macOS Mojave (10.14) - how to get a full installer without using the macOS Mojave Patcher Tool
Where to get the full offline-capable installer for macOS Mojave (.1 update)?
Closed ball not a manifold. My book on differential geometry claims that a closed ball in $\Bbb R^n$ can never be a differentiable manifold because of the boundary points. The book doesn't really give an explanation for why this is true. Could someone provide more details please? thanks Using Chrome's Element Inspector in Print Preview Mode? the following code will only make the qed not appear in the second proof. However, it it possible to make the qed symbol never appear at the end of the proofs without having to specify it locally every time?  \documentclass{article} \usepackage{amsthm} \begin{document} \begin{proof} This has the QED symbol. \end{proof} \begin{proof}\renewcommand{\qedsymbol}{} This hasn't. \end{proof} \begin{proof} And this has it again. \end{proof} \end{document} Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens) I don't know if this is a well-known fact, but I have observed that every number, no matter how large, that is equally divided by $9$, will equal $9$ if you add all the numbers it is made from until there is $1$ digit. A quick example of what I mean:  $9*99 = 891$ $8+9+1 = 18$ $1+8 = 9$  This works even with really long numbers like $4376331$ Why is that? This doesn't work with any other number. Similarly for $11$ and alternating digits sums. What would make a question popular with high views? I was wondering what might be making my questions less attractive to users?  I get very low views most of the time. What should be done to increase a question's popularity? How to add System.Windows.Interactivity to project? Itemize: Identation is different between first and second line Is $0$ a natural number? Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number?  It seems as though formerly $0$ was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers. After learning about the  datasets I've working with the following layers, from the USA data   Country boundaries State boundaries County boundaries City boundaries ZipCode/Postcode boundaries   What I am trying to find is the equivalent (where appropriate) of the same data for various countries.  Is there any free administrative boundaries available as shapefiles for other countries? Area of intersection between two circles Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres of the circles? In Windows, 'removable' drives cannot be partitioned, without the partitions not appearing and receiving drive letters, apart from the first partition.  Partitioned flash drives work fine in Linux.  What I want to do is partition a 8GB flash drive into two, with the first partition containing various boot disc images, which can be selected to boot from, and have various portable apps, documentation, utilities, scripts, etc, on the other partition.  I currently do this using two separate flash drives, but I want to be able to use a single flash drive for everything, which I keep on my keyring.  It is not possible to do this without having at least two partitions, as the ISO boot selector for the boot disc images will not work otherwise.  I know there is a method where you can flip a bit, using Lexar's USB Format Tool, which fools Windows into thinking that the partitions are on a fixed hard drive.  However, this apparently makes it difficult to eject the flash drive.  Flash drives with  from SanDisk had two partitions, presenting itself to the host system as a USB hub with a CD drive and standard USB mass storage device attached.  This is what I would like to emulate, if possible. Narration cartoon about a town that has weird paranormal occurrences in it The company I work for has asked me to attend a training class on the other side of the country.  However my situation is my drivers license expired a few days ago. I do however have a separate printed email stating that the license has been renewed.  This drivers license is my only ID that shows both my name &amp; photo.  Is it possible to be able to board a flight with the expired drivers license and the printed email showing that it was renewed? Quantum teleportation and no-communication theorem According to the Wikipedia article for the :     In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listeners to use their radio receiver to send messages to the other listener. This analogy is imprecise, because quantum entanglement suggests that perhaps a message could have been conveyed; the theorem replies 'no, this is not possible'.   According to the Jet Propulsion's recent article on quantum teleportation:   they can effect an entangled photon (B) with another photon (A) to change the state of the other entangled photon.  Doesn't this contradict what the no-communication theorem states ? Find the equation of the plane knowing that it passes through 3 points Why do some materials reflect (metals) and other materials reflect and refract (glass) from the quantum perspective? Recently I was asked to explain the difference between reflection and total internal reflection from a purely conceptual standpoint (no math).    Let me explain what I already know.  Reflection and refraction at the quantum level are the same thing.  Light is a photon.  A photon is a discrete particle that has wave characteristics (a finite wave traveling like a bullet).  As the photon travels it collides with electrons in the matter of the medium it is traveling in.  Depending on the energy of the photon and the allowed energy bands of the medium the photon cause the electron to jump up a level.  If the photon is absorbed then the medium will increase its motion (at the macro scale increasing its temperature).  If the photon is not absorbed it will be re-emitted (really as a new photon). I have read and watched Feynman's QED lectures and book and have a pretty good understanding of his process for determining how all these paths come together to give the net path of the photon.  The general rule of thumb is that the photon wants to take the path which requires the least amount of time.  I understand how this principle goes to explain refraction and reflection.    What I don't seem to understand is why does one material seem to cause a higher percentage of refraction compared to another (metal vs. glass).  What about the electron configuration of a the medium changes the net effect of the absorption and re-emissions of the photons?  Is there a change in the probability of the photon being re-emitted in a reverse direction?  Is there a farther distance the photon can travel before being incident onto an electron?  This is the part where my understand breaks down.    When you have hit the critical angle in a medium that refracts and the light completely reflects, are the photons moving is the same manner as they would be in a material that always reflects? How does this connect to the question in the previous paragraph?  I know I have a bunch of mini questions embedded in answering this one larger question.  Any help on any of the parts would be greatly appreciated? Using GParted to remove windows partition I am trying to build an executable jar program which depends on external jar downloaded. In my project, I included them in the build path and can be run and debug within eclipse.  When I tried to export it to a jar, I can run the program but I can't when I try to press a button which includes function calls and classes from the external jar. I have edited the environment variables (Windows XP) CLASSPATH to include paths of all the external jar, but it doesn't work.  A point to note is that I got compile warnings while exporting my executable jar, but it doesn't show up any description about the warnings.  Would someone kindly provide a thorough guide on how to include an external jar program using eclipse? I want to find out the number of possible combinations of $x$ numbers that sum to $y$. For example, I want to calculate all combination of 5 numbers, which their sum equals to 10.  An asymptotic approixmation is also useful. This question seems to be very close to number partitioning, with the difference that a number can be 0. See:    All possible partitions for sum 10 and 3 positions that can be zero, are 63 possiblities: (numbers shown as 3 digits)  019 028 037 046 055 064 073 082 091 109 118 127 136 145 154 163 172 181 190 208 217 226 235 244 253 262 271 280 307 316 325 334 343 352 361 370 406 415 424 433 442 451 460 505 514 523 532 541 550 604 613 622 631 640 703 712 721 730 802 811 820 901 910 How to resize my dual-boot partitions I have a dual-boot laptop with both Windows 10 and Ubuntu 16.04.  Currently, the Windows side has too much disk space, and I want to resize things so that the Ubuntu side has more.  Firstly, I went into the Windows disk management and shrunk the Windows partition by 20GB. I then wanted to expand the Ubuntu partition, but it seemed like this option was greyed out.  Can I expand the Linux partition from Windows or do I need to be in Ubuntu or do I need to create a boot disk and do it that way?  Or do I need third party software?  Any help gratefully received.