Yang's model as triply special relativity and the Snyder's model–de Sitter special relativity duality

We show that if Yang's quantized space–time model is completed at both classical and quantum level, it should contain both Snyder's model, the de Sitter special relativity and their duality.     

Fabrication of uniform porous alumina materials by radio frequency (RF) magnetron sputtering

Fabrication of porous materials with uniform pore size distribution remains a challenge. In this paper, a kind of uniform porous alumina material was fabricated on a template of polystyrene microspheres by radio frequency (RF) magnetron sputtering. Surface of samples was observed by scanning electron microscopy (SEM), and the phase of porous materials was confirmed by X-ray diffraction (XRD). The pore size distribution of samples was tested by mercury intrusion method.     

Complete classification of the direction loci for three-wave collinear quadratic parametric interactions in biaxial acentric crystals

One new topological classification of the phase-matching direction loci for sum/difference frequency generation in biaxial acentric crystals is presented. Based on nine fundamental axial wave constant mismatches, 12 locus indices are used to distinguish permissible direction loci. Totally 66 kinds of combined loci belonging to 30 main classes are found and categorized by a set of ternary-digit class symbols or equivalently by sequence numbers. They are well illustrated in a classification diagram, indicative of 170 possible transitions among the loci. By an analysis of the dispersion of refractive indices, the historic “optically well-behaved crystals” are redefined and improved with simplified classification diagrams and corresponding schematic stereographic projections.     

POSITIVE SOLUTION TO THREE-ORDER BOUNDARY VALUE PROBLEM WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE

By cone theory and the fixed point index,we study the existence of positive solutions to a three-order boundary value problem with dependence on the first order derivative.     

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded degree.The results generalize the analogous results on a homogeneous tree.     

Stability and bifurcation in a discrete system of two neurons with delays

In this paper, we consider a simple discrete two-neuron network model with three delays. The characteristic equation of the linearized system at the zero solution is a polynomial equation involving very high order terms. We derive some sufficient and necessary conditions on the asymptotic stability of the zero solution. Regarding the eigenvalues of connection matrix as the bifurcation parameters, we also consider the existence of three types of bifurcations: Fold bifurcations, Flip bifurcations, and Neimark–Sacker bifurcations. The stability and direction of these three kinds of bifurcations are studied by applying the normal form theory and the center manifold theorem. Our results are a very important generalization to the previous works in this field.     

AOR iterative methods for rank deficient least squares problems

In this paper we study the semiconvergence of accelerated overrelaxation (AOR) iterative methods for the least squares solution of minimal norm of rank deficient linear systems. Necessary and sufficient conditions for the semiconvergence of the AOR and JOR iterative methods are given. The optimum parameters and the associated convergence factor are derived.     

Fractional Lévy processes on Gel’fand triple and stochastic integration

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel’fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.      

Z-矩阵的预条件方法

通过对方程组Ax=b的系数矩阵施行初等行变换，该文提出了解线性方程组Ax=b的一种新的预条件Gauss Seidel迭代方法，理论上证明了新的预条件Gauss Seidel迭代方法较经典的Gauss Seidel迭代法收敛速度快. 该文提出的新预条件方法推广了文［1-2］中提出的预条件方法，具体的数值例子说明了新预条件方法的有效性.