Spatial decay estimates for heat-conducting fluids

Received August 29, 2001 / Published online November 15, 2001     

A fast method to block-diagonalize a Hankel matrix

In this paper, we consider an approximate block diagonalization algorithm of an n×n real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a new fast approach to compute the factorization in O(n ²) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511–523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur complementation adapted to the n×n real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness of our approach.     

Thermodynamic stability,critical points,and phase transitions in the theory of partial distribution functions

We consider the stability of the minimum of the thermodynamic potential treated as a functional of partial densities or correlation functions. We show that the loss of stability is related to critical points of thermodynamic functions. Curves or points of phase transitions of the first kind are determined by comparing the thermodynamic potentials of different phases, and the condition for loss of stability with respect to density fluctuations can be taken as the phase transition criterion only approximately. Phase transitions of the second kind are related to the loss of stability with respect to the pair correlation fluctuations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 512–523, June, 2008.     

On numerical approximation using differential equations with piecewise-constant arguments

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for stability and oscillation of a class of linear delay equations with continuous and piecewise constant arguments. This research was partially supported by Hungarian NFSR Grant No. T046929.     

四角对称晶场中3d3离子零场分裂理论研究

分别采用完全对角化方法和微扰方法讨论了微小磁相互作用对四角对称下基态⁴B₁态和第一激发态²E 态零场分裂的影响. 结果表明,⁴B₁态零场分裂与微小磁相互作用参量成线性关系,²E 态零场分裂主要由二重态决定,磁相互作用和四角晶场对²E 态零场分裂的贡献相比较,四角晶场的作用是主要的.     

矩阵对角化方法研究~(40)Ca~(35)Cl分子的超精细结构

采用矩阵对角化方法计算了~(40)Ca~(35)Cl分子的超精细结构能级,借助有效哈密顿算符获得了~(40)Ca~(35)Cl分子基态超精细能级的本征值.计算结果表明,得到的跃迁光谱数据与实验值符合的很好,误差仅在0 k Hz～90 k Hz,并好于之前的理论计算值.希望这些数据能为以后激光冷却~(40)Ca~(35)Cl分子提供有力的理论依据.     

OSCILLATION CRITERIA FOR SECOND ORDER DIFFERENCE EQUATIONS OF NEUTRAL TYPE WITH MIXED ARGUMENTS

In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.     

Advanced differential equations with nonlinear boundary conditions

We investigate the existence of solutions for advanced differential equations with nonlinear boundary conditions. Sufficient conditions when the problem has extremal solutions or a unique solution are formulated. Linear advanced differential inequalities are also discussed.     

三个非全同耦合谐振子哈密顿量的退耦合

对于哈密顿量为H＝∑^3i=11/2miP^2i 1/2k1(q2-q1-q0)^2 1/2k2(q3-q2-q0)^2的三个非全同耦合振子，我们打到一个方法使其对角化，给出了体系坐标和动量的变换式。