A new binary relation to compare viability of winning coalitions and its interrelationships to desirability relation and blockability relation

This paper aims to propose a new type of binary relations, called the viability relation, defined on the set of all coalitions in a simple game for a comparison of coalition influence, and to investigate its properties, especially its interrelationships to the desirability relation and the blockability relation. The viability relation is defined to compare coalitions based on their robustness over deviation of their members for complementing the inability of the desirability relation and the blockability relation to make a distinguishable comparison among winning coalitions. It is verified in this paper that the viability relation on a simple game is always transitive and is complete if and only if the simple game is S-unanimous for a coalition S. Examples show that there are no general inclusion relations among the desirability relation, the blockability relation and the viability relation. It is also verified that the viability relation and the blockability relation are complementary to each other. Specifically, the blockability relation between two coalitions is equivalent to the inversed viability relation between the complements of the two coalitions.     

均值限制相似优势粗糙集及决策分析模型研究

针对不完备信息系统中的偏好多属性决策问题,提出了一种基于均值限制相似优势粗糙集的决策分析模型.首先提出了均值限制相似优势关系的概念;然后在均值限制相似优势关系下得到知识的粗糙近似和属性约简,给出了分类决策规则.与相似优势关系和限制相似优势关系比较研究的结果表明:均值限制优势关系的分类精度和质量介于二者之间,而分类误差率则优于相似优势关系和限制相似优势关系,得到的决策规则可信度更高,决策模型与实际情况更加相符.     

On the duality and the derivation relations for multiple zeta values

We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values whose first components are 2’s are deduced from the derivation relation, which is known as a subclass of the extended double shuffle relation.     

Equality of proofs for linear equality

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose arrows correspond to diagrams. Edges in these diagrams join occurrences of variables that must remain the same in every generalization of the proof. It is found that assumptions about equality of proofs for equality are parallel to standard assumptions about equality of arrows in categories. They reproduce standard categorial assumptions on a different level. It is also found that assumptions for a preordering relation involve an adjoint situation.      

Influence of cubic nonlinearity on the dispersion relation for long waves on a water surface

The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg—de Vries equation.     

Calculating Exact Transitive Closure for a Normalized Affine Integer Tuple Relation

An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and output tuples of a normalized relation. The approach permits for calculating an exact transitive closure for a relation when the constraints of this closure are represented by both affine and non-linear forms. An example of calculating the exact transitive closure of normalized affine integer tuple relation is presented.     

On α-Relation and Transitivity Conditions of α

The main tools in the theory of hyperstructurs are the fundamental relations. The fundamental relation on hyperring was introduced by Vougiouklis at the fourth AHA congress (1990). The fundamental relation on a hyperring is defined as the smallest equivalence relation so that the quotient would be the ring. Note that, generally, the commutativity in the ring are not assumed. In this article, we introduce a new strongly regular equivalence relation on hyperring so that the quotient is a commutative ring. Also we state the condition that is equivalent with the transitivity of this relation and finally we characterize the complete hyperring (with the fundamental relation as commutative).     

Matrix relation algebras

Square matrices over a relation algebra are relation algebras in a natural way. We show that for fixed n, these algebras can be characterized as reducts of some richer kind of algebra. Hence for fixed n, the class of n × n matrix relation algebras has a first–order characterization. As a consequence, homomorphic images and proper extensions of matrix relation algebras are isomorphic to matrix relation algebras. Received July 18, 2001; accepted in final form April 24, 2002.     

投资控制模型在技术进步分析中的应用

经济增长与技术进步的关系历来是国内外学者关心的热门问题.本文研究了经济增长与技术进步的关系,总结了技术进步的测算方法,提出了一个基于投资控制模型的测算技术进步的方法.     

Small integral relation algebras generated by a partial order

The main purpose of this note is to exhibit a concrete representation for a four atom relation algebra which was known to be representable without an actual representation having been found. Along the way, representations are given for all integral relation algebas with four atoms which are generated by a partial order.     

A relation between convolution type operators on intervals in sobolev spaces

We construct an operator relation between convolution type operators with or without a reflection on a union of finite intervals and corresponding Wiener-Hopf operators. This relation is the reult for several other relations between intermediate operators constructed for that purpose. The presented relations are obtained with the help of different extension methods that annulate particular actions of the related operators. All the operators are defined in Bessel potential spaces or Sobolev spaces. In particular, the final relation enables us to derive properties from a Wiener-Hopf operator to the intial one. An example of application of the presented results is done in a differaction problem by a union of two strips     

Achievable hierarchies in voting games with abstention

It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley–Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable in the class of complete VGA. The aim of this paper is twofold. Firstly, we show that all hierarchies are achievable in a subclass of weighted VGA, the class of weighted games for which a single weight is assigned to voters. Secondly, we conduct a partial study of achievable hierarchies within the subclass of H-complete games, that is, complete games under stronger versions of influence relation.     

Decision-making with a fuzzy preference relation

In most decisio-making problems a preference relation in the set of alternatives is of a fuzzy nature, reflecting for instance on the fuzziness of experts estimates of the preferences. In this paper, the corresponding fuzzy equivalence and strict preference relations are defined for a given fuzzy non-strict preference relation in an unfuzzy set of alternatives which are used to introduce in a natural way the fuzzy set of nondominated alternatives. Two types of linearity of a fuzzy relation are introduced and the equivalence of the unfuzzy nondominated alternatives is studied. It is shown that unfuzzy nondominated solutions to the decision-making problem exist, provided the original fuzzy relation satisfies some topological requirements. A simple method of calculating these solutions is indicated.     

Linear wave dispersion relation of a magnetized relativistic rectilinear electron beam-dielectric system

A general dispersion relation is derived for a relativistic rectilinear electron beam of arbitrary momentum distributions interacting with a dielectric in a guide magnetic field, on the basis of Maxwell equations and the relativistic Vlasov equation. The instability occurs when the beam velocity exceeds the wave phase velocity in the medium. The linear wave dispersion relation, growth rate, spatial growth rate are studied analytically for delta and Lorentzian distributions of beam momentums in detail. The results are of importance for a new kind of high-power microwave generation or amplification devices based on anomalous Doppler effect.     

Some models for deriving the priority weights from interval fuzzy preference relations

Interval fuzzy preference relation is a useful tool to express decision maker’s uncertain preference information. How to derive the priority weights from an interval fuzzy preference relation is an interesting and important issue in decision making with interval fuzzy preference relation(s). In this paper, some new concepts such as additive consistent interval fuzzy preference relation, multiplicative consistent interval fuzzy preference relation, etc., are defined. Some simple and practical linear programming models for deriving the priority weights from various interval fuzzy preference relations are established, and two numerical examples are provided to illustrate the developed models.     

Second structure relation for q-semiclassical polynomials of the Hahn Tableau

The q-classical orthogonal polynomials of the q-Hahn Tableau are characterized from their orthogonality condition and by a first and a second structure relation. Unfortunately, for the q-semiclassical orthogonal polynomials (a generalization of the classical ones) we find only in the literature the first structure relation. In this paper, a second structure relation is deduced. In particular, by means of a general finite-type relation between a q-semiclassical polynomial sequence and the sequence of its q-differences such a structure relation is obtained.     

Viscous potential flow analysis of interfacial stability with mass transfer through porous media

The interfacial stability with mass transfer, surface tension, and porous media between two rigid planes will be investigated in the view of viscous potential flow analysis. A general dispersion relation is obtained. For Kelvin-Helmholtz instability, it is found that the stability criterion is given by a critical value of the relative velocity. On the other hand, in the absence of gravity the problem reduces to Brinkman model of the stability of two fluid layers between two rigid planes. Vanishing of the critical value of the relative velocity gives rise to a new dispersion relation for Rayleigh-Taylor instability. Formulas for the growth rates and neutral stability curve are also given and applied to air-water flows. The effects of viscosity, porous media, surface tension, and heat transfer are also discussed in relation to whether the system is potentially stable or unstable. The Darcian term, permeability’s and porosity effects are also concluded for Kelvin-Helmholtz and Rayleigh-Taylor instabilities. The relation between porosity and dimensionless relative velocity is also investigated.     

Exact enumeration of acyclic deterministic automata

A linear recurrence relation is derived for the number of unlabelled initially connected acyclic automata. The coefficients of this relation are determined by another, alternating, recurrence relation. The latter determines, in particular, the number of acyclic automata with labelled states. Certain simple enumerative techniques developed by the author for counting initially connected automata and acyclic digraphs are combined and applied. Calculations show that the results obtained in this paper improve recent upper bounds for the number of minimal deterministic automata (with accepting states) recognizing finite languages. Various related questions are also discussed.     

Valued preference-based instantiation of argumentation frameworks with varied strength defeats

A Dung-style argumentation framework aims at representing conflicts among elements called arguments. The basic ingredients of this framework is a set of arguments and a Boolean abstract (i.e., its origin is not known) binary defeat relation. Preference-based argumentation frameworks are instantiations of Dung's framework in which the defeat relation is derived from an attack relation and a preference relation over the arguments. Recently, Dung's framework has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another argument. In this paper, we instantiate this extended framework by a preference-based argumentation framework with a valued preference relation. As particular cases, the latter can be derived from a weight function over the arguments or a Boolean preference relation. We show under some reasonable conditions that there are “less situations” in which a defense between arguments holds with a valued preference relation compared to a Boolean preference relation. Finally, we provide some conditions that the valued preference relation shall satisfy when it is derived from a weight function.     

Brownian motion, quantum corrections and a generalization of the Hermite polynomials

The nonequilibrium evolution of a Brownian particle, in the presence of a “heat bath” at thermal equilibrium (without imposing any friction mechanism from the outset), is considered. Using a suitable family of orthogonal polynomials, moments of the nonequilibrium probability distribution for the Brownian particle are introduced, which fulfill a recurrence relation. We review the case of classical Brownian motion, in which the orthogonal polynomials are the Hermite ones and the recurrence relation is a three-term one. After having performed a long-time approximation in the recurrence relation, the approximate nonequilibrium theory yields irreversible evolution of the Brownian particle towards thermal equilibrium with the “heat bath”. For quantum Brownian motion, which is the main subject of the present work, we restrict ourselves to include the first quantum correction: this leads us to introduce a new family of orthogonal polynomials which generalize the Hermite ones. Some general properties of the new family are established. The recurrence relation for the new moments of the nonequilibrium distribution, including the first quantum correction, turns out to be also a three-term one, which justifies the new family of polynomials. A long-time approximation on the new three-term recurrence relation describes irreversible evolution towards equilibrium for the new moment of lowest order. The standard Smoluchowski equations for the lowest order moments are recovered consistently, both classically and quantum-mechanically.