1.

Cartesian closed categories of FƵdomains





Min Liu Bin Zhao《数学学报(英文版)》,2013年第29卷第12期


A subset system Z assigns to each partially ordered set P a certain collection Z（P） of subsets. In this paper, a new kind of subset systems called directable subset systems is introduced. For a directable subset system Z, the concepts of FZwaybelow relation and FZdomain are introduced. The wellknown Scott topology is naturally generalized to the Zlevel and the resulting topology is called FZScott topology, and the continuous functions with respect to this topology are characterized by preserving the suprema of directed Zsets. Then, we mainly consider a generalization of the cartesian closedness of the categories DCPO of directed complete posets, BF of bifinite domains and FS of FSdomains to the Zlevel. Corresponding to them, it is proved that, for a suitable subset system Z, the categories FZCPO of Zcomplete posets, FSFZ of finitely separated FZdomains and BFFZ of bifinite FZdomains are all cartesian closed. Some examples of these categories are given.

2.

An L0（F,R）valued Function＇s Intermediate Value Theorem and Its Applications to Random Uniform Convexity





Tie Xin GUO Xiao Lin ZENG《数学学报(英文版)》,2012年第28卷第5期


Let (Ω , F , P ) be a probability space and L0 ( F, R ) the algebra of equivalence classes of real valued random variables on (Ω , F , P ). When L0 ( F, R ) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0 ( F, R ) to L0 ( F, R ). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module ( S, · ) is random uniformly convex iff Lp ( S ) is uniformly convex for each fixed positive number p such that 1 p + ∞ .

3.

Scott连续自映射不动点的注记





奚小勇 李永明《数学研究及应用》,2011年第31卷第1期


It is discussed in this paper that under what conditions, for a continuous domain L, there is a Scott continuous selfmapping f ： L → L such that the set of fixed points fix（f） is not continuous in the ordering induced by L. For any algebraic domain L with a countable base and a smallest element, the problem presented by Huth is partially solved. Also, an example is given and shows that there is a bounded complete domain L such that for any Scott continuous stable selfmapping f, fix（f） is not the retract of L.

4.

ON THE EMBEDDING OF TOP IN THE CATEGORY OF STRATIFIED LTOPOLOGICAL SPACES 被引次数：1





LAI Hongliang ZHANG Dexue《数学年刊B辑(英文版)》,2005年第26卷第2期


§1. Introduction and PreliminariesLet L be a complete lattice. An Ltopology on a set X is a subset τ of LX closed withrespect to ?nite meets and arbitrary joins. (X,τ) is called an Ltopological space. The Ltopology τ is called strati?ed if it contains all the constant maps from X to L, and in this case(X,τ) is called a strati?ed Ltopological space. A continuous map between two Ltopologicalspaces (X,τX) and (Y,τY ) is a function f : X ?→ Y such that f←(λ) = λ ? f ∈ τX…

5.

Zero divisors and prime elements of bounded semirings





Tongsuo Wu Yuanlin Li Dancheng Lu《Frontiers of Mathematics in China》,2014年第9卷第6期


A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A bounded semiring is a semiring equipped with a compatible bounded partial order. In this paper, properties of zero divisors and prime elements of a bounded semiring are studied. In particular, it is proved that under some mild assumption, the set Z（A） of nonzero zero divisors of A is A ／ {0, 1}, and each prime element of A is a maximal element. For a bounded semiring A with Z（A） = A ／ {0, 1}, it is proved that A has finitely many maximal elements if ACC holds either for elements of A or for principal annihilating ideals of A. As an application of prime elements, we show that the structure of a bounded semiring A is completely determined by the structure of integral bounded semirings if either ｜Z（A）｜ = 1 or ｜Z（A）｜  2 and Z（A）2 ≠ 0. Applications to the ideal structure of commutative rings are also considered. In particular, when R has a finite number of ideals, it is shown that the chain complex of the poset I（R） is pure and shellable, where I（R） consists of all ideals of R.

6.

THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA





周惊雷 李庆国《数学物理学报(B辑英文版)》,2010年第30卷第3期


Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain： （i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.

7.

Hypercontinuous Posets





Wenfeng ZHANG Xiaoquan XU《数学年刊B辑(英文版)》,2015年第36卷第2期


The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.

8.

ON THE EQUIVALENCE PRINCIPLE FOR CONTRACTIVE MAPPINGS





丁协平《数学年刊B辑(英文版)》,1984年第2期


The main result is:Theorem 1.Let T be a continuous selfmapping of a complete metric space(X,d)andhave the unique fixed point property.If there exists n:X→N(the set of all positive integers)which is locally bounded such that for each x∈X and for all r∈N,r≥n(x),D(O_T(T~(n(x))x,0,r))≤(?)(D(O_T(x,0,r))),orD(O_T(T~(n(x))x,0,r))≤(?)(D(O_T(x,0,r))),where(?),and(?)are contractive gauge functions,then(a)T has a unique fixed point x~*;(b)For each x∈X,T~nx→x~* as n→∞;(e)There exists a neighborhood U(x~*)of x~* such that(?)T~n(U(x~*))={x~*};(d)x~*is stable;(e)For any given C∈(0,1)there exists a metric d~* topologically equivalent to d suchthat T is a Banach contraction under d~* with Lipschitz constant C.By Theorem 1 it is shown that many contractive type mappings defined in[1—26]aretopologically equivalent to each other.

9.

MAXIMAL SUBSPACES FOR SOLUTIONS OF THE SECOND ORDER ABSTRACT CAUCHY PROBLEM





Guoxiang Chen Meiying Wang《分析论及其应用》,2007年第23卷第3期


For a continuous, increasing function ω: R → R \{0} of finite exponential type, this paper introduces the set Z(A, ω) of all x in a Banach space X for which the second order abstract differential equation (2) has a mild solution such that [ω(t)]1u(t,x) is uniformly continues on R , and show that Z(A, ω) is a maximal Banach subspace continuously embedded in X, where A ∈ B(X) is closed. Moreover, Az(A,ω) generates an O(ω(t))strongly continuous cosine operator function family.

10.

The hyperspace of the regions below of all latticevalue continuous maps and its Hilbert cube compactification





YANG Zhongqiang Department of Mathematics Shantou University Shantou 515063 China《中国科学A辑(英文版)》,2005年第48卷第4期


Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.

11.

The Analytic Solution of Operator Equation of the First Kind 被引次数：2





崔明根 邓中兴 吴勃英《数学进展》,1988年第1期


Let W_2~1[a,b]≡W_2~1 = {u(x) u(x) is absolute continuous real function on [α,b],and u' (x)∈L~2[α,b]}. Set inner product

12.

Characterization in Approximation with Restricted Ranges





许树声《数学进展》,1992年第1期


Let [a,b] be a compact set containing at least n+1 points,C the set ofall continuous real valued functions defined on with uniform norm If φ_n=span{φ_1,…,φ_n),φ_i∈C([a,b])and φ_1,…,φ_n is an extended Chebyshev system of order,r(1≤r≤n),then we call K={q∈φ_n:l(x)≤q(x)≤u(x),x∈[a,b]} the set ofgeneralized polynomials having restricted ranges,where l and u are extended real

13.

Ergodic Retraction Theorem and Weak Convergence Theorem for Reversible Semigroups of NonLipschitzian Mappings





Liu Chuan ZENG《数学学报(英文版)》,2006年第22卷第2期


Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F（T） of T in C is nonempty. It is shown that if G is right reversible, then for each almostorbit u（.） of T, ∩s∈G ^CO{u（t） ： t ≥ s} ∩ F（T） consists of at most one point. Furthermore, ∩s∈G ^CO{Ttx ： t ≥ s} ∩ F（T） is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F（T） such that PTs  TsP = P for all s ∈ G and Px ∈^CO{Ttx ： s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u（t） ： t ∈ G} to a common fixed point of T.

14.

A CHARACTERIZATION OF l~1(Γ) TYPE BANACH SPACES





肖远辉《数学物理学报(B辑英文版)》,1993年第1期


In this paper it turns out that a Banach lattice X is order isomorphic to l~1(Γ) for some nonempty set Γ iff it is a Schur space and all the infinitely dimensional, separable and closed ideals of X are order isomorphic.

15.

The Saturation Property of Cosine Operator Function





《数学研究与评论》,1991年第3期


Let X be a Banach space and B(X)the algebra of all bounded linearoperators on X.{C(t);t∈R}is a strongly continuous cosine operator functionon X with infinitesimal generator A[1].Lemma I For each f,X,one has:

16.

Regularity for quasilinear degenerate elliptic equations with VMO coefficients





Shen Zhou Zheng《数学学报(英文版)》,2008年第24卷第11期


In this paper we establish an interior regularity of weak solution for quasilinear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1  n/q, 1  n/γ}.

17.

双诱导映射■集合范畴的L_b余等值子和L_b正则满态射(英文)





张红 汤建钢 李国华《数学季刊》,2012年第2期


In this paper,it gives the definition of the category of ■sets and biinduced maps whose true value set is a Locale,a complete Heyting algebra.In this category it defines the L_bmonomorphisms and the L_bepimorphisms.Especially,it gives the definition,the judgmental theorem of L_bcoequalizers.Furthermore,it defines L_bregular epimorphisms and proves the judgmental theorem.At the end it concludes a result:the category of ■sets and biinduced maps is finitely cocomplete.

18.

REGULARITY OF H~1 ∩L~(n((γ1)/(2γ))) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS





何旭东 陈宝耀《数学物理学报(B辑英文版)》,1990年第2期


Let us consider the following elliptic systems of second orderD_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R~n, n≥3 (1) and supposeⅰ) A_i~α(x, u, Du)≤L(1+Du);ⅱ) (1+p)~(1)A_i~α(x, u, p)are H(?)ldercontinuous functions with some exponent δ on (?)×R~N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R~N)∩L~(n(γ1)/(2γ))(Ω, R~N), B(x, u, Du)is ineasurable and B(x, u, p)≤a(p~γ+u~τ)+b(x), where 1+2/n<γ<2, τ≤max((n+2)/(n2), (γ1)/(2γ)ε), (?)ε>0, b(x)∈L2n/(n+2), n~2/(n+2)+e(Ω), (?)ε>0.Remarks. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey Space.Let assumptions ⅰ)ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H~1 weak solutions of (1) under controllable growth condition B≤α(p~γ+u~((n+2)/(n2))+b, 0<γ≤1+2/n and the H~1∩L~∞ weak solutions of (1) under natural

19.

一类LFuzzy拓扑空间——1.LFuzzy点的邻近构造





李中夫《数学研究与评论》,1982年第2卷第1期


Suppose (L_{0},≤) is a poset (i.e. partially ordered set) with an order reversing involution λ→λ′ and has an all element 1. Let L={bb is a subset of L_{0} and satisfies the condition: if λ∈b,μ≤λ then μ∈b} then (L,?,∩,∪) is a complete and distributive lattice. L is called the lattice induced from poset L_{0}. There is a mapping α→a′={λ∈L_{0}λ′(?)a} of a lattice L onto L. The mapping is clearly order reversing involution.

20.

SOLVING δb^ ON PARABOLIC LAMINATIONS





王刚《数学物理学报(B辑英文版)》,2014年第6期


Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s 〉 N and any continuous v ∈∧^（0,1）X×L^×s, there exists a continuous u ∈ L^×s solving δb^u = v.

