Relative time/space - Two clock thought experiment
The real meaning of time dilation
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$ Downloading from the main Ubuntu archive is slow even when it's not release day, how can I get apt-get to automatically use a mirror that is close to me? Often confusion arises when the  spell is used, an  is worn, or the 's anti-magic ray is employed, whether a given character's ability will still function.   The spell does give you some guidelines on how to adjudicate the effects of the loss of magic but says very little about how to determine what is affected.  In short, how do I tell if an ability is magical? What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory?  Some subjects off the top of my head that probably need covering:   Differential geometry, Manifolds, etc. Lie groups, Lie algebras and their representation theory. Algebraic topology. What exactly does ARM sell to vendors? Assumptions:   Computer architecture: Describes how the different modules of a processor interact with each other. A computer architecture is defined using vhdl files Computer Organization: Describes the physical layout of the processor modules on silicon. A computer organization is defined using a set of photo masks (and manufacturing process eg chemical, that goes at each step) Computer Organization, therefore, requires that the fab process be taken into account. ARM is not in the fabrication business, therefore it does not sell photo masks.     My question(s):   What exactly is ARM selling to a vendor (eg: freescale)? For a SoC (System On Chip), (eg: ), which part is ARM and which is Freescale? Who did the integration? Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.   This is what I got so far. I figured that since $p,q$ are bigger than $5$, there are only odd primes for this conjecture. Then I can rename $p=2m+1,q=2n+1,m,n∈Z$.  We want to show $(p^2-q^2 )=24k,k∈Z$. By substituting $2m+1$ for $p$ and $2n+1$ for $q$, we get  $((2m+1)^2-(2n+1)^2)$. If we expand it, we get $4(m^2+n^2+m-n)$ Q. I think I can make $4(m^2+n^2+m-n)$ look like $24k$. How should I approach ?  And my prof. commented that "I would take this proof in small steps.  Rather than trying initially to prove that $24 | p^2-q^2$, look at the progress you already have.  You proved $4 | p^2-q^2$.  Can you prove 8 is a factor?  What about 3?  Then see if you can put together what you have to get 24 as a factor."  I am stuck here. Any helps? Why Doesn't a Bootable USB Boot This question is asked often in Ask Ubuntu, sometimes with few hints about the situation.   Please provide a list of possible reasons to help troubleshoot the problem. By conservation of energy, the solid is left in a lower energy state following emission of a photon.  Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium is a statement of the mean behaviour of the system, not a statement that the internal energy is constant on arbitrarily short timescales.  The energy has to come from somewhere during emission, and go somewhere during absorption.  Energy in a solid can be stored as kinetic and potential energy of electrons and nuclei, either individually or in collective modes such as phonons and plasmons.  In thermal equilibrium energy will be stored more or less in various forms depending on the temperature and material.  However, even if most of the thermal energy in a particular solid at temperature $T$ is stored in the form of phonons, it could be that phonons primarily interact with light indirectly via electrons, e.g. a phonon excites an electron in a phonon-electron interaction, which can interact with light via the EM field.  Given that light is an EM field, it makes sense to me that it is emitted and absorbed by charged particles.  The electron-photon interaction is probably dominant for visible and ultraviolet light, given that metals are opaque, while semiconductors and insulators are transparent to (visible and UV) light with energy lower than their bandgap. However, once you get into energies in the IR and below, or X-rays and above, other mechanisms apparently take over.  For example, on the high-energy end of the spectrum I've heard that gamma rays can interact directly with nuclear degrees of freedom, which is reasonable considering that gamma rays are emitted during a lot of nuclear reactions.  A review of  might give clues to important light-matter interactions over a broad range of wavelengths.  Whether all of the these processes are involved in blackbody emission is a somewhat different question.  What physical processes mediate energy transfer during blackbody emission, and in which energy ranges are the various processes dominant? Given the following image:   $\hskip{1.5 in}$   Supposing $A(100, 300)$ and $B(300, 100)$, how can I find the angle $\alpha$ between A and B?  On a side note, what's the main difference between a point and a vector? translating a point to a vector is as simple as Point = Vector? Sometimes I find articles where the terms are interchangable How can I get the size of an array from a pointer in C? Second order partial of $f(x,y)=\frac{xy(x^2-y^2)}{x^2+y^2}$ Consider the function $f(x,y)=\dfrac{xy(x^2-y^2)}{x^2+y^2}$ for $(x,y) \neq (0,0)$, $f=0$ otherwise.  I have to compute $\dfrac{d^2f}{dydx}(0,0)$.  I know that I have to calculate $\frac{df}{dx}$ first. But that is ,  $\frac{df}{dx} = \frac{\partial f}{\partial y}\frac{dy}{dx}+\frac{\partial f}{\partial x}$. When I put it in wolframalpha, it gives me this calculation, and also just $\frac{\partial f}{\partial x}$ as an alternative form.   Why do I just ignore the y'? I don't know what y(x) is, as a function of x.  y and x are independent functions, no? If column matches another file, print every line with match (awk/grep) The Megahertz Myth became a promotional tactic due to differences between the PC's INTEL 8086 processor and Apple's Rockwell 6502 processor.  The 8086 ran at 4.77MHz while the 6502 ran at 1MHz.  However, instructions on the 6502 needed fewer cycles; so many fewer, in fact, that it ran faster than the 8086.  Why do some instructions need fewer cycles?  And why can't the instructions of the 6502, needing fewer cycles, be combined with a fast cycling processor of the 8086?  Wikipedia's article for instructions per cycle (IPC) says     Factors governing IPC   A given level of instructions per second can be achieved with a high IPC and a low clock speed...or from a low IPC and high clock speed.   Why can't you have both high instructions per cycle and high clock speed?  Maybe this has to do with what a clock cycle is?  Wikipedia mentions synchronization of circuits?  Not sure what that means.  Or maybe this has to do with how a pipeline works?  I'm not sure why instructions in a short pipeline are different from instructions in a long pipeline.  Any insight would be great!  Just trying to understand the architecture behind the myth.  Thanks!  References: Java logical operator short-circuiting The following  (links to pdf) in the  has no provided source. The book  by Ash and Gross seems to use a similar style. Where can I find hints for typesetting publication standard articles/books as above in TeX. I looked around a bit but couldnt find much from else from keyword searches.  Particularly, I am looking at the chapter headings, title page design, and the mirror effect. Sorry for the title, as I dont really know what its called. Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$ a) Determine the number of ways to colour a 1 by n grid using the colours red and white if an even number of squares are to be coloured red.   Note that n is greater than or equal to 1 and the number of red squares could be 0.  I know I must consider the cases of n being even and odd, and determine the sum, from zero to n of the squares being red, where the number of red squares is even. But I just want to make sure I haven’t missed any arrangements by saying a) is $2^{n-1}$ when n is even and $2^{n-1}-1$ when n is odd.  b) Determine the number of ways to colour the squares using red, white and blue if an even number of squares are to be coloured red.  For this case, I can have arrangements including red only, white only, blue only, white and blue only, red and white only, red and blue only, and finally all three colours.  Thank you for any help provided. I'm reading a lot of documentation on sed, and am still stumped on my particular use case.  I want to replace this line in a conf file with my own line:  Replace this line: #maxmemory &lt;bytes&gt; with: maxmemory 26gb  This is what I tried:  sed s/maxmemory.*bytes.*/maxmemory 26gb/ /etc/redis/redis.conf  I get the error: sed: -e expression #1, char 30: unterminated `s' command  Which stumps me because I don't know what that means. So my question is:  How can I accomplish what I want? What does that error mean? (so I can learn from it) A malevolent computer with AI takes over a woman's house with the intent of hybrid computer/human procreation. The evil computer seals off the house with the woman in it and keeps her prisoner while it prepares. I read the tale sometime in the late 80's or the early 90's. It was one of many of my missing books that got yardsaled by my in-laws when I wasn't looking. It may also have been made into a movie, but I didn't see the film. , to correct a misspelled library enum in an answer. Since the edit was only one character, I also had to add a superfluous sentence to get over the character limit required to edit a post.  I've hit this problem before in other edits, always in code snippets. Since the edit limit exists to prevent trivial edits, and since there are many cases where one character code edits are not trivial (= to == etc), would it make sense to have a lower edit minimum inside code snippets?