无限Fuzzy关系方程的解集

对(0,1)格上的无限Fuzzy关系方程,给出其可解的充要条件.利用可达解与不可达解的概念,给出方程存在可达解与不可达解的充要条件.进一步,在解集非空时,刻画了方程的解集的结构及性质.     

完备Brouwer格上有限inf-αT合成关系方程的解集

讨论了完备Brouwer格上有限inf-αT(其中T为伪t-模)合成关系方程,给出了方程解集非空的充要条件.当方程infαTj∈J(αj,xj)=b中b为交既约元时,证明了方程解集中存在极大解的一个充分条件,并给出了方程解集的结构.     

无限模糊关系方程解集的性质

对[0,1]上sup-合成无限模糊关系方程的解集性质,特别是无限模糊关系方程的偏可达解的性质作了讨论.首先构造了方程的偏可达解,并获得了无限模糊关系方程存在偏可达解的充要条件,然后证明了当偏可达解集非空时,偏可达解集中每一个元素都存在严格小于它的偏可达解,进一步说明偏可达解集中每一个元都没有小于等于它的极小元.     

论域无限时完备完全分配格上@-Fuzzy关系方程解集的一些性质和结构

给出连续交既约元的概念，然后在论域无限时，对定义在完备完全分配格上的@-Fuzzy关系方程的解集的性质和结构进行了讨论。     

[0,1]格上无限inf-αR合成Fuzzy关系方程的解集北大核心

在[0,1]格上讨论了无限inf-αR合成Fuzzy关系方程的解集问题,从方程的系数出发,给出了方程存在可达解和不可达解的充要条件。进一步,在解集非空时,刻画了方程解集的结构。     

带一阶导数项多滞量二阶中立型方程解的振动的充要条件

考虑中立型方程其中p_i,r_j(i∈I,j∈J)为任意实常数,q_k,τ_i(k∈K,i∈J)为正常数,而ρ_j,σ_k(j∈J,k∈K)是非负常数。则方程(*)所有解振动的充要条件是它的特征方程无实根。     

关于丢番图方程X~2+4Y~4=pZ~4

设p为素数,p=4A~2+1+2|A,A∈N~*.运用二次和四次丢番图方程的结果证明了方程G:X~2+4Y~4=pZ~4,gcd(X,Y,Z)=1,除开正整数解(X,Y,Z)=(1,A,1)外,当A≡1(mod4)时,至多还有正整数解(X,Y,Z)满足X=|p(a~2-b~2)~2-4(A(a~2-b~2)±ab)~2|,Y~2=A(a~2-b~2)~2±2ab(a~2-b~2)-4a~2b~2A,Z=a~2+b~2;当A≡3(mod4)时,至多还有正整数解(X,Y,Z)满足X=|4a~2b~2A-(4abA±(a~2-b~2))~2|,Y~2=4a~2b~2A±2ab(a~2-b~2)-A(a~2-b~2)~2,Z=a~2+b~2.这里a,b∈N~*并且ab,gcd(a,b)=1,2|(a+b).同时具体给出了p=5时方程G的全部正整数解.     

不定方程x4-y4=n整数解求法探讨

求方程 x4- y4=n　 ( n∈ N)的整数解 ,至今还没见到一般方法 ,本文将给出这类不定方程一种解法 .文中字母 P表示质数集 ,符号 ( a,b)( a、b∈ Z)表示不定方程　　 x4- y4=n　 ( n∈ N) ( 1 )的整数解 .定理 1　若 n∈ P,则方程 ( 1 )没有整数解 .证明　假定方程 ( 1 )有整数解 ( a,b) ,定有　 a2 b2 =n,　 a2 - b2 =1 ,∵　 a、b∈ Z,| a| >| b| ,只有　　　 (± 1 ) 2 - 0 2 =1 ,∴　 a =± 1 ,　 b =0 ,　 a2 b2 =1 ,与 a2 b2 =n是质数相矛盾 ,故方程 ( 1 )没有整数解 .由费马定理知 ,有定理 2　当 n =m4( n∈ N)时 ,则方程 ( 1…     

一类奇异线性方程组的Cramer法则

在 [3]中 ,给出了一类奇异线性方程组Ax =b的唯一解x =Adb的Cramer法则。本文将其推广到带W 权Drazin逆Ad ,w,得到如下结果 :奇异线性方程组Ax =b的唯一解x =WAd,wWb的分量xj 可表示成xj=det (WA) (j→Wb) UV(j→ 0 ) 0 　det WAUV 0 　j=1,2 ,… ,n ,其中A∈Cm×n,W∈Cn×m,Ind(WA) =k1,Ind(AW ) =k2 ,rank(WA) k1=r 相似文献   

A∩B={x|x∈A或x∈B}?!

众所周知,AU∪B={x|x∈A或x∈B},但我们发现,用它来解下面的一道题,结果却是错误的,而用A∩B={x|x∈A或x∈B)求解,结果恰好是正确的,不信,请看题目求方程tgx·tgx/2=0的解集, 解法1 方程tgx·tgx/2=0的解集为{x|     

The solution sets of infinite fuzzy relational equations with sup-conjunctor composition on complete distributive lattices

This paper deals with sup-conjunctor composition fuzzy relational equations in infinite domains and on complete distributive lattices. When its right-hand side is a continuous join-irreducible element or has an irredundant continuous join-decomposition, a necessary and sufficient condition describing an attainable solution (resp. an unattainable solution) is formulated and some properties of the attainable solution (resp. the unattainable solution) are shown. Further, the structure of solution sets is investigated.     

On Products of Property b1

In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.     

The lattice of quasiorder lattices of algebras on a finite set

The quasiorders of an algebra (A, F) constitute a common generalization of its congruences and compatible partial orders. The quasiorder lattices of all algebras defined on a fixed set A ordered by inclusion form a complete lattice \({\mathcal{L}}\). The paper is devoted to the study of this lattice \({\mathcal{L}}\). We describe its join-irreducible elements and its coatoms. Each meet-irreducible element of \({\mathcal{L}}\) being determined by a single unary mapping on A, we characterize completely those which are determined by a permutation or by an acyclic mapping on the set A. Using these characterizations, we deduce several properties of the lattice \({\mathcal{L}}\); in particular, we prove that \({\mathcal{L}}\) is always tolerance-simple.     

格的模糊软理想

将模糊软集与格的模糊理想概念相结合,引入了格的模糊软理想的概念,给出了它们的若干代数性质.定义了格的模糊软同态(同构)概念,证明了格的一个模糊软理想在模糊软同构(同态)下的像(原像)仍为模糊软理想的结论.     

同伦群和上同调群的上乘积

<正> 在[1]中,作者研究了一个(N—1)维连通空间的同伦群和同调群的密切关系,那里所考虑的同伦群的维数是在(2N—2)以内,本文可以看成[1]的继续,我偿将考虑维数在(2N—1)以上而又在(3N—3)以下的同伦群,Betti 数;和上乘积的密切关系.我们     

The lattice of strict completions of a finite poset

For a given finite poset , we construct strict completions of P which are models of all finite lattices L such that the set of join-irreducible elements of L is isomorphic to P. This family of lattices, , turns out to be itself a lattice, which is lower bounded and lower semimodular. We determine the join-irreducible elements of this lattice. We relate properties of the lattice to properties of our given poset P, and in particular we characterize the posets P for which . Finally we study the case where is distributive. Received October 13, 2000; accepted in final form June 13, 2001.     

A new hybrid iterative method for mixed equilibrium problems and variational inequality problem for relaxed cocoercive mappings with application to optimization problems

In this paper, we introduce and study a new hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-Lipschitz continuous and relaxed (m,v)-cocoercive mappings in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm which solves some optimization problems under some suitable conditions. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab and Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl (2009). doi:10.1016/j.jmaa.2008.12.005] and Gao and Guo [X. Gao and Y. Guo, Strong convergence theorem of a modified iterative algorithm for Mixed equilibrium problems in Hilbert spaces, J. Inequal. Appl. (2008). doi:10.1155/2008/454181] and many others.     

二维Landau-Lifshitz静态方程组的渐近性质

在本文中，我们讨论了ｕ∧（－Δｕ＋λ（ｕ，ｎ）ｎ）＝０，｜ｕ｜＝１，ｘ∈Ｂ１和ｕ＝（ｘ１，ｘ２，０）ｘ∈Ｂ１的轴对称解ｕλ的渐近行为，其中Ｂ１是Ｒ２中单位圆，ｕ＝（ｕ１，ｕ２，ｕ３）．我们证明了ｕλｕ∞在Ｈ２Ｂ１＼Ｂε，Ｒ３中．