Some generalizations of the Caginalp phase-field system

Our aim in this article is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory of deformable continua proposed by Green and Naghdi. In particular, we obtain well-posedness results and study the asymptotic and spatial behaviours of the solutions.     

Micromechanics of coalescence in ductile fracture

Significant progress has been recently made in modelling the onset of void coalescence by internal necking in ductile materials. The aim of this paper is to develop a micro-mechanical framework for the whole coalescence regime, suitable for finite-element implementation. The model is defined by a set of constitutive equations including a closed form of the yield surface along with appropriate evolution laws for void shape and ligament size. Normality is still obeyed during coalescence. The derivation of the evolution laws is carefully guided by coalescence phenomenology inferred from micromechanical unit-cell calculations. The major implication of the model is that the stress carrying capacity of the elementary volume vanishes as a natural outcome of ligament size reduction. Moreover, the drop in the macroscopic stress accompanying coalescence can be quantified for many initial microstructures provided that the microstructure state is known at incipient coalescence. The second part of the paper addresses a more practical issue, that is the prediction of the acceleration rate δ in the Tvergaard-Needleman phenomenological approach to coalescence. For that purpose, a Gurson-like model including void shape effects is used. Results are presented and discussed in the limiting case of a non-hardening material for different initial microstructures and various stress states. Predicted values of δ are extremely sensitive to stress triaxiality and initial spacing ratio. The effect of initial porosity is significant at low triaxiality whereas the effect of initial void shape is emphasized at high triaxiality.     

Restricted T-Universal Functions

We prove the existence of a function which is holomorphic exactly in the unit disk and has universal translates with respect to a prescribed closed set E∂ and satisfies C^∞(∂ \E). If Q is a subsequence of ₀ with upper density d(Q)=1 then the function can be constructed such that in addition

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中国股市一期价格行为研究

本文运用 CJ统计量与一步 Markov转移概率矩阵研究了中国沪、深两市的一期价格行为 .实证结果表明 :大约自 1997年以来 ,一期价格行为表现出很强的随机性 .     

速度依赖于高斯曲率倒数的非参数曲面发展

本文考虑具边值条件的曲面发展问题．与以往的问题不同（见［１－４］），这里讨论是的曲面发展速度与曲面曲率成反比的情况．本文得到了描述这种曲面发展的非线性非一致抛物方程第一初边值问题解的存在性、唯一性和渐进性．     

Limit behaviour of solutions to equivalued surface boundary value problem for p‐Laplacian equations

In this paper, we discuss the limit behaviour of solutions to boundary value problem with equivalued surface for p‐Laplacian equations when the equivalued surface boundary shrinks to a point in certain way. Copyright © 2000 John Wiley & Sons, Ltd.     

Dependent interest and transition rates in life insurance

For market consistent life insurance liabilities modelled with a multi-state Markov chain, it is of importance to consider the interest and transition rates as stochastic processes, for example in order to consider hedging possibilities of the risks, and for risk measurement. In the literature, this is usually done with an assumption of independence between the interest and transition rates. In this paper, it is shown how to valuate life insurance liabilities using affine processes for modelling dependent interest and transition rates. This approach leads to the introduction of so-called dependent forward rates. We propose a specific model for surrender modelling, and within this model the dependent forward rates are calculated, and the market value and the Solvency II capital requirement are examined for a simple savings contract.     

一阶双曲型方程组解的衰减率

本文在研究波动方程时引入的整体Sobolev不等式推广到双曲组的情形．得到了一阶双曲组Cauchy问题解的几个衰减估计．特别是当初始资料给在指定的带权Sobolev空间中时,定理1．5的结果提供了最佳的衰减率．在定理的证明中我们将双曲组化到相应的一阶拟微分方程的情形,进而利用微局部分析建立所需要的估计．     

Asymptotic behaviour of solutions of the difference Schrödinger equation

We use the method of averaging and the discrete analogue of Levinson's theorem to construct the asymptotics for solutions of the difference Schrödinger equation. Moreover, we present the general form for the averaging change of variable.