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Перевод: tensor
[существительное] тензор
Тезаурус:
- We named C as the right Cauchy-Green deformation tensor.
- In fact, it has been shown by Nutku (1981) that the discontinuities in the derivatives of f and g on the boundaries of region IV indicate the presence of an infinite discontinuity in the Ricci tensor on these hypersurfaces.
- This can not be a curvature singularity, since the curvature tensor on it is zero.
- Such a possibility can only arise if the impulsive components of the matter tensor occurring on the boundary of region IV have negative energy density.
- It may be a C k (or C k- ) quasiregular singularity if all components of the Riemann tensor and its first k derivatives evaluated in an orthonormal frame parallel propagated along an incomplete geodesic ending at q are C (or C 0- ).
- This scheme describes the singularity structure of a space-time on which the Riemann tensor is C k .
- We define a Cartesian tensor of second rank as any quantity which transforms under the change of axes governed by the direction cosines in the following way:
- The non-vanishing terms represent the components of a rotation vector (more properly an anti-symmetric tensor) and a general deformation consists of terms such as which cause changes of length and which cause rotations.
- Dipole studies, least-squares fitting of predicted and observed peculiar velocities and the analysis of the covariance tensor of reconstructed differential motions give , and , respectively.
- The components of the Weyl tensor are initially all zero.
- Also the fold singularities in regions II and III that have a topological character, are quasiregular singularities since on them the curvature tensor is zero.
- No curvature scalars diverge in this case, yet some components of the Riemann tensor evaluated in a PPON frame along an incomplete curve do not tend to finite limits as the singularity is approached.
- Following an elegantly presented critique of the physical foundations of the theory, he introduces the mathematics (affine tensor analysis) that is required for the full formulation of the theory.
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