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	Tensor Information - tensor lamps
		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 of the brain.
		While tensors can be represented by multi-dimensional arrays of components, the point of having a tensor theory is to explain further implications of saying that a quantity is a tensor, beyond specifying that it requires a number of indexed components.
		Examples of physical tensors are the tensor analysis tensor fasciae latae energy-momentum tensor, the inertia tensor and the polarization tensor.
	www.inanot.com /Ina-Electronics_Topics_T-/Tensor.html (1961 words)

	Tensor - Gurupedia
		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.
		The "components" of the tensor are the indices of the array.
		This treatment has largely replaced the component-based treatment for advanced study, in the way that the more modern component-free treatment of vectors replaces the traditional component-based treatment after the component-based treatment has been used to provide an elementary motivation for the concept of a vector.
	www.gurupedia.com /t/te/tensor.htm (1125 words)

	Tensor field Info - Bored Net - Boredom (Site not responding. Last check: 2007-10-12)
		The general idea of tensor field combines the requirement of richer geometry - for example an ellipse varying from point to point - with the idea that we don't want our notion to depend on the particular method of mapping the surface.
		Since the tensor product concept is independent of any choice of basis, taking the tensor product of two vector bundles on M is routine.
		Starting with the tangent bundle - the bundle of tangent spaces - the whole apparatus explained at component-free treatment of tensors carries over in a routine way - again independently of co-ordinates, as mentioned in the introduction.
	www.borednet.com /e/n/encyclopedia/t/te/tensor_field.html (425 words)

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	Wikinfo \| Tensor
		In mathematics, a tensor is a certain kind of geometrical entity which generalizes the concepts of scalar, vector (spatial) and linear operator in a way that is independent of any chosen frame of reference.
		The tensor calculus achieved broader acceptance with the introduction of Einstein's theory of general relativity, around 1915, which is formulated completely in the language of tensors.
		The classical approach views tensors as multidimensional arrays that are n-dimensional generalizations of scalars, 1-dimensional vectors and 2-dimensional matrices.
	www.wikinfo.org /wiki.php?title=Tensor (1140 words)

	Nonlinear optical materials - Patent 5173546
		Component (I) of the present invention also includes di- or polyepoxides of aliphatic or cycloaliphatic compounds containing more than one epoxidizable unsaturated group, for example, the diepoxides of cyclohexadiene, butadiene and the like.
		The nonlinear optical response of a polymer is determined by the susceptibility of the polymer to polarization by an oscillating electromagnetic field.
		The most important polarization components of a medium in contact with an electric field are the first order polarization components, i.e., the linear polarization, the second order polarization, i.e., the first nonlinear polarization, and the third order polarization, i.e., the second nonlinear polarization.
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	Euclidean Tensors
		The 23 component of the antisymmetric tensor is the same as the 1 component of c, for example.
		If the components of an antisymmetric tensor are the infinitesimal velocities of points of a fluid relative to a certain point, then the associated vector is twice the infinitesimal angle of angular velocity of rotation, the vorticity, and is a pseudovector.
		Tensor analysis was developed by Ricci and others to work with Riemannian spaces, and was applied to the theory of relativity, especially the General Theory.
	www.du.edu /~jcalvert/math/eucltens.htm (5403 words)

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	Reference.com/Encyclopedia/Tensor field
		It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences and engineering.
		The general idea of tensor field combines the requirement of richer geometry — for example an ellipsoid varying from point to point, in the case of a metric tensor — with the idea that we don't want our notion to depend on the particular method of mapping the surface.
		A tensor density is the special case where L is the bundle of densities on a manifold, namely the determinant bundle of the cotangent bundle.
	www.reference.com /browse/wiki/Tensor_field (1764 words)

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		On the other hand, it is seen that when conventional vane tensors supplied by A Co. and B Co. are used, the number of fluffs is prominently increased with increase of the twisting tension.
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	Question about cause of curvature of spacetime Text - Physics Forums Library
		The number of components depends on the dimension of the space - and there are 16 non-unique components for a 4-dimensional rank-2 tensor.
		But ultimately, a tensor is a specific mathematical (in fact geometric) object whose components (and basis vectors) transform in a specific way.
		And the stress-energy tensor, which is something that exists regardless of a co-ordinate basis is spcified by 10 different components.
	www.physicsforums.com /archive/index.php/t-113730.html (1365 words)

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		Classical treatment of tensors - The following is a component-based "classical" treatment of tensors.
		See Component-free treatment of tensors for a modern abstract treatment, and Intermediate treatment of tensors for an approach which bridges the two.
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		The inertia tensor in the dynamics of rigid bodies is an excellent example of a rank-2 tensor where the associated ellipsoid aids in the visualization of the motion.
		Also, since the component of the angular velocity in the direction of the angular momentum is constant, the distance d from the origin O to the tangent plane is constant.
		From the equation giving the stress tensor in terms of the strain tensor, k and μ, find the relation between the traces of the strain and stress tensors, and from this the equation giving the strain tensor in terms of the stress tensor.
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	Intermediate treatment of tensors - Wikipedia, the free encyclopedia
		Similarly, a given numerical representation of a tensor only makes sense in a particular coordinate system.
		It is for this reason that the superscript indices of a vector are called contravariant.
		The transformation rule for covector components is covariant.
	en.wikipedia.org /wiki/Intermediate_treatment_of_tensors (1112 words)

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