Banach空间中一类非线性变分包含问题解的具混合误差项的Ishikawa迭代逼近

本文在实自反Banach空间的框架下,研究了一类具有Lispschitz条件的强增生型变分包含解的存在性、唯一性及其具有混合误差项的Ishikawa迭代程序的收敛性问题。在适当的条件下,证明了该迭代序列强收敛于变分包含问题的唯一解。其结果改进和推广了引文中相应的结果。     

Banach空间中强增生型变分包含解的迭代逼近问题

本文研究p-一致光滑的实Banach空间（1＜p≤2）中一类强增生型变分包含解的迭代逼近问题.在仅假设强增生映象的连续性与没有条件βn→0（n→∞）下,利用徐宗本等人给出的对偶映象Jp的Holder连续性,证明了具误差的Ishikawa迭代程序强收敛到这类变分包含的唯一解.     

Banach空间中一类非线性变分包含问题解的存在性和逼近问题

研究了Banach空间中一类强增生型变分包含解的存在性及其具有混合误差项的Ishikawa迭代程序的收敛性问题,并推广了前人的结果。     

非一致光滑的Banach空间中强增生型变分包含问题解的带误差的Ishik awa迭代逼近

研究光滑且自反的实Banach空间中强增生型变分包含问题解的带误差的Ishikawa迭代程序的收敛性，所得结果改进和推广了张石生（1999年）文中的相关结果。     

Hilbert空间中一般强混合变分包含的迭代算法

研究了Hilbert空间中求一般强混合变分包含逼近解的迭代算法。这类变分包含概括了若干熟知的变分不等式与变分包含成特例。结果是刘理蔚与李育强(2001)及Noor(1998)的结果的推广和改进。     

一类新的含极大η-单调映象的完全广义非线性隐拟变分包含

引入和研究了一类新的含极大η-单调映象的完全广义非线性隐拟变分包含。在Hilbert空间中使用极大η-单调映象的预解算子技巧,构造了新的扰动迭代算法,并证明了近似解序列强收敛于精确解。其所得结果是近期相关结果的改进和推广。     

Banach空间中一类含(H,η)-增生算子的集值变分包含组

本文我们在Banach空间中引入和研究了一类新的含(H,η)-增生算子的集值变分包含组。利用所定义的(H,η)-增生算子的预解算子,给出了此类变分包含组的迭代算法,并证明了由该算法生成的迭代序列的强收敛性。     

关于Browder-Petryshyn型严格伪压缩映射的复合迭代逼近方法

本文通过建立新的迭代格式,采用一些分析方法和技巧,研究了迭代序列逼近有限个BrowderoPetryshyn型严格伪压缩映射的公共不动点问题.在适当的条件下,证明了迭代序列强收敛到映射族的公共不动点,改进和推广了某些最新结果.     

时标上脉冲动力方程周期边值问题的拟线性化方法

本文研究了一类时标上脉冲动力方程周期边值问题解的收敛性问题.利用时标上一阶脉冲动力不等式、上下解和单调迭代技巧证明了该问题解的一致收敛性结果,并进一步采用拟线性化方法和分析技巧获得了该方程在周期边值条件下两个逼近解序列高阶收敛的充分性判据.本文所得结果发展了时标上动力方程定性理论的结果.     

Banach空间二阶积分-微分方程初值问题的唯一解

本文在一般Banach空间中利用半序方法和一个新的比较结果,研究了二阶积分-微分方程初值问题的唯一解。仅使用了一个上解或下解,在比较广泛的上控制条件下得到了显形式表达的逼近解的迭代序列及误差估计,本文没有使用任何紧性条件,改进并推广了最近的一些结果。     

增生算子方程的具误差的Ishikawa迭代序列的收敛率估计

设X是一实的Banach空间,T：X→Y是一Lipschitz的增生算子。本文证明了具误差的Ishikawa迭代序列强收敛到方程x Tx=f的唯一解：并得一个一般的收敛估计式。若T：X→X是一Lipschitz的强增生算子,则具误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解。本文结果推广和发展了现有的相应结果。     

A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

It is recognized that the convergence of FFT‐based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain‐based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress‐based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly, the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress‐based approaches. In this paper, we propose a new polarization‐based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress‐based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples. Copyright © 2011 John Wiley & Sons, Ltd.     

广义集值强非线性混合似变分不等式解的存在性与算法

本文延拓辅助原理的技巧,来研究一类广义集值强非线性混合似变分不等式。首先,利用Ky Fan引理,证明了这类混合似变分不等式的辅助问题解的存存性。其次,利用该存在性结果,给出了解这类混合似变分不等式的迭代算法。最后。既证明了这类混合似变分不等式解的存在性,又证明了由算法生成的迭代序列的收敛性。     

Constitutive models for ductile solids reinforced by rigid spheroidal inclusions

We study the effective constitutive response of composite materials made of rigid spheroidal inclusions dispersed in a ductile matrix phase. Given a general convex potential characterizing the plastic “in the context of J₂-deformation theory” behavior of the isotropic matrix, we derive expressions for the corresponding effective potentials of the rigidly reinforced composites, under general loading conditions. The derivation of the effective potentials for the nonlinear composites is based on a variational procedure developed recently by Ponte Castaneda (1991a, J. Mech. Phys. Solids 39, 45–71). We consider two classes of composites. In the first class, the spheroidal inclusions are aligned, resulting in overall transversely isotropic symmetry for the composite. In the second class, the inclusions are randomly oriented, and thus the composite is macroscopically isotropic. The effective response of composites with aligned inclusions depends on both the orientation of the loading relative to the inclusions and on the inclusion concentration and shape. Comparing the strengthening effects of rigid oblate and prolate spheroids, we find that prolate spheroids give rise to stiffer effective response under axisymmetric “relative to the axis of transverse isotropy” loading, while oblate spheroids provide greater reinforcement for materials loaded in transverse shear. On the other hand, nearly spherical “slightly prolaterd spheroids are most effective in strengthening the composite under longitudinal shear. Thus, the optimal shape for strengthening composites with aligned inclusions depends strongly on the loading mode. Alternatively, the properties of composites with randomly oriented spheroidal inclusions, being isotropic, depend only on the concentration and shape of the inclusions. We find that both oblate and prolate inclusions lead to significant strengthening for this class of composites.     

广义集值混合变分不等式的一类单调算法

本文利用一个新的技巧建立了广义集值混合变分不等式与新的不动点问题的等价性。利用这个等价性,我们提出和分析了一类解集值混合变分不等式和相关的优化问题的新算法。我们的结果统一和改进了该领域内的一些最新结果。