Stochastic differential equations with polar-decomposed L関y measures and applications to stochastic optimization

This paper is concerned with the optimal control of jump-type stochastic differential equations associated with polar-decomposed Lévy measures with the feature of explicit construction on the jump term. The concrete construction is then utilized for analysis of two portfolio optimization problems for financial market models driven by stable-like processes.      

瓦斯爆炸机理及预防措施

分析了瓦斯爆炸的条件,发生的主要反应及其反应机理,指出相应的预防措施及事后急救方法,并介绍合理利用瓦斯能源的途径。     

Tsallis Entropy for Loss Models and Survival Models Involving Truncated and Censored Random Variables

The aim of this paper consists in developing an entropy-based approach to risk assessment for actuarial models involving truncated and censored random variables by using the Tsallis entropy measure. The effect of some partial insurance models, such as inflation, truncation and censoring from above and truncation and censoring from below upon the entropy of losses is investigated in this framework. Analytic expressions for the per-payment and per-loss entropies are obtained, and the relationship between these entropies are studied. The Tsallis entropy of losses of the right-truncated loss random variable corresponding to the per-loss risk model with a deductible d and a policy limit u is computed for the exponential, Weibull, χ2 or Gamma distribution. In this context, the properties of the resulting entropies, such as the residual loss entropy and the past loss entropy, are studied as a result of using a deductible and a policy limit, respectively. Relationships between these entropy measures are derived, and the combined effect of a deductible and a policy limit is also analyzed. By investigating residual and past entropies for survival models, the entropies of losses corresponding to the proportional hazard and proportional reversed hazard models are derived. The Tsallis entropy approach for actuarial models involving truncated and censored random variables is new and more realistic, since it allows a greater degree of flexibility and improves the modeling accuracy.     

Toward a global maximization of the molecular similarity function: Superposition of two molecules

A quantum similarity measure between two molecules is normally identified with the maximum value of the overlap of the corresponding molecular electron densities. The electron density overlap is a function of the mutual positioning of the compared molecules, requiring the measurement of similarity, a solution of a multiple-maxima problem. Collapsing the molecular electron densities into the nuclei provides the essential information toward a global maximization of the overlap similarity function, the maximization of which, in this limit case, appears to be related to the so-called assignment problem. Three levels of approach are then proposed for a global search scanning of the similarity function. In addition, atom—atom similarity Lorentzian potential functions are defined for a rapid completion of the function scanning. Performance is tested among these three levels of simplification and the Monte Carlo and simplex methods. Results reveal the present algorithms as accurate, rapid, and unbiased techniques for density-based molecular alignments. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 826–846, 1997     

Balancing vectors and Gaussian measures of n-dimensional convex bodies

Let ‖·‖ be the Euclidean norm on R ⁿ and γ_n the (standard) Gaussian measure on R ⁿ with density (2π)^−n/2e. It is proved that there is a numerical constant c>0 with the following property: if K is an arbitrary convex body in R ⁿ with γ_n(K)≥1/2, then to each sequence u₁,…,u_m∈ R ⁿ with ‖u₁‖,…,‖u_m‖≤c there correspond signs ε₁,…,ε_m=±1 such that ∑^m_i=1ε_iu_i∈K. This improves the well-known result obtained by Spencer [Trans. Amer. Math. Soc. 289 , 679–705 (1985)] for the n-dimensional cube. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12: 351–360, 1998     

The hyper-Wiener Index of diamond nanowires

Carbon nanowires based on various structures have various applications. In this article, our focus is on diamond nano-wires, based on the structure of the diamond. Our goal is to characterize these nanowires by providing their hyper-Wiener index, one of the basic topological graph indices. The diamond is formed by carbon atoms in a compact structure: every atom has exactly four neighbors connected by covalent bonds according to the simplest three-dimensional polyhedron. Considering an atom in the center of a tetrahedron, its neighbors, the atoms connected to it by bonds, are located in the corners of the tetrahedron. In this article, this “diamond-grid” structure is analysed in the case that the graphs correspond to connected parts of sequences of unit cells, in this way forming nanowires of various lengths. By a combinatorial approach, a closed formula is proven for the hyper-Wiener index based on the graph-distances of every pair of carbon atoms (i.e., the minimal number of edges connecting the atoms), and this formula depends only on the size of the graph in terms of the number of unit cells included.     

Hilbert-Space-Valued Super-Brownian Motion and Related Evolution Equations

A stochastic partial differential equation in which the square root of the solution appears as the diffusion coefficient is studied as a particular case of stochastic evolution equations. Weak existence of a solution is proved by the Euler approximation scheme. The super-Brownian motion on [0, 1] is also studied as a Hilbert-space-valued equation. In this set up, weak existence, pathwise uniqueness, and positivity of solutions are obtained in any dimension d . Accepted 23 October 1998     

高能电子辐照对束测量系统的影响

在直线感应加速器束参数测量系统实验的基础上,给出了束参数测量系统的实验布局和特点,分析高能电子辐照对直线感应加速器中测量系统电子器件介电性能的影响和变化规律;进一步探讨电子器件介电性能受高能电子辐照后的抑制措施。针对电磁空间干扰情况,主要通过采用光纤传输控制信号的措施,能很好地传输窄脉冲,信号延时抖动小,达到了高速信号的可靠传输要求,利用紧凑嵌入式方法,提高了抗电磁干扰的能力,这样可以更好保护束参数测量电子器件。     

Shape and symmetry of heptacoordinate transition-metal complexes: structural trends

The stereochemistries of heptacoordinate transition-metal complexes are analyzed by using continuous symmetry and shape measures of their coordination spheres. The distribution of heptacoordination through the transition-metal series is presented based on structural database searches including organometallic and Werner-type molecular complexes, metalloproteins, and extended solids. The most common polyhedron seems to be the pentagonal bipyramid, while different preferences are found for specific families of compounds, as in the complexes with three or four carbonyl or phosphine ligands, which prefer the capped octahedron or the capped trigonal prism rather than the pentagonal bipyramid. The symmetry maps for heptacoordination are presented and shown to be helpful for detecting stereochemical trends. The maximal symmetry interconversion pathways between the three most common polyhedra are defined in terms of symmetry constants and a large number of experimental structures are seen to fall along those paths.     

An arrogance of technicians

A recent article in this journal, reflecting a commonly held view, has sought to denigrate the contribution that might be made by legal metrology to public confidence in chemical measurements. This article disputes those contentions.