I want to create object like this:    How can I achieve this?
I'm trying to figure out the best way to model the sphere-spiral here:    Is it possible to make this shape directly? Or do you have to make it as a cylinder and wrap it to a sphere?
Does there exist a function $f: \mathbb{R} \to \mathbb{R}$ having the following properties?   $f(x) = 0$ for all $x \le 0$. $f(x) = 1$ for all $x \ge 1$. For $0 &lt; x &lt; 1$, $f$ is strictly increasing. $f$ is everywhere $C^\infty$. The sequence of $L^\infty$ norms $\langle \left\lVert f \right\rVert_\infty, \left\lVert f' \right\rVert_\infty, \left\lVert f'' \right\rVert_\infty, \dots \rangle$ is bounded.   If we impose only the first four conditions, there is : for $0 &lt; x &lt; 1$, define $f(x)$ by $$ f(x) = \frac{e^{-1/x}}{e^{-1/x} + e^{-1/(1-x)}} = \frac{1}{1 + e^{1/x - 1/(1-x)}} $$ However, the derivatives of this function appear to grow quite rapidly. (I'm not sure how to verify this, but it seems at least exponential to me.)  If such a function does not exist, what is the smallest order of asymptotic growth that the sequence $\langle \left\lVert f \right\rVert_\infty, \left\lVert f' \right\rVert_\infty, \left\lVert f'' \right\rVert_\infty, \dots \rangle$ can have? At what time will the upcoming Ubuntu release be made available? Every six months a new Ubuntu version will be released. Does anyone know at which time this will be? I was trying to find a font which has obsolete jamo and the right combining behaviour. Yesterday I found out about , which seems to have both of these. However, when I use it in XeTeX, I get some seemingly-arbitrary hanja (or blank spaces) instead of the expected characters.  (I’m guessing the composing behaviour will fix itself when the right characters are selected. And yes, I know that Code2000 is working perfectly in this example, but unfortunately it is the ugliest font in the world. :p)  MWE:  \documentclass{article} \usepackage{fontspec}  % 1. precomposed: U+BB47 % 2. separate jamo: U+1106, U+116E, U+11BA % 3. obsolete [separate jamo]: U+113B, U+119F, U+11EB \newcommand\test[1]{#1 &amp; {\fontspec{#1}{뭇; 뭇; ᄻᆟᇫ}} \\}  \begin{document}  \begin{tabular}{rl} \test{Arial Unicode MS} \test{Batang} \test{Code2000} \test{Gulim} \test{GungSeo} \test{HeadLineA} \test{Nanum Brush Script} \test{Nanum Myeongjo} \test{Nanum Pen Script} \test{Noto Sans Korean} \test{PCMyungjo} \test{PilGi} \test{Adobe Gothic Std} \test{Adobe Myungjo Std} \test{Apple SD Gothic Neo} \test{AppleGothic} \test{AppleMyungjo} \end{tabular}  \end{document} Take a look at this example schematic:  The chip in question is the  and as you can see power is provided on both sides (with a 100nF cap to smooth noise I guess). Is this strictly required or could you put power into one side and just ignore the other? I know that I have just put power in one side and everything still seems to work fine but I feel uneasy with doing that. I feel that they would not waste pins that could be doing something useful by having an extra pair of power in/out pins. For what purpose does this PIC MCU (and others like it) have multiple power pins? Can I define keyboard shortcuts using the Super key? GNU find and masking the {} for some shells - which? The man page for GNU find states:    -exec command ;     [...] The  string `{}'  is  replaced  by the current      file name being processed everywhere it occurs in the      arguments to the command, not just in arguments where      it is alone, as in some  versions  of  find.     Both  of  these  constructions might need to be escaped      (with a `\') or quoted to protect them from expansion      by the shell.     That's from the man to find (GNU findutils) 4.4.2.   Now I tested this with bash and dash, and both don't need to have the {} being masked. Here is a simple test:  find /etc -name "hosts" -exec md5sum {} \;    Is there a shell, for which I really need to mask the braces? Note, that it doesn't depend upon whether the file found contains a blank (invoked from bash):   find ~ -maxdepth 1 -type d -name "U*" -exec ls -d {} \;  /home/stefan/Ubuntu One   This changes if the found file is passed to a subshell:  find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d {}' \;  ls: cannot access /home/stefan/Ubuntu: No such file or directory ls: cannot access One: No such file or directory   which can be solved by:  find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d "$0"' {} \;   in contrast to:   find ~ -maxdepth 3 -type d -name "U*" -exec bash -c 'ls -d "{}"' \;  /home/stefan/Ubuntu One   but that's not what the man page is talking about, is it? So which shell treats {} in a different way? Install macOS Sierra on VirtualBox? I’m trying to install macOS Sierra on VirtualBox, but can’t seem to make it work. For reference, here are the steps I took.   Downloaded the Install macOS Sierra app from the App Store. Used the inbuilt media creation executable, CreateInstallMedia on a disk image. Created a new VM with the default settings for an OS X El Capitan, plus 128 VRAM. Since VirtualBox refused to accept the DMG, I tried splicing out the InstallESD. VirtualBox now accepted it, but wouldn’t boot. I tried to boot through rEFInd, but still no luck. I tried to patch it both ways (base system and ESD) with iesd. No luck. When booting to GParted LiveCD, it flat-out refused to discover any of the installer CDs.   How can I patch the installer to work with VirtualBox? I don’t want to use pre-patched versions of either the installer or an existing installation, as though to avoid piracy. Can I put a metal safe weighing 2000 lbs in a 12x12 room? I have a 12'x12' upstairs bedroom. Can a 2000 lbs safe be placed in that room? The dimensions would be the same size as a queen size bed (60"x80").  Can you supply the math in your answer.  Thank you in advance  Danny What are best practices/important steps when the Windows Server machine hosting SQL Server 2008 R2 is moved to another domain?   What steps definitely/might need to be done for SQL Server before and after the new domain is joined? How to get Total Pupulation From Tables In Sqlserver? When an air-filled balloon is released without its opening tied up, it moves in a circular path rather than a straight line. Why is that? In the comedic music video  there are many clips of vintage scifi films, some of which I recognize.  This one however, of a large blue floating holographic head talking to some kind of military installation does not look at all familiar.  Does anyone recognize this film? How can I play the same world between PS4 and Mobile? Why is "bicycle" pronounced differently from other obviously related words? What constitutes protons? When I see pictures, I can't understand. Protons are made of quarks, but some say that they are made of 99% empty space. Also, in this illustration from Wikipedia, what's between the quarks? Given a $k$-manifold $M$, such that $\partial M$ is a $(k-1)$-manifold, there is a standard way in which $\partial M$ inherits the orientation of $M$. So if $M$ is oriented by the form field $\omega$, then $\omega_\partial=\omega(v_{\text{out}},v_1,\dots,v_{k-1})$ orients $\partial M$, where the $v_1,\dots,v_{k-1}$ are basis vectors for a tangent space on a point of the boundary, and $v_\text{out}$ is an outward pointing vector (see here: , which follows the exposition of Hubbard &amp; Hubbard).  In practice I find this very difficult to interpret. How can one find this $v_\text{out}$ in practice?   For instance, take $M$ to be defined by $z=x^2+y^2$ for $x\ge0$ (technically a manifold with boundary, in fact a half-paraboloid). It's a fact that $\partial M$ is defined by the parabola $z=y^2$. If $M$ is oriented by $dx\wedge dy$, how does this induce an orientation on the boundary (in fact we should obtain a 1-form that induces an orientation on the boundary)?   Note: I find the whole discussion of boundary orientation to be rather clumsy in its exposition. In the case of surfaces inducing orientations on boundary curves, I was originally taught to imagine that the normal vector that induces the surface orientation is me walking on the surface. This normal should walk along the boundary such that the surface lies to its left. OK - but how does this translate to the $v_{\text{out}}$ interpretation, so that we can generalize to other dimensions easily?)  Edit: An ideal answer would merge the intuitive approach with the rigorous approach, if possible. I would grateful to anybody who could help order my (at present confused) understanding! Finding Elevation Change, any method So, I think it'd be cool - for goal setting for example - if I could keep track of my elevation change.  The problem is, the local cyclocomputers I looked at seem to use barometric pressure to determine the change.  This is fine, unless some weather is moving in, which happens not infrequently in the Midwestern United States.  Or do some of them try to use an inclinometer, your speed, and some math you learn in Calculus II to keep track of your change?  That would seem more accurate!  I could try to use a GPS meter, but those things are expensive -  and based on back when I had service to my smart phone, not guaranteed to match my car's odometer for distance even - I've read from some other riders that the distance varies at least slightly from local measurement on a bike as well.   Alternatively, let's say that I ride along a known route.  Is there any good way of plotting that route for elevation change?  Thanks! I have a script which calls two commands:  long_running_command | print_progress   The long_running_command prints progress but I'm unhappy with it. I'm using print_progress to make it nicer (namely, I print the progress in a single line).  The problem: Connection a pipe to stdout also activates a 4K buffer, so the nice print program gets nothing ... nothing ... nothing ... a whole lot ... :)  How can I disable the 4K buffer for the long_running_command (no, I do not have the source)? My proof is very different from my reference, hence I am wondering is I got this right?  Apparently, $F$ is continuous, and the identity matrix is closed. Now we want to show that the preimage of continuous function on closed set is closed.  Let $D$ be a closed set, Consider a sequence $x_n \to x_0$ in which $x_n \in f^{-1}(D)$, and we will show that $x_0 \in f^{-1}(D)$.  Since $f$ is continuous, we have a convergent sequence $$\lim_{n\to \infty} f(x_n) = f(x_0) = y.$$  But we know $y$ is in the range, hence, $x_0$ is in the domain. So the preimage is also closed since it contains all the limit points.  Thank you. I have 3 fields ( Exposed filter ) 1 Country 2 State 3 City  When a respective Country is selected in the 1st field, I want the second filter ( Dropdown or autocompete ) to display states of the country selected in the 1st field &amp; when this is done based on the state selection , I want the 3rd field to show only the cities belonging to the state selected in the second field.  How can this be done ? any help ?