Search results for "TENSOR"
showing 10 items of 550 documents
Tensor Operators and the Wigner-Eckart Theorem
2007
In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant an…
Intrinsic characterization of space‐time symmetric tensors
1992
This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.
Annihilators of tensor density modules
2007
Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …
Théorie des spectres rovibroniques des molécules octaédriques : Hamiltonien et moments de transition
2002
This thesis is devoted to the treatment of rovibronic couplings of octahedral species for which the Born-Oppenheimer approximation is broken down. By using the octahedral formalism, a full effective rovibronic model is extended from works about molecules in a non-degenerate electronic state. This effective model is dedicated to molecules with an odd or an even number of electrons and it has been successfully applied to V(CO)6 and ReF6. For both of them we have four interacting vibronic sublevels attributed to a dynamical Jahn-Teller effect and giving rise to very complicated spectra. This model is validated by the overall agreement between predicted and observed band profiles. Moreover, an …
Rekurento neironu tīklu novērtēšanas sistēma
2021
Darba “Rekurento neironu tīklu novērtēšanas sistēma” ietvaros tika izstrādāta sistēma, kurā var uztrenēt rekurento neironu tīklu arhitektūras uz dažādiem uzdevumiem, tām automātiski piemeklējot optimālos tīkla parametrus, un pārbaudīt uz tiem sasniegtos rezultātus, ar mērķi objektīvi novērtēt konkrēta rekurentā neironu tīkla efektivitāti. Sistēmu ir paredzēts lietot dziļās mašīnmācīšanās pētniecībā, jaunu rekurento neironu tīklu izstrādē un testēšanā, lai noteiktu vai jaunizveidotie neironu tīkli ir labāki par jau eksistējošajiem uz konkrētiem uzdevumiem.
MuLiMs-MCoMPAs: A Novel Multiplatform Framework to Compute Tensor Algebra-Based Three-Dimensional Protein Descriptors
2019
This report introduces the MuLiMs-MCoMPAs software (acronym for Multi-Linear Maps based on N-Metric and Contact Matrices of 3D Protein and Amino-acid weightings), designed to compute tensor-based 3D protein structural descriptors by applying two- and three-linear algebraic forms. Moreover, these descriptors contemplate generalizing components such as novel 3D protein structural representations, (dis)similarity metrics, and multimetrics to extract geometrical related information between two and three amino acids, weighting schemes based on amino acid properties, matrix normalization procedures that consider simple-stochastic and mutual probability transformations, topological and geometrical…
More on Diagrams
2017
The aim of this chapter is to introduce and study additional structures on a diagram such that its diagram category becomes a rigid tensor category. The assumptions are tailored to the application to Nori motives.
On the vibrations of a mechanically based non-local beam model
2012
The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …
A mechanically based approach to non-local beam theories
2011
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…
On inductive dimensions for fuzzy topological spaces
1995
An approach to the dimension theory for fuzzy topological spaces is being developed. The appropriate context for this theory is not the category CFT of Chang fuzzy topological spaces or some of its modifications, but the category Hut introduced in the paper (this category is a slight extension of the category H of Hutton fuzzy topological spaces Hutton (1980). The frames of this category allow us to make exposition simple and uniform, and on the other hand to make it applicable in quite a general setting.