The book by Griffith on elementary particles reads:     A typical experiment starts out with beam of particles whose spin orientations are random, and simple counts the number of particles in a given direction.In this case the relevant cross section is the average over all initial spin configurations and sum over all final spin configuration.   I do not understand this explanation. If we do not know the spins of both initial and final particles shouldn't we take average for both? Why do we sum for final particles?

I am reading Halzen's book about quarks and leptons and on page 120 he talks about spin sums.  He says that in order to calculate the amplitude between unpolarized states we have to sum over FINAL spin states and average over INITIAL states. Why is this so? why not sum over initial states and average over finals, or sum over initial and final spin states and average also over initial and final states?


(Copied from )  Maybe I'm searching for the wrong thing, but I can't see how I can do this.  I have two servers:   Server A (has SQL Server 2012 installed)  Server B (has SQL Server 2014 installed)   Server A provides an API via IIS. The code both inserts and gets data from the database depending on the API call.  Server B does exactly the same for its local database.  I would like to have it so that the two databases are consistent copies of each other. I do believe this is what HA accomplishes.  So a load balancer, for example, might direct API calls to A sometimes, and B sometimes, but the data needs to be consistent either way.  I found some documentation on HA for SQL Server 2012, but not on how to do this for a mixed environment of 2012 and 2014.  Any help or pointers to documentation would be great! Thanks.


I have an object in a scene that uses multiple light sources, however, I only need the lights to hit the object and nothing else in the scene. Is there any way to fix this problem in Blender currently? Eevee is being used to render.

Is (or will be) there any sort of light linking in Cycles, or a method to get a light to affect only certain objects that doesn't involve compositing two or more different render layers? Sort of what 3Dstudio does with the Include/Exclude methods.


Find $\lim_\limits{n\to \infty}\underbrace{{\sin\sin\cdots\sin(x)}}_{n\text{ times}}$.  It is known that after the first sine, we get something in $[-1,1]$. If it is $0$ then it is constant and remains that way and so is the limit. Otherwise, $\sin x>0$ and therefore the sequence is monotonically non-increasing with an infimum $0$. Therefore converges to $0$. The is when $\sin x<0$, the sequence is monotonically non-decreasing and converges to the supremum, $0$.   I know there is the possibility of using the continuity of sine and and Heine definition of limits, but I want to understand why someone said it is incorrect.

I need your help with evaluating this limit:  $$ \lim_{n \to \infty }\underbrace{\sin \sin \dots\sin}_{\text{$n$ compositions}}\,n,$$  i.e. we apply the $\sin$ function $n$ times.  Thank you.


I have a problem with series $\sum_{k=1}^ \infty k*(\frac{1}{2})^{k+2}$ How can I solve it?

I know that the Series $\sum_{n=1}^\infty n \cdot x^n $ converges to $\frac{x}{(x-1)^2}$ but I'm not sure how to show it. I'm pretty sure that has been asked before, but I wasn't able to find anything...


Here is my regex that tries to match a valid URL:  ^(https?:\/\/((\b\w[^-][a-zA-Z0-9-]{1,33})\.){1,34}([[a-zA-Z0-9]{1,6})\/?)$   and I've tried to find way to make a simple solution to forbid the use of a hyphen '-' in the beginning and end of a group of letters and numbers. I'd tried to use \b\w[^-]. But it hasn't helped. For example, my regex matches this string, but it shouldn't

How can I check if a given string is a valid URL address?  My knowledge of regular expressions is basic and doesn't allow me to choose from the hundreds of regular expressions I've already seen on the web.


As you can see in the screenshot below, my system attempts (multiple times per day) to install an HP printer update that will never work. How do I stop this?

Every time Windows 10 runs updates (which I see no way to control), it updates my graphics driver.  I like the old one because it is faster.  So, I have to reinstall it.  This is getting to be a pain.  Is there any way to stop Windows 10 from updating it again?


I was , realising I previously , and in the google results, with the same page title I found:    http://www.simosh.com/article/dfaceeij-quantifier-quantifies-nothing-but-i-never-asked-for-a-quantifier.html   The page serves ads (some that AdBlock doesn't block!!!1!), and I see my username and profile picture, and the username and profile picture of the accepted answer, but there are no links to Stack Overflow or the question itself, and neither my profile page nor Christoph's. The related posts section has links but they go to e.g  http://www.simosh.com/article/dhbdcja-javascript-invalid-quantifier-in-regex.html`   They also have a pretty nice racket on the rest of SO: http://www.simosh.com/  There's nothing on those pages that allow me to get here from there; indeed they even say © 2016 Powered by Simosh.com. I'm not really sure the © has any meaning nor what it's referring to but fair enough.  Lastly, there are some links at the bottom of the page that trigger JavaScript alert();s. All of them are complete gibberish (mushy inspirational quotes, anyone?) except for the one titled Privacy statement:     Some of the informations on this site are from interent and all rights belong to their respective owners. If you think your copyright has been infringed, please contact us and we will remove them.~   [sic]  Is this a violation of Creative Commons / SE's license? If it is, I'll report it to SE, but I'd like to know here first if I am incorrect.

of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means:   Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow:   You have to provide . Simple links to the original post and author info are just fine. You have to  and allow other people to use your content, as long as they follow these very same rules. How meta!    (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.)  There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short).  In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery.  So, the question is: what can you do if you spot a SCRAPER?


I'm pretty new to programming, and I've looked at a bunch of of other questions/answers for a solution to this, but I'm still confused. Could somebody explain it in a very simple way?

I'm learning the Python programming language and I've came across something I don't fully understand.   In a method like:  def method(self, blah):     def __init__(?):         ....     ....   What does self do?  What is it meant to be?  Is it mandatory?  What does the __init__ method do?  Why is it necessary? (etc.)  I think they might be OOP constructs, but I don't know very much.


I would like to know what kind of speed implications using FileVault2 would have on my MBPr (late 2013). As there are much faster SSD's in these machines I want to know whether there is a noticeable speed difference compared older generations.

Never fancied enabling FileVault on previous Macs but now I'm running OS X on an SSD. Is there a noticeable decrease in speed?


I'm trying to make a div for my landing page of my website center in the very center of the screen, but it is not working.   Here is my code  CSS:  .centerDiv{ width:800px; margin:0 auto; border-radius: 5px; background:#111; padding:10px;}   HTML:

Title

Text will go here.

   Thanks.

Best way to center a <div> element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too?


Consider the random variables $Y$ characterised by a probability mass function (PMF) as follows: $$ Y=\begin{cases} -2 & \text{ with probability $\frac{1}{2}$}\\ 2 & \text{ with probability $\frac{1}{2}$}\\ 10 & \text{ with probability $0$} \end{cases} $$ Is this PMF considered symmetric around zero? I'm confused because  if I picture it it looks symmetric around zero (the last mass point does not appear as it has probability mass zero). However, from reading the , it does not seem so.

What's the definition of a symmetric distribution? Someone told me that a random variable $X$ came from a symmetric distribution if and only if $X$ and $-X$ has the same distribution. But I think this definition is partly true. Because I can present a counterexample $X\sim N(\mu,\sigma^{2})$ and $\mu\neq0$.  Obviously, it has a symmetric distribution, but $X$ and $-X$ have different distribution! Am I right? Do you guys ever think about this question? What's the exact definition of symmetric distribution?


I'm trying to reconcile the physical steps that go into the operation of an AC induction motor. Looking online, I either find broad and general explanations that I already know and understand, or very specific and math heavy explanations that get a bit overly detailed.  I understand synchronous motor operation and describe it in my head like this: "From standstill, voltage is applied to the rotor. This creates a current in the rotor which generates a magnetic field which starts to turn the rotor due to attraction to the magnets of the stator. At the start, the rotor has little movement relative to the stator's field, so little back-emf is created, allowing for maximum current to flow, and so the machine has max torque at the start. As it gets up to speed, the rotor's quick movement cuts through more of the stator's flux, and generates more intense back-emf, which fights the input voltage, limiting current into the rotor, and torque drops off until some balance of speed/torque is achieved with the load.  But when I try to create the same "story" of what happens in an induction motor, I must have some fundamental misunderstanding (probably about back-emf), because I run into this: "At standstill, an AC voltage is applied to the stator windings, quickly manifesting a rotating magnetic field. This induces a voltage in the rotor coils, creating a current that manifests its own magnetic field such that the induced voltage/field opposes what created it. Now the relative motion of the rotating stator field and rotor coil would be maximum at startup, creating maximum possible back-emf.... and that's where my thinking fails. If the back-emf is biggest at the start, it'll fight the input voltage the most at the start, which will result in the least current and least torque at the start... and the thing will never get up to speed."  Obviously that's wrong, but I don't see where. In a DC motor, it makes sense easily because input voltage, back-emf, and rotation, are all in the rotor. So when the rotor speed is low, it cuts less flux, and creates low back-emf. When the rotor speed is high, it cuts more flux, and creates higher back-emf. A nice feedback loop.  But it seems reversed for the induction case the way I'm thinking of it. At a low rotor speed, the rotor would cut through more flux, because the stator field is quickly rotating around it. This would create a higher back-emf in the rotor, fighting the input voltage, limiting the input current, reducing torque, and slowing the machine or keeping it from moving.   Then at a high rotor speed, the rotor would cut through less flux, because it's catching up to the rotational speed of the stator's field. This would generate less back-emf in the rotor, which would mean the input voltage isn't being fought as much, increasing current, increasing torque, speeding the device up.  So my thinking ends up with the opposite of a self stabilizing device. If it slowed down, it'd want to keep slowing to standstill, and if it sped up, it'd want to keep speeding up...  None of that is right, so I must be messing something up about how back-emf operates in an induction motor. And I think the inverse nature of how the rotor speeding up leads to amount of flux being cut to be lower is also tripping me up...  Thank you so much for any help with a layman's quest for understanding!

I was musing about electric motors after seeing one randomly on TV, and there's something I'm must be remembering incorrectly.  It's just a thought experiment, so I'm imagining some theoretical DC electric motor, with a constant RMS current/voltage feeding in, and some constant load on it causing it to spin at some constant rpm and produce some constant torque.  Since voltage x current = electrical power = motor's mechanical power, that's the cap on how much you can get out of the machine.   But I remember that the greater the difference in rotational speeds between the rotor and stator fields (slip?), the more force/torque will be exerted on the rotor.   So in the hypothetical, if the motor is doing its thing and is stable with the load, if you suddenly increased the frequency of the input voltage/current, that in my mind would result in suddenly increasing the difference in relative rotational speeds of the stator/rotor, meaning the stator would feel more force/torque on it, which would make it want to speed up and catch up to the stator field, speeding up the load.  But only frequency changed and not how much electrical energy is entering the device, so there's no way that's possible! So I MUST be wrong, I just don't see where the error in my thinking is...  What's wrong with my thinking, and what would actually happen if you increased the frequency like that?  (I'm not an electrical person by trade, so there's a limit to my knowledge of concepts/terminology.)  [EDIT: I failed to mention that by "frequency", I'm referring to how DC motors can be controlled with pulse width modulation, and those pulses go in at some frequency. Otherwise it wouldn't make sense to talk about "frequency" with direct motors]


What are Window Managers, Desktop Managers, Desktop Environments?   Which one do you need and Why?

I'm having a really hard time trying to understand what the differences between a desktop environment and a window manager are?  EDIT: From this :  There are basically three layers that can be included in the Linux desktop: X Windows – This is the foundation that allows for graphic elements to be drawn on the display.  builds the primitive framework that allows moving of windows, interactions with keyboard and mouse, and draws windows. This is required for any graphical desktop. Window Manager – The Window Manager is the piece of the puzzle that controls the placement and appearance of windows. Window Managers include: , , , , , etc. Requires X Windows but not a desktop environment. Desktop Environment – This is where it begins to get a little fuzzy for some. A Desktop Environment includes a Window Manager but builds upon it. The Desktop Environment typically is a far more fully integrated system than a Window Manager. Requires both X Windows and a Window Manager.  Examples of desktop environments are , , ,  among others)


I'm trying to make chat prefixes (like so):  Steve (Administrator): Hello   That is in the chat.  In this, Steve is the username and Administrator is the rank. I want to do this without plugins or mods, just commands. Is this possible?

How do you give people tags/prefixes on your Minecraft server? I have a server but I do not know how to make it say I am the owner in the chat.  Example: Owner Kieranpb7: <text>


I bought this Lemond frame online. I have an opportunity to get some components for it before I actually receive the frame. Hoping to get more info on the bike (model/year) in the hope of getting some kind of spec sheet. Any help is appreciated.

This is a canonical question that will hopefully encompass all of the questions we get asking us to determine what year a bicycle was manufactured (how old is my bike, how old is my frame, etc.). Each "answer" should address a different way to determine the manufacturing year of a bicycle. To some extent, these will also help you narrow down the model as well as it will tell you what distinguishing features to look at.  The span of answers would include things such as:      Skiptooth cranks Cartridge bottom brackets (BB30/90 etc) Elliptical chainring Quick releases versus contemporary through-axles How the steerer attaches to the fork (quill vs. threadless)  Braking system (especially with mountain bikes: v-brake, direct pull, etc.)   Shifting ramps and pins on cassettes/sprockets and chainrings (versus flat sprockets) Frame material (e.g., shift from tubular steel to use of CF and hydroformed aluminium)  Frame tubing type (e.g. Reynolds 531 tubing introduced around 1934, still used today; Reynolds 501 tubing introduced around 1983). So a frame with an original 501 decal can't be from the 70', 531 decal doesn't help as much because of the range of years produced. Also, see Decals.   *Decals: style/design, amount, placement, color, etc. can help not only determine models, but also year of manufacture. Many changed decal design for the same model bike often yearly, with special/limited editions even more specific. This applies only if decals are original or have been replaced with the identical design. Tubing decals (Reynolds, Columbus, etc.) also changed designs for same tubing made in different years, although the changes aren't made as often, and manufacturers didn't always put tubing Brand decals on every model. Earlier bikes tended to have less fancy, less colorful, less quantity of decals.   Headbadges: most early bikes had actual "badges", often quite detailed and fancy, made of metal, then plastic, and finally just using decals on the headtube. Most bikes lost their metal badges in the 60's and early 70's, although some brands still have actual badges to this day, but in general a real badge indicates an earlier model bike. Dropout style (including the later inclusion of lawyers lips) Presence or absence of CPSC reflectors (USA only) Manufacturing method (shift from lugs to TIG welding, for example)  Number of gears (shift from 2x5 ten-speed to 3x8, 2x9, 1x11, etc.)  Inspection of lug design: pantographs, cut-out, stampings, custom brazing/filing, chrome, fork crow n sweep, etc. Frame/Fork Braze-ons. Race bikes tended have less braze-ons the earlier the year of manufacture. Most 60's racers and earlier had few or none with cable guides/stops, shifters, bidons, etc. being clamp-on. By the 80's if it was clamp-on, it was a sign of very cheap models and most frames had braze-ons for all cables, with multiple bottle and accessory bosses depending on style and use.   and so forth. Please edit this question if you have an answer that isn't in the index above.   A couple of caveats:   A previous owner could have replaced or upgraded components on a bicycle, so this guide only applies to original equipment There is a delay between the introduction of a technology (such as indexed shifting) and when manufacturers start selling products that use it. Low-end manufacturers may continue using technology that is severely outdated (such as one-piece cranks, freewheels, or quill stems) because it is cheaper to do so. A number of bikes are built in a Retro style, but with modern components.  Dutch bikes, trendy coffee cruisers, and beach cruisers may be modern but appear to be 1950s styling.  These tend to have modern rims and brakes as a giveaway.     Note that bicycles.stackexchange does not do valuations of bicycles. How much your bicycle is worth depends on the location of the buyer and seller, how much the buyer wants the bike, etc. etc. etc.


This question from Physics For Scientists And Engineers 7th page 746.     After redrawing , Actually I cant see any two clear capacitors that we can be combined , First we cant combine $C$1 with $C$2 because the point $a$, and the same argument on $C$3 with $C$4 because the point $b$, And personally I cant combine any of $C$1 ,$C$2 ,$C$3 and $C$4 with $C$3 because I don't know where should I put the equivalent capacitor.  To be more clear , How we can solve these kind of circuit ?

I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series...


I read nearly all topics about collinearity but still have some questions...  I know: multicollinearity is a problem because if two predictors measure approximately the same it is nearly impossible to distinguish them. They overlap each other. But WHY (??) is centering helpful for this(in interaction)? How can center to the mean reduces this effect?

In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized.  (Standardizing consists in subtracting the mean and dividing by the standard deviation.)  In which other cases do I need to standardize my data?  Are there cases in which I should only center my data (i.e., without dividing by standard deviation)?


Say I have this   str="System IP is 9.9.9.9 on port 3442" str2="ip 192.168.0.9 is using port 222"   I would like to remove all substrings except for the one which contains periods which would leave me with :  9.9.9.9  192.168.0.9   Any ideas ?

How to extract a text part by regexp in linux shell? Lets say, I have a file where in every line is an IP address, but on a different position. What is the simplest way to extract those IP addresses using common unix command-line tools?


Let $z_1,z_2,z_3$  be three complex number such that :  $| z_1| = | z_2| = | z_3| = 1$ and $z^3_1 + z^3_2 + z^3_3 +z_1z_2z_3=0$  Then $|z_1+z_2+z_3|$ can take which of the following values ?  (A) $1$ (B) $2$ (C) $3$ (D) $4$    Using the triangle inequality I get $|z_1+z_2+z_3| \leq |z_1|+ |z_2| + |z_3| \leq 3$.   Using the inequality the answers should be (A), (B) and (C).  However, my book says that the answer is only (A) and (B). What is wrong in my method?


I want send argument to the function in the class but i got below error How Should i define a function can use the argument?      class Tistory:         def __init__(self, m_client_id, m_redirect_uri, m_user_id, m_password, m_blogname):             self.m_client_id = m_client_id             self.m_redirect_uri = m_redirect_uri             self.m_user_id = m_user_id             self.m_password = m_password             self.m_blogname = m_blogname      def wrtiePost(m_title, m_content, m_category, m_tag):         params = {             'blogName' : self.m_blogname,             'title' : m_title,             'content' : m_content,             'tag' : m_tag,             'category' : m_category,             'visibility' : '0',             #'published' : '',             #'slogan' : '',             #'acceptComment' : '1',             #'password' : '',             'access_token' : self.getAccessToken(),             'output' : 'json'         }         ....  if __name__== "__main__":     tistory = Tistory(g_client_id,g_redirect_uri,g_user_id,g_password, g_blogname)     #tistory.getAccessToken()     tistory.writePost(m_title="test",m_content="test",m_category="test", m_tag="test")   when I call the function in the class why i get below error?  Traceback (most recent call last):   File "/Users/chullee/github/tistory/class/tistory.py", line 113, in <module>     tistory.writePost(m_title="test",m_content="test",m_category="test", m_tag="test") TypeError: writePost() got an unexpected keyword argument 'm_title'

When defining a method on a class in Python, it looks something like this:  class MyClass(object):     def __init__(self, x, y):         self.x = x         self.y = y   But in some other languages, such as C#, you have a reference to the object that the method is bound to with the "this" keyword without declaring it as an argument in the method prototype.    Was this an intentional language design decision in Python or are there some implementation details that require the passing of "self" as an argument?


Is it possible to get or display the line number in TextEDit in macOS Big Sur? As I am using the editor for HDL (Hardware Descriptive Language) coding. If it's not possible, could you point me to an editor that supports line numbers that I could use with HDL files?

I'm looking for a programmers' editor. I know Xcode and I use it for application programming but I'm looking for something that will:   Syntax highlight PHP, SQL, Javascript (including jQuery) and CSS not required but would be nice; also Lua, Python, and Perl    IntelliSense type stuff, start typing and get all the functions/objects/variables it could be and any parameters. Xcode does this well for C/C++/Objective-C but looking for languages that are listed above. Would be nice if it worked with projects and not just files    Integrated with SVN, CVS, or GIT Had upload-to-server functionality built in   I am aware of  but am looking for other options before I drop 100 bucks.


I am new to Ubuntu and so far I have this problem: I've tried to install skype and couldn't do it. Then the software "app" stop working and I get an error of Failed to load the package list, followed by details:  E:Malformed entry 55 in list file /etc/apt/sources.list (Component),   E:The list of sources could not be read.   I'm really rookie at this, but I've tried my best figuring out through older ask ubuntu questions of the "E:Malformed entry 54"  but that is not working.   Please help.

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


The integral is:$$\int\sqrt{1+\sin x} dx$$  My first attempt was to multiply by:  $$\frac{\sqrt{1-\sin x}}{\sqrt{1-\sin x}}$$  giving: $$\int\frac{\sqrt{1-\sin^2(x)}}{\sqrt{1-\sin x}}dx$$ which is: $$\int\frac{\cos x}{\sqrt{1-\sin x}}dx$$ then make the substitution: $$u=1-\sin x$$ which gives $$\int\frac{-1}{\sqrt{u}}du$$ which gives: $$-2\sqrt{u}+c$$ so: $$I=-2\sqrt{1-\sin x}+c$$ but I am not sure if this is correct.  Also sorry if the formatting is a bit rubbish

To find:  $$\int \sqrt{1+\sin(x)} dx$$  What I  tried:  I put $\tan(\frac{x}{2}) = t$, using which I got it to:  $$I = 2\int \dfrac{1+t}{(1+t^2)^{\frac{3}{2}}}dt$$  Now I am badly stuck. There seems no way to approach this one. Please give a hint. Also, can we initially to some manipulations on the original integral to make it easy? Thank you.


Help me prove   $$\binom{n}{r} + \binom{n}{r-1} = \binom{n+1}{r}.$$

Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1}  $  Thanks in advance, my professor asked us to this a couple weeks ago, but I was enable to get to the right answer.   Good luck!  Here is what I got up to;  $\frac{(n+1)!}{(n-r)!(r+1)!} = \frac{(n)!}{(r)!(n-r)!} + \frac{(n)!}{(r+1)!(n-r-1)!}    $


Is there a way to show the short title in the TOC instead of the long version with an AMS document class?  For example, when I do:   \chapter[short version]{longer version that describes things in a verbose way}   Is there a way for showing the [short version] instead of the {...} in the TOC?

for my thesis I want to have a section appear differently in the ToC than in the text.  After googling a bit, I found \section[short]{long} as a proposed answer, but this does not seem to work for me.  Here is a MnotWE:  \documentclass[12pt,a4paper,reqno]{amsbook} \usepackage{fontspec} \setmainfont[SlantedFont={Latin Modern Roman Slanted},          SmallCapsFont = {Latin Modern Roman Caps},          ]{Latin Modern Roman}    \usepackage[activate=true,nocompatibility},final,tracking=true,factor=1100,stretch=10,shrink=10]{microtype}  \usepackage[bindingoffset=1cm]{geometry} \usepackage{polyglossia} \setdefaultlanguage{english} \usepackage{csquotes}  \title{\textsc{Some Title}} \author{me}  \begin{document} \maketitle \frontmatter \tableofcontents \mainmatter  \part[toc part]{normal part} \section*[toc section]{normal section} some text  \end{document}   It just takes "toc part" as normal and as ToC heading for the \part command.  For the section I am interested in the starred version. Here the [toc section] part of the command seems to be completely ignored.  I use LuaLaTeX to build my document. Does anyone have a suggestion how to get a \section* appear with a different title in the ToC?


I am modeling a architecture environment in blender and everything was working fine but must have accidently hit a hot key that I was not aware of. Now when I go to manipulate an object whether it be just moving it around, extruding or grabbing a vertex(face or edge) it now jumps to a full blender unit before moving and so on and so forth. I was wondering if anyone knew how I could change it back to the smooth fluid motion of before?

My cursor is moving by every selection by large increments!  Normally when I use Blender, I am able to select and move objects to any coordinate. Now, all of the sudden, when I select an object or mesh the selection moves by an inch or so in each direction.  How do I reset it to normal?


I saw  which explains that when running a command in parentheses it actually runs the command in a subshell, which is a child process of the original shell. Running the following experiment: // one shell with PID 5344 ~$ (find /)  // another shell ~$ ps l F   UID     PID    PPID PRI  NI    VSZ   RSS WCHAN  STAT TTY        TIME COMMAND ... 0  1000    5344    5333  20   0  10888  5220 do_wai Ss   pts/0      0:00 bash 0  1000    5384    5333  20   0  10888  5140 do_wai Ss   pts/1      0:00 bash 0  1000    7239    5344  20   0  10860  3444 -      R+   pts/0      0:00 find / 4  1000    7240    5384  20   0  11400  3224 -      R+   pts/1      0:00 ps l   We can see that find / is a child of 5344, with no other shell in between. Wheres running: // one shell with PID 5344 (cd /; find /)  // second shell ~$ ps l F   UID     PID    PPID PRI  NI    VSZ   RSS WCHAN  STAT TTY        TIME COMMAND ... 0  1000    5344    5333  20   0  10888  5220 do_wai Ss   pts/0      0:00 bash 0  1000    5384    5333  20   0  10888  5140 do_wai Ss   pts/1      0:00 bash 1  1000    7379    5344  20   0  10888  3036 do_wai S+   pts/0      0:00 bash 4  1000    7380    7379  20   0  10864  3536 -      R+   pts/0      0:01 find / 4  1000    7381    5384  20   0  11400  3184 -      R+   pts/1      0:00 ps l     Now we can see that other shell in between. My guess is that it is some optimization of bash: In the first case, it doesn't really have to spawn another shell, so it just doesn't do it. In the second case, since the commands include cd /, which will have affect on the current shell, it has to spawn another process. Is that so?

Consider the two following bash commands. One creates a subshell and the other does not.   No subshell  $ bash -c "sleep 10000 "   pstree output:  bash,100648   └─sleep,103509 10000   With subshell  $ bash -c "sleep 10000; sleep 99999 "   bash,100648   └─bash,103577 -c sleep 10000; sleep 99999       └─sleep,103578 10000   Is this some kind of an optimization ? Bash looks at the command and skips the process creation for simple commands. It looks like the simple command is spawned by the parent terminal’s bash.     Bash version I am using is   $ bash --version GNU bash, version 4.2.46(2)-release (x86_64-redhat-linux-gnu)   Though, I think the same can be observed in bash 3.X too.     Some more examples.  With builtins the subshell gets spawned. Builtins are not executed in the parent bash.  $ bash -c "read"  bash,100648   └─bash,104336 -c read     Same behavior with sleep can be reproduced with top and with output redirect.   $ bash -c "top -b " bash,100648   └─top,104392 -b   And   $ bash -c "top -b > /dev/null " bash,100648   └─bash,104420 -c top -b > /dev/null       └─top,104421 -b


If you don't have access to the source code of a struct or class, is there a way to know the members of that struct or class? Specifically, i want to know the names, order, and data types of the members.

I'd like to be able to introspect a C++ class for its name, contents (i.e. members and their types) etc. I'm talking native C++ here, not managed C++, which has reflection. I realise C++ supplies some limited information using RTTI. Which additional libraries (or other techniques) could supply this information?


Context I need to make a mapping function. That maps range of int to an object. ex) if 10 > x >= 5: # map to y. What I tried map_list = [] step = 5 for i in range(100): # range(0, 500, 5)     lower_bound = i * step     upper_bound = (i+1) * step     map_list.append(lambda x: upper_bound > x >= lower_bound)  Problem I went through the map_list with the value 158 which is inside the mapping range. But all of the lambdas in the list returned False. While debugging, i passed 500 through the list and it all returned True. And more debugging, I found out that the lambdas were using the value of last upper_bound and lower_bound variables. What I need  Why is the lambda using a primary value as reference? I Another way to use lambda OR Another way to map (I want the evaluation of the bounds outside of the lambda for readability)

While I was investigating a problem I had with lexical closures in Javascript code, I came along this problem in Python:  flist = []  for i in xrange(3):     def func(x): return x * i     flist.append(func)  for f in flist:     print f(2)   Note that this example mindfully avoids lambda. It prints "4 4 4", which is surprising. I'd expect "0 2 4".   This equivalent Perl code does it right:  my @flist = ();  foreach my $i (0 .. 2) {     push(@flist, sub {$i * $_[0]}); }  foreach my $f (@flist) {     print $f->(2), "\n"; }   "0 2 4" is printed.  Can you please explain the difference ?    Update:   The problem is not with i being global. This displays the same behavior:  flist = []  def outer():     for i in xrange(3):         def inner(x): return x * i         flist.append(inner)  outer() #~ print i   # commented because it causes an error  for f in flist:     print f(2)   As the commented line shows, i is unknown at that point. Still, it prints "4 4 4".


I have a Document library with PDF files. I am trying to move this file to another document library using SPD 2013 Workflow. But it is not copied to the destination.

I want to move files from the Library into its folder (Which is in the same library). How can I do this using sharepiont Designer 2013


I have the .afm and .pfb files for the Garamond Light Condensed fonts, I follow the instructions available  for installation.  When I try to use them in my document they are not found by pdflatex; my log file contains  LaTeX Font Info:    Try loading font information for T1+pgm on input line 60. LaTeX Font Info:    No file T1pgm.fd. on input line 60.   and  LaTeX Font Warning: Font shape `T1/pgm/m/n' undefined   I am using TeX Live 2013 on Ubuntu, installed with TeX tools rather than apt-get.  This worked fine in TeX Live 2012. Why doesn't it work in TeX Live 2013?

Frequently there are questions about, how to manually install a font, what very often means “Type1 font”. So I thought, we should write a general answer about the several aspects to regard.  Beside the usual approach for  it seems, that for fonts further steps are necessary. What are these steps? Or better:  How to manually install fonts and their associated support files in TeX distributions?


¡Hi everyone!  I have a question, let me introduce the problem:  "Let be $M$ a right $R$-module, and $I$ ideal of $R$,     if $I \subseteq Ann(M)$. Show $M$ has a natural structure like right $(R/I)$-module."  My two questions is:    What means "Natural structure" Why i need $I \subseteq Ann(M)$?   Thanks.

Suppose that $I$ is a two-sided ideal in the ring $R$, and that $M$ is a module over the quotient ring $R/I$. Why can we naturally regard $M$ as a $R$-module that is annihilated by $I$? Conversely, suppose that $M$ is a $R$-module annihilated by $I$. Why is $M$ naturally a module over $R/I$?


When I try to update my Ubuntu 20.04 LTS from terminal I get this error message, any help please? N: Ignoring file 'rethinkdb.list.save.1' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension N: Ignoring file 'rethinkdb.list.save.2' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension E: Type '“deb' is not known on line 1 in source list /etc/apt/sources.list.d/signal-xenial.list E: The list of sources could not be read.

Every once in a while I see users having issues to update due to errors like this:  E:Type 'ain' is not known on line 1 in source list /etc/apt/sources.list.d/some-ppa.list'   with varying types/line numbers/source list files (often after removing a PPA).  How can such an error be fixed?


I want to show that some subsets of the rationals are dense in $[0,1]$. Right now I have the set $$P =\bigcup_{n \in \mathbb{N}} \{ \frac{k}{2^n} : 1 \leq k \leq 2^n \}$$ If I can show that this is dense in $\mathbb{Q} \cap [0,1]$ then I'm done since $\mathbb{Q} \cap [0,1]$ is dense in $[0,1]$. I want to find a sequence $(x_n)_n \subset P$ which converges to an element $\frac{p}{q} \in \mathbb{Q} \cap [0,1]$.

How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?


Some questions on Stack Overflow get repeated many times, for example basic Java IO questions.  Maybe I'm being the devil's advocate, but isn't there a possible hidden benefit to having dupes? I.e., then we attract more Google queries? Also - it allows some newbies to build reputation?  I guess what I'm asking is, do the  negatives of dupes to Stack Overflow really outweight the positives,  when it comes to having duplicates?   Edit: Just want to clarify that I'm supporting what Kate said.(in light of the current situation regarding closures vs. deletions. ) , Keeping dupes around while still closing them. I do see a benefit to, when the situation exists, directing users to high-quality dupes versus low-quality dupes. Although I'm not sure that we have a reliable way to differentiate what exactly qualifies a post as the "canonical duplicate." But overall, my original intent was more aligned with avoiding deletion(but allow closure).

(currently deleted (visible only to 10kers)) is a great example of a duplicate question that should not be deleted. [Note: this question was later merged into , which resulted in the original being hard-deleted. This issue with merging  ] The titles of the duplicates are completely different.  Having duplicates around greatly aids search hits on the site. We need to keep questions like this around for the benefit of the community. Both questions have around 4K views.  They are both relevant.  I cannot believe that a question with over 3K views is being deleted. Edit Search for python continue line and python line break in google.  Both answers are top hits.  They should both be open.


I am trying to add multiple values for the same output "Maths book". I think I am missing something basic on how to format values in brackets.
Set the variable to different value and then try...

I have a group of strings in Javascript and I need to write a function that detects if another specific string belongs to this group or not.  What is the fastest way to achieve this? Is it alright to put the group of values into an array, and then write a function that searches through the array?  I think if I keep the values sorted and do a binary search, it should work fast enough. Or is there some other smart way of doing this, which can work faster?


I am seeking some help to find research papers (preferably in the area of Markov chains) for my undergraduate research for reference. Any guidance on how to find research papers in general for undergraduate level research will be much appreciated. Thanks in advance

OK, I know this is a pretty basic question but I haven't been able to come up with any really satisfactory solutions. (I have searched around on this site, but none of the related questions precisely answer my problem.) I'm a first-year PhD student working mostly in evolution, phylogenomics, and conservation biology. I'm looking for basic tips on how I can become more effective at finding papers when I need to research a subject for any of the usual reasons like developing a methodology or drafting a proposal.  Right now I seem to be pretty bad at this. My search strategy pretty much consists of putting likely keywords into Web of Science and Google Scholar, and then looking at whatever papers appear that seem like they might be relevant to my query. Frequently this fails to yield satisfactory results, even when the subjects that I am researching seem like they ought to have a significant body of existing work behind them. I know I must be able to do better, because I see other people coming up with papers that I don't seem to be able to find.  What are some basic best practices for conducting a literature search? I feel like this is a big gap in my existing skillset, and something that will really hold me back if I don't get on top of it soon. Again, I realize that this is a pretty remedial-level question and I appreciate your patience and guidance here.


I need lil clarity , I am sort of lil new to ubuntu [ a week old :)]. I am exploring the OS and really finding it awesome . Meanwhile, I did come up with some basic doubts which needs clarity . I would be thankful to any body who can give me clarity.  Just some info before my question   I know ubuntu comes with server as well as with desktop versions  I installed the ubuntu desktop version 15.04 version  While, I was going through few youtube videos on ubuntu, I came across people referring other desktops on ubuntu like cinnamon , lxde , unity , etc     My questions   So my confusion started from here, Are they referring to an interface as a desktop ? Ubuntu /linux though they are operating system by themself.Do they still have the ability to have different desktops on top of them? Is it something like a skin, i can choose different versions? what command should i use to find what desktop i have on top of my ubuntu?

This question exists as it fills a specific criterion.  While you are encouraged to help maintain its answers, please understand that "big list" questions are not generally allowed on Ask Ubuntu and will likely be closed per the . More information on the .   What kind of desktop environments or shells are there for Ubuntu users to install?  Please list a desktop environment or shell for each:   a description on why you like or suggest it (features, performance, etc.). a good screenshot, preferably of it running on Ubuntu and showing off some of its features. the minimal requirement for it to be usable, If there's any setting to lower it's requirement (Like kde's low-fat profile); how to enable the said setting some instructions on how to set it up if in the repositories, please provide a software centre link


I think I have almost got to the solution: Let us start by considering two cases: $n\geq8$ and $n<8$. 1: $n\geq8$ $2^8+2^{11}+2^n$=$2^8(1+2^3+2^{n-8})=2^8(9+2^{n-8})$.......Factoring $2^8$ and                               simplifying terms inside the bracket. Now since $2^8$ is already a perfect square,$(9+2^{n-8})$ has to be a perfect square as well for $2^8+2^{11}+2^n$.Therefore we can write the following equation: $9+2^{n-8}=x^2$ =>$2^{n-8}=x^2-9$ =>$2^{n-8}=(x-3)(x+3)$ Hence, (x-3) and (x+3) are factors of a power of 2. The only factors of a power of 2,say $2^k$, is 2 and any $2^g$ where $g\leq k$. Therefore, $x-3=2^y$.......equation 1 $x+3=2^z$.......equation 2  (Product of $2^y$ and $2^z$ is $2^{n-8}$)* Subtracting equation 1 from 2 gives: $2^z-2^y=(x+3)-(x-3)$ =>$2^z-2^y=6$ (let us say $y<z$) $2^y(2^z-1)=6$. The factors of 6 that multiply to 6 are (1,6) and (2,3). So,  $2^y$ and $2^z-1$ have to be equal to 1 and 6 or 2 and 3. Out of these, for $y,z$ to be integers, 2 and 3 can only fit the equation. Hence y=1;z-y=2 or z=3.From *, $2^{n-8}=2^{y+z}=2^{3+1}=2^4$. Since $2^{n-8}=2^4$,$2^n=2^{12}$ If $z<y$, $2^z(1-2^y)=6$. Again following the same rules we must have $(2^z,1-2^y)=(1,6)$ or (2,3). None of them satisfy the equation when $x$ and $y$ are integers. Hence we can conclude that when $n\geq8$ , the only n that can make $2^8+2^{11}+2^n$ a perfect square is $n=12$. 2:$n<8$ Sub case 1: $n$ is odd. Since $n$ is odd, $n$ could be expressed as $2l+1$, where $l$ is an integer. Therefore, $2^8+2^{11}+2^n=2^8+2^{11}+2^{2l+1}=2^{2l+1}(2^{8-n}+2^{11-n}+1)=2*2^{2l}((2^{8-n}+2^{11-n}+1)$, Since there is a $2$ outside the bracket,$(2^{8-n}+2^{11-n}+1)$ must contain atleast one power of 2 and it is obvious that $(2^{8-n}+2^{11-n}+1)$ cannot be a power of 2. In this problem, I was not able to prove that there is no $n\leq 8$ such that n is even which can be a solution to the problem . Can someone help me out with it? I arrived with three different solutions for proving that, only to realize their defects.

I need some ideas (preferable some tricks) for solving these two problems:     Find the largest number $n$ such that $(2004!)!$ is divisible by   $((n!)!)!$      For which integer $n$ is $2^8 + 2^{11} + 2^n$ a perfect square?   For the second one the suggested solution is like this  : $ 2^8 + 2^{11} + 2^n = ((2^4)^2 + 2\times2^4\times2^6 + (2^ \frac{n}{2})^2 ) \Rightarrow n=12$  But I can't understand the approach,any ideas?


I am trying to prove the following function is continuous for all irrationals: $f(x) = \begin{cases} 0,  & \text{if $x$ is irrational} \\ 1/n, & \text{if $x = m/n$} \end{cases}$ The question assumes $m/n$ is in lowest terms. I have shown that it is discontinuous for all rationals, and now I believe I have to either use the $\epsilon-\delta$ definition of continuity or sequential continuity to show the function is continuous for when $x$ is irrational. I split my attempt into two cases: Our value of $x$ is irrational, then I want: $$\forall \epsilon > 0, \exists \delta > 0, |x-a|<\delta \implies |f(x) - f(a)| < \epsilon$$ $a$ is irrational here. Using that $x$ is irrational I get that $f(x) = 0$ as does $f(a)$ so no matter the $\delta$ we have our condition for continuity  satisfied as $0 < \epsilon$ for all $\delta$ Our value of $x$ is rational i.e. $x = \frac{m}{n}$ subbing in we want: $$\forall \epsilon > 0, \exists \delta > 0, |\frac{m}{n}-a|<\delta \implies |\frac{1}{n}| < \epsilon$$ I am struggling to find the $\delta$ necessary. I am able to bound $|\frac{m}{n}-a|$ by $1+2|a|$ if I say that $\delta \le 1$. However I do not know how to find a $\delta$ to yield the second inequality. Should I change my approach to sequential continuity?

Consider the function:  $f(x)= \begin{cases}  1/n \quad &\text{if $x= m/n$ in simplest form} \\ 0 \quad &\text{if $x \in \mathbb{R}\setminus\mathbb{Q}$}  \end{cases} $  Prove that the function is continuous at every irrational point and also that the function is not continuous at every rational point.  Also, we can say that the function is continuous at some point $k$ if $\displaystyle\lim_{x \to k} f(x)=f(k)$.  I was thinking of doing an epsilon delta proof backwards using the fact that $\mathbb{Q}$ is dense in $\mathbb{R}$ for rational points and irrational points.  Any ways on how to expand on this are welcome.


I want to understand what mounting is. It is used in different contexts and situations and I can't find resources which:   Describe the mount concept Explain the actions taken by the computer/OS/utility when a mount is performed How and in which situations mount is used Which features in the Linux mount command are of frequent use and some examples   ( I hear mount applied to diverse entities directories, flash drives, network card, etc )

I've heard the term "mounting" when referring to devices in Linux. What is its actual meaning? How it handling now unlike older versions?  I haven't done that manually via the command-line. Can you give the steps (commands) for mounting a simple device in Linux?


Let $f(x)$ be twice differentiable in $(a,b)$ and suppose that $f'(a)=f'(b)=0$. Prove that there exist at least one point $\mu$ in $(a,b)$ such that   $$ |f''(\mu)|\geq\frac{4}{(b-a)^2}[f(b)-f(a)]. $$     I tried Rolle's theorem. Since $f'(a)=f'(b)=0$, there exists at least one $\mu \in (a,b)$ such that $$ f''(\mu)=0. $$ I also wrote the right hand side as $$ \dfrac{f(b)-f(a)}{(\dfrac{b-a}{2})^2}=\dfrac{\dfrac{f(b)-f(\dfrac{b+a}{2})+f(\dfrac{b+a}{2})-f(a)}{\dfrac{b-a}{2}}}{\dfrac{b-a}{2}} $$ But I do not know how to do next.

Let ${\rm f}:\left[a, b\right]\to\mathbb{R}$ be twice differentiable, and suppose   $$\lim_{x\to a^{+}} \frac{{\rm f}\left(x\right) - {\rm f}\left(a\right)}{x - a} = \lim_{x\to b^{-}}\frac{{\rm f}\left(x\right) - {\rm f}\left(b\right)}{x - b} =0 $$  Show that there exists $\xi \in \left(a, b\right)$ such that $\displaystyle{% \left\vert\vphantom{\Large A}\,{\rm f}''\left(\xi\right)\right\vert \geq \frac{4\left\vert\vphantom{\Large A}% \,{\rm f}\left(a\right) - {\rm f}\left(b\right)\right\vert} {\left(b - a\right)^{2}}}$.  I don't know how to start. Any hints ?.


I want to select the number of rows which are greater than 3 by rownum function i_e "(rownum>3)" for example if there are 25 rows and I want to retrieve the last 22 rows by rownum function. but when I write the   select * from test_table where rownum>3;   it retrieve no row. can any one help me to solve this problem. thanks in advance

Is there a way to make an Oracle query behave like it contains a MySQL limit clause? In MySQL, I can do this: select *  from sometable order by name limit 20,10  to get the 21st to the 30th rows (skip the first 20, give the next 10). The rows are selected after the order by, so it really starts on the 20th name alphabetically. In Oracle, the only thing people mention is the rownum pseudo-column, but it is evaluated before order by, which means this: select *  from sometable where rownum <= 10 order by name  will return a random set of ten rows ordered by name, which is not usually what I want. It also doesn't allow for specifying an offset.


I have new flat bars and grips. What's the easiest way to slide the grips onto the bars?

I just spent the last 10 minutes trying to put a new set of grips on to my mountain bike handlebars..  The old ones came off fairly agreeably and I've got the new ones 80-90% of the way on, however, at this point both my hands are stinging from the aggressive twisting and pushing - I have tried gloves, but I feel it's best left till my hands don't hurt anymore.  Is there a tried and tested way of doing this? Or is there a knack to this that I am missing?


char *func1 = "Open file"; char *func2 = "Write to file";  printf("%s", func1); open_file(); printf("...test_passed.\n");   How can I format the printf so that the "test_passed" string is right-aligned on the same line that contains the first string?  Open file ........ test_passed. Write to file .... test_passed.

As of now I'm using below line to print with out dot's  fprintf( stdout, "%-40s[%d]", tag, data);   I'm expecting the output would be something like following,   Number of cards..................................[500] Fixed prize amount [in whole dollars]............[10] Is this a high winner prize?.....................[yes]   How to print out dash or dot using fprintf/printf?


Why does the following code result in three times true?  I was excepting false for the second step.      function foo() {         this.bar = function () { };     };      console.log("foo - defined : " + typeof window.foo !== 'undefined');     console.log("bar - defined : " + typeof window.bar !== 'undefined');      foo();      console.log("bar - defined : " + typeof window.bar !== 'undefined');

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


Suppose $\tau(n)$ is the number of divisors of a natural number $n$ and $s(G)$ is the number of subgroups of a finite group $G$. Is it always true, that $s(G) \geq \tau(|G|)$ for any finite group $G$?   This statement is true for finite abelian groups (follows from the classification of finite abelian groups and the fact, that $s(G \times H) \geq s(G)s(H)$). But is it true in general?

If $G$ is a finite group of order $n,$ and the number of divisors of $n$ is $k,$ can $G$ have fewer than $k$ subgroups?  A cyclic group $G$ of order $n$ has exactly one subgroup for each divisor of $n$, so in this case $G$ has exactly $k$ subgroups.  For the alternating group $G=A_4,$ $n=12$ and $k=6.$ There is no subgroup of order $6$ in $A_4,$ yet there are ten subgroups, which exceeds $k=6$ for this case. I began to wonder if there could be a group for which so many divisors of the order of $G$ had no subgroups of that order, that there wound up being fewer subgroups in $G$ than the number of divisors of $|G|,$ hence my question.


I wonder if questions about a feature that any SE site has on other metas belong on the StackOverflow meta.  For example, this question here:   It's asking about following a user, which applies to all other SE sites. Does this mean it's off-topic on English and Usage meta and should be moved to StackOverflow meta?

I'm mostly active on  and we have a separate . Most of my questions on IT Security meta have answers with links here. So my question is, where am I supposed to post what i.e. feature request, bug report, behavior questions?


Why are the diaphragms on audio speakers usually a cone with a dome in the centre? I don't know much about acoustics but my guesses would be:   it just empirically sounds better, the design was found through trial and error an acoustically better shape (perhaps a flat panel or a larger dome) is not structurally rigid for vibration, the cone shape is rigid and relatively flat the cone/dome somehow causes interference effects that give directionality to the sound waves   Could someone shed light on the physics behind this design choice?

This is related to another question I just asked, but they are different enough I thought it deserved its own spot. Speaker elements seem to always be shaped like a cone with a portion of a sphere at the center. What is the physics reasoning behind this shape being so standard? Is it a precise shape that all speaker elements share (e.g. parabaloid + sphere), or just kind of a general shape that "works well"? Does it work just as well for any light solid, or is it actually tuned to the speed at which sound propogates through the speaker element?


I want someone to check my proof. Suppose every proper subgroup is cyclic,but G is not cyclic. Since subgroup is cyclic,It generator must exist in subgroup. Then all element in subgroup exist in G;it included the generator of subgroup. then G has generator and cyclic  contradict my assumetion  therefore if every proper subgroup is cyclic G is cyclic

I am having difficulty seeing if it is the case that if all subgroups of a group are cyclic, that the group itself is cyclic.


I have tried to run the updater to install 14.04. It aborts half-way through with the error message there is too little space in the /boot folder. It recommends emptying the trash and running apt-get clean. I emptied the trash and ran apt-get clean, but this apparently accomplished nothing. Same problem. Inspecting the /boot folder seems to show there are a lot of older files left over from interim updates, but since I don't know what may be vital, I haven't attempted deletion. Is apt-get clean broken? And if so, is my only recourse a clean install? That would be annoying.

My /boot partition is nearly full and I get a warning every time I reboot my system. I already deleted old kernel packages (linux-headers...), actually I did that to install a newer kernel version that came with the automatic updates.  After installing that new version, the partition is nearly full again. So what else can I delete? Are there some other files associated to the old kernel images?  Here is a list of files that are on my /boot partition:  :~$ ls /boot/ abi-2.6.31-21-generic         lost+found abi-2.6.32-25-generic         memtest86+.bin abi-2.6.38-10-generic         memtest86+_multiboot.bin abi-2.6.38-11-generic         System.map-2.6.31-21-generic abi-2.6.38-12-generic         System.map-2.6.32-25-generic abi-2.6.38-8-generic          System.map-2.6.38-10-generic abi-3.0.0-12-generic          System.map-2.6.38-11-generic abi-3.0.0-13-generic          System.map-2.6.38-12-generic abi-3.0.0-14-generic          System.map-2.6.38-8-generic boot                          System.map-3.0.0-12-generic config-2.6.31-21-generic      System.map-3.0.0-13-generic config-2.6.32-25-generic      System.map-3.0.0-14-generic config-2.6.38-10-generic      vmcoreinfo-2.6.31-21-generic config-2.6.38-11-generic      vmcoreinfo-2.6.32-25-generic config-2.6.38-12-generic      vmcoreinfo-2.6.38-10-generic config-2.6.38-8-generic       vmcoreinfo-2.6.38-11-generic config-3.0.0-12-generic       vmcoreinfo-2.6.38-12-generic config-3.0.0-13-generic       vmcoreinfo-2.6.38-8-generic config-3.0.0-14-generic       vmcoreinfo-3.0.0-12-generic extlinux                      vmcoreinfo-3.0.0-13-generic grub                          vmcoreinfo-3.0.0-14-generic initrd.img-2.6.31-21-generic  vmlinuz-2.6.31-21-generic initrd.img-2.6.32-25-generic  vmlinuz-2.6.32-25-generic initrd.img-2.6.38-10-generic  vmlinuz-2.6.38-10-generic initrd.img-2.6.38-11-generic  vmlinuz-2.6.38-11-generic initrd.img-2.6.38-12-generic  vmlinuz-2.6.38-12-generic initrd.img-2.6.38-8-generic   vmlinuz-2.6.38-8-generic initrd.img-3.0.0-12-generic   vmlinuz-3.0.0-12-generic initrd.img-3.0.0-13-generic   vmlinuz-3.0.0-13-generic initrd.img-3.0.0-14-generic   vmlinuz-3.0.0-14-generic   Currently, I'm using the 3.0.0-14-generic kernel.


If $(X,\mathcal {B},\mu)$ and $(X,\mathcal{B}'\mu')$ are measure spaces on the same set $X$, we say that the latter is a refinement  of the former if $\mathcal{B}\subset \mathcal{B}'$ and $\mu'\downharpoonright_\mathcal{B}=\mu$.   Any measure space admits a refinement to a complete measure space via , and the resulting measure space is the coarsest refinement of the original measure space to a complete measure space. This implies that it is possible for a complete measure space to admit a further refinement, and such an example can be found in .   Now the  Lebesgue measure space $(\mathbb{R}^d,\mathcal{L}(\mathbb{R}^d),m_d)$ is complete; but unlike the above example above, many subsets of $\mathbb{R}^d$ are Lebesgue measurable and I was wondering if it admits a further refinement. Does it?

My question is the following :   is there a $\sigma$-algebra $\mathcal{T}$ (of subsets of $\mathbb{R^n}$) that contains strictly the $\sigma$-algebra $\mathcal{L}$ of  Lebesgue measurable sets (in $\mathbb{R}^n$), and such that there is a measure on $\mathcal{T}$ that extends the usual Lebesgue measure on $\mathcal{L}$ ?  I guess not, but I did not find a reference.


Say I have a trapezoidal prism (a six-sided object with 4 trapezoidal faces and a rectangular top and bottom) like this one .    I need to apply a displacement modifier to one trapezoidal face using an image containing the texture/normals, such as .    In other words, I need to take an image that is the same shape as the face and use it to create the actual 3D texture using a displacement modifier (the resulting object will be 3D printed).  I know how to do this on a simple plane/surface, but I'm running into trouble in this scenario.  The main problems seem to be:   How do I apply the displacement modifier to only one selected face, without affecting the rest of the object, and When I apply the image, how do I force the image to fit correctly onto the surface, as they have the same proportions but may not be the same size?   Edit: This has been flagged as a possible duplicate of .  I did see that question before posting mine, but it did not help me.  It does not cover how to apply displacement modifiers to only one face without altering the object, and does not touch upon the second part of my question at all.

How can I apply a modifier only to a part of an object? I want to model a goblet with a pedestal, and if I add a subsurf, the pedestal, of course, gets an unwanted round shape. How can I avoid that? I have tried Googling it, but, to my surprise, found nothing.


I understand the technical difference between the two, but I don't understand why one is better to use than the others? Can anyone give me an example that would help me distinguish an advantage one has over the other?  For example: If I was making an rpg game, and I was working on some healing items. What would the uml diagram look like. Would I be using an interface for items, and then healing items or abstract classes.

This may be a generic OOP question. I wanted to do a generic comparison between an interface and an abstract class on the basis of their usage.   When would one want to use an interface and when would one want to use an abstract class?


I need to compare a value in my current sheet with a value from another sheet in the same workbook. The name of the sheet can be found by getting values from two cells within my current sheet, but I cannot create a formula which combine cell values to a sheet name?  This is what I do instead     =SUM(E25;-('0501F9011C00_1 Discard'!E25))   The value 0501F9011C00 can be found in my current sheet cell B8and the value 1can be found in my current sheet cell B10  I tried solving it using a formula as follow, but it will not allow !E25 in this formula     =SUM(E25;-(CONCATENATE(B8;"_";B10;" Discard")!E25))   Is it possible to do what I try to do without using VBA?

In excel 2007, I have a formula in a cell like the following:  =COUNTIFS('2008-10-31'!$C:$C;">="&'$A7)   Now I want to make the name of the sheet ('2008-10-31') be dependent on the value of some cell (say A1). Something like:   =COUNTIFS(A1!$C:$C;">="&'$A7) // error   Is there is way to do this? Or do I have to write a VBA-Macro for it?


I was wondering whether you could take a move action in the middle of your  action (similar to moving between attacks), but the answers to  say no.  However, can you cast the spell as part of the  action and use a trigger of "when I stop moving" or "when I move to that spot" (or something similar) and then expend the your reaction for the turn to release the spell?  And does this actually avoid triggering  or a  if the casting takes place out of sight or out of range?           When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time o f 1 action, and holding onto the spell’s magic requires concentration.              When a creature within 5 feet of you casts a spell, you can use your reaction to make a melee weapon attack against that creature.              Casting Time: 1 reaction, which you take when you see a creature within 60 feet of you casting a spell   You attempt to interrupt a creature in the process of casting a spell.

Suppose I am within counterspell range of an enemy mage (who has counterspell) and want to guarantee that my spell won't be countered.   Could I do so entirely on my turn by moving behind full cover, then casting the spell with the ready action using a trigger of "when I have an unobstructed line of effect to the enemy mage", and then moving out from cover and releasing my spell?   Using my reaction seems like a fairly (or even unfairly) low cost to be able to deny a counterspell, but maybe the requirement for full cover is enough to make it a justifiable reward for making good use of the environment.


I'm trying to solve a problem involving a symmetric circulant matrix. I've solved it one way, but it's been suggested to me that there's a more elementary way of solving it, but I can't seem to find it. Let $a,b\in \mathbb{R}$, and denote $$ D_n = \begin{vmatrix} a&b&\cdots &b\\ b&\ddots &\ddots&\vdots \\ \vdots & \ddots & \ddots & b \\ b& \cdots & b & a \end{vmatrix} $$ the $n\times n$  determinant with $a$ on the diagonal, and $b$ everywhere else. Find $D_n$. Now I'm pretty sure I solved it, but it requires a theorem that I'm supposed to prove in a later problem. That is :  Theorem: If $A$ is an $n\times n$ circulant matrix, that is such that: $$ A=\begin{pmatrix} a_0&a_1&a_2&\cdots & a_{n-1}\\a_{n-1} & a_0 & a_1 & \cdots & a_{n-2} \\ a_{n-2} & a_{n-1} & a_0 & \cdots & a_{n-3} \\ \vdots & \vdots & \vdots & \vdots & \vdots \\  a_1 & a_2 & \cdots & a_{n-1} & a_0 \end{pmatrix} $$ with $a_i\in \mathbb{C}$ for all $i\in{0,\ldots,n-1}$. Then $$ \det A = \prod_{i=1}^n P(\omega_i)$$ with $\omega_i^n=1, \, \omega_i\in \mathbb{C}$ and $P(z)=a_0+a_1z+\cdots + a_{n-1}z^{n-1}$  So here $D_n$ is indeed the determinant of a circulant matrix, and $P(z)=a+bz+\cdots +bz^{n-1}=a+b(z+\cdots z^{n-1})$. Next we note that if $\omega^n=1$, $\omega\neq 1$, then $1+\omega+\omega^2+\cdots +\omega^{n-1}=0$. So for the $n$-th roots of unity $w_i$ s.t. $w_i\neq 1$ we have $P(w_i)=a+b(w+w^2+\cdots +w^{n-1})=a-b$. Also $P(1)=a+(n-1)b$. So we can conclude that $$ \det A = \prod_{i=1}^n P(\omega_i)=(a-b)^{n-1}(a+(n-1)b) $$ Now as I said in the beginning, it was suggested that there was a solution involving only elementary row operations and noticing that the sum of the coefficient of each row is $a+(n-1)b$. I think one can show using elementary row operations that $$ D_n=\begin{vmatrix} a-b&b-a&0&\cdots &0\\ 0 & \ddots &\ddots & \ddots & \vdots \\ \vdots & \ddots & \ddots & \ddots & \vdots \\ 0 &\cdots & \cdots& a-b & b-a \\ b & b & \cdots & b & a \end{vmatrix}.$$ So here the $D_n$ is really close to being upper triangular which would allow to compute the determinant easily. And we can notice that the diagonal does have $(a-b)$ $n-1$ times so that if for some reason we could do something so that the last line is $0$ everywhere except the last coefficient which would be $a+(n-1)b$ we'd be done. But I don't see it. So I'll take any help.

\begin{array}{rrrrr|r}     b & a & a & \cdot \cdot \cdot & a \\     a & b & a & \cdot \cdot \cdot & a \\     a & a & b & \cdot \cdot \cdot & a \\     \cdot & \cdot & \cdot & \space & \cdot\\ \cdot & \cdot & \cdot & \space & \cdot\\ a & a & a & \cdot \cdot  \cdot & b   \end{array}  I have the above matrix $A\in M_{n\times n}(F)$ where $F$ is a field and $n\geq1$, $a,b\in F$.  I'm trying to find out how to use row operations to make it into an upper triangular matrix in order to figure out the determinant. But I'm not sure how I would approach it.


When I build the document the output is perfect, however, all other pages but the first have a consistent and significant amount of vertical spacing after the header that the first page does not have. Additionally, I get some Missing number, treated as zero and Illegal unit of measure errors (coincidentally, one for each \newpage), but I don't know if that's related.  \documentclass[12pt]{article}  \usepackage{amsmath,amsthm,amssymb,fancyhdr}  \addtolength{\textheight}{1.5truein} \addtolength{\topmargin}{-.75truein}  %\setlength{\textheight}{9.5truein} %\addtolength{\topmargin}{-.75truein}  \setlength{\oddsidemargin}{0.3truein} \setlength{\evensidemargin}{0.3truein} \setlength{\textwidth}{5.9truein}  \addtolength{\oddsidemargin}{-0.5truein} \addtolength{\evensidemargin}{-0.5truein} \addtolength{\textwidth}{1.0truein}  \newcommand{\argmin}{\mathop{\rm argmin}}  \newcommand{\real}{\ensuremath{\mathbb{R}}}  \newcommand{\comment}[1]{} \newcommand{\vsph}{\vspace{.40cm}} \newcommand{\vsp}{\vspace{.80cm}} \newcommand{\vecc}[1]{\mbox{\boldmath $#1$}} \newcommand{\utilde}[1]{\underset{\widetilde{}}{#1}} \newcommand{\G}{\,|\,}  \def\EE{ {\rm I} \kern-.15em {\rm E} }  \newcounter{qnum} \newcounter{pnum}[qnum]   \newcommand{\topic}[1]{\vsph \hrule \vsph \mbox{} \hfill { \it #1}   \hfill \mbox{} }  % \newcommand{\QQ}{\vsph \hrule \vsph \stepcounter{qnum} {\noindent \bf %     Problem \theqnum.} \hspace{.2cm} } \newcommand{\QQ}{\vsp \stepcounter{qnum}                 {\noindent \bf Problem \theqnum.} \hspace{.2cm} }  %\newcommand{\QQ}[1]{ %\pagebreak[2] %\vsph \hrule \vsph \stepcounter{qnum} {\noindent \bf %    Problem \theqnum.}\hspace{.05cm} (#1) \hspace{.15cm} }   \newcommand{\PP}{\stepcounter{pnum} \item[{\bf (\alph{pnum})}]\, }   \newenvironment{parts}{   \begin{list}{}{\setlength{\topsep}{2.0ex}\setlength{\itemsep}{1.5ex}       \setlength{\leftmargin}{2.3em}\setlength{\labelsep}{0.8em}}   }{\end{list}}  \def\god{{\buildrel {\cal D} \over \longrightarrow}} \def\goas{{\buildrel {\rm a.s.} \over \longrightarrow}}  \def\r{\rightarrow} \def\p{\stackrel{p}{\r}} \def\d{\stackrel{d}{\r}} \def\argmax{\mathop{\rm argmax}}  \newcommand{\var}{\mbox{Var}}   \usepackage{amsfonts}  \newcommand{\RR}{\mathbb {R}}  \newcommand{\eps}{\varepsilon}   \newenvironment{clist} {%\vspace{-1cm} \begin{list}{$\bullet$} { %\setlength{\topsep}{0.0cm} %\setlength{\itemsep}{0.0cm} %\setlength{\parsep}{0.0cm}} \setlength{\topsep}{.1cm} \setlength{\itemsep}{.1cm} \setlength{\parsep}{.1cm}} }{\end{list}}  \setlength{\headheight}{70pt} % make header taller  % \fancypagestyle{plain}{} % Change default page style \pagestyle{fancy} \fancyhf{} % clear all header and footer fields \fancyhead[C]{       \vspace{0.1in}       \bf {\large Ph.\ D.\ Qualifying Exam\\                   Tuesday, January 3, 2012\\}       \vspace{.2in}       Put your solution to each problem on a separate sheet of paper.       \vspace{.4in} }  \renewcommand{\headrulewidth}{} % make line under header disappear  \begin{document}  \QQ     Applied Statistics (STA5166) \hspace{0.2in} \newline ({\bf Note: Need a Chi-Square table for this problem.})  \vspace{0.1in}    A study was conducted to determine whether the age of customers is related to the type   of movie he or she watches. A sample is shown in the following table.  \vspace{0.1in}  \begin{tabular}{cccc} \hline Age            &  Documentary & Comedy  &  Mystery\\ \hline 12-20          & 24 & 19 & 18 \\ 21-40          & 35 & 46 & 58 \\ 41 and over    & 23 & 60 & 49 \\ \hline \end{tabular}  \begin{parts} \PP  Given that the total sample size $n=332$ is fixed, what is the distribution of the nine categories?  What are the mean value and variance of each cell frequency? Run a chi-square test of independence and draw your conclusion. Use $\alpha=0.05$.  % \vspace{0.05in}  \PP  Run a chi-square test of  "Comedy" verse "Mystery".  Use $\alpha=0.05$.   \end{parts}  \newpage  \QQ    Applied Statistics  (STA5166)  etc...

My LaTeX file compiles fine. However, in reading my .log file, I see many repeated instances of  Package Fancyhdr Warning: \headheight is too small   Looking for it in google, I found some 'fixes', but first I'd like to know what the error is about.  What is fancyhdr? What is \headheight? What does the error mean?


Copying content is one thing, but copying content without referring to or quoting the original is just plain rude and violates the cc-wiki license and the clearly laid out  of this and related sites. When someone or some site does this, what action should we undertake towards the SO team to signal this? Should we worry at all?  Example of a full-copy [of a post and its thread][2] without linking back, violating cc-wiki and claiming it under their own cc-wiki. http://www.answerspice.com/c119/1540246/what-can-you-do-in-msil-that-you-cannot-do-in-c%23-or-vbnet Example of [the same post and only the accepted answer][3], with correctly linking back. http://efreedom.com/Question/1-541936/What-can-you-do-in-MSIL-that-you-cannot-do-in-C#-or-vb-NET The same .

NB The following is a community-generated list of websites that republish Stack Exchange content without attributing it properly. It is no longer being maintained, because the procedure for reporting such sites has changed; see the duplicate for more information. There are a number of license-violating clones of Stack Exchange sites popping up that use Stack Exchange's  data without following our Creative Commons attribution terms. Those terms are , and are also included as a .txt file in every data dump we produce.  Google now has  in search results. Also, you can :  The option to block a site appears when you click a search result and then navigate back to the search results page. Click the "Block" link next to that result to block all pages within the site's entire domain.   This post was created as an attempt to organize information originally posted . You may also be looking for .


I am implementing callback functions in this way:  typedef void (*callback)()   Its works fine and i can pass arguments to such callbacks:  void Call(int X){    printf("Input: %d", X); } void PrintSomething(callback F){    printf("Something");    F(10); }   But i can not shake the feeling that I am doing something wrong. Is my method memory safe ? Is any other good method for implementing callbackfunctions with parrameters ?

From the reading that I have done, Core Audio relies heavily on callbacks (and C++, but that's another story).    I understand the concept (sort of) of setting up a function that is called by another function repeatedly to accomplish a task.  I just don't understand how they get set up and how they actually work.  Any examples would be appreciated.


I have just set up an EC2 instance to play around with and am testing file permissions; however, I notice that the execution bit is not being passed down to the lower level (read and write are, just not execution).  [ec2-user@server www]$ touch web/hi [ec2-user@server www]$ ls -l web/ total 4 -rw-rw-r-- 1 ec2-user apache  0 May 27 19:02 hi -rwxrwxr-x 1 ec2-user apache 43 May 27 05:15 index.php [ec2-user@server www]$ getfacl --all-effective web/ # file: web/ # owner: ec2-user # group: apache # flags: -s- user::rwx group::rwx other::r-x default:user::rwx default:group::rwx default:other::r-x   What am I missing to get the execution bit to pass down?

When I use setfacl to manage on what permissions should the children files / directories have, for some reason the files have all the permissions except the execute ("x") one.  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ getfacl . # file: . # owner: someuser # group: webs # flags: -s- user::rwx group::rwx other::rwx default:user::rwx default:group::rwx default:other::rwx  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ touch file someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ mkdir dir someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ ls -l total 4 drwxrwsrwx+ 2 someuser webs 4096 paź 31 13:35 dir -rw-rw-rw-  1 someuser webs    0 paź 31 13:35 file   I thought it has something to do with umask but changing it in various ways never gives the expected result unless I'm missing something.  How can this be fixed?


I own an ecommerce website built with Magento that has many images in the homepage for promotional banners. What is the best way to improve load speed? Reducing the file size sacrifice quality, so is there any other way?  Here are some information:

I have a WordPress site which is 90% based on images.  I've installed Wp-Super-Cache, now it seems to load a little bit faster.   I've made a speed test on Pingdom Tools:   Page size 4.7MB Load time 5.09s Requests 153 Perf. grade 74/100   And also the Time Spent per Content Type:   Image    88.23%     So the problem is obviously the images.   My plan is to try as much as I can to optimize the images in terms of size, and then to add CDN support.  Is this enough in terms of improving the loading of images?


In one of Oasis's songs — Cigarettes and Alcohol — there are two sentences that make me confused:     All I found was cigarettes and alcohol   ...and...     All I need is cigarettes and alcohol   Why would is and was be correct in these sentences instead of are and were, since they're referring to more than one thing?

I hope you can enlighten me. I get varying answers in Google and I need to find out which is the correct grammatical structure for these sentences.     The rest of the staff is/are on leave at the moment.      The rest of my family is/are arriving late.


$\frac{ \sqrt{1+\sin(x)}+\sqrt{1+\cos(x)} }{ \sqrt{1-\sin(x)}+\sqrt{1-\cos(x)} }=\sqrt2+1\,\forall x\in [0,\pi/2]$ the fraction of square roots may be simplified using double angle formulas.. though i wouldn't recommend showing the derivative to be 0...

Here is the question:     $$\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}} = \;?$$   ()  I think we need to simplify it writing it in summation sign as you can see here:  $$\frac{\sum\limits_{n=1}^{99} \sqrt{10 + \sqrt{n}}}{\sum\limits_{n=1}^{99} \sqrt{10 - \sqrt{n}}}$$  or in Wolfram Alpha input in comments.  I can compute it too! It's easy to write a script for this kind of question. I need a way to solve it. How would you solve it on a piece of paper?


If $f:S\to T$ and $g:R\to S$ are functions such that $f \circ g$ is injective, then prove that $g$ must be injective.     I dont know how to prove it. I only know that composition of two injective functions is an injective function and composition of two surjective functions is surjective.

Let $f$ and $g$ be functions such that $f\colon A\to B$ and $g\colon B\to C$. Prove or disprove the following a) If $g\circ f$ is injective, then $g$ is injective  Here's my proof that this is true. Let $A = \{4,5\}$, $B = \{3,9\}$, $C = \{1,2\}$ $f(4) = 3$; $f(5) = 9$ $g\circ f(4) = 1$ and $g\circ f(5) = 2$ Since no 2 elements map to the same element in the range $g\circ f$ and $g$ are both injective.  b) If $f$ and $g$ are surjective, then $g\circ f$ is surjective.  Here's my proof that this is true. Let $A = \{1,2\}$, $B = \{4\}$, $C = \{5\}$, $f(1) = 4$; $f(2) = 4$ $g\circ f(1) = 5$ and $g\circ f(2) = 5$. Since no elements are left unmapped then $g\circ f$ and $f$ and $g$ are surjective Are these proofs valid? **Edit: Ok so I revised my proof for a. I will disprove it using a counterexample. Let A = {4}, B = {3,9}, C={1}. g∘f(4) = 1 and g(3) = 1 and g(9) = 1 g∘f is injective but g is not injective because 3 and 9 both map to 1. Is that a valid disproof? Now I'm just having some trouble disproving or proving b. If anyone could lend some tips. Also this is not homework. Just reviewing for an exam.


Video is to visual as audio is to...?  Just wondering what would be appropriate.  For example, I could say something like "the visual effects in that video were awesome!" But how about audio? "The audio effects in that piece of audio were awesome!" Doesn't sound so good...  EDIT: Just thought up 'auditory', would that be correct?

I'm looking for a term for audio in form of the word visual.  Visual is defined as      of or relating to the sense of sight   What could you call the sense of hearing? Also, what do you call this form of a word? (i.e verb, noun...)  It should fit the x in the following sentence:     Is it possible to fall in love with someone without visual or x contact?   I'm not a native English speaker, so I couldn't find the terms for searching this.


Looking for a command for this calligraphic phi    (\varphi is not the same and \mathcal{\varphi} does not work).  Solutions working under mathjax are more preferred.

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


I’m using Ubuntu 14.04.  I’m having trouble clearing out a file.  I’m getting permission denied even though I’m using sudo.  Here’s what’s happening …  myuser@mymachine:~$ sudo chmod 755 /var/log/unicorn/unicorn.log myuser@mymachine:~$ sudo echo '' > /var/log/unicorn/unicorn.log -bash: /var/log/unicorn/unicorn.log: Permission denied myuser@mymachine:~$ ls -al /var/log/unicorn/unicorn.log -rwxr-xr-x 1 rails root 304746186 Dec 31 15:08 /var/log/unicorn/unicorn.log   What evil demonic possessions have taken over and how can I conquer this crazy file?

When using sudo to allow edits to files, I regularly get 'permission denied'.  For example, my mouse is jittery and sluggish, so I want to disable polling:  sudo echo "options drm_kms_helper poll=N">/etc/modprobe.d/local.conf   I'm prompted for a password, and then get:  bash: /etc/modprobe.d/local.conf: Permission denied   So I tried to do a temporary change to disable polling by using:  sudo echo N> /sys/module/drm_kms_helper/parameters/poll   Yet again the system responded with:  bash: /sys/module/drm_kms_helper/parameters/poll: Permission denied   Any ideas?


Q. Let $P(x)$ be a non-constant polynomial whose coefficients are   positive integers. If $P(n)$ divides $P(P(n)-2015)$ for every natural   number $n$, prove that $P(-2015)=0$.   In one of the sources, the solution given is as follows: Note that $P(n)-2015-(-2015)=P(n)$ divides $P(P(n)-2015)-P(-2015)$ for every positive integer $n$. But $P(n)$ divides $P(P(n)-2015)$ for every positive integer n.   Therefore, $P(n)$ divides $P(-2015)$ for every positive integer $n$. Hence $P(-2015)=0$.  I am not able to understand that how $P(n)-2015-(-2015)=P(n)$ divides $P(P(n)-2015)-P(-2015)$. Please help me out.

Let $P(x)$ be a nonconstant polynomial whose coefficients are positive integers. If $P(n)$ divides $P(P(n) - 2015 )$ for every natural number n, then prove that $$P (-2015) = 0$$  I've observed that the proof depends on  $ P(n)$ divides $ P(P(n)-2015)-P(-2015)\,$ but I cannot see how to prove that. Could someone please elaborate on how to proceed.


could someone please explain to me the following question:  Let $f,g$ be continuous functions from $\mathbb{R}$ to $\mathbb{R}$ and suppose that $f(r) = g(r)$ for all $r \in \mathbb{Q}$. Is it true that $f(x) = g(x)$ for all $x \in \mathbb{R}$?  My claim is that it should be true since $f$ and $g$ are continuous from $\mathbb{R}$ to $\mathbb{R}$, so if $f(x) \neq g(x)$ for all $x \in \mathbb{R}$ then it cant be continuous on $\mathbb{R}$?   So, is my claim correct and if it is how am I supposed to prove it (please give me some hints) Also, if my claim is wrong, could you please explain to me as to why its wrong`

Akhil showed that the  is the same as the continuum, using as a step the observation that continuous functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.  This isn't an obvious step, so why is it true?


Let say we have 2 similar apples separated by a distance apart, just their mass energy alone is sufficient to cause bending in the space-time. I think it is this bending in the space-time that cause both the apples to accelerate but there shouldn't be any external forces to induce the acceleration, I've skimmed at the math it just says no bending no acceleration and that's not helping. I like to understand how bending in space-time cause the apple to accelerate?  [edit]okay I know the math shows that time is a vector(or scalar or even tensor*) too but that makes the matter even worst for me!  *just want to insured myself!

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


As an object moves faster, its time runs slower by factor X.  I get why this is the case, but I'm not sure why distance is decreased by factor X as well.  Questions:  1)  Why does a moving object's travel distance decrease by factor X as its time decreases by factor X?  The explanation I've heard is that because of v = d/t, since the moving object's speed is constant from different reference frames, its distance must decrease as time decreases.  But I thought motion was relative?  2)  Why does the object's physical length, from the reference frame of an observer, decrease by factor X?  Even if the object travels a smaller distance from part 1), I'm completely lost on how that would affect its length.  Also, I'm aware of the unification between space and time in General Relativity, but I'm learning about Special Relativity and would prefer an explanation in that realm.

I was in argument with someone who claims that length contraction is not "real" but only "apparent", that the measurement of a solid rod in its rest reference frame is the "real length" of the rod and all other measurements are somehow just "artificial" and "apparent". Seemed to me like a bad conversation about poorly defined words and not really relevant to physics, but then some quotes were offered:  ...so that the back appears closer to the front. But of course nothing has happened to the rod itself.  (Rindler)  The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.  (Resnick & Halliday) At the same time, the  insists that length contraction and time dilation are "real", with observable consequences:  Time and space dilation are often referred to as ‘perspective effects’ in discussions of STR. Objects and processes are said to ‘look’ shorter or longer when viewed in one inertial frame rather than in another. It is common to regard this effect as a purely ‘conventional’ feature, which merely reflects a conventional choice of reference frame. But this is rather misleading, because time and space dilation are very real physical effects, and they lead to completely different types of physical predictions than classical physics. [...] However, this does not mean that time and space dilation are not real effects. They are displayed in other situations where there is no ambiguity. One example is the twins' paradox, where proper time slows down in an absolute way for a moving twin. And there are equally real physical effects resulting from space dilation. It is just that these effects cannot be used to determine an absolute frame of rest.  I went through a lot of Einstein, Minkowski and Lorentz original material, and didn't find anything about what is "real" and what is not. Finally, I know about muons, where the effects of SR seem to be very real (from , but I had seen it in a physics class before):  When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and muon neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a velocity near the speed of light. Although their lifetime without relativistic effects would allow a half-survival distance of only about 456 m (2,197 µs×ln(2) × 0,9997×c) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. Both effects are equally valid ways of explaining the fast muon's unusual survival over distances.  So which is which? Why do Rindler, Resnick & Halliday use the word "apparent"?


I want to make a dvd for my old windows ME computer to upgrade to ubuntu. Please help!!!

I would like to see a full how-to guide on how to install Ubuntu.


I am creating one jasper report by connecting it with database. In which I have to hide table column depending upon the data I get after executing the query. How to do that?

I'd like to show/hide a column at runtime based on a particular condition. I'm using "Print when expression" to conditionally show/hide this column (and it's header) in my report. When the column is hidden, the space it would have occupied is left blank, which is not particularly attractive.  I would prefer if the extra space was used in a more effective manner, possibilities include:   the width of the report is reduced by the width of the hidden column the extra space is distributed among the remaining columns   In theory, I could achieve the first by setting the width of the column (and header) to 0, but also indicate that the column should resize to fit its contents. But JasperReports does not provide a "resize width to fit contents" option.  Another possibility is to generate reports using the Jasper API instead of defining the report template in XML. But that seems like a lot of effort for such a simple requirement.


I have a very basic interaction model with this setup: Y = $\beta_0$ + $\beta_1$ Var_1 + $\beta_2$ Var_2 + $\beta_3$ Var_1 * Var_2 + Controls + $\epsilon$  Y = Continuous variable Var_1 = Continuous variable Var_2 = Indicator variable (i.e., 1 or 0)  In this model, $\beta_3$ is significant--but joint test of $\beta_1$ + $\beta_3$ (i.e., when Var_2 = 1) is insignificant. How do I interpret the interaction term when the total effect isn't significant? Edit: My post has been identified as a potential duplicate, but I don't think that this is the case because those links appear to be concerned with the interpretation of main effects when an interaction effect makes the main effects insignificant. I'm interested in the interpretation of a significant interaction effect when the total effect (i.e., $\beta_1$ + $\beta_3$) is insignificant.

I have two non-significant main binary variables in my binary logistic regression model, but their interaction is significant. The variables are centered and no multicollinearity is the case (all VIFs about 1.0). The main variables are nonsignificant, but their interaction is. I want to interpret that significant interaction of two non-significant estimates.   It would read something like this: the effect of the variable A is less visible in the level 1 of the variable B (B1) and more visible in the second level of B (B2). Or I can say the same thing about the effect of B being less visible in A1 and more visible in A2...  However, the problem is that neither the effect of A, nor the effect of B are significant! So the above interpretation, although seemingly correct, sounds inconsistent or strange. (How a non-significant effect is supposed to be boosted by the other variable?)...   On a second thought, it seems that it is actually possible. For example, if I exclude cases with B2 from my sample, now the effect of A in the sample would show up as significant (it is B2 cases in the sample that disallow A to appear as significant)... This is getting more clear in my head now, but do you still have something other than the above interpretation in mind?


Does there exist a set $A$ such that $A \in A$?  The empty set doesn't work. Also, it seems clear that if $A$ exists, then it must be infinite.  If no such set exists, then is there a simple proof of this?

I am trying to understand   How can a set contain itself? Can you show example of set which is not a set of all sets and it contains itself.


I just wanted to know if its gramatically correct to say what animal is this? or which animal I this?

Most of the time one or the other feels better, but every so often, "which" vs. "what" trips me up.   So, what's the exact difference and when should you use one or the other?


Question:   10 people, split into team of 6, team of 4=(10C4)=(10C6).   And into teams of 5,5= (10C5)/2  I don't understand why one divides by 2 in the second case. Say I choose am team of 6 by (10C6), whatever left is a team of 4. Why is the same not true for choosing a team 5?

In how many different ways can you split $10$ people into two groups with the same amount of people?  My attempt: Since the order in which you choose someone doesn't matter, I chose to calculate the combinations: $10 \choose 5$


Is there any way to know from where a function is called in Android ??  In my application (Its a huge one, that's source code is downloaded from the internet.) a set of functions executing. I cant figure out from where they are called !  Is there any ways ??

I need to find the caller of a method. Is it possible using stacktrace or reflection?


I was wondering about generic installations of all applications in linux. And what that means? Well, when I was using windows I knew that if I want to install an application I am double-clicking the .exe file and then next,next,next.  In linux, I have understood that maybe there is a common (not generic) way to install any application. Installing from source maybe? Well is there any step by step method that can be used to install  application like in windows or not?  I am asking because I do not want to keep asking the google, how to? So, I have managed to install recently from source freecad from  and I think that it would be a very nice start as common method, right?  But the thing then is where to find the right source and when an application has a very unique method of installation!


I'm an American, and I'm traveling to the Czech Republic later this summer for a few weeks. I have a Visa debit card from a local credit union for use in ATMs and a Visa credit card from CapitalOne. Both of these cards have a magnetic strip only: no chip.   Are these cards sufficient for use in the Czech Republic? Do ATMs and retail locations use magnetic strip readers, or are chip cards required?

I'll be visiting the UK in a few weeks, and I understand that the UK credit/debit card system works on a "chip-and-pin" system. As far as I can ascertain via Google, US cards don't have this system on them. I've also read on some websites that certain readers will not process cards without the chip-and-pin, but I'm not sure how widespread such readers are.   With that in mind, is it likely that my US-issued card  will be generally usable in the UK and other countries with the chip-and-pin system, or should I be ready to exchange cash? In addition, does credit/debit make a difference in this regard?


Will 64 bit ubuntu work on my p4 pc with x86-64 bit architechture? I'm currently using it as live usb

What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit?


As per the title, I don't understand why it is grammatically incorrect to say "me and John went to the park" as opposed to "John and I went to the park." Is any help on this available?

Is it improper to say "me and Person X"?  I always hear it said as "Person X and I", but have personally learned to say "me and Person X".  Is there a difference between the two versions and is one of them incorrect? "Person and I" just sounds more formal to me.


If $\lim _{n \rightarrow \infty} \frac{1^{n}+2^{n}+3^{n}+4^{n}+\dots+n^{n}}{n^{n}}=k,$ then $\left[\frac{10}{k}\right]=\ldots$ (Where [.] denotes G.I.F)  I was able to calculate using Stolz-Cesàro lemma, it came out to be $\frac{e}{e-1}$. But can there be another method for students who are not yet exposed to Stolz-Cesàro lemma?

I can show that the following limit exists but I am having difficulties to find it. It is $$\lim_{n\to \infty} \sum_{k=1}^n \frac{k^n}{n^n}$$ Can someone please help me?