Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416–422]. Given mth-order, n-dimensional realvalued symmetric tensors A and B, the goal is to find λ ∈ R and x ∈ Rn,x = 0 such that Axm−1 = λBxm−1. Different choices ...

The impact of Lorentz violation on the dynamics of a scalar field is investigated. In particular, we study the dynamics of a scalar field in the scalar-vector-tensor theory where the vector field is constrained to be unity and time like. By taking a generic form of the scalar field action, a generalized dynamical equation for the scalar-vector-tensor theory of gravity is obtained to describe th...

In the past few years, successive improvements of the asymptotic complexity of square matrix multiplication have been obtained by developing novel methods to analyze the powers of the Coppersmith-Winograd tensor, a basic construction introduced thirty years ago. In this paper we show how to generalize this approach to make progress on the complexity of rectangular matrix multiplication as well,...

Let V be the standard two-dimensional representation of the algebraic group G = SL(2,C), and write Vn = SymnV for the irreducible (n+1)-dimensional representation of G on the nth symmetric tensor power of V . Also write Wn = V ⊗n for the nth tensor power of V (which has dimension 2n). Then, as virtual representations, it is known that each Vn can be written in terms of W0, . . . , Wn as Vn = Wn...

We compute the power spectra in the cosmic microwave background and cold dark matter (CDM) fluctuations seeded by strings, using the largest string simulations performed so far. We find that local strings differ from global defects in that the scalar components of the stress-energy tensor dominate over vector and tensor components. This result has far reaching consequences. We find that cosmic ...

‎‎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...

Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors. A higher-order generalized singular value decomposition technique successfully captures the common features of the same organ from multiple animals in genomi...

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...