On uniqueness of （fuzzy） relation in some generalized rough set model

In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.     

Multilinear Singular and Fractional Integrals

In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give （L^v, L^q）, （H^p, L^q） boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.     

行为NA的随机变量阵列加权和的完全收敛性

In this paper we obtain theorems of complete convergence for weighted sums of arrays of rowwise negatively associated （NA） random variables. These results improve and extend the corresponding results obtained by Sung （2007）, Wang et al. （1998） and Li et al. （1995） in independent sequence case.     

Anticipative Stochastic Differential Equations with Non-smooth Diffusion Coefficient

In this paper we prove the existence and uniqueness of the solutions to the one-dimensional linear stochastic differential equation with Skorohod integral Xt（ω）=η（w）＋∫^t 0 asXs（ω）dWs＋∫^t 0 bsXs（ω）ds, t∈[0,1] where （Ws） is the canonical Wiener process defined on the standard Wiener space （W,H,u）, a is non-smooth and adapted, but η and b may be anticipating to the filtration generated by （Ws）. The intention of the paper is to eliminate the regularity of the diffusion coefficient a in the Malliavin sense, in the existing literature. The idea is to approach the non-smooth diffusion coefficient a by smooth ones.     

The Compact Quantum Group Uq（2） （Ⅱ）

In this paper, we first prove that the θ-deformation Uθ（2） of U（2） constructed by Connes and Violette is our special case of the quantum group Uq（2） constructed in our previous paper. Then we will show that the set of truces on the C^＊ -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ.     

广义非线性隐似变分不等式

A new class of generalized nonlinear implicit variational-like inequality problems （for short, GNIVLIP） in the setting of locally convex topological vector spaces is introduced and studied in this paper. Under suitable conditions, some existence theorems of solutions for （GNIVLIP） are presented by using some fixed point theorems.     

Dimension of Maximal Attractors for the m-dimensional Cahn-Hilliard System

On the basis of the existence of the maximal attractor of the m-dimensional Cahn-Hilliard system in the product spaces （L2（Ω））^m and （H2（Ω））^m, in this paper, its Hausdorff dimension is estimated by calculating the orthogonal projection of the linear variational operator of the system.     

量子代数${\cal U}_q(f(K,H))$的量子伴随作用

Let H = uq（sl（2）） or u（sl（2））. By means of the standard basis of polynomial algebras, the Glebsch-Gordan formula and quantum Clebsch-Gordan formula are proved by a unified method, and the explicit formula of the decomposition of V（1）^n into the direct sum of simple modules is given in this paper.     

构造二元向量值有理插值函数的一种新方法

At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.     

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω） （k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.     

On a student-related optimal control problem

In a recent paper (Ref. 1), Cheng and Teo discussed some further extensions of a student-related optimal control problem which was originally proposed by Raggettet al. (Ref. 2) and later on modified by Parlar (Ref. 3). In this paper, we treat further extensions of the problem.This paper is a modified and improved version of Ref. 4. It is based, in part, on research sponsored by NSF.     

L-fuzzy群理论的数理逻辑基础

Zadeh在文[1]中引入Fuzzy集概念之后，这一概念被Goguen[2]推广，真值域由单位闭区间被更一般的格所代替。Rosenfeld[3]将Zadeh的思想引入到群论中，提出Fuzzy群概念，真值域为格的Fuzzy群被称为L—fuzzy群[4]。本文的目的是用数理逻辑的语言陈述L—fuzzy群理论，构造L—fuzzy群的形式数学系统，从而建立L—fuzzy群理论的数理逻辑基础。     

Forbidden sets and stability in some rational difference equations

In this paper, we solve open problem (5) submitted by Sedaghat in his paper, On third order rational difference equations with quadratic terms, J. Differ. Equ. Appl., 14(8) (2008), pp. 889–897. We also confirm conjecture (6) in the mentioned paper.     

Evolution Problems involving non-stationary Operators between two Banach Spaces II. Ancillary results

This paper is a direct continuation of the first paper in this series[Quaestiones Math. 8 (1985), no. 2,], which deals Kith the evolution problem [B(t)u(t)]' = A(t)u(t), Bu(0) = y. whereas in the first paper existence and uniqueness results were presented, this paper contains the ancillary results formulated in the first paper. These results describe the properties of B(t)-evolutions with non-stationary generating pairs, as well as of the solution operator of [B(t)u(t)]' = Au, Bu(0) = y.

The notation of the first paper is assumed throughout and is used without further note. Citation of results from the first paper is made by equation number. The numbering of this paper follows that of the first paper in sequence.     

Comments on “A note on “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets””

In a recently published paper “A note on “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets””, Khalil and Hassan pointed out that assertions (3) and (4) of Theorem 3.2 in our previous paper “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets” are not true [2]. Furthermore, they introduced the notions of a generalized trapezoidal interval type-2 fuzzy soft subset and a generalized trapezoidal interval type-2 fuzzy soft equal and used these two notions to correct the flaw in assertions (3) and (4) of Theorem 3.2 in our previous paper. In this paper, we show by a counterexample that Khalil and Hassan's correction is incorrect and provide the modified versions of assertions (3) and (4) of Theorem 3.2, along with a strict proof. In addition, Khalil and Hassan pointed out by a counterexample that assertions (3)–(6) of Theorem 3.5 in our paper are not true and proposed the corrections of those assertions. In this paper, we show that Khalil and Hassan's counterexample and corrections are incorrect and provide a new example to verify the inaccuracies of assertions (3) and (5) of Theorem 3.5 in our paper. Moreover, we offer the modified versions of assertions (3) and (5) of Theorem 3.5 and prove them. Finally, Khalil and Hassan's statement that assertions (4) and (6) of Theorem 3.5 in our previous paper are not true is proven to be incorrect, i.e. assertions (4) and (6) of Theorem 3.5 in our previous paper are true.     

近代非线性回归在电力系统负荷短期预测中的应用

本文就河北省１９８５—１９９０年春节期间每小时用电量的统计数字用非线性回归模型（Ｇｏｍｐｅｒｔｄｚ）处理了６年中同日同一时间的耗电量，建立了回归模型，并预测了１９９１年同一时间的用电情况。实际表明本文的结果是可信的．     

THE STATIONALRITY ANDSPECTRAL REPRESENTATION OFONE CLASS OF NON-NEGATIVEINTEGER-VALUED TIME SERIES

1.IntroductionLet{x,}beatimeseriesdefinedonprobabilityspace(fi,r,P),satisfyingwhere(1)ac(t,s,j)isarandomfieldwithvalue1or0,t,sEI={0,FI,12,'.},jeN{1,2,'.},andsatisfies(i)p{ry(t,s,j)=0}=1whens>t;(l'2)(n)ac(tl,sltif)andn(t2,s2,j2)aremutuallyindependentwhenif/jZorsl/s2;(iii)Forfixeds,i,n(t,s,i)fort2sisanonhomogeneousMarkovChainwithtransitionRevisedJune23,1997.tNowworkinginU.S.A.frominstituteofSystemsScience,theChineseAcademyofSciences,Beijing100080,China.probabilityandinitialdistribution…     

Corrigendum to “A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets” [Appl. Math. Model. 37 (2013) 4948–4971]

The aim of this paper is to show by counterexamples that assertions (3) and (4) of Theorem 3.2, and assertions (3) and (5) of Theorem 3.5 in a previous paper by the authors [Appl. Math. Model. 37 (2013) 4948-4971] are incorrect and offer their modified versions.     

关于分离性和同胚关系的一些推广

1963年Norman Levine引入了半开集和半连续函数的概念。1972年S.Gene Crossley等又引入不定函数和前半开函数,定义了半同胚,讨论了一系列的半拓扑性质。以后出现了不少有关半开集和半同胚方面的论文。作者拟在这里进一步引入两类分离性和几种新的同胚,并且指出在一定意义下有些名称应当改变。 首先,我们在这里利用半开集,产生一种分离手段——半开集分离性,从而定义一系列新的拓扑空间,它们之间及它们与T_(i-)型拓扑空间(i=0,1,2,3,4)之间有着一定的联     

A new grey prediction model FGM(1, 1)

The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), abbreviated as FGM(1, 1), which is based on the existing GM(1, 1) but modelled with data including the first-entry’s messages of the original series. A proof concerning this subject has been presented by other authors. However, the algorithm of their direct proof is too complicated. A more compact algorithm is presented in this paper to prove the first entry of the original series ineffective to the modelling values and forecasts by GM(1, 1). Then, an arbitrary number can be inserted in the front of the original series to extract the messages from its first entry. Only a few data (usually fewer than ten) are used for model building. This paper deals with the effectiveness of the first entry of the original series by GM(1, 1).