"兰氏"平方律作战毁伤过程兵力损耗率系数战例求解理论

如何求得著名的“兰氏”平方律战斗动力学方程中双方兵力损耗率系数，这是作战模拟应用研究领域中一个久攻未克的难题。本文提出了以作战结果来逆向研究作战过程中双方兵力损耗率系数的思想。阐述了对于不变的作战双方在相同（相近）的作战环境与作战条件下相继进行的作战序列里，双方各自的兵力损耗率系数不变（波动不大）的公理，论证了揭示作战序列内部规律的两条定理。据此，建立了兵力损耗率系数的战例求解理论与方法。运用这一理论与方法，据以往发生的作战过程其数值特征可以求得未来相似或相同作战过程中双方兵力损耗率系数的具体取值，首次解决了作战模拟研究领域中兵力损耗率系数的具体取值这一难题。     

关于格蕴涵代数公理的一个注记

设在一个非空集合L上有一个二元运算→和两个零元运算O与I，除此之外没有其它已知的代数结构，利用这三个运算可以在L上定义一个一元运算′和两个二元运算∨和∧（定义2．1）。本文证明了只要这些运算满足格蕴涵代数的公理（不包括有余格的公理），（L，∨，∧，′）就是一个有泛界O，I的有余格（定理2．2）。因此在定义格蕴涵代数时可以在一个没有任何代数结构的非空集合上定义蕴含运算而不必在一个有泛界的有余格上定义蕴含运算，而且在这两种定义方式中蕴含运算所满足的条件是相同的。     

Equivalence of axioms for bankruptcy problems

The bankruptcy problem is concerned with how to divide the net worth of the bankrupt firm among its creditors. In this paper, we investigate the logical relations between various axioms in the context of bankruptcy. Those axioms are: population-and-resource monotonicity, consistency, converse consistency, agreement, and separability. In most axiomatic models, they are not directly related. However, we show that they are equivalent on the class of bankruptcy problems under minor additional requirements. Received: April 1998/Revised version: January 1999     

Geometric torsions and invariants of manifolds with a triangulated boundary

Geometric torsions are torsions of acyclic complexes of vector spaces consisting of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a three-dimensional manifold with a triangulated boundary. These invariants can be naturally combined into a vector, and a change of the boundary triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued at their common boundary, these vectors undergo scalar multiplication, i.e., they satisfy Atiyah’s axioms of a topological quantum field theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 98–114, January, 2009.     

The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters

Let X be an infinite set and let and denote the propositions “every filter on X can be extended to an ultrafilter” and “X has a free ultrafilter”, respectively. We denote by the Stone space of the Boolean algebra of all subsets of X. We show:

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A capital allocation based on a solvency exchange option

In this paper we propose a new capital allocation method based on an idea of [Sherris, M., 2006. Solvency, capital allocation and fair rate of return in insurance. J. Risk Insurance 73 (1), 71-96]. The proposed method explicitly accommodates the notion of limited liability of the shareholders. We show how the allocated capital can be decomposed, so that each stakeholder can have a clearer understanding of their contribution. We also challenge the no undercut principle, one of the widely accepted allocation axioms, and assert that this axiom is merely a property that certain allocation methods may or may not meet.     

几类基于L*上二元聚合算子的蕴涵

L*是区间值模糊与Atanassov意义下的直觉模糊集的基本格。本文首先基于单位区间上的三角模与三角余模,引入L*上两组对偶的二元聚合算子,然后,类似于剩余蕴涵与强蕴涵的构成方法,利用引入的对偶聚合算子生成几类L*上的蕴涵,并对其性质进行讨论。     

State Property Systems and Orthogonality

The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva–Brussels approach to the foundations of quantum mechanics (Aerts, D. International Journal of Theoretical Physics, 38, 289–358, 1999; Aerts, D. in Quantum Mechanics and the Nature of Reality, Kluwer Academic; Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B. International Journal of Theoretical Physics, 38, 359–385, 1999), and the category of state property systems was proven to be equivalent to the category of closure spaces (Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B., International Journal of Theoretical Physics, 38, 359–385, 1999; Aerts, D., Colebunders, E., van der Voorde, A., and van Steirteghem, B., The construct of closure spaces as the amnestic modification of the physical theory of state property systems, Applied Categorical Structures, in press). The first axioms of standard quantum axiomatics (state determination and atomisticity) have been shown to be equivalent to the T₀ and T₁ axioms of closure spaces (van Steirteghem, B., International Journal of Theoretical Physics, 39, 955, 2000; van der Voorde, A., International Journal of Theoretical Physics, 39, 947–953, 2000; van der Voorde, A., Separation Axioms in Extension Theory for Closure Spaces and Their Relevance to State Property Systems, Doctoral Thesis, Brussels Free University, 2001), and classical properties to correspond to clopen sets, leading to a decomposition theorem into classical and purely nonclassical components for a general state property system (Aerts, D., van der Voorde, A., and Deses, D., Journal of Electrical Engineering, 52, 18–21, 2001; Aerts, D., van der Voorde, A., and Deses, D. International Journal of Theoretical Physics; Aerts, D. and Deses, D., Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation, and Axiomatics, World Scientific, Singapore, 2002). The concept of orthogonality, very important for quantum axiomatics, had however not yet been introduced within the formal scheme of the state property system. In this paper we introduce orthogonality in an operational way, and define ortho state property systems. Birkhoff's well known biorthogonal construction gives rise to an orthoclosure and we study the relation between this orthoclosure and the operational orthogonality that we introduced.     

Quantum Theory from Four of Hardy's Axioms

In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of quantum theory from five reasonable axioms. Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy's assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his work can be easily reconciled with a Bayesian interpretation of quantum probability.