Search results for "TENSOR"

Tensor product characterizations of mixed intersections of non quasianalytic classes and kernel theorems

2009

Mixed intersections of non quasi-analytic classes have been studied in [12]. Here we obtain tensor product representations of these spaces that lead to kernel theorems as well as to tensor product representations of intersections of non quasi-analytic classes on product of open or of compact sets (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Remarks on (Q, P, Y)-Summing Operators

2003

Abstract unavailable at this time... Mathematics Subject Classification (1991): 47B10. Key words: Summing operators; injective tensor product. Quaestiones Mathematicae 26(2003), 97-103

Invertibility in tensor products of Q-algebras

2002

Vectors, Tensors, Manifolds and Special Relativity

2015

Assuming that the reader is familiar with the notion of vectors, within a few pages, with a few examples, the reader will get to be familiar with the generic picture of tensors. With the specific notions given in this chapter, the reader will be able to understand more advanced tensor courses with no further effort. The transition between tensor algebra and tensor calculus is done naturally with a very familiar example. The notion of manifold and a few basic key aspects on Special Relativity are also presented.

Equivalences involving (p,q)-multi-norms

2014

A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches

2015

We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying co…

The Bernstein Basis and its applications in solving geometric constraint systems

2012

International audience; This article reviews the properties of Tensorial Bernstein Basis (TBB) and its usage, with interval analysis, for solving systems of nonlinear, univariate or multivariate equations resulting from geometric constraints. TBB are routinely used in computerized geometry for geometric modelling in CAD-CAM, or in computer graphics. They provide sharp enclosures of polynomials and their derivatives. They are used to reduce domains while preserving roots of polynomial systems, to prove that domains do not contain roots, and to make existence and uniqueness tests. They are compatible with standard preconditioning methods and fit linear program- ming techniques. However, curre…

Classifying Healthy Children and Children with Attention Deficit through Features Derived from Sparse and Nonnegative Tensor Factorization Using Even…

2010

In this study, we use features extracted by Nonnegative Tensor Factorization (NTF) from event-related potentials (ERPs) to discriminate healthy children and children with attention deficit (AD). The peak amplitude of an ERP has been extensively used to discriminate different groups of subjects for the clinical research. However, such discriminations sometimes fail because the peak amplitude may vary severely with the increased number of subjects and wider range of ages and it can be easily affected by many factors. This study formulates a framework, using NTF to extract features of the evoked brain activities from time-frequency represented ERPs. Through using the estimated features of a ne…

Three-dimensional architecture of the whole human soleus muscle

2018

Background Most data on the architecture of the human soleus muscle have been obtained from cadaveric dissection or two-dimensional ultrasound imaging. We present the first comprehensive, quantitative study on the three-dimensional anatomy of the human soleus muscle in vivo using diffusion tensor imaging (DTI) techniques. Methods We report three-dimensional fascicle lengths, pennation angles, fascicle curvatures, physiological cross-sectional areas and volumes in four compartments of the soleus at ankle joint angles of 69 ± 12° (plantarflexion, short muscle length; average ± SD across subjects) and 108 ± 7° (dorsiflexion, long muscle length) of six healthy young adults. Microdissection and …

Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level.

2007

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing …