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A metric tensor is a (symmetric) (0, 2)-tensor; it is thus possible to contract an upper index of a tensor with one of the lower indices of the metric tensor in the product. This produces a new tensor with the same index structure as the previous tensor, but with lower index generally shown in the same position of the contracted upper index.
the tensor of two diagrams as the composition of whiskerings ′ = (′) ′. Note that because the diagram is in generic form (i.e. each layer contains exactly one box) the definition of tensor is necessarily biased: the diagram on the left hand-side comes above the one on the right-hand side.
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems [1] and fluids. [ 2 ] [ 3 ] Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties.
The strain rate tensor E(p, t) is symmetric by definition, so it has only six linearly independent elements. Therefore, the viscosity tensor μ has only 6 × 9 = 54 degrees of freedom rather than 81. In most fluids the viscous stress tensor too is symmetric, which further reduces the number of viscosity parameters to 6 × 6 = 36.
Others like CamStudio can be used to record the screen activity. [2] The most popular pieces of slide producing software are Microsoft PowerPoint, Prezi, Apple Keynote, Google Slides and ClearSlide. [3] PowerPoint is currently the most popular slides presentation program. LibreOffice Impress is a FOSS alternative.
In combination with polarizers, it can be used as a shutter or modulator. The values of K depend on the medium and are about 9.4×10 −14 m·V −2 for water, [citation needed] and 4.4×10 −12 m·V −2 for nitrobenzene. [10] For crystals, the susceptibility of the medium will in general be a tensor, and the Kerr effect produces a ...
In mathematics, a tensor is a certain kind of geometrical entity and array concept. It generalizes the concepts of scalar , vector and linear operator , in a way that is independent of any chosen frame of reference .
A dyadic tensor T is an order-2 tensor formed by the tensor product ⊗ of two Cartesian vectors a and b, written T = a ⊗ b.Analogous to vectors, it can be written as a linear combination of the tensor basis e x ⊗ e x ≡ e xx, e x ⊗ e y ≡ e xy, ..., e z ⊗ e z ≡ e zz (the right-hand side of each identity is only an abbreviation, nothing more):