Exchange Relation Planar Algebras

An inclusion of II ₁ factors NM of finite index has as an invariant, a double sequence of finite-dimensional algebras known as the standard invariant. Planar algebras were introduced by V. Jones as a geometric tool for computing standard invariants of existing subfactors as well as generating standard invariants for new subfactors. In this paper we define a class of planar algebras, termed exchange relation planar algebras, that provides a general framework for understanding several classes of known subfactor inclusions: the Fuss–Catalan algebras (i.e. those coming from the presence of intermediate subfactors) and all depth 2 subfactors. In addition, we present a new class of planar algebras (and thus a new class of subfactors) coming from automorphism subgroups of finite groups.     

An M/M/1 Driven Fluid Queue – Continued Fraction Approach

This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264].     

The Homogeneous Hamilton–Jacobi and Bernoulli Equations Revisited, II

It is shown that the admissible solutions of the continuity and Bernoulli or Burgers' equations of a perfect one-dimensional liquid are conditioned by a relation established in 1949–1950 by Pauli, Morette, and Van Hove, apparently, overlooked so far, which, in our case, stipulates that the mass density is proportional to the second derivative of the velocity potential. Positivity of the density implies convexity of the potential, i.e., smooth solutions, no shock. Non-elementary and symmetric solutions of the above equations are given in analytical and numerical form. Analytically, these solutions are derived from the original Ansatz proposed in Ref. 1 and from the ensuing operations which show that they represent a particular case of the general implicit solutions of Burgers' equation. Numerically and with the help of an ad hoc computer program, these solutions are simulated for a variety of initial conditions called compatible if they satisfy the Morette–Van Hove formula and anti-compatible if the sign of the initial velocity field is reversed. In the latter case, singular behaviour is observed. Part of the theoretical development presented here is rephrased in the context of the Hopf–Lax formula whose domain of applicability for the solution of the Cauchy problem of the homogeneous Hamilton–Jacobi equation has recently been enlarged.     

集对Fuzzy格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处）,并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样,与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应,软代数在集对 Ｆｕｚｚｙ 格中有表示,在理论上是很完美的     

关于Fuzzy Drazin子半群

本文引进了ＦｕｚｚｙＤｒａｚｉｎ子半群的概念,并讨论了它们的一些代数性质,改进并推广了［５］、［６］、［８］、［１０］及［１１］中的许多重要结果     

带模糊约束的最小费用流问题

本文首次提出了带模糊约束的最小费用流问题,建立了相应的数学模型并给出了求解这一模型的有关算法。最后,给出了一个具体实例。     

模糊广义判断矩阵的一致性检验及合成排序

决策评价过程中往往包含诸多不确定性、随机性和模糊性,广义判断下的ＡＨＰ－ＧＪＡＨＰ是一种广义ＡＨＰ,Ｆｕｚｚｙ 环境下的ＧＪＡＨＰ决策方法是应用集值统计的方法,在区间判断标度基础上确定模糊判断矩阵元素的正模糊数表示,并根据模糊集理论的扩展原理,求得Ｆｕｚｚｙ 环境下的模糊排序权值向量。本文给出模糊广义判断矩阵的一致性定义,讨论了各类判断形式条件下的一致性检验法与Ｆｕｚｚｙ 环境下递阶层次结构中的合成排序问题     

综合函数与扩展原理

本文首先对合情扩展映射的公理化条件的完备性与独立性进行讨论,之后给出了扩展原理的一般形式及合情扩展映射的等价定义。最后,利用综合函数,特别是变维综合函数列,给出了扩展原理的一些具体形式     

复Fuzzy函数的Buckley导数与Buckley积分

本文对Ｊ．Ｊ．Ｂｕｃｋｌｅｙ在［１］、［２］中给出的实变量复Ｆｕｚｚｙ数值函数的导数与积分加以推广,引出复变量复Ｆｕｚｚｙ数值的导数与积分概念,为研究Ｆｕｚｚｙ复分析打下一定的基础。     

On fuzzy subgroups and fuzzy ideals under triangular norms

In this communication, we explicitly point out that the principal results of Liu 1982 basically deduced from the definition of binary operation ° on the set F(X) of all fuzzy subsets of X, also hold if one uses the weaker definition of product under triangular norm °_t. Fuzzy ideals with respect to the triangular norms are also defined.