impossible to work with.   I've been interested in Ubuntu for a while, so, would I be able to use something like Debian to clear my HDD and OS and then install Ubuntu and start fresh?


Find the Fitch Style Proof for the following argument: $((A \rightarrow B) \rightarrow A) \rightarrow A)$ I am quite unsure on how to apply the famous rules of natural deduction. Would welcome any comprehensive proofs.

Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$? I started with the hypotheses $(p \implies q) \implies p$ and $\sim p$. However, from these hypotheses I did not get the desired contradiction to solve the question.  Thanks sb45


when I run mount, I can see my hard drive mount as fuseblk.  /dev/sdb1 on /media/ecarroll/hd type fuseblk (rw,nosuid,nodev,relatime,user_id=0,group_id=0,default_permissions,allow_other,blksize=4096,uhelper=udisks2)   However, fuseblk doesn't tell me what filesystem is on my device. I found it using gparted but I want to know how to find the fs using the command line utilities.

Possible Duplicate:             How can I quickly check the filesystem of the partition? Can I do that by using df?


I have an Hp Pavilion dv7 64bit system, 6gb memory, Ubuntu 12.10 partitioned with Win7,AMD Phenom(tm) II N640 Dual-Core Processor × 2 , 650g HDD.  This is what i'm getting through Terminal, same type of warning when going through software center.  I've tried re-installing OS and it is MADDENING!  chris@ubuntu:~$ sudo apt-get install wine [sudo] password for chris:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine : Depends: wine1.4 but it is not going to be installed E: Unable to correct problems, you have held broken packages.  The following is the warning from Software Center: The following packages have unmet dependencies:  wine1.4: PreDepends: dpkg (>= 1.15.7.2~) but 1.16.7ubuntu6 is to be installed          Depends: libc6 (>= 2.14) but 2.15-0ubuntu20.1 is to be installed          Depends: wine1.4-amd64 (= 1.4.1-0ubuntu1) but 1.4.1-0ubuntu1 is to be installed          Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not going to be installed

Every time I try to install "WINE" VIA the Software Center on Ubuntu 12.10, I get this error:  The following packages have unmet dependencies:  wine1.4: PreDepends: dpkg (>= 1.15.7.2~) but 1.16.7ubuntu6 is to be installed          Depends: libc6 (>= 2.14) but 2.15-0ubuntu20 is to be installed          Depends: wine1.4-amd64 (= 1.4.1-0ubuntu1) but 1.4.1-0ubuntu1 is to be installed          Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not going to be installed   When I try installing it VIA the terminal, this is what I get:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine1.4 : Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not installable            Recommends: gnome-exe-thumbnailer but it is not going to be installed or                        kde-runtime but it is not going to be installed            Recommends: ttf-droid            Recommends: ttf-mscorefonts-installer but it is not going to be installed            Recommends: ttf-umefont but it is not going to be installed            Recommends: ttf-unfonts-core but it is not going to be installed            Recommends: winbind but it is not going to be installed            Recommends: winetricks but it is not going to be installed E: Unable to correct problems, you have held broken packages.   how do I fix this?


while True:     question = input('Enter the secret word: ')      if question in ['happy', 'Happy', 'HAPPY']:         print('Great Job!')      else:        print('Try again!')    This code works but what if the user types HaPpY. My computer won't recognize and will say Try again! How do I prevent this?

How can I do case insensitive string comparison in Python?  I would like to encapsulate comparison of a regular strings to a repository string using in a very simple and Pythonic way. I also would like to have ability to look up values in a dict hashed by strings using regular python strings.


DoubleAA (a mod for over a year) seems to have to vote extra times to undelete a post.          Shouldn't it just say his name once?  Week has passed and five more have been added... this is getting out of control!

I just saw a post (deleted)  which was deleted by  but is shown as:   deleted by Charles, Gordon♦, Gordon♦ 1 min ago   How is it that one person (whether a mod or not) can vote twice on the same post?


How it should look:   The above picture is a startup file that is working perfectly!  But the file which I am working on is looking strange! And it is actually:  When it was a new file, it had all the options, but now they disappeared!  How do I fix this?     Also when I am in Edit Mode it does not show assign button to assign   material on selected faces

I have my object selected and don't know why the settings are not there. I've tried different objects and it's the same problem. Can somebody help? Edit: I can see all the settings in the Shading tab..


The TikZ user guide (version 3.18b, page 1042) says this:  ifthenelse(x,y,z) This returns y if x evaluates to some non-zero value, otherwise z is returned.  It would appear that both y and z are first evaluated and then returned, which is (to me) a surprise; a TeX \if does not evaluate the unused option -- so why does TikZ bother to evaluate an unused option? I discovered this in a vain attempt to avoid division by zero: \documentclass{article}  \usepackage{tikz}  \begin{document}  \pgfmathsetmacro{\foo}{0}  \pgfmathsetmacro{\foobar}{ifthenelse(equal(\foo,0),0,1)}\foobar  %% Both return the error: "You've asked me to divide `1' by `0'..." % Uncomment the following to see the problem: %\pgfmathsetmacro{\foobar}{ifthenelse(equal(\foo,0),0,1/\foo)}\foobar %\pgfmathsetmacro{\foobar}{ifthenelse(greater(\foo,0),1/\foo,0)}\foobar  \end{document}  There are a number of non-TikZ approaches (for the moment I have settled on \ifdim\foo pt=0...\else...\fi). Just wondering what a more TikZ-idiomatic approach might be.

Consider having to compute some value using an operation that might not be defined for certain values, like e.g. the tangent function. To avoid raising exceptions, I tried using pgfmath's ifthenelse(<expression>, <true code>, <false code>), like in the following example:  \documentclass[tikz, border=2mm]{standalone} \usepackage{xifthen}  \begin{document}  \begin{tikzpicture}     \foreach \D [count=\C] in {85,...,95}     {   \pgfmathsetmacro{\goodAngle}{ifthenelse(or(\D<=86, \D>=94), 1, 0)}         \pgfmathsetmacro{\Tan}{ifthenelse(\goodAngle == 1, tan(\D), 0)}         %\ifthenelse{\goodAngle = 1}         %   {   \pgfmathsetmacro{\Tan}{tan(\D)}}         %   {   \pgfmathsetmacro{\Tan}{0}}         \node[right] at (0,-\C*0.7) {\D$^{\circ}$, \goodAngle, \Tan};     } \end{tikzpicture}  \end{document}   I expected this to only compute the tangent of the given angle if it was previousely determinded to be a good angle (it would have been sufficient to exclude just 90°, but here I excluded anles from 87° to 93°), but it appears to be evaluating both expressions which obviousely fails for 90°. The result is the same when doing it in "one step", that is without computing the \goodAngle first, as well as using the shorthand notation for ifthenelse (which is <expression> ? <true code> : <false code>). To check that it's not my thinking that is flawed, I used the \ifthenelse macro from the xifthen package, which, as expected, only evaluates the correct expression. If one uncomments the three commented lines and comments out the line above like this  \begin{tikzpicture}     \foreach \D [count=\C] in {85,...,95}     {   \pgfmathsetmacro{\goodAngle}{ifthenelse(or(\D<=86, \D>=94), 1, 0)}         %\pgfmathsetmacro{\Tan}{ifthenelse(\goodAngle == 1, tan(\D), 0)}         \ifthenelse{\goodAngle = 1}             {   \pgfmathsetmacro{\Tan}{tan(\D)}}             {   \pgfmathsetmacro{\Tan}{0}}         \node[right] at (0,-\C*0.7) {\D$^{\circ}$, \goodAngle, \Tan};     } \end{tikzpicture}   one obtains the expected result:    This behaviour is not limited to the tangent function, it also emerges for e.g. simple division by zero, like in   \begin{tikzpicture}     \foreach \D [count=\C] in {-5,...,5}     {   \pgfmathsetmacro{\goodValue}{ifthenelse(or(\D<=-2, \D>=2), 1, 0)}         \pgfmathsetmacro{\byZero}{ifthenelse(\goodValue == 1, 1/\D, -1)}         %\ifthenelse{\goodValue = 1}         %   {   \pgfmathsetmacro{\byZero}{1/\D}}         %   {   \pgfmathsetmacro{\byZero}{-1}}         \node[right] at (0,-\C*0.7) {\D, \goodValue, \byZero};     } \end{tikzpicture}   Is this expected behaviour (I doubt it), or is this a bug? Are there facilities in pgfmath who work like a try ... except statement, or even better, a non- exception approch that lets me catch specific error types, like a try ... except ErrorType1 ... except ErrorTypeN ... finally construct? If not, does something like this exist at all in the world of TeX, and is it even possible?


I'd like to write the following equation:    I don't know which symbol is used for the P in the numerator. I have tried \mathcal{}, \mathfrak{}, and \mathsrc{}, but it wasn't any of these.  Could someone also recommend notation to describe the power density vector?

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


Is there anything similar to MS Windows' command-line tool  for Ubuntu's command line?

How do I kill all processes running by my own non-root account?  I have some spinning smbd  processes that I caused from my windows machine and so I telnetted into the linux server and I want to kill those spinning processes.   I don't have authority to restart services or reboot the machine.


What if I installed an .exe game with a trojan using wine on my Ubuntu? Would this allow the hackers to hack into my device just like what happens usually on Windows? What about the viruses that work behind the scenes in the background, backdoors, the trojans that store a file inside the registry, startup folder and I don't know what else -- will my Ubuntu be hacked just like what happens in Windows?   Extra question: Should I install anti-virus on my Ubuntu?

Can wine as a whole or the windows applications installed via wine pose some kind of risk to an Ubuntu installation? This question arose in my mind when I read this answer to my earlier question :     Try installing PlayonLinux from   playonlinux.org and install IE via   PlayonLinux. and use IE only for those   pesky sites :) - Received 1 downvote      And enjoying the risks of IE? No   thanks - This comment received 2   upvotes   I believe this PlayOnLinux works as a frontend to wine making installing tasks easier.  In totality, I want to know if it is safe to install Internet connecting applications like IE via Wine? Is there any remote possibility of being subject to more online attacks and virus threats this route. I plan to use IE only for browsing websites not accessible with other browsers, like the one in earlier question.


I'm reading the tutorial on LaTeX by overleaf, and in their section  they have some example code:  \documentclass{article} \usepackage{graphicx} \graphicspath{ {images/} }  \begin{document} The universe is immense and it seems to be homogeneous,  in a large scale, everywhere we look at.  \includegraphics{universe}  There's a picture of a galaxy above \end{document}   When explaining the \includegraphics{universe} part of that they say:  The \includegraphics{universe} command is the one that actually included the image in the document. Here universe is the name of the file containing the image without the extension, then universe.PNG becomes universe. The file name of the image should not contain white spaces nor multiple dots.  My question really comes down to this: If I had in that folder both universe.png and universe.jpg what would be chosen? Why?

When using 's \includegraphics you can specify the file extension or not. For generic use and perhaps portability, extensions are commonly dropped. The types of "approved" inclusions and their order of precedence depends on the driver/compiler being used. What are these driver-defaults?  Related:


I ask this because from my understanding, they both are same, because they both denote variance along most important dynamics. So their corresponding values should be the same, but as clearly seen in matlab this is not the case.   why latent values returned by pca matlab are not singular values ?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SVD and PCA?  Or in other words, how to use SVD of the data matrix to perform dimensionality reduction?


I'm new at coding and am wondering if there is any way that one can split a list into two parts? I had thought previously that I could use the .split() function but quickly learned that it will only work if you are splitting strings.  Any suggestions/clarifications would be greatly appreciated. All of the websites that I have found online use things like pandas or numpy which I am not familiar with/not supposed to use.

I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it.


I know that would can't be used to refer to a past state, while used to can. How about in this sentence?     When he lived in Paris, he _____ walk on the banks of Seine River   I find that both would and used to can be appropriate to fill the gap. What is the correct answer, because the question only allows 1 answer. Thank you

"Would " & " Used to ".  They both are used for repeated action in the past tense. Then what is the difference between them?


In Java, in the body of an interface, must methods and variables be declared as having public access? If so, what could be gained from declaring the interface access without the 'public' access modifier i.e. leaving access as the default access?  As an example, what could be gained from writing  interface DefaultAccess {   as opposed to  public interface PublicAccess {   ?

Should methods in a Java interface be declared with or without the public access modifier?  Technically it doesn't matter, of course. A class method that implements an interface is always public. But what is a better convention?  Java itself is not consistent in this. See for instance Collection vs. Comparable, or Future vs. ScriptEngine.


I have a doubt related to back to back connection of PN diode....  Does  exactly as transistor?  It looks like a small doubt... But I want detailed information about it. So, can anybody explain about it in detailed manner?

Another form of the question is: will joining two diodes with wires (pn-np) make a transistor-equivalent?  I read that they are not equivalent, but why?


I'm trying to remake this fancy theorem/definition/lemma environnment, but I've got no any where to begin. Is it a known package or rather a homemade redesign?

this is a follow up to the problem described .  I have the same problem and the proposed solution does not completely solve the problem. I mean, it does solve the problem but also creates another one. The new problem is that the theorems, lemmas and the rest are placed in such as way that they are not cut (of course), but this leaves then big empty spaces in many pages. So the problem is that, the problem described  does not seem to be fully resolved using the nocut option.   Do you any of you have a good idea on how to solve this?  Thanks!


I tried installing a theme using the following lines:  sudo add-apt-repository ppa:noobslab/themes sudo apt-get update sudo apt-get install vimix-flat-themes   Needless to say the theme did not install as expected and I would like to remove what was installed. Any assistance would be greatly appreciated, thanks.  Here is the source web page i followed:

I've added many PPAs using the add-apt-repository command. Is there a simple way to remove these PPAs? I've checked in /etc/apt/sources.list for the appropriate deb lines but they aren't there.   This is on a server system so a command line solution would be great!


These might be the same scenario.   I am a pastor.  I find a lottery ticket in the collection plate.  The next day it wins big.  I want to cash in the ticket on behalf of the church.  My church is a tax exempt institution.  Must it pay tax on the winnings? I win the powerball lottery.  I am afraid of so much money and want to donate the winning ticket to my college and wash my hands of the situation.  The college wants to claim the ticket winnings as a tax exempt organization.  Can it do this?

US 501(c)3 Private Foundations are typically controlled by the primary donator, so that is a nice perk, but in exchange for that perk I realize the tax deductions for donating are significantly lowered than for charities. Aside from being lower, the tax code doesn't recognize appreciated property and only allows for a deduction based on the donating taxpayer's cost-basis: ie. the price they paid for the property no matter its current market value.  When there is a significant delta of price paid vs current redeemable value, it seems this can still be a perk for the donating taxpayer in some circumstances, such as with lottery tickets that are known winners already.  If the donating taxpayer pays $1 for the ticket. Their cost basis is $1. If the ticket is now worth $100,000,000 but has not been redeemed, is it accurate that the donating taxpayer can donate this to their private foundation for a deduction at cost basis, and the private foundation can redeem the $100,000,000 ticket completely exempt from all lottery withholding income taxes?   (Other taxes unique to private foundations are known and outside the scope of this question.)  Most literature I can find is about appreciated marketable securities, and occasionally real estate. It doesn't seem that the tax code specifies any distinction between property, but it also doesn't seem the answer to this question is part of the general collective conscious even if it really is that obvious if my understanding is already correct.


I fitted lasso regression to "diabetes" data from Efron paper (2004).  I had the plot of the coefficients path, but how to know which the best model from this fitting/plot?

Following is the plot of glmnet with default alpha(1, hence lasso) using mtcars data set in R with mpg as the DV and others as the predictor variables.  glmnet(as.matrix(mtcars[-1]), mtcars[,1])     What can we conclude from this plot regarding different variables, especially am, cyl and wt (red, black and light blue lines)? How would we phrase the output in a report to be published?  I thought of following:   wt is the most important predictor of mpg. It is negatively affecting the mpg. cyl is a weak negative predictor of mpg. am may be a positive predictor of mpg. Other variables are not robust predictors of mpg.    Thanks for your thoughts on this.  (Note: cyl is the black line which does not reach 0 till very close to it.)  Edit: Following is plot(mod, xvar='lambda') which shows x-axis in order reverse of above plot:


I recently decided I wanted to learn Linux, so I found an old computer and installed Ubuntu 18.04 on it. However, the external wifi device does not work (ralink technology corp. mt7601u wireless adapter). What do I do to get it working?  EDIT: I'm just gonna buy another one. Sorry for wasting everyone's time

I am trying to install a Ralink wifi adapter in Ubuntu Desktop 14.04.  The system is not detecting the wifi.   lsusb lists the device as:  Bus 002 Device 004: ID 148f:7601 Ralink Technology, Corp.  I have the rt2800 USB driver listed in "/etc/modules"; Following some instructions on the web, I tried this command:  echo 148F 7601 | sudo tee /sys/bus/usb/drivers/rt2800usb/new_i  lsmod | grep rt2800 returns the following:  rt2800usb              26581  0  rt2x00usb              20041  1 rt2800usb rt2800lib              83150  1 rt2800usb rt2x00lib              48886  3 rt2x00usb,rt2800lib,rt2800usb mac80211              545990  3 rt2x00lib,rt2x00usb,rt2800lib crc_ccitt              12627  1 rt2800lib


I'm not a physics guy, but this is something I have always wondered about. If a clock flown by an object of high mass runs slower, what is the effect of this in regards to the density of the universe. It seems to me that as the universe expands, it would lose density and therefore clocks would run faster as the universe expands. Is this correct? And if so, could this create the perception of an accelerating expansion in a hypothetical universe of constant expansion. I want to understand the things I believe in, and I believe in the big bang. It seems that if the universe were a singularity at some point that a nearby clock would be running infinitely slow. Would the first few seconds of the big bang be perceived as slow, maybe from a distant view, despite much happening in the first few seconds? (I'm not sure how the human brain perceives time). Forgive my complete lack of understanding. I'm just curious if and how this is accounted for in the models.

At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time.  If so, could it be that the time periods just after Big Bang which are usually considered happening in small part of a second (such as the Planck epoch), in reaity took billons of year (or may be, infinity) but due to time dilation appear to us as spanning only microscopic parts of a second? Could it be that the age of the universe is dramatically underestimated?


The code seems correct and straight forward to me, I'm using the basic indexOf method for an array i created.  Why won't this code:  public int indexOf(X s) {             for (int i = 0; i <= arr.length-1; i++)     {         if (arr[i] == s)         {             return i;         }      }             return -1; }   pass this test:  @Test public void testIndexOf() {     BetterArray<String> b = new BetterArray<String>();      for (int i = 0; i < 20; i++)         b.add("str" + i);      assertEquals(0, b.indexOf("str0"));     assertEquals(19, b.indexOf("str19"));     assertEquals(-1, b.indexOf("not found")); }

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


[table name:franchise  I have two inputs in php latitude and longitude with this value i need to fetch nearest frachise from franchise table.  please see image for table info.  Ex: 25.271631753161955-Latitude  55.31605750322342-Longitude  I want to select nearest franchise using given latitude and longitude.]

I've got a working PHP script that gets Longitude and Latitude values and then inputs them into a MySQL query. I'd like to make it solely MySQL. Here's my current PHP Code:  if ($distance != "Any" && $customer_zip != "") { //get the great circle distance      //get the origin zip code info     $zip_sql = "SELECT * FROM zip_code WHERE zip_code = '$customer_zip'";     $result = mysql_query($zip_sql);     $row = mysql_fetch_array($result);     $origin_lat = $row['lat'];     $origin_lon = $row['lon'];      //get the range     $lat_range = $distance/69.172;     $lon_range = abs($distance/(cos($details[0]) * 69.172));     $min_lat = number_format($origin_lat - $lat_range, "4", ".", "");     $max_lat = number_format($origin_lat + $lat_range, "4", ".", "");     $min_lon = number_format($origin_lon - $lon_range, "4", ".", "");     $max_lon = number_format($origin_lon + $lon_range, "4", ".", "");     $sql .= "lat BETWEEN '$min_lat' AND '$max_lat' AND lon BETWEEN '$min_lon' AND '$max_lon' AND ";     }   Does anyone know how to make this entirely MySQL? I've browsed the Internet a bit but most of the literature on it is pretty confusing.


Here are some of my observations:   many new users are often technically strong enough to contribute. new users are often "forced" to use an answer as the only way of contributing.   I believe injustice is done to the technically strong and motivated new users.  So a possible solution could be: (Numbers with prepended ~ are up to optimization and discussion)   Allow new users to comment. Only experienced users (rep > ~1000 from answering) can see the comment first, no one else can. Experienced users can upvote, downvote the comment.    If a comment gets a Netto of ~-2 the comment could be considered spam and the 50 rep rule should be applied to the new user. If a comment gets a Netto of ~+2 the comment could be considered valuable and becomes visible to the world. The new user can now continue to contribute.  If the new user's comments get accepted ~5 times, his comments can be seen by the world directly. However, they should still be open for voting until rep 50 is reached.      We cannot prevent users from posting spam on the site. (They can always use the answer for this.) We can maximize the contribution by giving the technically strong new users a shot.

I've seen so many should-be-a-comment "edits" or "answers" in the review queues by new users, and it's pretty obvious that to them this was the only way to somehow interact with a question due to their lack of allowance to leave a comment. And sometimes (just sometimes) this comment would contribute something useful. So it's a shame to waste reviewers' time to first figure out that a suggested "edit" / "answer" should actually be a comment and then not exactly having tools to turn the former into an actual comment. If the new user would instead have had the possibility to clearly indicate that they wanted to leave a comment which would then be put into a simple "comments (by low-rep users)" review queue, where reviewers could maybe even leave one of the (more specific) automated comments à la "You should ask this as a new question" (where new question might even not only link to the "ask question" site but put the users comment into the title or body). And until approval the comment would by default by hidden by a "on hold" line that only higher-rep users, say >500, could toggle to view (and vote to approve directly in place). This is typical practice in many blogs' comments, and I think since we're community reviewing anyway this might be improve the hijacking situation. edit Note that by design those automated comments would not need to trigger a notification to the post's OP but only to the commenter. Whether the un-reviewed comment should already trigger a notification to the OP or not is a different question. I propose not, since the obvious once-in-a-while spam comment would be easier detected by a reviewer who is currently concentrating on specifically determining the validity of a comment. edit2 As noted in  these auto-replies should not clutter the original post - once a comment has been determined "Actually I want to ask a new question" they (and the reply) won't show up below the post except for the original commenter who will also be notified if they registered.  In summary:  Low-rep user posts a comment -> Below the post there will be a "1 comment under review" link and that comment will be added to the comment-review queue (see images below). No notification will be triggered for the OP, since the high likelihood of an unjustified comment was the reason for comments originally not being post-able by just anyone If a reviewer approves the comment, it will show up like any usual comment and now a notification to the OP (and @replied-to users) will be sent If a reviewer rejects the comment (with an optional reason as reply), it won't be shown below the original post as "under review" anymore. It, together with the reply, will be visible to the original commenter who will be notified, but no one else will be bothered by it edit3 As per : The commenter will not be able to post further comments until their comment is either reviewed or self-deleted. As , a negative review/flag should refute that user's ability to comment any more (or reduce a very low contingent of unreviewed comments allowed)


I have a MacBook Pro, always plugged, I put it to sleep during the night. Is  that the best thing to do if I want to maintain a high number of remaining charges, while also keeping a healthy battery?   Or should I turn it off at night instead of sleep, plug it off, or something else?

My friend told me that I need to disconnect the power cord when the battery is fully charged. Otherwise, I will shorten the life of the battery.  Other people say you should drain it once a month or point out that for long term storage, you should charge it to 50% and then periodically (3 to 6 months) bring it back to 50% and store it again.  I am going to use my laptop at home 90% of the time. So, I plan to have the power cord connected all the time.  I'd prefer to just plugging in my MacBook Pro and letting it be on charge long term and occasionally taking it away from the charger when I'm not at home or my desk.  Are these specific recommendations worth the inconvenience?


I have an Ubuntu Mate 16.04.1 installed on a pen drive and I would like to use a different MAC address when I boot this system.  To be more specific I'd like to use always the same address, and to change that before connecting to the network.  I read a lot of guide but none of them works for me. I tried to use macchanger but when I connect to the network my MAC turn back to the original one.  If someone can help I will really appreciate. Thank you

My router can do port-forwarding based on MAC addresses. That is, a specific MAC will get a specific IP, for which I can configure a set of ports to be forwarded. In order to easily change that set of ports, I'd like to have different connections in the Network manager.  How do I change the MAC address for a network connection?


Are there truths that the scientific method cannot explore, but maybe alternative methods can? Does the scientific method subsume all possible valid ways to obtain true knowledge? Or are there alternative methods to explore truths that lie beyond the space of truths reachable by the scientific method due to its methodological constraints?

I am not talking about miracles, religious revelation, or artistic expression, but something more mundane. There is a lot of "empirical" evidence that the Riemann hypothesis is true, the scare quotes indicate that the source of the evidence is "mathematical intuition". In psychology there are mental states that no one sees, touches, hears, smells or tastes, qualia with their perceptual fullness that can not be conceptualized or directly communicated, and abilities/skills "know how" with the same problem. In linguistics Kripke's theory of reference relies on "modal intuitions" to decide the truth of counterfactuals. But an empirical counterfactual is an oxymoron, especially when it is embedded into an entire "possible world".  Freudian psychoanalysis and Husserlian phenomenology are attempts to deal with some of them systematically, but they are traditionally confined to the fringe of science at best. The mainstream approach is empirical second hand, but behaviorism in psychology and linguistics, and nominalism in mathematics, were not very productive.   According to the naturalized epistemology there is no a priori "first philosophy" of science, methodology is subject to the "tribunal of experience" and revision, just as the science itself. Should it apply to non-empirical experience? Sense empiricism has served science well for centuries, and was fully embraced by Quine.  takes him to task for it:     "Cognitive science is an empirical science working to unearth the mechanisms through which natural language constitutes itself. That account has had to recognize the indispensability of mental states, of beliefs, if it is ever to become adequate to the problem... There is still too much "first philosophy" in Quine. We must rescue naturalized epistemology from its own founder".    Note the use of "empirical" together with "mental states".  Questions: Does naturalized epistemology dictate that natural science should relax sense empiricism, and approach non-empirical phenomena partly first hand? If so, how can the scientific method be adapted to introspective/intuitive phenomena that are not readily reproducible, manipulable, measurable, and/or publicly accessible? What would play the selective role of empirical testing? Can there be non-empirical (more likely, not entirely empirical) natural science?


This works:  declare @ids varchar(50) = '1, 2, 3' create table #test  (id int) exec('insert into #test select userid from users where userid in(' + @ids + ')')   This doesn't:  declare @ids varchar(50) = '1, 2, 3' create table #test  (id int) insert into #test select userid from users where userid in(@ids)   It (kinda obviously) returns:     Conversion failed when converting the varchar value '1, 2, 3' to data   type int.   Is there an elegant way to make the query work without using exec(), like I try to do in the second piece of code?

How do I parameterize a query containing an IN clause with a variable number of arguments, like this one?  SELECT * FROM Tags  WHERE Name IN ('ruby','rails','scruffy','rubyonrails') ORDER BY Count DESC   In this query, the number of arguments could be anywhere from 1 to 5.  I would prefer not to use a dedicated stored procedure for this (or XML), but if there is some elegant way specific to , I am open to that.


Let S be the equivalence relation defined on $P$({1, 2, 3, 4}) defined by XSY if and only if |X| ≡ |Y| (mod 2). Write down the equivalence classes of S.   So the absolute value of any set in $P$({1, 2, 3, 4}) will be any of 0, 1, 2, 3, 4  Aka |X| and |Y| can only equal 0, 1, 2, 3, or 4.  For |X| and |Y| to be congruent (mod 2), |X| - |Y| must be divisible by 2.  So would the equivalence classes just be every 5 different sets, each containing subsets with the same absolute value? As in one set for absolute value 0, one set for absolute value 1, etc. all the way to 4?  I'm confused by what equivalence classes actually are, or what the answer to this would even look like. Thanks for any help.

Let $S$ be the equivalence relation defined on $\wp(\{1, 2, 3, 4\})$ defined by: $$XSY\text{ if and only if } |X|\equiv|Y|\;\mod 2$$ Write down the equivalence classes of S.  I understand that equivalence classes have relations where it is reflexive, symmetric and transitive but how are you supposed to write equivalence classes?


I'm fairly new to programming and c#. I have a problem with a simple calculator program I'm trying to write in visual studio c#. I want to convert my text with numbers and math operators into a number. All my attempts so far have led to no success. I have tried:  Double.Parse() Convert.Int32() Convert.Double()  Here are some images of my code:   Any help would be much appreciated, if there is any extra information you need I would be happy to provide it. -Retro_Goat

If I have a string with a valid math expression such as:  String s = "1 + 2 * 7";   Is there a built in library/function in .NET that will parse and evaluate that expression for me and return the result? In this case 15.


I asked this  some times ago and the given solution perfectly worked for me. Now I am trying to draw the same thing in a slide and it's not working.   Here's the code I used:  \begin{frame}  \frametitle{Almost Complex Structure on a Riemann Surface}  \begin{itemize}  \item   <1-> So, we get a diagram: \\  \begin{center}  \begin{tikzcd}[row sep = huge, column sep = huge] T_p M \arrow[r, "J"] \arrow[d, "d\varphi_p", swap] \arrow[dd, bend right = 100, "d\psi_p", swap] & T_p M \arrow[d, "d\varphi_p"] \arrow[dd, bend left = 100, "d\psi_p"] \\  \mathbb{C} \arrow[r, "M_i"] \arrow[d, "d(\psi\circ\varphi^{-1})_0", swap]                             & \mathbb{C} \arrow[d, "d(\psi\circ\varphi^{-1})_0"]                       \\  \mathbb{C} \arrow[r, "M_i", swap]                  & \mathbb{C}                                \end{tikzcd}\\  \end{center}  \end{itemize}  \end{frame}

I have a problem with tikz-cd. When I try to compile in beamer it doesn't work and I no have idea why. Can someone help-me, please?  \documentclass[aspectratio=169]{beamer}  \usetheme{Warsaw} \theoremstyle{plain} \setbeamercovered{transparent} \usefonttheme[onlymath]{serif}  \usepackage[brazil]{babel} \usepackage{tikz-cd}  \tikzset{   every picture/.prefix style={     execute at begin picture=\shorthandoff{"}   } }  \begin{document}  \frame{\titlepage} \section{Motivation}  \begin{frame} \[\begin{tikzcd}[column sep=small] Y \ar[dr, "\displaystyle{p_G}"'] \ar[rr, "\displaystyle{p}"]& &  X \\ & Aut(Y|X)\bs Y \ar[ur, "\displaystyle{\widetilde{p}_G}"'] & \end{tikzcd}\] \end{frame}  \end{document}


Does anyone have a quick method of denesting square roots?     Problem: To quickly denest $\sqrt{5+2 \sqrt{6}} \qquad \tag{1}$   As an aside, this comes from solving the polynomial     $$x^4-10x^2+1=0$$   Since the elements of the Galois group must send an element of the kernel to another element of the kernel, we can show that four different permutations give us exactly the four-group of Klein.  The roots of the $(1)$ can be shown to be $\{\sqrt{2}+\sqrt{3},\sqrt{2}-\sqrt{3},-\sqrt{2}+\sqrt{3},-\sqrt{2}-\sqrt{3}\}$ all of which arise from the denesting of $\pm \sqrt{5\pm2 \sqrt{6}}$.  Other than brute force, does anyone have a quick way to denest square roots, I find this part of the the solution to Galois problems takes a long time, and detracts from the most fun part, the permutations of the symmetries of the roots.

I have recently read some passage about nested radicals, I'm deeply impressed by them. Simple nested radicals $\sqrt{2+\sqrt{2}}$,$\sqrt{3-2\sqrt{2}}$ which the later can be denested into $1-\sqrt{2}$. This may be able to see through easily, but how can we denest such a complicated one $\sqrt{61-24\sqrt{5}}(=4-3\sqrt{5})$? And Is there any ways to judge if a radical in $\sqrt{a+b\sqrt{c}}$ form can be denested?  Mr. Srinivasa Ramanujan even suggested some CRAZY nested radicals such as: $$\sqrt[3]{\sqrt{2}-1},\sqrt{\sqrt[3]{28}-\sqrt[3]{27}},\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}, \sqrt[3]{\cos{\frac{2\pi}{7}}}+\sqrt[3]{\cos{\frac{4\pi}{7}}}+\sqrt[3]{\cos{\frac{8\pi}{7}}},\sqrt[6]{7\sqrt[3]{20}-19},...$$ Amazing, these all can be denested. I believe there must be some strategies to denest them, but I don't know how.  I'm a just a beginner, can anyone give me some ideas? Thank you.


Is the End Times connected to 40k or is it a complete different story? Because the Old World is hardly High-Terra and the corruption that Archaon brought is not the purity of High-Terra.

Is the 40k just Fantasy in the future? They exists in parallel worlds or Fantasy is an enclosed space quadrant of universe in 40k?


I need a ftp for mac since my current viper ftp is corrupting my xml files. So just wanted to know if we have efficient FTP for mac users.

Since Cyberduck uses Java, it's out for me.  Any replacement for Mavericks that is good, has similar to WinSCP functionality and has an option to try before I buy?


How can I prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$  I have tried substitute $x,y$ for numbers, which turns out right, but I don't know how to reason here.  Thanks in advance!

I am having trouble with this problem from my latest homework.  Prove the arithmetic-geometric mean inequality. That is, for two positive real numbers $x,y$, we have $$ \sqrt{xy}≤ \frac{x+y}{2} .$$ Furthermore, equality occurs if and only if $x = y$.  Any and all help would be appreciated.


I am a Swiss citizen. I am planning on going to San Diego from Zurich on November 8-15. Would I be able to do a day-trip to Tijuana and then come back? The trip to Mexico would be by land.  Would I be eligible to re-enter the US?  Thank you!

I am Australian and planning to travel to the US in November for a month. I will be flying into the US and as part of my trip then driving to Mexico for a week and then back to the US. Can I get a visa waiver for this or because I will be entering from Mexico 'by land' do I need some other sort of visa?


The following question seems to be very elementary and must be a folklore, but we are not able to find an answer.  Let $f: [0,\infty)\to \mathbb R$ be a continuous function such that for every $a>0$, $$ \lim_{n\to+\infty} f(na) = 0, $$ where $n$ is restricted to be integer.   Does this imply that  $$ \lim_{t\to+\infty} f(t) = 0, $$ where $t$ is allowed to be real?

Suppose that $f$ is a continuous and real function on $[0,\infty]$. How can we show that if $\lim_{n\rightarrow\infty}(f(na))=0$ for all $a>0$ then $\lim_{x\rightarrow+\infty} f(x)=0$?


Searching for a solution(tool) for comparing two images (1. expected image, 2. real time captured image) to identify difference with high accuracy for automation testing to integrate it with VB.net.  If it also supports OCR functionality then one more problem of mine will be solved.

In my team, we use Selenium for automation of functional testing. We also do a lot of manual regression testing to make sure the appearance of the rendered web pages is ok. I would like to develop a framework, that would allow comparing screenshots of the "base" live web page, and the web page on the test server after applying the software update. I believe this will drastically reduce the amount of manual regression testing we need to do.   I would like the framework to be able to detect portions of web pages that were rendered differently from each other. An example of such functionality can be  (first image in the article)  I have never worked with image processing and would need ideas on what algorithms are already publicly available that would help me with the task. From what I can see, the simple pixel-by-pixel comparison would not work well, because it does not account for the concept of elements.  Or am I approaching this problem from a completely wrong direction?


Though TeXlipse is a great tex editor, one complaint I have is the lack of hot keys for common  style formatting for characters such as bold italic. I found the preference of TeXlipse has an page on style completion which seems to deal with the problem. My understanding of the usage of this feature is:    select a word Press Ctrl+space (on windows, the key is Ctrl+Alt+space) A window pops up and I can choose the format style listed in the style completion page in the preference.   However when I hit the enter to choose a format style, nothing happens? It seems that Eclipse ignores my action. Does anyone encounter this problem? And what is the alternative way to fast format characters using TeXlipse?

Are there any hotkeys to make a text bold or italic in TeXlipse plug-in? It is tiresome to type \textbf{} and \textit{} each time I need to emphasize some word. Most of other TeX-editors support standard Ctrl+B" and Ctrl+I, but in TeXlipse it doesn't work.


I am using a list of list as follows:  L = [['a', 4], ['b', 2], ['c', 13]]   I want to generate a new list for all the numbers which are in the second position in each set of the list:  L =  [4, 2, 13]   Is there any shortcut in python to get the above list?

I have a list of 2-item tuples and I'd like to convert them to 2 lists where the first contains the first item in each tuple and the second list holds the second item.  For example:  original = [('a', 1), ('b', 2), ('c', 3), ('d', 4)] # and I want to become... result = (['a', 'b', 'c', 'd'], [1, 2, 3, 4])   Is there a builtin function that does that?


I have a problem with ng-pattern.    function formCtrl($scope){} <script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js"></script> <div ng-app ng-controller="formCtrl">   <form name="myForm">     <input ng-model="sign_username"ng-minlength="6" ng-maxlength="15" ng-pattern="/[\p{L}0-9]+$/u" required>   </form>   {{myForm.$valid}} </div>     ng-minlength and ng-maxlength work correctly but when I use special characters ng-pattern still is positive.  I want to check if field contains only letters (unicode) and digits.

How can I use Unicode-aware regular expressions in JavaScript?  For example, there should be something akin to \w that can match any code-point in Letters or Marks category (not just the ASCII ones), and hopefully have filters like [[P*]] for punctuation, etc.


In coordinate geometry, points are defined by ordered pairs. However, I have never come across a rigorous definition of what an ordered pairs is, specially given the fact that the same element can occur twice in such a set but not in in sets defined in ZFC.

My book says  \begin{equation} (a,b)=\{\{a\},\{a,b\}\} \end{equation}  I have been staring at this for a bit and it doesn't make sense to me. I have read several others posts on this, but none made any sense to me.  For example,   Based on how my ignorant brain is viewing this, I don't see why the definition could not be.  \begin{equation} (a,b)=\{\{a\},\{b\},\{a,b\}\} \end{equation}  aka the power set. What is the significance of the {a} in that definition? Please keep things simple if possible. Normally definitions have a valid and clear reason for being defined that way.    Clarification  First, I understand what an ordered pair is. I just don't see how the set notation says that.   Second,  \begin{equation} (a,b) = \{\{a\},\{a,b\}\}=\{\{a,b\},\{a\}\} \end{equation} Sets don't preserve order, but ordered pairs do. How does the third part of the equality apply to the definition?  Third, another issue with the notation that I have starts with the Product Property of Sets  \begin{equation} \text{Let $X$ and $Y$ be sets} :\ X=\{a,b,c\}\text{ and }Y=\{a,d,e\}. \end{equation} \begin{equation} \text{Then }X \times Y = \{(a,a),(a,d),(a,e),(b,a),(b,d),(b,e),\dots,(c,e)\} \end{equation} If we look at the first ordered pair and our given definition we have  \begin{equation} (a,a)=\{\{a\},\{a,a\}\} \end{equation}   How can this be so, you can't have duplicates in sets? I guess what I am looking for in an answer, is not a proof or a definition of ordered pairs, but rather something like, "This notation says what it says because...". Except for the second to last point I get the terminology, I just don't get the connection between the two different uses of notation.


I have a list like this :  now, i want to use it, if the text1 = "A12345", then do something.   if the text1 = "B54321", do otherwise but i've tried like below, but it did not work,  how should i do that  private void buildRecyclerView(){         // Create recycler view.         mRecyclerView = findViewById(R.id.recyclerView);         mRecyclerView.setHasFixedSize(true);          mLayoutManager = new LinearLayoutManager(this);          // Create an adapter and supply the data to be displayed.         mAdapter = new ExampleAdapter(mExampleList);          // Give the recycler view a default layout manager.         mRecyclerView.setLayoutManager(mLayoutManager);          // Connect the adapter with the recycler view.         mRecyclerView.setAdapter(mAdapter);         //buat hilang dulu diawal         mRecyclerView.setVisibility(View.GONE);          mRecyclerView.addOnItemTouchListener(                 new RecyclerItemClickListener(this, mRecyclerView ,new RecyclerItemClickListener.OnItemClickListener() {                     @Override                     public void onItemClick(View view, int position) {                         Toast.makeText(menu_utama.this, "Clicked at pos " + position, Toast.LENGTH_SHORT).show();                         if (getText(0) == "A12345"){                             // do here                         }                     }                     @Override                     public void onLongItemClick(View view, int position) {                         // do whatever                     }                 })         );     }

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


Craster's sons being given as sacrifice is one that's really bothering me, because Craster gives them up as new born babies. So I've been wondering when they're changed to White Walkers. (I assume that's what happens, because I'm yet to read the books.)  Are they raised as humans till they're older and stronger by White Walkers? Or do White Walker babies age?

When Craster gives away the baby boys to the White Walkers, what happens? Do the baby boys become snacks at a White Walker party? Made into something else with magic?


Could someone help me on how to fix this bad encoding?  The right output would be Église (this is what I have in the DB), however I'm getting Ã‰glise in the html output.  After running mb_detect_encoding(), I get "UTF-8". I've tried utf8_decode() without success, so I'm kind of lost and would need some guidance. Thanks all!

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.


According to  query's answer, The Dragon Ball Super Broly movie is set after the Dragon Ball Super series. My query is, if its timeline is set after the Dragon Ball Super series, then why didn't Goku's U.I. triggered (Assuming it's spontaneous, and Goku still don't know how to trigger it whenever he wants) when he was pushed to the limit while fighting Broly, and instead he did the fusion with Vegeta?

In the tournament of power, Goku was pushed to his limits several times, and he awakened Ultra Instinct Omen, and Mastered Ultra Instinct. But in the battle with Broly (in which I would assume he was pushed to his limits too, since       not even with Vegeta was he able to defeat Broly in Super Saiyan Blue   He couldn't awaken Ultra Instinct, not even Omen Ultra Instinct, and in the new manga arc we see he was "Ultra Instinct-less" for several years. Why wasn't Goku's Ultra Instinct awakened in his battle with Broly?


Which is correct:        Electric power engineering student   Electrical power engineering student

What is the difference between electric and electrical and their usage?  For example, what is the difference between "electrical machine" and "electric machine"?


Per this answered question from 5 years ago,    I see that reputation will be retained for answers that   1) Have a score of 3 or greater and/or 2) have had exposure for 60 days.  In order for reputation to be retained for an answer to a deleted question, do BOTH conditions have to be fulfilled, or either?

One of my questions got closed, as it was very similar to some other posted questions (though I don't feel the linked questions answered what I was trying to ask).  There's no point to the question staying online, as it doesn't answer anything, so I was going to delete it - but if I do that will it remove the reputation of the helpful answerers I want to upvote?


I have been trying to open and see the visualization of a DXF file in Blender with the DXF importer addon. I managed to get it working once and I could see the details properly in the 3D viewport but now when I import the file it just appears in the outliner but no model is actually visible. What to do? It's basically a point cloud height map from a mapping service. Here is the file:

I try to import .obj files from this project:  - the files contain Polygon Mesh Data.  When I import the obj file into blender, the outliner shows a new mesh added, but nothing is visible in the 3D viewport:      Any help will be appreciated.


This problem is paraphrased from an old version of an exam that  I will be taking, and I have no idea how one would do solve it.     Let $p$ be a prime number, let $F$ be a field of characteristic $p$, and let $c$ be a field element      such that $\:x^{\hspace{.025 in}p}\hspace{-0.04 in}+(-c)\:$ has no roots in $F$. $\;\;\;$ Show that $\:x^{\hspace{.025 in}p}\hspace{-0.04 in}+(-c)\:$ is irreducible over $F$.   How would one solve that problem?

Assume that $F$ is a field and $\operatorname{char}(F)=p$. Let $a$ be an element in $F$ without $p$th root, then the polynomial $$x^{p^n}-a$$ is irreducible and inseparable over $F$ for all $n$.    I have proved the inseparable part by considering the derivative of the polynomial, but I'm having trouble with the irreducible part. Any help?


If it is easier, the user can be denied only deletion of one specific database instead of any database.

My scenario: I have some groups with full - and inappropriate - access to all Sql Server instances. I want to change that.  My Plan: Give full and automatic access to all databases (it is customer databases and this groups must be allowed to change any property if necessary).  Restrict permissions on Instance Level, because this groups should not be allowed to do any unexpected change on instance properties.  I don't want to create a user in databases, because our external customer could drop the user ( they have db_owner permission )  Someone have any idea? Tks


I watched the  about Zephyr ( Z ) sensei. In it they explain that someone killed his family and cut his arm off, later becoming a warlord. I searched online, but could not find another movie or episode where they reveal which warlord it was? Although I suspect Doflamingo or Mihawk because only they have cutting related skills.

So I just watched the One Piece Movie - The Battle of Z and it left me wondering who it was that killed Zephyr's crew (while he was in the Navy) and then became a warlord? It says he was a devil fruit user and that is why he acquired that weapon on/as his arm to take out all the devil fruit users he could.   Does it get explained anywhere in the manga? Any helpful information would be appreciated!


I'm trying to position an image to touch the right and bottom edges of the page. It's for a subtle background image. Any ideas on how to do this?

I am generating one report where I need to use background image. But I found that image always starts leaving some margin space to left side.    \documentclass{article} \usepackage{wallpaper} \usepackage{mdframed} \usepackage[top=2cm, bottom=2cm, outer=0cm, inner=0cm]{geometry} \begin{document}  Some content \ThisLRCornerWallPaper{1.0}{image.jpg} \end{document}    How can I use background image covering whole page?