Search results for "TENSOR"

Production of a tensor glueball in the reaction γγ → G2π0 at large momentum transfer

2018

Abstract We study the production of a tensor glueball in the reaction γ γ → G 2 π 0 . We compute the cross section at higher momentum transfer using the collinear factorisation approach. We find that for a value of the tensor gluon coupling of f g T ∼ 100 MeV, the cross section can be measured in the near future by the Belle II experiment.

Structure determination to calculate nonlinear optical coefficients in a class of organic material

1999

A class of molecules with intramolecular two-dimensional charge transfer upon excitation has been synthesized. It is expected that these materials should be prospective candidates for nonlinear optical (NLO) applications such as second harmonic (SHG) generation. In order to optimize the macroscopic NLO properties of the compounds, it is necessary to relate their first hyperpolarizability tensors at a molecular level to those at a crystal bulk level. This requires a complete structure determination and refinement. However, the growth of sufficiently large single crystals, which are needed for structural analysis and refinement by x-ray methods, is a time-consuming and sometimes impossible ta…

Tensor decomposition of EEG signals: A brief review

2015

Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposit…

Rotational Raman spectroscopy of ethylene using a femtosecond time-resolved pump-probe technique.

2005

154309; Femtosecond Raman-induced polarization spectroscopy (RIPS) was conducted at low pressure (250 mb at 295 K and 400 mb at 373 K) in ethylene. The temporal signal, resulting from the beating between pure rotational coherences, was measured with a heterodyne detection. The temporal traces were converted to the frequency domain using a Fourier transformation and then analyzed thanks to the D2hTDS software (http://www.u-bourgogne.fr/LPUB/shTDS.html) dedicated to X2Y4 molecules with D2h symmetry. The effective Hamiltonian was expanded up to order 2, allowing the determination of five parameters with an rms of 0.017 cm(-1). Special care was taken in the precise modeling of intensities, taki…

Conformation constraints for efficient viscoelastic fluid simulation

2017

The simulation of high viscoelasticity poses important computational challenges. One is the difficulty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high stiffness of the governing differential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables efficient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric fluids, which defines simple governing equations for a conformation tensor. The model can represent a diverse pa…

Physics, Techniques and Review of Neuroradiological Applications of Diffusion Kurtosis Imaging (DKI)

2016

In recent years many papers about diagnostic applications of diffusion tensor imaging (DTI) have been published. This is because DTI allows to evaluate in vivo and in a non-invasive way the process of diffusion of water molecules in biological tissues. However, the simplified description of the diffusion process assumed in DTI does not permit to completely map the complex underlying cellular components and structures, which hinder and restrict the diffusion of water molecules. These limitations can be partially overcome by means of diffusion kurtosis imaging (DKI). The aim of this paper is the description of the theory of DKI, a new topic of growing interest in radiology. DKI is a higher or…

Dipolar NLO-phores with large off-diagonal components of the second-order polarizability tensor

1997

Mixed intersections of non quasi-analytic classes

2008

Given two semi-regular matrices M and M' and two open subsets O and O' [resp. two compact subsets K and K'] of Rr and Rs respectively, we introduce the spaces E(M×M')(O × O') and D(M×M')(O × O') [resp. D(M×M')(K × K')]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.

Kernel theorems in the setting of mixed nonquasi-analytic classes

2008

Abstract Let Ω 1 ⊂ R r and Ω 2 ⊂ R s be nonempty and open. We introduce the Beurling–Roumieu spaces D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) , D ( M , M ′ } ( Ω 1 × Ω 2 ) and obtain tensor product representations of them. This leads for instance to kernel theorems of the following type: every continuous linear map from the Beurling space D ( ω 1 ) ( Ω 1 ) (respectively D ( M ) ( Ω 1 ) ) into the strong dual of the Roumieu space D { ω 2 } ( Ω 2 ) (respectively D { M ′ } ( Ω 2 ) ) can be represented by a continuous linear functional on D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) (respectively D ( M , M ′ } ( Ω 1 × Ω 2 ) ).

Defining relations of minimal degree of the trace algebra of 3×3 matrices

2008

Abstract The trace algebra C n d over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n , d ⩾ 2 . Minimal sets of generators of C n d are known for n = 2 and n = 3 for any d as well as for n = 4 and n = 5 and d = 2 . The defining relations between the generators are found for n = 2 and any d and for n = 3 , d = 2 only. Starting with the generating set of C 3 d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C 3 d is equal to 7 for any d ⩾ 3 . We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8. The proofs are based …