Fixed points of approximable maps

We present a simple proof of the Leray-Schauder type theorem for approximable multimaps given recently by Ben-El-Mechaiekh and Idzik. We apply this theorem to obtain a Schaefer type theorem, the Birkhoff-Kellogg type theorems, a Penot type theorem for non-self-maps, and quasi-variational inequalities, all related to compact closed approximable maps.

     

A Note on Orthogonal Multiplication

Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:Rk×Rn→Rn. In this paper,we shall discuss two extensions of the theorem.that is,the sufficient and necessary conditions about the existence of an orthogonal multiplication f:Rk×Rn→Rn 1or f:Rk×Rn→Rn 2     

Double image encryption by using Arnold transform and discrete fractional angular transform

Based on Arnold transform and discrete fractional angular transform, a double image encryption algorithm is designed. Two original images are regarded as the amplitude and phase of a complex function. Arnold transform is introduced for scrambling the pixels at a local area of the complex function. Subsequently the changed complex function is converted by discrete fractional angular transform. The operations mentioned will be performed many times. The amplitude of final output complex function is the encrypted image and its phase is regarded as the key of encryption algorithm. The parameters of the two transforms serve as the additional keys for enhancing the security. Some numerical simulations have been done to validate the performance of this encryption scheme.     

Entanglement complexity of lattice ribbons

We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as n, and similar results hold for the twist and writhe.     

连续体结构拓扑优化的一种改进变密度法及其应用

针对连续体结构拓扑优化设计变密度方法SIMP和RAMP,因惩罚函数选取的不合理而导致拓扑结构形式不甚合理的问题,本文提出了一种新的惩罚函数,并基于此函数导出了相应的迭代设计公式,几个典型考题的数值结果,说明了方法的可行性和有效性.     

Random coefficient differential equation models for bacterial growth

In the mathematical modeling of population growth, and in particular of bacterial growth, parameters are either measured directly or determined by curve fitting. These parameters have large variability that depends on the experimental method and its inherent error, on differences in the actual population sample size used, as well as other factors that are difficult to account for. In this work the parameters that appear in the Monod kinetics growth model are considered random variables with specified distributions. A stochastic spectral representation of the parameters is used, together with the polynomial chaos method, to obtain a system of differential equations, which is integrated numerically to obtain the evolution of the mean and higher-order moments with respect to time.     

联系数中差异度系数i的专家估测法及应用

在联系数中差异度系数i已有取值方法的基础上,给出了差异度系数i的专家估测取值方法、加权统计取值方法和频数统计取值方法以及它们在实际中的应用.     

新型生物黏附性材料巯基壳聚糖的合成与表征

巯基聚合物利用二硫键的形成, 以共价键黏附于黏膜表面, 可以延长药物在黏膜上的滞留时间, 有利于药物分子的吸收. 本文合成了一种新型巯基聚合物——N-乙酰基-L-半胱氨酸-g-壳聚糖(CS-NAC), 并进行了表征, 同时对材料的溶胀度、黏附性和细胞毒性进行了测试. 结果表明, 这种巯基聚合物具有较高的巯基含量, 最高可达到589.3 μmol/g; 具有快速的溶胀性能; 黏附性显著增强, 黏附时间和黏附力分别是壳聚糖的30和3倍; 无明显的细胞毒性. 因此, CS-NAC是一种很有应用前景的生物黏附性材料.