函数半群的产生集的最小基数

函数半群的产生集个数是函数半群科学中较为复杂的问题之一，通过对函数半群的研究，得到了函数半群中生成函数半群的最小基数。     

基于半群结构的多等级密钥分享方案

在信息管理与电子商务应用中,如何安全地将一个合法实体(比如一个公司)的密钥分配给其属下的若干部门具有非常重要的意义.通常在这类应用中各部门都需拥有自己的子密钥,而每个部门的每个人(或科室)都有不同的子密钥授权等级,即一个部门只要其中一部分被授权人根据他们的密钥授权等级适当联合就能获得所在部门的子密钥,而一旦得到每个部门的子密钥就能够恢复出公司完整的密钥.基于此,建立了一个满足这种要求的安全的密钥分享体制.与传统方法不同,利用代数中群与半群的结构理论,通过使个人的密钥授权等级对应于相应群的特定元素的阶从而给出了一种能实现这种多等级密钥分享的方案.该方案可用于需要多等级密钥分享的其它场合.     

扰动C半群的紧性

讨论了 C半群 {T( t) }t≥ 0 在有界线性算子 (或正算子 ) B的扰动下生成的拢动 C半群{S( t) }t≥ 0 的紧性 ,得到了 S( t) - T( t)是最终紧的一个充分条件     

素数阶群按树上有限交换幂零半群的单纯理想扩张

研究了素数阶群G按树上的有限交换幂半群N的单纯理论扩张S。给出了G按N的单纯理想扩张的存在条件、所有互不同构的这类扩张的数目以及两个此类扩张同构的充要条件。     

Optimal Control for Pennes' Bioheat Equation

The problem of Pennes' bioheat boundary control through a skin with its inner medium kept at a constant steady‐state temperature where the outer surface subjected to conductive condition is solved by different methods. Analytical and mild solutions of Pennes' boundary control problem yield a discrete optimization problem for temperature profile at the specific depth point as well as temperature profile at all points of the skin in the final time. The pointwise optimal control problem has been solved by discretized form of the unconstrained optimization problem using analytical solution for Pennes' boundary control problem. The analytical solution has been used to solve the optimal control problems via an unconstrained/constrained optimization in Methods I and II. In Method III first, Pennes' boundary control problem is solved using mild solution by strongly continuous semigroup theory. Then, nonlinear optimization problem with linear constraints is proposed to calculate the corresponding piecewise optimal control function. All methods, have been applied to a homogeneous tissue. Mathematical simulation is done to show the optimal controls for the related states when minimum effort is used.     

Lattice implication ordered semigroups

From the viewpoint of semantics, lattice implication algebras provide a basis to establish lattice-valued logic with truth value in a relatively general lattice. In this paper, we first introduce two notions of lattice implication n-ordered semigroup and lattice implication p-ordered semigroup, which induced by lattice implication algebras. Secondly, we study some of their basic properties and prove that a lattice implication n-ordered semigroup is a residuated semigroup, and a lattice implication p-ordered semigroup is an arithmetic lattice ordered semigroup. We also define the homomorphism mapping between lattice implication n-ordered semigroups. Finally, we discuss some properties of filters and sl ideals in lattice implication n-ordered semigroups and lattice implication p-ordered semigroups.     

一类半线性微分方程的调和伪概周期解

利用不动点理论，给出了一类半线性微分方程有界的调和伪概周期解存在的充分条件。     

异步自动机半群

首先给出异步自动机半群的定义,并讨论其基本性质.证明了如下结果：异步自动机半群的字问题在指数时间内可解,任一异步自动机半群具有唯一性的异步自动机结构,异步自动机半群具有“伙伴旅游者”的性质.     

Approximate controllability results for non-densely defined fractional neutral differential inclusions with Hille–Yosida operators

In this paper, we mainly focused the approximate controllability results for a class of non-densely defined fractional neutral differential control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of fractional differential inclusions with infinite delay where the linear part is non-densely defined and satisfies the Hille–Yosida condition. The main techniques rely on Bohnenblust– Karlin's fixed point theorem, operator semigroups and fractional calculus. Further, we extend the result to study the approximate controllability concept with nonlocal conditions. Finally, an example is also given for the illustration of the obtained theoretical results.     

Approximate controllability of stochastic nonlinear third‐order dispersion equation

In this work, we consider a class of control systems governed by the stochastic nonlinear third‐order dispersion equation in Hilbert spaces. We first prove the existence of mild solutions of stochastic nonlinear third‐order dispersion equation by using fixed point theory, infinite dimensional semigroup properties, stochastic analysis techniques, and then a new set of sufficient conditions are formulated which guarantees the approximate controllability of the main problem. Finally, an example is provided to illustrate the application of the obtained results.Copyright © 2012 John Wiley & Sons, Ltd.