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	Encyclopedia :: encyclopedia : Lattice (order) (Site not responding. Last check: 2007-11-01)
		Lattices constitute one of the most prominent representatives of a series of "lattice-like" structures which admit order-theoretic as well as algebraic descriptions, such as semilattices, Heyting algebras, and Boolean algebras.
		The set of compact elements of an arithmetic complete lattice is a lattice with a least element, where the lattice operations are given by restricting the respective operations of the arithmetic lattice.
		These conditions basically amount to saying that there is a functor from the category of sets and functions to the category of lattices and lattice homomorphisms which is left adjoint to the forgetful functor from lattices to their underlying sets.
	www.hallencyclopedia.com /Lattice_(order) (2277 words)

	Order theory - Wikipedia, the free encyclopedia
		Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering.
		It addresses readers who have basic knowledge of set theory and arithmetics and who know what a binary relation is, but who are not familiar with order theoretic considerations so far.
		Filters and nets are notions closely related to order theory and the closure operator of sets can be used to define topology.
	en.wikipedia.org /wiki/Order_theory (4023 words)

	particle physics - Hutchinson encyclopedia article about particle physics (Site not responding. Last check: 2007-11-01)
		Yukawa's theory was largely superseded from 1973 by the theory of quantum chromodynamics, which postulates that the strong nuclear force is transmitted by the exchange of gauge bosons called gluons between the quarks and antiquarks making up protons and neutrons.
		In 2003 scientists at the High-Energy Accelerator Research Organization in Tsukuba, Japan, discovered a new particle that could not be explained in terms of existing theories of energy and matter.
		The unknown particle, which the researchers classified as X(3872), was detected in the decay products of beauty meson particles; it weighed as much as a single atom of helium and lasted a billionth of a trillionth of a second, an unusually long lifetime for a subatomic particle of this size.
	encyclopedia.farlex.com /particle+physics (882 words)

	Neil Sloane (home page)
		This displays a certain 8-dimensional dataset by projecting it onto a sequence of 40 planes in 8-space that were obtained from the E_8 lattice (one of our Grassmannian packings).
		Mixed binary-ternary codes [pdf, postscript]: Suppose you want a set of vectors in which the first b coordinates are binary and the last t coordinates are ternary, and you want Hamming distance at least d between any two vectors.
		This data-base of lattices is a joint project with Gabriele Nebe, University of Aachen Our aim is to give information about all the interesting lattices in "low" dimensions (and to provide them with a "home page").
	www.research.att.com /~njas (1209 words)

	History of Imagination Engines, Inc.
		While studying theoretical solid state physics in graduate school, Thaler begins experimentation with lattice models of both ferromagnetic and ferroelectric materials using Ising models and crude Boltzmann Machines.
		He soon finds great fascination in raising the computational temperature of such lattices beyond their Curie points and watching the dissipation of memories frozen into them.
		In contrast, IEI's founder presented the theory, philosophy, and most importantly, the patented IEI technology required to produce a free-thinking and creative entity among the many TCP/IP nodes of the Internet.
	www.imagination-engines.com /history.htm (3465 words)

	Join
		Related Topics: JOIN, least, free, lattice, dictionary, calculus, command, relational, upper, SQL, database, bound, Look, theory
		In lattice theory, a join is a least upper bound
		theory, This, wish, Look, refer, internal, referred, dictionary, least, articles
	www.brainyencyclopedia.com /encyclopedia/j/jo/join.html (92 words)

	The Math Forum - Math Library - Topology (Site not responding. Last check: 2007-11-01)
		This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology.
		Fixed Point Theory and Applications sites; Mailing List; Conferences: previous and forthcoming; books on fixed point theory; other interesting sites on the Web; bibliography database; abstracts; papers on fixed point theory; general information.
		Subscribe to and join a free discussion about functionspaces and related topics.
	www.mathforum.org /library/topics/topology (2425 words)

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