关于GMP和GMT问题的最优解

进一步研究模糊推理的非模糊形式，在几个重要的逻辑系统中形式地讨论GMP(广义取式)和GMT(广义拒取式)问题的最优解。结果表明，GMP和GMT问题的三I解和一种新的三I解都是某种意义下的最优解。还讨论所给算法的还原性问题。     

(O,N)-蕴涵的新性质

重叠函数是一类特殊的非结合的二元聚类函数.利用重叠函数可以诱导出不同形式的模糊蕴涵.文[7]介绍了由重叠函数O和模糊否定N诱导出的模糊蕴涵—(O,N)-蕴涵,并对(O,N)-蕴涵的基本性质进行了研究,但尚存一些重要性质尚未得到研究.主要基于自同构φ和模糊否定N的相关性质对(O,N)-蕴涵进行深入研究,给出(O,N)-蕴...     

R蕴涵与I_(T,N)蕴涵关系的研究

着重研究了R蕴涵与T_(T,N)蕴涵之间等价的条件,给出了二者等价的若干定理,有助于更好地理解I_(T,N)蕴涵与R蕴涵之间的关系,丰富了模糊蕴涵理论的内容.     

模与环的(■,U)-M-凝聚性

设N是一个无穷基数,U是平坦的右R-模,M是左R-模.称左R-模N是((N),U)-M-凝聚的,如果对任意的B/A→Rm,其中0≤A相似文献   

SU(n,1)/S(U(n)×U(1))上的中心极限定理

Let G=SU(n,1),K=S(U(n)×u(1)),and for l∈Z,let{η)1∈Z be a one-Dimensional K-type and let E1 be the line bundle over G/K associated to η.In this work we obtain a central limit theorem for the space El.     

On algebras satisfying $x^2x^2=N(x)x$

The commutative algebras satisfying the “adjoint identity”: , where N is a cubic form, are shown to be related to a class of generically algebraic Jordan algebras of degree at most 4 and to the pseudo-composition algebras. They are classified under a nondegeneracy condition. As byproducts, the associativity of the norm of any pseudo-composition algebra is proven and the unital commutative and power-associative algebras of degree are shown to be Jordan algebras. Received January 26, 1999; in final form August 26, 1999 / Published online July 3, 2000     

环的左(N,U)-凝聚维数

设R和S是环,U是平坦右R-模,V是平坦右S-模.本文中我们证明了(N,(U,V))-lc.dim(R⊕S)=sup((N,U)-lc.dim R,(N,V)-lc.dimS).     

Left (N,U)-coherent Dimensions and Excellent Extensions of Rings

Let S be an excellent extension of a ring R and U a flat right 5-module. We show in this paper that the left (N, U)-coherent dimension of S is equal to that of R.     

环的左(N,U)-凝聚维数和Excellent扩张

Let S be an excellent extension of a ring R and U a flat right S-module. We show in this paper that the left (N,U)-coherent dimension of S is equal to that of R.     

On Henstock integral of fuzzy-number-valued functions (I)

In this paper, we define and discuss the (FH) integral for fuzzy-number-valued functions. Using a concrete structure into which we embed the fuzzy number space E¹, several necessary and sufficient conditions of integrability for fuzzy-number-valued functions are given by means of abstract function theory.     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G = SU(2,2), K = S(U(2)×U(2)), and for l∈Z, let {τl}l∈z be a onedimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.     

Algorithms for Computing U(N) Clebsch Gordan Coefficients

If V ^(m) is an irreducible representation space for the unitary group U(N), then the r-fold tensor product space, is in general reducible. Such a reducible representation can be reduced to a direct sum of irreducible representation spaces, albeit with multiplicity. Clebsch–Gordan coefficients are the overlap coefficients between an orthonormal basis in the tensor product space and an orthonormal basis in the direct sum space. Since such coefficients are basis dependent, bases in the U(N) irrep spaces must be chosen. In this paper we use the Gelfand–Zetlin basis, built out of the chain of subgroups U(N)⊃...⊃U(1). Our first result is to derive algorithms for generating Gelfand–Zetlin bases from Gelfand–Zetlin tableaux. Given these concrete basis realizations we develop algorithms for computing the Clebsch–Gordan coefficients themselves.      

U(3,Z_p),U(4,Z_p)及U(5,Z_p)的共轭类

通过计算相关矩阵的秩,求出了U(3,Z_p),U(4,Z_p)及U(5,Z_p)的共轭类.     

曲面到U（N）中有限的调和映射

本文证明了如果ｓ是从曲面Ω到Ｕ（Ｎ）中有限的调和映射，则Ａｚ，Ａｚ－是幂零的，并给出其逆不成立的反例。     

Hardy spaces H_L~p(R~n) associated with operators satisfying k-Davies-Gaffney estimates

Let L be a one-to-one operator of type ω having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k ∈ N. In this paper, the authors introduce the Hardy space HLp(Rn) with p ∈ (0, 1] associated with L in terms of square functions defined via {e-t2kL}t>0 and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schrdinger type operator L2 := (-Δ)k + Vk, where Δ is the Laplacian and 0≤V∈Llock(Rn). Moreover, as an application, for i ∈ {1, 2}, the authors prove that the associated Riesz transform ▽k(Li-1/2) is bounded from HLip (Rn) to Hp(Rn) for p ∈ (n/(n + k), 1] and establish the Riesz transform characterizations of HL1p (Rn) for p ∈ (rn/(n + kr), 1] if {e-tL1 }t>0 satisfies the Lr-L2 k-off-diagonal estimates with r ∈ (1, 2]. These results when k := 1 and L := L1 are known.     

Doob's Decomposition Theorem for Fuzzy (Super) Submartingales

Abstract

The notions of fuzzy random variables and fuzzy (super) submartingales are introduced. In this paper we provide the necessary and sufficient conditions of Doob's decomposition for fuzzy (super) submartingales. Finally, we discuss the decomposition of fuzzy (super) submartingales on R, and an example is given which explains that not every fuzzy (super) submartingale has Doob's decomposition.