本刊英文版Vol.30(2014),No.11论文摘要(英文)

<正>On Equivalence of Simple Closed Curves in Flat Surfaces Zong Liang SUN Abstract By explicit constructions,we give direct proofs of the following results:for any distinct homotopy classes of simple closed curvesαandβin a closed surface of genus g1,there exist a hyperbolic structure X and a holomorphic quadratic differential q on X such that     

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Submanifolds of Pn(l) with Splitting Tangent Sequence

Let l be a line in a projective space Pn. We consider the blowing up Pⁿ(l) of Pnalong l.Assume that X is a smooth closed subvariety of Pⁿ. If the strict transform of X in Pⁿ(l) has a splitting tangent sequence and dim X is at least 2, then X is a linear subspace of Pⁿ.     

关于纤维一般拓扑的一点注记(英文)

Some characterizations of paracompact maps are given in this note, and some equivalent statements of collectionwise normal maps are discussed. And also we show that if f ： X→Y is a closed collectionwise normal map, and f^-1（y） is a semistratifiable subspace of X for any y ∈ Y, then f is a paracompact map.     

本刊英文版Vol.21(2005),No.4论文摘要(英文)

Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.     

A VIEWPOINT TO MEASURE OF NON-COMPACTNESS OF OPERATORS IN BANACH SPACES

This article is committed to deal with measure of non-compactness of operators in Banach spaces. Firstly, the collection C(X)(consisting of all nonempty closed bounded convex sets of a Banach space X endowed with the uaual set addition and scaler multiplication) is a normed semigroup, and the mapping J from C(X) onto F(?) is a fully order-preserving positively linear surjective isometry, where ? is the closed unit ball of X*and F(?) the collection of all continuous and w*-lower semicontinuous sublinear functions on X*but restricted to ?. Furthermore, both ■ and ■ are Banach lattices and EK is a lattice ideal of EC. The quotient space EC/EK is an abstract M space, hence,order isometric to a sublattice of C(K) for some compact Haudorspace K, and(FQJ)C which is a closed cone is contained in the positive cone of C(K), where Q : E_C → E_C/E_K is the quotient mapping and F : E_C/E_K → C(K) is a corresponding order isometry. Finally, the representation of the measure of non-compactness of operators is given: Let B_X be the closed unit ball of a Banach space X, then■     

On equivalence of simple closed curves in flat surfaces

By explicit constructions,we give direct proofs of the following results: for any distinct homotopy classes of simple closed curves α and β in a closed surface of genus g 1,there exist a hyperbolic structure X and a holomorphic quadratic differential q on X such that lX(α) = lX(β),extX(α) = extX(β) and lq(α) = lq(β),where lX(·),extX(·) and lq(·) are the hyperbolic length,the extremal length and the quadratic differential length respectively.These imply that there are no equivalent simple closed curves in hyperbolic surfaces or in flat surfaces.     

Some Characterizations of Spaces with Weak Form of $cs$-Networks

In this paper, we introduce the concept of statistically sequentially quotient map:A mapping f : X → Y is statistically sequentially quotient map if whenever a convergent sequence S in Y, there is a convergent sequence L in X such that f(L) is statistically dense in S. Also, we discuss the relation between statistically sequentially quotient map and covering maps by characterizing statistically sequentially quotient map and we prove that every closed and statistically sequentially quotient image of a g-metrizable space is g-metrizable. Moreover,we discuss about the preservation of generalization of metric space in terms of weakbases and sn-networks by closed and statistically sequentially quotient map.     

本刊英文版Vol.28(2012),No.3论文摘要(英文)

<正>Closed 3-stop Center and Periphery in Graphs Linda EROH Ralucca GERA Steven J.WINTERS A delivery person must leave the central location of the business,deliver packages at a number of addresses,and then return.Naturally,he/she wishes to reduce costs by finding the most efficient route.This motivates the following: Given a set of k distinct vertices S = {x_1,x_2,…,x_k} in a simple graph G,the closed k-stop-distance of set S is defined to be     

On the Weak＊ Drop Property for Polar of Closed Bounded Convex Sets

We define and study the weak* drop property for the polar of a closed bounded convex set in a Banach space which is both a generalization of the weak* drop property for dual norm in a Banach space and a characterization of the sub-differentialmapping x→эp(x) from S(X) into 2^S(X*) that is norm upper semi-continuous and norm compact-valued.     

The Answer to a Problem Posed by Zhao and Ho

Zhao and Ho asked in a recent paper that for each T_0 space X, whether KB(X)(the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Top_κ of the category Top_0 of T_0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Top_κ.     

AN ITERATIVE PROCESS FOR FINDING APPROXIMATE SOLUTIONS TO NONLINEAR EQUATIONS OF STRONGLY ACCRETIVE OPERATORS

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.     

Existence of best simultaneous approximations in L_p(S, Σ, X) without the RNP assumption

Let(S, Σ, μ) be a complete positive σ-finite measure space and let X be a Banach space. We consider the simultaneous proximinality problem in Lp(S, Σ, X) for 1 p +∞. We establish some N-simultaneous proximinality results of Lp(S, Σ0, Y) in Lp(S, Σ, X) without the Radon-Nikody′m property(RNP) assumptions on the space span Y and its dual span Y*, where Σ0is a sub-σ-algebra of Σ and Y a nonempty locally weakly compact closed convex subset of X. In particular, we completely solve one open problem and partially solve another one in Luo et al.(2011).     

套代数模中的插值问题

Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.     

本刊英文版Vol.32(2016),No.6论文摘要（英文）

正On Proximinality of Convex Sets in Superspaces Li Xin CHENG Zheng Hua LUO Wen ZHANG Ben Tuo ZHENG Abstract In this paper,we show that a closed convex subset C of a Banach space is strongly proximinal(proximinal,resp.)in every Banach space isometrically containing it if and only if C is locally(weakly,resp.)compact.As a consequence,it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it,the metric     

Three-space problems for the bounded compact approximation property

In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP for each finite codimensional subspace Y∈X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p.     

Holomorphic Curves into ■~N(C) That Share a Set of Moving Hypersurfaces

Let F be a family of holomorphic curves of a domain D in C into a closed subset X in ■~N(C). Let Q_1(z),…, Q_(2t+1)(z) be moving hypersurfaces in ■~N(C) located in pointwise t-subgeneral position with respect to X. If each pair of curves f and g in F share the set {Q_1(z),…, Q_(2t+1)(z)}, then F is normal on D. This result greatly extend some earlier theorems related to Montel's criterion.     

On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces

Let B （resp. K, BC,KC） denote the set of all nonempty bounded （resp. compact, bounded convex, compact convex） closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem （F, G） is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC ／ G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B ／B° （resp. K ／ B°, BC ／B°, KC ／ B°） is a-porous in B （resp. K,BC, KC）. Moreover, we prove that for most （in the sense of the Baire category） closed bounded subsets G of X, the set K ／ B° is dense and uncountable in K.     

严格伪压缩映象的Ishikawa 迭代序列的收敛率估计

It is shown that any fixed point of each l.ipschitzian, strictly pseudocontractive mapping 7“ on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure. The argument in this paper provides a convergence rate estimate.Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results.     

Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori, Ⅱ

We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S~2×S~1 or RP~3#RP~3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni(2014) in an earlier paper.