Problem about points on an equilateral triangle
The vertices of an equilateral triangle are shrinking towards each other
"This computer currently has no detected operating systems" when installing find command: -or option doesn't work I want to execute a command for an each file that matches a pattern. But the command that seems to be right, doesn't work for me, I have no idea why.  $ find . -type f -name '*.c' -or -name '*.h' -or -name '*.cpp' -exec ls {} \; $ ls script.sh  test.c  test.h Transfer from JFK Terminal 2 to Terminal 4 I have family who does not speak English.  They are changing planes in JFK Airport and will most likely be transferring from Terminal 2 (Delta) to Terminal 4 (China Southern Airlines).  At first I thought that directing them to use the Airtrain would be best.  However, in doing more reading my understanding is that the Airtrain would mean they would need to go through security again.  I found this on Delta's site:   If they use the JITNEY Shuttle to change from Terminal 2 to Terminal 4, does that mean they would not need to re-clear Security?  Edit: They are flying TO China. They are going from Tampa -> NY JFK -> China. In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual? I've read in several places that one motivation for category theory was to be able to give precise meaning to statements like, "finite dimensional vector spaces are canonically isomorphic to their double duals; they are isomorphic to their duals as well, but not canonically."  I've finally sat down to work through this, and -  Okay, yes, it is easy to see that the "canonical isomorphism" from $V$ to $V^{**}$ is a functor that has a natural isomorphism (in the sense of category theory) to the identity functor.  Also, I see that there is no way that the functor $V\mapsto V^*$ could have a natural isomorphism to the identity functor, because it is contravariant whereas the identity functor is covariant. My question amounts to:     Is contravariance the whole problem?   To elaborate:   I was initially disappointed by the realization that the definition of natural isomorphism doesn't apply to a pair of functors one of which is covariant and the other contravariant, because I was hoping that the lack of a canonical isomorphism $V\rightarrow V^*$ would feel more like a theorem as opposed to an artifact of the inapplicability of a definition.  Then I tried to create a definition of a natural transformation from a covariant functor $F:\mathscr{A}\rightarrow\mathscr{B}$ to a contravariant functor $G:\mathscr{A}\rightarrow\mathscr{B}$. It seems to me that this definition should be that all objects $A\in\mathscr{A}$ get a morphism $m_A:F(A)\rightarrow G(A)$ such that for all morphisms $f:A\rightarrow A'$ of $\mathscr{A}$, the following diagram (in $\mathscr{B}$) commutes:  $$\require{AMScd}\begin{CD} F(A) @&gt;m_A&gt;&gt; G(A)\\ @VF(f)VV @AAG(f)A\\ F(A') @&gt;&gt;m_{A'}&gt; G(A') \end{CD}$$  This is much more stringent a demand on the $m_A$ than the typical definition of a natural transformation.  Indeed, it is asking that $m_A=G(f)\circ m_{A'}\circ F(f)$, regardless of how $f$ or $A'$ may vary. Taking $\mathscr{A}=\mathscr{B}=\text{f.d.Vec}_k$, $F$ the identity functor and $G$ the dualizing functor, it is clear that this definition can never be satisfied unless $m_V$ is the zero map for all $V\in\text{f.d.Vec}_k$ (because take $f$ to be the zero map). In particular, it cannot be satisfied if $m_V$ is required to be an isomorphism.     Is this the right way to understand (categorically) why there is no natural isomorphism $V\rightarrow V^*$?   As an aside, are there any interesting cases of some kind of analog (the above definition or another) of natural transformations from covariant to contravariant functors?  Note: I have read a number of math.SE answers regarding why $V^*$ is not naturally isomorphic to $V$. None that I have found are addressed to what I'm asking here, which is about how categories make the question and answer precise. ( was closest.) Hence my question here. 2D collision detection Let's assume I'm using this character.  (source: ) How would you implement collision detection for it? Using a bounding box doesn't seem to be a good approximation, because the bird's shape is nowhere near a square. I was thinking of having a sort of quad tree data structure inside the object that represents portions of the image. Each leaf could be either false (in case it covers the white/transparent space outside the bird) or true (in case it represents an area of the bird i.e. beak, eye etc). Then somehow test the only obstacle in the scene for collision with the bird. But my problems in my approach are:  I don't know how to initialize the quad tree. Once the quad tree is initialized, I'm not sure how to traverse &amp; use it once the obstacle is within the coordinates of the image.  How would you do collision detection with non-squarish characters? LE: The other approach I've seen was to use multiple bounding boxes. For example I'd have one or a few bounding boxes for the beak, then a few of them for the hair or the tail. But it can get tedious. If this is a valid approach in my case, how would I generate those bounding boxes? I doubt I'd have to have them hardcoded in my program. LE2: I care about fairly precise collisions. I can't imagine how a single bounding box or circle can at least approximate decently that shape, so this approach won't work. Wireless connection fails every few minutes I want to package my project in a single executable JAR for distribution.  How can I make a Maven project package all dependency JARs into my output JAR? Design simulates perfectly but won't work on FPGA Money transfer from India to USA My daughter is a US Citizen. We (parents)are also planning to permanently settle in US. We will go their as Permanent Resident,as per US Law. We have a house here in India worth Rs.2 Crores.  We want to sell it and take money with us. We have ordinary savings Bank account here in India.  My US Citizen Daughter is a Income Tax payer.  Now your advises are required as under:   What are the routes to take money from India to US and our tax liabilities Can I gift this whole amount to my US Citizen Daughter or what is the maximum limit of Gift amount.  What will be the tax liability on me and on my Daughter in case of Gift   Whether I have to show it in my Income Tax Return or in my Daughter's Tax Return. What US Income Tax Laws says. What will be the procedure to send money as Gift to my Daughter. Will the money will go directly from my Bank Act.to my Daughter's Bank Account. Will there will be wire transfer from bank to bank Can I send money through other money sender Certified Companies also.    Please advise. If there is something more on the subject to make me understand, please advise. Thanks, What free Remote Desktop (server) solutions are there? I know Ubuntu comes with a "Remote Desktop" option that appears to be a straightforward VNC server, and I'm trying to understand the alternatives. Here are the possibilities I've heard about so far:   VNC  VNC + SSH Tunnelling NX Server, free edition FreeNX NeatX X2Go X11 Forwarding over SSH xrdp    I'm coming at this from a Windows user's perspective: To the best of my experience, RDP (aka Terminal Services) is a reasonably secure (barring mitm/server spoofing), efficient desktop sharing protocol with well-supported clients, that can be exposed to the internet when necessary without major fears of intrusion. To the best of my knowledge straight VNC is none of those things, which is where I get confused - why wouldn't a better desktop sharing technology be developed or used in the open-source world? I know VNC can be wrapped with SSH, but that seems beyond the reach of a casual user. X11 forwarding over SSH may be more or less efficient, I have no idea, but is definitely even more complicated, and doesn't (as far as I know) give you access to already-running stuff (no desktop sharing as such, just remote application running).  So, I'd like any feedback/preferences amongst these or any other "Free" desktop sharing options, using these criteria and/or any others:   Security (esp. for access across internet) Efficiency (bandwidth usage, responsiveness, etc) Free-ness, as in Speech (not sure where RDP or FreeNX lie for this) Free-ness, as in Beer (are there any commercial solutions with usable dependable free offerings?) Ease of use (server and client side) Cross-OS Client availability Cross-OS Server availability Support for independent sessions and shared (and/or "Console") sessions Ongoing support/maintenance/development   Thanks! What is the 64-bit Firefox Beta PPA? I recently discovered that my computer is 64-bit. I have backed up my Home folder, and reinstalled Ubuntu. The reinstall wasn't nearly as painful as I thought. There is one thing that I can't quite seem to figure out: how do I get the 64-bit Firefox Beta build? I always get the Beta builds, but I want to take advantage of the 64-bit architecture of my computer.  says that Mozilla has come out with a 64-bit version of Firefox, but I can't seem to find it.  I do understand  of using a 64-bit browser, but I've decided to jump right in and do it anyway. (Flash and Java are already 64-bit, and who cares about Silverlight, since it's not for Linux anyway?)  There's only one issue, and it's a big one: I can't find the 64-bit Beta PPA!!! (I really hate using .tar.gz files, but I'd be willing to do that as long as I could still access Firefox via the Launcher. Oh, speaking of which, I don't understand .tar.gz files. Once, I managed to run one (the Dropbox Beta build,) but I have no idea whatsoever on how to install them: as in, click on the icon and go.) Test if a package (or package option) is loaded [french]{babel} (aka frenchb) is incompatible with some other packages, such as tikz, since it tries to insert \thinspace before semi-colons.  In order to make these two play nice, you have to call \shorthandoff{;} in the document.  Now I have a package that uses tikz and I would like to locally disable the semi-colon for babel, instead of disabling it for the whole document. I could hack the .sty of the package to do that, knowing that I'm using frenchb, but I would rather make something clean and portable.  Is there a way in my package that I can test if frenchb is loaded and disable semi-colon management with babel locally, so the package doesn't have to be hacked?  Edit:  Martin's solution gives me something like this in general:  \RequirePackage{ifthen} \newcommand{\@babel@loaded}{0} \AtBeginDocument{\@ifpackageloaded{babel}                                                    {\renewcommand{\@babel@loaded}{1}}                                                         {\renewcommand{\@babel@loaded}{0}}                                                       } \newcommand{\somecommandusingsemicolon}{   \ifthenelse{\@babel@loaded=1}{\shorthandoff{;}}{}     % code with semi-colon here }   and in the specific case of tikz:  \AtBeginDocument{\@ifpackageloaded{babel}   {%     \g@addto@macro\tikz@installcommands{%       \shorthandoff{;}%     }     \g@addto@macro\tikz@uninstallcommands{%       \shorthandon{;}%     }   }   {\relax} } Why 32bits OSs can't address more than 3.2/3.2 gb of memory? Don't know if this is the right place to ask this question.  I've been reading that 32bit OSs (like the Ubuntu i'm running right now) can't adress more than 3.2gb or 3.3gb of RAM memory.  I remember for my old Computer Architecture course that the memory limitation was 2^32 "pointers" (don't remember the right word). I mean, the memory was represented like an array where the CPU can acces it directly, but up to its limit. If the CPU is 32 bit, then it can address 2^32 words, if it's 64 bits 2^64, etc.  So, if what i said before is right, then, my OS should be able to address 2^32 = 4294967296 = 4Gb.  I'm thinking maybe some sort of space is reserved to the particular use of the Kernel, cache, buffering or swapping. But don't have the correct answer.  Can you give me a hint? I applied a survey consisting of 12 questions to 120 people and each questions include 4 nominal categories; I want to make comparison of people's answers according to their socio-demographic characteristics such as their educational level or socioeconomic status. All of my comparison criteria consist of nominal categories and number of categories change between 3 to 6. I cannot drop or combine comparisons; categories in other words number of categories are fixed.    My question is when I compare the frequency distribution of people's answers based on their education levels (for example) through chi-squared test, I got a warning that says (for instance) 7 cells have less than count five; minimum expected count is; 43.  I got this warning for almost my all questions - demographic characteristics comparisons.    Shall I underestimate this warning and use my test results or is there a different test I should use? If I should use a different test, which one? Why does the wire-frame material fades across the object? Why does the wire-frame material fades across the object?  Here is what I did - I created a new material and I selected on "Wire" and I made it shadeless. Then, I created a new material and assigned the new material on the on the object. However, doing it that way, it allows me to render both materials - "Wire" and "Surface". Then I get a fading result like this -    But I want all of the edges to be shown, not a fading result. How can I make that?  Here is the blend file if anybody wants to check it out - How does Ethernet know how long a frame is? Adapt Ubuntu to a high-DPI resolution screen How can I adapt Ubuntu to a high resolution display?  I have a display with 3200x1600px on only 11'' and everything looks really tiny. For a CDF that is not strictly increasing, i.e. its inverse is not defined, define the quantile function   $$F^{-1} (u) =\inf \{x: F(x) \geq u \},\quad 0&lt;u&lt;1. $$  Where U has a uniform $(0,1)$ distribution. Prove that the random variable $F^{-1} (u)$ has cdf $F(x)$.  In case of a strictly increasing CDF the proof is quite easy because the inverse is defined. Define $X=F^{-1} (u)$  $$ P\left[X&lt;x \right]=  P \left [F^{-1} (U) \leq x \right]= P \left[U \leq F(x) \right] =F(x)  $$  But how do I accomondate the nondecreasing CDF whose inverse is given by the quantile function? I am a begginer so any help is welcome. Thank you. Why won't my follower, Serana, follow me? I told my follower (Serana) to wait. But this is different. I told her to go somewhere and wait so it will activate the enemies. Well it did and I killed them. But Serana seems to be not following me anymore. I can't tell her to follow me. And she is constantly in a squatting position. The only thing I can do is tell her to wait somewhere else to move her. And I can't part ways because I'm doing a main quest and she has to be there. Can anybody give me a tip on what to do? Movie with "Where do the tubes go?" I'm trying to find a movie with an underground facility with people wearing white suits. The people have been affected such that they show no curiosity. There is one person that does and asks one of his co-workers where a tube leads to.      At the end there is an uprising where everyone gets to see the surface and sunlight.   What is the name of this movie?