On Strategic Defense in Stochastic Networks

This paper deals with the detection and prediction of losses due to cyber attacks waged on vital networks. The accumulation of losses to a network during a series of attacks is modeled by a 2-dimensional monotone random walk process as observed by an independent delayed renewal process. The first component of the process is associated with the number of nodes (such as routers or operational sites) incapacitated by successive attacks. Each node has a weight associated with its incapacitation (such as loss of operational capacity or financial cost associated with repair), and the second component models the cumulative weight associated with the nodes lost. Each component has a fixed threshold, and crossing of a threshold by either component represents the network entering a critical condition. Results are given as joint functionals of the predicted time of the first observed threshold crossing along with the values of each component upon this time.     

Jordan Algebras Over Algebraic Varieties

General results on the module structure of Jordan algebras over locally ringed spaces are obtained. Albert algebras over a Brauer–Severi variety with associated central simple algebra of degree 3 are constructed using generalizations of the Tits process and the first Tits construction.     

On an optimal control problem involving first order hyperbolic systems with boundary controls

In this paper, we consider an optimal control problem involving a class of first order hyperbolic systems with boundary controls. A computational algorithm which generates minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated. Moreover, a necessary and sufficient condition for optimality is derived and a result on the existence of optimal controls is obtained.     

A Modified Tikhonov Regularization for Linear Operator Equations

We construct with the aid of regularizing filters a new class of improved regularization methods, called modified Tikhonov regularization (MTR), for solving ill-posed linear operator equations. Regularizing properties and asymptotic order of the regularized solutions are analyzed in the presence of noisy data and perturbation error in the operator. With some accurate estimates in the solution errors, optimal convergence order of the regularized solutions is obtained by a priori choice of the regularization parameter. Furthermore, numerical results are given for several ill-posed integral equations, which not only roughly coincide with the theoretical results but also show that MTR can be more accurate than ordinary Tikhonov regularization (OTR).     

Synthesis,crystal structures and magnetic properties of five new metal(II) compounds constructed with isomers of aminobenzonitrile and dicyanamide ligands

Five new compounds formulated as [Ni^II(dca)₂(para-ABN)₂(H₂O)₂] (1), [Cu^II(dca)₂(para-ABN)₂(H₂O)₂] (2), [Cu^II(dca)₂(para-ABN)₂]_n, (3), [Cu^II(dca)₂(ortho-ABN)₂]_n, (4) and [Cd^II(dca)₂(meta-ABN)₂]_n (5), where dca = dicyanamide and ABN = aminobenzonitrile, have been synthesized and characterized by single crystal X-ray diffraction studies and low temperature (300–2 K) magnetic measurements. The structural analyses revealed that 1 and 2 are isomorphous where dca and para-ABN both act as monodentate ligands. 3 consists of infinite double stranded chains of Cu(II) ions connected through the para-ABN bridges whereas 4 and 5 consist of infinite double stranded chains of Cu(II) and Cd(II) respectively, connected through μ_1,5-dca bridges. The compounds extend their geometries to three-dimensional for 1–3 and 5 and two-dimensional for 4 through hydrogen bonding interactions. All the metal ions Ni²⁺, Cu²⁺ and Cd²⁺ are located on inversion centres and have distorted octahedral coordination geometries. The variable temperature magnetic susceptibility measurements show that the global feature of the χ_MT versus T curves for 3 and 4 is characteristic of very weak antiferromagnetic interactions and between 300 and 2 K the best fit parameters were determined as J = −2.35 and −5.1 cm⁻¹, respectively.     

铀的原子模型

在U价电子采用(5s4p3d4f)/[3s3p2d2f]收缩基函数,原子实采用相对论原子实势进行处理的条件下,通过B3LYP杂化交换-相关泛函对U₂分子的电子态和势能数据进行了第一性原理计算．结果表明U₂分子的基态电子态为X⁹∑⁺_g ．同时用Murrell-Sorbie解析势能函数对对势数据进行拟合．在自旋极化水平和广义梯度近似下,采用密度泛函理论(DFT)和Perdew-Burke     

岩体工程地质动力学基本原理

本文简要介绍了岩体工程地质动力学的基本原理。文章认为岩体工程地质动力学的任务是揭示岩体与各类工程地质动力因素的作用规律,其主要研究内容包括:岩体物质和结构的动力学成因与特性,岩体赋存的地壳动力学环境,岩体的动力学行为与过程,以及岩体工程防灾原理等。岩体工程地质动力学的基本观点包括:岩体及其特性是地球动力学作用结果的"动力成因观"、岩体的工程行为是岩体与动力学环境相互作用结果的"动力作用观",以及工程地质防灾的基本途径是调节岩体与环境的相互作用过程的"过程调节观"。文章在动力作用观的框架下,系统阐述了岩体的动力学成因与特性,岩体赋存的地壳动力学环境特征,岩体的基本力学行为,高地应力环境岩体特性与力学行为,岩体动力学响应,岩体中地下水的作用规律等。