Fock Space Realizations of Imaginary Verma Modules

This work expands to the setting of the results of H. Jakobsen and V. Kac and independently D. Bernard and G. Felder on the realization of , in terms of infinite sums of partial differential operators. We note in the paper that, in the generic case, these geometric constructions are just realizations of the imaginary Verma modules studied by V. Futorny. Presented by A. VerschorenMathematics Subject Classifications (2000) Primary: 17B67, 81R10.     

Problems and prospects in the ab initio treatment of pure and defective crystals

Accurate Hartree-Fock LCAO calculations for moderately complex crystalline systems are now feasible; a number of important applications may be envisaged in the areas of material science and technology. Some critical aspects of the corresponding computer schemes are discussed which are of fundamental importance in determining the cost of the computation. Data are provided concerning actual computations which are indicative of the kind of periodic systems that can (or cannot) be treated at present. The result of a perfect-crystal ab initio HF study can be used as an input for treating with the same approximation local-defect problems, by use of suitable embedding techniques. A scheme of this kind is presented, and its computational implications are discussed: due to the intrinsic complexity of this problem, it may be foreseen that the study of defects in crystals will be a typical application of supercomputers in the area of quantum chemistry.This paper was presented at the International Conference on The Impact of Supercomputers on Chemistry, held at the University of London, London, UK, 13–16 April 1987     

Von Neumann entropy and entropy squeezing of a two-level atom and the superposition of squeezed displaced fock states

The work presents some aspects of studying the two-level atom in a Kerr media interacting with a single-mode electromagnetic field, which is the superposition of squeezed displaced Fock states. We discuss the effect of the new field on quantum entropy and the entanglement of the atom-field system in the two-photon process. The exact results are employed to perform a careful investigation of the temporal entropy evolution. The position and momentum entropy squeezing of the optical field are investigated. The general conclusions obtained are illustrated by numerical results.     

Introductive Backgrounds to Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems

Introductive backgrounds to a new mathematical physics discipline—Quantum Mathematics—are discussed and analyzed both from historical and from analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered. The Authors devote their article to their Friend and Teacher academician Prof. Anatoliy M. Samoilenko on occasion of his 70 years-Birthday with great compliments and gratitude to his brilliant talent and impressive impact to modern theory of nonlinear dynamical systems of mathematical physics and nonlinear analysis     

X-ray and computational structural study of neutral <Emphasis Type="Italic">bis</Emphasis>(<Emphasis Type="Italic">N,N,N</Emphasis>′,<Emphasis Type="Italic">N</Emphasis>′-tetramethylthiophosphoramidoyl)-methylamine

The structure of bis(N,N,N′,N′-tetramethylthiophosphoramidoyl)-methylamine 1 has been determined by single-crystal X-ray diffraction. The compound 1 crystallizes in the monoclinic system, with a space group P2₁/c, a = 11.836(2) Å, b = 11.659(2) Å, c = 12.796(5) Å and β = 95.28(3)°, V = 1758.3(5) Å³ and Z = 4. The X-ray crystallographic data have been assessed by semi-empirical and ab-initio density functional theory and by Hartree–Fock molecular orbital methods. A comparative study of the results of the different methods is given.     

Composition operators on noncommutative Hardy spaces

In this paper we initiate the study of composition operators on the noncommutative Hardy space , which is the Hilbert space of all free holomorphic functions of the form

     

偶数维复Clifford代数中的Dirac旋量空间

本文引入了偶数维欧氏空间的复结构及Witt基,在此基础上讨论了偶数维复Clifford代数中的Dirac旋量空间.由Fock空间的结果我们得到了Dirac旋量空间视为复Clifford代数中极小左理想,最后我们研究了Dirac旋量空间的对偶空间.     

On the Fock space of metaanalytic functions

We develop the theory on the Fock space of metaanalytic functions, a generalization of some recent results on the Fock space of polyanalytic functions. We show that the metaanalytic Bargmann transform is a unitary mapping between vector-valued Hilbert spaces and metaanalytic Fock spaces. A reproducing kernel of the metaanalytic Fock space is derived in an explicit form. Furthermore, we establish a complete characterization of all lattice sampling and interpolating sequence for the Fock space of metaanalytic functions.