Discussions - sci.math | Google Groups

	(a_n,b_n) nested open intervals for all n > n_0 show either a_n=A or b_n=A
	Let (a_n,b_n) be a sequence of nested open intervals. Assume that intersection of all (a_n, b_n) is empty. Let A=Sup a_n=Inf b_n Show that there exists an n_0 such that for all n > n_0 either a_n=A or b_n=A. Proof: If r,s >= n_0 the x_r, x_s both belong to (a_n0, b_n0) . therefore \|x_r - x_s\| <= b_n0 - a_n0... more » By TheGist - 12:59am - 1 new of 1 message

	-- boundary of an open set
	If U is a nonempty, non-dense open subset of R^n, with n > 1, must the boundary of U contain a nontrivial path? quasi By quasi - 12:23am - 1 new of 1 message

partition function

i'm trying to find the number of non negative integral solutions of the equation a + 2b + 3c + 4d = n ,i find it is equation to the partition of n into at most 4 parts. Wikipedia says this is the definition of partition . Can some one help me understand why is the number of non integral solutions to the above equation is equal to number of partions atmost... more »

By nikl...@gmail.com - Oct 6 - 3 new of 3 messages

	> Eigenvalue problem for sufficiently well-behaved functions
	Suppose f is a sufficiently well-behaved real-valued function (say, a smooth function with compact support) defined on the set of real numbers), and define T(f) = \integal _{-\infty}^x y f(y) dy What are the eigenvalues for T ? Which eigenvalues lead to square-integrable functions? I tried differentiating both sides of... more » By k.hofmann - Oct 6 - 2 new of 2 messages

	What does FLOPS mean?
	Wikipedia has an article about FLOPS, in this article, FLOPS = FLoating point Operations Per Second [link] But in another article about Cholesky decomposition ( [link] ) it says that the complexity of Cholesky Decomposition is about n^3/3... more » By Sean - Oct 6 - 3 new of 3 messages

	-- Eigenvalue problem for sufficiently behaved functions
	Suppose f is a sufficiently well-behaved function (say, smooth function with compact support) defined on the set of real numbers, and define T(f) = \integal _{-\infty}^x y f(y) dy What are the eigenvalues for T ? Which eigenvalues lead to square-integrable functions? I tried differentiating both sides of... more » By k.hofmann - Oct 6 - 1 new of 1 message

	orientation of galactic coordinate system centered at Earth's sun, looking from Earth's perspective? Ouch my brain exploded!
	I'm making an Earth simulator in Flash and still have several concepts to work out. I managed to plot stars in a sky looking from the Sun's position, and can make out constellations seen from our sky. Now if I virtually move to the Earth's position, and look at the sun, how will the galactic sphere of stars rotate?... more » By Ultrus - Oct 6 - 4 new of 4 messages

Deterministic vs Nondeterministic Turing machines.

... first of all, is there any generally accepted definition of non- deterministic Turing Machines? At least I have found almost nothing usable, including wiki-articles. So I will state my question in the following form: Is it true, that there exists ‘probabilistic’-TM, which could not be simulated with deterministic-TM at all?... more »

By Dmitriy Samsonov - Oct 6 - 1 new of 1 message

	about CNF converting
	Hi all, did somebody know if is possible to use a non deterministic algorithm in order to convert every boolean propositional formula into an equivalent CNF formula? Thanks a lot Regards By newbie - Oct 6 - 2 new of 2 messages

	Dedekind-MacNeille completion
	Let S be an (partially) ordered set. For A subset S, let above A = set of upper bounds of A. below A = set of lower bounds of A. The Dedekind-MacNeille completion of S is M = { below above A \| A subset S } If S is a Boolean algebra, then M is a Boolean algebra. In particular, when A subset S, what set B is there for which... more » By William Elliot - Oct 6 - 1 new of 1 message