Fractional Deng Entropy and Extropy and Some Applications

Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures.     

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     

铅对人体健康危害及其预防措施

着重阐述了铅的污染与对人体健康危害情况及应采取的预防措施。这些预防措施都是简单可行的,对于减少铅的污染,免受它的危害,增进人体健康都有十分重要意义。     

Stochastic Control Problems where Small Intervention Costs Have Big Effects

We study an impulse control problem where the cost of interfering in a stochastic system with an impulse of size ζ∈ R is given by c+λ|ζ|, where c and λ are positive constants. We call λ the proportional cost coefficient and c the intervention cost . We find the value/cost function V _c for this problem for each c>0 and we show that lim _{c→ 0+} V _c =W , where W is the value function for the corresponding singular stochastic control problem. Our main result is that This illustrates that the introduction of an intervention cost c>0 , however small, into a system can have a big effect on the value function: the increase in the value function is in no proportion to the increase in c (from c=0 ). Accepted 23 April 1998     

L 1 (μ, X) as a constrained subspace of its bidual

In this note we consider the property of being constrained in the bidual, for the space of Bochner integrable functions. For a Banach spaceX having the Radon-Nikodym property and constrained in its bidual and forY ⊂ X, under a natural assumption onY, we show thatL ¹ (μ, X/Y) is constrained in its bidual andL ¹ (μ, Y) is a proximinal subspace ofL ¹(μ, X). As an application of these results, we show that, ifL ¹(μ, X) admits generalized centers for finite sets and ifY ⊂ X is reflexive, thenL ¹ μ, X/Y) also admits generalized centers for finite sets.     

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     

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.      

Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

Four-qubit entanglement has been investigated using a recent proposed entanglement measure, multiple entropy measures （MEMS）. We have performed optimization for the nine different families of states of four-qubit system. Some extremal entangled states have been found.     

S.I.S.向量随机测度在弱拓扑及相容拓扑下的收敛性

本文主要研究ｓ．ｉ．ｓ．向量随机测度在弱拓扑及相容拓扑下的收敛性,给出了ｓ．ｉ．ｓ．向量随机测度在弱拓扑 容拓扑下的Ｖｉｔａｌｉ－Ｈａｌｍ－Ｓａｋｓ定理,作为应用,我们建立了Ｒ＾１－值有界可测函数关于Ｂａｎａｃｈ空间值ｓ．ｉ．ｓ．向量随机测度的随机积分的收敛定理,并得到了具ｔｙｐｅｐ的Ｂａｎａｃｈ空间中ｓ．ｉ．ｓ．向量随机测度的大数定律及中心极限定理。     

A Trajectory for Validating Computational Emulation Models of Organizations

Validation of complex simulation models is a challenging problem in computational organization theory research. In this paper, we describe a validation strategy suitable for emulation simulation systems, and show how a comprehensive validation consists of a sequence of steps that evaluate different aspects of a computational organizational simulation model. We demonstrate how this strategy can be applied to the evaluation of the Virtual Team Alliance (VTA), an emulation simulation system designed to guide managers charged with organizational change. VTA required a &201C;trajectory&201D; of successive validation experiments, before managers where willing to follow the recommendations of VTA. Ultimately, we believe this validation approach can be applied to a wide range of different simulation systems, and will make identification of the strengths and weaknesses of organizational simulations easier.