Let $I \subset \mathbb{R}$ be an open interval and $f: I\to \mathbb{R} $ is convex. (That is, whenever $a, b \in I$ and $0\leq t\leq 1$ then $$f((1-t)a + tb) \leq (1-t)f(a) +tf(b).$$ How can I prove that $f$ is differentiable almost everywhere? The proof of Alexandrov theorem or the contents in Rockafellar's "Convex analysis", Theorem 25.5 mentioned in  are too difficult for me, who is studying elementary real analysis. Are there any other proof of this? (I hope there is because it is the simplest case in which $ n =1$.)

Let $f:\Bbb R\to\Bbb R$ be a convex function. Then $f$ is differentiable at all but countably many points.   It is clear that a convex function can be non-differentiable at countably many points, for example $f(x)=\int\lfloor x\rfloor\,dx$.  I just made this theorem up, but my heuristic for why it should be true is that the only possible non-differentiable singularities I can imagine in a convex function are corners, and these involve a jump discontinuity in the derivative, so since the derivative is increasing (where it is defined), you get an inequality like $f'(y)-f'(x)\ge \sum_{t\in(x,y)}\omega_t(f')$, where $\omega_t(f')$ is the oscillation at $t$ (limit from right minus limit from left) and the sum is over all real numbers between $x$ and $y$. Since the sum is convergent (assuming that $x\le y$ are points such that $f$ is differentiable at $x$ and $y$ so that this makes sense), there can only be countably many values in the sum which are non-zero, and at all other points the oscillation is zero and so the derivative exists. Thus there are only countably many non-differentiable points in the interval $(x,y)$, so as long as there is a suitable sequence $(x_n)\to-\infty$, $(y_n)\to\infty$ of differentiable points, the total number of non-differentiable points is a countable union of countable sets, which is countable.  Furthermore, I would conjecture that the set of non-differentiable points has empty interior-of-closure, i.e. you can't make a function that is non-differentiable at the rational numbers, but as the above discussion shows there are still a lot of holes in the proof (and I'm making a lot of unjustified assumptions regarding the derivative already being somewhat well-defined). Does anyone know how to approach such a statement?


The problem is to find $\sqrt{(-1)\cdot(-1)}$ Approach 1 - $\sqrt{(-1)\cdot (-1)} = \sqrt{(-1)^2} = -1$ Approach 2 - $\sqrt{(-1)\cdot (-1)} = \sqrt{1} = 1$  Which is correct and why?

I know there must be something unmathematical in the following but I don't know where it is: \begin{align} \sqrt{-1} &= i \\\\\ \frac1{\sqrt{-1}} &= \frac1i \\\\  \frac{\sqrt1}{\sqrt{-1}} &= \frac1i \\\\  \sqrt{\frac1{-1}} &= \frac1i \\\\  \sqrt{\frac{-1}1} &= \frac1i \\\\  \sqrt{-1} &= \frac1i \\\\  i &= \frac1i \\\\  i^2 &= 1 \\\\  -1 &= 1 \quad !!? \end{align}


Consider the following class:  \NeedsTeXFormat{LaTeX2e} \ProvidesClass{sampleclass}  \LoadClass[ paper=a5, chapterprefix=true ]{scrbook}  \DeclareOption*{\PassOptionsToClass{\CurrentOption}{scrbook}} \ProcessOptions\relax   and the following document:  \documentclass[ ]{sampleclass}  \begin{document}     \chapter{Test} \end{document}   I am making the observation that the option chapterprefix=true has an effect on the document, while the option paper=a5 does not.  If I include the paper option in the document like this:  \documentclass[ paper=a5 ]{sampleclass}  \begin{document}     \chapter{Test} \end{document}   then it works. What is going on?  Edit: In the chat it was suggested the problem might be connected to the KOMA class so I just add the tag here to attract the KOMA experts.

I want to create a document class based on a KOMA-Script class. If myclass.cls contains the following  \ProvidesClass{myclass}[2011/08/31] \LoadClass[paper=a5]{scrartcl}   then compiling a document whose first line is \documentclass{myclass} generates the warning   LaTeX Warning: Unused global option(s):     [paper=a5].   The same problem occurs with scrbook and scrreprt. What am I doing wrong?


If $f(x)=\frac{x}{\sqrt{1+x^2}}$ prove by mathematical induction that $f(f(...f(x)...))$ = $\frac{x}{\sqrt{1+nx^2}}$.  (Noting that there are n $f$'s in the LHS)  I have no idea where to start with this one. Which method is best suited for proving this?   Thanks

We were asked to determine  the composition $f \circ f \circ f \circ \cdots \circ f $,  $n$ times, where $f(x)=\dfrac{x}{\sqrt{1+x^2}}$.  Has anyone an idea?


I'm new to Ubuntu and I tried to install something and the guide I was reading says to run a command that starts with  sudo add-apt-repository   but whenever I try to use the command then it says  bash: add-apt-repository: command not found   whether I start it with sudo or not, and I can't seem to find any help anywhere else.

I’m running Ubuntu 14.04. When I run:   sudo add-apt-repository ppa:ubuntu-wine/ppa   I get the following error:  sudo: add-apt-repository: command not found   I tried to run  sudo apt-get install software-properties-common   but it shows:  software-properties-common is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded.


I once had a book called Arena. Unfortunately that is a very common book title. Its cover was very similar to:    but that's a coincidence.  In the story, the main character (female), is invited to take part in an experiment. In the experiment she is transported to another world. (I'm pretty sure it was virtual reality.) The world has 3 sections:  The first section everything is fairly simple. You just have to stay on the path, and walk to the end, and insert the key into a door. But no one ever does. (The get off the path, and turn their keys into weapons etc). There is a town at the base of the wall (I think it is infinitely high, people try to climb it). Along the way there are safe houses that can be accessed with the keys.  The second area is (I think) a staging ground. There is a library and a team gathers to try and, I think cross the wasteland, and then get into a city (it was full of goblin equivalents).   The third area is the city and the wasteland. At the end, the main character makes it out, (There must be a gate at the center of the city).   One of her friends (male), was shot on the way, but she meets him back in real life but he has no memory. (Only people who legitimately escaped keep there memory). It was theorised the guys conducting the experiment must have been aliens because their technology was so advanced.  The book has at least one sequel. (I managed to hunt the book down once before when I when back to the library I first found it.) It was published during or before 2005.  On of my friends has had the exact same problem, trying to find it. (I mentioned this book I read, called "Arena", and he was like "I read a great book called Arena once, but I can't remember the author name, and there are so many others.". Eventually we worked out it was the same book.  Any help finding the author name would be appreciated.

This is a book I read about a decade ago. It is a science fiction type book and I got it in the young adult section of my public library. It is a standalone book, not a short story or collection of stories.  Characters The main character of the book is a youngish woman, I'm guessing younger than 30, but I can't remember her name. One of the other major characters/possible love interest is a man named Garth (I remember this name in particular because I had never heard of anyone named Garth and thought it was funny). They meet up with others along the way, somewhere around 10-20 people in total.  Plot The premise of the plot is that a bunch of people on Earth joined programs for "quitting smoking" or "quitting drugs" or "self-improvement". However, these programs were a front, and as soon as they attend their first meeting, they are told to go inside a room/device and suddenly find themselves transported to an alien planet. (One of the characters later jokes that it worked, because she hasn't smoked in weeks due to being on an alien planet with no cigarettes)  Once the main character meets up with other transported humans, they start trying to figure out what to do. They receive some sort of instructions from the aliens who put them there and they are told if they reach a certain place alive, they will be sent back to Earth.   A lot of the conflict centers around people arguing whether or not to follow the instructions they were given. The aliens themselves don't play a huge role until the end (other than giving instructions), and the book focuses more on what the people discover about themselves in the journey (which lasts weeks at least) to this mysterious end goal. I remember it as "a sci-fi sort of Pilgrim's Progress" (minus the heavily religious overtone), because all the different places/challenges they do are supposed to represent some real-life problem someone in the group was facing.  In the end, those that make it are returned to Earth with their memories wiped, but their bad habits gone.  For some reason I thought the title was "The Crystal Arches" for a long time, but I haven't had any luck finding it by that title. Possibly their end destination was a set of crystal arches or something.   I've asked this on a couple other internet sites but haven't had any luck. I didn't think to try here until I saw other questions like this.


The number of columns in the "Stack Exchange Network" in the footer varies. For example, the Science section has 2 columns, but there are still 10 more unlisted sites. Why don't they be listed? Apparently there are rooms for that, because in the Technology section it has 7 columns. Why is that?

New collapsing/expanding footer displays sites by catecories. E.g. Technology section is most solid and contains more then five columns each of them contains seven sites:        Other sections like Science have less items, only two non-full columns and more(10) link:        Seems there is possible to display all of science sites, so more link will not be actually needed.   Why the list of sites here is intentionally reduced? Is it possible to show all of them in this case?


I am writing a personal statement for the very first time and I'm worried that the suffix -wise may sound too laid-back for a text of such genre. The sentence I want to write is similar to this:  Teaching-wise, being bicultural can be an advantage in that it...  I appreciate your help!

I found myself writing the following in a bit of technical documentation:     The Trainers' and Students' clients have very little in common, both user interface-wise and code-wise.   At first, I wondered whether I should have written user-interface-wise, user interface-wise, user interface wise or user interfacewise... or some other combination. A quick Google search  however that the "-wise" suffix actually isn't one you can or should use on any word.  What do you suggest? I guess the easiest way out is rephrasing (e.g., not only for what concerns the user interface, but also for actual methods), but I wanted to learn whether appending "-wise" to arbitrary words is incorrect, frowned upon or merely a stylistic choice.


I am quite aware of  for editing questions and answers, but there are several cases that I would find useful to just copy the raw text of another question/answer. Some examples are:  Complex  entries about math formulas that I might want to integrate, modify, or copy. On the spot quick reminder of a special uncommon attribute (e.g., HTML)  Is this an already existing functionality?

Once a post has been edited, you can go into the revision list, and click "View Source".  If a post has not been edited (and I don't have the edit privilege) is there any way to see the raw Markdown?  The reason I ask I because of  - it's impossible to see the source markdown, and how it's different from the rendered Markdown.  Not exactly a huge issue, just curious!


Working out a few kinks in this code and for some reason my method validation check is not quite working. All I want it to do is to validate that the input from the user ONLY contains letters G, C, A, T before moving onto the method at_calculate which performs the maths on the input sequence. Any help/tips would be appreciated.  import re  from tkinter import *  class AT_content_calculator:      def __init__(self, master):         #initialising various widgets         frame_1 = Frame(master)         frame_1.pack()          self.varoutput_1 = StringVar()          self.label_1 = Label(frame_1, text="Please enter a DNA sequence:")         self.label_1.pack()         self.entry_1 = Entry(frame_1, textvariable=self.dna_sequence)         self.entry_1.pack()         self.output_1 = Label(frame_1, textvariable=self.varoutput_1)         self.output_1.pack()         self.button_1 = Button(frame_1, text="Calculate", command=self.validation_check)         self.button_1.pack()      def dna_sequence(self):         self.dna_sequence = ()      def validation_check(self):         #used to validate that self.dna_sequence only contains letters G, C, A, T         if re.match(r"GCAT", self.dna_sequence):             self.at_calculate()         else:             self.varoutput_1.append = "Invalid DNA sequence. Please enter again."             self.validation_check()      def at_calculate(self):         #used to calculate AT content of string stored in self.dna_sequence         self.dna_sequence = self.entry_1.get()         self.total_bases = len(self.dna_sequence)         self.a_bases = self.dna_sequence.count("A")         self.b_bases = self.dna_sequence.count("T")         self.at_content = "%.2f" % ((self.a_bases + self.b_bases) / self.total_bases)         self.varoutput_1.set("AT content percentage: " + self.at_content)  root = Tk() root.title("AT content calculator") root.geometry("320x320") b = AT_content_calculator(root) root.mainloop()

What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it.


How could I solve this error?? when I am trying to share my folder to Local network.

Why I am getting this error when I am trying to share my folder on a network.


I've been seeing tons of Pokémon, but every time I get one in a pokéball, it seems to escape.   I tried getting more storage for pokémon, and I even tried doing curve calls and waiting for the circle to get small. This has happened with around 30 pokémon in a row.   I should mention that I was in the car going about 70 miles per hour, maybe it was because we were driving really fast, and so the pokémon was far away?  Any ideas why this is happening?

I'm level 10 on Pokemon Go. I've caught at least 150 Pokemon, and had no problems. Now, every time I try to catch a Pokemon, no matter the level, it just rolls twice in the pokeball, breaks free, then runs away. Can anyone provide some insight on how to fix this problem?


What is the command to find out number of cores the process is running on at any instance ?  -Thanks

Is there any command in Linux to figure out, given a process, which processor the process is running? I am interested in figuring out the CPU busy and CPU idle time of that processor.


So I need to run one script, and I just drag & drop it to console, but console outputs this error:  matas@H81M-D2V:~/Desktop/gui$ '/home/matas/Desktop/gui/load.sh'  bash: /home/matas/Desktop/gui/load.sh: /bin/bash^M: bad interpreter: No such file or directory matas@H81M-D2V:~/Desktop/gui$ ^C matas@H81M-D2V:~/Desktop/gui$ ^C matas@H81M-D2V:~/Desktop/gui$    The script:  #!/bin/bash if [[ $(nvidia-settings -q '[gpu:0]/DigitalVibrance[DFP-1]' | grep 'Attribute.*1023\.') ]] then     nvidia-settings -a '[gpu:0]/DigitalVibrance[DFP-1]=0' > /dev/null     echo "Vibrance Disabled" else      nvidia-settings -a '[gpu:0]/DigitalVibrance[DFP-1]=1023' > /dev/null     echo "Vibrance Enabled" fi

I wanted to execute a shell script:  -rwxr-x--x 1 root root   17234 Jun  6 18:31 create_mgw_3shelf_6xIPNI1P.sh   I tried to do a standard procedure, but I got this error:  ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0  DEBUG   cd/etc/opt/ldapfiles/ldif_in ; ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0 **ERROR  sh: ./create_mgw_3shelf_6xIPNI1P.sh: /bin/bash^M: bad interpreter: No such file or directory**   What does it mean? I was doing this as the root user under the root group.  Does it mean that the file does not have the correct permission for the root user?


I have a string that comes in the format name = "1/2/2021", how can I convert this string to the format newName = "2021-2-1" original =  name day = original[0] month = original[2] year = original[4:8] combination = year + "-" + month + "-" + day  I have tried using this but brings wrong values when date or month changes to more than 2 characters

I've got a huge list of date-times like this as strings:  Jun 1 2005  1:33PM Aug 28 1999 12:00AM   I'm going to be shoving these back into proper datetime fields in a database so I need to magic them into real datetime objects.   This is going through Django's ORM so I can't use SQL to do the conversion on insert.


I recently got to know about OnyX to delete recent history on docs. How shall I use it? Will clicking on recent items delete all the recent items on doc or a particular recent item which I visited today? Please refer  for the image, I am talking about the "recent items" mentioned in the 1st picture?

I am not a very techie girl. I used my brother's macbook air and saw some of his personal things which I should haven't. And I realised that he could see that in recents. How to delete them? After surfing a lot, I got to know about the recent files stored in plist in preferences, by the name com.apple.recentfiles.plist or LSSharedfiles.plist but I couldn't find a file/plist named above. Kindly help! As mentioned above it is macbook air and again I do not know much :(


when I type any  command the terminal asks for password and then when I write nothing show up .. how can I solve that ?

When I'm about to install a program in the terminal it wants the password:  [sudo] password for xxx:   But when I start to type my password nothing happens. What should I do?


I would like to prove the statement on the title. I tried to prove it using the definition of multiply of matrices, however it seems like weak to me. Can't decide how to make a correct proof of the statement above.  Edit: Those ns are the same ns. So that, the dimension of the Matrix have to match the power to which it is raised.

Given an $n\times n$ upper triangular matrix $A$ with zero on main diagonal, show that $A^n = 0$.   I did some matrix operation and noticed that the diagonal moves up, ultimately all entries will be zero. Is there a nicer way to do it?


I have a database field is_enabled - which set to either 'Yes' or 'No'.  Following checkbox will have to set as checked if the db field is 'Yes'.  <input name="enab" type="checkbox"> <label>Enabled Status: </label>   JQuery:  $('[name=enab]').val(values.enab);   Anyone please help.

I'd like to do something like this to tick a checkbox using jQuery:  $(".myCheckBox").checked(true);   or  $(".myCheckBox").selected(true);   Does such a thing exist?


I have been issued a multiple-entry Schengen visa from the Italian consulate, is it possible to do transit in Holland for 2 hours as I am traveling on KLM?

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


I want to prove that any $\alpha(s)$ with arc parameter $s$ lying on a sphere with radius $R$ has curvature $k\geq1/R^2$. I tried so many times to prove it and at this point it's pissing me off really hard. The conditions of arc length parameter $$ |\alpha'(s)|=1 $$ and lying in the sphere $$|\alpha(s)|=R$$ should be enough to prove this by deriving those equations etc. The only thing I have found with this is that $$ \{\alpha,\alpha',\alpha\wedge \alpha' \} $$ is a basis of the curve at each point. This works for nothing to obtain the curvature $k$, as curvature is defined as $$k(s) = |\alpha''(s)| $$ or as the function such that $$ \alpha''(s) = k(s)N(s)$$ where $N$ is in a vector in the direction of $\alpha''$. I also tried methods such as starting first with plane curves of maximum radius, which gives me a curvature of $1/R^2$. Then saying that plane curves of less radius have curvature $1/\tilde{R}^2\geq 1/R^2$ as $\tilde{R}$ is smaller. But I don't have any clue for the other type of curves in the sphere. Note: I have seen many similar posts but none address this problem but other properties about the curvature of a curve in a sphere.

I'd like some hint for this problem: Show that every unit-speed curve $ \alpha : I \subset \mathbb{R} \longrightarrow \mathbb{R}^3$, whose image is in the sphere of radius $R$ , has curvature $\displaystyle k_{\alpha}(s)\geq \frac{1}{R}$ .


How would you prove the following using induction. n is a non negative integer  $$1+\sum_{i=1}^n i i!=(n+1)!$$  This be what I did  base case let $n=3$  $$1+1+4+18=(3+1)!$$  $24=24$  Hypothesis step let $n=k$  $$1+\sum_{i=1}^k i (i!)=(k+1)!$$  Induction step let $n=k+1$  $$1+\sum_{i=1}^{k+1} i (i!)=(k+1+1)!$$  so start on the left hand side and get  $$1+\sum_{i=1}^k i (i!)+(k+1(k+1)!)=(k+1)!+(k+1(k+1)!$$  and I am stuck.

Use induction to prove that    $\displaystyle\sum_{r=1}^n r\cdot r! =(n+1)! -1$   I first showed that the formula holds true for $n=1$.  Then I put n as $k$ and got an expression for the sum in terms of $k$.  I then found the sum till the $(k+1)$th term by adding the $(k+1)$th term to both sides of the equation and compared it to the sum expression I get by plugging $k+1$ into the sum expression given in the question - they don't match.


Imagine that I've got a big $N \times N$ boolean matrix (all entries are $0$ or $1$). At the beginning, the matrix is full of zeros.  Then, I execute the following algorithm  Matrix M empty of type N x N while (there is a 0 in M) {     Position pos;     do {         pos = random position in M     } while (pos is 1);     // Here pos is 0     mark pos as 1; }   I want the cost of the previous algorithm (suppose that "there is a $0$ in $M$" has no cost, and that "random position in M" has constant, i.e. $\Theta(1)$, cost).   My intuition says that it is $\Theta(\cdot)$ of $$ 1 + \textrm{Geom}\left(\frac{N^2 -1}{N^2}\right) + \textrm{Geom}\left(\frac{N^2 -2}{N^2}\right) + \cdots + \textrm{Geom}\left(\frac{1}{N^2}\right) $$

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?


I am a beginner programmer, learning Java and had a question, (I have seen many answers to this, and they seem to describe something different to what I want).  As far as I understand it, an interface is a thing, and you can have a class implement the thing, what that means is the class has to define the methods mentioned in the thing. So why not just define the methods anyway?

I have seen this mentioned a few times and I am not clear on what it means. When and why would you do this?   I know what interfaces do, but the fact I am not clear on this makes me think I am missing out on using them correctly.   Is it just so if you were to do:  IInterface classRef = new ObjectWhatever()   You could use any class that implements IInterface? When would you need to do that? The only thing I can think of is if you have a method and you are unsure of what object will be passed except for it implementing IInterface. I cannot think how often you would need to do that.   Also, how could you write a method that takes in an object that implements an interface? Is that possible?


I would try to make it as clear as possible. I have a relay, and it has five pins( NC, NO, C, and coil) like any basic relay.    Now, I want to apply a logic - when the input (I would say it BMS from now) is 230V ( the mains supply is on) the alarm system should not buzz ( the alarm work at 230V mains supply) and when the input(BMS) is cut off (0V) the alarm system should start buzzing. In short, the alarm should start when the input is 0V and should turn off when the input is 230V mains. I realized the best way I can achieve is by using a relay and 2 different mains supply. The BMS will control the coil of the relay. The second power supply mains will be connected to the NC pin of the relay. And the alarm (hooter) will be connected to the C or common pin of the relay. Now, we consider two cases.   Case 1:  The second power supply is On and BMS is also on.   When this is the case, the Coil of relay is high as we have connected BMS to the relay coil.  So, NO and C of the relay will be connected to each other. We have nothing connected in the NO pin so the C pin would be low and the alarm will not start. Exactly what we want.   Case 2: The second power supply is On and BMS is cut-off  In this case, the coil of the relay will be cutoff so NC and C of the relay will be connected to each other. The second power supply is connected to the NC pin and as it is shorted to C of the relay, it will start the alarm as it will receive the supply voltage from the second power supply. So, when the BMS is cut-off, the alarm starts. Still, exactly the case we want.   The problem is that the BMS will always be on usually and the relay will always be in the switched state( NO and C of the relay will be connected). It will be only when the BMS is cut-off the relay will come to normal state( NC and C of the relay are connected).   Now, coming to my question. As the relay will be in the switched state forever ( NO AND C is always connected), will it damage my relay? Will the self-life of the relay decrease in that case? I hope you got my question. If it will damage my relay, please read further. If not, I would not look for alternatives.   Please help if you have any alternative for achieving the same thing.   If there is any other way of the same functioning ( the alarm should start when the BMS is cut-off) without using relay or using relay but with different connections, please do let me know. I am open for suggestions and please do help. Thanks for reading as I know I wrote a whole story here. Thank you.

I have a mission-critical device, which involves a micro and mosfet controlling a pump. I want to implement a failsafe, so that if basically anything happens to the micro, or the mosfet blows, the system will engage and turn on a backup pump. The easiest way to do this, it would seem to me, would be to have an always-engaged (NC) relay that is disengaged by a failure, energizing the backup pump. So, my question is, is it a good idea to have a relay on continuously for what may amount to years? The extra 20ma for the coil is negligible in this application, but are there any other consequences to doing this?


From my point of view, high gas pressure input creates air rotation inside the tube. Due to the rotation, the kinetic energy in the air change to internal energy. The internal energy release as heat energy. The heat energy goes out and the cold air stay. The cold air flows back to the other end to create the cold air flow.  If what I am thinking is right, I don't understand why the inner vortex tube is cold. From the circular motion point of view, air needs more kinetic energy to rotate in a smaller radius than in a larger radius. This could draw a conclusion that the air in the inner tube rotates slower than the air in outer tube.   -HOWEVER  I read the following from   What is usually agreed upon is that the air in the tube experiences mostly "solid body rotation", which means the rotation rate (angular velocity) of the inner gas is the same as that of the outer gas. This is different from what most consider standard vortex behavior — where inner fluid spins at a higher rate than outer fluid. The (mostly) solid body rotation is probably due to the long length of time during which each parcel of air remains in the vortex — allowing friction between the inner parcels and outer parcels to have a notable effect.  =====  How I understand is difference from Wikipedia. Do I make some conceptual mistake? Please help

A  takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. .  Both linked sources are scarce with information about how and why this works. Now, I have two questions:   Why does it work, specifically why should the situation in the vortex lead to a transfer of thermal energy from the inner stream to the outer one? How efficient can it be?  How do you define the efficiency of a device that may be closer to Maxwell's Demon than to a heat pump? My feeling is that any analysis should not only take into account the sum of input energy (thermal and mechanical energy instream) and sum output (thermal energies and pressures of both gas streams), but also the Temperature differential that is created - since that contains an ability to create work.* If course it's pointless to create heat from high grade 8mech.) energy to transform it back to mech. energy - but it gives an idea on the worth of the output.


To re-define a command to contain itself (patching in TeX parlance) you usually use \let.  by @egreg says:     Never use \let on commands defined with \DeclareRobustCommand or commands defined with \newcommand and having an optional argument.   So a natural question is what should we do in such cases?  For example, how do I re-define \bibitem to add another command after it? This:  \let\old@bibitem\bibitem \def\bibitem{\old@bibitem\it}   does not work, and \show\bibitem shows why:  > \bibitem=macro: ->\@ifnextchar [\@lbibitem \@bibitem .   What should I do to achieve the effect?  I would prefer not to use packages such as xpatch because I am modifying a class which others will use, and I try to use as few pacages as possible to minimize possible conflicts.

Frequently I see users redefine macros using (for example)  \let\oldmacro\macro% Store \macro in \oldmacro \renewcommand{\macro}{%   % ...redefined \macro   \oldmacro% }   and other times they use  \usepackage{letltxmacro}% http://ctan.org/pkg/letltxmacro \LetLtxMacro{\oldmacro}{\macro}% Store \macro in \oldmacro \renewcommand{\macro}{%    % ...redefined \macro   \oldmacro% }   Why would one use \LetLtxMacro when \let works just as well? Or, more specifically, when would one use \LetLtxMacro and/or why?


What is $[\mathbb{Q}(\sqrt [3] {2}+\sqrt {5}):\mathbb{Q}]$? A straight forward way will be to just set $x=\sqrt [3] {2}+\sqrt {5}$, take powers and reach at a polynomial in $x$ and show the polynomial is irreducible. But the method is very tedious and seems to be hopeless. Any idea?

Is there a general or elegant way to approach this problem? One can show that $\sqrt 5+\sqrt[3] 2$ is a root of the hexic $x^6-6x^4-10x^3+12x^2-60x+17$, which should then be its minimal polynomial to get the result. I see no straightforward way to show this is irreducible, though. It has a root in $\mathbf{F}_4$, and to show it's irreducible over $\mathbf{F}_3$ already seems to require a lot of grunt work.  One thing I can do is rule out the possibility that $[\mathbf{Q}[\sqrt 5+\sqrt[3] 2]:\mathbf{Q}]=2$, because $[\mathbf{Q}(\sqrt 5,\sqrt[3] 2):\mathbf{Q}]=6$ and $\mathbf{Q}(\sqrt 5,\sqrt[3] 2)$ is the compositum of $\mathbf{Q}[\sqrt 5+\sqrt[3] 2]$ and $\mathbf{Q}[\sqrt 5]$, where the latter has degree two. But I don't seem to be able to play an analogous trick to rule out $3$, because I know of no general lower bound on the degree of a compositum.   Could there be some way to bring Galois theory into the picture? These extension aren't Galois, and so it's by no means clear to me how to reason from their normal closures, but perhaps that's the direction to go in. Suggestions are very much appreciated.


Question:                            Letting S be a planar graph.                  Demonstrate that there would exist a vertex of S whose degree                        would be no greater than 5, ie, $\leq 5$  I have just gotten started with Discrete Math Graph Theory and it would be a great help if someone could assist me in working out the steps to understand the problem and work through the answer with a detailed explanation? Thanks.

I am trying to prove the following statement, any help!?     Prove that every planar graph has a vertex of degree at most 5.


Is it possible to have a masters degree in business engineering or management engineering when you don't have a first degree? But i have more than 10 years professional experience

I have worked as translator for more than seven years in the industry. I have a background in cuisine for more than ten years. Now I would like to add an graduate degree related to Tourism, Hotel and Event Management to my professional experience.  Can I enroll in such a masters program without first acquiring a Bachelors degree?


I have recently upgraded to Ubuntu 18.04. I used to update youtube-dl via youtube-dl -U, but now I get the error:  youtube-dl: error: youtube-dl's self-update mechanism is disabled on Debian.  Please update youtube-dl using apt.   So will I always get the recent (stable!!) update by going   sudo apt update && sudo apt dist-upgrade -y   as for everything else, or will I have to add a new repository?

This error occurred when using youtube-dl:  [youtube] 1234567890A: Downloading webpage [youtube] 1234567890A: Downloading video info webpage ERROR: 1234567890A: "token" parameter not in video info for unknown reason;    please report this issue on https://yt-dl.org/bug.  Make sure you are using the latest version; type youtube-dl -U to update.    Be sure to call youtube-dl with the --verbose flag and include its complete output.    I tried to uninstall youtube-dl and reinstall it, but this error reoccurred.


everyone. I am afraid that my question is too trivial. But here it is. The Klein four group is the first counterexample to the the statement: "If all proper subgroups of a group are cyclic, then the group is cyclic." I am looking for other examples, if any. Are there?  Thanks in advance.

Does there exist some sort of classification of all minimal non-cyclic groups (non-cyclic groups, such that all their proper subgroups are cyclic)  I know the following classes of such groups:  1) $C_p × C_p$, where $p$ is a prime  2) $Q_8$  3) $\langle a,b | a^p = b^{q^m} = 1, b^{−1}ab = a^{r}\rangle$, where $p$ and $q$ are distinct primes and $r ≡ 1 \pmod q$, $r^q ≡1 \pmod p$.  (These three classes completely cover the case, when our group is finite: )  4)$C_{p^{\infty}}$, where $p$ is a prime  5)$(\{ \frac{n}{p^m}| m, n \in \mathbb{Z} \}, +)$, where $p$ is a prime  (These two classes completely cover the case, when our group is infinite abelian: )  6)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{p}$ for a fixed prime $p$ (Tarski monster groups)  7)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{\infty}$ ().  However, I do not know, whether there exists anything, that does not fall into these classes. I only know, that if such groups exist, they have to be infinite non-abelian.


As I understand it, if light is traveling at the speed of light, then from it's point of view space is fully compressed in its direction of travel.  Does that mean that from it's point of view, light isn't traveling through space, and has already arrived as soon as it's created?  Does that mean that light knows the future?

To an an external observer it appears that time has stopped for photon. But this relation is reflexive, so for an observer travelling with the photon it appears the universe has stopped everywhere.  Is this right?  Space also gets distorted parallel to the direction of motion, but not perpendicular to it.   Does this mean that for an observer travelling with a photon sees spacetime as a flat plane?  Note 1: I'm using language vividly not literally when I say a photon experiences space and time. Not that I'm against idealist or panpyschist interpretations of matter or energy come to that.  Note 2: Since it's been pointed out that an inertial frame can't be boosted into the frame of a photon and moreover there is no limiting behaviour here - no matter what frame you are boosted into, light will always appear to travel at c. Nevertheless, when an external observer watches a train chasing a photon by gradually increasing its speed, he will note that the train speed is approaching the speed of the photon (but will never match it) and when he looks at the clock inside the train he will not too that it is gradually slowing down (but never actually stops). Using this picture, we can attempt the thought experiment - if not one that can be carried out - of what a world looks like to a photon.


I was wondering the difference between two symbols (we can found the diagram page 2 at  )  Between the logic gate NOT (a triangle then a circle) and the other symbol (a circle then a triangle) which is located in the right of the CLOCK10  I searched on the internet but I only find information about the NOT gate (and nothing about the other one)  Thank you very much,

See , page 2: the internal logic diagram for the MM74HC138.    The diagram shows logic inverters with bubbles at the input or at the output. Is there an actual difference between them?


I am having trouble collecting my first troll mutagen in Witcher 3. I have found several trolls in the game, but none of them have dropped a single troll mutagen. I have received advise from others to re-kill the trolls by saving the game and reloading it. I have tried this several times, and none of my trolls re-spawned. In fact, when I revisit locations where trolls were slain, they never reappear. I am unsure if this is a bug in the pc version or something else.  What must I do to force troll respawn in Witcher 3?

I have played the Witcher 3, exchanged dialogue with 5 trolls already, and decided not to kill them. All 5 trolls were involved in specific quests. I have killed two trolls of which I did not exchange dialogue. I have yet to receive a Troll Mutagen.  How does one obtain a Witcher 3 Troll Mutagen from a non-quest specific troll, at least one of which you never exchange dialogue with?


How do you partition a set into X number of new sets all that have Y elements?  Example: How to partition 18 unique cards are divided to six persons, and each person gets 3 cards each. How many combinations are there?

Let's have 2 numbers, N and K, where K divides N. The number of K-combinations from a given set S of N elements is a well known formula. Let's concatenate N/K groups (resulting in N elements) such as the resulting set is N. How many possibilities are there, i.e. what's the formula?  For instance:    N=4, K=2, C(4, 2) = 6 {1,2},{1,3},{1,4},{2,3},{2,4},{3,4}   The 3 possibilities are:     {1,2},{3,4}   {1,3},{2,4}   {1,4},{2,3}   I generated these combinations and I think the number goes like this:  (4, 2): 3 (6, 3): 10 (6, 2): 15 (10, 5): 126 (9, 3): 280 (10, 2): 945 (14, 7): 1716 (12, 4): 5775 (15, 5): 126126 (15, 3): 1401400   Apparently, the result always divides with (N-1).


Using Primefaces 6.2 and JSF 2.3. I would like to send the visitor to a page (actually a navigation rule) in a new window (not tab) when ckicking on a menuitem. The user must be able to continue navigation in the new window. Thanks

I have a select box that calls window.open(url) when an item is selected.  Firefox will open the page in a new tab by default.  However, I would like the page to open in a new window, not a new tab.    How can I accomplish this?


I fail to understand why an increase in the number of particles does not increase the temperature in case of ideal gas? Let's assume the increase mechanism  magically adds more particles of the same gas with the same average kinetic energy. More particles create higher pressure -- there is more bumping into the walls: $$ p={\frac {nRT}{V}} $$ Gay-Lussac's law: $$ P_{1}/T_{1}=P_{2}/T_{2} $$ So if P2 = 2*P1 (due to more particles being added), T2 must also double, right? I know similar question have been asked before (e.g. ), but I would like to start a new discussion since those answers don't make it clear to me.

Basis is the ideal gas law:   This law only states a mathematical relationship between many variables. It does not state what happens if one of the variables changes.  So we pin down the volume and increase moles of air by pumping in more gas. n obviously changes, so does P. But what happens to T? Does the temperature change at all?


After a fresh install of 18.04, I've installed  rather than the APT package.  Now I'm trying to tweak GNOME extensions at , and it's showing me:    This is because of the way snaps are sandboxed, it doesn't have access to the system version of chrome-gnome-shell. I assume it's a similar problem to those in these threads:     Does anyone know if there's a solution to getting chrome-gnome-shell to work with the Firefox snap?    I found the same question has already been asked , but there's no answer there yet either.

Got an error from Firefox saying :      Although the GNOME Shell integration extension is active, the native host connector is not recognized. Please consult the installation manual.   Which is an error that seems to never happen, I'm using Ubuntu 18.04 (Dual Boot Windows 10), and yes GNOME shell is installed via   sudo apt-get install chrome-gnome-shell   I'm using Firefox v64.0.2 (64 bits) snap.  Could someone help?


I am making a self signed certificate using OpenSSL. I want to make the certificate in one go, means that it will not ask me for the input for Company Name, Common Name etc etc. Is there anyway to do this like a switch e.g. /noprompt or any other through which I can input my all fields in one go. Is it possible that the following command takes all arguments in this call which it takes after pressing enter  openssl x509 -req -days 30 -in request.pem -signkey key.pem -out certificate.pem

I am using following code to generate keys:  apt-get -qq -y install openssl; mkdir -p /etc/apache2/ssl; openssl genrsa -des3 -out server.key 1024; openssl req -new -key server.key -out server.csr; cp server.key server.key.org; openssl rsa -in server.key.org -out server.key; openssl x509 -req -days 12000 -in server.csr -signkey server.key -out server.crt; mv server.crt  /etc/apache2/ssl/cert.pem; mv server.key  /etc/apache2/ssl/cert.key; rm -f server.key.orig; rm -f server.csr   I have two questions:   How can I skip the passphrase prompting? Would it be reasonably safe for me to do so? (as in it should not be downright foolish like anyone should be able to hack the certificate) How do I avoid the prompting for the country name, organization etc. I hope I can give them on command prompt (the man page shows only top level options for OpenSSL)


If the (net) gravity (at the centre of the Earth) is $0$, then what is the pressure? Some say it's astronomically big, but how can that be? Is it because of the (high) temperature? I can't think of anything else. And how about a neutron star and a black hole then? What is the temperature at the centre of those?

The  has microgravity and is thought to be solid and almost 6000 degrees hot. What is the pressure like there? The confusing thing, for the common man I suppose, is that there's no gravity there, but lots of matter around it which does gravitate towards the center. How does that add up? Is the center just a gas cloud or is it highly compressed?  And I could add the aside question about what it is like in the microgravity center of a  or a black hole, but I don't expect anyone to know about that.


I know the title is not good i don't know how to explain that.   I have table like  Id    AvaibleSports 1     [1] 2     [1] 3     [2],[10] 4     [4],[10]   I know this is not the best way to store information but this is all i have right now. I need to filter rows based on avaible sports value.  For example when i filter for "1" i must get records 1 and 2. When i filter for "10", i need to get 3 and 4 back.  I tried to filter with like statement like this:  select Id, AvaibleSports FROM myTable wHERE AvaibleSports like '%[10]%'   but this is also returning records containing [1].   I also tried to filter like   select Id, AvaibleSports FROM myTable wHERE AvaibleSports like '%10%'   This is returning correct result for 10 but wrong result for 1.   How can i filter this correctly?

I am trying to filter items with a stored procedure using like. The column is a varchar(15). The items I am trying to filter have square brackets in the name.  For example:  WC[R]S123456.  If I do a LIKE 'WC[R]S123456' it will not return anything.  I found some information on using the ESCAPE keyword with LIKE but I do not understand how to use it to treat the square brackets as a regular string.


Ok,  I am really new to java (and programming in general) so don't be too surprised when you see something strange.  Basically what I am trying to do is change the order of array elements because I want to "remove" one element from the array.  For example participant 2 gets knocked out, I want to remove him. I want the participant with the highest index to replace participant 2 and then reset the highest index participants values to default.  Fighter k1=participant[jList1.getSelectedIndex()]; Fighter k2=participant[jList2.getSelectedIndex()];  k1.fightsWith(k2); if (k1.refresh()==true) {       if (k1.getHP()<=0) {     participant[k1.getID()]=participant[amount];     participant[k1.getID()].setID(k1.getID());     participant[amount].reset();     amount-=1;   } else if(k2.getHP()<=0){     participant[k2.getID()]=participant[amount];     participant[k2.getID()].setID(k2.getID());     participant[anzahl].reset();     amount-=1;   }    jList1Model.clear();   jList2Model.clear();   for (int i=0;i<amount;i++) {     if (participant[i].getID()<=20) {       jList1Model.addElement(participant[i].getName());       jList2Model.addElement(participant[i].getName());     }   }    }   The lines participant[k1.getID()]=participant[amount];  participant[amount].reset();     are giving me trouble here.   Exception in thread "AWT-EventQueue-0" java.lang.NullPointerException

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


I am just being introduced to logic in mathematics. Let $P$ be "He is an honest person." and $Q$ be "He can be the President.". My lecturer was saying that "only if" means $P\rightarrow Q$, while "if" means $Q\rightarrow P$. I simply cannot wrap my head around this.  So let us consider the following two sentences.   One can be the president only if one is honest. One can be the president if one is honest.   How are the two statements any different in meaning?  However, according to the definitions, the first statement is of the form $P\rightarrow Q$, while the second is of the form $Q\rightarrow P$ and I know that $P\rightarrow Q$ and $Q\rightarrow P$ clearly have different meanings.  Any explanations regarding the difference between both terms and how/when to use which will be greatly appreciated!

For some reason, be it some bad habit or something else, I can not understand why the statement "p only if q" would translate into p implies q. For instance, I have the statement "Samir will attend the party only if Kanti will be there." The way I interpret this is, "It is true that Samir will attend the party only if it is true that Kanti will be at the party;" which, in my mind, becomes "If Kanti will be at the party, then Samir will be there."   Can someone convince me of the right way?  EDIT:  I have read them carefully, and probably have done so for over a year. I understand what sufficient conditions and necessary conditions are. I understand the conditional relationship in almost all of its forms, except the form "q only if p." What I do not understand is, why is p the necessary condition and q the sufficient condition. I am not asking, what are the sufficient and necessary conditions, rather, I am asking why.


Simplify: $\displaystyle\frac{\frac{a}{x}-\frac{a}{y}}{\frac{a}{x}+\frac{a}{y}}$  I did $\displaystyle\frac{ay}{xy}-\frac{ax}{xy}=y-x$ on top in underside. I did $\displaystyle\frac{ay}{xy}+\frac{ax}{xy}=ay+ax=a(y+x)$.  My final answer is $\displaystyle\frac{y-x}{ay+ax}$. Is this correct?  I posted question before but now just bit different. Please explain in steps so I understand this form and solve my other problems.

Frist I solved this equation $\displaystyle \frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{xy}}$ by multiplying $xy \left(\frac{xy}{x}+\frac{xy}{y}\right)=y+x$ The answer is correct.  Next equation was:    $$\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$$  I made the bottom multiplied and got $x^2 y^2.$ So I made the up also multiply and got     $$\frac{\frac{y^2}{x^2}-\frac{x^2}{y^2}}{\frac{1}{x^2y^2}}.$$   Now I'm stuck.  So now I doubt I did the first one the right way. I might have gotten the answer right but not the correct way to get it. Im sorry if Im confusing. Can someone help me with the two were I go wrong?


I deleted some old questions of mine with no answers from stackoverflow.com. Is this OK?, as I don't want a question ban.

Last week I wrote a , and I noticed that no one has answered it nor comment it (it only has one comment). Maybe my question is too broad, too complex or too strange, I am not sure, because it's my first question on the site and my first time making a game, so I'm not sure how to explain it. But the important thing is that I posted the question 8 days ago, and I still doesn't have an answer. Also, I don't know how much time it usually could take, but I never saw a question that didn't have an answer in less than 4 days (without being downvoted or closed), so I am starting thinking that maybe I shall delete my own question. Shall I delete it? Actually the question doesn't have any answer, and maybe it would never have one, so it's just trash. It takes space in the site, making the search of other questions on the site slightly more difficult and it doesn't provide useful information. Does it have any positive use on Stack Exchange?


Looking at , I was wondering if there is a way to set a whole row of a tabular to math mode (without repeating $...$ for every cell) or a whole row of an array to text mode (without repeating \text{...} for every cell).  In  this setting is done for a bold/italic/any-other-switch rows but can it be done also when the cell content should be the argument of a macro or the body of an environment?  \documentclass{article} \usepackage{amsmath}  \begin{document}     For example, how to set, once for all, the second row to text here:      \[     \begin{array}{*{14}{c}}     \dfrac{17}{91} & \dfrac{78}{85} & \dfrac{19}{51} & \dfrac{23}{38} & \dfrac{29}{33} & & & & & & & & & \dfrac{55}{1} \\[10pt]     \text{A} & \text{B} & \text{C} & \text{D} & \text{E} & \text{F} & \text{G} & \text{H} & \text{I} & \text{J} & \text{K} & \text{L} & \text{M} & \text{N} \\     \end{array}     \]      Or the first row to math here:     \begin{center}     \begin{tabular}{*{14}{c}}         $\dfrac{17}{91}$ & $\dfrac{78}{85}$ & $\dfrac{19}{51}$ & $\dfrac{23}{38}$ & $\dfrac{29}{33}$ & & & & & & & & & $\dfrac{55}{1}$ \\[10pt]         A & B & C & D & E & F & G & H & I & J & K & L & M & N \\     \end{tabular}        \end{center}  \end{document}

It is possible to format the column entries of a tabular in an argument-style fashion using the lrbox environment to   store the column cell in a box (say) \mybox; and supply \mybox as an argument to some other macro.   Here is a short example illustrating this fact*:  \documentclass{article} \usepackage{array}% http://ctan.org/pkg/array \begin{document} \newsavebox{\mybox} \begin{tabular}{c>{\begin{lrbox}{\mybox}}c<{\end{lrbox}\fbox{\usebox{\mybox}}}c}   One & Two & Three \\ \hline   1 & 2 & 3 \\   4 & 5 & 6 \\   7 & 8 & 9 \\ \hline \end{tabular} \end{document}     The above example uses the  to achieve this column-specific formatting. More specifically, each cell in the column is supplied as an argument to \fbox. Does there exist an equivalent automation that would yield    \documentclass{article} \begin{document} \begin{tabular}{ccc}   One & Two & Three \\ \hline   1 & 2 & 3 \\   \fbox{4} & \fbox{5} & \fbox{6} \\   7 & 8 & 9 \\ \hline \end{tabular} \end{document}   without having to specify \fbox for each entry in the row?  As a start, I know that the  provides \rowfont[<alignment>]{<font specification>}. However, this only applies macros <font specification> to each cell in a row and these macros can't take the cell contents as an argument. Moreover, you need to use the tabu environment in order to use this. So that's a little restricting. Also, trying to decipher the  macros for colouring a tabular or array row is just confusing.  The UK TeX FAQ entry on  modifies the row entries via column specifications and therefore requires the addition of "subtle" identifiers like  \begin{tabular}{|$l|^l|^l|}   to initiate $ and propagate ^ whatever row style is defined. Is there a way around this or at least a cleaner alternative that doesn't use columns to format entries in a row? In particular, a solution should provide an lrbox-style flexibility, since the contents of the cell in the to-be-styled row could be anything, even a paragraph (say).  * There are other alternatives, as indicated by the post .


I have lines of equations that run over the boundary of the PDF, I would like them to fit in the PDF. However, this is what happens instead:   I have the code:  \documentclass[11pt,fleqn]{article} \setlength {\topmargin} {-.15in} \setlength {\textheight} {8.6in}  \usepackage{amsmath}    \usepackage{amssymb} \usepackage{amsthm}  \renewcommand{\labelenumii}{\theenumii.}  \newcommand{\mname}[1]{\mbox{\sf #1}} \newcommand{\pnote}[1]{{\langle \text{#1} \rangle}}  \begin{document}  \medskip  \noindent  \subsection*{Required Problems}  \begin{enumerate}    \item \textbf{[10 points]} Prove by weak induction that \[\sum^{n}_{i=0}i^2 = \frac{n(n+1)(2n +1)}{6}\] for all $n \in \mathbb{N}$.  \bigskip  \begin{proof} Let $P\,n \equiv \sum^{n}_{i=0}i^2 = \frac{n(n+1)(2n +1)}{6}$. Proving $P\,n$  for all $n \in \mathbb{N}$ by weak induction.  \emph{Base case}: $n = 0$.  \begin{align*} P\,0 & \equiv \sum_{i=0}^{0} {i}^2 = \frac{0(0+1)(2*0 +1)}{6} &  \pnote{definition of $P$}\\      & \equiv 0^2 = \frac{0(0+1)(2*0 +1)}{6} & \pnote{definition of $\sum_{i=m}^{n} f\,i$}\\      & \equiv 0 = \frac{0(1)(1)}{6} & \pnote{arithmetic}\\      & \equiv 0 = 0         & \pnote{arithmetic} \end{align*}  \emph{Induction step}: Assuming $P\,n$. Proving $P\,(n + 1)$.  \begin{flalign*} P\,(n+1) & \equiv \sum_{i=0}^{n + 1} {i}^2 = \frac{(n+1)(n+2)(2(n+1) +1)}{6} & \pnote{definition of $P$}\\          & \equiv {(n+1)}^2 + \sum_{i=0}^{n} {i}^2 = \frac{(n+1)(n+2)(2(n+1) +1)}{6} & \pnote{definition of $\sum_{i=m}^{n} f\,i$}\\          & \equiv {(n^2+2n+1)} + \sum_{i=0}^{n} {i}^2 =  \frac{(n^2+3n+2)(2n+3)}{6} & \pnote{arithmetic}\\          & \equiv {(n^2+2n+1)} + \sum_{i=0}^{n} {i}^2 =  \frac{(2n^3+9n^2+13n+6)}{6} & \pnote{arithmetic}\\           & \equiv {(n^2+2n+1)} + \frac{n(n+1)(2n +1)}{6} =  \frac{(2n^3+9n^2+13n+6)}{6} & \pnote{induction hypothesis}\\          & \equiv \frac{(6n^2+12n+6)}{6} + \frac{(n^2+n)(2n +1)}{6} =  \frac{(2n^3+9n^2+13n+6)}{6} & \pnote{arithmetic}\\          & \equiv \frac{(6n^2+12n+6+2n^3+n^2+2n^2+n)}{6} =  \frac{(2n^3+9n^2+13n+6)}{6} & \pnote{arithmetic}\\          & \equiv \frac{(2n^3+9n^2+13n+6)}{6} =  \frac{(2n^3+9n^2+13n+6)}{6} & \pnote{arithmetic}\\ \end{flalign*}  \end{proof}    \end{enumerate}   \end{document}   Please realize that I am a complete beginner to LaTeX.

I often see output from TeX with the warning overfull hbox, badness 10000. What does this message mean?


The question I have is the use of the word "to" in the phrase "to December 28". Does the "to" definitely include December 28th, or is it (as I think it is) ambiguous?  The way it reads, I feel it is ambiguous as to whether hours worked and record on December 28th will be included in the live payroll processing date of December 29th.  I think a less-ambiguous word choice would be "through" instead of "to".

The quiz covers all the material up to the week of the quiz Sept.30 - Oct.6.    Does this mean that September 29 is the last date, or that the week Sept.30 - Oct.6 is included in this span?


I have a site where some code was injected into a very large number of php files and removing them manually is not feasible due to the number of files.  I can search for a variable name from the injected code in all files and it gives me a list of the affected ones, but I can't put the actual code in the search as it contains double quotes, single quotes and all types of characters.  Here is what I used for the search:  grep -Ril "ljdcvhg" 'path-to-site-folder'  Is there any way to search for the entire php function / injected code and remove? Please note I'm very new to linux.  I was going to put the hack code in here, but I'm not sure if that is allowed or not.  Any help is appreciated.


Gödel's second incompleteness theorem concerns the question of proving consistency of certain axiomatic systems. But what set of axioms is used to prove Gödel's second incompleteness theorem itself? Is there a possibility that the set itself is proven inconsistent in the future?

For example, consider the proof using Rosser's trick as shown on wikipedia.  That proof isn't inside the arithmetical theory T, but in some higher level meta-theory. So if I wanted to do meta-reasoning about Godel's proof (or Rosser's etc), I would need a system that could refer to or even encode statements like "For any fixed arithmetical theory $T$, let Proof$_T(x,y)$..." In what formal system would the statement "For any fixed arithmetical theory $T$..." exist? It obviously wouldn't be in $T$ itself since that would be tantamount to a proof that $T$ is consistent that is inside $T$, in which case $T$ would be inconsistent by Godel's second incompleteness theorem, thus making $T$ useless as a formal system. Is it second order logic? ZFC?


I need to add a p7b root ca to Ubuntu, in order to connect to services/servers for my company.  Based on what I have found on the internet, it seems that I need to convert this file to either .crt or .cer. I used the following commands to convert the file:  openssl pkcs7 -inform der -in cert.p7b -out cert.cer openssl pkcs7 -inform der -in cert.p7b -out cert.crt   I then moved these files (I actually tried them one at a time) into /usr/share/ca-certificates/mycompany, and then added mycompany/cert.cer and mycompany/cert.crt to the /etc/ca-certificates.conf. After performing update-ca-certificates I still get root CA warning that the certificates/chain isn't in the system.   The only direction my company has given is for both Windows and adding this file into the OSX keychain. Any help is appreciated, because I don't like disabling https while using remote services/tools for my company.

Excuse my poor English and my ignorance about Ubuntu and Linux world in general.  I just received a .p7b file in order to connect with a private site through HTTPS. Using MS Windows, I just have to double-click that file and install it, but doing that with Ubuntu pops up a window where I could see all the details of certificate, then there were two buttons: "Close", that is the only one I can press, and "Import", that is gray and therefore useless.  So I searched around the Internet for a solution, then copied the .p7b file in /usr/local/share/ca-certificates/ and ran update-ca-certificates with root permission. Nonetheless, if I tried to connect that site, Chrome gives me a NET::ERR_CERT_AUTHORITY_INVALID.  If I run againt update-ca-certificates, output is still the same it was the first time:  Updating certificates in /etc/ssl/certs... 7 added, 7 removed; done. Running hooks in /etc/ca-certificates/update.d...  Adding debian:Entrust.net_Secure_Server_CA.pem Adding debian:GTE_CyberTrust_Global_Root.pem Adding debian:RSA_Root_Certificate_1.pem Adding debian:Thawte_Premium_Server_CA.pem Adding debian:Thawte_Server_CA.pem Adding debian:ValiCert_Class_1_VA.pem Adding debian:ValiCert_Class_2_VA.pem Removing debian:Entrust.net_Secure_Server_CA.pem Removing debian:GTE_CyberTrust_Global_Root.pem Removing debian:RSA_Root_Certificate_1.pem Removing debian:Thawte_Premium_Server_CA.pem Removing debian:Thawte_Server_CA.pem Removing debian:ValiCert_Class_1_VA.pem Removing debian:ValiCert_Class_2_VA.pem done. done.   Then I'm totally stuck... can you help me please? Thanks!


I have to encrypt a code with XXTEA algorithm.  cipher = 16 byte key = 8 byte  Example : key: 0xAA 0xBB 0xCC 0xDD 0xAA 0xBB 0xCC 0xDD 0xAA 0xBB 0xCC 0xDD 0xAA 0xBB 0xCC 0xDD  msg : 0xFF 0xFF 0x87 0x30 0xFF 0xFF 0x87 0x30  And I expect this encrypted result  : 0X24 0x81 0xCE 0x89 0xA5 0x58 0x57 0x35  Now I'm using this code :   But for me is more difficult to use this code with hexadecimal byte values, because the byte function gives me the wrong value.  How can I implement an algorithm that accepts hexadecimal value and return encrypted value in a byte array  EDIT : I know how convert hex dump string to byte array (i learned it on stackoverflow =D ), but my problem is that if I use byte[] encrypt(byte[] data, byte[] key) I obtain a wrong result.

I am looking for a way to convert a long string (from a dump), that represents hex values into a byte array.  I couldn't have phrased it better than the person that posted .  But to keep it original, I'll phrase it my own way: suppose I have a string "00A0BF" that I would like interpreted as the  byte[] {0x00,0xA0,0xBf}   what should I do?  I am a Java novice and ended up using BigInteger and watching out for leading hex zeros. But I think it is ugly and I am sure I am missing something simple.


I'm sorry about the title - I'm not sure which rules of grammar apply to this question.   I'm trying to decide the correctness of the following sentences.     1) The carpenter will bring a hammer and be able to use it.   2) The carpenter will bring a hammer and will be able to use it.     Sentence 1) looks like it could be parsed incorrectly as:      The carpenter will bring [a hammer] and the carpenter will bring [be   able to use it].   Sentence 2) could suffer from a similar parsing error.  Is either sentence grammatically correct, in that the sentence parses to the following?     The carpenter will bring a hammer and the carpenter will be able to use the hammer.

Should I use the second "will" in constructions like this one: "it will definitely help you and will make the text more readable"  And should I write "to" before every infinitive in enumeration, or only before the first one, e.g. "it helps to develop and test" or "it helps to develop and to test"? Could this example be influenced by the fact that "help" can go with to-invinitive and bare infinitive, and with other verbs the rule would be different?


I upgraded to Ubuntu 18.04.  Now I would like to change the clock looks.  Up to now it looks like this:    I would like to see dd.mm to see the date of today.  How to do this?

On previous versions I had the date displayed. Now it just shows the current day but not the day's number or the month.   Is there a way to customize the clock or tray/taskbar more in GNOME shell on Ubuntu 17.10 and later?


From my main c# app, I start many slave process with Process.Start method. (on the same PC)  Just before starting those slave process, I serialize some data (I have serialized class) in XML files which are passed in the arguments of Process class.   In each slave process, those data are deserialized and a computation is done. A new serialization is done to XML in order to send result to the main process.  My apps works but the performance are very bad. The time of serialization/deserialization operation is too long because the size of each XML file is about 1,5 Mo...  I really need a high-performance for this simple communication between main app and slave process.  How can I easily modify my code to improve this performance ? Nb : in the future my main process will be in 64 bits and the slaves process in 32 bits.  I have heard that some apps allows to virtualize hard disk in RAM ? Does it exist ? Is it free ?  I have heard of WCF, Named Pipe, Memory Mapped, etc but I seems to be heavy to use ....?

Should I use Named Pipes, or .NET Remoting to communicate with a running process on my machine?


I have wrote the following in LaTeX:  \begin{align} & \tan(\Gamma_{4}) =  \begin{cases} \frac{x_{T3} - x_{T2}}{y_{T3} - y_{T2}} & \text{if} \qquad x_{T3}>x_{T2} \\ \\ \frac{x_{T2}-x_{T3}}{y_{T2}-y_{T3}} & \text{if} \qquad x_{T3} < x_{T2} \end{cases} \\ & (T_{2})_{Calc}: ((x_{T2})_{Calc},(y_{T2})_{Calc}) = (x_{T3} - (y_{T3}-y_{L2}) \cdot \tan(\Gamma_{4}),y_{L2}) \end{align}   and I obtain the following results:    The thing is that the text inside the fraction becomes very small compared to the other equations.  Is there a way to make them have the same size as the rest?

what should I do to stop the cases environment compressing the first line of the following? \begin{equation} \alpha_{mn} = \begin{cases} \frac{16\mu^2}{mn\pi^2\left[\pi^2(m^2/a^2 + n^2/b^2) - \mu^2\right]} &\mbox{for } m \mbox{ and } n \mbox{ odd;}  \\ 0 &\mbox{for } m \mbox{ or } n \mbox{ even;} \end{cases} \\[1ex] \end{equation}  I'm not sure to do tex on this site, but if anyone tries it they see the first case is compressed because it's a fraction.


My Minecraft openings keep crashing when I start it. Here is my crash reports: ---- Minecraft Crash Report ---- // I feel sad now :(  Time: 28-7-17 15:46 Description: Initializing game  org.lwjgl.LWJGLException: Pixel format not accelerated     at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)     at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(WindowsPeerInfo.java:52)     at org.lwjgl.opengl.WindowsDisplay.createWindow(WindowsDisplay.java:247)     at org.lwjgl.opengl.Display.createWindow(Display.java:306)     at org.lwjgl.opengl.Display.create(Display.java:848)     at org.lwjgl.opengl.Display.create(Display.java:757)     at org.lwjgl.opengl.Display.create(Display.java:739)     at ave.ap(SourceFile:534)     at ave.am(SourceFile:363)     at ave.a(SourceFile:310)     at net.minecraft.client.main.Main.main(SourceFile:124)   A detailed walkthrough of the error, its code path and all known details is as follows: ---------------------------------------------------------------------------------------  -- Head -- Stacktrace:     at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)     at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(WindowsPeerInfo.java:52)     at org.lwjgl.opengl.WindowsDisplay.createWindow(WindowsDisplay.java:247)     at org.lwjgl.opengl.Display.createWindow(Display.java:306)     at org.lwjgl.opengl.Display.create(Display.java:848)     at org.lwjgl.opengl.Display.create(Display.java:757)     at org.lwjgl.opengl.Display.create(Display.java:739)     at ave.ap(SourceFile:534)     at ave.am(SourceFile:363)  -- Initialization -- Details: Stacktrace:     at ave.a(SourceFile:310)     at net.minecraft.client.main.Main.main(SourceFile:124)  -- System Details -- Details:     Minecraft Version: 1.8.8     Operating System: Windows 10 (amd64) version 10.0     Java Version: 1.8.0_25, Oracle Corporation     Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation     Memory: 66176680 bytes (63 MB) / 157487104 bytes (150 MB) up to 1060372480 bytes (1011 MB)     JVM Flags: 6 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx1G -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M     IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0     Launched Version: 1.8.8     LWJGL: 2.9.4     OpenGL: ~~ERROR~~ RuntimeException: No OpenGL context found in the current thread.     GL Caps:      Using VBOs: Yes     Is Modded: Probably not. Jar signature remains and client brand is untouched.     Type: Client (map_client.txt)     Resource Packs: lucas     Current Language: ~~ERROR~~ NullPointerException: null     Profiler Position: N/A (disabled)     CPU: <unknown>

Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.


Someone can help me to do like this exemple :

I want to add a box in a tabularx table that would frame several cells vertically. There is this post that shows how to frame cells horizontally (), but I cannot figure out how to do to have the box extend over several rows. Here is what I would roughly like to get (but with a nice box):  Column 1 & Column 2 & Column 3                       +-----+ bla      & bla      & |bla  |                       |     | bla      & bla      & |bla  |                       +-----+   Any idea of how I could do that?  Edit: the solutions proposed below are very nice. But they are compatible with the tabular environment only, it seems, and not with tabularx and booktabs. Below is the code I have used. Does anyone have an idea of how to extend these solutions to the tabularx style? If not, then I will just rewrite all my tables using the simple tabular style.        \documentclass{article}    \usepackage{tabularx, booktabs}    \usepackage{tikz}    \usetikzlibrary{calc}     \newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node (#1) {};}    \newcommand{\DrawBox}[1][]{%         \tikz[overlay,remember picture]{         \draw[black,#1]            ($(left)+(-0.5em,2.0ex)$) rectangle            ($(right)+(0.75em,-0.75ex)$);}           }     \begin{document}    \begin{table}[H]    \centering     \begin{tabularx}{0.3\textwidth}{Y*{4}{c}}         \toprule          & Masc  & Fem & Neut\\          \midrule  \cline{4-4}         Nom & hic & haec & \multicolumn{1}{|c|}{hoc} \\          Acc & hunc & hanc & \multicolumn{1}{|c|}{hoc} \\ \cline{4-4}         \bottomrule      \end{tabularx}     \end{table}      \begin{table}[H]    \centering     \begin{tabularx}{0.3\textwidth}{Y*{4}{c}}         \toprule          & Masc  & Fem & Neut\\          \midrule           Nom & hic & haec & \tikzmark{left}hoc \\          Acc & hunc & hanc & hoc\tikzmark{right} \\          \bottomrule      \end{tabularx}       \end{table}     \end{document}


10th of June i've made an update and now I'm no more able to login. Unfortunately I don't know wat was included in this update. My PC looks like logging in, but, after a few seconds, it comes back to the login screen and ask me again and again the password (or to select another account).

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


I'm confused as to why the below will output "1".  If I use var to declare a in myFunc that should limit the scope of a to that function.   Calling "a" in the anonymous function (in the setInterval call) is a different function so why is that considered with the scope of myFunc?  Is it only because the function is anonymous? I would expect a to be available to another function unless bind() was used.  myFunc = function(){      var a = 1;      var int = setInterval(function () {          console.log(a);      }, 5);      }

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


I have two instances of SQL server namely Adventure and instance 2. Now  I cannot start SQL server from services for Adventure but the instance2 is fine. Once i go through the log file it showed SQL evaluation is expired.   Does SQL licence expire for a single instance?

This is a  about Licensing.    Questions on licensing are off-topic on Server Fault.  If your question has been closed as a duplicate of this question, then this is because we want to help you understand why licence questions are off topic rather than just telling you "it just is". In all likelihood, this question will not address your question directly, it was not meant to.    I have a question regarding software licensing. Can the Server Fault community please help with the following:   How many licenses do I need? Is this licensing configuration valid? What CALs do I need to be properly licensed? Can I run this product in a virtual environment? Can I downgrade this product to an earlier version? Am I entitled to feature X with license Y?


I understand this is a single threaded example and this would lock in a multi-threaded example. But given the execution sequence, shouldn't the lock be consumed by the parent, therefore starving the child even in a single thread situation?  class Program {     static readonly object Lock = new object();      static void Main(string[] args)     {         Console.WriteLine("Main start");         Parent();         Console.WriteLine("Main end");         Console.ReadLine();     }      static void Parent()     {         lock (Lock)         {             Console.WriteLine("Parent start");             Child();             Console.WriteLine("Parent end");         }     }      static void Child()     {         lock (Lock)         {             Console.WriteLine("Child start");             Console.WriteLine("Child end");         }     } }   Console output     Main start   Parent start   Child start   Child end   Parent end   Main end

Will the following code result in a deadlock using C# on .NET?   class MyClass  {     private object lockObj = new object();      public void Foo()     {         lock(lockObj)         {               Bar();         }     }      public void Bar()     {         lock(lockObj)         {            // Do something          }     }         }


Let  $r\in \Bbb R$ such that  $r + \frac{1}{r}\in \Bbb N$, Prove by induction that $r^n + \frac{1}{r^n}\in \Bbb N$ for every $n\in \Bbb N$.  I've done some expansions for $(r+\frac{1}{r})^n$ for $n = 2,3$ and I can see how it holds.  I am having trouble showing it for all $n.$

Assume that $x+\frac{1}{x} \in \mathbb{N}$. Prove by induction that $$x^2+\frac1{x^2}, x^3+\frac1{x^3}, \dots , x^n+\frac1{x^n}$$ is also a member of $\mathbb{N}$.  I have my base, it is indeed true for $n=1$..  I can assume it is true for $x^k+x^{-k}$ and then proove it is true for $x^{k+1}+x^{-(k+1)}$ but I'm stuck there.


It is quite easy to show that (by using residue theorem) $$\int_0^{\infty} \frac{1}{1+x^n}dx = \frac{2 \pi i^{1+2/n}}{n(e^{2 \pi i / n} - 1)} $$ for $$n \ge 2$$  Is there any possibility to simplify $$\frac{2 \pi i^{1+2/n}}{n(e^{2 \pi i / n} - 1)}$$ or it is best result?  Thanks in advance!


I was wondering if it is possible to repurpose this ancient computer with a version of ubuntu?  BrandLenovo CPU2.1-GHz AMD Accelerated Processor A6-4455M Card Slots2-1 card reader Display Size14 Graphics CardAMD Radeon HD 7520G Graphics Hard Drive Size500GB Hard Drive Speed5,400rpm Hard Drive TypeSATA Hard Drive Native Resolution1366x768 Operating SystemWindows 8 Optical DriveNone Optical Drive Speedn/a Ports (excluding USB)USB 2.0, Headphone/Mic, HDMI, Ethernet, USB 3.0 RAM4GB Size13.25 x 9.5 x 0.33-0.83 inches Touchpad Size4.25 x 2.75 inches USB Ports3 Wi-Fi802.11b/g/n

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


first-timer here.  I will try to explain this as clearly as possible, as I'm not an engineer or anything.   My Router: ASUS RT-AC87U - DD-WRT firmware installed, SNMP enabled.  Topology:  I have two switches off the router. behind switch 1: 2 W8 Desktops  behind switch 2: TV, Roku, Xbox.   On wireless: 2 Rokus, 4 iPhones, W8 laptop, chromebook, 2 Kindles  What I'm looking to do: I would like to be able to see traffic data to each individual IP I choose, particularly the rate at which it's flowing. Mostly because there are some devices sucking large amounts of data and I want to understand what they are, where they are receiving the data from and at what rate. And partly because I'm a geek and granular data is just something I prefer.  I installed PRTG and put an SNMP trap on my router, but the data isn't very useful to me. It put probes on there like eth0, vlan1, vlan2, br0 etc.  I tested with my machine when no other device in the house was streaming. What I saw was about 30K kbps, on eth0 and about half of that on vlan1. I'm sure there's an explanation for this that I don't understand, but at the end of the day - I stil can't get what I need when two different traps are displaying 2 different speeds for only 1 device. Plus the wireless devices are mostly what I'm interested in.  Is there a way I can configure the traps so it's 1:1? Will it require scripting? Do I need another solution besides PRTG? Is any of this even possible on a home router?   I will thank you all in advance for any insight/solutions you can provide, and I'll apologize as well if this is a redundant question that I couldn't find the thread to.  Thanks.

I have in my home a standard Comcast cable internet connection.  I have it going from the wall to a cable modem, and from the modem to a late-series Linksys router, which provides wired and wireless networking.  The vast majority of the users are wireless connections.  For day-to-day tasks, this connection is fully sufficient for all my needs.  However, on regular occassions, we have social gatherings that involve many people bringing laptops and other PCs and using the network and internet simultaneously, frequently for gaming.  I have no administrative oversight over these machines;  they have been known to be riddled with spyware and/or bloatware or be running torrents, legal or otherwise.  The only reason I care is that on a regular basis, one of the machines will flatline my internet bandwith, and consume it all in order to upload/download/spam people/whatever.  When this happens, the latency of the connections for gaming and the like becomes unacceptable, and everyone suffers.    My question is:  Is there a system I can set up whereby I can easily monitor the various systems connected to my wireless connection, see how much bandwith each one is using, and for what ends?  That way, at a glance, I can spot the offending machine and kick it from the connection, without having to go from machine to machine, checking each one's "bandwith used" properties manually, and dealing with the owner's indignant protests all the while.  I understand this will likely involve 3rd-party software and/or hardware;  my issue is I don't even know where to begin.


For example, I can run ln, nano, and programs I installed over apt like sl or worms without having to give the full path. However, when I build a program/package/software manually/using make/using something else, I have to invoke it using the full path, in my case ~/ghc/bin/ghc. How do you tell bash, or for that matter, sh, which names exist?  I know how to do this on Windows, but as far as I know, there's no equivalent of %PATH% in Linux/Unix/Ubuntu (in my case).

How to add something to PATH ? I have added like   PATH=$PATH:/home/example export PATH   and it works until I restart , after that when  I type env in PATH there is no /home/example.


I tried uninstalling PCL 1.7.2 which I had installed  (without sudo apt-get) but when I tried to remove them using the apt-get remove , terminal showed me those files cannot be uninstalled because they were not installed in the first place.    How can I check if the files were installed correctly if I installed files using cmake How can I uninstall a file that I manually installed using cmake? How are the files installed using apt-get vs cmake different?   Note - similar question but using apt-get remove:

I used source code to build one package such as below:  ./configure --prefix=/usr --sysconfdir=/etc --localstatedir=/var --libexecdir=/usr/lib --with-package-name="Myplugin" --with-package-origin="http://www.ubuntu.org/" --enable-gtk-doc --disable-static make make install   But unfortunately, i discovered that its the latest version, and has lot of bugs, so i need to remove it/uninstall it. But how can i do so? I tried make clean; make uninstall but still i see it exist:  # pkg-config --list-all | grep Myplugin myplugin-.... $ ls /usr/lib/myplugin/libXYZ.so exist....   How do you remove this now?


I am struggling with deleting apex classes that my org no longer uses. Why is this an issue? I would like to delete fields that are in the class (so now I cannot delete the field). What is the fastest way for deleting?

I cannot install Eclipse, even if I wanted to.  It is not approved software for my org.  How can test classes be deleted from production, using deployments? There no 'active' checkbox when I am editing the classes in sandbox mode, so I can't just deactivate the test class, and i cant deploy a deleted class to prod...  how the heck is this done?  I dont want to use ANT or special software.  SF must have a native way to achieve this.  And if not...  then I am very disappointed in humanity.


I am trying to find references on processing carried out inside the camera before the image is stored in RAW format. I am quite sure that some denoising is performed at the hardware level after the gain (that in photography we call ISO).  Are there any reference on the possible processing carried out before RAW image are produced?

Recently I came across a debate about whether it's fair to call RAW 'unprocessed' or 'unaltered' sensor data of a DSLR. As far as I know, the analog sensor data is processed into a digital RAW file using the ISO setting, a process during which the Bayer-sensor data is demosaiced as well. However, those are just the necessary steps for saving a digital file while maintaining maximum quality.  Are those assumptions correct? If so, are there any additional steps that need to be performed between the sensor receiving light and the saving of the RAW file? And can those be reasonably be described as an 'alteration' of the sensor data, or is it fair to say that a RAW file holds the unaltered sensor data?


Let $f:[a,b]\to \mathbb R$ such that it reaches its maximum and minimum in any closed sub-interval of $[a,b]$.  In addition:  $$|f(x)-f(y)| \leq 4|x-y|$$  holds for any $x,y$ in the interval. How would you prove that the function is integrable using the fact that Riemann's condition (i.e. $U-L < \epsilon$ for any epsilon)?

We suppose that $f : [0, 1] \rightarrow \mathbb{R}$ is a Lipschitz function with constant $K$. We want to show that $f$ is integrable on $[0, 1].$  I've been trying to use the Darboux criterion of integrability by trying to show that, for $\epsilon > 0$, $$S^*(f,P) - S_*(f, P) < \epsilon,$$ where $S^*(f, P)$ and $S_*(f, P)$ are the Upper and Lower Riemann Sums, respectively.  This is what I have so far: $$\sum_{i=1}^n M_i (x_i - x_{i-1})- \sum_{i=1}^n m_i (x_i - x_{i-1}) = \sum_{i=1}^n (M_i - m_i) (x_i - x_{i-1})$$ $$\le \sum_{i=1}^n K (x_i - x_{i-1}).$$ because $|f(x) - f(u)| \le K|x-u| \le K |1|$, since $x\in [0, 1]$. Then, $$\sum_{i=1}^n K (x_i - x_{i-1}) = K.$$ However, this is only a single upper bound, not an arbitrary $\epsilon.$ Can I get some pointers about how to proceed? Thanks!


I'm in the process of designing an iOS app menu, and the online version of this menu does not contain icons. After doing some R&D i've noticed that many iOS app menus do contain icons. From a UX perspective is it necessary to include them? I find the UI to appear a lot less cluttered without them

Are there any rules on when to use icons vs. icons with text vs. just text links in a web application?  For example:    vs.   save  vs.  save    Extra question: Is  save -or- save  preferable?


I need a formula for the summation of the series $a+2a^2+3a^3+...$ upto nth term. Is there any way to simplify it?

I want to know the general formula for $\sum_{n=0}^{m}nr^n$ for some constant r and how it is derived.  For example, when r = 2, the formula is given by: $\sum_{n=0}^{m}n2^n = 2(m2^m - 2^m +1)$ according to   Thanks!


I want to send to server (php) a request AJAX from an api javascript:   JS File :  var commit = new Object();  commit.id= this.id; commit.action = this.doCommit; commit.vrp= this.vrp; $.post(this.ajaxURL, commit);   with this code i can send a request but in mode asynchroun. I searched on internet and I found a solution :   $.ajax({     type: 'POST',     url: this.ajaxURL,     data: commit,     async:false });   I don't know if it is the best solution, or I can precise async:false in a  $.post request, if yes , how ?.

I have a JavaScript widget which provides standard extension points. One of them is the beforecreate function. It should return false to prevent an item from being created.   I've added an Ajax call into this function using jQuery:  beforecreate: function (node, targetNode, type, to) {   jQuery.get('http://example.com/catalog/create/' + targetNode.id + '?name=' + encode(to.inp[0].value),    function (result) {     if (result.isOk == false)          alert(result.message);   }); }   But I want to prevent my widget from creating the item, so I should return false in the mother-function, not in the callback. Is there a way to perform a synchronous AJAX request using jQuery or any other in-browser API?


I am a South African travelling to Canada with 2 passports. Passport one is expiring 2 days after I leave Canada and has a valid visa in it.  Passport 2 is a new passport. is this okay

I recently renewed my passport. I also have an expired passport which has my Canada visa (visitor's) valid for another three years. I have already used my Canadian visa which is multiple entry. I am planning to visit Canada this summer.  Since my valid Canadian visa is in my old/expired passport, do I need to renew/transfer my Canada visa or can I simply travel with valid visa in old passport?


on my database I've properly set up the Collation to utf8_general_ci in the case for the Japanese Characters may insert into the table. but when I tried to insert a Japanese character and viewing the table data in my phpMyAdmin database, It posted like this characters--> ãƒ™ãƒƒãƒ‰ãƒ¡ã‚¤ã‚¯(å®¢å®¤æ¸…æŽƒ)ã®ãŠä»•äº‹   How can I setup the phpMyAdmin to display the right Japanese characters?  on my HTML page I set up like this <meta charset="utf-8">  em I wrong?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I'm trying to install puttygen on an Amazon Linux server. puttygen is provided by the putty package available in EPEL, but installation fails with it unable to find several required C libraries:  Error: Package: putty-0.63-7.el6.x86_64 (epel)            Requires: libgtk-x11-2.0.so.0()(64bit) Error: Package: putty-0.63-7.el6.x86_64 (epel)            Requires: libatk-1.0.so.0()(64bit) Error: Package: putty-0.63-7.el6.x86_64 (epel)            Requires: libgdk_pixbuf-2.0.so.0()(64bit) Error: Package: putty-0.63-7.el6.x86_64 (epel)            Requires: libgdk-x11-2.0.so.0()(64bit)   Currently I'm installing putty on a Centos 6 box, then copying the binary /usr/bin/puttygen on to the Amazon Linux box. This works for my use-case, but I'm not keen on circumventing the package manager in this way. Is there a 'proper' way of doing things?

I have generated and downloaded a private .pem key from AWS. However, to use Putty in order to connect to the virtual machine, I must have that key in .ppk format. The process of conversion is detailed in roughly 20 lines here:      I am using Linux Mint (an Ubuntu distro) and I know I can use puttygen in the terminal. However, I have no idea how to use this tool, nor how to configure the needed parameters. When I type puttygen --help I get   PuTTYgen unidentified build, Aug  7 2013 12:24:58 Usage: puttygen ( keyfile | -t type [ -b bits ] )                 [ -C comment ] [ -P ] [ -q ]                 [ -o output-keyfile ] [ -O type | -l | -L | -p ]   -t    specify key type when generating (rsa, dsa, rsa1)   -b    specify number of bits when generating key   -C    change or specify key comment   -P    change key passphrase   -q    quiet: do not display progress bar   -O    specify output type:            private             output PuTTY private key format            private-openssh     export OpenSSH private key            private-sshcom      export ssh.com private key            public              standard / ssh.com public key            public-openssh      OpenSSH public key            fingerprint         output the key fingerprint   -o    specify output file   -l    equivalent to `-O fingerprint'   -L    equivalent to `-O public-openssh'   -p    equivalent to `-O public'   But I have no idea whatsoever on how to do what the website tells me to do and all my tentatives failed so far.  How do I do what the website tells me to do, using puttygen on the terminal?


I am working on a project where I have to monitor Vehicle fuel levels using an ADC of a micro controller. My fuel signal is a 0-12V signal & my 10 bit ADC is 0-3.6V range. I have 2 questions :-   Is only putting resistor divider for 0-12V to 0-3.6V sufficient? Do I need to take care of anything else here? How do I calculate resolution of 10 bit ADC after I drop down the voltage as mentioned in point 1 using a divider circuit?

I am working on a BLDC sensorless motor. I need to detect BEMF Zero-cross event. My Motor is working on 24 Volt power.  Now I need to detect the back E.M.F. As refered in .  My MCU is working on 5V. And ADC range is 0 to 5V. I need to convert the BEMF feedback signal to ADC channed in this.  As we know voltage divider rule says:   In Figure I :-- Now signal (U) which I need to feed is applied at the middle of the two resistors R1 & R7. So what is the value of voltage VU ?   In Figure II :-- Sum of U,V,W  is applied at the middle of the two resistors R11 & R15. So what is the value of voltage VN ?  Also, what are the roles of capacitors C1 & C4?  Please can someone explain the MATH behind this ?


Obviously the opacity isn't what I want lol. I'm a little stuck on how to merge   Little bit closer, but it's still transparent...

I have multiple scenes each with different objects. I want to combine all these scenes in the compositor but when they render, all the objects from each scene overlap each other and are all transparent, so I can see all the objects when some should be hidden behind others.   To join my scenes I'm using a mix node with add.


Let $f:\mathbb{\Omega}\to\mathbb{\Omega}$ be an analytic function such that there exist $z_0$ and $z_1$ $\mathbb{R}$-linearly independent$f(z+z_0) = f(z)$ and $f(z+z_1) = f(z)$ for all $z$. Show that $f$ is constant.  I can show that $f(nz_0+mz_1) = f(0)$ for $n$ and $m$ natural numbers, and I know that if  I could show it for $n$ and $m$ rational, it will be enough to conclude. But I'm not really sure how to continue or whether that's the right way or not (maybe I could use the maximum modulus principle o some similar theorem). Any help will be appreciated

Let $f: \Bbb C \to \Bbb C$ be an entire (analytic on the whole plane) function such that exists $\omega_1,\omega_2 \in \mathbb{S}^1$, linearly independent over $\Bbb R$ such that: $$f(z+\omega_1)=f(z)=f(z+\omega_2), \quad \forall\,z\in \Bbb C.$$Prove that $f$ is constant.   The intuition seems clear to me, we have the three vertices of a triangle given by $0$, $\omega_1$ and $\omega_2$. All points in the plane are one of the vertices of that triangle under a suitable parallel translation. The constant value will be $f(0)$, fine. Throwing values for $z$ there, I have found that $$f(n\omega_1) = f(\omega_1) = f(0)=f(\omega_2) = f(n\omega_2), \quad \forall\, n \in \Bbb Z.$$  I don't know how to improve the above for, say, rationals (at least). Some another ideas would be:   Checking that $f' \equiv 0$. I don't have a clue of how to do that. Write $w = a\omega_1+b\omega_2$, with $a,b \in \Bbb R$, do stuff and conclude that $f(w) = f(0)$. This approach doesn't seem good, because I only have a weak result with integers above. Finding that $f$ coincides with $f(0)$ on a set with an accumulation point. This seems also bad: the set on with $f$ coincides with $f(0)$ by which I found above is discrete.    Nothing works and this is getting annoying... And I don't see how analyticity comes in there. I'll be very thankful if someone can give me an idea.  (On a side note.. I know that this title is not informative at all. Feel free to edit if you come up with something better.)


whenever i login into the app ,I am starting sync adapter.It will sync data for every 12 hours.Right now  it is working fine in android kitkat and lower versions but when i login into my app and current os android lollipop,it is crashing please help me  error Log:   12-03 10:56:10.205: E/AndroidRuntime(10000): FATAL EXCEPTION: IntentService[Sync service]     12-03 10:56:10.205: E/AndroidRuntime(10000): Process: com.sample.example, PID: 10000     12-03 10:56:10.205: E/AndroidRuntime(10000): java.lang.IllegalArgumentException: error unparceling Bundle     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.content.ContentResolver.validateSyncExtrasBundle(ContentResolver.java:1835)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.content.SyncRequest$Builder.build(SyncRequest.java:490)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at com.sample.example.BeatsSyncAdapter.configurePeriodicSync(SampleSyncAdapter.java:129)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at com.sample.example.sync.BeatsSyncAdapter.onAccountCreated(SampleSyncAdapter.java:177)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at com.sample.example.sync.BeatsSyncAdapter.getSyncAccount(SampleSyncAdapter.java:168)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at com.sample.example.sync.BeatsSyncAdapter.initializeSyncAdapter(SampleSyncAdapter.java:190)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at com.sample.example.service.SampleSyncService.onHandleIntent(SampleSyncService.java:22)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.app.IntentService$ServiceHandler.handleMessage(IntentService.java:65)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.os.Handler.dispatchMessage(Handler.java:102)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.os.Looper.loop(Looper.java:135)     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.os.HandlerThread.run(HandlerThread.java:61)     12-03 10:56:10.205: E/AndroidRuntime(10000): Caused by: java.lang.NullPointerException: Attempt to invoke virtual method 'java.util.Set android.os.Bundle.keySet()' on a null object reference     12-03 10:56:10.205: E/AndroidRuntime(10000):    at android.content.ContentResolver.validateSyncExtrasBundle(ContentResolver.java:1819)     12-03 10:56:10.205: E/AndroidRuntime(10000):    ... 10 more

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