We now come to the persistent field appearing in the 2nd rank

tensor field equations when matter is absent.

Generally, the vanishing of

tensor field h means that the Reeb foliation of [M.

Now we recall from a paper of Hall-da Costa [28] that the existence of a covariant constant second-order

tensor field, other than the metric tensor, must exclude some spacetimes, in particular, perfect fluids.

Then, we prove precise results regarding the definition of the Hilbert

tensor field (Theorem 1).

where [LAMBDA] is a fourth order tensor, called the mobility tensor which is essentially the inverse of the relaxation time of the polymer fluids, c is the conformation tensor, [rho] is the fluid density, Q is anisotropic viscosity matrix that is related to viscous dissipation, L is coupling parameter between the velocity gradient field and the structural

tensor field, and A is Helmholtz free energy function represented by a combination of invariants of the conformation tensor, which can be written as follows based on the Hookean model:

An n-dimensional differentiable manifold M is said to admit an almost para-contact Riemannian structure ([phi], [xi], [eta], g), where [phi] is a (1, 1)

tensor field, [xi] is a vector field, [eta] is a 1-form and g is a Riemannian metric on M such that

tau]] of the vector field Z represents the controlled process (it is also possible to replace it by a transport of an arbitrary

tensor field along the flow [c.

where a, b, c, d are scalars of which b [not equal to] 0, c = 0, d [not equal to] 0 and A, B are two non-zero 1-forms such that A(X) = g(X,U) and B(X) = g(X, V); U, V being mutually orthogonal unit vector fields and D is a symmetric (0, 2) type

tensor field with zero trace which satisfies the condition D(X, U) = 0, [for all]X.

n] = (M, g) where g (the fundamental tensor) is a distinguished

tensor field on [?

denote the Christoffel symbols of the first type attached to tensor f and if we introduce the distinguished

tensor fieldIn 1968 Yano and Sawaki (10) defined and studied a

tensor field W of type (1, 3) which includes both the conformal curvature tensor C and the concircular curvature tensor [~.

A sampling of paper topics includes real-time hand gesture recognition system based on Q6455 DSP board, a model of data reduction based on

tensor field, fast path searching in real time 3D game, and policy-gradient based actor-critic algorithms.