timo

That's wrong. Test it for m=5, g=1 and a=0, for example.

Concerning Guantanamo Bay I see a few differences: - He was probably arrested within the US, not captured by the US military on the other end of the world. - He wasn't captured in a war, err ... I mean during liberation of a democracy-seeking nation from unlawful combatants. - There's probably no US official who has an interest in torturing him; it's not very likely that he knows about the terror plans of his fellow racists. - He has had a trial. - Most importantly: The US laws concerning this case are probably quite clear. @Pangloss: In the German Nazi scene 88 stands for "Heil Hitler" (H is the 8th letter of the alphabet), I think. EDIT: The 14 seems a US thing:

How about any standard textbook used in university courses?

I don't see your problem. What if [math]y_0[/math] was called c? Do you think that would make a difference? Does "solve [math] ce^{-kt} = \frac c2[/math] for t" look easier to you? If so, then solve that. If not, then there must be something special about the [math]y_0[/math] that you did not tell us. The way the problem is stated it is just some non-zero constant.

What you say is roughly a typical description of Hawking Radiation (never heard "illusion" in that context, though), so in that sense it indeed is what I called radiation above. But this explanation does not make sense to me (or I just don't understand it) so I expect that it is an explanation that is simplified to the point of being wrong. That's why I simply said that black holes are assumed to radiate off stuff.

I cannot but the mechanism by which black holes are believed to lose mass is called "Hawking Radiation". Maybe you'll have some luck with Wikipedia or Google.

Considering that the derivatives are all polynomials I would expect that the construction of a potential function by straightforward integration (also polynomials) either leads to a potential function or a contradiction at some point. Neither do I have a sketch for a proof of that statement (I'd expect that you can actually construct an algorithm for this case) on my notebook not am I completely sober at the moment, though.

1) Not exactly a dumb question. 2) I'd not call it "another form of energy" but "some state with the same energy". Might sound like the same but the difference is that the former statement sounds like energy was something like a substance while the latter statement considers energy to be the property of something which in my opinion is a more defensive and more reliable statement. 3) General Relativity has the nasty habit that total energy must not be conserved, as far as I know. But the mechanism by which this violation of conservation of energy occurs is not accounted to causing something to pop out of nothing, though (still: as far as I think or remember from my relativity classes). 4) Conservation of energy is not unique to thermodynamics and should not be thought of as a consequence of thermodynamic laws. Instead, consider it as a very basic property of nature which is so important that it explicitly gets re-mentioned in thermo. I think it is fair to say so. But note that to my knowledge no one (in the scientific community outside the scope of having to attract public interest or funding) really claims the big bang to be the universe being emerged out of nothing. Technically, you trace the current state of the universe back in time. Then, according to current knowledge, all points in space must have had a distance of zero at some time in the past -> this is called the big bang. However, when going arbitrarily close to that point in the past you encounter physical environments in which the current mathematical framework do describe nature is not expected to work. So it is not really clear what happened close to the big bang and, in effect, what the big bang really is. I am not sure if at the moment this is more than a brain teaser/cramp: Assuming there really is a point where the universe begins, do the laws of the universe really have to hold before the existence of the universe?

1) I'd start with [math]\Phi = \int 2xy + 3z^2 dx \ + C[/math] for a start, i.e. you integrate [math]\frac{\partial \Phi}{\partial x}[/math] over x to get [math]\Phi[/math], not over z. 2) Your constant can still depend on x and y, i.e. [math]\Phi = \int 2xy + 3z^2 dx \ + C(x,y)[/math]. 3) What happens when you do the same for y and z?

There is no known reason/mechanism for an upper mass of a black hole, as far as I know. There is a trivial limit on the lower mass (zero). Black holes are often believed to lose mass over time by radiating off stuff, even to mass=0 where they then cease to exist. In that sense, there is an end to a black hole, but not in the sense that you seemed to have in mind: The reason stars have "an end" is that there's a process going on (fusion of whatever stuff) that creates a pressure countering the gravitational attraction. This process has a limited runtime (at some point you are out of stuff for the process) and after that runtime gravitation will do what it was prevented to do before. No such process stabilizing a black hole against gravitational collapse -a black hole is already as collapsed as anything can be- exists.

In this case the best way would be to know what the integral over and the derivative of a polynomial function looks like. Not sure if this is homework so I'll not give a potential. It should be straightforward to find one by playing around with possible choices a bit.

In which case "gradient field" is the term you want to look up. The vanishing of the integral over any closed path is a property of a gradient field.

There is no need to consider equation 1 for my statement: If there is no solution that satisfies x+a+b+c = 19 then there is no solution that satisfies both, x+a+b+c=19 and equation 1. I did not give the solution because that did not seem to be intended by TheDrBrainac; he would probably have given his solution, then. But as a remark: The question about the smallest value is rather trivial to solve by using brute force; ~10 lines of computer code.

I have some doubts about your solution, then. The first composite naturals are 4, 6 and 8. a=b=c=x=4 is not a solution. Having one of them equal 6 and the others being 4 would give a value of 9. Having 2 sixes and two twos already gives 10. Having three fours and 1 eight also gives a result of 10. All other combinations should give even higher results. If you leave out the "composite" criterion then there is a solution with a lower value.

I don't see how the question makes any sense. You probably missed to include some restrictions, e.g. what type of numbers a, b and c are and what type of function x is. And x seeming to be a function depending on some parameter in the first equation but not in the term you want to minimize is pretty suspicious, too.

I'd love to have the option (or just the feature without selecting it) that threads started by people on my ignore list are not shown to me in the first place or at least marked as "save time by not clicking here".

Consider pouring ink into boiling water. I would imagine that cold water poured in boiling water might behave roughly like the ink.

I have quite a few spontaneous ideas: 1) Get into contact with someone who has a tabletop fusion reactor lying around. 2) Publish your idea on your homepage and hope someone sees it. 3) Publish your idea somewhere else and hope someone sees it. 4) If you're more interested in the money than in the science you could look for people who invest in high-risk startup enterprises. 5) Wonder if the fact that you don't know who to contact about an idea about nuclear fusion might also say something about your expertise in fusion and reconsider the likeliness of your idea to work. 6) Verify if tabletop fusion reactors actually do exist. 7) Post your idea here and wait for comments. Of course, not all the ideas might be an option to you. It would also be important to know how important getting rich with your idea is for you.

I think it doesn't take a science degree to figure that a group of terrorists is more likely to get take their nuke to a major city to blow it up there than to launch one to space to disrupt electricity. Not to mention that my computer has died of less spectacular reasons before. And if the evil communists invade your country then there's more to worry about than not being able to access facebook. In effect, I think there is no need for you to protect against an EMP attack. I am afraid I do not understand how EMP is supposed to work, either. But I would be interested how the pulse intensity compares to having my mobile lying on my laptop.

The matrix A in question has an eigenvalue of zero and hence is not invertible. Since [math] Av_0 = 0 [/math] (as given in the text) you immediately get [math] AAv_0 = A0 = 0 [/math] for [math]v_0 \neq 0 [/math].

AAx = 0 does not imply x=0. x=0 is not the same as "no solution". So I don't think that will help here.

I find it very sad when the attitude "I am against [this] war" ends at "but contributing to it is an economically safe and well-paid job". Makes weapon manufacturers look like honorable businessmen.

There's plenty of proposals in the reviews. I liked the idea of putting it into a box together with a vial of poison and a cat.

I have no clue about the legality or accordance with forum rules (trading chemical is not really the forum intent). But in any case you won't get as good reviews as Amazon.

Thanks for the replies so far. I'll probably comment on them as soon as I can spare the time to consider them and formulate a reply/statement. Until then, further comments and discussion are highly welcome. This thread is not supposed to be about the forum organization on sfn but more towards the question what people in general (or in particular) do consider "theoretical physics" to be.