I have an Early 2011 Quad Core i7 Mac. Due to hyperthreading, a lot of programs report 8 "cores".  If I were to write a program that executes in parallel, could I kick off 8 instances of this program or just 4?  I get I can start as many threads as I want, but would I be seeing 4 or 8 instances of the program execute in parallel?
I'm new in this computer terms. So anyone can explain to me what "virtual cores" and "hyperthreading" are at greatest detail a layman can understand?  People told me that virtual cores are imaginary cores acting like a physical core. If that is so, then can I make my AMD v105 processor single core a dual core processor?   Is it also possible to hyperthread my CPU? Are these functions built in?
What is the main difference between an inner class and a static nested class in Java? Does design / implementation play a role in choosing one of these? Retry a task multiple times based on user input in case of an exception in task Every finitely generated algebra over a field is a Jacobson ring Knowing that the polynomial ring in $n$ variables over a field $k$ is a Jacobson ring, how can we prove from it that every finitely generated $k$-algebra is a Jacobson ring?   EDIT: We define a ring to be Jacobson if every prime ideal is an intersection of maximal ideals. I have been wondering why anyone ever thought that we could find an expansion for eigenstates of some perturbed Hamiltonian in terms fo those for the basis Hamiltonian. My lecturer insisted that this was because the eigenstates of the Hamiltonian are complete', however from my (limited) understanding of the mathematical basis of QM:   When you are given a Hamiltonian, it comes with the Hilbert space of functions of which it acts (subject to some conditions we impose, such as the Lebesgue square-integrability of functions) When you are given another Hamiltonian, there is no guarantee that it will act on the same Hilbert space Therefore, that the zeroth order Hamiltonian has eigenstates forming a complete basis for the space on which ti acts does not guarantee that these same eignestates form a complete basis for the Hilbert space on which the purturbed Hamiltonian acts.   As a simple example. I can imagine adding a small perturbing magnetic field to a Hamiltonian in which there initially is none, such that we lose the degeneracy in the eigenstates accounting for different spins of a particle. One could say that we have the same Hilbert space before and after but we lose degeneracy; or I would have been tempted to say that our initial Hilbert space did not have these extra dimensions corresponding to the spin states. So rather than the eigenstates of the basis Hamiltonian also forming a complete basis for the purtubed Hamiltonian, but having eigenvalue degeneracy which is lifted on the purtubration, I would have said that our Hilbert space has changed. After all, if we take the former view (i.e. a basis accouting for spin but with degeneracy) then it seems like for any problem we would need to know and account for EVERY possible system property that can be discerned. This doesn't seem reasonable to me....  NOTE:  1) My question was asked here previously:   although there is only a discussion and no conclusive answer given. I see that the distinction is important in relativistic QM, and the case of adding a potential onto a free particle Hamiltonian seems to be a special one. Although I am still not sure what the answer is for general purturbations.  2) Similar question here:   but it seems to completely avoid answering the question. Why did Obi-Wan Kenobi choose that moment to appear to Luke? In The Empire Strikes Back, Luke Skywalker violently escapes from the lair of a wampa ice creature, finds himself in the middle of a life-threatening snowstorm on an inhospitable planet, collapses from cold and fatigue, and will likely be dead in a few minutes. As :     Luke lies face down in the snow, nearly unconscious. Slowly he looks   up and sees Ben Kenobi, barely visible through the blowing snow. It is   hard to tell if Kenobi is real or a hallucination.     Why did Obi-Wan Kenobi choose this moment to appear to Luke and deliver rather important instructions concerning next steps in his Jedi training?  It seems lucky that Luke remembered anything of the encounter at all. He probably thought he was hallucinating. Why is "cupboard" pronounced with a silent "p"? My homework has this problem:     Prove that there exist irrational numbers $x$ and $y$ such that $x +  y$ is rational.   There is an easy solution that I found on mathbitsnotebook.com:     \begin{align} \left(2+6\sqrt{7}\right) + \left(-6\sqrt{7}\right) = 2.\end{align}   Can we prove the same without using subtraction? Why do I need 50 reputation to comment? What can I do instead? What is the reason for the top secret two space newline markdown weirdness? I need help to calculate the  Fourier transform of this funcion  $$b(x) =\frac{1}{x^2 +a^2}\,,\qquad a &gt; 0$$ Thanks. Is there a way to tell Nautilus not to generate previews of PDF files? I tend to download lots of articles as PDFs, and I find that when I browse a directory of these Nautilus takes 1 minute to load the directory. I assume that's because it's generating previews of their front pages. That feature is useless to me, alas.  I'd like to tell it not to do that. What's the shelf life on crushed specialty grains? Any nice, stable ways to keep a window 'Always on top' on the Mac? I am looking for a stable way to keep any window 'always on top' on OSX.  , an app that does that requires SIMBL/easySIMBL, which it seems is not very stable.  Are there any better solutions? It's actually surprising that there is no native way to implement this. I have a stubborn folder that someone must have created accidentally and that has persisted all this time. I can see it with:  # find /var/www/html -maxdepth 1 -type d   which gives me:  /var/www/html /var/www/html/files /var/www/html/.?   unfortunately the question mark there is not the actual character ?, it merely seems to denote that there is no proper glyph and/or translation for that character. So something like rmdir is out of the question. My system has UTF-8 as the default locale as so many modern Ubuntu systems, but admittedly the folder in question may have originated on a RHEL or CentOS box (tared up and unpacked).  # env|grep LANG LANG=en_US.UTF-8   When trying to cd .\? (as mentioned before it is not actually ?) I get auto-corrected to . by bash and actually end up in /var/www/html/. for some reason. Now if I can't "name" this folder usefully, I cannot access it in any way. How can I get rid of it without putting the whole system in jeopardy?  Now I installed detox already but that only seems to act on files, not folders, according to its documentation and besides it still requires that I be able to name the object somehow to do something with it. While my code is compiling, I usually like to go through some reviewing and especially the late answers.  What I do see a lot in answers to old questions is the self-defense mechanism     ""   As if there is something fundamentally wrong with answering old questions. This leads me to two questions/thoughts:   Should we edit phrases like that out of the answer? (Given it's a good/valid answer to begin with, without any of the likely "old answer" problems. I realize the example linked to has its flaws.) Should we perhaps explicitly encourage answering old unanswered questions somewhere in the FAQ? (I'm unaware of any such recommendation, but might have read over it. Let me know if I did) I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$   Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I get $p= 0/0$. How does it make sense?   Can you tell me that where I am wrong? Windows 7 Automatic Log-on with a Default User Account? I have two User Accounts for my Windows 7 with no password requirement. I frequently use one of those accounts; so I would like Windows to log-on automatically with that account without the need for user input.  P.S. I don't prefer installing/using a third-party software for that purpose; especially those that place at low levels before Windows log-on. Where does "pay through the nose" originate? Why are local variables not initialized in Java? Was there any reason why the designers of Java felt that local variables should not be given a default value? Seriously, if instance variables can be given a default value, then why can't we do the same for local variables?  And it also leads to problems as explained in :     Well this rule is most frustrating when trying to close a resource in a finally block. If I instantiate the resource inside a try, but try to close it within the finally, I get this error. If I move the instantiation outside the try, I get another error stating that a it must be within a try.      Very frustrating. How do I install an SSH private key generated by PuTTYgen?