区间集上的格蕴涵代数、FI-代数、MV-代数的研究

区间集是一个新的重要的研究方向,在近似推理、模糊控制等领域中有着广泛的应用。在区间集上,重新定义了区间蕴涵今,构造了格蕴涵代数,讨论了格蕴涵代数的一系列性质。同时在区间集上也重新定义了可换FI-代数和MV-代数,证明了格蕴涵代数、FI-代数和MV-代数3种不同的代数系统是等价的。     

Worst case bounds on the point-wise discretization error in boundary element method for the elasticity problem

In this work, point-wise discretization error is bounded via interval approach for the elasticity problem using interval boundary element formulation. The formulation allows for computation of the worst case bounds on the boundary values for the elasticity problem. From these bounds the worst case bounds on the true solution at any point in the domain of the system can be computed. Examples are presented to demonstrate the effectiveness of the treatment of local discretization error in elasticity problem via interval methods.     

TREE-LIKE HIERARCHY OF SYSTEMS

In this paper the concepts of tree-like hierarchy of systems and linked hierarchy of systems are introduced. The concepts can be seen as generalizations of those of time systems and linked time systems, respectively; moreover, the concepts can be used to establish models of social organizations and of the development of a cultural entity. Some open questions are posed.     

Interval optimization of dynamic response for structures with interval parameters

This paper presents an interval optimization method for the dynamic response of structures with interval parameters. The matrices of structures with interval parameters are given. Combining the interval extension of function with the perturbation theory of dynamic response, the method for interval dynamic response analysis is derived. The interval optimization problem is transformed into a corresponding deterministic one. Because the mean values and the uncertainties of the interval parameters can be elected as the design variables, more information of the optimization results can be obtained by the present method than that obtained by the deterministic one. The present method is implemented for a truss structure and a frame structure. The numerical results show that the method is effective.     

A note on functions associated with Gödel formulas

We give a characterization of functions associated with formulas of Gödel logic, following what has been done by McNaughton for Lukasiewicz logic.     

Tensor products of MV-algebras

 The structure of MV-module over a PMV-algebra was defined in [5]. In this paper we test this notion in the important problem of scalar extension. The tensor product ⊗ _mv defined in [11] is generalized and another tensor product, ⊗ _o , is studied in relation with the corresponding tensor product of ℓ-groups [9]. Using tensor products we get the free MV-modules over a totally ordered PMV-algebra. Dedicated to Prof. Ján Jakubíik on the occasion of his 80th birthday     

An algorithmic approach to resolutions

We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modified to construct minimal projective resolutions of linear modules over Koszul algebras.     

彝文输入法自由编码方案的推广及应用

简述并探讨基于自由拆分模式的彝文输入法编码优化方案,从文字字形结构特点出发,运用自由拆分模式的形码编码方案,对比分析规范彝文文字和云南部分少数民族文字,探究其共性,以实现自由编码方案在云南少数民族文字中的推广和应用,从而为云南少数民族地区文字信息化处理的研究提供方法和内容上的参考。     

On interval fuzzy S-implications

This paper presents an analysis of interval-valued S-implications and interval-valued automorphisms, showing a way to obtain an interval-valued S-implication from two S-implications, such that the resulting interval-valued S-implication is said to be obtainable. Some consequences of that are: (1) the resulting interval-valued S-implication satisfies the correctness property, and (2) some important properties of usual S-implications are preserved by such interval representations. A relation between S-implications and interval-valued S-implications is outlined, showing that the action of an interval-valued automorphism on an interval-valued S-implication produces another interval-valued S-implication.     

有理Bézier曲面的区间隐式化

本文依据以往的研究引入了有理Bézier曲面的区间隐式化的概念,即找到一条较低次的区间代数曲面使得给出的有理Bézier曲面落在该区间代数曲面内,并使得该区间代数曲面的宽度达到最小．文中给出了一个通过解一个带有线性限制条件的二次优化问题来计算一有理Bézier曲面的区间代数曲面的算法,并用实例演示了该算法．     

Meet continuity properties of posets

In this paper we consider a number of properties of posets that are not directed complete: in particular, meet continuous posets, locally meet continuous posets and PI-meet continuous posets are introduced. Characterizations of (locally) meet continuous posets are presented. The main results are: (1) A poset is meet continuous iff its lattice of Scott closed subsets is a complete Heyting algebra; (2) A poset is a meet continuous poset with a lower hereditary Scott topology iff its upper topology is contained in its local Scott topology and the lattice of all local Scott closed sets is a complete Heyting algebra; and (3) A poset with a lower hereditary Scott topology is meet continuous iff it is locally meet continuous, iff it is PI-meet continuous.     

Computing on a free tree via complexity-preserving mappings

The relationship between linear lists and free trees is studied. We examine a number of well-known data structures for computing functions on linear lists and show that they can be canonically transformed into data structures for computing the same functions defined over free trees. This is used to establish new upper bounds on the complexity of several query-answering problems.This work was started when the author was at Brown University, Providence, RI. It was partly supported by NSF Grant MCS 83-03925. A preliminary version of this work has appeared in theProceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, West Palm Beach, FL, October 1984, pp. 358–368.     

Weak pseudo-Wajsberg and weak pseudo-MV algebras

 We introduce and study a generalization of pseudo-Wajsberg and pseudo-MV algebras. The weakening of the axioms leads to the existence of two lattice structures, and of two multiplicative monoid structures. Some categorical equivalences are established.     

N-可分效应代数

引入了N-可分效应代数的定义,证明了N-可分效应代数是区间效应代数且N-可分效应代数可嵌入到可分效应代数中.     

Comparison of finite element and pendulum models for simulation of sloshing

The pendulum model is a cost effective tool for the simulation of sloshing. However, the accuracy and applicability of the model has not been well established. In this article, we compare the simulation results obtained from the pendulum model and a more complicated finite element model for sloshing of liquids in tanker trucks. In the pendulum model, we assume that the liquid in the tanker is a point mass oscillating like a frictionless pendulum subjected to an external acceleration. In the finite element model, we solve the full Navier-Stokes equations written for two fluids to obtain the location and motion of the free surface. Stabilized finite element formulations are used in these complex 3D simulations. These finite element formulations are implemented in parallel using the message-passing interface libraries. The numerical example includes the simulation of sloshing in tanker trucks during turning.     

Cartesian product of compressible effect algebras

In the paper, we prove that is compatible with p}, the set of commutant of p, and , the projection commutant of a, are all normal sub-effect algebras of a compressible effect algebra E, and is a direct retraction on E} is a normal sub-effect algebra of an effect algebra E. Moreover, we answer an open question in Gudder’s (Rep Math Phys 54:93–114, 2004), Compressible effect algebras, Rep Math Phys, by showing that the cartesian product of an infinite number of E _i is a compressible effect algebra if and only if each E _i is a compressible effect algebra. This work was supported by the SF of Education Department of Shaanxi Province (Grant No. 07JK267), P. R. China.     

Theorems on the structure of finite dimensional estimation algebras

In this paper we proved several theorems concerning the structure of finite dimensional estimation algebras. In particular, under proper technical assumptions, we proved the following: (1) The observation of a filtering system must be linear if the estimation algebra is finite dimensional. (2) All elements of a finite dimensional estimation algebra belong to a special class of polynomial differential operators. (3) All finite dimensional estimation algebras are solvable.     

Transformational reducibility and synthesis of algorithms and programs of symbolic processing

This paper deals with the algebra of algorithmics in the context of developing modern means of transformation and synthesis of algorithms and programs in object-oriented environments. This report was first presented by the author in English at the conference ECI-2005 (Kosice, Slovakia). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 165–173, September–October 2006.     

Finite derivation type for Rees matrix semigroups

This paper introduces the topological finiteness condition finite derivation type   (FDT) on the class of semigroups. This notion is naturally extended from the monoid case. With this new concept we are able to prove that if a Rees matrix semigroup M[S;I,J;P]$M[S;I,J;P]$ has FDT then the semigroup S$S$ also has FDT. Given a monoid S$S$ and a finitely presented Rees matrix semigroup M[S;I,J;P]$M[S;I,J;P]$ we prove that if the ideal of S$S$ generated by the entries of P$P$ has FDT, then so does M[S;I,J;P]$M[S;I,J;P]$. In particular, we show that, for a finitely presented completely simple semigroup M$M$, the Rees matrix semigroup M=M[S;I,J;P]$M=M[S;I,J;P]$ has FDT if and only if the group S$S$ has FDT.     

Letterplace ideals and non-commutative Gröbner bases

In this paper we propose a 1-to-1 correspondence between graded two-sided ideals of the free associative algebra and some class of ideals of the algebra of polynomials, whose variables are double-indexed commuting ones. We call these ideals the “letterplace analogues” of graded two-sided ideals. We study the behaviour of the generating sets of the ideals under this correspondence, and in particular that of the Gröbner bases. In this way, we obtain a new method for computing non-commutative homogeneous Gröbner bases via polynomials in commuting variables. Since the letterplace ideals are stable under the action of a monoid of endomorphisms of the polynomial algebra, the proposed algorithm results in an example of a Buchberger procedure “reduced by symmetry”. Owing to the portability of our algorithm to any computer algebra system able to compute commutative Gröbner bases, we present an experimental implementation of our method in Singular. By means of a representative set of examples, we show finally that our implementation is competitive with computer algebra systems that provide non-commutative Gröbner bases from classical algorithms.