生态系统的参数确定问题

通过不同观测数据研究捕食者—被捕食者生态系统参数确定问题.研究了四种情形1.观察数据无误差,并已知一个参数值.这种情况下,参数可由其相轨线和最小二乘法精确确定.2.观察数据无误差,但所有参数未知.此时仅靠相轨线的研究,无论给出多少组精确数据,都无法精确确定这些参数.通过原非线性模型的数值计算和网格搜索法,至少需要4组数据,同样得到了精度较高的参数值.3.当观测数据有误差时,根据解的周期性,引入标准周期的概念,在一个标准周期里讨论参数的确定问题,并利用标准周期内的捕食者与被捕食者的数量均值与系统的平衡点的关系对参数进行修正,然后使用网格法进行搜索,进一步提高了参数的精度.4.当观测时间也有误差时,先选取相对最优的随机正态数对观测时刻进行修正,然后再利用3.的方法估计参数.     

基于贝叶斯网络的多态故障树分析方法

针对多态系统故障树分析的难点,通过一个多态雷达系统的实例给出了一种基于贝叶斯网络的多态故障树分析方法.首先根据多态故障树的结构建立贝叶斯网络的拓扑结构,然后根据多态逻辑算子对其进行定量化,进而利用贝叶斯网络分析多态故障树顶事件概率、部件重要度及其它结果.最后通过对实例的分析说明了基于贝叶斯网络的多态故障树分析方法有更强的建模分析能力.     

A spatial decay in the linear theory of microstretch piezoelectricity

The electromagnetic theory of microstretch elasticity is an adequate tool to describe the behavior of porous bodies, animal bones and solids with deformable microstructures. In this paper we study the linear theory of microstretch piezoelectricity. First, we establish a spatial decay estimate. Then, we obtain an upper bound for the amplitude term.     

A priori estimates for a singular limit approximation of the constitutive laws for chiral media in the time domain

The equations for the evolution of electromagnetic fields in chiral media, in the time domain, are nonlocal in time. In this work we study the validity of a singular limit (local in time) approximation for these nonlocal in time equations, by estimating the size of the difference of the fields as predicted by both models. In particular, we establish an a priori estimate for this difference, depending on the time horizon, properties of the domain, spatial properties of the initial data and the source terms and the chirality measure β of the approximating model.     

Global Existence of Solutions in H4 for a Nonlinear Thermoviscoelastic Equations with Non-monotone Pressure

We consider a one-dimensional continuous model of nutron star, which is described by a compressible thermoviscoelastic system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We will prove that, despite a possible destabilizing influence of the pressure, which is non-monotone and not always positive, the presence of viscosity and a sufficient thermal dissipation can yield the global existence of solutions in H ⁴ with a mixed free boundary problem for our model.      

Coercive Estimates

Mathematical Notes -     

Quasistatic anti-plane motion in the simplest theory of nonlinear viscoelasticity

We consider a very simple model in the framework of differential viscoelastic materials which are isotropic and incompressible. In this model the Cauchy stress tensor is split in an elastic part and a dissipative part. The elastic part is derived from a strain-energy density function only of the first invariant of the Cauchy–Green strain tensor. The dissipative part is like the Navier–Stokes equations: linear in the stretching tensor with a constant viscosity parameter. For this model we provide some time and spatial estimates in the quasistatic approximations for the equations governing anti-plane shear motions. Several explicit examples for specific form of the strain energy are produced. Our results impose analytical restrictions on the mathematical properties of the strain energy to ensure a physical behavior in the creep and recovery experiments. Moreover, we show polynomial decay for the spatial behavior in the class of stress-hardening (or strain-stiffening) materials. For stress-softening materials a Phragmen–Lindelof alternative is proved.     

Applying Bayesian neural networks to identify pion, kaon and proton in BES Ⅱ

The Monte-Carlo samples of pion, kaon and proton generated from 0.3 GeV/c to 1.2 GeV/c by the 'tester' generator from SIMBES which are used to simulate the detector of BES Ⅱ are identified with the Bayesian neural networks (BNN). The pion identification and misidentification efficiencies are obviously better at high momentum region using BNN than the methods of X2 analysis of dE/dX and TOF information.The kaon identification and misidentification efficiencies are obviously better from 0.3 GeV/c to 1.2 GeV/c using BNN than the methods of X2 analysis. The proton identification and misidentification efficiencies using BNN are basically consistent with the ones of X2 analysis. The anti-proton identification and misidentification efficiencies are better below 0.6 GeV/c using BNN than the methods of X2 analysis.     

A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations

In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control.     

Some remarks concerning the Fourier transform in the space L 2(ℝ n )

For the Fourier transform in the space L ₂(?²) of square integrable multivariable functions, two practically useful estimates are proved in certain classes of functions characterized by a generalized continuity modulus.