Filter Diagonalization with Finite Fourier Transform Eigenfunctions

Below, we briefly report on the progress in the development of the Filter Diagonalization technique when filtering is carried out with the aid of Finite Fourier Transform (FFT) eigenfunctions. During recent years interest in these functions, also known as ‘prolates’, or ‘slepians’, has increased among scientists doing research in the field of signal processing. The main explanation to this follows from the set of very special extremal and orthogonality properties exibited by the FFT eigenfunctions. Recent results of Walter and Shen on sampling with prolate spheroidal functions will necessary produce a new wave of interest. In the presented, Filter diagonalization machinery, we show that the sampling formula of Walter and Shen simplifies essentially the computation of matrix elements as certain 2D–integrals involving FFT eigenfunctions.     

First findings of monocrystalline aragonite inclusions in garnet from diamond-grade UHPM rocks (Kokchetav Massif, Northern Kazakhstan)

The crystal field effect and microscopic origins of the Zeeman g-factors g(//) and g(⊥) for (6)S(3d(5)) state ions at tetragonal symmetry crystal filed, taking into account the spin-spin (SS), the spin-other-orbit (SOO), and the orbit-orbit (OO) magnetic interactions besides the well-known spin-orbit (SO) magnetic interaction, have been investigated using the microscopic spin Hamiltonian theory and the complete diagonalization method (CDM). It is found that the g(//)(±1/2)≠g(//)(±5/2) and g(⊥)(±1/2)≠g(⊥)(±5/2), where the g-factors g(//)(±1/2) and g(⊥)(±1/2) express the g-factors of the ground state |M?(s)=±1/2), whereas the g-factors g(//)(±5/2) and g(⊥)(±5/2) express the g-factors of the ground state |M?(s)=±5/2). It is shown that although the SO magnetic interaction is the most important one, the contributions to the shifts of g-factors Δg(//)(=2.0023-g(//)) and Δg(⊥)(=2.0023-g(⊥)) from other three magnetic interactions including the SS, SOO, and OO magnetic interactions are appreciable and should not be omitted, especially for the shifts of g-factors Δg(//)(±5/2) and Δg(⊥)(±5/2). The individual contributions to the shifts of g-factors arising from the spin quartet states and spin doublet states have been studied. The investigations show that the Δg(//)(±1/2) and Δg(⊥)(±1/2) primarily result from the spin quartet states, whereas Δg(//)(±5/2) and Δg(⊥)(±5/2) from the spin quartet states as well as the combined effects between the spin quartet states and the spin doublet states. The contribution to the shifts of g-factors from the net spin doublet states is zero.     

Cr3+：MgAl2O4晶体EPR参量及其电子精细光谱的研究

考虑了SS(Spin-Spin)作用和SOO(Spin-Other-Orbit)作用，采用完全对角化方法，结合自旋Hamiltonian理论，研究了Cr³⁺∶MgAl₂O₄晶体EPR参量及其吸收光谱，理论与实验符合甚好. 在此基础上，进一步研究了⁴A₂(3d³)离子EPR参量的微观起源. 研究表明，EPR参量起源于四种微观机制：(1) SO(Spin-Orbit) 耦合机制；(2) SS耦合机制；(3)SOO耦合机制；(4) SO～SS～SOO总联合作用机制. 在这些机制中，SO机制是最主要的.     

Cauchy problems for linear thermoelastic systems of type III in one space variable

The goal of the paper is to analyse properties of solutions for linear thermoelastic systems of type III in one space variable. Our approach does not use energy methods, it bases on a special diagonalization procedure which is different in different parts of the phase space. This procedure allows to derive explicit representations of solutions. These representations help to prove results for well‐posedness of the Cauchy problem, L^P–L^q decay estimates on the conjugate line and results for propagation of singularities. Copyright © 2005 John Wiley & Sons, Ltd.     

SINGULAR PERTURBATION OF TWO─POINT BOUNDARY VALUE PROBLEM FOR NONLINEAR SYSTEM

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＴＷＯ─ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＣｈｅｎＹｕｓｈｅｎ（陈育森）（ＦｕｊｉａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙＦｕｑｉｎｇＢｒａｎｃｈ，福建师范大...     

Phase transitions and reflection positivity for a class of quantum lattice systems

We prove a form of reflection positivity in planes containing sites for a class of quantum lattice systems. As an application, a proof is given of a phase transition for the Fisher-stabilized Ising antiferromagnet in an external magnetic field with parallel and transverse components, both by the method of infrared bounds and by a suitable version of the Peierls argument. We also discuss the spherical model in an appendix.     

Convergence Analysis of the Block Householder Block Diagonalization Algorithm

This paper develops algebraic and convergence properties of the left and right block reflectors used in the block diagonalization algorithm. Several numerical illustrations are reported.AMS subject classification (2000) 65F20, 15A23.Submitted December 2002. Accepted October 2003. Communicated by Per Christian Hansen.     

Acceleration of self-consistent-field convergence by combining conventional diagonalization and a diagonalization-free procedure

A new scheme that combines conventional matrix diagonalization with the recently proposed diagonalization-free algorithm has been developed to obtain the density matrix for the next self-consistent-field iteration from the Fock matrix of the current iteration. In this manner, the advantages of the two methods are combined. The more rapid convergence of the diagonalization-free algorithm for density matrices rather close to self consistence and the more robust convergence of the conventional matrix diagonalization further away from self-consistence. The scheme has been implemented in the one- and two-component self-consistent-field procedures in the program system TURBOMOLE. The number of iterations is typically reduced by about 10%, but savings are usually much larger for slowly converging cases.