Polynomials in one variable with infinitely many roots.

Can a non-zero polynomial in one variable have infinitely many roots ? Can a non-zero polynomial in one variable have uncountably many roots ?  Motivation: over $\mathbb Z/12\mathbb Z$, $X^2-4$ has 4 roots. When it comes to polynomials with coefficients over an integral domain, the answer is clearly negative (in that case, a polynomial can't have more roots than its degree). What happens with a ring that has zero divisors ?


matplotlib Error: No module named matplotlib even though it is installed

I have been through the process of installing matplotlib on my Ubuntu 12.04 computer. However, when I try to run a test program, I get the following error:   Traceback (most recent call last):   File "../py33/test.py", line 2, in <module>     import matplotlib.pyplot as plt ImportError: No module named 'matplotlib'   I am trying a sample program from matplotlib's website (basic_example). I just don't understand why it says there is not module matplotlib, even though I have definitely installed it (using sudo apt-get install python-matplotlib, and have done sudo apt-get build-dep python-matplotlib; I also tried pip install matplotlib, as I was told to do that, after installing Python itself, if I wanted to install other binaries).


Bootstrapping the sample range - When the bootstrap fails

I'm trying to convince myself that bootstrapping fails when estimating extreme order statistics (and thus functions thereof). This is a classic shortcoming of the bootstrap laid out in some detail by Chernick (2007, 2011). The reasoning for this is that other methods have been proposed to get around the issue of extreme values, such as the $m$-out-of-$n$ bootstrap. Consider bootstrapping sample range $R = X_{(n)} - X_{(1)}$ from a $N(5, 1.5)$ distribution from $n$ = 100 observations. This is easily accomplished in R as follows. set.seed(1991)  x <- rnorm(100, 5, 1.5) # simulated data r <- max(x) - min(x) # true value = 10.02242  f <- function(x, i) {    return(max(x[i]) - min(x[i]))  }  library(boot)  y <- boot(x, f, R = 10000)  plot(y) # histogram and QQ plot  boot.ci(y) # confidence intervals Intervals :  Level      Normal              Basic          95%   ( 8.97, 13.40 )   (10.02, 13.55 )    Level     Percentile            BCa           95%   ( 6.50, 10.02 )   ( 7.12, 10.02 )   Calculations and Intervals on Original Scale Some BCa intervals may be unstable  The true range is captured in two of the above intervals. I also notice that the true/bootstrapped value is often the endpoint of the CI. I don't think this is a random occurrence, since R sometimes warns users of this, but I still consider the endpoint value falling within the interval.' Here are the plots of the bootstrap distribution. This is what I'm getting at. Looking at these, it suggest something might be wrong -- and indeed this is the case. The below plots look nothing like your typical bootstrap distribution when $n$ is large. Typically, when we bootstrap "nice" (smooth) statistics like the sample correlation say, the plots end up approximating a Gaussian distribution quite closely.  Besides checking whether or not bootstrap confidence intervals capture the true parameter value (and looking at the distribution plots), is there any other evidence suggesting that the traditional bootstrap fails in the case of estimating the sample distribution of extreme order statistics? I'm thinking that interval coverage could also be examined, but is this typically done (or is there enough proof in the intervals and plots themselves)? Edit - In response to duplicate question Many responses to similar questions on CV are quite theoretical. While I appreciate and understand the theory behind the bootstrap, many researchers in other fields do not and would appreciate applied answers that use simulations/real examples in R.


TeX Live Manager crashes with "Unknown docfile tag"

Today my TeX Live 2013 stopped updating packages. I use tlmgr to update packages but it's crashing with the following error:  $ sudo tlmgr update Unknown docfile tag:  texmf-dist/doc/latex/pythontex/pythontex_quickstart.pdf details=""Quick start" documentation" at /usr/local/texlive/2013/tlpkg/TeXLive/TLPOBJ.pm line 127, <TMP> line 127939.   The command   sudo tlmgr update --self --all --reinstall-forcibly-removed   does not fix it.


What is the best word to refer to the person that I (directly) supervise, in the context of a corporate workplace? The closest I can think of is employee, but that doesn't directly convey a direct supervisor relationship.  Other options I can think of are apprentice (usually used to refer exclusively to someone who is still learning where I come from), underling (patronizing), and worker (again not specific).  For example when describing a project:   My employee designed the front-end of the system while I worked on the critical business logic.


Is there a way to monitor the amount of processing power used in a program in Python?  My goal is to kill a program if someone is using too much power while connecting to my server in case of malicious intent.


Here is the output of ifconfig -a: lo: flags=73<UP,LOOPBACK,RUNNING>  mtu 65536     inet 127.0.0.1  netmask 255.0.0.0     inet6 ::1  prefixlen 128  scopeid 0x10<host>     loop  txqueuelen 1000  (Local Loopback)     RX packets 4653  bytes 433590 (433.5 KB)     RX errors 0  dropped 0  overruns 0  frame 0     TX packets 4653  bytes 433590 (433.5 KB)     TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  wlx34e894d6ef11: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500     inet 192.168.86.40  netmask 255.255.255.0  broadcast 192.168.86.255     inet6 fe80::e7d2:d7bc:ea13:327  prefixlen 64  scopeid 0x20<link>     ether 34:e8:94:d6:ef:11  txqueuelen 1000  (Ethernet)     RX packets 737205  bytes 1091181187 (1.0 GB)     RX errors 0  dropped 148  overruns 0  frame 0     TX packets 334745  bytes 34779005 (34.7 MB)     TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  Here is the output of sudo nano /etc/network/interfaces: auto lo iface lo inet loopback allow-hotplug eth0 iface eth0 inet dhcp  Here is the output of ethtool eth0: Settings for eth0: Cannot get device settings: No such device Cannot get wake-on-lan settings: No such device Cannot get message level: No such device Cannot get link status: No such device No data available  Here is the output of sudo lshw -C network: *-network UNCLAIMED           description: Ethernet controller    product: Intel Corporation    vendor: Intel Corporation    physical id: 1f.6    bus info: pci@0000:00:1f.6    version: 00    width: 32 bits    clock: 33MHz    capabilities: pm msi bus_master cap_list    configuration: latency=0    resources: memory:d1200000-d121ffff *-network    description: Wireless interface    physical id: 1    bus info: usb@1:12    logical name: wlx34e894d6ef11    serial: 34:e8:94:d6:ef:11    capabilities: ethernet physical wireless    configuration: broadcast=yes driver=r8188eu ip=192.168.86.40 multicast=yes wireless=IEEE 802.11bgn  Here is the output of sudo lspci -v: 00:1f.6 Ethernet controller: Intel Corporation Device 0d4c        Subsystem: Dell Device 09a6        Flags: bus master, fast devsel, latency 0, IRQ 255        Memory at d1200000 (32-bit, non-prefetchable) [size=128K]        Capabilities: [c8] Power Management version 3        Capabilities: [d0] MSI: Enable- Count=1/1 Maskable- 64bit+  Output of lspci -knn | grep Eth -A3: 00:1f.6 Ethernet controller [0200]: Intel Corporation Device [8086:0d4c]        Subsystem: Dell Device [1028:09a6] 01:00.0 Non-Volatile memory controller [0108]: Micron Technology Inc Device [1344:5405]        Subsystem: Micron Technology Inc Device [1344:0100]  How can I fix this?


In most Emacs major modes targetting compiled programming languages, C-c C-c invokes make. In AucTeX, it lets me choose between any of  BibTeX  Biber   Check   ChkTeX  Clean   Clean All   File Index   LaTeX   Other   Print   Queue   Spell   View Xindy   These options are generally fine, but sometimes compiling my document requires more complex steps; in these cases, I use a Makefile.  How can I extend the list displayed by AucTeX to include a Make option?  TeX-command-list and TeX-run-compile seem relevant, as C-c C-c invokes TeX-command-master, which presents entries from `TeX-command-list.


How does attacking a target affected by the sleep spell work?

The  spell description says:  Starting with the creature that has the lowest current hit points, each creature affected by this spell falls unconscious until the spell ends [...]  So an  creature has penalties, and these two in particular are why I am confused:   The creature drops whatever it’s holding and falls prone.  [...]  Attack rolls against the creature have advantage.   But when you look at the rules for the  condition:  An attack roll against the creature has advantage if the attacker is within 5 feet of the creature. Otherwise, the attack roll has disadvantage.  The unconscious condition says that attack rolls against my target have advantage, but the prone condition says that if I'm not within 5 feet I have disadvantage on my attack. Do these cancel out?


how to schedule a salesforce job every 3 months?

Someone know how to cron a salesforce job every 3 months, on the 1st at 9am? any ideas?


What causes this NPE in org.apache.catalina.connector.CoyoteWriter.flush()?

private void respond(String response) {      httpServletResponse.setContentType("application/json");     httpServletResponse.setCharacterEncoding("UTF-8");      try {         PrintWriter out = httpServletResponse.getWriter();          out.print(response);         out.flush();      } catch (IOException ex) {         log.error("Error while writing response",ex);     }  }   This code throws null pointer at out.flush(). httpServletResponse is instance variable. I have verified that response is not null. This function is being called from inside Apache's aync http client lib's CloseableHttpAsyncClient.execute.completed().  LOG:  Caused by: java.lang.NullPointerException: null     at org.apache.coyote.http11.InternalNioOutputBuffer.flushBuffer(InternalNioOutputBuffer.java:234) ~[tomcat-coyote.jar:8.0.14]     at org.apache.coyote.http11.InternalNioOutputBuffer.addToBB(InternalNioOutputBuffer.java:189) ~[tomcat-coyote.jar:8.0.14]     at org.apache.coyote.http11.InternalNioOutputBuffer.commit(InternalNioOutputBuffer.java:177) ~[tomcat-coyote.jar:8.0.14]     at org.apache.coyote.http11.AbstractHttp11Processor.action(AbstractHttp11Processor.java:739) ~[tomcat-coyote.jar:8.0.14]     at org.apache.coyote.Response.action(Response.java:179) ~[tomcat-coyote.jar:8.0.14]     at org.apache.coyote.Response.sendHeaders(Response.java:341) ~[tomcat-coyote.jar:8.0.14]     at org.apache.catalina.connector.OutputBuffer.doFlush(OutputBuffer.java:331) ~[catalina.jar:8.0.14]     at org.apache.catalina.connector.OutputBuffer.flush(OutputBuffer.java:313) ~[catalina.jar:8.0.14]     at org.apache.catalina.connector.CoyoteWriter.flush(CoyoteWriter.java:98) ~[catalina.jar:8.0.14]     at com.thruport.aje.rotator.reward.async.RewardRequest.respond(RewardRequest.java:185) ~[output/:na]     at com.thruport.aje.rotator.reward.async.RewardRequest.lambda$new$2(RewardRequest.java:131) ~[output/:na]     at java.util.concurrent.CompletableFuture.uniApply(CompletableFuture.java:602) ~[na:1.8.0_121]     ... 8 common frames omitted


When I log in to my machine per ssh, the banner says: "no mail". Other times, it says "you have mail", even though I have no new mail. Obviously, I don't need to be informed about mail which I have already read. This information is completely useless. Can I disable it all together ?  I am using Debian Wheezy


Are 401k Employer Match amounts subject to FICA or any other tax?

When my employer makes a contribution to an employee 401k account, are any taxes payed by the employee (e.g. FICA)?  And does the employer match amount show anywhere on the employee's W-2 or 1040?


Bash - meaning of the semicolon after the command

A list is a sequence of one or more pipelines separated by one of the   operators ‘;’, ‘&’, ‘&&’, or ‘||’, and optionally terminated by one of   ‘;’, ‘&’, or a newline.   I can't find an explanation, what does semicolon (;) do after the last command. For instance, what's the difference between the following two commands:  a;b;c  a;b;c;  ?


I had applied for standard visitor visa to see my daughter (British citizen)''s family  including kids (British citizens) and her husband (Indian citizen on ILO) 0n 18/5/2018 and got refusal as above . While i had visited uk in 2008 and returned back in 2 months (different sponsor).I am unable to understand the refusal  noti ce because of folowing reason's :- 1 ECO has claimed to have considerd interview with applicant and sponsor but no interview has been conducted with me and sponsor. 2. Reason of refusal has been left blank for explanation with a dot mark.  3.name of ECO has not been entered. 4.General refusal wording is written in which reasons are also not entered .These wordings clearly show that reasons must be entered but it is not done.moreover refusal writing guidance also mentions explanation of any refusal to be entered in refusal notice.  In the light of above I want to ask if this refusal notice is justified and do all general refusal wordings  mentioned in refusal notice apply to me or are they general one?? To whom should I write for explanation.? No such activity was done on my part that such deception charges may apply to me . Are there chances that appllication and supporting documents  of some other person may have been considered for me . What should I do .kindly suggest .thanks


Why does cron silently fail to run sudo stuff in my script?

I have a script run from a non-privileged users' crontab that invokes some commands using sudo. Except it doesn't. The script runs fine but the sudo'ed commands silently fail.   The script runs perfectly from a shell as the user in question. Sudo does not require a password. The user in question has (root) NOPASSWD: ALL access granted in /etc/sudoers. Cron is running and executing the script. Adding a simple date > /tmp/log produces output at the right time. It's not a permissions problem. Again the script does get executed, just not the sudo'ed commands. It's not a path problem. Running env from inside the script being run shows the correct $PATH variable that includes the path to sudo. Running it using a full path doesn't help. The command being executed is being given the full path name. Trying to capture the output of the sudo command including STDERR doesn't show anything useful. Adding sudo echo test 2>&1 > /tmp/log to the script produces a blank log. The sudo binary itself executes fine and recognizes that it has permissions even when run from cron inside the script. Adding sudo -l > /tmp/log to the script produces the output:       User ec2-user may run the following commands on this host:   (root) NOPASSWD: ALL    Examining the exit code of the command using $? shows it is returning an error (exit code: 1), but no error seems to be produced. A command as simple as /usr/bin/sudo /bin/echo test returns the same error code.  What else could be going on?  This is a recently created virtual machine running the latest Amazon Linux AMI. The crontab belongs to the user ec2-user and the sudoers file is the distribution default.


c# extend String Class with static method

I was wondering if there is a way to extend the string class with a method called GenerateRandom() which generates a random string. Maybe this would look like  string.CreateRandom();   As I have read there is no way than creating an instance of a string and then calling the extension method. Maybe there is one and you know it.  Thanks for your help!


Counterexamples for $G \times H$ isomorphic to $G$ implies $H$ trivial.

I am interested in the following question:  Does $G \times H \cong G$ necessarily imply that $H$ is trivial?  In order to demonstrate it is not, I attempted to construct an example, but I am not entirely sure it is valid:  Let $G = \langle \mathbb{Z}; [a,b] \ (\forall a,b \in \mathbb{Z})\rangle$.  Then $G \times G = \langle \mathbb{Z} \cup \mathbb{Z}; \ \{[a_1, b_1]\} \cup \{ [a_2, b_2]\} \cup \{[a_1,b_2]\}\rangle$, where my notation is intent to convey that the direct product presentation has the abelian relations from the "first" copy of G, the abelian relations from the "second" copy of G, and the required abelian relations which commute generators of the "first" copy with those of the "second" copy.    In this example, since our cardinalities are equal, $|\mathbb{Z} \times \mathbb{Z}| = |\mathbb{Z}|$, and since this implies that commuting all elements of $G$ and commuting all elements of the same cardinality generating set $G \times G$ requires a bijection between the relator sets, then we should have a bijective group homomorphism $\phi : G \rightarrow G \times G$ so that we have isomorphism, but obviously $G$ is not trivial.  Therefore this provides the necessary counterexample to the original statement.  My first question is: is there anything wrong with this proof?  My second question is: if there is nothing wrong with the proof, is there a more standard way of constructing this type proof?  In general, it would seem that whenever you have isomorphic generating sets and isomorphic relator sets, then this should be enough to describe any number of counterexamples to the claim that $H$ must be trivial.  Is this true?  Finally, since direct products can be viewed as the products in the category Ab, and since all final objects must be isomorphic, would there be an easier way (or maybe just an insightful way) of construct this argument entirely in a category theoretic context?  Thanks!


How do I get this neat avatar + rep + badges image?

The other day, I saw the blog of an SO member. In it, there was an image of his SO avatar and his reputation and badges. It looked cool. Is there any easy way for me to get something like that, tailored to me?


Match text between two words with grep on multiple lines

I know there's the a syntax you can use, like:  grep -oP '.word1.*?word2'   but this doesn't work on multiple lines. So here's an example input:  user1:x:1001:1001::/home/user1home:/bin/bash user2:x:1002:1002::/home/user2home:/bin/bash user3:x:1003:1003::/home/user3home:/bin/bash user4:x:1004:1004::/home/user4home:/bin/bash   The command I tried to use was:  grep -oP '.1002:1002.*?user4home'   My desired output would be something like this:  1002:1002::/home/user2home:/bin/bash user3:x:1003:1003::/home/user3home:/bin/bash user4:x:1004:1004::/home/user4home


Are there a distinct number of solutions to: $a^n-b^n=2^{100}$ If a, b and n are positive integers greater than 1 I have tried to solve it with code but it takes to long.  for ($a=3; $a -lt 5000; $a++) {     for ($b=2; $b -lt $a; $b++){         for ($n=2; $n -lt 200; $n++) {             $x=[bigint]::Pow($a,$n)-[bigint]::Pow($b,$n)             if ( [bigint]::Pow(2,100) -eq $x) {write-host $a,$b,$n}             }         }    }


Can somebody actually find out my name on a Stack Exchange community?

So recently I tried answering back and to somebody's post on SO. However, he replied back to me with my real name, which is not public. I am just wondering, from where did he get the name, since my username is no way telling my complete name, then how did he get the same?  Am I missing out some settings or something here?


Can this proof be written without invoking the Axiom of Choice?

I have two questions. First of all, I have defined the set $\mathbb{N}$ using the axioms of ZFC, and I have also defined arithmetic on it. I have also proven the induction principle and I am free to use it.   I am now trying to prove the following: a set is finite if and only if it is in bijection with a natural number. I have shown by induction that every natural number is finite, so only one direction remains. For your information, in my framework a set is defined to be infinite if it is in bijection with a proper subset of it.  I have also proven the following fact: if a set contains an infinite subset, then it is infinite. So here is my proof: (the set is denoted by $S$)  If $S$ is empty then there is nothing to prove. So, let $S$ be a non-empty finite set. For the sake of contradiction, suppose $S$ is not in bijection with a natural number. We will show that there is an injective map $f:\mathbb{N}\to S$, and hence $S$ will contain an infinite subset, which will imply that $S$ is itself infinite, and hence a contradiction will be obtained.   First, we show that for every non-zero $n\in\mathbb{N}$, there is a subset of $S$, which we denote by $S_n$, such that $n$ is in bijection with $S_n$. Moreover, we will show that $S_{n}\subset S_{n + 1}$ for every $n\in\mathbb{N}$. This we show by induction.   For the base case, consider $1 = \{0\}$. Choose any $s_0\in S$, and consider the map $0\mapsto s_0$. So, $1$ is in bijection with the set $S_1 = \{s_0\}$. Now, suppose $n\in\mathbb{N}$ is in bijection with some subset $S_n\subset S$, and let this bijection be $\theta$. Clearly, $S - S_n$ is non-empty, otherwise it would contradict our assumption that $S$ is not in bijection with a natural number. So, there is some $s_{n}\in S - S_n$. Consider the map that sends any $m < n$ to $\theta(m)$, and maps $n$ to the element $s_n$. Let $S_{n + 1} = S_n\cup\{s_n\}$. So this map is a bijection from $n + 1$ onto $S_{n + 1}$, and also $S_n\subset S_{n + 1}$ (where the inclusion is proper). So by induction, this statement is true for all $n\in\mathbb{N}$.    Now, we construct an injection from $\mathbb{N}$ into $S$ as follows. By our hypothesis, every set $S - S_n$ is non-empty. Let $f:\mathscr{P}(S)\to S$ be a choice function as guaranteed by the axiom of choice. Then consider the following map: $0\mapsto s_0$ and $n\mapsto f(S_{n + 1} - S_{n})$ for every $n\ne 0$. This is easily seen to be a one-one map from $\mathbb{N}$ into $S$. This completes the proof.   Now I have two questions: I wanted to confirm whether the induction step is valid or not. And second and more importantly, can this proof be written without invoking the Axiom of Choice?  I have been thinking hard about it, but still no progress.


Movie with giant spider-like alien robots kidnapping people

Giant robots with an oval-looking head with a few of long legs (like spider) but bigger  Lighting strikes down into the middle of the road and that’s how they came They climbed out and starting shooting lasers that would desintegrate the humans they kill but their clothes are not gone A family (the main characters) go and try to run and they live but they go to a big ferry or ship. They make it on but those alien robots come and flip the ship, taking all passengers into the water, taking them with their long arms inside of them. The alien robots are either killing them or storing them but they throw out their clothes.  The family finds a little underground house or something, but the son or boy goes to help someone else up the hill. So he goes and leaves the family but I think he dies. the father and daughter hide in the underground bunk house, but the alien robots have moving arm eyes or something, looking for people to capture and kill or take.   I don’t think this is from War of the Worlds.


Probability of $x^2+bx+c=0$ having real roots

Consider the quadratic equation $x^2+bx+c=0$, where $b$ and $c$ are   $Uni∼[0,1]$. Let $p(b)$ represent the probability that the given   equation has a real solution for a fixed value of$ b$.       What is $p(1/2)$?      What is the probability that$ x^2+bx+c=0$ has a real solution ?   $p(1/2)$ = prob $x^2+bx+c=0$ has a real solution)  now $x^2+bx+c=0$ has a real solution if discriminant $≥0$  i.e., $1−16c≥0$ which   is same as $c≤1/16$. since $C∼UNI[0,1]$ the $p(c)≤1/16=1/16$  Is this correct and how to do the second part?


How do i make meshes separate from eachother?

All parts work as their own in edit mode, count as one in object mode. Looking to make them all separate.


Why does a wind turbine have only three blades?

Why not four or five or even more?  Intuitively, the more leaves the more power.  So, what is the reason?


Why does illuminance stay the same for a given f-stop even when focal length changes?

I'm trying to wrap my head around the math/physics of how illuminance on the film/sensor plane remains equal for a given f-number regardless of the focal length of the lens.  Since a longer lens will have a larger entrance pupil at a given f-stop than a shorter lens at the same f-stop, how can the light falling on the film/sensor be equivalent?  Empirically, I know this to be true.  Say I take an incident meter reading (not reflected/TTL) off my subject, and get f/5.6 at 1/100s, I'll get proper exposure at the point at which i took the meter reading with that setting whether I use a 50mm lens or a 200mm lens (obviously composition will be different).    Wikipedia's  reads:     A 100 mm focal length f/4 lens has an entrance pupil diameter of 25   mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of   50 mm. The 200 mm lens's entrance pupil has four times the area of the   100 mm lens's entrance pupil, and thus collects four times as much   light from each object in the lens's field of view. But compared to   the 100 mm lens, the 200 mm lens projects an image of each object   twice as high and twice as wide, covering four times the area, and so   both lenses produce the same illuminance at the focal plane when   imaging a scene of a given luminance.   I'm not sure I agree with the explanation on wikipedia.  The film/sensor doesn't care how big the image is that falls outside the bounds of the sensor; the film/sensor "sees" what it sees, and that's it.


Simplest known solution to "World's Hardest Easy Geometry Problem"?

I've seen multiple solutions to this well-known problem (posed, among other sites, at ). None of the solutions are particularly simple. I was wondering if trigonometry (which the site I mentioned instructs you not to use) would yield an easier solution. Can anybody provide one?  EDIT: Multiple users have marked this as a duplicate question. The question they are referring to is far more general and probably far more difficult. All the answers that were given to it either lacked proofs or were incorrect. I'm looking for a specific, detailed, simple proof for this particular problem that takes advantage of trigonometry instead of elementary geometry.


What should we do about a question where the OP answered it in the question itself?

I am talking about following question:   As we can see, the OP has found the answer and he has updated it in the question itself. What should we do when encountering such questions?


Are the words biology and Ecology ever interchangeable?

I often hear people use the word "Ecology" when i think they mean "biology." This got me wondering: are the words ever interchangeable, or are these people really just that frequently using the wrong word?   My understanding is biology is the broader study of life while Ecology is the more specialized study of life interacting with other stuff (life + earth).


If $H$ is a subgroup of $S_n$ contains transpositions $(1,2), (1,3), ..., (1,n)$ then $H = S_n$

I have a question concerning permutations.  I'm starter in group theory and would appreciate some ideas. I read something about generators but I didn't understand very well how these work with permutations:     Show if $H$ is a subgroup of $S_n$ contains transpositions $(1,2), (1,3), ..., (1,n)$ then $H = S_n$.


Install Windows 7 from USB in Ubuntu 16.04 LTS

I prepared a Windows 7 ISO file, bootable pendrive by using DISKS.  Here's my system configuration.        Currently Ubuntu is running on my system (only one OS) When I am trying to install the Windows 7 using a penddrive, it is showing no device is found. But am able to view the pendrive data/details once I'm logged into the system.  Is this problem due to partition issues?  Please give some guidance/suggestions on how to install Windows 7.


What is the indefinite integral of $\lfloor x^{-1} \rfloor$?

I am trying to find the indefinite integral of $\lfloor \frac 1x \rfloor$  My attempt  Please be aware that what comes after this sentence is nothing more than my work. It makes to me, and a lot of it contains made up notations, a lot of which I have made up and are very difficult for me to explain and/or define clearly. If it makes no sense to you, feel free to ask, but since those things are tangential to the question, feel free to also ignore them and refer purely to my above queston.  So, since this is a piecewise constant function, I used the method of jump series to integrate it. I found the implied integral to be $x\lfloor x \rfloor$.  This means that the integral now equals $x\lfloor \frac 1x \rfloor - JS(x \lfloor \frac 1x \rfloor)$  Now, the piecewsie constant component troubles me. Because the function is infinite at 0, I cannot shift all of the disconnected pieces to line up with x = 0 held fixed (physically I mean). That would make the function infinite everywhere. Plus, I am not sure if the integral is divergent. I think the floor chops away enough area to make it finite. However, it throws me off.  Extra question  Assuming that the answerer understands my writing (or at least can understand my progression of computation), could the answerer find and compute JS(x * floor(1/x))? It shouldnt be too hard. (After all, it is just a matter of solving for it in the expression earlier mentioned involving it). If you cannot find it (doesnt reveal itself explicitly) or the weird notation confused you, feel free to ignore this "extra question". Its not relevant to the original question at the very top of this post, and as I said, these later sections pertain to my attempts, not neccessarily the solution that one finds. As they say, more than one way to skin a cat. Dont have to like my method to skin the cat. :p  Definitions (to help clarify things)  Implied Integral: A form of symbolic integration that holds all symbols of the form $\lfloor f(x) \rfloor$ constant. Implied Integration varies by piece-wise constants rather than constants. Eric Stucky more formally defined this concept  (note, I did not write that paper. 'Assistance' is merely credit to me making up this integral.)  Jump Series: The portion of a piece-wise continuous function (bounded or unbounded) that consists purely of jump discontinuities. The Jump Series will be a piece-wise constant function varying by a real number constant. If there is a jump from an infinite value to a finite value that cannot in some way be reduced down, we still consider the Jump Series to be existing, but either 'diverging' or 'unbounded'.  Integration Method of Jump Series: A method of integration where regular integration is split into an implied integral of the function being integrated minus the jump series of the aforementioned implied integral. This method is guaranteed to work so long as the final integral has a closed form. All of the operators involved are guaranteed to exist so long as the original function being integrated exists; however, the degree to which they can be expressed is... unknown.


Where is the delete button account button in Thunderbird 17.0.8?

How I can remove an account in my Thunderbird? I have Thunderbird 17.0.8.


Graphics problem when viewing in user perspective

When I view my scene in "User Perspective" mode, my graphics are glitched out (both solid and texture modes).  When I switch to ortho everything looks fine, so does the final render.  On the left is a plain old vanilla sphere (no modifications) - on the right is a cylinder with holes cut out.    I'm using 2x GTX-770 graphics cards (CUDA) in preferences.  Any Ideas?  Cheers.


The objective is to have assignment rules fired on a Lead record creation. It seems the rule can be assigned only when using "update" DML in an "after insert" trigger. Why does another DML must be executed after insert to have lead assignment rule assigned?   //Does not work trigger LeadTrigger on Lead (before insert) {         for (Lead l : Trigger.new) {                 Database.DMLOptions dmo = new Database.DMLOptions();         dmo.assignmentRuleHeader.useDefaultRule = true;         so.setOptions(dmo);     } }   //Works: Records must be *updated* in after insert trigger in order to have the rule assigned trigger LeadTrigger on Lead (after insert) {     List<Lead> ls = new List<Lead>();      for (Lead l : Trigger.new) {         ls.add(new Lead(id = l.id));     }      Database.DMLOptions dmo = new Database.DMLOptions();     dmo.assignmentRuleHeader.useDefaultRule = true;     Database.update(ls, dmo); }   Moreover, testing of the rule assignment fails even though the rule has been assigned to the Lead. We cannot test assignment rule outcome (ownerId=defaultQueueId for example) since the rule will change on PROD eventually.  //Test method failing for a lead *having* rule assigned:     public static void assertDefaultAssignmentRules(SObject sobj) {     Database.DMLOptions dmo = sobj.getOptions();      System.assertNotEquals(null, dmo, 'DMLOption is null');     System.assert(dmo.assignmentRuleHeader.useDefaultRule, dmo); }


Why can we add "a number of" before nouns?

In the following sentence:     The city is populated by many people.   "many" can be replaced by something like "a great number of" (let us leave the perceived differences between the meanings of these two modifiers out of discussion):     The city is populated by a great number of people.   I understand that this replacement does not change the object "populating the city" from the original "people" to a "number", but rather shows the ability of expressions in the form "[numeral] of" to provide information about the quantity of nouns they modify.  Is this ability due to some special qualities of nouns such as "number", "quantity", "fraction", &c., or is it just one usage of the preposition "of"?


How can I remove a directory of many files quicker?

How can I remove a directory of many files fast?  For example, I backup my hard drive on an external drive, and when I need to release the space occupied by some very old backup on the external drive, I want to release the space as soon as possible. rm -r /very/old/backup takes very long to finish running.  Thanks.


Battery charge status decreases while plugged in charging

so I have a 2019 MacBook Pro 16" on Catalina 10.15.5.  I recently got it back from the shop - upper case replacement for bad keyboard that included replacing the battery as part of the repair.  Now I've noticed that while its plugged in and 100% charge and I'm using it, the battery charge actually decreases.  For instance last night I opened it, it was plugged in at 100%. I used it to make an email and print a few pages for 15 minutes and the charge actually decreased to 93%.  The icon shows when plugged in. I have looked at  but Battery Health Management is not turned on so it seems to be something else in my case. How can I diagnose and solve this issue? PS: I'm using an OEM 96W power adapter.


Only a few characters of an arabic word in a different color

Can we get for example only the last character of an arabic word written in a red color.  I use the arabi package with pdfLatex


How to remove entry of ubuntu 12.04 from Windows bootloader while used (wubi installation)?

A few months I decided to install Ubuntu 12.04 on my PC alongside with my Windows 7 partition. In order to do that and avoid any mistake, I followed the steps of  tutorial.  Everything was going well until I decided to update to the 12.10 release. I don't know what happened, but after I updated my Ubuntu, it stopped working, it didn't even launched, when I turned on my PC and choose to run "Ubuntu 12.04" on the Grub Screen, a weird messaged appeared.  Well, so I decided to install the Ubuntu 12.10 and forget about the 12.04 partition, no problem.  I erased the partitions used for the Ubuntu 12.04 with EaseUS partition Manager.   However, when I start my PC, there is still the option of "Ubuntu 12.04" to chose, is that bad?  And what about now, can I use the  of Ubuntu to install the Ubuntu 12.10 ? What should I do to have Ubuntu 12.10 and Windows 7 in dual boot again?


Is RSA in a ECB-like-mode safe for bulk encryption?

Let's say I would like to communicate with my friend using asymmetric/public-key encryption, e.g. RSA.  (Note: I do realize that in practice this is done through an intermediate symmetric key, but this question assumes we only use asymmetric encryption.)  Say I try to do this: I slice up my data into 2n-byte blocks (padding with zeros [edit: padding appropriately] if necessary), append the block index to the block (to prevent the same plaintext from turning into the same ciphertext), then use my friend's public key to encrypt each block separately.  Is this a secure scheme, or does the fact that I'm re-using the key make it susceptible to some kind of attack? If so, is it used in practice in any existing algorithms? If not, is there any way to make it safe, aside from using a symmetric key?


Can you help me prove that every planar graph can be expressed as a union of (maximum) five forests?  Ι used induction on the number of vertices. A planar graph $G$ has at most $3|V|-6$ edges, so there is at least one vertex $v$ of degree 5 or less.  Let $\{w_1,\ldots, w_j\}$; $j \le 5$ be $v$'s neighbors in $G$.  Then let $F_1,\ldots, F_5$ be the 5 edge-disjoint forests (some may be empty) such that $\cup_{j=1}^5 F_i = E(G \setminus \{v\})$. How do I prove that $F_1,\ldots, F_5$ exist?  Then for each $i \le j$ set $F'_i = F_i + \{v,w_i\}$, and (if $j$ is strictly less than 5) for each $i \in \{j+1,\ldots, 5\}$ set $F'_i=F_i$. Then each $F'_i$ is also a forest, and that each edge of $G$ is in one of the $F'_i$s.  Special thanks to user Mike for the answer.


In how many different ways can we place 8 identical rooks on a chess board?

In how many different ways can we place 8 identical rooks on a chessboard so that no two of them attack each other and none of them is on main diagonal?  I have tried many ways to solve it and I am quite sure it should be done by few cases. But I can't come up with any idea.


Grammar: Did Jim ask you whether you are a virgin? VS Did Jim ask you whether you were a virgin?

How do I form a question based on the following details:  At 1pm on Sunday Jim: Are you a virgin? Jane: Yes  nothing happened from 1pm to 9pm  At 9pm on Sunday: Did Jim ask you whether you were a virgin?  or   At 9pm on Sunday: Did Jim ask you whether you are a virgin?


New Ubuntu versions on older Compaq Presario

Does latest versions of Ubuntu work on older computers like a Compaq Presario that was preinstalled with Windows Vista


Can a regular expression itself be parsed with a regular expression?

I am reading the code of a regular expression parser, and start to wonder if the syntax of regular expression is itself regular, and can be expressed with another (quite complicated) regular expression?  rere = "" # the regular expression of regular language match1 = re.match(rere, "[a-z]+@[a-z]+.com") # True match2 = re.match(rere, ")az[") # False    I don't see any recursive structure in regular expression syntax, so I think maybe this is doable?  If it is, what does the expression look like? If not, why?


Volume shader results different on cpu/gpu

I was trying to do some tutorials and experiments for Volume shader. In a final render as well as in viewport I am getting totally different results with GPU and CPU. What is strange, when GPU (gtx 970) is used the Volume is very noisy and the quality is much lower (it looks very flat). This is first time i saw such difference in CPU vs GPU result. What is going on?


Default program not listed in windows10 settings

TL;DR: read only bold text + check pictures.   I was trying to change .txt files default program to visual studio code, the problem is, that when I open settings in windows 10 and try to change it there, visual studio code is not listed in the default programs and there is no browse button, so that I could pick any program I want via the path to it.     I have also tried to change the default app in right MB -> open with -> choose another app, but no luck, there was no permanent option.      How are you supposed to change the default program than?


I am reading the PHP documentation for boolean.  One of the comments says 0=='all' is true.    I want to know how it becomes true.  The documentation says all non-empty strings are true except '0'.  So 'all' is true and 0 is false.  false == true should be false.  But:  if(0=='all'){     echo 'hello'; }else{    echo 'how are you '; }   prints 'hello'.


Why does dynamic_cast(VAR) only work when VAR is on the heap?

#include <iostream>  enum types { INTEGER, DOUBLE, BOOL, STRING };  class Descriptor {  public:     Descriptor(types type):         _type{type}     {}     types &type() { return _type; }       virtual ~Descriptor() = default;  private:     types _type; };  class Number: public Descriptor {  public:     Number(types descType):         Descriptor(descType)     {}      virtual ~Number() = default;      int intValue; };   void printValue(Descriptor t) {    auto cast = dynamic_cast<Number *>(&t);   if (cast == nullptr) {     std::cout << "Err" << std::endl;   } else {     std::cout << "Works" << std::endl;   } }   int main() {    Number t =  Number(INTEGER);   t.intValue = 1;    printValue(t); }   The output is always Err. However when I change Number (in main) to be allocated on the heap with new the cast works and is able to access any functions within class Number?  Whats the difference in casting a stack object? When I tried to use static cast and access "intValue" it just gave me a garbage value. Is it possible to cast a stack object?


I'm aware of English's unpredictable nature in wording, but this phrase got me thinking.  What is the origination of the phrase word up... a lot of times shortened to just word!  I understand the meaning of the phrase to be:   Great! Alright! Ok! I agree! That's awesome!   , but how did word end up being a synonym for these?


I was looking through a bike catalogue at one of the high-end road bikes (a ) and I couldn't help but notice that this bike is advertised with specific tyres for front and rear wheels.  This was a new one to me, I've not known any other bike to have this and, as far as I can see, tyre manufacturers don't make front and rear tyres - they're just tyres! So my next question was, "what's the difference?"  The two tyres are the same size (700x23) and it turns out that the difference is in the tread patterns [edit: I now realise this is incorrect]. The front tyre is described as sticky 60/64/60 durometer. The rear described as durable and fast 64/70/64 durometer.  I was just wondering if anyone knew what these values actually mean? (left/centre/right thickness?) Or is it something proprietary to Giant?  Just to be clear, I understand why you might put different tyres on front and back, I understand that the difference between these two might be unnoticeable to all but the best cyclists, its those numbers I'm interested in understanding.


I do not understand as I wrote in a previous question:    solution:    I see that we can scale:   $u_k$ but I do not understand why it is legal to say $a_k + b_k = 1$ what is $a_1 = 20$ and $b_1 = 1$ then $a_1 + b_1 \ne 1$?


Which is right: dad's corner or dads' corner? I see dad's corner used regularly so I am assuming that's right, but in my mind dad's is singular whereas the corner belongs to multiple dads as it's a place for dads to go to meet.


I have a new website that I tried to list in DMOZ, but as of now it's still not listed.  Please tell me what I have to do so that my website will get listed in DMOZ.


Can some weapons not fuse with each other? Because when I tried to fuse the Aurum Club and the Palutena Bow it didn't work and this also happened with the Doom Cannon and the EZ Cannon. And I'm pretty sure I have all the weapons. And also I'm asking if these specific weapons can fuse. Not why they can't. And tell me what they fuse into if they can.


Bash, execute command after invoking a new shell

I am trying to make a script like this:  #!/bin/bash sudo -s something...   When I execute it, I get a new shell but something is executed only when I exit the shell created by sudo -s, not inside it.  Any help?


I want my games that have function that can changes the character colors.I have try a few times.I can make it changes colors in the menu but the colors doesnt change when I click start button. Can any body help me please.


Why are my US Google rankings so much worse than UK rankings and what can I do about it?

My site address is  My Google rank for people searching from the UK is currently 14th - which considering the last 10 years I've been ranking at 18/19/20 or lower is much better. But For people searching from around the world - specifically the USA - I understand my rank is somewhere on page 3. So how would I go about improving my international standing? PS. I'm hoping my rank in the UK has more improvements to make in future updates. EDIT Here's some detail of what sort of things that I've done over the years to try and improve rankings:  Got rid of a directory listing of about 750 noindexed demo pages which didn't have a lot of content beyond a canvas or SVG chart example and the JavaScript code that creates it. This was in August 2019. In the December 2020 Google update my site moved up to 14th position in the UK for the search that I'm targeting - "javascript charts". It still remains in a page 3 ranking for the USA.  I've added an extensive About page:   I used to have a forum which I removed - but since then I've re-added one. This time I'll be making sure the titles are good quality (a lot of people who post messages don't have English as their first language for example).  All/most of the pages have good titles and meta descriptions.  All the pages have been spell checked. When I did this the site started moving up but about 2 weeks later it was pulled back to 18/19/20 overnight. This was before I removed the demo pages. My sight isn't good so I made a lot of spelling and grammar errors!  All of the pages have a set of breadcrumb links.  All pages use HTTPS and gzip compression.  For improved usability, the font size and the CSS line-height have been increased.  I've added an FAQ to the site (  ) which also uses schema. This was a recent addition; this year.  For pretty much all support requests I usually ask people if they could link to me. I usually get positive responses.  The URLs of the pages used to be quite long, but I've shortened them and added 301 redirects from old to new. An example of the new URL style is:    Which is a page about the Google Sheets connector.  I frequently use online performance tools like  ( I just ran a test and got 5 A grades testing from the UK).  I have a spider tool on my computer (Xenu spider) which I use frequently to look for 404 pages. There shouldn't be any legitimate 404 pages currently.  I've tried to "flesh out" pages and make them more verbose (without adding useless crap).  The footer contains links to various key pages on the site - such as the canvas and SVG sections of the website, the FAQ, the support forum, the Twitter and Facebook pages.  The site has Twitter and Facebook pages which are kept up-to-date and relevant, closely mirroring what gets posted on the websites blog (  ).  The pages are quick to load and render, not using complicated HTML so they render consistently across browsers and platforms.  I've added unique Twitter/Facebook meta/Og tags for each page.  The site works well on mobile. No problems reported on GSC. For smaller screens the nav bar turns into a hamburger menu.  Certain JavaScript libraries are positioned to enhance speed - eg charts that aren't immediately visible are created by code that's positioned at the bottom of the page.  Certain HTML5 tags are used (fwiw) eg /.  Summary blocks have been added to the top of each page that use the meta description.  I used to change the design of the site quite often - but I no longer do this. According to the waybackmachine the last significant change to the design of the front page was between August 25th and September 15th in 2019.   There's probably more - I'm always tinkering with something - but this should give a pretty good impression I think. If there's more that you need to know then let me know.


Is it possible to replace the audio of an existing video with a new track? I have some videos that I want to do some audio cleanup on. Can I replace the old audio with the new once I've cleaned it up?


How can I Tex this equation?  I try to have exactly the same result but for the moment I only succeeded in having intersecting lines... Thanks!


How can I share files over a Windows network?

I have a media computer which I recently reformatted to Ubuntu 10.04. I am probably just missing something obvious but I can't figure out how to share folders and files, so that I can browse to them on my Windows computers in order to copy files to/from the computer.  How do I do this?


Detect if a method is annotated with a given attribute only knowing the attribute type as string (Swashbuckle/Swagger)

Linq offers a method to filter an enumerable for a given type.  public static IEnumerable<TResult> OfType<TResult>(this IEnumerable source);   But this means I need to now the type (and have access to it) at compile time. In order to let someone define the type as string how would I call this having the type only as string?  Sure, I could write my own function (since the  isn't that heavy).  I am just curious if there is a way to call without writing my own method. The compiler complains on everything I tried so far.  In my case I have one lib defining an attribute and a second lib allowing to something if the attribute is set. But the filtering library does not know the first library, so I would need to pass this as string.  Well, in detail I am trying to write a Swagger/Swashbuckle operation filter adding the infos for typical pagination. Unfortunatly the pagination itself is in an (replaceable) pagination library. So I need to pass the information which attribute defines that this methods supports pagination from the pagination library to the Swagger/Swaschbuckle library (or define it as value in the configuration).  The code itself does only check if the attribute is set (thats all where I need the type).    public void Apply(Operation operation, OperationFilterContext context)   {     bool paginationSupported = context.ControllerActionDescriptor       .GetControllerAndActionAttributes(inherit: true)       .OfType<MyTypeAsString>() //???       .Any();      if (paginationSupported) // do stuff   }


Java Regex: Find insertion, deletion, substitution counts

I have an algorithm that works with  insertion, deletion and substitution counts of a word compared to a format. I can find these counts in Python like below, fuzzy_counts give me these error counts:   import regex regex_pattern = r"([0-9]{6}){e}" word = '12345' regex_object = regex.fullmatch(regex_pattern, word, regex.ENHANCEMATCH) print(regex_object)   Output:   <regex.Match object; span=(0, 5), match='12345', fuzzy_counts=(0, 0, 1)>   However I need this same thing in Java.  Thanks for the help.


"Markdown editing help" button in the question asking view is misplaced

Just posted a bug report, and found another one :p    (lame hand-drawn cursor coz windows doesn't capture the real cursor)  Oh yeah, I'm on Firefox.


Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?

I would like to solve the beginner's standard exercise which claims that a point of $\mathrm{Spec} \ R$ is closed iff it is a maximal ideal.  The reverse implication is easy. The direct one seems much subtler. If $P = V(I)$ then, since there exist a maximal ideal $M$ containing $P$, it would follow that $\{P, M\} \subseteq V(I) = P$, whence $P=M$. In order to show the existence of $M$ I applied Zorn's lemma to the set of ideals containing $P$.  The question is the following: is there any other proof of the above implication that does not (indirectly) use the axiom of choice? My concern is that I may be using a cannon to shoot a fly. Also, it would be the first time that I see closedness of points to require the axiom of choice. If the axiom is indeed needed in general, are there "nice" classes of rings for which we could get away without it?


How to remove the face that intersects throught the cylinder

I need to remove the face inside this cylinder intersecting with my cube. I've tried to use the knife, project knife with a circle, tried adding a boolean and union/intersect.. nothing does it. The cylinder is scaled down towards the bottom and there is also an angle to the cube. still not working. Please help ! and all those object are currently a single piece.


I want to create a table as shown below. Can someone provide me an MWE?


Splitting shapefile with counties into single boundary lines

I'm a beginning QGIS user and have a shapefile with polygons of all the county borders in Holland.  When I style this shapefile with a non-fill and a dashed line, all the adjacent (overlapping) lines are almost solid instead of dashed. This is because adjacent county borders are duplicates.  How do you get rid of those lines? tried to set the polygon shapes to lines and tried several geometry tools. Is this even possible? Or do you have to remove, clip all the double lines by hand?


How can I record sound before outputting?

I have some apps that I want to record the output sounds locally before outputting to speaker, Bluetooth or any other output. So I get clean unadulterated audio, before any audio output mods.  My devices are rooted, some have custom ROMs.   Is there a way to do this internally, without any programming/coding knowledge? Can this be accomplished? Preferably with out hooking to PC as that prevents local saving.   include steps.  include references      Please excuse lack of tags, limited on choices.


Upgrading pre-release version of Ubuntu 18.04 LTS

I wanted to test a number of ideas and programs as early as possible on Ubuntu 18.04 server in preparation for a possible upgrade of a number of systems from Ubuntu server 16.04 LTS.  My question is if an early version of Ubuntu 18.04 (dec 2017), fully upgraded e.g. once / week will be equivalent to the official version released in april -18? If so, I might use the upgraded 18.04 copy as a template for my servers, saving some time and testing.


Unable to follow release upgrade instructions to upgrade from 19.04 to 19.10

I am trying to upgrade from 19.04 to 19.10 following  instructions. When I come to Select the 3rd Tab called 'Updates', I get the following message:  Unable to download updates: failed to refresh cache: E: The repository 'http://security.ubuntu.com/ubuntu disco-security Release' no longer has a Release file.   How can fix this?


Issues with centering captions for two figures side by side

After following the code for the solution of  I am struggling to get the second line of the captions to stay centered. Normally the first line of text is always centered but once there are two or more lines the text switches to the "justified" alignment (block text). I have tried putting both \begin{center} and \centering within the minipage but neither do anything to the captions, nor do they produce any errors.  Here's my code. Although I checked all the packages and commands and don't think they interfere but I'll add them just in case anyone notices a problem.  \documentclass{article} \usepackage[margin=0.75in]{geometry} \usepackage[utf8]{inputenc} \usepackage{multicol} \usepackage{amsmath} \usepackage{hyperref} \usepackage{gensymb} \usepackage{float} \usepackage{biblatex} \usepackage{mwe} \usepackage{natbib} \usepackage{graphicx}  \renewcommand\thesection{\Alph{section}} \newcommand{\HRule}[1]{\rule{\linewidth}{#1}}  \begin{document}  \begin{figure}[H] \centering \begin{minipage}{0.45\textwidth}     \centering     \includegraphics[width=\textwidth]{log-hhcf.png}     \caption{Logarithmic graph for HHCF gold sample.}     \label{log-hhcf} \end{minipage}\hfill \begin{minipage}{0.45\textwidth}     \centering     \includegraphics[width=\textwidth]{hhcf.png}     \caption{HHCF for gold sample with all the relevant fitted lines and functions.}     \label{hhcf} \end{minipage} \end{figure}  \end{document}   I get this:    Anyone know another way to center the text of the captions on my figures?


I have some monitors left that I want to use. However my GTX980 is fully occupied. Can I throw in an old AMD card I have laying around to drive some secondarily, aka non important displays? Or do I need to stick with NVidia cards? The main monitors would be connected to the 980 for gaming etc, the others would just be used for reading Does anyone run a setup like this? If so, any problems you've encountered? Thanks for the feedback!


Real analysis : Problem related to inverse

Let $f:[0,\infty)\rightarrow [0,\infty) $ be a continuous strictly increasing function and $g=f^{-1}$. Let $a,b>0$ and $a\neq b$. Then how $\displaystyle\int_{0}^af(x)dx+\int_0^bg(y)dy\geq ab.$ Any hint will be appreciated.


How to access a private network behind a router? Can't port forward

I have a video surveillance system (a bunch of IP cameras, with private IPs) behind a router in a distant location. The only ISP that's available at that location has provided me with a 3G/4G USB dongle (so basically mobile Internet). Apparently this dongle (which connects to the router) does some routing/magic by itself (and is not configurable) so I can't use the router to do port forwarding (not in anyway that helps at least). This means that while the cameras have Internet access (so can push information to me), I can't access them directly over the Internet (so basically, no live feeds).  I'm thinking of getting around this by putting a low power computer (software doesn't really matter much in this question, but I'll use Linux) in the same subnet as the IP cameras - let's call this computer A; I also have a VPS rented somewhere that is publicly accessible via the Internet - let's call it B.  I think that this setup should allow me to work around the issue with my live feeds. At least conceptually if I get A to open a tunnel to B then via B I should have access to A's network.  Presuming the above works (I don't see why not, but .. that's why I'm asking) can you guys recommend a system that can accomplish the above with at little fuss as possible? I mean .. should I set-up a VPN with A as a VPN client and B as a VPN server; then anyone who wants to view the cameras simply connects to the VPN server installed on B?  I think this should work, but maybe there's an easier way than setting up VPN on every computer from where I want to check the cameras.  I'm not directly interested in the software (I'm sure that exists and I'll manage to configure it) but rather the networking concepts.   The ideal situation would be that I'd connect to B on (for example) port 8080 and that traffic will automatically be routed from B through a tunnel to A, at which point A will feed data obtained from camera "1" through that connection; then 8081 from camera "2" and so on.


How many nodes to use Maas/Juju for Openstack (Juno)?

I want to do a Proof of concept (Multi node) on MAAS/juju and I'd like to know how many nodes juju needs to install Openstack ? How many NIC ? How many network 1,2,3 ? it is possible with 1 network ?  Can I control where the controller, the compute or cinder will be install on my maas cluster ? (which server?)  I don't want to use devstack or other tools "all-in-one" sorry to ask but on all my researchs, it's still not clear !


I'm looking for a word that means "to make music" without regard to how the music is made (vocal or instrumental), like "to sing" means to make music by passing air over the vocal chords. Example sentences:  I am going to ____. Let's ____.  I would like it to not require an object( for example "play" would work, but the meaning is unclear without stating what is being played). EDIT: To clarify, I am looking for a single word meaning to play music, not a word meaning to write music, although it should be able to apply to improvising(playing and composing music simultaneously). EDIT2: "Make Music" does not work because it is unclear (it could mean to compose or to play music) and sounds too formal for common use.


How do I assign last month's date (year and month only - 2016-07) as a variable?

I am having trouble with using date as a variable in a bash script. I will admit that I have zero experience writing anything – in bash or otherwise – but I’ve been tasked with figuring this out. I have seen some other posts on here that come close to what I am looking for, but I haven’t been able to figure it out yet.  I need to move hundreds of log files from one directory to an archive directory named with the year and month (numerically) of last month, eg., 2016-07. I want the script to look in the archive directory to see if the directory for last month is there and, if not, create it and then move the logs into it. I’m using RHEL 5.11.  From the command prompt this gives me what I need:  date +%Y-%m –d “last month”   Which returns: 2016-07  I just can't get it work as a variable. I've tried the following (amongst other things):  last_month=date +%Y-%m -d "last month" last month=(date +%Y-%m -d "last month")


Change all associations from gedit to another application

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


What's a good way to reduce the output from a 9V battery to the 1.8V to 5V required by an ATmega328 controller? The context is a small robotics platform with low power requirements (very slow movement).


Open PDF when USB is plugged in Windows 7

I have a PDF file on an USB drive (named test.pdf placed in root). How do I get it to open automatically as soon as I plug in the USB drive? No dialog or anything, just open the PDF directly after the UBS drive is plugged in.  Windows 7 and autorun.inf is not working for me.


I'm looking for a program that saves the recent clipboard items (plain text would be enough) for Ubuntu 14.04.  Thanks for any help !


Browsing the internet from the command line

How can I browse the Internet from the command line in Ubuntu?


How can I create a bootable USB stick with Linux and FAT32 from macOS

I want to put 2 partitions on my USB stick: first one (so Windows can see it) with FAT32 (so also macOS can write to it) and a second one, bootable with  on it.  I started looking how to partition the stick and I discovered that Disk Utility will not let me create partitions on the USB stick (the button is disabled), let alone configure the partition as bootable in the MBR.  There is plenty of ways to do that on GNU/Linux, other also works on Windows but I didn't find anything for macOS. Is there any free (as a beer) way to do that?


After applying a mirror and subsurf, there is a clear edge at mirror axis rather than a smooth overflow

I've applied a mirror and then a subsurf to the model, however the mirror doesnt flow smoothly and instead there is a "seam" in the center as seen above. The modifier settings are shown in the image below:


How can I compute the orbit of one body around another?

I'm attempting to have a planet (with a known mass and radius) orbit it's sun (also with a known mass and radius). It doesn't have to be 100% realistic, but it should be possible that the sun have more than one planet orbit it at a time.  What equations should I use to accomplish this?


How does one create the symbol for EMF (electromotive force) used in physics for a LaTeX document? It is like \varepsilon but uppercased.


How to migrate code from SVN to GIT without losing commits history?

I would like to know the recommended way to move our code from a SVN repository to a GIT repository, so that we transition our developers team & start using GIT.  Can we do the transition and keep all the commits done in the SVN repository ?  Also, our team is happy with SVN currently, but, they don't know that branching in GIT is much easier than SVN, where can I find a practical example that proves power of GIT in branching ?


Lenovo Thinkpad T440p - wifi interface not listed

I recently purchased a Lenovo Thinkpad T440p, where I installed Ubuntu 13.04, with the following networking options:   WiFi card Intel Dual Band Wireless 7260AC with Bluetooth 4.0 3G/HSPA+ built-in module (Ericsson N5321)   When I run ifconfig, I get only eth0 and lo listed.  When I run lspci:  00:00.0 Host bridge: Intel Corporation Haswell DRAM Controller (rev 06) 00:01.0 PCI bridge: Intel Corporation Haswell PCI Express x16 Controller (rev 06) 00:01.1 PCI bridge: Intel Corporation Haswell PCI Express x8 Controller (rev 06) 00:02.0 VGA compatible controller: Intel Corporation Haswell Integrated Graphics Controller (rev 06) 00:03.0 Audio device: Intel Corporation Haswell HD Audio Controller (rev 06) 00:14.0 USB controller: Intel Corporation Lynx Point USB xHCI Host Controller (rev 04) 00:16.0 Communication controller: Intel Corporation Lynx Point MEI Controller #1 (rev 04) 00:16.3 Serial controller: Intel Corporation Lynx Point KT Controller (rev 04) 00:19.0 Ethernet controller: Intel Corporation Ethernet Connection I217-LM (rev 04) 00:1a.0 USB controller: Intel Corporation Lynx Point USB Enhanced Host Controller #2 (rev 04) 00:1b.0 Audio device: Intel Corporation Lynx Point High Definition Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation Lynx Point PCI Express Root Port #1 (rev d4) 00:1c.1 PCI bridge: Intel Corporation Lynx Point PCI Express Root Port #2 (rev d4) 00:1d.0 USB controller: Intel Corporation Lynx Point USB Enhanced Host Controller #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation Lynx Point LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation Lynx Point 6-port SATA Controller 1 [AHCI mode] (rev 04) 00:1f.3 SMBus: Intel Corporation Lynx Point SMBus Controller (rev 04) 02:00.0 VGA compatible controller: NVIDIA Corporation GK208M [GeForce GT 730M] (rev a1) 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. Device 5227 (rev 01) 04:00.0 Network controller: Intel Corporation Device 08b2 (rev 83)   Here is the output of uname -a  Linux flo-ThinkPad-T440p 3.8.0-19-generic #30-Ubuntu SMP Wed May 1 16:35:23 UTC 2013 x86_64 x86_64 x86_64 GNU/Linux   It seems the required firmware is included with Kernel 3.10+ if I understand well what's written at  and my kernel is currently at 3.8 something.  Do I need to find the right backport to actually enable WiFi or is there something easier to do?  Thanks in advance!


Systemd backed tmpfs | How to specify /tmp size manually

I mount /tmp on tmpfs using:  sudo systemctl enable tmp.mount sudo systemctl start tmp.mount   But this way /tmp takes up all the free RAM:  $ df -h /tmp Filesystem      Size  Used Avail Use% Mounted on tmpfs           3.9G   12K  3.9G   1% /tmp $   How do I tell systemd tmp.mount to use only 1G? I know I can alternatively not use systemd and manually add an entry to /etc/fstab and specify the size there. But I don't want to do that. I want to use systemd backed tmpfs.


What's the best way to send a signal to all members of a process group?

I want to kill a whole process tree.  What is the best way to do this using any common scripting languages? I am looking for a simple solution.


Working with sets, set difference, union and intersection

I am asked to prove that  $$ A \setminus (B \cap C) = (A\setminus B) \cup (A\setminus C). $$  However I am only finding this to be not true. How would I prove this?


So, I have CHROMEBOOK, and I want install Ubuntu. I download ubuntu files (~1GB), ISO format, but, I dont know, how to put there files to my USB? Just help me please :)


What happened to Tauriel after the events of the Battle Of the Five Armies?

I know this is probably a difficult question to answer, since as far as I know Tauriel is a character that was created just for the movies, but if anyone has any quotes from the director or cast or producers or whatever, I would love to know what happens to her. She was one of my favorite characters, and I feel like they kind of just left us hanging with her.


How is the determinant related to the inverse of matrix?

Whenever I needed to find the inverse of a matrix, I was told to check if its determinant is not zero. However, once I directly applied the Gauss-Jordan's method for finding the inverse of matrix whose determinant was zero. The inverse matrix that I got looked pretty normal like any other (if there wasn't a mistake).  I want to know how does the determinant of the matrix is related to inverse of matrix or why is that if determinant is zero then inverse doesn't exist? What exactly is inverse?


This question was asked on Philosophy.SE, but if it's somehow possible to answer questions that are put on hold, that's a network wide issue.  Link:   Question was put on hold 2015-05-19 14:28:44Z. Answer was posted 2015-05-19 17:33:38Z.


Show multiple awardable badges in the list of available badges even if the badge has been awarded

Recently I’ve suddenly got a second  badge. This badge can be awarded multiple times, but currently if the user already have one the badge is not shown in the list of available:        My request is to add badges which can be awarded multiple times and can be tracked to the list of available badges with an ability to track them.


Can tomato sauce with cooked pork in it be eaten after sitting out in pot and a/c overnight?

I made tomato sauce with browned pork roast pieces in it and cooked it for around 6 hours and left overnight by mistake until the next morning. Lots of sodium and water. My apartment a/c is set at 75 degrees C. Can this be safely eaten after reheated to boiling for an hour and then refrigerated before eating for dinner that night?


How do I get Braid to recognize my Xbox 360 controller?

Supposedly Braid has support for the Xbox 360 controller (as it's an XBLA port), but it refuses to recognize mine.  The controller shows up among my Devices & Printers, and works perfectly in Super Meat Boy, but Braid is totally oblivious.  Edit: It somehow fixed itself after I played SMB, but I have no idea how.  I didn't unplug/replug it between Braid, SMB and back again (though I had much earlier), or really do anything else at all.


How to exchange a heavy box of mixed-denomination coins?

I'm living in the UK and I'm about to move flat. In the five years in my current flat I've accumulated around 20kg of mixed coins - from £0.05 to €2 at a glance. Are there any easy ways to exchange this with a bank or other institution/individual for some reasonable approximation of its worth?


Alternate proof to number of monomials in a given degree - "more" rigorous, formal

Let $s$ be the number of variables and $n$ be the degree of the monomials we want to count in $R[X_1,\dots,X_s]$. Then show, that the count is    $$\delta(n,s):=\binom{s-1+n}{s-1}.$$   The question is a duplicate, but I have so far not been satisfied with any of the seen answers. Not here, not on google/lecture notes etc.. So here goes a proof using as little combinatorics as possible - the only proof with very little combinatorics involved I have seen here used that the substitution  $$R[[X_1,\dots,X_s]]\to R[[X]], X_i\mapsto X$$  is a well-defined homomorphism - something I have only seen as a statement in Zariski's "Commutative Algebra" Volume II...  So here goes my question + answer.


Is PVC Schedule 40 pipe safe to use in a potable water supply?

I have not had a problem for nine years and never noticed what my plumbing pipes used. My hot and cold water feed away from heater use "Bristol 1120 Schedule 40 PVC.  480 PSI 73 deg." Is there strong evidence that I have been using this type of piping in danger to my family's heath. Should it be removed immediately?


Why does testfor sometimes output an error?

Because there are so many questions asking about this, but not closed as duplicates, I decided to make a uniting question here:  There are two three four basic situations here:   Why does the /testfor command (I have) always output an error (not listed below)?   Why does the /testfor command (I have) always output the entity UUID is an invalid format?   Why does the same /testfor command sometimes output the entity UUID is an invalid format instead of found [x] and sometimes not? Why does the /testfor command not output anything?


Creating a special symbol to use in align environment

This is a bit of a silly question, but, is there a way of creating new symbols in LaTeX? Is it possible to make an emoji TeX-able? I want to label Burgers' equation in an align environment with a hamburger (like the burger emoji you may find on your smart phone).


Squatting company registered similar domain after I registered mine, am I able to dispute this?

In 2010 I registered a .net domain name (my family surname). At this time I was very young and it was my first experience with domains/websites, etc.  Around 15 days after registering my domain, a well known squatting company registered the .com equivalent of my domain.  From this it is pretty clear that they were simply monitoring for .net registrations, and would then snap up the .com equivalent.  They are now selling the .com domain for $4,000. It just has a parked domain page with 'For Sale' info, etc.  My .net domain does not represent a registered company or trademark, it is just my family name.  Do you I have any recourse to dispute this based on the fact that they registered it in response to me registering the .net version? Or perhaps because it is my (probably not unique) family name?


Is there an unspoken loophole in complex number theory?

I'm a high school student, who started learning about complex numbers literally today. Sorry if I say anything naive.  My question is this:  sqrt(-1) x sqrt(-1) = sqrt(1) = 1        [simple algebraic manipulation]    however i = sqrt(-1), and is literally defined as i^2 = -1  yet the algebraic result says that i^2 = 1 ??  have i done a mistake somewhere? if not, can someome explain this?


How can I hard-code a URL with translations in a template?

I already followed .  In the template file I have this code.  {{ 'About Us'|t }}   I am using multiple languages, so it should work fine with /th/about-us.  I want to achieve it directly in the template file. How can I do it?


Looking at Rey's staff, it sure looks like it is made of lightsabers as parts.   Are they actually lightsabers? Did she get them (or the whole weapon) from scavenging?


Q:: Could anyone please explain in further detail about "pass-by value" in a program?

I'm a student just starting to learn Programming for C++. We've recently gone over a term called "Pass-by value" in our lectures and I'm a little confused about what it means and what it's meant do. I've asked my professor and even looked over my materials multiple times, but I just can't get it. I understand that it stop the argument from being changed, and it mainly uses the 'void' header, but that is about it. Could anyone go into further detail about this? It would help tremendously.


During the latest gaming session our level 3 Rogue was Two-Weapon fighting with a Rapier in the main-hand and a scimitar in the off-hand.  At the completion of our gaming session I contested the application of the Two-Weapon fighting rules as it seemed unbalanced.  Once I got home I reviewed the PHB and various RPGStack and Reddit but couldn't find a concrete answer.  My interpretation of the PHB Reference rules below is that although any class/character can technically wield a weapon in their off-hand, only those who have been granted a Bonus Action for which no explicit bonus action have been defined would be allowed to actually attack.  So in the case of a Rogue the Bonus Actions granted under Cunning Action allow for specific actions (none of which are attack).  The alternate interpretation would be the rules under Two-Weapon Fighting, perhaps it should be written      you receive a bonus action to attack with a different light melee weapon that you’re holding in the other hand.   This would, in my opinion, explicitly grant the Bonus Action to any character/class who is Two-Weapon Fighting.  After thorough review does it boil down to application of the rules-as-written and determining a house-rule to apply in our campaign?    References  Page 189 of PHB : Bonus Actions  Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. The Cunning Action feature, for example, allows a rogue to take a bonus action.      You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus   action. You otherwise don’t have a bonus action to take.   You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available. You choose when to take a bonus action during your turn, unless the bonus action’s timing is specified, and anything that deprives you of your ability to take actions also prevents you from taking a bonus action.  Page 96 of PHB  A Rogue receives cunning action at level 2, You can take a bonus action on each of your turns in combat.      This action can be used only to take the Dash, Disengage, or Hide action.   Page 195 of PHB  Two-Weapon Fighting (Combat Rules)  When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.  Page 165 of PHB  Dual Wielder  (Feat)  You master fighting with two weapons, gaining the following benefits:   You gain a +1 bonus to AC while you are wielding a separate melee weapon in each hand. You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren't light. You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.


How can I accomplish gradient effects in Photoshop?

I'd like the gradient to have more depth like the red  graphic has


append .mp3 at end of every file in a folder

I have a folder with multiple files in it, and I want to append .mp3 extension at end of each file.  is there any way to rename all these files with one command.?


$$\int^{\infty}_{0} e^{-at^2}  \cos(2 x t) \, dt = \frac{1}{2} \sqrt{\frac{\pi}{a}} e^{\frac{-x^2}{a}}$$ for Re$(a)>0$,  for all real value greater than zero.  I took this equation from the book, , Equation number $7.4.6$


Necessary and sufficient condition for $f \in L^{p}$

Let $(X,\mathscr F,\mu)$ be a finite-measure space and $f$ a measurable function, and define: $E_{n}=\{x \in X;\; (n-1)\leq |f(x)| <n \}$ Show that $f \in L^p$ iff $\sum_{n \in \mathbb{N}}n^p\mu(E_n)$<$\infty$ My attempt: I already showed that $\int |f|^p d\mu<\sum_{n \in \mathbb{N}}n^p\mu(E_n)$ but I can't see how to show that it will be finite


I want to display the number in fax format. If the user enter the number as 12345678910 it need to be formated as (1234)(567)(8910) can it be possible through formula field without writing trigger. If possible please help me how can we achieve it through formula field or please suggest me any other best way to achieve it.


Where can I find good documentation on "msconfig" and "services.msc" for Windows 7?

Running Windows 7  I'm trying to boost the startup speed of my computer and I'm going through "msconfig" and "services.msc" to disable some applications from starting up automatically when the computer turns on.  There are some good sites that document the entries found in the "Processes" tab of the task manager.  You can find out if they are safe to kill, who the manufacturer is, and what the process in question is used  for.  Are there any sites that list startup processes &| services that are safe to kill?  For example, there is an entry in msconfig that just says "Computer Browser" - pretty vague, but seems like something to not kill.  On the other hand, there is an entry in msconfig that says "Extensible Authentication Protocol" - pretty specific and seems like it shouldn't be killed, but how can I know for sure?  Does anyone know if there are any websites documenting the "killable" items listed in both msconfig & services.msc?


Let $I_n=\int_0^1{\frac{x^n}{x+1}dx}$ , $n>0$  Show that $\lim_{n->\infty}{(n+1)I_n} = \frac{1}{2}$  All I could do was to show that the $I_n$ is decreasing.


Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.

Prove that   $$\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0.$$   I'm not really sure how to proceed. I know that I should not try L'Hôpital's rule (tried that) but not sure how I would incorporate into the Squeeze Theorem or how I would use continuity.  Thanks!  Edit: Turns out I was really dumb and you do use L'Hôpital's rule twice. I made the mistake of differentiating the whole quotient rather than the function on top and the bottom of the vinculum separately.


I can't help but wonder...  Config:  mathieu@mathieu-UX21E:~/$ python --version Python 2.7.5+   Code:  import logging logger = logging.getLogger('x')  def main():     print logger     logger = 2  if __name__ == "__main__":     main()   Output:  mathieu@mathieu-UX21E:~/$ python ./manager.py  Traceback (most recent call last):   File "./manager.py", line 9, in <module>     main()  File "./manager.py", line 5, in main     print logger UnboundLocalError: local variable 'logger' referenced before assignment   Obviously, I would expect that print statement to access the globally-defined logger variable. Is there something I did not understand about the python variable scoping rules ?  Also, obviously, the logger = 2 statement should not do much. However, if I remove it, the undefined variable exception disapears.


I am having a problem in understanding what happens when i put negative value to step in case of slicing.  I know [::-1] reverses a string. i want to know what value it assign to start and stop to get a reverse.  i thought it would be 0 to end to string. and tried  f="foobar"  f[0:5:-1]---> it gives me no output. why?  and i have read start should not pass stop. is that true in case of negative step value also?  can anyone help me to clear my doubt.


This is a follow-up question to  and probably an even more naive question. If I'm understanding the answer correct, professors need funding to do research, but once they get it, the university takes some of the grant as overheads (to pay for office space, electricity, etc), and the cut the university takes is substantial.  Given that then, why do professors need universities? One could just apply for the grant as per normal, and once one gets it, buy a slightly bigger house and convert one of the rooms into a lab. One loses nothing to overheads, gets to work from home, has zero teaching duties, can choose to settle anywhere (no two-body problem!), and can even monitor an experiment 24/7. This gets even easier if one works in a field that doesn't need a physical lab. Further, presumably the grant covers postdoc salaries, so one would still be able to pay for postdocs (although probably not PhD students since a professor without a university will not be able to award a degree).   The obvious answer is that one cannot apply for a grant without a university, but Google indicates that's not the case, e.g.  only looks at one's previous accomplishments & potential applications of the research result, both of which are independent of the university. I suppose one could lose journal access, but there's always stuff like arXiv / ResearchGate, emailing the authors of the desired paper, or even Scihub (oops). It's conceivable that not working for a university loses one some prestige, since one can no longer claim to be a professor. However even then I'd expect at least some academics to choose this path, valuing the convenience & extra research funding over prestige.  If the answer to this varies from field to field, I'm most interested in the sciences.


Why does the classical Noether charge become the quantum symmetry generator?

It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this be the case mathematically?  For clarity let's assume we are doing canonical quantization, so that Poisson brackets become commutators. I assume that the reason has something to do with the relationship between classical Hamiltonian mechanics and Schrodinger's equation. Perhaps there's a simple formulation of Noether's theorem in the classical Hamiltonian setting which makes the quantum analogy precisely clear?  Any hints or references would be much appreciated!  Mathematical Background  In classical mechanics a continuous transformation of the Lagrangian which leaves the action invariant is called a symmetry. It yields a conserved charge $Q$ according to Noether's theorem. $Q$ remains unchanged throughout the motion of the system.  In quantum mechanics a continuous transformation is effected through a representation of a Lie group $G$ on a Hilbert space of states. We insist that this representation is unitary or antiunitary so that probabilities are conserved.   A continuous transformation which preserves solutions of Schrodinger's equation is called a symmetry. It is easy to prove that this is equivalent to $[U,H] = 0$ for all $U$ representing the transformation, where $H$ is the Hamiltonian operator.  We can equivalently view a continuous transformation as the conjugation action of a unitary operator on the space of Hermitian observables of the theory  $$A \mapsto UAU^\dagger = g.A$$  where $g \in G$. This immediately yields a representation of the Lie algebra on the space of observables  $$A \mapsto [X,A] = \delta A$$  $$\textrm{where}\ \    X \in \mathfrak{g}\ \ \textrm{and} \ \  e^{iX} = U \ \  \textrm{and} \ \  e^{i\delta A} = g.A$$   $X$ is typically called a generator. Clearly if $U$ describes a symmetry then $X$ will be a conserved quantity in the time evolution of the quantum system.  Edit  I've had a thought that maybe it's related to the 'Hamiltonian vector fields' for functions on a symplectic manifold. Presumably after quantization these can be associated to the Lie algebra generators, acting on wavefunctions on the manifold. Does this sound right to anyone?


Whenever I try to meditate on the Whitcher 3 it says "you cannot do this now". Any help? I'm not on a horse or anything I'm just in the city of Novigrad and I can't meditate.


Dealing with violations of assumptions of OLS regression, normality and linearity of residuals

I am trying to do OLS regression to identify value-added predictors of an outcome. I've chosen predictors that are all zero-order correlates of my outcome. Then I began checking assumptions for each of those predictors. A few of my predictors are skewed above a guideline of >.8, and so I have attempted to transform those with power transformations, going down the ladder for positive skew (e.g. sqrt, and then natural log). These transformations successfully reduce the skew. However, after I make a trasnformation, I check graphical representations of residuals with the transformed variable and Y, such as the normal QQ plots and the plot of fitted residuals with a lowess curve. These graphics are either unchanged, or worse. As in, the tails of the normal QQ line are still curved, and the lowess curve is much less flat.  For example, here are the plots of the nontransformed variable. Lowess curve looks good, but QQ line is curvy at tails.   And here are plots of log transformed variable. Lowess curve is no longer flat and QQ line is still curvy!   Am I supposed to continue moving down the ladder and visually checking these assumptions as I go? Are increasingly powerful transformations likely to improve my problem? Should I instead ignore the guideline of skew above .8 (Tabachnik and Fidell)?


Is there a name for the extent of an object in a 4th and higher spatial dimensions? (width, height, depth, …)

If width is the extent in the first dimension, height in the second and depth in the third, is there a name for the extent of an object in the fourth spatial dimension?   And what about a five, sixth and higher dimensions?


How to solve the error : "Sorry, installation of this driver failed. Please have a look at the log file for details: /var/log/jockey.log"

I have recently installed Ubuntu 12.04  and on updating driver from GUI additional driver, it prompts me for the missing of broadcom driver . on accepting the download option. the message get prompted   Sorry, installation of this driver failed.  Please have a look at the log file for details: /var/log/jockey.log   i am new with ubuntu can any one suggest how can i over come this issue and get wifi network enabled on my compaq presario kernel 3.8


If we have a collection of Linux computers on a LAN, how to write shell script to shutdown all computer

I have lab and in that ,collection of Linux computer are connected in LAN. i want how to writ e shell script to shut down all PC when we run that shell script.


Ubuntu installed some updates, and after the restart, I cannot log in.  It seems to accept, but then beeps and returns to the login screen.  All of the users, including guest do the same thing.  I was looking at some other posts here, and tried some of the suggestions without success.  I looked at the .xsession-errors file but I don't understand the error:  X Error of failed request:  BadValue (integer parameter out of range for operation)   Major opcode of failed request:  155 (GLX)   Minor opcode of failed request:  3 (X_GLXCreateContext)   Value in failed request:  0x0   Serial number of failed request:  34   Current serial number in output stream:  35 openConnection: connect: No such file or directory cannot connect to brltty at :0 upstart: gnome-session (Unity) main process (1751) terminated with status 1 upstart: unity-settings-daemon main process (1737) killed by TERM signal upstart: Disconnected from notified D-Bus bus upstart: logrotate main process (1601) killed by TERM signal upstart: update-notifier-crash (/var/crash/_usr_bin_compiz.1001.crash) main process (1669) killed by TERM signal upstart: update-notifier-crash (/var/crash/_usr_bin_compiz.1002.crash) main process (1671) killed by TERM signal upstart: bamfdaemon main process (1730) killed by TERM signal upstart: hud main process (1735) killed by TERM signal upstart: indicator-bluetooth main process (1795) killed by TERM signal upstart: indicator-power main process (1796) killed by TERM signal upstart: indicator-datetime main process (1797) killed by TERM signal upstart: indicator-application main process (1844) killed by TERM signal upstart: job window-stack-bridge failed to stop   Thanks, David


Is/Are list with 2nd person and 3rd person

Should you use is or are here:     I can't tell is you or Amanda is/are the best.   I know with you it would be are.  I know with Amanda it would be is.   And I know with a list of Amanda and Dave it would be is.  But I'm unsure in this particular situation, mixing 2nd and 3rd person.


What’s the Accepted Procedure for questions that have been answered on another Stack Exchange site?

“” on Stack Overflow seems (to me) to be asking much the same question as “” on Super User. That second question , but of course that’s not on Stack Overflow, and I’m not sure that such a question doesn’t belong on Stack Overflow (nor even that it instead doesn’t belong on Super User).  I don’t necessarily like the idea of an answer simply saying “See the answer to this question on Super User” (and indeed, although I did attempt to post such an answer, it was deemed Trivial and converted to a comment), but in the case of a user coming across this question (say) by means of searching, I’d like there to at least be a link to the answer on Super User so that the question isn’t a dead end. What’s generally supposed to be done in this sort of case?


Why does strcat not work properly if you pass it a constant?

I am new to C. I have been searching for hours to find an answer to this problem but no luck. Your help would be greatly appreciated.  I need to write a function that takes the file path as argument (I am calling this argument WorkingDir below)  This function  void test1(char *WorkingDir) {     FILE *out_file1;     out_file1 = fopen(strcat(WorkingDir,"Th.txt"), "wt");      // the above attempts to open file   /WorkingDir/Th.txt     fclose(out_file1); }   called as  test1("/my/directory/")   does not work (it does not set the path as required), although this one works just fine  void test2(char *WorkingDir) #argument is not used anywhere {     char path[100]="/my/directory/";     FILE *out_file1;     out_file1 = fopen(strcat(path,"Th.txt"), "wt");     fclose(out_file1); }   Thank you all for your answers. An important detail that I did not mention is that I am calling the C function from R. To pass a string from R to C requires char ** argument. So this function sets the path as required:  void test101(char **WorkingDir){     const int MAX_PATH = 300;     char path_name[MAX_PATH + 1];     snprintf(path_name,MAX_PATH,"%s%s",*WorkingDir,"Th.txt"); }   The above function uses your inputs. Thank you for them.


Show that $\sum\limits_{n=1}^\infty\frac{\sqrt{a_n}}{n^p}$ converges for p > $\frac{1}{2}$

Let    $\sum_{n=1}^\infty{a_n}{}$   be a convergent series of positive terms.   Show that  $$\sum_{n=1}^\infty\frac{\sqrt{a_n}}{n^p}$$   converges for p > $\frac{1}{2}$


Could you help me to prove  $$ |e^{i\theta} -1| \leq |\theta| $$  I am studying the proof of differentiability of Fourier Series, and my book used this lemma. How does it work?


Why doesn't current return via the grounding conductor when it's connected in the panel?

Since the neutral wire and ground wire are connected in the main fuse box then why doesn't some of the returning electricity flow through the ground wire to earth?


Good introductory book about Group Theory?

I am looking for a good introductory book about Group Theory for physicists.


Derivation of binomial coefficient in binomial theorem.

How was the binomial coefficient of the binomial theorem derived?  $$\frac{n!}{k!(n-k)!}$$


Which statement is true about the following sequence: $f(1)=1,f(2n)=f(n),f(2n+1)=f(n)+f(n+1)$

ETA: In case someone notices the similarity, this question is not a duplicate of .     Which statement is true about the sequence $\{f(n)\}$:    $$ \left\{  \begin{array}{l} f(1)=1 \\  f(2n)=f(n) \\  f(2n+1)=f(n)+f(n+1) \end{array} \right.  $$   a)All prime numbers appear in $\{f(n)\}$   b)All Mersen primes appear in $\{f(n)\}$   c)A finite set of primes appear in $\{f(n)\}$   d)Just primes of the form $4t-1$ appear in $\{f(n)\}$     It's seen that $f(2n)=1$ but I'm not sure that $f(2n+1)$ generates which primes...


What do the curvature and torsion measure?

Consider a smooth surface for simplicity. What does its curvature measure? What does its Gaussian/Riemannian curvature measure? What does its torsion measure?  What does the Ricci curvature measure?


Searching for a specific book about dragons

I believe it was a trilogy. It was set in a universe where dragons are pitted in fights against each other for humans' benefit, and the main character was a stableboy who helped to take care of dragons. I remember early on in the first book he gets injured by a dragon, and a woman who is taking care of his wounds comments on how otherwise unscarred his back is, which embarrasses him.   At some point he discovers that he has an empathic connection with dragons (!?) and everything goes down south when a dragon he'd been helping his mentor figure prepare gets injured ("hamstrung") and has to be put down. As the mentor administers a mercy killing to the dragon, the main character was visualizing a candle being snuffed out.   One of the novels ended with the main character and his female traveling companion both developing an empathic/psychic bond with their dragons and with each other; when their dragons communicate with them, they hear/see/feel it in rainbows.  I remember discovering it in a middle school library; I believe it's young adult. It wouldn't have been published any later than 2005


How to order an array by inner array key value?

I have an array of arrays.  I want to order these arrays by their ['date'] field.  So the latest is at index [0].  How can I do this?  Here is an example of my print_r  $array=    (     [0] => Array         (             [date] => 01/05/2013 12:00             [location] => Town Hall             [minutes] => mydomain.com             [agenda] =>          ),  [1] => Array         (             [date] => 09/05/2013 12:00             [location] => Town Hall             [minutes] => mydomain.com/walker             [agenda] =>          )  )


It's now been almost four years since Stargate Universe flopped, and as far as I'm aware there's been no word of anything else in that universe since then. I can understand this being the case with the TV series'; but I'm wondering if there are other media, especially novels. I can think of several things that are begging for it such as Universe's continuation and the Stargate going public. Does anyone know if there's any new novels set after Universe, or any other plans in place?  I'm aware that  basically asks the same, but since it was answered shortly after that happened the question was still somewhat up in the air. I'm hoping things have changed since then.


I am struggling to understand how option processing works in classes. As a MWE  foo.tex:  \documentclass[draft,figures]{foo} \begin{document}   \includegraphics{example-image} \end{document}   foo.cls:  \ProvidesClass{foo} \RequirePackage{foo} \LoadClassWithOptions{article} \RequirePackage{graphicx}   foo.sty  \ProvidesPackage{foo} \RequirePackage{etoolbox} \newbool{foo@figures} \DeclareOption{figures}{\booltrue{foo@figures}} \ProcessOptions\relax \ifbool{foo@figures}{\PassOptionsToPackage{final}{graphicx}}{}   When I process foo.tex with pdflatex the log shows     LaTeX Warning: Unused global option(s):       [figures].   but I also see the graphic, which means that I am passing the final option to the graphicx package. Why does LaTeX think the figures option is unused?  Moving \LoadClassWithOptions to before the package is loaded gets rid of the warning. In my real use case, the class that is being loaded, loads the graphicx package and therefore I need to load the package before loading the class.