Rule for specific symbols
Pattern Match symbols that begin with same letter?
Suppose $k$ is a field that is finitely generated as a ${\mathbb Z}$-algebra.  (That is, $k$ is a quotient of ${\mathbb Z}[X_1,\dots,X_n]$ for some $n$). Does it follow that $k$ is finite? Extracting the function from InterpolatingFunction object In the  library, they are overloading the () operator.  Is this a convention in C++? For callbacks, etc.?  I have seen this in code of a co-worker (who happens to be a big Boost fan). Of all the Boost goodness out there, this has only led to confusion for me.  Any insight as to the reason for this overload? Why commutator subgroup is normal to G? If $G$ is a group and $G'$ is generated by $\{xyx^{-1}y^{-1}|x,y\in G\}$, then $G'\trianglelefteq G$ and  $G/G'$ is Abelian.  At first, I thought this is easy because I thought $g[x,y]g^{-1}=[gxg^{-1},gyg^{-1}]$. But it was a mistake. I could not prove that it is also subgroup of G and $G/G'$ is abelian. I need help. Multiple workspaces on Ubuntu 18.04.1 LTS and later with GNOME Shell Any idea how to have more than 2 workspaces on Ubuntu 18.04.1? What's the significance of conditional and absolute convergence? I know how to find if a series is conditional or absolute convergence by taking the absolute value and seeing if that absolute sum converges (then the original sum is absolute). If the absolute diverges but the original converges, then that's conditional.   But my question is: is there a significance? Is absolute convergence series bigger than absolute? Does a series being absolute or conditional affect rate of convergence, or radius? Does it affect symmetry?   Looking at Google, I only found tests on how to find if it's absolute or conditional. But I want to find meaning or significance. Or at least more mathematical properties. python: restarting a loop i have:  for i in range(2,n):     if(something):        do something     else:        do something else        i = 2 **restart the loop   But that doesn't seem to work. Is there a way to restart that loop?   Thanks What is the direction of stack growth in most modern systems? I am preparing some training materials in C and I want my examples to fit the typical stack model.  What direction does a C stack grow in Linux, Windows, Mac OSX (PPC and x86), Solaris, and most recent Unixes? Let $x, y$ and $z$ be real numbers such that $x^2+ y^2+ z^2= 1$. Find the   maximum and minimum values of $2x + 3y + z$ .       How can I able to solve the problem? Thanks for your help. How to divide an image into blocks in MATLAB? What does the plus sign do in '+new Date' After closing paint the last used settings went back to default. I want them to be saved. Like the selected Brush-Tool, Color, Line-strength, etc.  Either after every usage or I define one I use most. Maybe through the registry or by start parameters? Can I do anything about a Nikon d750 taking 5 minutes to power on after taking saltwater damage? I have had a Nikon d750 for a year or so, and 6 months ago it took on a bit of saltwater damage. It still works, but twice in the past it wouldn't power on, once for two weeks and once for two days.   Now it is at a point where it takes around 5 minutes to power on, and when i switch the camera to 'off' or standby, it completely powers off as if the battery drops out, then it takes another 5 mins or so for it to power back on, if it does at all. So I have switched the standby timer in the settings to 'infinity' so it just stays powered on.  I am taking it in to have it looked at, I just hope the damage isn't too fatal. I wonder if anyone has experienced anything similar to this, or can help me diagnose the actual problem. I have tried different batteries, and everything else possible really. Camera itself works fine, just power issues.  thanks in advance. Where do the X-Men get all their money/funding? Charles Xavier's father was a "wealthy nuclear scientist". In the beginning, Charles personally bankrolled the Xavier Institute/X-Men using his family's money.   This included, but was not limited to things like upgrading the mansion to house the training levels, providing a helicopter (the predecessor to the Blackbird jet), providing and replacing uniforms, providing health care for injured students, and rebuilding/repairing the mansion and parts of the Danger Room  repeatedly.  These have all been recurring costs. The mansion has been damaged or outright destroyed a ridiculous number of times. X-Men can't get into a fight without someone's uniform getting damaged.   In one of the more recent stories (I believe it was an early issue of Wolverine &amp; The X-Men), a comment is made about how the X-Men are pretty much bankrupt.  Where has all this money come from over all these years?   Xavier may have had a large war chest to start with, but no other income has ever been mentioned to my knowledge. Student's tuition could account for some of it, but there's no way that's going to fund everything. How I can identify which process is making UDP traffic on Linux? I want to make a persistent live Ubuntu USB drive with more than 4GB of storage.   I know there is an option of installing directly on the drive but I don't want to do this as it will restrict the drive from working on different computers.   One option is to make an additional partition with extra space but if I do this how can I get newly installed software to be stored on this partition? IBM Slack links broken Does anyone know where I can find working Slack invite links to any of IBM's Slack pages? The Slack links on  are all broken. Thank you. Suppose I am given a $2$x$2$ matrix $A=$ \begin{pmatrix} a &amp; b \\ c &amp; d \end{pmatrix}  And an initial vector $x_n$ = \begin{pmatrix} x_0 \\ y_0\end{pmatrix}.  Under repeated iteration $x_{n+1} = Ax_n$, we find that $x_{n+1}$ converges to a line in the direction of the $eigenvector$  of $A$ of the form $X$= $[u,mu]$ where $m$ is the slope of the line.  I know that this process somehow also involves the largest $eigenvalue, \lambda,$ of $A$, though I am unsure how it connects.  My question is: How does the largest eigenvalue connect to this repeated iteration, how do I find the slope of the line of convergence $m$, and what is meant by the "direction of the eigenvector"? Imagine a black hole that is fast-approaching its final exponential throws of Hawking evaporation. Presumably, at all points in this end process there will remain a region that identifiably remains &quot;the black hole&quot; until the the very end, as opposed to huge swarm of fundamental particles that is being radiated out from it. As the mass of the black hole descends to that of individual particles, it would seem entirely feasible that the very last fermionic Hawking radiation event available to the almost-deceased black hole could leave it with an unbalanced charge, e.g. -1, and an unbalanced spin, say 1/2. It would also have some kind of mass of course, but that aspect of the final residue could be fine-tuned to any specific value by photon emissions of arbitrary frequencies. After photon emission mass trimming, the resulting black hole residuum would reach a point where it is no longer be able to evaporate into any known particle, because there is no longer any lower-mass option available to it for removing the -1 charge and 1/2 spin. The black hole residuum will at that point be stuck, so to speak, stuck with exact charge, spin, and mass features of an electron. And so my question: Is it an electron? And if so, by equivalence, is every electrons in the universe really just a particular type of black hole that cannot evaporate any further due to the constraints of charge and spin conservation? And if so, why are charge and spin so uniquely combined in such black hole remnants, so that e.g. a remnant of -1 charge and zero spin is not permitted, at least not commonly, and the mass is forced to a very specific associated level? Is there anything in the current understanding of general relativity that would explain such a curious set of restrictions on evaporation? The full generalization of this idea would of course be that all forms of black hole evaporation are ultimately constrained in ways that correspond exactly to the Standard Model, with free fundamental particles like electrons being the only stable end states of the evaporation process. The proton would be a fascinating example of an evaporation that remains incomplete in a more profound way, with the three quarks remaining incapable of isolated existence within spacetime. The strong force, from that perspective, would in some odd sense have to be a curious unbalanced remnant of those same deeper constraints on the overall gravitational evaporation process. This may all be tautological, too! That is, since Hawking radiation is guided by the particles possible, the constraints I just mentioned may be built-in and thus entirely trivial in nature. However, something deeper in the way they work together would seem... plausible, at least? If an electron is an unbalanced black hole, then the particles given off would also be black holes, and the overall process would be not one of just particle emission, but of how black holes split at low masses. Splitting with constraints imposed by the structure of spacetime itself would be a rather different way of looking at black hole evaporation, I suspect. (final note: This is just a passing thought that I've mulled over now and then through the years. Asking it was inspired by  by Ben Crowell. I should add that I doubt very seriously that that my wild speculations above have anything to do with Wheeler's concept of geons, though.) Minecraft crashes on launch with EXCEPTION_ACCESS_VIOLATION, Problematic frame: ig4dev32.dll or ig4dev64.dll or ig4icd32.dll or ig4icd64.dll When I try to launch Minecraft 1.7.4 or newer, the game crashes on startup, and the game output screen says this:  #  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=*, pid=*, tid=* # # JRE version: Java™ SE Runtime Environment (7.0_51-b13) (build 1.7.0_51-b13) # Java VM: Java HotSpot™ Client VM (* mixed mode, sharing windows-* ) # Problematic frame: # C  [ig4dev32.dll+0x3e88] OR # C  [ig4dev64.dll+0x55ec] OR # C  [ig4icd32.dll+0x104a77] OR  # C  [ig4icd64.dll+0x84930a]   This happens with both Java 7 and 8.  What causes this error, and what can I do to fix the issue?