‎‎The tensor product is the fundemental ingredient for extending one-dimensional techniques of filtering and compression in signal preprocessing to higher dimensions‎. ‎Woven frames play ‎ a crucial role in signal preprocessing and distributed data processing‎. Motivated by these facts, we have investigated the tensor product of woven frames and presented some of their properties. Besides...

Computing the electromagnetic fields produced by an aboveground radiating antenna has been one of the most basic problems in radioengineering for the past century. If the antenna in question is a dipole (i.e., it can be thought of as a pair of electric charges of equal magnitude but opposite sign, separated by some relatively small time-varying distance), the radiated fields are given by the so...

the ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, linton and banaschewski with nelson defined and studied the tensor product in an equational category and in a general (concrete) category k, respectively, using bimorphisms, that is, defined via the hom-functor on k. also, the so-called sesquilinear, or on...

‎the object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎at first we prove that a quasi-conformally flat spacetime is einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎einstein's field equation with cosmological constant is covariant constant‎. ‎next‎, ‎we prove that if the perfect...

In this paper instability of planar anisotropic sheet metal during a few forming processes is investigated for the first time. For this reason components of the constitutive tangent tensor for planar anisotropic sheets are developed. By using the above tensor location of necking is predicted. Direction of the shear band is also predicted using the acoustic tensor. A finite element program is pr...

We present a new numerical scheme to solve efficiently scattering problems involving an elongated and flat heterogeneous dielectric material assumed be invariant along direction of space. The technique consists compressing the integral operators integro-differential formulation with so-called quantized tensor train (QTT) algorithm whose use is rather original in this context. show that it allow...

It is shown that the set of equations known as “Maxwell’s equations” perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing topological defects as dislocations and disclinations, in the case of constant and homogenous expansion. The analogy between these two physical system...