Approximation by a class of modified Szász-Durrmeyer operators

We modify Szász-Durrmeyer operators by means of three-diagonal generalized matrix which overcomes a difficulty in extending a Berens-Lorentz result to the Szász-Durrmeyer operators for second order of smoothness. The direct and converse theorems for these operators inL _p are also presented by Ditzian-Totik modulus of smoothness.This project is supported by Zhejiang Provincial Foundation of China.     

Compensated Compactness, Paracommutators, and Hardy Spaces

LetB₁: ⁿ× ^N₁→ ^m₁,B₂: ⁿ× ^N₂→ ^m₂andQ: ^m₂→ ^m₁be bilinear forms which are related as follows: ifμandνsatisfyB₁(ξ, μ)=0 andB₂(ξ, ν)=0 for someξ≠0, thenμ^τQν=0. Supposep⁻¹+q⁻¹=1. Coifman, Lions, Meyer and Semmes proved that, ifuL^p( ⁿ) andvL^q( ⁿ), and the first order systemsB₁(D, u)=0,B₂(D, v)=0 hold, thenu^τQvbelongs to the Hardy spaceH¹( ⁿ), provided that both (i)p=q=2, and (ii) the ranks of the linear mapsB_j(ξ, ·) : ^N_j→ ^m₁are constant. We apply the theory of paracommutators to show that this result remains valid when only one of the hypotheses (i), (ii) is postulated. The removal of the constant-rank condition whenp=q=2 involves the use of a deep result of Lojasiewicz from singularity theory.     

Medium-range structural order in liquid Ni20Al80 alloy: Experimental and molecular dynamics studies

In this Letter, structural properties of liquid Ni₂₀Al₈₀ have been studied through molecular dynamics (MD) simulations, and results agree well with X-ray experiments. The prepeak in the structure factor manifests the existence of medium-range structural order (MRSO) in liquid Ni₂₀Al₈₀. Analyses in MRSO reveal the dominance of ideal icosahedra and defective icosahedra which, furthermore, form clusters and share common atoms.     

Study on a Cross Diffusion Parabolic System

This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity.     

Non-equilibrium grain boundary cosegregation of Mo and P

The segregation of P at grain boundaries is believed to be an important cause of temper embrittlement in steels. As an alloy element, Mo may reduce the embrittlement. However, the concentration measured by Auger electron spectroscopy at the grain boundary in 2.25Cr1MoV and 12Cr1MoV showed that the concentration of P increased with that of Mo, which indicates that Mo and P cosegregated to the grain boundary in Cr-Mo steels.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.     

Evolution of Weighted Networks by Duplication-Divergence Mechanism

The duplication and divergence process is ubiquitous in nature and man-made networks. Motivated by the duplication-divergence mechanism which depicts the growth of protein networks, we propose a weighted network model in which topological evolution is coupled with weight dynamics. Large scale numerical results indicate that our model can naturally generate networks with power-law-like distributions of degree, strength and weight. The degree-strength correlation is illustrated as well. These properties are in agreement well with empirical data observed in real-world systems. Furthermore, by altering the retention probability δ, weighted, structured exponential networks are realized.     

Improvement of least-squares finite difference method on simulating slider air bearings in head disk systems

Least-squares finite difference (LSFD) method, one of mesh-free methods, is used to solve slider air bearings problem through discritizing the generalized Reynolds equation into nonlinear systems of algebraic equations. Two approximation schemes for the linearization of these equations are presented and compared. And, some new techniques to search supporting points for the reference node in the mesh-free method were proposed and explored. Therefore, these improvements eliminate some potential limitation of the LSFD method previously published and further facilitate its employment in complex slider models. Advanced step slider as an example of negative pressure sliders is simulated and verified using the improved LSFD mesh-free method in head disk systems.