D.C.隶属函数模糊集及其应用(II)——D.C.隶属函数模糊集的万能逼近性

本文是D.C.隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D.C.隶属函数模糊集,建立了D.C.隶属函数模糊集对模糊集的万有逼近性。探讨了D.C.隶属函数模糊集与模糊数之间的关系,给出了用D.C.隶属函数模糊集逼近模糊数的-εC e llina逼近形式,得到模糊数与D.C.函数之间的一个对应算子,指出了用模糊数表示D.C.函数的问题。     

Explicit characterizations of orthogonality in lS(C)

In a previous paper, the author used a notion of orthogonality introduced in another article to establish characterizations for orthogonality in the spaces l_S^p(C), 1?p<∞, thus obtaining generalizations of the usual characterization of orthogonality in the Hilbert spaces l_S²(C), via inner products. In this paper we make explicit these characterizations for some of the spaces l_S^p(C). We finish by presenting some remarks and open problems.     

Polynomial Rings over Non-noetherian Power Series Rings

ＰｏｌｙｎｏｍｉａｌＲｉｎｇｓｏｖｅｒＮｏｎ┐ｎｏｅｔｈｅｒｉａｎＰｏｗｅｒＳｅｒｉｅｓＲｉｎｇｓＣｈｅｎＨｕａｎｙｉｎ（陈焕艮）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ，４１００...     

Implications between strong large cardinal axioms

The rank-into-rank and stronger large cardinal axioms assert the existence of certain elementary embeddings. By the preservation of the large cardinal properties of the embeddings under certain operations, strong implications between various of these axioms are derived.     

On Normal Integral Bases

in this paper, let K = Q ( ) be an abelian number field,where mi's are distinct square-free integers and Gal (K/Q ) (Z/2Z )n+1, and let k Q(M). When k is imaginary or k is real and has a unit of norm -1, we give a necessaryand sufficient condition for K/k to have a normal integral basis.     

Second-Order Optimality Conditions in Set Optimization

In this paper, we propose second-order epiderivatives for set-valued maps. By using these concepts, second-order necessary optimality conditions and a sufficient optimality condition are given in set optimization. These conditions extend some known results in optimization.The authors are grateful to the referees for careful reading and helpful remarks.     

On differential inclusions with prescribed attainable sets

In this article, the inverse problem of the differential inclusion theory is studied. For a given ε>0 and a continuous set valued map t→W(t), t∈[t₀,θ], where W(t)⊂Rⁿ is compact and convex for every t∈[t₀,θ], it is required to define differential inclusion so that the Hausdorff distance between the attainable set of the differential inclusion at the time moment t with initial set (t₀,W(t₀)) and W(t) would be less than ε for every t∈[t₀,θ].     

基于SPA联系数的大连产业结构演化规律研究

SPA联系数是把研究对象各种测度联系起来加以系统性地描述、计算、分析的一种结构函数,其一般形式为a+bi+cj,用于城市第一产业、第二产业、第三产业相互联系和演化规律的研究有其合理和创新之处,其特点是把城市第一产业、第二产业、第三产业看成一个系统.用于大连产业结构演化规律研究后发现,大连市在1978~1999年20年间经历了稳定——剧烈调整——稳定这样三个阶段.在今后的10~20年间,对于第三产业的投资仍将处在首位.     

多元Kantorovich算子L_p范数下的渐近展开

本文给出了高维单纯形上Kantorovich算子在Lp（1＜P＜∞）范数下的高阶渐近展开公式．     

Trees, set compositions and the twisted descent algebra

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the linear span of set compositions (the twisted descent algebra). Among others, a number of enveloping algebra structures are introduced and studied in detail. For example, it is shown that the linear span of trees carries an enveloping algebra structure and embeds as such in an enveloping algebra of increasing trees. All our constructions arise naturally from the general theory of twisted Hopf algebras.