Tensor product semigroups

Structure tensors are used in several PDE-based methods to estimate information on the local structure in the image, such as edge orientation. They have become a common tool in many image processing applications. To integrate the local data information, the structure tensor is based on a local regularization of a tensorial product. In this paper, we propose a new regularization model based on the non-local properties of the tensor product. The resulting non-local structure tensor is effective in the restitution of the non homogeneity of ...

We analyze the boundary element Galerkin method for weakly singular andhypersingular integral equations of the first kind on open surfaces. We show thatthe hp-version of the Galerkin method with geometrically refined meshes convergesexponentially fast for both integral equations. The proof of this fast convergence isbased on the special structure of the solutions of the integral equations which possessspecific singularities at

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V⊗k. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V⊗k are isomorphic to the categories of weak, weak admissible and ordinary V-modules, respectively. The main result is an explicit construction of the weak g-twisted V⊗k-modules from weak V-modules. For an arbitrary permutation automorphism g of V⊗k the category of weak admissible g-twisted modules for V⊗k is semisimple and the simple objects are determined if V is rational. In addition, we extend these results to the more general setting of γg-twisted V⊗k-modules for γ a general automorphism of V acting diagonally on V⊗k and g a permutation automorphism of V⊗k.

Tensor product decompositions with optimal separation rank provide an interesting alternative to traditional Gaussian-type basis functions in electronic structure calculations. We discuss various applications for a new compression algorithm, based on the Newton method, which provides for a given tensor the optimal tensor product or so-called best separable approximation for fixed Kronecker rank. In combination with a stable quadrature scheme for the Coulomb interaction, tensor product formats enable an efficient evaluation of Coulomb integrals. This is demonstrated by means of best separable approximations for the electron density and Hartree potential of small molecules, where individual components of the tensor product can be efficiently represented in a wavelet basis. We present a fairly detailed numerical analysis, which provides the basis for further improvements of this novel approach. Our results suggest a broad range of applications within density fitting schemes, which have been recently successfully applied in quantum chemistry.

We investigate the possibility of transforming, under local operations and classical communication, a general bipartite quantum state on a d A x d B tensor-product space into a final state in 2 x 2 dimensions, while maintaining as much entanglement as possible. For pure states, we prove that Nielsen’s theorem provides the optimal protocol, and we present quantitative results on the degree of entanglement before and after the dimensional reduction. For mixed states, we identify a protocol that we argue is optimal for isotropic and Werner states. In the literature, it has been conjectured that some Werner states are bound entangled and in support of this conjecture our protocol gives final states without entanglement for this class of states. For all other entangled Werner states and for all entangled isotropic states some degree of free entanglement is maintained. In this sense, our protocol may be used to discriminate between bound and free entanglement.

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.

We show how to reduce free independence to tensor independence in the strong sense. We construct a suitable unital *-algebra of closed operators `affiliated' with a given unital *-algebra and call the associated closure `monotone'. Then we prove that monotone closed operators of the form $$ X'= \sum_{k=1}^{\infty}X(k)\bar{\otimes} p_{k}, X''=\sum_{k=1}^{\infty} p_{k}\bar{\otimes}X(k) $$ are free with respect to a tensor product

control has been lost [4]. In order to extend the flight envelope a common approach is gain scheduling. In which several linear models of the quadrotor are obtained for different trim points and then number of Liner Time Invariant (LTI) controllers are derived for each point. As operating conditions vary, the global controller is estimated by interpolating gains of the

This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space'' and its rational powers. Positive spaces are 1-dimensional ``semi-vector spaces'' without the zero vector. A direct approach to this subject might be sufficient. On the other hand, a broader mathematical understanding requires

Abstract Given two semi-regular matricesM andM′ and two open subsets Ω and Ω′[resp. two compact subsetsK andK′] of ℝ r and ℝ s respectively, we introduce the spacesE (M× M′)(Ω× Ω′) andD (M× M′)(Ω× Ω′)[resp. D (M× M′)(K× K′)]. In this paper we study ...