I'm making a game engine and got stuck at one point.  g.drawImage(BPaint.g2dToImage(bgo.render()), 100, 100, null);   does NullPointerException, even though I check EVERYTHING that connects to Image parameter. The code is used in paintComponent(Graphics) method, written below.  @Override public void paintComponent(Graphics g){     g2d = (Graphics2D) g;     g2d.setColor(Color.BLACK);     g2d.fillRect(0, 0, getWidth(), getHeight());     BWindow current = BWindow.getCurrentBWindow();     if (current != null) {         for (BGO bgo : current.getBGOs().getBgos()) {             g.drawImage(BPaint.g2dToImage(bgo.render()), 100, 100, null);         }     } }   This is pretty forward, but you may be stuck while reading at 2 methods - bgo.render() and BPaint.g2dToImage.  BGO is game object, which has Graphics2d method  public Graphics2D render(){     if (bgsu == null) {         return sprite.getGraphics();     } else {         return bgsu.getRule();     } }   Ignoring BGSU, because it is null, and not used, sprite is an object containing Graphics2D that I want to get. Now to BPaint.g2dToImage(Graphics2D), a method turning Graphics2D to Image.  public static Image g2dToImage(Graphics2D g){     JLabel j = new JLabel();     j.paintAll(g);     return j.createImage(null); }   After checking everything that should not be null, I don't really know the cause. I hope you can tell me. Below is full stacktrace of NPE. (line 34 is line of method in beginning)  java.lang.NullPointerException at sun.awt.image.ImageRepresentation.startProduction(ImageRepresentation.java:732) at sun.awt.image.ImageRepresentation.drawToBufImage(ImageRepresentation.java:807) at sun.java2d.pipe.DrawImage.copyImage(DrawImage.java:1021) at sun.java2d.SunGraphics2D.drawImage(SunGraphics2D.java:3318) at sun.java2d.SunGraphics2D.drawImage(SunGraphics2D.java:3296) at bdk.bjgl.components.BGraphics.paintComponent(BGraphics.java:34) at javax.swing.JComponent.paint(JComponent.java:1056) at javax.swing.JComponent.paintToOffscreen(JComponent.java:5219) at javax.swing.RepaintManager$PaintManager.paintDoubleBuffered(RepaintManager.java:1572) at javax.swing.RepaintManager$PaintManager.paint(RepaintManager.java:1495) at javax.swing.RepaintManager.paint(RepaintManager.java:1265) at javax.swing.JComponent._paintImmediately(JComponent.java:5167) at javax.swing.JComponent.paintImmediately(JComponent.java:4978) at javax.swing.RepaintManager$4.run(RepaintManager.java:824) at javax.swing.RepaintManager$4.run(RepaintManager.java:807) at java.security.AccessController.doPrivileged(Native Method) at java.security.ProtectionDomain$1.doIntersectionPrivilege(ProtectionDomain.java:75) at javax.swing.RepaintManager.paintDirtyRegions(RepaintManager.java:807) at javax.swing.RepaintManager.paintDirtyRegions(RepaintManager.java:782) at javax.swing.RepaintManager.prePaintDirtyRegions(RepaintManager.java:731) at javax.swing.RepaintManager.access$1300(RepaintManager.java:64) at javax.swing.RepaintManager$ProcessingRunnable.run(RepaintManager.java:1720) at java.awt.event.InvocationEvent.dispatch(InvocationEvent.java:311) at java.awt.EventQueue.dispatchEventImpl(EventQueue.java:756) at java.awt.EventQueue.access$500(EventQueue.java:97) at java.awt.EventQueue$3.run(EventQueue.java:709) at java.awt.EventQueue$3.run(EventQueue.java:703) at java.security.AccessController.doPrivileged(Native Method) at java.security.ProtectionDomain$1.doIntersectionPrivilege(ProtectionDomain.java:75) at java.awt.EventQueue.dispatchEvent(EventQueue.java:726) at java.awt.EventDispatchThread.pumpOneEventForFilters(EventDispatchThread.java:201) at java.awt.EventDispatchThread.pumpEventsForFilter(EventDispatchThread.java:116) at java.awt.EventDispatchThread.pumpEventsForHierarchy(EventDispatchThread.java:105) at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:101) at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:93) at java.awt.EventDispatchThread.run(EventDispatchThread.java:82)


In  one can find the following symbol:    I have tried to Detexify it to no avail. What is this symbol/font?  It appears many times in the following excerpt:

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


When creating an android game for example space invaders. How big would the sprites have to be? The Enemy ships and player ship and boss ships. So they fit on the android phone and is playable. I'm confused between resolution and this.    Thanks.

For instance, the Motorola Droid is as wide as the G1, but has more height.  Should I try to spread the UI out across the extra height found on the Motorola Droid?  How do others handle this problem?  I'm not using OpenGL, but a SurfaceView for a 2D game.


I am using Windows 8.1 Pro and have a drive that I think may be dying, so I ran 4 different repair tools on it. And now WD Data Lifeguard shows no disk errors at all after a full test. I’m still concerned about the stability of the disk, but I would like to try using it again with the knowledge that any data on it could be destroyed at any time.  Is there a way I can monitor the disk access reads/writes or whatever information I would need to be able to tell if the hard disk drive is in fact going bad? I don’t mind having a program run in the background to monitor as I’ll likely only be using it for a few weeks at most.

I've seen programs in the past that were able to check the SMART status of a hard disk drive but it wasn't easy for me to find. Also, I think I had to boot into the CD in order to check on it. What is your preferred method for getting this data to hopefully preempt any disk failures?


We are currently in the process of creating Hardware-Test-Boards where we want to "plug-in" our PCB's and do a couple of tests. Our Boards have a rather complicated shape and are mostly surface mounted. Thus we have a hard and error-prone time to figure out, how to automate our tests due to connectivity issues.  Recently I found something on the Omega2s that would perfectly fit our needs.    The HDK of the Omega2s features those nifty little springs to plug in the sourface-mounted Omega2s which are holding it snug in place.  But we are unable to find those Springs on e.g. Mouser and Digikey.   How are they called? Where do I find some?  (We already have a footprint, just one hole and a long-hole).

Here's a module with castellated pads attached to an eval board:  (source: ) Looking closely at the wires interfacing with the castellated pads, they're clearly soldered to the eval board. However, they don't look like they're soldered to the module, but rather they're being pressed against the pads with the tension in the wire. It also looks like the free end of the loops are protruding down into a channel cut in the PCB. Do these kind of connectors/metal loops have a name?


I am designing a web application with plug able component architecture (plugins). My requirement is to add new plugin jar (classes) into application without restarting the application, it should be dropped in web application's lib or plugin directory and application should able to pick it up.  I tried this with tomcat server but it can not load the jar file dropped into its lib directory once its started.  Can anyone suggest a best way to do this ?

Why is it so hard to do this in Java? If you want to have any kind of module system you need to be able to load JAR files dynamically. I'm told there's a way of doing it by writing your own ClassLoader, but that's a lot of work for something that should (in my mind at least) be as easy as calling a method with a JAR file as its argument.  Any suggestions for simple code that does this?


I have a limit, $\sqrt x$, in which I consider only values of $x\in\mathbb{R}$. If I then consider values of $x$ approaching zero, I know that:  $$\lim_{x\rightarrow 0^{-}}\sqrt x$$  does not exist, and that:  $$\lim_{x\rightarrow 0^{+}}\sqrt x$$  does exist, so I can then conclude that the limit does not exist and I understand that, but does this mean that the limit is not well defined as $x$ approaches $0$ as well?   Thanks.

What is the limit of $\sqrt x$ as $x$ approaches $0$? I asked a few people and they all gave me two different answers. Some said that the limit is $0$, and other say that the limit is not defined because the right-hand limit is $0$ while the left-hand limit is undefined. I'm confused. please help!!


I've been getting alot of segv crashes in gnome-shell and although the apport window has alot of info, it's not very user friendly (window is really small, no way of searching, no way of saving a copy to text file etc).   Is there a way I can access the information available to apport directly from the terminal? Does gnome-shell save traceback logs somewhere?  I know there's a logfile for apport in /var/log but that log file doesn't offer nearly the same level of detail.

So, if there is some problem with my computer, be it hardware or software, what are the major log files and where are they located?  Also, is there a generic location where log files of the other packages might be located?


Hi guys recently I got stuck with PHP preg_match_all(). I'm really bad on REGEXP, I had to find:  var nx = (100000 + x) * 23452;   with preg_match_all(), I do this:  preg_match_all('/var nx = (100000 + x) * (.*);/', $html, $token); return $token[1][0];   I want output like this on my array:  23452   Please anyone help me, with explanation will be appreciate. Thanks.

I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps?


By the definition of square root, we can take square root of $16$ as $\pm4$.  But in problems, why do we take $16^{\frac12}$ as $4$?  And also how can we say, if $a^m=b^n$ then $a=b^{m/n}$?  Because when we take $x^2=a$, we solve it as $x=\pm{a^{1/2}}$.

Why $f(x) = \sqrt{x}$ is a function (as I found in my textbook) since for example the square root of $25$ has two different outputs ($-5,5$) and a function is defined as "A function from A to B is a rule of corre- spondence that assigns to each element in set A exactly one element in B.", so $f(x) = \sqrt{x}$ is not a function?


General relativity states (in simplified vocabulary) that mass curves the space-time, being gravity one of the observable effects of this curvature. Is there any theory or works starting on the premise: mass (particles) IS a curvature of the space-time ?

Can matter be described as the result of the curvature of space, rather than the curvature of space being the result of matter, and energy being the cause of the curvature of space?


Given that $x_n\geqslant 0$, $x_{n+1}\leqslant x_n+\dfrac{1}{n^2}$, prove this sequence converges. I want to prove by The monotone bounded convergence theorem. $$ 0\leqslant x_n=\displaystyle\sum_{i=1}^{n-1}(x_{i+1}-x_i)\leqslant\displaystyle\sum_{i=1}^{n-1}\dfrac{1}{i^2}<\dfrac{\pi^2}{6} $$ My question is how to prove the sequence is monotonous.

Let $x_n$ be a sequence of the type described above. It is not monotonic in general, so boundedness won't help. So, it seems as if I should show it's Cauchy. A wrong way to do this would be as follows (I'm on a mobile device, so I can't type absolute values. Bear with me.) $$\left|x_{n+1} - x_n\right| \leq \frac{1}{n^2}.$$ So, we have $$ \left|x_m -x_n\right| \leq \sum_{k=n}^{m} \frac{1}{k^2}$$ which is itself Cauchy, etc., etc. But, of course, I can't just use absolute values like that. One thing I have shown is that $x_n$ is bounded. Inductively, one may show $$ \limsup_{n \to \infty} x_n \leq x_k + \sum_{k=n}^{\infty} \frac{1}{k^2},$$ although I'm not sure this helps or matters at all. Thanks in advance.  Disclaimer I've noticed that asking a large number of questions in quick succession on this site is often frowned upon, especially when little or no effort has been given by the asker. However, I am preparing for a large test in a few days and will be sifting through dozens of problems. Therefore, I may post a couple a day. I will only do so when I have made some initial, meaningful progress. Thanks.


I love the interesting tags feature on the site.  It really helps me see questions on the site that I can answer.  I do wish that I had a bit more power though.  I would like to be able to set up and relationships for interesting tags.    For example, I might be interested in questions tagged  and .  I can't answer all C# questions, and I can't answer all regex questions, but I could probably answer almost all  questions.

There are many tags that can have multiple uses.  This is fine and good.  However, it would help in finding questions that I can actually answer if there was a way to join tags for my Interesting Tags and Ignored Tags.  Here is an example to make it clearer:    Tags:  Generics and .Net    or  Tags: Generics and Java    The first one I can help with.  The second one I know very little about.  I know a bit about Java in general, so I don't want to add that to my ignore list, but I am not much help with a deep Java Generics issue.  This would also help some with categorization.  There are tags like [wpf-binding].  That tag is used because databinding can be for WPF or other things.  This leads me to tag my WPF Databinding questions with both (wpf-binding and databinding)  Anyway, I am not dying to have this feature, it just hit me as a good idea so I thought I would throw it out there.


I have installed a managed package that has some static resources along with other features. I want to include a static resource to my vf page, but i get an error message: "Error: Field $cscfga__Resource.jQuery_min does not exist. Check spelling" I declare the static resources as follows: <apex:includeScript value="{!$cscfga__Resource.jQuery_min}" /> <apex:includeScript value="{!$cscfga__Resource.cs_messaging}" />   And i have checked that spelling is correct. What could be going wrong?

Is it possible to access a static resource of a managed package in your local environment?  Thanks


We are asked to compute $\lim \limits_{n \to \infty} \displaystyle\frac{| \sum_{k=1}^n (-1)^k \sqrt{k}|}{\sqrt{n}}$  This appears to converge to $0.5$ by numerical evidence . I tried squeeze theorem but to no avail.

I'm trying to show that $$\lim_{n\to \infty} x_n=\lim_{n\to \infty}\frac{1}{\sqrt n}\left|\sum_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}.$$ Assuming $\lim\limits_{n\to\infty} x_n=x$ exists, we have  $$x_{2n}=\frac{\sqrt{2n-1}(-x_{2n-1})+\sqrt {2n}}{\sqrt {2n}}$$  Letting $n\to \infty$,  $$\quad \quad x=-x+1$$ $$x=\frac{1}{2}$$  But I'm stuck on proving the existence of $\lim x_n$. Any idea?    Update: I just solved the problem using sandwich theorem + integral test. Still, I would like to see a continuation of my initial idea, i.e. proving     $\{x_{2n}\}$ is monotonically increasing (similarly, $\{x_{2n+1}\}$ is monotonically decreasing)


This is pretty weird now. I am trying to kill a process by using its pid but it is not working at all.  root@machineA:/home/david# ps aux | grep modelling david  5075  0.0  0.0 1285420 29404 ?       Dl   21:05   0:01 /opt/modelling/bin/http root   8730  0.0  0.0   8096   936 pts/4    S+   22:43   0:00 grep --color=auto modelling   Below is the way I am kiiling the process.    root@machineA:/home/david# kill -9 5075   And then if I do the ps again. I can see the same result back again.  root@machineA:/home/david# ps aux | grep modelling david  5075  0.0  0.0 1285420 29404 ?       Dl   21:05   0:01 /opt/modelling/bin/http root   9062  0.0  0.0   8100   936 pts/4    S+   22:44   0:00 grep --color=auto modelling      Does anyone know what is happening? This was working fine earlier and it has started happening few hours back and I am not sure what's wrong?     Update:-  I did top and it is showing as D instead of Z which is uninterruptible sleep  5075 david  20   0 1255m  28m  13m D    0  0.0   0:01.09 http

I have a process I can't kill with kill -9 <pid>. What's the problem in such a case, especially since I am the owner of that process. I thought nothing could evade that kill option.


I performed a git commit command and it gave me the following reply:  7 files changed, 93 insertions(+), 15 deletions(-) mode change 100644 => 100755 assets/internal/fonts/icomoon.svg mode change 100644 => 100755 assets/internal/fonts/icomoon.ttf mode change 100644 => 100755 assets/internal/fonts/icomoon.woff   I know files can have user / group / other rwx permissions and those can be expressed as three bytes, like "644" or "755". But why is git showing six bytes here?  I've read the following articles but didn't find an answer:

I saw a code change at work, where the mode values were changed from 777 to 0777 to make nfs setattr work. What is the difference in the 2 values?


i have an object, which has multiple values. one of its field is timestamp. While creating the object, i have converted the input string to timestamp.  DATETIME_FORMAT = '%d-%b-%y %H.%M.%S.%f %p'  class CustomObject:     def __init__(self, input_data):         entry_list = [entry.strip() for entry in input_data.split(',')]         self.field_one = entry_list[0]         self.field_two = entry_list[1]         self.field_timestamp = datetime.strptime(entry_list[2], DATETIME_FORMAT)   There is list of CustomObject which I want to sort based on field_timestamp. How would i do that?   I was looking at sorted function but it takes in a lambda as an expression. In this case, i don't have an expression, i just have one field which i will be using to sort. how should it be done?

I've got a list of Python objects that I'd like to sort by an attribute of the objects themselves.  The list looks like:  >>> ut [<Tag: 128>, <Tag: 2008>, <Tag: <>, <Tag: actionscript>, <Tag: addresses>,  <Tag: aes>, <Tag: ajax> ...]   Each object has a count:  >>> ut[1].count 1L   I need to sort the list by number of counts descending.  I've seen several methods for this, but I'm looking for best practice in Python.


I have a string var x = 2019-02-14T21:06:06.400Z  Another string y = 2019-02-14T21:06:06.44500Z  I need to remove content after the dot i cant slice it because the dot might come after 4 or 5 or 6 or n characters

I have this string  'john smith~123 Street~Apt 4~New York~NY~12345'   Using JavaScript, what is the fastest way to parse this into  var name = "john smith"; var street= "123 Street"; //etc...


Im in holidays in Malaysia and it is god damn hot. You cannot leave your hotel/car and go out. All this because of the sun.  I we were to capture all the heat (solar panels, ...) would this help make the Earth cooler / fight global warming ?  Edit : see one of my comments, I mean use the heat to conduct some endothermic reactions (e.g solar panel -> electricity -> electrolyte)

I guess that energy will be used up and, at the end, will contribute to heat the earth, so I see no big differences...  please explain your point of view.


In the past days, I used VLC to watch video tutorials. But, occasionally, the video couldn't play correctly and had screen stuck problems. I thought that I perhaps needed to update my system and the software. So I used the command: sudo apt upgrade  trying to fix problem, but, unfortunately my computer also held those problems. The system and VLC are both on the last version. Last night, I used Ubuntu Software to remove VLC. And from some forums I found that I should run: $ sudo apt-get autoremove vlc $ sudo apt-get auto clean"  etc (because I wanted to uninstall it completely to reinstall later). But after uninstalling VLC, I am incapable of enabling it again. This the reason why I can't install VLC again. yann@yann-Matrimax-PC:~$ sudo apt-get install vlc [sudo] password for yann:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies: vlc : Depends: libgles1-mesa (>= 7.8.1) but it is not going to be installed or libgles1 E: Unable to correct problems, you have held broken packages. yann@yann-Matrimax-PC:~$ ^C   My system is Ubuntu 16.04 LTS, and I run VLC 2.2.5. Could you can help me to solve those troubles? Thanks :)

After upgrading from 10.04 to 12.04 I am trying to install different packages.  For instance ia32-libs and skype (4.0).  When trying to install these, I am getting the 'Unable to correct problems, you have held broken packages' error message.   Output of commands:  sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.   After running this:  sudo dpkg --configure -a foo@foo:~$ sudo apt-get install -f Reading package lists... Done Building dependency tree        Reading state information... Done 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.


$1+2+3.......$so on $ = -1/12.$ I have seen a few proofs of this result. And I hope most of you are familiar with them.   Why string theorist use this ambiguous result in string theory, when assigning a value to a divergent sum is not acceptable to many mathematician?  If this result is true; does it consolidate the belief that nature of ultimate reality cannot be perceivable by human mind.

This youtube video from Numberphile,   shows how the value is derived. In the video, one interviewee claims that "this result is used in many areas of physics". In the video, only string theory is mentioned.  Which areas of physics use or depend on the sum $$1 + 2 + 3 + 4 + 5 + 6+ 7+\ldots= -1/12?$$


I've been studying the EPA's procedures for calculating Method Detection Limits (MDLs) based on .   After calculating the MDL, they give the constants for calculating a confidence interval for the MDL      according   to the following equations derived   from percentiles of the chi square over degrees   of freedom distribution ($\chi^2$/df).      LCL = 0.64 MDL      UCL = 2.20 MDL    Based on an example at , I found that $\sqrt \frac{df}{\chi^2(\alpha/2, df)} $ and $\sqrt \frac{df}{\chi^2(1 -\alpha/2, df)} $ give the constants for the MDL limits.  I confirmed this using R with   # The EPA document anticipates a sample size of 7, or 6 df sqrt(6 / qchisq(.975, 6)) # 0.6443934 sqrt(6 / qchisq(.025, 6)) # 2.202066   I'm afraid I don't understand the derivation, however.  It seems to be a chi-squared variable divided by it's degrees of freedom would be the same as a chi-square variable divided by a constant, which has a Gamma distribution.  So I'm fairly certain I'm missing something obvious and would appreciate any help in understanding the derivation of the confidence interval for the MDL.

This is a very basic question. Why do we use a chi square distribution? What is the meaning of this distribution? Why is this the distribution used for creating a confidence interval for the variance?   Every place I google for an explanation just presents this a fact, explaining when to use chi, but not explaining why to use chi, and why it look the way it does.  Many thanks to anyone that can point me towards the right direction and that is - really understanding why I am using chi when I am creating a confidence interval for the variance.


One of my players is considering multiclassing warlock/cleric. I have not played warlocks or had other players use them so I am looking into the casting mechanics. After looking at other threads I think I have the idea down. Something like a warlock 1/cleric 5 would have the cantrips and 1 warlock slot that can cast at first level and the cleric would provide up to 3rd level spell slots. my confusion comes from  Pact Magic: If you have both the spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the spellcasting class feature, and you can use the spell slots you gain from the spellcasting class feature to cast warlock spells you know.  so they would be able to cast warlock spells up to 3rd level with the cleric 3rd level slot, as evident from answers to , but would they also be able to cast fireball (in the case of a light domain cleric) using their warlock slot but doing so at 1st level? If so how would this translate to an end game build? would the cleric then have the equivalent to 2 9th level slots? I am assuming this does not work this way and the initial build listed essentially just has a slightly expanded spell list and an extra 1st level slot that comes back on a short rest, but I just want to make sure I am not missing something so I can explain this fully in the future.

Can my player’s multiclass Warlock 1/Sorcerer 8 cast the higher level sorcerer spells from with their warlock pact magic spell slots?  My player argued that he could now cast his 4th level sorcerer spells with his level 1 warlock  spells slots. I think he interpreted pact magic as "highest spell slot possible",  so he figures that since he has 4th level spell slots, he interprets that the warlock spell slots are 4th level slots now too.


Is there a way to add "open as administrator", when I right-click on a folder, because there are some folders you cannot access graphically because that would need administrator privileges?

I want to have a root privileges on some directories. How can I do this?


;) I have a small problem... When creating a multi output device in the application "MIDI" on the mac, i don't have any problems at all. Now i want to make Videos (YouTube) and wanted to output the computer audio to the "Build in output" and to "Soundflower". It works fine, but the only problem is, that if i want to change the volume with the volume keys i can't because its locked (view Image).  So I went to google and searched for solutions and found the way to just change the volume on the different devices manually. But isn't there a easier solution? I just want to be able to change the volume with the keys again and use that multi output device.  Greetings  PS: please don' mind my english because i am from Switzerland... ;)

When creating either an Aggregate Device or a Multi-Output Device in Audio MIDI Setup and setting it as the default audio output device, the volume control is greyed out and locked at maximum intensity. Why is that and how can it be bypassed?


When I try to install any version of Wubi,appears message which asks  me to Burn DVD E. And no choice to change it,or reject. Regards, M.Shahbazov

Is there any Windows installer (wubi) for Ubuntu 14.04 LTS?  When I mount the .iso file with Daemon Tools and run wubi.exe, it just asks me if I want to reboot (I think that's useful only when the .iso  is burned on CD), so is there no "real" installation?


I've tried taking the log of both sides (but am left with $k\ln{x}=x\ln{k}$).

What are the roots of $$f(x) = x^a - a^x$$ for real $a > 0$?   Case 1: For $0 < a < 1$ there is 1 solution, $x=a$. Case 2: For $1\le a < e$ there are 2 solutions: $x=a$ and $[x>a]$. Case 3: For $a > e$ there are 2 solutions: $x=a$ and $[x < a]$.     if we let b = a^(1/a). x = b^^ [use mathematica for tetration] or using the basic operators,  x = b^(b^(b^...))...) for a > e, this solves for the non-simple root < a  but for a < e it solves for  x = a i am looking for a similar solution for a < e


Let $B$ be the set of all the upper bounds of the non-empty bounded subset $A\subseteq\Bbb R$. Prove that $\inf B=\sup A$.   I divided it into two areas ($\inf B>\sup A$, $\inf B<\sup A$) and tried to show a contradiction. Is it the right approach? How can I prove it?

Let $A$ be a nonempty and bounded below, and define $B= \{b\in \mathbb{R}: b$ is a lower bound for $A\}$. Show sup$B$ = inf$A$.   So far I have: Let $A$ be nonempty and bounded below. This implies $\exists l \in A, \forall a \in A, l\leq a$ and $l =$ inf$A$. Let $B = \{b\in \mathbb{R}: b$ is a lower bound for $A\}$ and let $M=$ sup$B$. This implies $\exists b\in B, \forall b \in B, b\leq M$. By definition of $B$, we know inf$A \in B$. Since $b\leq$ sup$B$, with sup$B$ the largest element in $B$, we have inf$A \leq M =$ sup$B$, so inf$A \leq$ sup$B$.  I realize I have to prove that sup$B \leq$ inf$A$ to get that sup$B$=inf$A$. I am having trouble doing so.   Part B: Use (a) to explain why there is no need to assert that greatest lower bounds exist as part of the Axiom of Completeness.


I hope I'm right in thinking this is the site where you post general computer-related problems...  A problem I have when playing games (since you won't be pressing multiple keys simultaneously anytime else) is that when I press and hold Up/Left keys together with another key, that last key fails to 'work' or it hinders the arrow keys and doesn't let them work. This doesn't happen with any other arrow key combination, e.g. Up/Right or Down/Left.  The weird thing is that same thing happens when I'm using WASD instead of the arrow keys! Meaning W+A+smth else doesn't work. Perhaps this problem is for all such sets of four keys.  If someone knows what my problem is, I'd appreciate the help. (My reflexes are fast so I can circumvent this obstacle, but it's quite annoying and totally unnecessary)

I hope I'm right in thinking this is the site where you post general computer-related problems...  A problem I have when playing games (since you won't be pressing multiple keys simultaneously anytime else), is that when I press up/left and then another key, it fails to 'register' as if that last key is never pressed. This doesn't happen when I'm pressing any other two arrow keys, e.g. down/left or up/right. The weird thing is that when I'm playing with WASD instead of the arrow keys, i still have this problem! Meaning W+A+another button doesn't work.  If anyone knows what I should, I'd appreciate the help. (My reflexes are fast and I can always circumvent this problem, but it's quite annoying and shouldn't exist to begin with!)


Let G be the group of 2*2 matrices [ a  b ; c  d] where a,b,c,d are integers modulo p, p is prime number, such that ad-bc≠0. G forms group under relative to matrix multiplication. What is o(G)? Let H be the subgroup of the G defined by H= { (a  b; c  d) €G | ad-bc=1} . What is order of H?  I got the direct formula for computation, but How can we get that relation or is there any simple way to do this??

I've just left an exam of algebraic structures, and one of the questions asked to compute the order of $SL_2(\mathbb{Z}/ 5\mathbb{Z})$ (the 2x2 matrices with determinant $1$ over the field $\mathbb{Z}/ 5\mathbb{Z}$). The answer should be $120$, and a friend of mine could achieve that, but by methods of raw counting. My question is: Is there a way to compute the order of $SL_2(\mathbb{Z}/ n\mathbb{Z})$ for all $n$?  OBS: Although $120=5!$, I believe this is purely a coincidence.


I need to draw 3D grid with nodes on it using Tikz. Moreover, would it be possible to construct it simply by 3 nested loops? So that I could mark some node by hollow circle and some with solid circle... The viewpoint is also important for visual clarity.    The linked duplicate have a lot of new command and setting a lot of macros. It should not be that complicated. I want to do it with basic instruction set so that code would remain easy to understand; and easy to recall...  The other difference is that only selected nodes will be marked with solid circle, not all the nodes. The above linked answer does not help in this regard either...

I need to draw a 3d isometric grid/lattice using tikz that is not visually confusing. It needs to be at least 6x6x6 but possibly bigger. I sort of would like to have it fade into the background or contracts in size as it goes into the screen. I will put small text nodes at each coordinate. For any example dots will suffice.  It is analogous to  except in 3D. The main issue is somehow figuring out how to make sure it is easily seen in 3D.


Is there a proof that the $n$-th root of $2$ is irrational for every $n \in \mathbb{N}$? Thanks.

Possible Duplicate:          Will every $n^{th}$ root of $2$ be an irrational number? If yes, how can I prove that?


I made a total mistake here. Anyway I ran chmod -R 777 /* and immediately regretted my decision.  I had to boot into single user mode to and ran chmod -R 755 /etc/* in order to login to the server.  The only problem is ssh now and obvious security issues.  How do I get SSH working again?

This is a  about File Permission and Why 777 is "destructive".   I'm not asking how to fix this problem, as there are a ton of references of that already on Server Fault (reinstall OS). Why does it do anything destructive at all?  If you've ever ran this command you pretty much immediately destroy your operating system. I'm not clear why removing restrictions has any impact on existing processes. For example, if I don't have read access to something and after a quick mistype in the terminal suddenly I now have access well... why does that cause Linux to break?


I know this might be an obvious question as we all know that the answers (beside $(x,y)=(1,1)$) are $(x,y)=(2,4)$ but the problem is, how is this exactly solved?  Tags might be inaccurate so feel free to edit my question at will.  By the way so far I tried this:  $x^y = y^x \rightarrow y\log x=x\log y $  Later on,I tried to draw their graphs and see where they intercept,but well ... no use.  A hint would be highly appreciated.

We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\neq y$) which satisfies the equality $x^y = y^x$?


Let's assume $Y=\sum_{i=1}^{N}\alpha_iX_i^2$.  where $X_i$ has Gaussian distribution with mean $0$ and variance $1$, i.e., $\mathcal{N}(0,1)$ and $\alpha_i$s are constants.  When $\alpha_i$s are all $1$, the distribution of $Y$ is Chi-Squared. My question is what is the distribution of $Y$ when $\alpha_i\neq 1$?

I have  that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by  describing a method for the summation of a general set of Gamma random variables. I have tried implementing  method but have yet to have success.  What does the summation of a general set of Gamma random variables look like? To make this question concrete, what does it look like for:  $\text{Gamma}(3,1) + \text{Gamma}(4,2) + \text{Gamma}(5,1)$  If the parameters above are not particularly revealing, please suggest others.


Let $f: X \longrightarrow Y$ a map, if $\:\operatorname{Dom}(f)$ is a countable set, show that $\operatorname{Ran}(f)$ is a countable set.

One of my homework problems asks to prove that if $f:X\to Y$ is a function and $A$ is a countable subset of $X$, then $f(A)$ is countable.  I believe I have a valid proof by partitioning the set A into equivalency classes based in image under $f$. Then using that partition as domain for a choice function $C_f$ back to $A$. So now the function $f$ restricted to the domain (range $C_f$) $f|_{range(C_f)}$ maps to $f(A)$ 1-1 and onto. Therefore  $$|f(A)|=|range(C_f)|\leq |A|=\aleph_0$$ $\therefore f(A)$ is a countable set. $\quad \blacksquare$  My problem is that I used the axiom of countable choice $AC_\omega$ in my proof but that isn't a part of the course I am taking. Does anyone have a simpler proof or one that does not involve Choice?


I am writing a large document (thesis proposal) that I would like to break into separate files, with the following directory structure:  . |-- ch/ |   |-- chapter1.tex |   |-- chapter2.tex |   |-- somemacros.sty |   |-- moremacros.sty | |-- main.tex   The main.tex file calls \usepackage{ch/somemacros}, which in turn requires the moremacros package.  Unfortunately, compiling this will fail to find ./moremacros.sty because it simply doesn't exist there.  I hesitate to hard code the directory structure into the packages, since some of these macros are written for use outside of this particular document (e.g., subject-specific mathematical notation).  But i also hesitate to develop these macros in a separate VCS repository, since I'm developing them as needed while writing the proposal document.  How can I handle this problem?  Is there a solution that meets my constraints? Also feel free to (try to) convince me that these constraints are unnecessary (e.g., "use a better directory structure", "use a separate repository", etc.).

Over the years I've written some libraries. These libraries sometimes depend on each other.  As a result, the "tex" directory is structured as follows:  tex ├── library |   ├── library1.sty |   ├── library2.sty |   └── library3.sty ├── project1 |   ├── master.tex |   ├── chapter1.tex |   └── chapter2.tex ├── project2 |   └── article.tex └── project3     └── paper.tex   The libraries depend on each other. As a result, in every library that depends on another library, this is part of the header:  %library2.sty \ProvidesPackage{library2} \RequirePackage{../library/library1}   In other words, the library is imported from the "root of every project". This is not a good design choice. What if someone copies the libraries in the folder of the root of a project, or what if the folder "library" is renamed...  It is however reasonable the "active directory" still remains in the project root.  What can be done to resolve such library dependencies?


Time and again I'll create a question on the Android app, only to find I'm asked which SE site... Despite already selecting this first.  It seems like the tag selection goes right to site selection even if site is already selected?

I'm using the official Stack Exchange mobile app for iOS or Android, and  My app crashed! It doesn't look good on my new smartphone. It won't run after I updated my device. I noticed another bug. I have an idea for a new feature which is currently not in the app.  How do I report bugs with or request features for the iOS and Android apps? Also:  I've used the built-in functionality of the app to report a bug or submit a feature request. Did I do the right thing? The app prompted me to post on Meta after an error occurred. Should I post about it here? I'm wondering why the latest version is from 2017. I've heard rumors that the apps are no longer supported; is that true? I can't find the app on my device's app store anymore! Where did it go?     We get a lot of bug reports from users about the mobile apps, which are unsupported, and at the moment, there is no centralized Q&A pair for those to be closed as duplicates of (the relevant answers are spread across multiple unrelated questions). This question is an FAQ proposal, to serve as a directly-related duplicate target for those questions.


I have read a sentence including occur in New Concept English,  a well-known English reference book focusing on rules of British English. And in order to fully grasp the word, I tried to make a sentence with it, but in the middle, I was greatly confused by the tense.     It suddenly occurred to me that he [is/was] a considerate leader.   Supposing that the truth is he is definitely a considerate manager, and while I was doing something yesterday, the thought slipped into my mind. Which tense is more appropriate? And please explain in detail, thanks!

Possible Duplicates:             My wife and I were disagreeing about this today:        Did you know Fred was a doctor?   Did you know Fred is a doctor?      I was arguing for (1) based on what seemed to "sound right."  My wife claimed that, since Fred is currently alive and still practicing medicine, present tense should be used.  However, we agreed that the negation of these sentences uses was:     I didn't know Fred was a doctor.   Here I think everyone would agree that is would sound wrong!  So which is correct between (1) and (2)? And why? Is this some kind of subjunctive?


On a Mac Lion 10.7.5 I have 5 USB external disk and I'm not using them all the time so I want to prevent it to mount at boot and only mount the one I need when needed.  How can I achieve this ?  Thank you

My iMac (mid-2010 model, Snow Leopard) has a problem with S.M.A.R.T status: Failing and it has become read-only. Because I didn't want to waste money on the repair, I bought an external HD, so the internal HD is now unnecessary. How can I disable mounting the internal Macintosh HD at boot?


I  I want to create this symbol. any one help me.

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


How do I do this question using the pigeonhole principle? Of course, I could just list down values of $k$ such that $2^k-1$ is divisible by 11. For example $k = 10$ would nicely solve the question but it requires listing and when the divisor gets bigger (For example show that there exists a $k$ where $2^k-1$ is divisible by 21, it's harder and much more complicated to solve it.  Are there any hints how I can use pigeonhole principle to solve this question?

Let $n$ be some positive odd number. Prove, in terms of the pigeonhole principle, that there exists some positive integer $k$ such that $n\mid 2^k-1$.


I'm running this code with JDK 1.4 and 1.5 and get different results. Why is it the case?  String str = ""; int test = 3;  str = String.valueOf(test); System.out.println("str[" + str + "]\nequals result[" + (str == "3") + "]");  if (str == "3") {     System.out.println("if"); } else {     System.out.println("else"); }   outputs:   on jdk 1.4  str[3] equals result[true] if  on jdk 1.5  str[3] equals result[false] else

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


I'm sure this has been explained somewhere, but I have never found it so, here I go:  Let's say I have an object that contains functions move, attack, defend. How can I add them to a unit-object, without adding them one at a time, or adding a sub.object: units.commands = commands, rather: units = commands OR units.prototype = commands.  Another simple example:      var one = function  () {         this.a = 1;     };     var two = function  () {         this.z = 1;     };     var jee = new one(),     jee2 = new two();     jee = jee2;     console.log(jee); // Should have z AND a.

I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects.


I've installed Ubuntu twice on virtualbox successfully and after messing around with it for a while I wanted to install it on my old xp netbook to give it new life and also cuz Linux is kinda cool! The problem is that no matter what I try I cannot get it to install! NOTES: It's a 32 bit machine running on BIOS and it's hard drive has windows xp (im not planning on dualbooting but idk if wiping it first will help much) First I just flashed the latest iso (20.04) on a flash drive with rufus, all it gave me was a grub menu at the start, when I press start ubuntu it just did the black screen with blinking underscore, and the test ram gave me error symbol grub_efi_secure_boot not found nomodenset also didn't work Eventually I realized that this is a 32 bit machine and that I used a 64 bit so I got the first 32 bit image that popped up during search (). This got me a bit further, as I can now get to the "keyboard equals happy person in bubble" screen. It gets me to the splash loading screen with the 5 dots but then just stays there forever. Again, neither nomodeset nor using the "happy person in bubble menu" (im sorry i rly don't know what to call it hhhh) options will get me past the loading screen. Any suggestions on what to try?

I'm thinking about installing Ubuntu Desktop, but I don't know what flavor is the best for my system. What are the minimum and recommended hardware requirements? What kind of CPU? How much memory? Should I have Hardware Acceleration? What flavor should I use?  This is an attempt of a canonical answer. My answers have the "official  requirements", the recommended are a mix of official sources and opinion based (along with the answer it's told the source). You can comment or edit if you feel that the information is obsolete or incomplete. It is a good rule of thumb that any system capable of running Windows Vista, 7, 8, x86 (Intel) OS X will almost always be a lot faster with any Ubuntu flavor even if they are lower-spec than described below.


How do I get emails when someone comments on my question?  I read that you need to click the Stack Exchange icon in the top left, but all I get are communities ().

I could not find a solid documentation to this question.  Is there a way to subscribe by email to a given question's answers and comments?  For example, this is a question which I answered:    People are adding comments to my answer.  Is there a way to get email notifications about new comments so I can read and relate to them quickly?


If this has already been discussed or this is not the right place to ask let me know and I will delete this question.  That being said, the first two months of me using SO, the push notification system(reputation changes, comments, live tracking of votes and answer acceptance) was flawless.   However, in the past month, I notice up and again that it is clearly off. For example, I will be in a question tab and post an answer and monitor that question only to realize there have been alot of changes on this page such as votes and new answers and comments. However, to get those updates I have to keep refreshing the page. What is more peculiar is I can glimpse reputation changes for that question in another tab being updated correctly, but not for the post itself.  What gives?

Since some time in the last two or three weeks, upvotes do not show in the top bar the way they used to (like, +10 on the achievements dropdown image for an answer upvote), at least on Super User. I have to click on the achievements dropdown image or go into my profile to see the recent reputation change. This was also network-wide, so it readily alerted me to voting going on on questions on other sites, sometimes causing me to revisit and improve them.  The reputation count (next to the avatar) is updated, but this is far from obvious.  I really miss reputation changes being somewhat prominently displayed. Where did that feature go?  Edit: It looks like this might affect only questions on sites other than the one I am currently browsing. Either way, an explanation of the intended behavior from someone in the know would certainly be appreciated! All the seemingly relevant posts I found were years old.


Cantor’s theorem states that $|\mathcal{P}(A)| > |A|$ for any set $A$.  As a special case of this, we have $|\mathcal{P}(\mathbb{N})| > |\mathbb{N}|$. If we denote the power set of the naturals by $\mathcal{P_1}$, then $|\mathcal{P}(\mathcal{P_1})| > |\mathcal{P_1}|$. Now denote the power set of $\mathcal{P_1}$ by $\mathcal{P_2}$. Applying the theorem again, we have $|\mathcal{P}(\mathcal{P_1})| > |\mathcal{P_2}|$. We can repeat this process forever, with each power set, $\mathcal{P_n}$, having strictly greater cardinality than the last, $\mathcal{P_{n-1}}$.  Clearly this shows that there is an infinite number of different cardinalities of infinite sets (an infinity of infinities). My first thought is then to wonder about the nature of this infinite quantity.  I have two questions:   What is the cardinality of the set of different cardinalities of infinite sets? In other words, what kind of infinity is the number of kinds of infinity? It seems like it would be countable infinity to me, as we clearly have a bijection between the naturals and these cardinalities. However, my question below may cause a problem with this argument. In performing this iterative process on $\mathbb{N}$, are we actually covering all possible kinds of infinity? Can we be sure that there don’t exist any kinds of infinity that won’t at some point be generated by this process?   A side question regarding the definition of ‘uncountable’: Does uncountable infinity refer to any infinity that isn’t $|\mathbb{N}|$, or is it strictly $|\mathbb{R}|$?  I hope this question makes sense and that I’m not asking something pointless or unanswerable.

It's pretty straightforward to say that there is an infinite number of different sizes of infinity, but then I thought, "What size of infinity is that?"  My thoughts are that the number of unique cardinalities is equivalent to the number of real numbers, based on the fact that the cardinalities can always be ordered by increasing size. I don't really know how to prove this, though. It's mostly based on intuition, which isn't very reliable when talking about uncountably infinite sets.  I originally asked a somewhat related  at a different (and not math-oriented) forum, and the users there told me that it is not possible to talk about the number of cardinalities without talking about the set of all sets, which forms a paradox. If a set were to contain all of the different sizes of infinity, it would have to contain its own power set, which isn't possible.  However, I'm not completely convinced that it is not possible to talk about a set of all of the cardinalities. Sure, a cardinality represents a size of infinity, but I think that it should be possible to have a set of the cardinalities without having the set actually contain the various infinities. Would this avoid the above paradox?  So, is it possible to measure the number of different sizes of infinity, and what would that size be?


I am new to JavaScript and I am making and idle game and what I want to do is to change the value of a variable inside a function wich is called by an event listener like this:  const foo = (x) =>{     x = x + 1; } foofoo.addEventListener("click", function(){foo(x)})   where x is a variable is this possible?

The primitive types (number, string, etc.) are passed by value, but objects are unknown, because they can be both passed-by-value (in case we consider that a variable holding an object is in fact a reference to the object) and passed-by-reference (when we consider that the variable to the object holds the object itself).  Although it doesn't really matter at the end, I want to know what is the correct way to present the arguments passing conventions. Is there an excerpt from JavaScript specification, which defines what should be the semantics regarding this?


I got asked to prove this which makes no sense to me “Proof if a and b are two arbitrary numbers then (a,b) are divisors of lcm(a;b)” Isn’t this a part of the definition of lcm? What is there to prove?

Is $$d_1\mid n,d_2\mid n\iff [d_1,d_2]\mid n$$ true ? And if yes, how can I prove it ? I recall that $[d_1,d_2]$ is the least common multiple.  My tries  For the implication : Let $d_1\mid n$ and $d_2\mid n$. Then, $d_1d_2\mid n^2$. By the way, since $d_1,d_2\mid n$, we have that $(d_1,d_2)\mid n$ where $(d_1,d_2)=:\gcd(d_1,d_2)$  and thus $$[d_1,d_2](d_1,d_2)\mid n^2.$$  Question: How can I get $[d_1,d_2]\mid n$ from this?  For the converse, since $d_1,d_2\mid [d_1,d_2]\mid n$, the claim follow.


I am unable to get my MacBook Pro to boot. It turns on, and the Apple logo + loading bar appear however after a minute or so of loading it eventually changes to a white/grey screen and just hangs.   The machine is a 15-inch MacBook Pro from early 2011 running OSX 10.10.5.   I have booted in verbose mode and I couldn't spot anything untoward however similar behavior was observed, just in verbose mode.  I can get to a shell with cmd+s but I'm not too familiar with OS X so I'm not sure where to begin looking for hints about the failed boot.  I tried to enter recovery mode by booting and holding alt and was able to get the screen up where you pick the recovery drive, but I experienced the same failed boot behavior as described above.  Prior to all this the laptop had a bit of an episode where the video went very funny, top half of the screen at the bottom, and the bottom at the top with some horizontal bars of random colors, like colorful TV static... And it flashes a bit like this just before it hangs at boot... leading me to think it might be something video card related but this is my only clue so far...  Can anyone help me as to where to go from here? Such as boot logs found from the command line, or diag commands I can run?

I am somewhat new to caring for Macs, but one has been left in my care and I have not been able to restore it to working order yet. Here are the symptoms:   The MacBook Pro would hang with a "white screen" during the boot process. A bit of boot splash would show up, but the gray background would at some point just hang. Booting recovery mode did not work, as far as I remember. Boot from a Ubuntu 14.04.2 USB stick works, provided one attaches "nofb nomodeset" to the kernel commandline (though I put that one down to insufficient driver support). I have no idea whether or not these usually work out-of-the-box. Using parted from the aforementioned stick, I was able to see three partitions, one EFI Boot, one large main partition and one labeled Recovery. It seemed strange that the recovery was recoognized as HFS+, as I expected, but the "main" partition was not mountable and did not show a filesystem type. I also discovered that the drive in question was an OCZ Vertex3 256 GB, which I assume is not standard? The previous owner could have upgraded it. At this point, I decided to wipe the drive and try with a fresh installation. I removed the SSD from the MacBook, pulled a full disk image from my desktop just in case (which went without any read errors) and used hdparm to do an SATA enhanced erase, leaving me with a "fresh" disk. Then I put it back in. I started internet recovery, which loaded, showing me the global and everything. Afterwards, it rebooted, showing me the Apple Logo. But then I run into the original "white screen" again. I've tried resetting the NVRAM on boot, which succeeded because it turned the boot chime back on, but even then, running internet recovery again just causes it to hang on the white screen. There seems to be either very high CPU or GPU usage on the white screen, as the fans start wailing pretty intensely, also the body gets very hot in a very short time. For funsies, I installed Ubuntu onto the MacBook, which works (after smoothing over a few hiccups, fortunately I have lot more experience doing that). Recovery mode (Cmd+R) and Apple Hardware Test (D?) I have not been able to run. The former suffers the same white screen issue as described above.   Currently, my only vague guess is a GPU issue, that may be circumvented by Ubuntu by using the not completely feature complete open source radeon drivers. But that is a wild guess. Any input is appreciated.


Let $R$ be the quotient ring $\mathbb{Z}_3 [x] / I$, where $I= <x^2-1>$ . I need to find how many are the nilpotent elements of $R$, i.e. the elements $a \in R$ for which there exists a natural $n$ such that $a^n=0_R$ .   Let $f(x)+I \in R$ be a nilpotent element. Then, for some $n$,  $(f(x)+I)^n = 0+I = I $. Can someone tell me what's the direct conclusion of the last equality?  Is it right to imply that $(f(x))^n \in <x^2 -1>$ ? I need a clue to proceed to the solution. Thank you.

We have the ring $\displaystyle R=\mathbb{Z}_3[x]/I, \ I=(x^2-1)\mathbb{Z}_3[x]$ is a principal ideal. The question is to find the elements $a\in R$ such that $a^n=0_R$ for some $n\in\mathbb{N}$.    I'm trying to understand the form of the elements in $R$.  Firstly, the elements of $R$ have the form $f(x)+I, \ f(x)\in\mathbb{Z}_3[x]$. By the euclidean division there exist $\pi(x)\in\mathbb{Z}_3[x]$ and $a,b\in\mathbb{Z}_3$ such that $f(x)=\pi(x)(x^2-1)+(ax+b)$. The elements of the form $ax+b$ where $a,b\in\mathbb{Z}_3$ are the following:  $$A=\{0,1,2,x,x+1,x+2,2x,2x+1,2x+2\}$$  (Is that a correct approach to examine the form of the elements in $R$?)  We have that $x^2-1=(x+1)(x-1)=(x+1)(x+2)$ in $\mathbb{Z}_3[x]$. If $f(x)^n+I=0+I$ then $f(x)^n\in I\Rightarrow (x+1)(x+2)\mid f(x)^n$. By looking at the polynomials in $A$, this is true if $f(x)=0$. But how can I check what happens to the $n-$th power of the rest of the polynomials?  Secondly, I 'm trying to find the invertible elements of $R$. Now we are looking for elements $f(x)\in A$ such that $\gcd(f(x),x^2-1)=1$. Are these $\{1,2,x,2x\}$? How can I find the inverse of $2x$?   Thank you in advance.


Hi I have the following problem:  Let $R$ be a ring and $S\subset R$ multiplicatively closed and $M$ be an $R$-module. Show: $M$ is flat $\Leftrightarrow S^{-1}M$ is a flat $S^{-1}R$-module.  I think I can show $"\Rightarrow$" but for $"\Leftarrow"$ I don't know how to start. Can someone help me please?

Let $M$ be a flat $S^{-1}A$-module. I want to show that $M$ is flat as an $A$-module.    $\newcommand{\tp}{\otimes}$ My "best" attempt is the following: Let $$0 \to N_1 \to N_2 \to N_3 \to 0$$ be exact (of $A$-modules). Then, $$0 \to S^{-1}N_1 \to S^{-1}N_2 \to S^{-1}N_3 \to 0$$ is exact, and as $M$ is flat, $$0 \to S^{-1}N_1 \tp_{S^{-1}A} M \to S^{-1}N_2 \tp_{S^{-1}A} M \to S^{-1}N_3 \tp_{S^{-1}A} M \to 0$$ is flat, and due to $S^{-1}N_i \tp_{S^{-1}A} M = S^{-1}N_i \tp_{S^{-1}A} S^{-1}M = S^{-1}(N_i \tp_A M)$ $$ 0 \to S^{-1}(N_1 \tp_A M) \to S^{-1}(N_2 \tp_A M) \to S^{-1}(N_3 \tp_A M) \to 0 $$ is exact. But I don't know why $$ 0 \to N_1 \tp_A M \to N_2 \tp_A M \to N_3 \tp_A M \to 0 $$ is exact, which would imply the flatness of $M$ as an $A$-module.


When I first watched numberphile's  I thought the sum actually equalled $\frac{-1}{12}$ without really understanding it.  Recently I read some wolframalpha pages and watched some videos and now I understand (I think), that $\frac{-1}{12}$ is just an associative value to the sum of all natural numbers when you analytically continue the riemann-zeta function. 3Blue1Brown's  really helped. What I don't really understand is why it gives the value $\frac{-1}{12}$ specifically. The value $\frac{-1}{12}$ seems arbitrary to me and I don't see any connection to the sum of all natural numbers. Is there any intuition behind why you get $\frac{-1}{12}$ when analytically continue the zeta function at $\zeta(-1)$?  EDIT(just to make my question a little clearer): I'll use an example here. Suppose you somehow didn't know about radians and never associated trig functions like sine to $\pi$ but you knew about maclaurin expansion. By plugging in x=$\pi$ to the series expansion of sine, you would get sine($\pi$) = 0. You might have understood the process in which you get the value 0, the maclaurin expansion, but you wouldn't really know the intuition behind this connection between $\pi$ and trig functions, namely the unit circle, which is essential in almost every branch of number theory.  Back to this question, I understand the analytic continuation of the zeta function and its continued form for $s < 0$ $$\zeta(s)=2^s\pi^{s-1}\sin\frac{\pi s}2\Gamma(1-s)\zeta(1-s)$$ and how when you plug in s = -1, things simplify down to $\frac{-1}{12}$ but I don't see any connection between the fraction and the infinite sum. I'm sure there is a beautiful connection between them, like the one between trig functions and $\pi$, but couldn't find any useful resources on the internet. Hope this clarified things.

$\displaystyle\sum_{n=1}^\infty \frac{1}{n^s}$ only converges to $\zeta(s)$ if $\text{Re}(s) > 1$.  Why should analytically continuing to $\zeta(-1)$ give the right answer?


As Thunderbolt 3 incorporates controller and has 40Gbits bandwidth, I believe it should be possible to link two PC with in a network.  I have an Intel NUC/Linux.

When plugging thunderbolt cable between two mac computers, it's possible to setup a high speed network connection between them (depending on the thunderbolt version it can be up to 40Gbps).  I was wondering if anyone tried to do something similar between linux and mac?  The goal is to have 10Gbps+ connection between linux and mac.


I have not seen this as an option in the media and wondered if this has been considered and rejected.   Unless the virus has shown to be mutating frequently, this option would allow low-risk groups to be exposed in an isolated environment, they would be able to get treatment if necessary. But if as expected, the majority get over the infection without adverse affects, they can be free from having to practice social distancing and/or isolation.  The first groups could be health workers and other essential personnel like the national guard. These people could then go about doing essential work without fear of catching it or spreading it.  Over time we could significantly reduce the number of people who would be forced to practice social distancing and/or isolation.  We could even consider having Covid-19 zones where people could get exposure, become immune and then be allowed to leave the zone.  This would reduce the stress on healthcare systems overall.

In forest management, a controlled burn is “used for hazard reduction [to] decrease the likelihood of serious hotter fires” []. In backfiring strategy, “firefighters attempt to halt the advance of a wildfire (…) by burning up fuel in its path” [].  Could the same strategy be used to fight the Coronavirus?  E.g. in my native country (Norway), most hotels are now closed. If, for the sake of the argument, we assume that 1) humans become immune after having fallen sick to the virus and 2) people under 25 do not become seriously ill, what is the counterargument to inviting people in the age group 15-25 to mass isolate in said hotels for e.g. 1 month, for the purpose of kickstarting herd immunity?  (In the meantime, they would also be off the streets, presumably posing less of a risk to the more vulnerable population, and students would have a chance of colocating.)   the matter (in Norwegian) hypothesizing that a controlled burn could decrease the death toll in Norway from 60.000 to 2.000 individuals.


I'm trying to say:  In simulations specific effects can be switched on or off to determine their impact.   This switched on or off seems to me rather clumsly. Is there a single verb with that meaning? I don't think toggle really works, but could be wrong.

I'm looking for a word that describes "to enable or to disable".  found the hypernyms mode and state, but I am looking for a verb. I.e. a word for "(potentially) change mode/state".  I guess to switch is a good match, but unfortunately in JavaScript (my target language), switch is a reserved keyword.  What alternatives are there?


I want to determine the quantile of a probability density function (PDF). I do not know the distribution, but I have a sample that was generated from it.   I estimate the quantile of the distribution as the quantile of the sample. How can I give an uncertainty that tells me how much the quantile of the sample fluctuates around the quantile of the PDF?

I have a distribution of samples with a small number of values in each one (less than $10$). I have calculated the median for each sample, which I want to compare with a model and obtain the difference between the model and the median of each sample. To have a consistent result, I need an error on this difference.  It results that finding the standard deviation in such a case can be quite hard, at least for a non-pro like me (see for example ).  I have found  which says how to calculate confidence intervals for the median, even if there is no official reference quoted.  It seems reasonable to me, but I can't really judge, so I would like to know:   are those formulas correct? There is a reference for that? What about if I want to find CI different from $95\%$?   Thanks in advance  EDIT: I have also found . Now, I do not know much about bootstrapping, but it would be good to have an address on its validity.


In terminal I just type firefox and then Firefox starts, but I can not return to  command mode anymore.  How can I come back to command mode? I have already tried :q or exit, but neither work.

On the CLI, sometimes a command I type takes a while to complete, and sometimes I know when that's about to happen. I'm a bit confused on "backgrounding" and such in Linux.  What is the most common (or user-friendly way) of telling the CLI that I don't want to wait, please give me back my prompt immediately. And if it could give me a progress bar or just busy-spinner, that would be great!


I am a self funded PhD student and have been told by my supervisor that her name should be first on any future journal I will be publishing during my studies under her supervision as "this is the only thing she gets from her PhD students".  I am just wondering if the ordering of author names matter? She is going to help me only by proof writing my article. All research will be done by myself.   Is she legally allowed to say it? Should I accept it?

I understand that in a lot of big-lab fields it is common for the principal investigator to append their name to a paper even if they did not write the paper, design the experiment, or collect data since they spend energy securing funding, and managing the whole lab. What about for small labs?  What are the requirements for a supervisor to be included as an author on a paper, as opposed to just appearing in the acknowledgements? If you are working on your own projects independently of your supervisor, but using funding provided by your supervisor (how does this change when the funding provides resources versus just your salary), are you suppose to add them as authors or just acknowledge the source of funding?


I have a Dell Dimension E510. Its most important gaming specs are:   Intel Pentium 4 3.0GHz CPU 1 GB of RAM (with a max of 4 GB) ATI Radeon X300 with 128 MB   Typically I enjoy playing Counter Strike Source online, but find that it is often difficult to play due to delays. Other games I like to play are Guild Wars, and find that it is ok for the most part. I have the greatest difficult with Battlefield 2.  I have looked on amazon and have found that for about $60 I can upgrade to a 1GB video card, and for another $60 I can max out my RAM to 4 GB. However, I do not want to upgrade without first understand where my slow down is.  How can I determine where the resources are needed? I typically attempt to open up the Windows Task Manager to view the CPU and Memory utilization. I have not found a way to monitor video card metrics. The CPU hovers around 60% and the memory can get under 50 MB under certain circumstances.  Additionally, I have further concerns that my wireless connection to the desktop is less than optimal. How could I understand if: (1) a sub-optimal internet connection makes the game slow, or (2) a sluggish system is due to something other than network resources?  While upgrading both the video card and memory is not a tremendous amount of memory ($120), I would hate to upgrade and not see a difference in game play.

What is a reliable, but not too time-consuming way to determine if a certain game is limited by the graphics card or by the processor speed?  I have some preconceptions about whether I'm mostly GPU or CPU limited, but I'd like to verify if I'm right about that. I have some ideas how I would go around and test that but performing accurate benchmarks is notoriously tricky and I don't have much experience with it.   So I'm wondering what would be an easy way to determine the bottleneck, having only one computer with a certain configuration available? What tools would I use for that purpose?  It would also be interesting to determine if the amount of VRAM on my graphics card is a limiting factor.


We applied for a tourist VISA for 5 people,  who are Me,  My Mother,  My Father,  My Brother's close friend and a cousin of mine. Me and my parents got the VISA.  However,  My brother's friend's and my cousin's got refused.  The purpose of us visiting the UK is to meet my brother (non resident)  and sister in law (British Resident) and to attend their blessings ceremony in the UK. We attached the sponsorship  letter, pay slips and invitation from my brother and sister in law. I want to ask, should we reapply for my brother's friend?  As you can see in the refusal letter its mentioned that the business provisional registration is of 26/6/17, which is true but its because GST got introduced in INDIA in june'17. He has his business registration documents which are 9 months old as he started his business at that time.  The other concern is income tax return,  as he is new into the business or work,  he was not aware of the tax submission earlier,  and then he was waiting for the GST to be introduced,  so that he can file the ITR correctly. Another consern is his bank statement not matching with his income stated, is because he has other savings which he got after his father passed away in june 2015. He has his mother and 2 sisters to take care of in INDIA. His mother has the source of income from the interest of fixed deposits worth INR 25,00,000 and the rent which she recieves from the property which his father owned and after his father's death it got transferred in the name of his mother and himself.  He is the owner of the house in which he stays with his family.  This house was gifted by his father to himself, when he was alive.  Me and my brother's friend are in a relationship from last 8 year and are soon planning to get married. He has clear intention to return to India as hismother and sister are depebt on him,  not financially but because of his mother's health conditions. We also missed mentioning his family's dependancy on him and abouf the bank balance which he got after his father's demise.  Request you to suggest what should we do?  As I never thought of visinting the UK without my boyfriend. Should we reapply?  Are there any chances of getting VISA if reapply?  Is it that if they refuse to give VISA to my boyfriend twice, the possibility of him getting VISA in the future gets minimal?

Many of the UK visa refusals we see here share a common pattern and the prevailing reasons refer to V 4.2 (a) and (c).    I do understand that, while the applicants may describe very different individual circumstances, there's a consistent pattern and, broadly, fall into specific categories:    Credibility (lifestyle, lack of ties, visit history, lies & omissions) Funding (insufficient funds, provenance of funds, funds parking) Sponsorship (family, friends, employer)   Question: What most commonly triggers a UK visa refusal where V 4.2 (a) and (c) are given as the grounds?  Secondarily: Given that there is a clear pattern, to what extent are these refusals predictable? Does sponsorship make a difference? Is there a set of personal circumstances, however abstract, where a refusal is all but guaranteed? For example, why do those we see here on TSE who sought entry for the PLAB or British Army appear to be refused with a common theme? Is there a uniform shortcoming or is it just discrimination?   PLAB: What is about applications for a visa, for the purpose of sitting the Professional and Linguistic Assessments Board (PLAB) exam, that seem to invite refusals. After all, the test is given so that international medical graduates can show that they qualify to practise medicine in the UK. The first part, PLAB 1, can be taken in centres outside of the UK. However, PLAB 2 can be taken only in the UK. Why can't you can't get a visa just to sit the exam, promising that you'll leave immediately after?    British Army: Since Commonwealth citizens are eligible to apply online to join, even those who don't reside in the UK, why is it so difficult to get a visa just to attend an interview to see whether you are suitable? Even with an invitation from the Army, such visa applications seem to be unsuccessful. Isn't a career in the British Army a valid reason?     Lastly:  After such a refusal, what approaches would increase the chance of a successful application?


Is there an application that doesn't allow me to move icons on the home page when I long press them in order to prevent accidental movements?  So for instance if I long press the Camera icon on the main screen I'd like nothing to happen while this application I'm asking about is active/installed.  LE: Of course I search the Play store and haven't found such an app.

I had recently gifted my Mom a Nexus 7, with a hope that she will like to read books. She is old with poor eye sight and can't read English that great. I find her eager to learn and she had made a good progress in reading few books. Since she is not used to these gadgets, I am trying to keep settings in  her tablet constant. Recently I observed that the shortcut in home screen for PDF reader disappeared and resulting in discontinued  reading till my arrival. The frequency of this sort of interruption has increased now a days. Rather than finding how the shortcut is being deleted, I think preventing changes to home screen is sensible.  Hence, I would like to know about any means to keep the icons or shortcuts in  home screen  and in launcher  constant, immune to long press and drag and drop operations.  Device info: Nexus 7, running stock 4.2.1, unrooted, but willing to root if required.


I have to write short script to replace line in file. Some of the lines contains slashes and left square brackets (probably right also).   I know that another delimiter should be used to replace line with slashes.  My code:  sed -i -e "s|${oldLine}|${newLine}|g"   This throws an error because line contains [.   Example String in line to change (oldLine variable):  // List exampleList = [   Example how like should look after change:  List exampleList = [   How to make it works when there are some chars like [  To reproduce:  sed -i -e 's|// List exampleList = [|List exampleList = [|g' test.txt

In my bash script I have an external (received from user) string, which I should use in sed pattern.  REPLACE="<funny characters here>" sed "s/KEYWORD/$REPLACE/g"   How can I escape the $REPLACE string so it would be safely accepted by sed as a literal replacement?  NOTE: The KEYWORD is a dumb substring with no matches etc. It is not supplied by user.


I am using Ubuntu Server 16.04. Everytime I log in, I need to manually run my script: /home/user/ini.sh. This script calls other scripts that need sudo permissions, so I get the prompt, insert my password and done. Now I want to configure a way to run the script automatically when the system starts.  I have used crontab -eand added the line  @reboot /home/user/ini.sh   This does not seem to work. I have tried different options as suggested by other users in , ,  or .  @reboot user    /home/user/ini.sh @reboot root    /home/user/ini.sh @reboot sh      /home/user/ini.sh */1 * * * *     /home/user/ini.sh ....   adding SHELL=/bin/bash... But I cannot get it to work. I have also tried  @reboot echo "yes" > /home/user/yes.txt   And the file is created - empty though, with no content inside (this demonstrates something is working but I am making a mistake somewhere).  Where is my error?    EDIT  I have also unsuccessfully tried to sudo crontab -e and use  @reboot root    /home/user/ini.sh

Is it possible to run a  job which needs the  command?  Like:   sudo rm somefile


In Skyrim, I really want to get a Daedric weapon, but I am only level 40. Could someone please help me get one without smithing or using the Atronach Forge?


I have a HP e9300z, Have Windows 7 on it currently. x64 bit. I wish to Dual Boot Ubuntu with Windows 7, when i do  the windows setup , do not even get the options to Install Alongside with, Just install or Something else. Someone in another forum said something with the HP BIOS, can not find where to change anything. So what do i have to do so Ubuntu sees my HDD with Windows? Manually make partition? Only have 1 partition my C: Windows. Thanks.

I would like to install Ubuntu alongside Windows 7 on a HP G62 Notebook. Although I have installed  Ubuntu in a dual-boot many times before, I found out that this model has already four partitions.    Partitions:   SYSTEM (NTFS, 199MB, used 66.59MB) Partition without any tag: NTFS (579GM, used 129GB)  RECOVERY (NTFS 16.74 GB, used 2.42GB)  HP_TOOLS (FAT32, 103.34 MB, used 13.23MB)   Since I am not an expert with partitions I would like to get advice on how to do this.  My first idea is this one:   Free some space from /dev/sda2 (I don't know if could also free some other space) delete the HP_Tools partition (I have already created a backup) create an extended partition with the free space in #1 containing three parititions: swap (1gb); / (EXT4, 30GB);  /home (EXT4, 120GB)   Another option is to use wubi instead.  What do you think? Is there any other way to achieve this?  PS: I really think this HP policy of using 4 partitions is not a coincidence  PS: I tried using gparted from the live CD and I got a warning message saying that if I freed some space from /dev/sda2 I could create serious issues in the system


public class Main{          public static void main(String[] args){             double value = 0.12;             double sum = value + value + value;             System.out.println(sum);         } }   output: 0.036000000000000004  why output is not 0.036 ? How I am getting the trailing 4 after a bunch of zeros ?

public class doublePrecision {     public static void main(String[] args) {          double total = 0;         total += 5.6;         total += 5.8;         System.out.println(total);     } }   The above code prints:  11.399999999999   How would I get this to just print (or be able to use it as) 11.4?


How do I create a graphical shortcut to run a program in awesome WM? An icon I can click to launch a program?  Right now, I can only run Firefox by either:   launching a terminal, then typing "firefox &", pressing Super+R and typing firefox, editing config files to add a keyboard shortcut.

In older versions it was easy to create a launcher on my desktop. All I had to do is right click on my desktop and select the "create launcher" option.  How can I create such launchers now?


Why a test charge is always positive. WHy cant we assume the test charge to be negative? Just that if we assume it to be negative test charge, will the electric field turns to be negative?   Additional Details reply: does it mean that if we put a negative charge as a test charge near a positive charge source, it shows that the positive charge actually exerts a field pointing inward? before, if we put a positive charge near a positive source, it means field radially outward,how if we change the test charge to a negative charge?  Thanks in advance!

Is there any difference between using a positive versus a negative charge to test an electric field?


Currently, when I run the Update Manager in 12.04.1 LTS , I get since some weels:    How can I update from this state?  Update   $ sudo apt-get update Get:1 http://at.archive.ubuntu.com precise Release.gpg [198 B] ... Hit http://at.archive.ubuntu.com precise-backports/universe Translation-en Fetched 198 B in 1s (146 B/s) Reading package lists... Done W: GPG error: http://at.archive.ubuntu.com precise Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key

The computer gave me this output in a window:  E: Encountered a section with no Package: header E: Problem with MergeList /var/lib/apt/lists/archive.ubuntu.com_ubuntu_dists_natty_main_binary-i386_Packages E: The package lists or status file could not be parsed or opened.   How can I fix this?


I installed MySQL some days ago on my Windows machine. Today I noticed that it modified my PATH to just:  C:\Program Files\MySQL\MySQL Shell 8.0\bin\  I had a lot of other items added to my PATH over the course of time and I lost all that. Is there any way I could revert back?

I installed an application that screwed my PATH variable. Now I cannot run anything from the command prompt. Is there any way I can restore PATH variable?


At the beginning of this year we lunched a lot of massive data deletions (millions of rows per week) in our production database. Also, there is an automatic integration of new data (insert/updates) of 10 to 25 .CSV files per day with a global/average size of 400MB. We noticed that reading performance on data even with full using of index became too slow. We have about 122GB of daya with 60GB of RAM and I configured 48GB for the Innodb buffer pool (please check details in images). Is the deletion affect buffer pool performance ? What is the best/fast way to resolve that issue ? Thank you for your help.   **  (UPDATED)  ** It's not really a fragmentation issue, I added a 3rd image for more information. (updated) It is not indexes (the use is about 90% - 100%) but the bad way the app is using the db model made is too bad.

I have a table in mysql with a lot of INSERT and SELECT at every second. And there is a bulk delete of some older data once in a day. Do I need to reindex the table after delete? I want to increase the performance. Can anybody suggest some tips? Using 'innodb' as engine. Do I need to change it? I think its better for concurrent insert and select. pls give your suggestions. Do I need reindexing?  Thanks in advance..


This is a purely academic question, because this will never happen.  If a PID is stored as type pid_t, and not some arbitrary-precision type, then there is a limit to the number of PIDs that can exist at one time. Is there a defined behavior for when PIDs overflow?  Will the 65536th process kill /sbin/init and create a kernel panic? Or is there some safety measure in place?

What is the maximum value of the Process ID?  Also, is it possible to change a Process ID?


In my lecture notes I have that the distribution of a random variable $Y$ is said to be in the exponential family if it can be written as $f(y;\theta)=exp(a(y)b(\theta)+c(\theta)+d(y))$, where $a,b,c$ and $d$ are fixed functions. If we have (in the exponential family form) that $a(y)=y$, then the distribution is said to be in canonical form and then $b(\theta)$ is the called the natural parameter and $b$ is called the natural link function. Then we have shown that for a random variable $Y$ in exponential family form we have $\mathbb{E}(a(Y))=\frac{-c'(\theta)}{b'(\theta)}$ and $var(a(Y))=\frac{b''(\theta)c'(\theta)-c''(\theta)b'(\theta)}{[b'(\theta)]^{3}}$.  I am now working on the following problem: the gamma pdf of r.v. $Y$ is given by   $\begin{equation} f(y) = (s^{a}\Gamma (a))^{-1}y^{a-1}e^{y/s} \end{equation}$,               where $y \geq 0$, $s$ is the scale parameter, $a$ the shape parameter. The first question asks me to reparameterise this pdf by setting $a=1/\phi$ and $s=\mu\phi$, and hence show that it is a member of the exponential family. So after introducing $a=1/\phi$ and $s=\mu\phi$ into the pdf and rearranging I get   $ f(y) = exp((\frac{1}{\phi}-1)log(y)-\frac{y}{\mu\phi}-\frac{1}{\phi}log(\mu\phi)-log(\Gamma(1/\phi))=exp(a(y)b(\theta)+c(\theta)+d(y))$,   where $a(y)=y$,$b(\mu)=-\frac{1}{\mu\phi}$,$c(\mu)=-\frac{1}{\phi}log(\mu\phi)$ and $d(y)=(\frac{1}{\phi}-1)log(y) - log(\Gamma(\frac{1}{\phi}))$, where we treat the (dispersion) parameter $\phi$ as a nuisance parameter. Is that correct?   The next question says: deduce that the canonical link for the gamma is $\theta=\frac{1}{\mu}=\eta=\textbf{X}\beta$. So I'm thinking since $f$ is in a canonical form, the canonical parameter is $b(\mu)=-\frac{1}{\mu\phi}$ and so ignoring all the constants of proportionality we have that the canonical link, in its simplest form, is $\frac{1}{\mu}$, as required. Does that make sense? I still don't have a good enough understanding of link/canonical link functions, I'm afraid.  Then the next question asks me to deduce further that the variance function is $b''(\theta)=-1/\theta^{2}=-\mu^{2}$. I don't really know how to do this. Why is this the variance function? What is $\theta$ here? A canonical link? That clearly doesn't make sense. Or is just the dummy variable for our parameter of interest ( $\mu$ in our case )? I've tried to differentiate $b(\mu)$ w.r.t. to $\mu$ but it doesn't work. I'd really appreciate some help.

I have $X_1,X_2 ... X_n$ Gamma-distributed r.v with density:    First of all I showed, that Gamma distribution belongs to exponential family and can be represented in form     I found, that for Gamma distribution $B(\theta) = log(\theta)$ where $\theta$ is $\alpha/\beta$  Then we know, that moment generating function of the random variable $T(X)$ is given by $$M(t)=\exp\{B(\theta+t)-B(\theta)\}$$  Natural sufficient statistics for Gamma distribution is:    But I didn't understand what should I do next? Because Natural sufficient statistics is two dimensional it confuses me:  $M(T) = exp[log(\theta + T) - log(\theta)]$  and $T = [s,t]^\intercal$


I would like to draw three tables side by side with three different captions. My tables are below  \documentclass[11pt,a4]{article} \begin{document} \begin{table}[!t] \renewcommand{\arraystretch}{1} \caption{Common Differentially Expressed and Non Differentially Expressed genes by } \label{table:6} \centering \begin{tabular}{|p{2.5cm}|p{2.5cm}|p{2.5cm}|} \hline { Method} & { \centering  Differentially Expressed Genes} & {Non differentially Expressed Genes}  \\ \hline Fooooo and AW    & 14923 & 4715   \\ \hline  Fooooo and Fiiiiis  & 14923 & 4715   \\ \hline Fooooo and Fiiiiis  & 12700 & 4720  \\ \hline Fooooo and Fiiiiis & 15179 & 3624 \\ \hline Fooooo and Fiiiiis  & 14904 & 4711  \\ \hline Fooooo and Fiiiiis  & 14904 & 4711  \\ \hline Fooooo and Fiiiiis  & 12682 & 4716  \\ \hline Fooooo and Fiiiiis  & 15159 & 3623 \\ \hline \end{tabular} \end{table}   \begin{table}[!t] \renewcommand{\arraystretch}{1} \caption{Common Differentially Expressed and Non Differentially Expressed genes by } \label{table:7} \centering \begin{tabular}{|p{2.5cm}|p{2.5cm}|p{2.5cm}|} \hline { Method} & { \centering  Differentially Expressed Genes} & {Non differentially Expressed Genes}  \\ \hline Fooooo and AW    & 15546 & 3889   \\ \hline Fooooo and Fiiiiis   & 15546 & 3889   \\ \hline Fooooo and miiii  & 13296 & 4307  \\ \hline Forgery and minP & 15554 & 1977 \\ \hline Haaaaa and Fffffff  & 15538 & 4071  \\ \hline Haaaaa  and ffffff  & 15538 & 4071  \\ \hline haaaaaaa  and tttt  & 13296 & 4307  \\ \hline haaaaaaa  and ssssss  & 15554 & 1977 \\ \hline \end{tabular} \end{table}   \begin{table}[!t] \renewcommand{\arraystretch}{1} \caption{Common Differentially Expressed and Non Differentially Expressed genes } \label{table:8} \centering \begin{tabular}{|p{2.5cm}|p{2.5cm}|p{2.5cm}|} \hline { Method} & { \centering  Differentially Expressed Genes} & {Non differentially Expressed Genes}  \\ \hline aaa and BBB  & 10193 & 2060   \\ \hline BBBBB and CCCCC  & 10193 & 2060   \\ \hline CCCCC and DDDDD & 10193 & 360 \\ \hline EEEE and FFFF  & 10177 & 2059  \\ \hline GGG and HHHHH & 10177 & 2059  \\ \hline IIIIIIIII nd JJJJJJ  & 10177 & 360  \\ \hline \end{tabular} \end{table} \end{document}

I have three tables and I need that the three tables stays side by side.  I tried with this approach but the tables are overlapping each other.  \begin{table}[!htb]\tiny     \begin{minipage}{.20\linewidth}     \caption{First Table}      \label{tab:first_table}       \centering          \begin{tabular}{ccccc}     \toprule     {\bf Library} & {\bf Comedy} & {\bf Scary} & {\bf Others} \\     \midrule     Library1 & $23$ & $233$ & $3295$ \\     Library2 & $843$ & $0$ & $0$ \\     Library3 & $11$ & $1$ & $0$ \\     Library4 & $1$ & $0$ & $0$ \\     \midrule     {\bf Total} & $878$ & $234$ & $3295$ \\     \bottomrule     \end{tabular}     \end{minipage}%     \begin{minipage}{.20\linewidth}       \centering         \caption{Second Table}     \label{tab:second_table}         \begin{tabular}{ccccc}     \toprule     {\bf Library} & {\bf Comedy} & {\bf Scary} & {\bf Others} \\     \midrule     Library1 & $954$ & $40$ & $0$ \\     Library2 & $32$ & $0$ & $1$ \\     Library3 & $11$ & $132$ & $110$ \\     Library4 & $1$ & $30$ & $67$ \\     \midrule     {\bf Total} & $998$ & $202$ & $178$ \\     \bottomrule     \end{tabular}           \end{minipage}%     \begin{minipage}{.20\linewidth}         \centering         \caption{Third Table}     \label{tab:third_table}             \begin{tabular}{ccccc}     \toprule     {\bf Library} & {\bf Comedy} & {\bf Scary} & {\bf Others} \\     \midrule     Library1 & $483$ & $27$ & $2$ \\     Library2 & $848$ & $220$ & $3$ \\     Library3 & $121$ & $12$ & $40$ \\     Library4 & $13$ & $0$ & $0$ \\     \midrule     {\bf Total} & $1465$ & $250$ & $45$ \\     \bottomrule     \end{tabular}     \end{minipage}  \end{table}


This code  \documentclass{scrartcl} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{amssymb,amsmath} \usepackage{amsthm} \usepackage{dsfont} \usepackage{empheq} \theoremstyle{plain} \newtheorem{lemma}{Lemma} \newenvironment{lemmaqed} {\pushQED{\qed}\lemma} {\popQED\endlemma}  \begin{document} \begin{lemmaqed} \begin{itemize}   \item $a^2+b^2=c^2$   \item $a^2+b^2=c^2$ \end{itemize} \end{lemmaqed}  \begin{lemmaqed} \begin{align*} a^2+b^2=c^2 \end{align*} \end{lemmaqed}  \begin{lemmaqed} $a^2+b^2=c^2$ \end{lemmaqed} \end{document}   creates the output My problem is: The qed symbol should be at the place indicating by Lemma 3, so on the right at the same line. This is not the case in Lemma 1 and 2. How can I change this?

I have two questions. 1. Can I delete the red-colored space? 2. If I use enumerate in proof, QED symbol appears the next line of the end, as above. If I do not want to type manually \qedhere, should I use ntheorem?  \documentclass[a4paper]{article} \usepackage[scale=0.75]{geometry}  \usepackage[english]{babel} \usepackage[utf8x]{inputenc} \usepackage{amsmath} \usepackage{amsthm} \usepackage{amssymb} \usepackage{textcomp} \usepackage{enumitem} \setlist[enumerate]{nosep, label=(\arabic*)}  \theoremstyle{definition} \newtheorem{lem}{Lemma}  \begin{document}  \begin{lem} \begin{enumerate} \item xxxx \item yyyy \end{enumerate} \end{lem} \begin{proof} \begin{enumerate} \item xxxxxxxxxxxxxxxxxxxxxxxxx. xxxxxxxxxxxxxxxxxxxxxxxxx. xxxxxxxxxxxxxxxxxxxxxxxxx. xxxxxxxxxxxxxxxxxxxxxxxxx. xxxxxxxxxxxxxxxxxxxxxxxxx. xxxxxxxxxxxxxxxxxxxxxxxxx.  \item yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. yyyyyyyyyyyy. \end{enumerate} \end{proof}  \end{document}


Don't want to waste money on buying windows 7, so the laptop is going to be ordered without an OS. Is it possible to buy a physical copy (CD) of Ubuntu?

I need to upgrade my existing Ubuntu system, and I also want to install Ubuntu on a new laptop.  I would like to have an installation CD or DVD to do both of these.  Where exactly I can order or request an Ubuntu installation CD/DVD/USB?


I installed Ubuntu using a pendrive. Everything worked well the first time after which there was a request to update the system. Once the update happened (don't know what the update was for - I'm a first time Linux user), I'm unable to login to the system. It's a dual boot by the way and the windows 10 works just fine. Please advice. Attached is the pic of the error.

Upon trying to upgrade from 10.10 to 11.04 all seemed to go well until the restart. This error message is what comes up:  Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0)   How do we fix that?


I want to install Kitkat 4.4 on my Samsung Star Pro S7262 (rooted). I could't find a solution by googling. If it is not possible or not available for my phone right now, please suggest me any other version which is greater than jellybean 4.1

There are several reasons to be looking for a ROM:   Upgrading or downgrading your stock ROM Looking for firmware from a different region/language Flashing a custom ROM for different features, removing bloat, etc.   But where can one find ROMs in the first place?  What sites are likely to have the ROM I need?  ; please add to the wiki answer instead of posting separate answers.  See also:


I was reviewing close votes when I found that the trick review test showed modified scores and details and if you open the question link on new tab, you can view the actual question. If you get to see the question on which the test was based, it reveals its a trick review. Should this be fixed? Perhaps a fake link for the fake question? This is the  where I found this.  Congratulations! This was only a test, designed to make sure you were paying attention. You passed. For reasonable questions, Leave Open is appropriate.

I recently received this rather amusing message while reviewing a user's first post:  Congratulations! This was only a test, designed to make sure you were paying attention. This post has already been removed, but thanks for taking time to leave feedback for the author.   What is the purpose of this test? How does the audit work? What happens if I fail? Why was the system expecting me to negatively review a good post, or positively review a bad post? A review is obviously an audit. Should I report it? Do review audits count toward the Reviewer badge? Do robo-reviewers dream of electric sheep?


Let's say we have a class with a function template.  Header file Sort.hpp with the class definition:  #ifndef TEST_SORT_HPP #define TEST_SORT_HPP  #include <vector> using namespace std;  class Sort { public:     template <typename T>     static void mergeSort(vector<T>& arr); };  #endif //TEST_SORT_HPP   Source file Sort.cpp with the function implementation:  #include "Sort.hpp"  template <typename T> void Sort::mergeSort(vector<T> &arr) {     // the implementation is irrelevant at the moment }   This structure would not work for . As also stated in the referenced answer, there are ways to work around this issue, if I do not want to include the implementations straight into the header file.  However, those solutions do not work for me:   If I add #include "Sort.cpp" in the end of the header file (before #endif), I get the error: redefinition of 'static void Sort::mergeSort(std::vector<T>&)' I do not know in advance all the types the sort is used for and cannot declare them explicitly in the end of the source file. I also cannot remove #include "Sort.hpp" from the Sort.cpp file, because then 'Sort' has not been declared   How is this actually done to make it work?  What are the best practices for organizing code into files in case of:   ... creating class templates with unknown types (unlimited)? ... creating class templates where it is known which certain types will be used?

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.)


Which particles could be waves? Electrons and photons are both particles and waves (electricity and electromagnetic radiation). Could other fermions or bosons be both particles and waves?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' that everything is made up out of particles, whether those are photons, electrons, or maybe even strings. That light for example, also shows wave-like properties, why does that even matter? Don't we know that everything is made up of particles? In other words, wasn't Young wrong and Newton right, instead of them both being right?


Suppose that the conclusion of a particular argument is ‘Grass is green and it is not the case that grass is green.’ Without knowing anything more about this argument – in particular, without knowing what its premises are – is it possible to tell whether it is valid or invalid? Explain your answer.

I have an argument with the conclusion: 'The sky is blue and it is not the case that the sky is blue'.  Without knowing the premises of this argument, am I right in saying this argument is invalid since the this conclusion is necessarily false?


Why is it “the” Port Authority Bus Terminal, but not “the Penn Station”?

Last week in college, a student [with a thick South Asian accent] asked me:     "Excuse me, where can I find the room 401?".   I realized that to my native English ears, the word "the" sounded non-native. This had me realize that we sometimes use no article.  I am learning French; in French, we seem to always use some kind of article before nouns. It surprised me, at that moment, to realize that English doesn't always do the same! (That, and using the definite article in "the room 401" seems to make sense if I think about when definite articles are used).  Is there a grammatical name or concept for this "no article" aspect of our language? Are there any websites that can explain this to me?


I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question.  I've had a lot of physics experiments involving springs, unintentionally dismantled a hair clipper once, helped my dad repair his car, and all of them have very identical springs.   Here's an image of a variety of springs that are used for multiple purposes:     So, what's with the spiral/helical shape? And why are they "curled"  in circle-like shapes. Why not triangle, square or any other geometric shape? What exactly is the physics behind this.

Why are springs coiled the way they are? Why not some other shape? Is the shape due to its elasticity or something?


The code that I want to use is  private void removeInstance (BaseClass b) {     // some more code     b = null; }   b can be of an instance of a subclass of BaseClass. For example  public class C extends BaseClass {/* Some Code */}   This is what should be possible.  C c = new C (); // some code removeInstance (c);   However it currently does not set c to null as c is cast to BaseClass in this example.  I want to be able to set an instance to null from the base class in one way or another.

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?