三层薄板的热屈曲测量及特征反演

The paper presents a new study on a tri-layer thin plate.Shadow moiré implemented with an advanced phase unwrapping technique is employed to obtain actual flexural deformation of a real-life plate sample subjected to thermal loads.An analytical model is re-formulated to provide the plate with global closed-form solutions of the plate deflection as well as the interfacial stress and strain.With the measurements and the solutions available,an inverse iterative approach is developed to evaluate and maximize th...     

带投资的时依更新风险模型中破产概率的一致渐近估计

本文考虑索赔额过程与索赔时间过程具有相依性的更新风险模型.假定保险公司将其盈余投资到金融市场中,该投资的价格过程服从几何L′evy过程.当索赔额分布属于L∩D时,本文得到有限时间总索赔额现值尾概率的一致渐近估计,同时也得到有限时间破产概率的一致渐近估计.     

Bernstein-Sikkema-Bézier算子的点态逼近

讨论了Bernstein-Sikkema-Bézier算子点态逼近的等价定理,首先利用插项的的方法证明了正定理,然后应用讨论算子逼近的常规方法给出了其逼近的逆定理.     

由Lévy过程驱动的反射型倒向随机微分方程

证明了由Lévy过程驱动的反射型倒向随机微分方程在局部Lipschitz系数下的解的存在唯一性,并且研究了解的稳定性质.此外,当系数满足Lipschitz条件以及反射壁正则时,证明了过程K的正则性.     

某种局部凸空间上的Bishop-Phelps定理

本文通过在局部凸空间上引入新拓扑的方法,给出某种特殊局部凸空间上的另一种形式的Bishop-Phelps定理.     

关于Bernstein多项式的一类不等式及其应用

In this paper a class of new inequalities about Bernstein polynomial is established. With these inequalities,the estimation of heights,the derivative bounds of Bézier curves and rational Bézier curves can be improved greatly.     

带形状参数的T-Bézier曲线

给出了n阶带形状参数的三角多项式T-Bézier基函数.由带形状参数的三角多项式T-Bézier基组成的带形状参数的T-Bézier曲线,可通过改变形状参数的取值而调整曲线形状,随着形状参数的增加,带形状参数的T-Bézier曲线将接近于控制多边形,并且可以精确表示圆、螺旋线等曲线.阶数的升高,形状参数的取值范围将扩大.     

Judging or setting weight steady-state of rational Bézier curves and surfaces

Many works have investigated the problem of reparameterizing rational Bézier curves or surfaces via Mbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after Mbius transformation. What's more the users of computer aided design softwares may require some guidelines for designing rational Bézier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway.The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational Bézier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal parametric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational Bézier surfaces with compact derivative bounds.     

Branching particle systems in spectrally one-sided Lévy processes

We investigate the branching structure coded by the excursion above zero of a spectrally positive Lévy process. The main idea is to identify the level of the Lévy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump- Mode-Jagers (CMJ) branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Lévy process is established by a time reversal approach. Properties of the measurevalued processes can be studied via the excursions for the corresponding Lévy processes.     

Intrinsic contractivity properties of Feynman-Kac semigroups for symmetric jump processes with infinite range jumps

Let (X_t)_t≥0 be a symmetric strong Markov process generated by non-local regular Dirichlet form (D, D(D)) as follows: D(f,g)=∫?d∫?d(f(x)-f(y))(g(x)-g(y))J(x,y)dxdy,?f,g∈D(D), where J(x, y) is a strictly positive and symmetric measurable function on ?d×?d. We study the intrinsic hypercontractivity, intrinsic supercontractivity, and intrinsic ultracontractivity for the Feynman-Kac semigroup TtV(f)(x)=Ex(exp?(-∫0tV(Xs)ds)f(Xt)),?x∈?d,f∈L2(?d;dx). In particular, we prove that for J(x,y)≈|x-y|-d-al{|x-y|≤1}+e-|x-y|l{|x-y|>1} with α ∈(0, 2) and V(x)=|x|λ with λ>0, (TtV)t≥0 is intrinsically ultracontractive if and only if λ>1; and that for symmetric α-stable process (X_t)_t≥0 with α ∈(0, 2) and V(x)=log?λ(1+|x|) with some λ>0, (TtV)t≥0 is intrinsically ultracontractive (or intrinsically supercontractive) if and only if λ>1, and (TtV)t≥0 is intrinsically hypercontractive if and only if λ≥1. Besides, we also investigate intrinsic contractivity properties of (TtV)t≥0 for the case that lim inf?|x|→+∞V(x)<+∞