Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.     

一种多模态信息融合的视频检索模型

针对包含复杂语义信息的视频检索的需要,提出了一种基于关系代数的多模态信息融合视频检索模型,该模型充分利用视频包含的文本、图像、高层语义概念等多模态特征,构造了对应于多个视频特征的查询模块,并创新地使用关系代数表达式对查询得到的多模态信息进行融合。实验表明,该模型能够充分发挥多模型视频检索及基于关系代数表达式的融合策略在复杂语义视频检索中的优势,得到较好的查询结果。     

赋范格H蕴涵代数和模糊格H蕴涵代数

在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。     

逻辑代数[0,1]上的度量结构

在4种逻辑代数中分别建立了逻辑度量,讨论了其性质,并对它们之间的关系进行了详尽地讨论;又对4个逻辑度量空间的结构及其性质进行了详细地讨论,并得到一些好的结果。     

使用基于进程代数的方法建立软件体系结构的安全模型

安全体系结构集成了软件体系结构与信息安全两大领域的研究,基于进程代数的语言适合描述基于并发交互构件的软件体系结构的一系列重要性质。使用基于进程代数的描述语言对结构中各组成元素和整体拓扑构形分别建模,形成安全的软件体系结构。     

The rest stays unchanged (concurrency and state-based specification)

Pre-/postconditions have been extensively used in program specification, e.g. Z [Spi89], VDM [Jon86], and proof, e.g. Hoare logic, Dijkstra's guarded commands [DiF88]. In [ScP86, SPB90] the authors introduced neutral and central relations to formalise the concept of the rest stays the same. In this paper we abstract away from the specific definition of neutral relation given in [SPB90], through the mechanism of relational boolean algebras. This leads to the definition of implicitly central relations which are easier for the user in practical examples and facilitate the use of pre-/postcondition reasoning about truly concurrent behaviour.     

Stability analysis for linear time-varying systems using bicoprime factorization

This paper presents a bicoprime factorization (BCF) approach to deal with various stability problems for linear discrete time-varying (LTV) systems within the framework of nest algebra. Based on the bicoprime factorization, we give necessary and sufficient conditions for (strongly) simultaneous stabilization of three systems, which generalize similar results for systems by coprime factorization (CF). Finally, when the bicoprime factorization for the plant and controller has additive perturbations, we derive sufficient conditions using the norm inequality for robust stability of the system.     

多光谱图像Clifford拟微分算子及应用

采用Clifford代数理论处理多光谱图像不同于传统代数的处理方法,其可有效利用光谱层之间的联系信息.本文通过分析Clifford微分,提出了多光谱图像的Clifford拟微分算子,丰富了多光谱图像处理的Clifford代数理论体系.在边缘识别仿真实验中,与最大熵法相比较,本文提出的以Clifford拟微分算子理论为核心的边缘检测算法识别模糊边界能力更强.在医学CT影像辅助诊断边缘检测实验中,新算法能有效凸显病灶,提高了诊疗准确性和诊断效率.     

基于策略代数系统的策略间关系分析

当前分析策略之间关系的研究多集中于访问控制策略,主要根据主体、目标和动作三元组上的重叠关系来划分策略冲突类型,存在划分标准不明确,冲突分类不完善等问题.采用策略代数系统来对策略进行描述,能表示Ponder中的授权策略(访问控制策略)和职责策略.分析了策略对应组成部分间所有可能存在的关系,包括离散、相等、包含、部分包含和交叉等五种,在这些关系的基础上指出了可能存在的冲突,并给出了相应的冲突消解方案.     

姚氏百万富翁问题的高效解决方案

姚氏百万富翁问题是安全多方计算的典型问题,但已有解决方案多数存在效率低的问题。通过采用０编码与１编码,将百万富翁问题转换为集合交集问题,提出一种基于可交换加密函数的百万富翁问题高效解决方案,并进行了安全性证明。该方案无需复杂的模指数运算,加解密运算为O(n),通信轮数为4,整体性能优于其他方案。