I've been looking forward to know which is this kind of font in LaTeX. I've tried with these changes in my preamble document:  \renewcommand*\rmdefault{cmss} \usepackage{pifont} \usepackage{amsfonts}   But that doesn't work. I attached an image as I want to see in my pdfLaTeX document   Can anybody help me please?

Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag.


I have thought about quantum entanglement for some time, and I still don't quite understand the reasoning behind the conclusion that entangled particles somehow can communicate their state to each other instantaneously, even though they are separated by a substantial distance (e.g., the communication would happen faster than the speed of light).  From what I gather, the assumption is that each entangled particle is in a superposition of all possible states, and that upon observation of one of the particles, it immediately (and randomly?) converges to only one of the permissible states.  If the second (entangled) particle is observed, at the same or at a different time, the second particle is observed to have the same state as the first particle.  Is this interpretation correct?  Based on the first two answers that I have seen, I will add somewhat to my question.  Yes, I realize that quantum entanglement seems to violate Einstein's laws, or he wouldn't have called it "spooky action at a distance".  And no, I don't want a lesson in tensor calculus as my answer.  The jist of my question is: What observational evidence and logic leads physicists to conclude that there is "spooky action at a distance", rather than conclude that the individual particles are somehow correlated with each other?  Round 3: There is approximately a 50% probability that I am about to get to the bottom of the answer that I am looking for, but (in the finest quantum tradition), I'm not sure yet.  Anyway, here goes.  Based on LENGTHY replies here (for those who went to the effort, thanks), and a bit of background research, I wasn't aware that the quantum state of two entangled particles could not be described independently.  I'm not sure why this is, but given this "fact", it makes perfect sense that the physicists from several decades ago didn't like the conclusions that they were drawing.  Is it correct that the quantum states of two entangled quantum particles cannot be independently specified?  Or is this a case where I can specify either one of the particles, but to specify them as entangled I necessarily have to specify both together?  Chris Drost - thanks for the clarification.  The occasional text that refers to "communication between particles", "spooky action at a distance" (yes, this quote is decades old), etc., now makes a good deal more sense in the context of the mathematical framework that you described.

Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that does?


I know that using a higher amperage charger will make a device charge faster.  But is there a limit to how high the current can be?  Could too high a current damage the battery?.  Could I use a 24watt (5v/4.1A) USB charger (intended to charge USB-C devices such as my Nexus 5x) to charge an iPhone?.  I'd use a USB-A to USB-C cable for connection.

I have an iPhone 4 and an iPad.  Since the iPad really charges best off the wall charger I keep it plugged in, but I usually just charge the iPhone off the computer.  Although frequently if the iPad is charged I will charge the iPhone with the wall charger.  Now the Apple sales rep said he heard from someone who heard from someone that that would burn out the phone because the iPad charger is 10 watt instead of 5 watt.  It is true that it is twice as many watts.  I said that I thought it shouldn't burn out the phone because a device should only pull as many watts as it needs, so the watts were irrelevant.  He said that made sense, but he didn't really know.  So I thought I would ask the experts.  Has anyone had their iPad charger fry an iPhone or iPod?  Am I correct in my understanding of watts in chargers?  Is there an official word about the iPad charger causing trouble with other devices?  Have I already voided my warranty?


I'm trying to find an easy way to generate Color ID maps in blender to use in Quixel, Substance painter or designer. But there doesn't seem to be any sure shot easy way. I don't have access to Maya or 3ds max but I do have substance bundle, zbrush and 3D coat. I do all my modelling and UV mapping work in blender, So It would be really helpful if I can easily generate quality color id maps for my assets before putting them in substance for texturing. I've tried assigning different emissive materials on the mesh and trying to bake textures in cycles. But its really time consuming for complex meshes.I also tried using  with a low poly mesh with red, green and blue materials applied on different faces but it gives a black and white result something like this.  Please help me with this.

All of the most powerful texturing applications require a color ID map (Substance Designer, Substance Painter, Quixel DDO). I've been using a Maya plugin called Nightshade Blockout to export color maps for use in these programs. Nightshade may be one of the most-used plugins for texture artists abroad, simply because it's referred and linked by those giants.      I would hope it's as simple as assigning a material color and baking the texture, but it's safe to assume such a map wouldn't come with edge padding (extending the boundaries of each color island by a certain number of pixels, to hide seams during the texturing process).   If there is a Blender workflow/plugin for this, I would love to know about it!  Thanks for reading,  Allen


Introduction Often people who receive down votes are uncertain why they are receiving them. This is in part because those giving the down votes do not wish to comment publicly for fear of revenge down voting (and the general social stigma of publicly saying "This sucks because" 1) and also because writing comments takes time. Therefore I propose2 radio buttons to select from a number of common reasons for down voting. Related proposals A related solution;  also sets out to solve this problem, however that does not solve the effort issue and also introduces the risk that when comments are anonymous people may feel able to say anything Mock up On clicking the downvote the following would appear to allow you to select a reason for downvoting  On hovering over the score the OP of the question (and possibly everyone else) would see a bar chart of why people down voted. Suggested options On a question  Is confusing/unclear Does not show research effort Contains too much irrelevant information I disagree with the idea(meta only) Other / I'd rather not say  On an answer  This is wrong This is unclear This is technically correct but is dangerous or bad practice I disagree(meta only) Other / I'd rather not say  We don't tell people how to vote Voting is entirely at the discretion of the voter and that is why I have included the Other / I'd rather not say option as a catch all for "the rest" Why not have a free form "other" Without having to be publically accountable for their comments (or reasons) people could get very nasty. It is for this reason that Other wouldn't ask for more information Minimising clicks Other would be selected by default so assuming you didn't want to give feedback this would only add 1 extra click 1 I’m sorry, I forgot this was the internet. There is no stigma to saying things suck 2 I say I'm proposing this, but I thought I had seen this before, I couldn't find it on search however so if so this idea needs a duplicate just for search terms

Preamble: I know that 'give a reason when downvoting' is a very common request, and I assure you that I have read these posts and the discussions in them and my request is very different. This isn't about encouraging people to comment and is more about gathering metrics.  I'd like to see a feature whereby people who are downvoted get some better feedback on why they were downvoted, especially given that people rarely leave comments in practice.  So my suggestion is that when user clicks on the downvote, they are prompted to pick from a short list (No more than 5) of common reasons. It would be a popup that replaces the existing "Please consider adding a comment" box.  The user receiving the downvote would see how many people downvoted them for each reason, but not who did it. It would significantly address the issue of people being too lazy to comment or not wanting to comment (for fear of retaliation or any other reason) while helping to ensure the user gets useful feedback.  Perhaps the downvote could also be weighted based on whether or not a reason is picked.  For questions the list might look something like:   Not a question Not relevant to the subject area Trivial question with no research effort Poorly asked question Other   And for answers, this might be:   Nonconstructive or not an answer Incorrect or dangerous answer Poor explanation Doesn't answer the original question Other


Have anyone experienced this?     String or binary data would be truncated   Raised during ALTER INDEX; even in CREATE TABLE. I'm not having this problem in other databases. I may have reconfigured something as this is only a test database.    All I am seeing in the internet is regarding length of strings inserted by INSERT statement exceeds in the length of defined data type.

I have created a linked server (PostgreSQL). When I try to import data from SQL Server to linked server I get the following error:     String or binary data would be truncated   Even though I am familiar with this error, I have never faced it for the text data type. There is only text datatype in my table.  I would like to know is there are any limitation in linked server?  I have created a test table with a text column. When I try to insert from my linked server I can't insert more than 4000 characters. For testing purpose only I did this but actually I need to import data from SQL to p-sql.  Created following table in p-sql using pg admin  create table test_sql ( col text )   When I try to then inserted values  insert into linkedserver.database.schema.table (col)  values ('4001 char')   but it fails to insert.  I have successfully created linked server with below query:  EXEC master.dbo.sp_addlinkedserver @server = N'Test_server', @srvproduct=N'PostgreSQL Unicode(x64)', @provider=N'MSDASQL', @provstr=N'Driver=PostgreSQL Unicode(x64);uid=postgres;Server=######;database=test_db;pwd=password;SSLmode=disable;PORT=5432'


Is it possible for me to show  $a=7\beta-7\alpha,\ b=3\alpha-2\beta$  If I know that   $\alpha=4a+b,\ \beta=19a+b$  in $mod\ 26$  Any help would be much appreciated, I'm new to modular arithmetic, so still figuring things out.

I know a bit about the Chinese Remainder theorem but what do I do in the case I was asked to solve a system of congruences such as this with two variables:  $3x + y = 7$ (mod 8)  $4x + 3y = 1$ (mod 8)


I get nullpointer exception every time I tried to run this code,but I do not see anything wrong with this.So here is the code:  @Override     protected Void doInBackground(Void... params) {         // Create an array         arraylist = new ArrayList<HashMap<String, String>>();         // Retrieve JSON Objects from the given URL address         jsonobject = JSONfunctions.getJSONfromURL("http://www.focusyazilim.net/json/main.json");          try {             // Locate the array name in JSON             jsonarray = jsonobject.getJSONArray("worldpopulation");              for (int i = 0; i < jsonarray.length(); i++) {                 HashMap<String, String> map = new HashMap<String, String>();                 jsonobject = jsonarray.getJSONObject(i);                 // Retrive JSON Objects                 map.put("şehir", jsonobject.getString("rank"));                 map.put("ülke", jsonobject.getString("country"));                 map.put("nüfus", jsonobject.getString("population"));                 // Set the JSON Objects into the array                 arraylist.add(map);             }         } catch (JSONException e) {             Log.e("Error", e.getMessage());             e.printStackTrace();         }         return null;      }   What can be the problem that can cause nullpointer exception? Here is the error:

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


I'm wondering if there is any difference in runtime at lock vs syncronized. I have learnd that syncronized is a slow operation and outdated at Java. Today I saw the lock at C# and I'm wondering if they are the same and lock is something I "want" to avoid same as in Java or maybe he is much faster and I want to use it...  Thanks!

Do these two keywords have exactly the same effect, or is there something I should be aware of?


What is the most better way to use Python 2.7 code if I have installed Python 3 already?  I've never used a Python 2.7 because I am new in Python and most video tutorials and web topics said it's better to use Python 3. But when I try to run code who is for 2.7 and not exist for Python 3, sometimes it's not working. What is the better option. To use Python 2 and 3 both on my PC. Or to try looking for Python 3 code only. Or to modify somehow Python 2.7 code? These are the errors:  IPython 6.1.0 -- An enhanced Interactive Python.  runfile('C:/Users/G/Desktop/image_recognition/new_test/GemData.py', wdir='C:/Users/G/Desktop/image_recognition/new_test')  Traceback (most recent call last):    File "C:\ProgramData\Anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 2862, in run_code     exec(code_obj, self.user_global_ns, self.user_ns)    File "<ipython-input-1-02441e959cce>", line 1, in <module>     runfile('C:/Users/G/Desktop/image_recognition/new_test/GemData.py', wdir='C:/Users/G/Desktop/image_recognition/new_test')    File "C:\ProgramData\Anaconda3\lib\site-packages\spyder\utils\site\sitecustomize.py", line 710, in runfile     execfile(filename, namespace)    File "C:\ProgramData\Anaconda3\lib\site-packages\spyder\utils\site\sitecustomize.py", line 101, in execfile     exec(compile(f.read(), filename, 'exec'), namespace)    File "C:/Users/G/Desktop/image_recognition/new_test/GemData.py", line 19     print "error: image not read from file \n\n"        # print error message to std out                                                ^ SyntaxError: Missing parentheses in call to 'print'. Did you mean print(print "error: image not read from file \n\n"        # print error message to std out)?

I'm running Windows and the shell/OS automatically runs Python based on the registry settings when you run a program on the command line. Will this break if I install a 2.x and 3.x version of Python on the same machine?  I want to play with Python 3 while still being able to run 2.x scripts on the same machine.


As the heading says, why would Voldemort want a child? I've got the following arguments against the matter:   Voldemort was planning for immortality, so he hardly would need an heir. Thinking of an heir would be acknowledging the fact that he could die, something he always refused to do. Even if Delphi was supposed to be a follower than an heir, why would Voldemort risk having a child when he had so many Death Eaters? Voldemort has no family sentiment(murdered his paternal relatives, got Morfin framed, denied that his mother was a Muggle,etc) so what would make him think that a child of his would be useful or special? I say this because many answers would say that Voldemort wanted a new right-hand man, but Voldemort, who never trusted or got attached to anyone, was unlikely to make an exception for his child. If Voldemort did want a right-hand man, could be not put it off till he was absolutely sure he had won? After all, he still had to kill off Harry, his first priority, his obsession. Surely he would think of a child after "settling down" into his rule, rather than go for it in the middle of a war? Voldemort always wanted to be the sole object of worship for his followers. Surely having a child had the possibility of creating a new leader for his followers ( for example: "Why follow Voldy, he's so harsh, let's back Delphi in a coup, she's liberal"). It could cause unnecessary undermining of his authority and create secondary centres of power, while Voldemort likes keeping things centralized around himself. If all he wanted was a capable assistant, why would he go for a child? Pardon the similie, but isn't it like commissioning a $200000 lawnmower... to mow the lawn? Too much effort for a simple matter. Finally, he, the lone wolf, would prefer to operate alone. Surely having a child would elevate both the child and its mother to a higher level than master-servant? Wouldn't he foresee the unnecessary complications of placing them closer to himself, at least in others' view? (For example: "Bella is his favorite, grumble grumble...")   P.S.: Despite all my arguments, I welcome any answer that is logical and addresses the questions I raise.

In The Cursed Child,      Delphi is revealed to be Voldemort's daughter.   As she explains:      Delphi:  I am from the future. The child of Bellatrix Lestrange and you [(Voldemort)]. I was born in Malfoy Manor before the Battle of Hogwarts. A battle you are going to lose. I have come to save you. (Harry Potter and the Cursed Child - p.307 - Little, Brown - Act Four, Scene Eleven)   But why? Why did     Voldemort, of all people,   have a child in the first place?     He does not love, he considers himself supreme, he is arrogant, he does not need a right-hand man/woman, and he has absolutely every intention of immortality. Even with the Potter boy chipping away at his Horcruxes, surely he would feel no need for an heir?


I'm doing a gap year to learn english in London. I'm accepted in an accredited school (for 8 month) and i have sufficient funds to go (my parents will pay for me) My Father has a new bank account ( 1 month old ) with more than 50 000 pounds. Is it a good enought proof of financial stability ?  I also have a bank account where i receive approximatively 2000 pounds every month from my family but sometimes i go over and use 100 pounds more (so i go under 0)  Any advice on how to go from there to have a good chance to get my short term STUDENT visa ?  Thank you

The UK Visas and Immigration Directorate publishes  that provides helpful tips that can result in successful visa applications. Section 2 of this guidance opens is entitled "other documents you may want to provide" (emphasis mine).  Section 2: other documents you may want to provide – all visitors This section provides guidance on the types of documents that you may want to provide to help us consider your application against the Immigration Rules. Previous travel documents/passports, which show previous travel. Financial documents showing that you have sufficient funds available.  These must clearly show that you have access to the funds, such as:  bank statements building society book proof of earnings such as a letter from employer confirming employment details (start date of employment, salary, role, company contact details) where a third party (who is either in the UK or will be legally in the UK at the time of your visit) is providing financial support to you e.g. a business, a friend or a relative, documents to show that they have sufficient resources to support you in addition to themselves and any dependant family should be provided   The first item is "bank statements" and this ties in with the , which says...  evidence that you can support yourself during your trip, eg bank statements or payslips from the last 6 months  (Note 'eg' is a Latin abbreviation meaning "for example"; this appears to be optional rather than a fixed requirement.) Question: How should someone interpret this such that the chances of success are maximized? How many statements should I submit? What are they looking for and what do my bank statements tell about me?


Here is the error:   E: The package libpam-systemd needs to be reinstalled, but I can't find an archive for it.   When I try to update Ubuntu 14.04, I receive the following pop-up windows:     Could not initialize the package information   An unresolvable problem occurred while initializing the package information.      Please report this bug against the 'update-manager' package and include the following error message: E:The package libpam-systemd needs to be reinstalled, but I can't find an archive for it."     I reviewed the following post:   When I attempted to input sudo apt-get install aptitude into Terminal, I received the exact same error message.  Per request, full verbatim results from Terminal:

I get this error whenever I try to install programs using the terminal:  home@ubuntu:~$ apt-get install myunity E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Also I'm unable to install updates using the terminal.


I have a file that contains date values. I want to be able to pull the last line of the file, formatted like "'2018-09-18 16:42:57'" add 1 day to it and store that into a variable. The code I have right now looks like the following, but it does not work:  start_date=$(tail -n 1 run_dates.txt) start_date=$(start_date -d "+1 day")   What is the correct syntax to do this?

I need to do date arithmetic in Unix shell scripts that I use to control the execution of third party programs.   I'm using a function to increment a day and another to decrement:   IncrementaDia(){ echo $1 | awk ' BEGIN {         diasDelMes[1] = 31         diasDelMes[2] = 28         diasDelMes[3] = 31         diasDelMes[4] = 30         diasDelMes[5] = 31         diasDelMes[6] = 30         diasDelMes[7] = 31         diasDelMes[8] = 31         diasDelMes[9] = 30         diasDelMes[10] = 31         diasDelMes[11] = 30         diasDelMes[12] = 31 } {         anio=substr($1,1,4)         mes=substr($1,5,2)         dia=substr($1,7,2)          if((anio % 4 == 0 && anio % 100 != 0) || anio % 400 == 0)         {                 diasDelMes[2] = 29;         }          if( dia == diasDelMes[int(mes)] ) {                 if( int(mes) == 12 ) {                         anio = anio + 1                         mes = 1                         dia = 1                 } else {                         mes = mes + 1                         dia = 1                 }         } else {                 dia = dia + 1         } } END {         printf("%04d%02d%02d", anio, mes, dia) } ' }  if [ $# -eq 1 ]; then         tomorrow=$1 else         today=$(date +"%Y%m%d")         tomorrow=$(IncrementaDia $hoy) fi   but now I need to do more complex arithmetic.   What it's the best and more compatible way to do this?


It seems that in Rudin's functional analysis (P168, Thm6.27) that the Dirac distribution $\delta_0$ on $R^1$ can write as $$  \delta_0=f_0+f'_1+f''_2, $$ for $\{f_i\}_{i=0}^2\in C(R^1)$, there $'$ should be understand as derivative of distruibution of course.  My problem is, can we write down $f_i$ exactly?

It seems from Rudin's functional analysis (P168, Thm6.27), the Dirac distribution $\delta_0$ on $R^1$ can be written as $$  \delta_0=f_0+f'_1+f''_2, $$ for $\{f_i\}_{i=0}^2\in C(R^1)$, there $'$ should be understand as derivative of distruibution of course.  My problem is, can we write down $f_i$ exactly?  The Dirac distribution is defined as $$  \delta_0(\phi)=\phi(0),\quad\phi\in C_0^\infty(R) $$


I summoned an ender dragon in minecraft realms (in the overworld) and it just sits there and makes a lot of noise. I have tried many things to remove it but it will not work. (Cheats are on!) It does not move or shoot fireballs it just makes a lot of noise and stays in one place. Please someone help me I really need to remove this...

So I used the command /summon EnderDragon ~ ~ ~ {NoAI:1} so that I would have an Ender Dragon that would just sit there.    I then wanted to get rid of it, but doing /killall EnderDragon didn't work, neither did /killallnpc, and I can't seem to do any damage, even with a diamond sword and maximum strength using commands.    I'm not sure why I can't get rid of it; I think it's because the dragon has no AI, but I need to get rid of it somehow, any ideas?


Let $f:\mathbb{R} \mapsto [0,+\infty]$ , $\lambda$ the Lebesgue measure in $\mathbb{R}$ and $f\in L^1(\lambda)$. Show that the function $F(x)=\int \limits_{-\infty}^xf(t)dt$ is continuous.  I tried to use the $\epsilon- \delta$ definition of continuity but I am not sure that will work, or how it will work. Any ideas?

I'm learning about measure theory, specifically the Lebesgue integral of nonnegative functions, and need help with the following problem.       Let $f:\mathbb{R}\to[0,\infty)$ be measurable and $f\in L^1$. Show that $F(x)=\int_{-\infty}^x f$ is continuous.   I know is isn't much but the only thing a could think of is that given $x, y \in \mathbb{R}$ with $x < y$ we note that $F(x) \leq F(y)$, i.e. $F$ is increasing. So maybe we can apply one of the convergence theorems of Lebesgue integration theory.    I was also wondering if this problem can be solved using only Riemann integration theory.


My UI is corrupted (after going into sleep mode).   What do I do to reset this without rebooting? I tried: - change screen resolution - change ubuntu theme  That did not fix it. Thanks!

NB: Nvidia has released an official fix; please see ,  and/or .  Upon waking up Ubuntu 16.04 from Suspend, the following graphical glitches appear around all windows, context menus, and similar:      This is currently known to affect the following NVIDIA cards running the proprietary drivers:  NVIDIA GeForce 610M, driver version 375.39, 340.102 NVIDIA GT 630M, driver version 375.39 NVIDIA GTX 650, driver version 375.39 NVIDIA GT 740M, driver version 378.13 NVIDIA GTX 745, unknown driver version NVIDIA GTX 850M, driver version 375.39, 378.13 NVIDIA GT 940M, driver version 375.39 NVIDIA GTX 950M, unknown driver version NVIDIA GTX 960M, driver version 378.13 NVIDIA GTX 970, driver version 375.39 NVIDIA GTX 970M, driver version 375.39 NVIDIA GTX 980 TI, unknown driver version NVIDIA GTX 1060, driver version 375.26, 375.39, 378.09 NVIDIA GTX 1070, driver version 378.09  The above above list has been sourced from reports from other users here on AU,  thread, and  thread. NB: This is be no means an exclusive list. It probably effects nearly all Nvidia cards.  Furthermore, this issue has been replicated on a clean install where the only change was a software update and the installation of the latest NVIDIA drivers.  What is going on, and how can it be resolved?


I wish to reformat a Windows 7 partition, reclaiming it for use under Ubuntu 14.04 already running on the machine. Windows is no longer needed.   The partition is mounted in Ubuntu and its files accessible to Ubuntu, but as mentioned no longer needed. How can I most safely go about this?   And also, Will this consequentially screw up the boot process? To the point of boot - the machine started as Windows 7, then had Ubuntu 12 installed via Wubi, later Wubi was discarded of and the Ubuntu partition became a regular Ubuntu partition. The machine is still dual boot, but as mentioned Windows will no longer be needed.

I want to keep Ubuntu but remove Windows.


How can you prove or disprove that any even number is the sum of two primes?

Show that every even natural number grater than $2$ can be expressed as a sum of two prime numbers. No idea how to prove this. Can you help? thanks


I have Ubuntu 16.04 LTS and tried to install Virtual Box on my system. I downloaded setup for 16.04 directly from Oracle site, ran through Ubuntu Software of course, and I suspected already when it didn't start install on one click, I needed to click twice, then I got install icon on my dock, which didn't load for about 10 minutes. I restarted, then I got error message on picture.   Question 1: How to fix that error? Question 2: How do I get clear install of Virtual Box?

I have unistalled and reinstalled the Ubuntu Software Center as per info I found in a similar thread and I got the same response about line 91 or something like that.  I just tried to upload a screen shot but since I'm new it won't allow me to.  I also can not figure out how to cut and paste anything so I have to hand type what the error screen says, both when I attempt to open the software center and nothing happens, when I try to enter commands into the terminal to uninstall, reinstall, whatever I get the same following:  COULD NOT INTITIALIZE THE PACKAGE INFORMATION An unresolvable problem occured while initializing the package information Please report t:his bug against the 'update-manager' package and include the following error message: 'E: Malformed line 91 in source list/etc/apt/sources.list (dist parse)  E: The list of sources could not be read.,  E: The package list of status file could not be parsed or opened.   How do I report bugs?  What can be done about this.  I have searched and everything everyone says to do leads me back to the same line error message.  So, I don't know how to get to line 91 in the source list; to tell you what it says. Sorry, I'm really new to this. That is what I need is to find out how to get there and fix what it says. I would really like to NOT have to re partition my hard drive and start from scratch, so I'm really looking forward to getting this problem solved. I need to be able to install new software.


I am having the same issue with three separate monitors! I am quite frustrated that no part of the live cd will load for kubuntu 16.10. I get my bios splash screen, then the initial cd loading screen (ruler = CD), the Kubuntu logo, and finally the above message (or some variation on that depending on the monitor I'm using).  What is the deal? What is the default resolution for this thing? I have no problems with resolutions of 1680x1050 on all of my three monitors using windows. I have been searching for solutions, but I don't think there is one - they all require you to boot some type of command prompt and even with Ctrl-Alt-F1 I need to login (and I don't know the password for the live-cd).

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


An object has a location (or center) (x, y, z) and a size (or dimensions) (width, height, length). What is a single word for both? I thought of "measurements" but it's not so accurate.

I am developing an application and can not figure out a proper abstract term that would fit an interface that defines an object as Movable and Resizable (In essence, something that has a defined size and defined position). Calling it Movable and resizable is kind of silly. Layout was a term that came to my mind but it is not good as layout is something that is responsible for defining position and size, not containing it. Thanks a lot.


I had my first day of Linear Algebra today, and we got introduced to matrices, one thing that kept nagging me though, was that I kept seeing matrices written in a few different styles, namely  $$ A = \left[ \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right] $$  as well as   $$ B = \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right) $$  and on really rare occasions I've even seen   $$ C = \left\{ \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right\} $$  So my question is, which of these is considered most correct to use? $A$, $B$, or $C$?

When I first learned linear algebra, both the professor and the book used brackets like [ and ] to enclose matrices. However, in my current differential equations textbook, matrices are enclosed by parenthesis, and I suddenly realize everybody else are using them too.  So are brackets/parenthesis for enclosing matrices always totally interchangeable?


So, I've somehow managed to wreck my Ubuntu machine (Ubuntu 16.04) by installing some software.   Now, when I try to log in, the screen just goes black for a bit and then takes me back to log in screen. Same happens when I try to log in with a different desktop environment, as I was using Gnome Shell instead of the Unity environment.    I can, however, log in as a guest but it won't connect to the internet.  So, can someone please advise me as to the best method for recovering all my stuff? I want to get all my stuff off then reinstall Ubuntu 17. I don't suppose there's any way to do this as a guest, or will I need to do it via BIOS or some other thing?

I installed Ubuntu on a hard drive that had Windows XP installed so I could dual-boot the two operating systems. Everything was fine but now I can't boot into XP or Ubuntu. I had some important documents in the Ubuntu partition and the hard drive is still working, so how can I recover those files from a working Ubuntu installation? Where should I look for the broken Ubuntu installation?


I'm working on fairly new Mac Mini, running OS X 10.9.4 and VMWare Fusion Pro 6.0.4.  For software testing purposes, I want to install both a OS X 10.7 Lion and OS X 10.8 Mountain Lion inside a virtual machine. I have access to the developer downloads under .    I can find numerous packages saying, for example "OS X Lion 10.7.2 Build XXXXX", but all of them seem to updates and are relatively small in size (~ 700 MB). I can't seem to find any image that would allow me to install a fresh 10.7 or 10.8 inside a new VM.  So how exactly do I go about creating those two virtual machines on my OS X 10.9 host?

I have a MacBook with Lion installed.  I bought VMWare Fusion 4 because I want to create a Lion VM.  As far as I can tell I need to point VMWare to the Lion installer that is downloaded from the App Store, but that file deleted itself after Lion was installed.  How do I re-download the Lion installer (and keep it around) to create a VMWare Fusion 4 virtual machine?


It seems like most statistics books over-complicate the examples of most concepts.   For example, I encountered recently a text that illustrates singular values decomposition with visual recognition, instead of the simpler idea of finding the best way to rotate an ellipse to calculate the lengths of its axes.   This confuses not only the less experienced mathematicians, but even those who have a good understanding of the underlying concepts, which are often elementary.  Is there a text that explains statistical concepts with toy examples, instead of dazzling one with huge numbers and large amount of data?  EDIT: As pointed out in the commentaries, I must specify that I am looking for a book that is more on the applied side, more geared towards machine learning/hypothesis testing, yet with toy examples. I want it to be comprehensive, covering all of the major topics. I a am a fan of Introduction to Statistical Learning so far, but the examples in it are not to my liking, as they seem overly complicated.

To give you some background, I have a grasp on the basics of statistics and probability theory and even remember touching Bayes theorem at the university data mining course. But being a few years away from the university made my math got extremely rusty (so much for last-minute pre-exam cramming). While I remember various random basic concepts, there are a lot of gaps in my understanding of them.  What would be a good material (a book, a site, or otherwise equally accessible medium) to revise the fundamentals and go beyond basics? I'd like a book that can be actually read as a book (most statistics books are really dry and are close to being reference material, rather than a book).


I've just found that method in xsd dataset.  [System.Diagnostics.DebuggerNonUserCodeAttribute()]         protected override System.Xml.Schema.XmlSchema GetSchemaSerializable() {             global::System.IO.MemoryStream stream = new global::System.IO.MemoryStream();             this.WriteXmlSchema(new global::System.Xml.XmlTextWriter(stream, null));             stream.Position = 0;             return global::System.Xml.Schema.XmlSchema.Read(new global::System.Xml.XmlTextReader(stream), null);                         }   It creates 3 streams, but not using "using" clausule/closing them. Why is that? It also says, at the top of the file, that   //     Changes to this file may cause incorrect behavior and will be lost if //     the code is regenerated.   So I believe I shouldn't fix it myself. Can anyone explain? :) Thanks

I have the following code:  MemoryStream foo(){     MemoryStream ms = new MemoryStream();     // write stuff to ms     return ms; }  void bar(){     MemoryStream ms2 = foo();     // do stuff with ms2     return; }   Is there any chance that the MemoryStream that I've allocated will somehow fail to be disposed of later?    I've got a peer review insisting that I manually close this, and I can't find the information to tell if he has a valid point or not.


EDIT: As already explained in the original question, re.escape() is not a solution for this use case. This is therefore not a duplicate of . Please read the question before closing as a duplicate!  Java allows the use of \Q and \E to escape blocks of characters, instead of only escaping characters one at a time. .  Is there an equivalent for this in Python? I've reviewed the  and couldn't find it, but I want to make sure I'm not missing something.  I know there's re.escape() which will automatically escape all non-ASCII characters, but this doesn't work for my use case.  My use case is effectively taking a user-supplied string of format foobarbaz<c> and turning it into a regex that will match foo followed by a number then bar then another number then baz then another number. It would then capture the values of , , and <c>. Also, it's possible that foo, bar and baz could instead be strings containing regex special characters, such as in the case of $.cities[].name.  Java code is something like this:  String key = "foobarbaz<c>";  String keyRegex = "^\\Q" + key + "\\E$"; Matcher m = Pattern.compile("<.*?>").matcher(key);  while (m.find()) {     keyRegex = keyRegex.replace(m.group(), "\\E([0-9]+)\\Q"); }  keyPattern = Pattern.compile(keyRegex);

I want to use input from a user as a regex pattern for a search over some text.  It works, but how I can handle cases where user puts characters that have meaning in regex? For example, the user wants to search for Word (s): regex engine will take the (s) as a group.  I want it to treat it like a string "(s)" .  I can run replace on user input and replace the ( with \( and the ) with \) but the problem is I will need to do replace for every possible regex symbol. Do you know some better way ?


The questions along the side need spoiler alerts if they relate to movie/tv series plot lines:    See the Game of Thrones question

I've noticed that occasionally "hot questions" from SciFi and the Movies & TV network contain major spoilers about the movie/show discussed.  The Matrix spoilers:      (just now there's something about Cypher betraying Morpheus in the Matrix, which is a big deal for people who haven't seen the movie).   I like browsing through those but fear that one day one of these questions will spoil a show I'm excited about and yet to finish   Breaking Bad spoilers:      (like the finale of Breaking Bad, imagine a question asking why did one character betray another at the end or something).   Can users posting such questions be asked to label those with a tag (such as 'spoilers') and then somehow have the network hide those from the "hot questions" list? Or possibly format them differently?  Similarly, this could apply to the Arcade network too.  P.S. Love how this question spikes in popularity around the time GoT starts running again. I swear it should be fairly simple technically to ban questions that have a tag that says 'spoilers' from appearing in the Hot Network Questions.  P.P.S. Oh, and with every fresh release of Star Wars (The Last Jedi being the most recent one)!  P.P.P.S. Another year, another Game of Thrones, another spike in popularity!


In a day, we have different names for different times of it. For example, morning, afternoon, night, evening, noon.  I need a hypernym for them all. What word should I use?

I'm applying tags to a set of recorded data files, and I have to classify by when the recording appears to be taken (if it's light or dark).  TimeOfDay: Day TimeOfDay: Night TimeOfDay: Dusk  TimeOfDay: Dawn TimeOfDay: Night/Day # (the recording spans both Day and Night)   Is there another term to describe "time of day"?  Edit: As per the comments, removed most of the specific constraints - question now focuses on the terminology.


I'm trying to do some caluclation for each value of the list in the main thread as below  for (int i = 0; i < list.size(); i++) {                 //Do some task             }   Bur I'm getting the ConcurrentModificationException on list.size().  It is the simple java.util.List  Caused by: java.util.ConcurrentModificationException                                                                         at java.util.AbstractList$SubAbstractList.size(AbstractList.java:360)                                                                         at java.util.Collections$SynchronizedCollection.size(Collections.java:440)   How to solve this ?  Complete code :  private List<Double> computeValue(@NonNull List<Double> list1, List<Double> list2) {         List<Double> computedList = new ArrayList<>();             for (int i = 0; i < list1.size(); i++) {                 computedList.add(-((list1.get(i) + list2.get(i)) / 2));             }         return computedList;     }

We all know you can't do the following because of ConcurrentModificationException:  for (Object i : l) {     if (condition(i)) {         l.remove(i);     } }   But this apparently works sometimes, but not always. Here's some specific code:  public static void main(String[] args) {     Collection<Integer> l = new ArrayList<>();      for (int i = 0; i < 10; ++i) {         l.add(4);         l.add(5);         l.add(6);     }      for (int i : l) {         if (i == 5) {             l.remove(i);         }     }      System.out.println(l); }   This, of course, results in:  Exception in thread "main" java.util.ConcurrentModificationException   Even though multiple threads aren't doing it. Anyway.  What's the best solution to this problem? How can I remove an item from the collection in a loop without throwing this exception?  I'm also using an arbitrary Collection here, not necessarily an ArrayList, so you can't rely on get.


Look at the code below. Although the catch clause itself throws an exception, the finally block's return statement causes that exception to be swallowed. This method will return 420 even if something goes wrong in the catch block.  private static int foo() throws Exception {     try {         throw new Exception("try");      } catch (Exception ex) {         throw new Exception("catch");     } finally {         String s = "";         return 420;     }   }

I was surprised recently to find that it's possible to have a return statement in a finally block in Java.  It seems like lots of people think it's a bad thing to do as described in ''. Scratching a little deeper, I also found '' which shows some pretty horrible examples of other types of flow control in finally blocks.  So, my question is, can anyone give me an example where a return statement (or other flow control) in a finally block produces better / more readable code?


I want to export equations from LaTeX to PowerPoint (if possible as vector graphic, e.g. .svg). I use Windows7 / Office 2010 and ShareLaTeX. Since I would like to export every equation, I tried:  \usepackage[active,tightpage]{preview} \PreviewEnvironment{equation} \begin{equation}     \dot x = f(x(t)) \end{equation} \begin{equation}     x(t_0) = x_0 \end{equation}   But I have no idea, how to convert the .pdf into a .svg-file.  Would be great, if somebody could help.

What websites allow users to quickly and simply convert mathematical equations into SVG without having to install or run any software?


if $\gcd(a,b)=1$  is it true that, $$a^{\phi(b)}+b^{\phi(a)}=1\mod ab$$  I think the answer is yes, but I am not exactly sure about my reasoning  $a^{\phi(b)}=1\mod b$  and $b^{\phi(a)}=1\mod a$  by Euler's theorem.  The question asks if  $$ab| a^{\phi(b)}+b^{\phi(a)}-1$$  So what would a better way of seeing this be?

I would like to prove the following equality: $$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}$$if $\gcd(l,k)=1$. What methods can I use? Thank you for your help.


I have a following air itinerary/PNR printout. How do I decode this? What does each line and column signify?     TK 693 V 14MAY 7 CAIIST HK1       3  0240 0550   32B E 0 M   SEE RTSVC                                                                        2  TK 661 V 14MAY 7 ISTTUN HK1       I  0830 0925   333 E 0 M   SEE RTSVC                                                                       3  TK 664 V 21MAY 7 TUNIST HK1       M  1700 2145   321 E 0 M   SEE RTSVC                                                                       4  TK 692 V 22MAY 1 ISTCAI HK1       I  0035 0145   32B E 0 M   SEE RTSVC

What do the abbreviations mean in the following itinerary:     2  EK 641 L 29NOV 2 KBLDXB HK1       I  1630 1905   *1A/E*                      3  EK 344 L 29NOV 2 DXBKUL HK1       3  2140 0835+1 *1A/E*                      4  MH 704 V 30NOV 3 KULMNL HK1       M  1245 1630   *1A/E*                      5  UA 184 Y 01DEC 4 MNLGUM HK1       1  2255 0440+1 *1A/E*                      6  UA 155 Y 02DEC 5 GUMTKK HK1          0820 1008   especially, the numbers (2,2,3,4,5) before KBLDXB, KULMNL.... The letters and numbers before time (I, 3, M, 1) *1A/E*?


I've been reading through Zorich's "Analysis I" book recently, and I came across this nice little exercise.  Let $f: [0,1]\to \mathbb R$ be a continuous function such that $f(0)=f(1)$. Show that    for any $n\in \mathbb N$ there exists a horizontal closed interval of length $\frac 1n$ with endpoints on the graph of this function; if the number $\ell$ is not of the form $\frac 1n$ there exists a function of this form on whose graph one cannot inscribe a horizontal chord of length $\ell$.   The first part can be proven like this: Consider $g: [0,(n-1)/n] \to \mathbb R$ given by $g(x) = f(x) - f(x+1/n)$. Then   $$\sum_{k=0}^{n-1} g(k/n) = 0$$  and therefore either all of these points are zero or there exists both a point where $g$ is positive and a point where $g$ is negative. By continuity, there must then also be a point where $g = 0$. So we are done.  Now, the second statement seemed rather counterintuitive, and I have given it some time now, but don't see a counterexample for $\ell < 1/2$.  (For $\ell > 1/2$ the function $f(x) = \sin(2\pi x)$ will do.)  Can anyone help me out?  Cheers,

Let $f \in C[0,1]$ and $f(0)=f(1)$.   How do we prove $\exists a \in [0,1/2]$ such that $f(a)=f(a+1/2)$?  In fact, for every positive integer $n$, there is some $a$, such that $f(a) = f(a+\frac{1}{n})$.  For any other non-zero real $r$ (i.e not of the form $\frac{1}{n}$), there is a continuous function $f \in C[0,1]$, such that $f(0) = f(1)$ and $f(a) \neq f(a+r)$ for any $a$.  This is called the Universal Chord Theorem and is due to Paul Levy.  Note: the accepted answer answers only the first question, so please read the other answers too, and also this answer by Arturo to a different question:     This is being repurposed in an effort to cut down on duplicates, see here: .  and here: .


i created a minecraft-hosting.pro paid server for forge 1.15.2 and am unable to login to it in multiplayer. it shows that my server is online and I am running forge 1.15.2 on launcher. however i keep getting the invalid session (try restarting your game) every time i try to login. i can login to my bfs server, but not my own. Please help.  i have done the java 8 update, and can now no longer open Minecraft forge 1.15.2, however i can open latest release 1.1.5.2.

When I try to connect to servers or join up on lan worlds in Minecraft it says "Failed to Login : Invalid session (Try restarting your game)". Multiplayer used to work fine but now keeps coming up with this error. Can anybody help?


Recently I am having problems with my USB drive which can't be formatted, Even though I tried disk part and it recognized and showed my 14 GB flash drive on the list still I get: DISKPART> list disk    Disk ### Status         Size     Free     Dyn  Gpt   --------  -------------  -------  -------  ---  ---   Disk 0    Online          111 GB  1024 KB    Disk 1    Online           14 GB      0 B  DISKPART> select disk 1  Disk 1 is now the selected disk.  DISKPART> clean  DiskPart has encountered an error: The system cannot find the file specified. See the System Event Log for more information.  DISKPART>

I have a USB flash drive, which I may have mucked up, so I used DISKPART's CLEAN to clean it up. I created a simple volume, and tried to format it. (This is all using Windows' disk management.) I was told The system cannot find the file specified.  So I tried using DISKPART (as an admin):   DISKPART> select volume 9  Volume 9 is the selected volume.  DISKPART> format recommended  DiskPart has encountered an error: The system cannot find the file specified. See the System Event Log for more information.  DISKPART>   As you can see, no luck.  When I plug the drive in, the computer makes a beep noise as though it has recognised something, but nothing appears in My Computer  How can I format the disk so I can use it again?


The exact question is $ABC$ is a triangle. Find the locus of $P$ if $PA^2 + PB^2 = PC^2$. I have solved similar questions in Coordinate geometry where coordinates of the sides were given and I know the locus is a line, but I'm not able to conlude anything in the general case. I tried using, $PA^2 + PB^2 + PC^2=GA^2+GB^2+GC^2+3PG^2$ But couldn't proceed further, I also tried to draw medians to AG from P but arrived at the same equation.

Find the locus of all points inside $\triangle ABC$ such that $PA^{2}+PB^{2}=PC^{2}$. At first, i tried finding a right angled triangle and then tried to go on applying Pythagorean Theorem and finding other trivia but that didn't seem to work. I think the locus is most likely to be some line segment rather than an arc of some circle as that seems to be quite unrelated seen from an Euclidean perspective. Applying Apollonius' Theorem and Stewart's Theorem on some triangles might be the key to this problem although i could not find such triangles. I don't know whether this can be solved by trigonometry or not but since this is a problem from a chapter on euclidean geometry, i am sure that there is some clever way to look at this problem.


Im trying to show that the sum $\sqrt{2} + \sqrt[3]{5}$ is irrational.  Ive seen proofs that the terms are both irrational but for the sum I dont know.  Any help would be much appreciated.

Prove: $\sqrt{2}+\sqrt[3]{5}$ is irrational    I have tried to look at $1+\sqrt{2}+\sqrt[3]{5}$ but I can see how to continue


I was reading the book  Algebra: Chapter 0 , by Paolo Aluffi, and came across the following assertion, in page 290, Exercise 5.9:     It is in fact much harder to factor integers than integers polynomials.   What I want to know is:   What exactly is the meaning of easier. Why is that so? Because it seems quite unintuitive for me that finding a factorization of a high degree polynomial (with a lot of big integer coefficients) should be easier than factoring the degree of polynomial itself.

There seems to be a consensus that factorization of integers is hard (in some precise computational sense.) Is it known whether polynomial factorization is computationally easy or hard?  One thing I originally thought was that if we could factor polynomials easily, then we could factor $n$ by finding a polynomial $p(x)$ with $p(m)=n$ for some $m$, then "easily factorizing" $p$ to get $p(x)=q(x)\cdot r(x)$. Then $q(m)\cdot r(m)$ would be a factorization of $n$. But we wouldn't get any information if one of these happened to be 1.  Does anyone have a solution or a reference for this problem? (I searched online, but all I could find was how to do factorization like in high school problems.)


I am trying to invite my son (IOS Pocket Edition) to my realms server (mac osx).   I keep getting the response "Could Not Invite The Provided Name" when I try to invite him. His name is all regular characters with no spaces . . . just letters and numbers.  Are the two game types incompatible, and if they are Is it possible to create the same type of 24/7 available server that is only open to him and other invitees like the OSX realms?   Thanks in advance for any clarification.

My kids are playing Minecraft on 2 PCs, creative mode.  They are connected by the way of one of them starts a single player game on the other one than joins that game over the LAN.  Can I, using Minecraft PE on my iPad, join their game as well?


We have a server with 300+ websites on it, and it has gotten an abuse letter from spamcop. We have investigated the logs, and searched for the PHPMailer version stated in the mail and all came up with nothing.  I was wondering if there is a chance for some sort of phpmailer script that is obfuscated or encoded, and how to find it. I am running NeoPi and Web Shell Detector, but so far nothing comes up.  Is there a way to monitor the outgoing port 25 and filter it with the domain name? The domain which the emails are supposed to be coming from is clean, I am suspecting that another code is using this domain because of its DKIM,SPIF etc.  Return-Path: <dianne.l@*****.com> X-Original-To: x Delivered-To: x Received: by truhi.net (Postfix, from userid 132)     id 5BB8510057D; Sat, 29 Jul 2017 11:35:05 +0300 (EEST) X-Spam-Checker-Version: SpamAssassin 3.4.1 (2015-04-28) on truhi.net X-Spam-Level:  X-Spam-Status: No, score=0.0 required=3.1 tests=HTML_MESSAGE autolearn=ham     autolearn_force=no version=3.4.1 Received-SPF: None (mailfrom) identity=mailfrom; client-ip=**.**.**.***; helo=a.**.com; envelope-from=dianne.l@*****.com; receiver=<UNKNOWN>  X-Greylist: delayed 319 seconds by postgrey-1.36 at truhi; Sat, 29 Jul 2017 11:35:04 EEST Received: from a.**.com (mail.**.com [**.**.**.***])     by truhi.net (Postfix) with ESMTP id 0D6C4100164     for <x>; Sat, 29 Jul 2017 11:35:02 +0300 (EEST) Received: by a.**.com (Postfix, from userid 33)     id 3075E922488; Sat, 29 Jul 2017 11:29:35 +0300 (IDT) To: x Subject: Enter our club as a lover Date: Sat, 29 Jul 2017 11:29:35 +0300 From: "Dianne L." <dianne.l@*****.com> Message-ID: <7fee________________________c316@www.*****.com> X-Mailer: PHPMailer 5.2.23 (https://github.com/PHPMailer/PHPMailer) MIME-Version: 1.0 Content-Type: multipart/alternative;     boundary="b1_7feee464828bc148486a4b82f280c316" Content-Transfer-Encoding: 8bit

This is a  about Fighting Spam.   Also related:                    There are so many techniques and so much to know about fighting SPAM. What widely used techniques and technologies are available to Administrator, Domain Owners, and End Users to help keep the junk out of our inboxes?  We're looking for an answer that covers different tech from various angles. The accepted answer should include a variety of technologies (eg SPF/SenderID, DomainKeys/DKIM, Graylisting, DNS RBLs, Reputation Services, Filtering Software [SpamAssassin, etc]); best practices (eg mail on Port 25 should never be allowed to relay, Port 587 should be used; etc), terminology (eg, Open Relay, Backscatter, MSA/MTA/MUA, Spam/Ham), and possibly other techniques.


$$ \displaystyle \int_{0}^{1}\dfrac{\ln(x)\ln(1+x)\ln(1+x+x^{2})}{(1-x)(1+x^{2})}\,dx$$ I posted this on I&S but there was no response , so posting it here. Wolfram gave $-0.223434$, can it be evaluated in terms of special functions functions?

This problem was posted in I&S   $$ \int_{0}^{1} \dfrac{\log x \log (1+x) \log (1+x+x^{2})}{(1-x)(1+x^{2})}\,\mathrm{d}x \approx -0.223434.$$  I am not sure if there exists a closed form but it seems worth trying. I am completely clueless on how to start with this beast. It is worth saying that$$1-x^3= (1-x)(1+x+x^2).$$ That seems to go no where. I think the integral can be represented as the derivative of the integral representation of the Hypergeometric function but I am not comfortable with that. Any ideas ?


How many antisymmetrical relations are there on Set $B$ if Set $B = \{1,2,3\}$?  I believe its three?

I know that given a set $A = \{1, 2, 3, ... , n\}$, the total number of relations on $A$ is $$2^{n^2}$$ The number of reflexive relations is $$2^{n^2 - n}$$ The number of symmetric relations is $$2^{{n+1}\choose 2}$$ But how can I find the number of anti-symmetric relations? With a small set, say $n = 4$, it can be easy to just brute force it. Is there another way (perhaps using the inclusion-exclusion principle?)


Some SEO articles have suggested "You should never have more than one H1 tag on a page."   Can I use H1 tags more than once? Can I use an H1 tag in each section tag or article?

Is is true
 tag should not have more than 1 on every page for SEO?   Every pages on the header, it includes and
 tag. Website Name which show an image from logo class, like this:

      Website Name

   and I also include
 on the contact page, help, etc and article page for example:
Contact Us

Name of the Article Title here
   On the homepage, it just has one
 for the logo Site Name... other pages have 2
 tags


I have to find how many times the word shell is used in a file. I used grep "shell" test.txt | wc -w in order to count how many times that word has been used, but the result comes out 4 instead of 3. The file content is:  this is a test file for shell_A shell_B sh shel and  shell_C script project

I have a large JSON file that is on one line, and I want to use the command line to be able to count the number of occurrences of a word in the file. How can I do that?


I have just installed the virtualbox application on my Ubuntu 14.04 OS (host OS). I then installed another Ubuntu 14.04 "inside" the VM i.e. the guest OS. The problem is the resolution is tiny and unusable and I need to increase the resolution "inside" the guest OS  here is what I have tried already  starting with a brand new install of Ubuntu 14.04 "inside" the VM  Install and configure the virtualbox guest additions   sudo apt-get install virtualbox-guest-additions-iso - (run from inside the guest OS) this seemed to attempt to modify/build kernel modules, and there were some failures. Then set x86 virtualization settings (again inside the guest OS)   Go to System settings → Software and Updates → Additional drivers Use x86 virtualization solutions... then reboot VirtualBox    Then what am I supposed to do - from there?  I have tried going into (from the host) virtualbox application -> file -> preferences -> display, then apply a "hint" of say 800x600. But when I start the virtual box the res. is still something like 640 x 480  If I go into the guest OS'es display settings - there is still no option  I have also googled for a solution and see there are answers, but they are outdated, give various solutions that dont work for me

I've recently installed Ubuntu on Oracle's Virtualbox.  Now I want to install the guest additions.  I started up my Ubuntu guest OS, clicked "Devices" and chose "Install Guest Additions". Nothing happened, and I don't see the CD icon on my desktop.  How can I make this work?


When I installed Ubuntu Studio 19.10, I didn't add password for login. Now anytime I try to do something with the terminal it asks for my sudo password but of course I have no way of finding out what that is, since:  a) GRUB does not appear for me at all when I boot system b) I cannot open etc/sudoers  Totally new user...have installed Ubuntu in light of world events, covid and love for open source community.  THANK YOU!

I'm working on a Ubuntu system, and my client has completely forgotten his administrative password. He doesn't even remember entering one; however it is there.  I've tried the suggestions on the website, and I have been unsuccessful in deleting the password so that I can download applets required for running some files. Is there a solution?


I have code on JavaScript.  var a = [];  for (var i = 0; i < 5; i++) {     a[i] = function () {         alert(i);     }; }  a[2]();   If I invoke a[2]() I expect to see a message with 2 but instead of this I see 5.  To fix it I can rewrite it like this:  for (var i = 0; i < 5; i++) {     (function (v) {         a[i] = function () {             alert(v);         }     })(i) }   But I cannot understand how does it work. So why I need to wrap my function code to closure?

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


Given image files  lights000.rgbe lights001.rgbe lights002.rgbe ... lights899.rgbe   Are all located in a single subfolder. What is the best way to read one file then the next?  Given that my read command for .rgbe is called readHDR(char* filename)  I have seen several questions regrading this problem but they all use OpenCV. I am not using opencv and .rgbe is not even a supported OpenCV file extension so that method wouldn't even work.  I saw the following code from a different question:  char* Dataset_Dir( "C:/Data/" ); // Or take it from argv[1] cv::Mat normal_matrix; std::vector<cv::Mat>* image_stack; for( int i=1; i<=endNumber; ++i ) {     // Gives the entire stack of images for you to go through     image_stack->push_back(cv::imread(std::format("%s/%03d-capture.png", Dataset, i), CV_LOAD_IMAGE_COLOR));       normal_matrix = cv::imread(std::format("%s/%03d-capture.png", Dataset, i), CV_LOAD_IMAGE_COLOR); }   But I cannot find any information on the std::format command or the Dataset_Dir.  Any advice for even how to split the file name string into three parts would be really helpful.  Split into:   char Name = "lights";  int Num  = "000";  char File = ".rgbe;

I'm trying to iterate over the words of a string.  The string can be assumed to be composed of words separated by whitespace.  Note that I'm not interested in C string functions or that kind of character manipulation/access. Also, please give precedence to elegance over efficiency in your answer.  The best solution I have right now is:  #include <iostream> #include <sstream> #include <string>  using namespace std;  int main() {     string s = "Somewhere down the road";     istringstream iss(s);      do     {         string subs;         iss >> subs;         cout << "Substring: " << subs << endl;     } while (iss); }   Is there a more elegant way to do this?


Since gravity is so similar with the Yang-Mills theory, the Christoffel connection is the gauge potential, the Riemann curvature is the field strength, then why is quantising gravity so difficult when we already have a successful quantum yang-mills theory? I know by dimensional analysis, we can deduce that Einstein theory is not renormalizable. But are there something else truly essential that make quantising gravity so difficult?

It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest.


Let $f: K \rightarrow \mathbb  R$ be a locally Lipschitz mapping on a compact subset $K$ of $\mathbb R^n$. Is it then $f$ Lipschitz?

I need to prove:  Let $A$ be open in $\mathbb{R}^m$, $g:A \longrightarrow \mathbb{R}^n$ a  locally lipschitz function and $C$ a compact subset of $A$. Show that $g$ is lipschitz on $C$.  Can anyone help me?


I'm new to shell scripting. I'd like to know if there's a command similar to "echo" for displaying text in a terminal, but instead of simply displaying it immediately, it actually types it, like if someone was actually typing on the terminal?   I'd also appreciate it if someone could point me to pages explaining simple scripting like menus and such.

I am writing a script, which I would like to spice up a bit.  What I need, is a loop, which takes one letter at a time, including space, and then write it on the screen, like an old typewriter would do.  I would write some kind of pause/sleep between the typing, so it would look retro like.


I was fascinated when I heard that the most intuitive laws of arithmetic are no longer necessarily valid when it comes to the sum of an infinite sequence, which be denoted  by $$S = \sum_{n=0,1,2,...}a_n$$ There are different ways of convergence, and particularly interesting I find Riemann's rearrangement theorem, which states that for conditionally convergent series, it is possible to rearrange the series to converge to any given value.  Since this is all about the sum of a countably infinite set of numbers, I wonder whether there is a similar field of study on the sums of uncountably infinite sets of numbers, which could be written like this:  $$S = \sum_{x\in\mathbb{R}}a_x$$ Or if interpreted as the sum of all values of a function $f(x)$: $$S = \sum_{x\in\mathbb{R}} f(x)$$  Some minor observations are that:   if $f$ is continuous and $f(x)\ge 0$ for $x\in [a,b]$ then $S_{[a,b]}=\sum_{x\in [a,b]}f(x) \to +\infty$ (and the opposite if $f(x)\le0$ in $[a,b]$) The integral of $f(x)$ in $[a,b]$ seems to be the sum $S_{[a,b]}$ diveded by the number of already counted values of $f$, however this seems not quite right because we are talking about an uncountably infinite amount of numbers and we have no notion of transitioning from countably to uncountably infinite values.   Is there any study on the sum of uncountably infinite sets of numbers?

Can we add an uncountable number of positive elements, and can this sum be finite?   I always have trouble understanding mathematical operations when dealing with an uncountable number of elements. Any help would be great.


Is there any good book where the equivalence of AC to the statement "Any surjection has a right inverse" is proved (and maybe other equivalences)? I could do $AC \Rightarrow$ "Any surjection has a right inverse" by myself but I have no idea for the other direction.

This is a problem from Tao's Analysis I.  We are asked to show that the axiom of choice is equivalent to the statement that for any sets $A$ and $B$ for which a surjection $g:B\to A$ exists, an injection $f:A\to B$ exists.  I have proven that the axiom of choice implies the statement , but I am having difficulty with the other implication. The hint given in the book is to use the previous exercise, which says that the axiom of choice is equivalent to the statement that if $I$ is a set, $\forall\alpha\in I$ $X_\alpha$ is a non-empty-set and $\forall \alpha,\beta\in I, \alpha\neq \beta\implies X_\alpha\cap X_\beta=\emptyset$, then there exists a set $Y$ with $\forall \alpha\in I ,|Y\cap X_\alpha|=1$.  To use the previous exercise we need disjoint sets, so we consider the sets $\{\alpha\}\times X_\alpha$ instead of just $X_\alpha$. I think then we should find a set $Y$ with $\forall \alpha \in I,|Y\cap(\{\alpha\}\times X_\alpha)|=1$, perhaps by using that there is some surjection between two sets and so by assumption some injection which goes the other way, whose image is suitable as a set $Y$. I think that is the idea, but I can't figure out exactly what these functions should be.  If I am incorrect, please correct me. Any help is appreciated.


The loss of energy of a capacitor is independent of length of wire connecting it to voltage source $$(\frac{1}{2}×CV^2)$$So where and when is the coverted into heat?

A capacitor is charged. It is then connected to an identical uncharged capacitor using superconducting wires. Each capacitor has 1/2 the charge as the original, so 1/4 the energy - so we only have 1/2 the energy we started with. What happened? my first thoughts were that the difference in energy is due to heat produced in the wire. It may be heat, or it may be that this is needed to keep equilibrium.


Am trying to install Bibletime v2.9.2. I purged v2.8, added the crosswire ppa (ppa:pkgcrosswire/ppa) to my software sources and did a sudo apt-get update.  Since I don't have a fast internet connection, I wanted to know the Bibletime version available before installing it via terminal. I'd be glad if anyone can point me in the right direction.  Thanxs.

How can I check the version of the available package in the Ubuntu repositories without installing it?


Here i have list with product name and product price but i want to take only the products price from the list and calculate the total price of all products. How can i do it ?  For example i have a list: all_products = ['food',1000,'pasta',500,'beer',400] how can i do : 1000+500+400 = 1900

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.


Although I'm sure a lot of you tired of seeing this question, but I'm never really get the answer that suits my situation.  I will fly with Qantas from Dublin to Sydney. My Qantas flight back to Europe will end at London Heathrow, and I will transfer at LHR to British Air for the last leg to Dublin (11th July QF1 to BA828).   Full itinerary detail (all time is local time):  1.QF1 Sydney (10/06 15:55) (stop at Changi Singapore approx 100min) to London (11/06 06:25) 2.BA828 London (11/06 08:25) to Dublin (11/06 09:50)  I am not sure whether I will passing UK immigration and custom or not, since Qantas told me I need to re-check my baggage, even though I do all the booking in one booking refernece (all of them under the same booking reference and I can see the British Airways flight in my "Manage Booking" Qantas website).  I have Indonesian passport and Irish Residence Permit Stamp 2. I visited  and this sentence: "You must also have an Irish biometric visa (marked ‘BC’ or ‘BC BIVS’ in the ‘Remarks’ section)" made me unsure whether I am exempt from transit visa or not. Ireland abolished re-entry visa () so there is nothing in my Passport to confirm the remarks section as showing my Irish Residence Permit card would replace the Re-Entry visa  Is there anyone that can confirm whether I need/not need UK transit visa?

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


Iam making a basic calculator with 3 functions. Iam using a Scanner-utility to help me interact with the calculator. You enter the first number, then it saves it to a variable, You enter a second number and that is also saved to a variable. Then after that it asks you what you want to do with the numbers. You can choose between Multiply, Add, Subtract. But none of them seem to work, and i dont know why, but iam guessing that the String that is inserted after the question isnt saved or maybe iam using wrong method.   import java.util.Scanner;  public class MainClass {     private static final String Multiply = null;     private static final String Add = null;     private static final String Subtract = null;      public static void main(String[] args)     {         MainClass mainObject=new MainClass();         mainObject.Calculator();         }      public void Calculator()     {         double firstnumber;         double secondnumber;         double result;         String word1="Multiply";         String word2="Add";         String word3="Subtract";          Scanner scan=new Scanner(System.in);         System.out.println("Enter first number");         firstnumber=scan.nextInt();         System.out.println("Enter second number");         secondnumber=scan.nextInt();         System.out.println("What do you want to do?");         String operator=scan.next();          if(operator==word1)         {             result=firstnumber*secondnumber;             System.out.println(result);           }         else if(operator==word2)         {             result=firstnumber+secondnumber;             System.out.println(result);         }         else if(operator==word3)         {             result=firstnumber-secondnumber;             System.out.println(result);         }     } }

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?


How to prove the following :   Given $(X, \tau)$ a topological vector space on $\mathbb{R}$,  If {0} is closed then $\tau$ is separated.  Thank you.

On page 146, James Munkres' textbook Topology(2ed),  Show that $G$ (a topological group) is Hausdorff. In fact, show that if $x \neq y$, there is a neighborhood $V$ of $e$ such that $V \cdot x$ and $V \cdot y$ are disjoint.  Noticeably, the definition of topological group in Munkres's textbook differs from that in .  A topological group $G$ is a group that is also a topological space satisfying the $T_1$ axiom, such that the map of $G \times G$ into $G$ sending $x \times y$ into $x \cdot y$ and the map of $G$ into $G$ sending $x$ into $x^{-1}$, are continuous maps.


I'm using Windows 10 Home 64-bit. I have a program that was manually deleted from the “Program Files” folder, but it still shows it in the “Programs and Features” list, and when I click uninstall it shows an error message saying that Windows cannot find the uninstaller:    I've seen many other s in this SE saying that from the registry editor I should go to:  HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall   for me, it was in  HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows\CurrentVersion\Uninstall\   then go the key to be deleted by locating the key name created by the program, then finally delete the selected registry key and its values.  Where that worked, and no more issue in the add or remove programs panel, but I pressed Ctrl+F and typed in the 'application's name' and tried to search for in the registry editor, so I found many results    and in those locations for example:  HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\LowRegistry\Audio\PolicyConfig\PropertyStore\c24b033a_0   ,  HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Compatibility Assistant\Store   ,  HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Layers   Should I worry about these values? would they have been removed if I had used the proper way of uninstallation? should I manually delete them? is their existence necessary? or should just ignore them?

So I'm cleaning out an old computer, and several of the programs it thinks it has were actually installed on an old drive, that's now gone. For some of them, it prompts to get rid of them because it can't find the drive, so that's all well and good.  But, for LibreOffice and a couple of others, it tries to run the LibreOffice Uninstaller, and only quits with a fatal error when the LibreOffice uninstaller can't find the drive.   The difference here is that in the first case, Windows can't even find the drive with the uninstallers on them, so it prompts to remove them; but in the second, its found the uninstallers on the local disk somewhere and is trying to run them, prompting a fatal error when the uninstaller can't find them.  What should I do here? How can I remove what's left of these programs/erase their names from the family tree?  Thanks!  evamvid


Definition: A topological space $X$ is called Hausdorff  space if for each $x_1,x_2 \in X$ (they are distinct) we can always find neighborhoods $U_1,U_2$ of $x_1,x_2$  such that $U_1 \cap U_2 = \varnothing $.  Is this definition equivalent to say that the following set   $$ \mathcal{D}  = \{ (x,x) : x \in X \}$$  is closed in $X \times X $ ??  Im having difficulties seeing why this istrue. Any help would be greatly appreciated.

Let $X$ be a topological space. The diagonal of $X \times X$ is the subset $$D = \{(x,x)\in X\times X\mid x \in X\}.$$   Show that $X$ is Hausdorff if and only if $D$ is closed in $X \times X$.   First, I tried to show that $X \times X \setminus D$ is open using the fact that $X \times X$ is Hausdorff (because $X$ is Hausdorff), but I couldn't find an open set that contains a point outside $D$ and is disjoint to it...


I just upgraded a cloud server to 14.04 and grub2 going to a grub rescue prompt on boot.  I have attempted to follow the instructions here:   But the system will not boot.  I can do a ls / and it displays the /boot directory.  The root partition appears to be set to the correct drive.  When I do a insmod normal it gives me error: file not found  I am not even seeing a linux.mod or normal.mod files in my grub directory.  I am thinking that the grub install may have failed.  What steps would be recommended to rescue this server?  Again this is on a vmware esx system so booting from a cd is going to be quite complicated.  What files should I have in the grub and boot folder?  What insmod command should I be running to set the kernel and boot commands?

I installed Windows 7, which ate Ubuntu's boot file. When starting up the computer, it now goes straight to Windows, without giving me the option of booting Ubuntu.   How can I get Ubuntu back?


In the preamble of the main.tex file I've written \renewcommand{\exp}[1]{ \exp \left( {#1} \right) } so that the math function \exp automatically includes the round brackets. In the file I wrote simply $ \exp{qV/kT} $. When I compile with pdflatex I get an error that says: TeX capacity exceeded, sorry [input stack size=5000] $ \exp{}. What does that mean?  I'm on Win7, TEXLive2013, TexStudio 2.6.6.  From the log file:    (./cap7_formule.tex  ! TeX capacity exceeded, sorry [input stack size=5000].  \exp #1-> \exp \left                        ( {#1} \right )   l.2 $ \exp{}          $  If you really absolutely need more capacity,  you can ask a wizard to enlarge me.

I'd like to "add to" an existing command by writing something like  \renewcommand{\somecommand}{\begin{something}\somecommand\end{something}}   but (not surprisingly) I get errors about being "too deeply nested".  Is there a way to take an existing command, add to it (by appending or prepending additional commands or text), and then have that "augmented" command replace the existing command?


I think the question itself is self-explanatory. But I will just elaborate on it. I already had Sublime Text 3 installed on my Ubuntu, and then I installed the beta version of Sublime Text 4. I downloaded the .deb package for Sublime Text 4 and then ran the command sudo dpkg -i sublime-text_build-4101_amd64.deb. After installation, I realized that it might override my current one. I looked up and found there was exactly two software with the same name and icon. Now when I am uninstalling by using the command sudo apt-get remove sublime-text, there is only one of them. Then I ran this command to get the details of the package apt-cache show sublime-text and this is the output: Package: sublime-text Status: install ok installed Priority: optional Section: editors Installed-Size: 47906 Maintainer: Sublime HQ Pty Ltd <support@sublimetext.com> Architecture: amd64 Version: 4101 Depends: libgtk-3-0 Description: Sublime Text is a sophisticated text editor for code, markup and prose Description-md5: ### Build-Depends: libgtk-3-0  Package: sublime-text Priority: optional Section: editors Installed-Size: 34033 Maintainer: Sublime HQ Pty Ltd <support@sublimetext.com> Architecture: amd64 Version: 3211 Depends: libgtk-3-0 Filename: files/sublime-text_build-3211_amd64.deb Size: 9835156 MD5sum: ### SHA1: ### SHA256: ### SHA512: ### Description: Sublime Text is a sophisticated text editor for code, markup and prose Description-md5: ###  So it shows there are two versions. How do I uninstall any one of them? From  I tried apt-cache policy sublime-text and this is the output: sublime-text:   Installed: 4101   Candidate: 4101   Version table:  *** 4101 100         100 /var/lib/dpkg/status      3211 500         500 https://download.sublimetext.com apt/stable/ Packages   Output for snap list | grep -i sublime: sublime-text       3211                        97     latest/stable    snapcrafters  classic  [Solved] One of the Sublime Text was installed using apt and the other with snap. So I uninstalled the snap one with the command sudo snap remove sublime-text

I've discovered that I have two different version but same package installed. For example the following is the two linux-firmware installed. Package: linux-firmware Architecture: all Version: 1.187.10 Multi-Arch: foreign Priority: optional Section: misc Origin: Ubuntu Maintainer: Ubuntu Kernel Team <kernel-team@lists.ubuntu.com> Bugs: https://bugs.launchpad.net/ubuntu/+filebug Installed-Size: 545755 Provides: atmel-firmware Conflicts: atmel-firmware Breaks: linux-firmware-raspi2 (<= 1.20190819-0ubuntu2), linux-firmware-snapdragon (<= 1.2-0ubuntu1) Replaces: atmel-firmware, linux-firmware-snapdragon (<= 1.2-0ubuntu1), linux-restricted-common Filename: pool/main/l/linux-firmware/linux-firmware_1.187.10_all.deb Size: 102768040 MD5sum: 819c7933a41766c75fb90fdf43424660 SHA1: faed33f1f9914d92a35bc15cdad854f10af42639 SHA256: 758bbb4d01c38186f26fd67fb35f624c66d559fab7c0269222efe901ba98dd53 SHA512: d82df37e09acf1e1953d497d0781c336cc476d495509a09dbeade152923af920878589d2960f7e078cc4226563ae3d801147fca32497f59445533db8682a72a4 Description-en: Firmware for Linux kernel drivers  This package provides firmware used by Linux kernel drivers. Description-md5: 7a047bff9e44dce458a300976c12f9da Task: ubuntustudio-desktop-core, ubuntustudio-desktop  Package: linux-firmware Architecture: all Version: 1.187 Multi-Arch: foreign Priority: optional Section: misc Origin: Ubuntu Maintainer: Ubuntu Kernel Team <kernel-team@lists.ubuntu.com> Bugs: https://bugs.launchpad.net/ubuntu/+filebug Installed-Size: 522910 Provides: atmel-firmware Conflicts: atmel-firmware Breaks: linux-firmware-raspi2 (<= 1.20190819-0ubuntu2), linux-firmware-snapdragon (<= 1.2-0ubuntu1) Replaces: atmel-firmware, linux-firmware-snapdragon (<= 1.2-0ubuntu1), linux-restricted-common Filename: pool/main/l/linux-firmware/linux-firmware_1.187_all.deb Size: 98718284 MD5sum: b9d9ab13f41f316a33f406d5145939ce SHA1: 875ed1bb7f9738965cc5edcb435237812fb2fa4b SHA256: cb27d20f8a11ddd89ca4d0de9f6c2b3abf6266a1005f774ec8b11fc1983a7893 Description-en: Firmware for Linux kernel drivers  This package provides firmware used by Linux kernel drivers. Description-md5: 7a047bff9e44dce458a300976c12f9da Task: ubuntustudio-desktop-core, ubuntustudio-desktop  As you can there are two versions: Version: 1.187.10 Version: 1.187 Can I remove one ? For example 1.187 ?


Supposed I have written a program, and I want to make sure that its code will not be changed (for now, let's assume we are using an interpreted / scripting language, so "just compile it" is not a valid answer).  So I would like to detect if someone changes the code. How can I do this reliably?  The most obvious way is to hash the code, put the hash into the code, and verify it - but of course this does not work, as it is pretty easy to simply rehash the code. You would have to know the hash in advance and put it into it while calculating the hash, but this is a chicken-egg problem, obviously.  Are there any other options that are reliable?

I need to write a small program that can detect that it has been changed. Please give me a suggestion!  Thank you.


Let $f(x)=x^4+ax^2+b \in K[x]$ (With char $K\neq 2$) be irreducible with Galois group $G.$  If $b$ is not a square in $K$ and $b(a^2-4b)$ is a square in $K$, then $G \cong \mathbb{Z}_4$.  My attempt:  I know if $f$ (irreducible) separable quartic polynomial with Galois group $G$. Let $\alpha, \beta, \gamma$ be the roots of the resolvent cubic of $f$ and let $m=[K(\alpha, \beta, \gamma):K]$ then  $m=2\Leftrightarrow G\cong D_4, \text{or } G\cong \mathbb{Z}_4$; in this case $G\cong D_4$ if $f$ is irreducible over $K(\alpha, \beta, \gamma)$ and $G\cong \mathbb{Z}_4$, otherwise.  So the resolvent cubic is  $$h(x)=x^3-2ax^2+(a^2-4b)x=x(x^2-2ax+(a^2-4b))$$ then $\alpha=0$, $\beta=a+\sqrt b$, $\gamma=a-\sqrt b$ since $b$ is n ot a square in $K$ we can conclude $K(\alpha, \beta, \gamma)=K(\sqrt b)$ then $m=2$ but I have some troubles to proof $f$ is reducible over $K(\sqrt b)$  Futhermore if neither $b$ nor $b(a^2-b)$ is a square in $K$ then $G\cong D_4$... in this case $f$ need to be irreducible over $K(\sqrt b)$ but I have troubles here too :(  My main question is how can I prove $f$ is reducible/irreducible over $K(\sqrt b)$ thanks :).  EDIT: To decide if $f$ is irreducible over $K(\sqrt b)$ we set up a hypothetical factorization $$f(x)=(x^2+px+q)(x^2+rx+s)$$ and read off the algebraic conditions imposed on the coefficients: $$r+p=0, \ ps+qr=0,\ qs=b , \ s+q+pr=a$$ Therefore $r=-p$, $s=q=\pm\sqrt b$, $p=\sqrt{\pm2\sqrt b -a}$ and $r=-\sqrt{\pm2\sqrt b -a}.$ Then $$f(x)=(x^2+(\sqrt{\pm2\sqrt b -a})x+\sqrt b)(x^2-(\sqrt{\pm2\sqrt b -a})x+\sqrt b)$$ Any suggestions to continue demonstrating the irreducibility/reducibility of $f$?

The following facts are standard: an irreducible quartic polynomial $p(x)$ can only have Galois groups $S_4, A_4, D_4, V_4, C_4$. Over a field of characteristic not equal to $2$, depending on whether or not the discriminant $\Delta$ is a square and whether or not the resolvent cubic $q(x)$ is irreducible, we can distinguish four cases:   If $\Delta$ is not a square and the resolvent cubic is irreducible, then the Galois group is $S_4$. If $\Delta$ is a square and the resolvent cubic is irreducible, then the Galois group is $A_4$. If $\Delta$ is a square and the resolvent cubic is reducible, then the Galois group is $V_4$. If $\Delta$ is not a square and the resolvent cubic is reducible, then the Galois group is either $D_4$ or $C_4$.   How can we resolve the ambiguity in the last case? For $p$ a monic polynomial in $\mathbb{Z}[x]$, I know the following approaches:   In the simplest cases one can work directly with the splitting field. But this is rare, although it can work if $p = x^4 + ax^2 + b$ for some $a, b$.  If $p$ has two complex roots (equivalently, if the discriminant is negative), there is a transposition in the Galois group, so the Galois group is $D_4$. If $p$ factors as the product of two linear factors and an irreducible quadratic factor modulo a prime, there is a transposition in the Galois group, so the Galois group is $D_4$.    In practice, the last two often work to identify a Galois group of $D_4$ (and in principle it must eventually work by the Frobenius density theorem). But I don't know a corresponding practical way to identify a Galois group of $C_4$. There is a criterion due to Kappe and Warren which I learned about from one of Keith Conrad's expository notes . However, in an upcoming exam I'm taking, I'll only be able to cite results proven in the course, and this criterion isn't one of them.   So what are my other options in general?


I am well aware of the fact that the template function basically gets compiled at the point when there is a specific invocation. But in this question I am looking for something different.  I have the following source files :  a.cpp :  template <class T> void g(T x) {     cout<<x<<"  g#1\n" ; } void f() ; main() {     g(10) ;     g('c') ;     f() ; }   b.cpp :  template <class T> void g(T x) {     cout<<x<<"  g#2\n" ; } void f() {     g(11) ; }   Now when I compile the code as :  g++ a.cpp b.cpp   all the three calls to g (2 in main and one in function 'f') are resolved via the template function defined in a.cpp.  But when I compile the code as :  g++ b.cpp a.cpp   the call g(10) in main and g(11) in function 'f' are resolved via the template function defined in b.cpp while the call g('c') in main is resolved via the template function defined in a.cpp  Of course if the template function defined in either of the two files is removed there is a compiler error reported by that particular file.  Can someone please provide an explanation for all these observations  In particular I want to know what kind of function call resolution is taking place during object file generation a.o and b.o. My query is as to how is the call resolved at compile time, i.e when I say :  g++ -c a.cpp   and  g++ -c b.cpp   and then what happens when I say :  g++ a.o b.o

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I'm using a map service which shows points for oil and gas wells.  It's useful to view them in ArcMap, but what I'd really like to do is be able to export them for use in another program, such as AutoCAD.    I don't have the option to right-click and export any of the layers.  I can't select the layers or view an attribute table.    Is this typical behavior with a map service, or is there some way I can export these points (with attributes) to a separate layer?  I'm using ArcMap 10.2 (Basic).  The map service is located .

Looking at this information page for a dataset hosted on esri.com:   Trying to figure out how I can get access to the raw data (either raw lat/lng coordinates or SHP).  It looks like the data is available, I just can't figure out how to pull it from this interface.


Is It normal to keep log file larger than data file?  I know why my log file is large, it is because I have a huge modification and locking occurred on a specific time, and caused my log file to be large.. as i'm using log shipping, I normally take log backups every 10 minutes.  What I'm asking is "Is it normal to see Log file larger than data file as my data file is about 7,216 GB and my log file is about 9,930 GB?" I'm afraid there is a standard ratio between log and data file? I don't want to shrink my log file because I have enough space on my hard disk.

how I can shrink tempdb log file when reaching a specific size?? I'm scheduling job to shrink tempdb but still I face a problem of disk space due to tempdb is full!


I purchased a Canon SX50 and immediately found I enjoyed photography. It made me happy. Anyway, I am now fortunate enough to be able to buy myself a camera, and I want to make the switch to SLR. I like photographing the following... Wildlife My pets (reptiles)  My child - as he darts about the garden (sports mode?) Loved getting shots of the moon (but feel a lens capable of these shots would be VERY costly) Weather - Lightning - Heavy Rain etc Landscapes Moving water  So, my next question is, would you choose Canon or Nikon, and what models would you go for. Although I am new to photography, I really want to develop myself, which is why I'm thinking go for a high end model so I don't need to upgrade any time as this will probably be the only ever time I have such funds - So I need to choose wisely.  Please please please help...I'm so tired from reading heaps of threads and reviews all night, every night :/  Thanks

I am thinking of buying a digital SLR camera. What things should I be looking for?


Suppose $a$ is a positive integer which is coprime to 10. Show that $$a^{2001} \equiv a \pmod {1000}$$   I know it has something to do with the Fermat-Euler theorem.   $\phi(1000) = 400$ and $a^{400}\equiv 1 \pmod {1000}$  However, I do not know how to proceed from here to show the congruence

I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great.


There's a bunch of symbolic links in /dev/block directory. And I figured out that they're pointing block device files in /dev. I wonder meaning of their names(8:0, 8:1, 11:0, 11:1, ...)

file /dev/* prints the description of a bunch of files as "block special (M/N)" and "character special (M/N)", where M and N are numbers. For example:  $ file /dev/null /dev/null: character special (1/3)   man file doesn't seem to document these, but refers vaguely to man stat, which seems to refer to these as major and minor device types. apropos 'device type' finds nothing. So what do these numbers mean?


I know that torque will cause an object to rotate about its centre of mass. I am curious why this is so.  Suppose we have a string of particles that are held in a line by electromagnetic forces of attraction such that they resemble a rod. The rod is floating in space. If we were to apply a perpendicular force at one end of the rod, it should start rotating about its centre of mass.  As such: Why does the object rotate about its centre of mass? I know that this is intuitive if there is a pivot supporting the centre of the rod. However, in this case there isn't, yet the object still behaves as though it is pivoted at the centre.  Why are the particles at both ends of the rod accelerating in opposite directions? If a perpendicular force was applied at one end of the rod, shouldn't the rod experience translational motion, as though it is being dragged forward by the end where the force was applied?  More specifically, I would like to know how the individual particles in the rod are "pulling and pushing" each other when the rod is rotating.

Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis which is perpendicular to the force and which goes through the center of mass.  What is the proof of this?


For example I have a list of dates in A2 through A31 (1st April to 30th April) and want to count the number of weekdays.  In B2 to B31 I could use =WEEKDAY(A2,2)<6 to give true or false. Then separately  count the trues.  Is there anyway to do it all in 1 cell with something similar to =COUNTIF(A2:A31,WEEKDAY(A2,2)<6)?

I have column with dates in column U. I changed them to "ddd" format, so now they are Mon, Tue etc.   I am trying to count how many times Mon is in cells between cell U2 and U1048576. I tried =COUNTIF(U2:U1048576,Mon) and =COUNTIF(U2:U1048576,"Mon"). Result is always 0. I tried same thing but searching for a number and it works. How do I do same thing for weekdays ?


I have a fresh installation of Ubuntu 18.10. Using the disc management tools in Windows I was able to shrink the volume and give myself 200G for Ubuntu.   I am trying to mount the Windows partition so that I can place my music (abt 240G) and my photos (abt 400G) on the Windows partition and have full access to all the files. So far, even when using the examples below, "Permissions" says I have full access, yet I cannot change anything on that partition.  Using the examples in:    I have edited my /etc/fstab:       # Example:     # Windows Partition - targetted for /media/win7     # UUID=UUIDOFPARTITION  /media/win7    ntfs-3g     defaults,locale=en_US.utf8,windows_names,umask=7000,uid=1000,gid=1000,user  0   0     #     # first solution:     # UUID=82B86F5AB86F4C2B /Windows ntfs-3g defaults,local=en_US.utf8,windows_names,umask=7000,uid=1000,gid=1000,user 0 0     # The above did not work.      #     # second solution:     # Example:     # UUID=0123456789ABCDEF    /mnt    ntfs-3g    rw,exec,async,auto,user,locale=en_US.utf8,windows_names,umask=7007,gid=654    0    0     #      # My next solution:     # UUID=82B86F5AB86F4C2B /Windows ntfs-3g rw,exec,async,auto,user,locale=en_US.utf8,windows_names,umask=7007,gid=1001, 0 0     UUID=82B86F5AB86F4C2B /Windows ntfs-3g rw,exec,async,auto,user,locale=en_US.utf8,windows_names,umask=7007,uid=1000,gid=1001, 0 0   This did not result in being able to read and write to the NTFS partition on the single hard drive. I tried with and without the uid=1000. I created the group and added myself to 'ntfs-access' with gid="1001" (quotes removed).

Why is everybody keep mentioning to disable Fast Boot on Windows 8 if you have installed alongside Ubuntu? Is it something that is recommended only for UEFI machines or is it a suggestion for Legacy BIOS machines as well? Is it because it makes the Windows partition inaccessible from Linux or there is another more serious reason to disable it?


Let $A_n$ be a sequence of independent events with $$lim_{n \to \infty}P(A_n)=0.$$ Suppose that  $$\sum_{n=1}^{\infty}P(A_n^c \cap A_{n+1}) < \infty.$$ Will the events $A_n$ cease to occur eventually with probability one?  I think that the question is asking to show that  $$P(A_n\ i.o.)=0$$ And I tried to prove that $$\sum_{n=1}^{\infty}P(A_n)<\infty$$ So that I can use the Borel-Cantelli Lemma.  But I did not get nowhere. I am kind of confused about all these operations includes limits, sets, and interplays between them, as well as the $limsup$ and $liminf$ stuff. Hope someone could help me.

Practice problem for exam:     Let ${A_n}$ satisfy $\sum\limits_{n=1}^\infty P(A_n \cap A^c_{n+1}) < \infty$ and $\lim\limits_{n\to \infty} P(A_n) = 0$.  Show that $P(\lim \sup A_n) = 0$.    I can see that it is sufficient to show that $P\left(\sum\limits_{n=1}^\infty A_n\right) < \infty$ and then apply the Borel-Cantelli lemma, but I am having trouble showing this from the information given.  I see an almost identical problem here: , however the hint there is not enough for me to make headway, and this problem is also different in which term gets the complement inside the first sum.


Alright so, it follows the curve but they wont follow in line, they will all rotate at the same time not following the line, the primary will follow it but the rest in the array will copy the first and not follow the array correctly.

What order are these modifiers applied in? I would think the Armature would be applied first, followed by Lattice. Or is it the other way around?