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Topic: Tensor product of fields

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	A (Site not responding. Last check: 2007-11-07)
		the vector product of a pseudo-tensor and a psuedo-vector is a pseudo-tensor.
		The divergence of a vector field is a scalar field, the divergence of a tensor field is
		a vector field, the divergence of a tensor field is a vector field, the divergence of a
	www.cchem.berkeley.edu /jsngrp/Che250/HW1.htm (958 words)

	Tensor product of fields - Wikipedia, the free encyclopedia
		In mathematics, the theory of fields in abstract algebra lacks a direct product: the direct product of two fields, considered as ring (mathematics) is never itself a field.
		As a ring, it is sometimes a field, and often a direct product of fields; it can though contain non-zero nilpotents (see radical of a ring).
		Each such field is a representative of an equivalence class of (essentially distinct) field embeddings for K and L in some extension of M. When K is a number field, this result can be combined with Dirichlet's unit theorem to yield the rank of the group of units of K. edit]
	en.wikipedia.org /wiki/Tensor_product_of_fields (655 words)

	Tensor - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		Tensors may be written down in terms of coordinate systems, as arrays of scalars, but are defined so as to be independent of any chosen frame of reference.
		In the field of diffusion tensor imaging, for instance, a tensor quantity that expresses the differential permeability of organs to water in varying directions is used to produce scans, for example of the brain.
		Note that the word "tensor" is often used as a shorthand for tensor field, which is a tensor value defined at every point in a manifold.
	www.bexley.us /project/wikipedia/index.php/Tensor_calculus (1625 words)

	Tensor product of R-algebras - Wikipedia, the free encyclopedia
		In mathematics, there is a construction in abstract algebra of the tensor product of commutative rings; which puts a ring structure on the tensor product as abelian groups of two commutative rings R and S.
		We observe the multilinear nature of the product
		This construction is of constant use in algebraic geometry: working in the opposite category to that of commutative R-algebras, it provides pullbacks of affine schemes, otherwise known as fiber products.
	en.wikipedia.org /wiki/Tensor_product_of_R-algebras (171 words)

	PlanetMath: tensor (Site not responding. Last check: 2007-11-07)
		A tensor is the mathematical idealization of a geometric or physical quantity that may be represented relative to a given frame of reference as an array of numbers
		Examples of physical tensors are the energy-momentum tensor, and the polarization tensor.
		Tensor field concepts, which typically involved derivatives of some kind, are discussed elsewhere.
	planetmath.org /encyclopedia/Tensor.html (852 words)

	THE MEANING OF "TENSOR"
		In group theory, there is an additional important combining form called a "semidirect product", a typical example of which is the combining, in an affine Euclidean space, of a group of rotations with a group of translations.
		Roughly, according to a classical theorem (Levi's theorem) on the subject, any Lie group is a semidirect product of a solvable algebra by a semisimple algebra, meaning that the structure problem is broken into determining the structure problems for solvable and semisimple algebras.
		Tensor Product The tensor product grows from the idea of the "Cartesian Product" of the one dimensional x-axis as a vector space, and the one dimensional y-axis in elementary algebra to form the two dimensional Cartesian plane.
	graham.main.nc.us /~bhammel/MATH/tensor.html (1952 words)

	Tensor - FreeEncyclopedia (Site not responding. Last check: 2007-11-07)
		In mathematics, a tensor is a certain kind of geometrical entity which generalizes the concepts of scalar, vector and linear operator in a way that is independent of any chosen frame of reference.
		Tensors are of importance in differential geometry, physics and engineering.
		Note that the word "tensor" is often used as a shorthand for tensor field, a concept which defines a tensor value at every point in a manifold.
	openproxy.ath.cx /te/Tensor.html (864 words)

	Tools of Tensor calculus - Tensors and Forms
		As we have stressed in the Introduction a tensor in TTC is handled as a single (geometric) object, so, in addition to the components, one has to input also the basis elements.
		The notation for tensors follows a rather straigthforward generalization of the notation for vectors and 1-forms that we have seen in the previous chapter.
		Tensors of type (0, q) which are antisymmetrics on all q indices are called exterior q-forms.
	baldufa.upc.es /xjaen/ttc/tutorial/tens.htm (1223 words)

	Tensor (intrinsic definition) (Site not responding. Last check: 2007-11-07)
		In differential geometry an intrinsic geometric statement may be described by a tensor field on a manifold, and then doesn't need to make references to coordinates at all.
		The same is true in general relativity, of tensor fields describing a physical property.
		(The term "tensor" is sometimes used as a shorthand for "tensor field".) For instance, the curvature tensor is discussed in differential geometry and the stress-energy tensor is important in physics and engineering.
	www.free-download-soft.com /info/add-in.html (750 words)

	Compositum
		Therefore the compositum is isomorphic to the tensor product iff the tensor product embeds in e.
		Since the tensor product is essentially the cross product of s and t, with r in common, every pair generator used to build u has to have an s component of 0 or a t component of 0.
		The field extension t(x)/t has dimension equal to the degree of g, or less, yet x is a root of p, which is irreducible, hence the dimension of t(x)/t equals the degree of p.
	www.mathreference.com /ring-alg,compos.html (1678 words)

	Straightening Bases for Tensor Products (Site not responding. Last check: 2007-11-07)
		Corresponding to each of these tableaux, there is a tensor $e_{\bf T}$ in $\bigotimes^3 V$ that is an element of the straightening basis for $\bigotimes^3 V$ (but, because there are not enough of them, these are not all of the elements of the straightening basis).
		Thus the tensor $P(\sigma_{T'})(e_{\bf T})$ is the element of the straightening basis corresponding to the pair $[{\bf T}, T']$.
		\bigskip The representative tensor $e_{\bf T}$ is the tensor product of $k$ elements of the Grassmann algebra, each of those $k$ elements constructed in turn by taking the wedge product of the basis elements of $V$ with indices from the corresponding row of ${\bf T}$.
	www-cse.ucsd.edu /~gill/Research/StrBasTeX.html (5259 words)

	PlanetMath: scheme (Site not responding. Last check: 2007-11-07)
		In order to extend algebraic geometry to deal with fields that are not algebraically closed, it is necessary to generalize the notions of affine variety and projective variety.
		A scheme in some sense captures the equations defining an algebraic object, so that the points of that object can be examined over many different fields.
		In fact, the points of such an object take a secondary role: this is neccesary because, for example, over a finite field most curves have no points at all until you pass to a suitable field extension.
	planetmath.org /encyclopedia/Scheme.html (654 words)

	Tools of Tensor Calculus
		There is no restriction about the number of coordinate systems (or manifolds...) defined simultaneously, their dimension or the type of the tensor fields.
		Tensor and exterior calculus: tensor product, interior product, symmetrization and antisymmetrization, exterior product, Lie and exterior derivatives.
		TTC can handle explicit tensor calculus (the tensors involved are known linear combinations of a known basis) and symbolic index tensor calculus (the tensors involded are only known through its properties like symmetries of some index and others
	baldufa.upc.es /xjaen/ttc (212 words)

	Tensor product of fields (Site not responding. Last check: 2007-11-07)
		This kind of result can be proved in general using the ramification theory of algebraic number theory.
		Each such field is a representative of an equivalence class of (essentially distinct) field embeddings for K and L in some extension of M. Examples
		K is the product of (a copy) of K, and a splitting field of X
	www.sciencedaily.com /encyclopedia/tensor_product_of_fields (608 words)

	Are Perceptual Fields Quantum Fields (Site not responding. Last check: 2007-11-07)
		We examine a handful of mathematical parallels between the visual field and its concomitant quantum field, and argue for an identity between the two fields.
		Feigl’s “immediately experienced qualities, or their configurations in the various phenomenal fields” might then be identified with ‘observables, or their configurations, in various quantum fields’ - what amounts to a mind/brain identity theory wherein the matter of the brain is viewed at the quantum level.
		This means that independently of the choice of frame of reference, the same field theory is the object of our investigation; changing from one frame to another the fields transform covariantly according to the rule imposed by the principle of relativity.
	www.marilia.unesp.br /atividades/extensao/revista/v3/artigo2.html (8464 words)

	Tensor Field Visualization
		Our technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression and expansion.
		The method is based on two steps: first we define a positive definite metric, with the same topological structure as the tensor field; second, the resulting metric is visualized.
		The eigenvector fields are represented using a texture-based approach resembling LIC methods.
	graphics.cs.ucdavis.edu /~lfeng/research/tensor (194 words)

	vector matrix tensor
		Matrix and tensor constructions from a generic SU(n) vector...
		What is a tensor and can any examples of their use be given?...
		The evaluation of the elastic and piezoelectric tensors with...
	www.scienceoxygen.com /math/511.html (131 words)

	Integral Geometry of Tensor Fields
		This section of integral geometry can be considered as the mathematical basis for tomography of anisotropic media whose interaction with sounding radiation depends essentially on the direction in which the latter propagates.
		A theorem on conjugate tensor fields on the sphere
		Readership: This book will be of value and interest to mathematicians, engineers, computer scientists and physicists who are working in the fields of lightconductor technology, plasma physics, tomography and liquid crystals.
	www.brill.nl /product.asp?ID=10872 (377 words)

	Continuous Tensor Products of Hilbert Spaces and Generalised Random Fields, by R. F. Streater and A. Wulfsohn; current ... (Site not responding. Last check: 2007-11-07)
		Continuous Tensor Products of Hilbert Spaces and Generalised Random Fields, by R. Streater and A. Wulfsohn; current algebras and groups.
		The infinite tensor product is generalised to a tensor product of certain Hilbert spaces over a topological index set.
		The criterion for positivity of characteristic functionals of generalised random processes is used to construct two distinct types of continuous tensor products.
	www.mth.kcl.ac.uk /~streater/wulfsohn.html (195 words)

	Tensor Product Computations (Site not responding. Last check: 2007-11-07)
		A Program that tells whether or not a given 4x1 matrix is factorable into a tensor product of two 2x1 matrices.
		To work the tensor product program, input four different complex numbers into the four Text Fields in the form of a+bi.
		To normalize the vector, press the "Normalize" button, and to clear all the fields, use the "Clear" button.
	www.williams.edu /crypto/applets/Quantum.html (199 words)

	Tensor contraction
		Traceless cartesian tensor forms for spherical harmonic functions: new theorems...
		From Vectors to Tensors (RuÃz-Tolosa)-Springer Linear and Multilinear Algebras,...
		Join Tensors: on 3D-to-3D alignment of Dynamic Sets...
	www.scienceoxygen.com /math/521.html (143 words)

	NCA 110.02 - C. Gauthier: Quantum effects due to extra space multiconnectivity (Site not responding. Last check: 2007-11-07)
		We have shown [3] that this multiconnectivity generates a discontinuous gauge which provides a geometrical interpretation for the apparent discretization of fields, the wave- corpuscle duality and the wave function collapse.
		should be a round number, that is a number which is the product of a considerable number of comparatively small factors ([10], p.
		131 and references therein) is that the restriction of the unified field theory considered here to quantum phenomenology should be exempt of infrared divergence ([15], p.
	www.sif.it /cimento/toca/110.02/04/04.html (4739 words)

	[No title]
		Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Conformally-Optical Metrics: Schwarzschild Black Holes by N.G. Phillips and B.L. Hu.
		After the introduction of early versions of Mathematica, Parker and Christensen began to work together to create a general purpose tensor analysis package that was powerful yet easy-to-learn and use.
		In the early 1990's, MathTensor was introduced as a commercial product licensed to MathSolutions, Inc., a Delaware S-Corporation, with offices in Chapel Hill, North Carolina and Milwaukee, Wisconsin.
	smc.vnet.net /MathTensor.html (496 words)

	what is a tensor - Page 5 - Physics Help and Math Help - Physics Forums
		I notice some dork with my same handle has maintained there is no such thing as a tensor, since "to tensor" is a verb.
		equals the product of the order of the subgroup fixing a point, times the order of the orbit of that point.
		I suspect the tiny handful of group members who have a clue what you've been talking about are already up to their eyebrows in algebra texts.
	www.physicsforums.com /showthread.php?p=316293 (1434 words)

	Amazon.com: Books: Rich Dad, Poor Dad: What the Rich Teach Their Kids About Money--That the Poor and Middle Class Do ... (Site not responding. Last check: 2007-11-07)
		Based on the principle that income-generating assets always provide healthier bottom-line results than even the best of traditional jobs, it explains how those assets might be acquired so that the jobs can eventually be shed.
		Third, experts in the fields he talks about generally agree that his advice is bad.
		Product offered violates Amazon.com's policy on items that can be listed for sale.
	www.amazon.com /exec/obidos/tg/detail/-/0446677450?v=glance (2493 words)

	Love and Tensor Algebra - Stanislaw Lem (Site not responding. Last check: 2007-11-07)
		Where dyads tread the fairy fields of Venn,
		The inverse of my verse, a null domain.
		I hear the tender tensor in thy sigh.
	www.ee.duke.edu /~wrankin/misc/tensor.html (101 words)

	Amazon.com: Finding Nemo (Collector's Edition) (2003): DVD (Site not responding. Last check: 2007-11-07)
		Along the way he hooks up with a scatterbrained blue tang fish named Dory (Ellen DeGeneres), who's both helpful and a hindrance, sometimes at the same time.
		Faced with sharks, deep-sea anglers, fields of poisonous jellyfish, sea turtles, pelicans, and much more, Marlin rises above his neuroses in this wonderfully funny and nonstop thrill ride--rarely does more than 10 minutes pass without a sequence destined to become a theme park attraction.
		Pixar continues its run of impeccable artistic and economic success (their movies include Toy Story, A Bug's Life, Toy Story 2, and Monsters, Inc).
	www.amazon.com /exec/obidos/tg/detail/-/B00005JM02?v=glance (1885 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Energy Citations Database (ECD) Document #6361925 - Confinement through tensor gauge fields
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		For a journal article, please see the Resource Relation field.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=6361925 (112 words)

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