On Orbits and Bi-invariant Subsets of Binary $$G$$ -Spaces

Mathematical Notes - Orbits and bi-invariant subsets of binary $$G$$ -spaces are studied. The problem of the distributivity of a binary action of a group $$G$$ on a space $$X$$ , which was posed in...     

(N)-空间和度量空间的mssc-映象

本用度量空间的mssc-映象给出了N-空间一些刻画，证明了空间X是N-空间当且仅当X是度量空间的序列覆盖(序列商)mssc-映象，肯定地回答了关于N-空间的一个猜想．     

On Robustness of Orbit Spaces for Partially Hyperbolic Endomorphisms

In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space(the inverse limit space) M~f of f is topologically quasi-stable under C~0-small perturbations in the following sense: For any covering endomorphism g C~0-close to f, there is a continuous map φ from M~g to Multiply form -∞ to ∞ M such that for any {y_i }_(i∈Z) ∈φ(M~g), y_(i+1) and f(y_i) differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense: For any pseudo-orbit {x_i }_(i∈Z),there is a sequence of points {y_i }_(i∈Z) tracing it, in which y_(i+1) is obtained from f(y_i) by a motion along the center direction.     

A Note on $$\aleph$$ -Spaces and g-Metrizable Spaces

In this paper, we give the mapping theorems on -spaces and g-metrizable spaces by means of some sequence-covering mappings, mssc-mappings and π-mappings.     

Orbit Spaces of Free Involutions on the Product of Two Projective Spaces

Let X be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on X and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration ${X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}}$ . We also give an application of our result to show that if X has the mod 2 cohomology algebra of the product of two real projective spaces (respectively, complex projective spaces), then there does not exist any ${\mathbb{Z}_2}$ -equivariant map from ${\mathbb{S}^k \to X}$ for k ≥ 2 (respectively, k ≥ 3), where ${\mathbb{S}^k}$ is equipped with the antipodal involution.     

On Graded Distributive Modules

ＯｎＧｒａｄｅｄＤｉｓｔｒｉｂｕｔｉｖｅＭｏｄｕｌｅｓ￥ＣｈｅｎＱｉｎｇｈｕａ（陈清华）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｊｉａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｆｕｚｈｏｕ，３５０００７）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅ...     

关于分配格的判定问题

针对分配格判定时容易出错这一教学难题,提出可以利用学生专业特点从而结合计算机这一工具来帮助解决,并通过一个典型例子来具体说明,该例子同时也指出了教材习题解答书中的一处错误.认为本文提出的这一教学思想对于离散数学的教学有一定的启示.     

A Four for the Price of One Duality Principle for Distributive Spaces

In this paper we consider topological spaces as generalised orders and characterise those spaces which satisfy a (suitably defined) topological distributive law. Furthermore, we show that the category of these spaces is dually equivalent to a certain category of frames by simply observing that both sides represent the idempotents split completion of the same category.     

Constructions of Small Complete Caps in Binary Projective Spaces

In the binary projective spaces PG(n,2) k-caps are called large if k > 2^n-1 and smallif k ≤ 2^n-1. In this paper we propose new constructions producing infinite families of small binary complete caps.AMS Classification: 51E21, 51E22, 94B05     

Classification and Constructions of Complete Caps in Binary Spaces

We give new recursive constructions of complete caps in PG(n,2). We approach the problem of constructing caps with low dependency via the doubling construction and comparison to lower bounds. We report results of the exhaustive classification (up to projective equivalence) of all caps in PG(n,2) for n≤ 6. Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)     

The Long-Eight-Figure Spines of Lens Spaces and Binary Trees

There is a conjecture that the long-eight-figure spines of lens spaces are minimal in the class of almost special spines. In the work the embedding of these spines into the lens spaces with respect to the lenses' natural presentations is described effectively via flypes of binary trees.     

Lifts of Diffeomorphisms of Orbit Spaces for Representations of Compact Lie Groups

A structure of the group of diffeomorphisms for the orbit space of an orthogonal representation G> O(V) of a compact Lie group G is studied. For a finite G, it is proved that each diffeomorphism of the orbit space V/G has a smooth lift to V and the component group of the group of Diff(V/G is described, especially in the case when G is a finite Coxeter group. Similar results are obtained for the isotropy representations of some symmetric spaces.     

On Complementary Spaces of the Lizorkin Spaces

Let S(Rⁿ){\cal S}(R^n) be the Schwartz space on R ⁿ . For a subspace V ì S(Rⁿ)V\subset {\cal S}(R^n), if a subspace W ì S(Rⁿ)W \subset {\cal S}(R^n) satisfies the condition that S(Rⁿ){\cal S}(R^n) is a direct sum of V and W, then W is called a complementary space of V in S(Rⁿ){\cal S}(R^n). In this article we give complementary spaces of two kinds of the Lizorkin spaces in S(Rⁿ){\cal S}(R^n).     

Polyspherical Coordinate Systems on Orbit Spaces with Applications to Biomolecular Shape

A general theory of molecular internal coordinates of valence type is presented based on the concept of a Z-system. The Z-system can be considered as a discrete mathematical generalization of the Z-matrix (a molecular geometry file format familiar to chemists) which avoids the principal disadvantage of Z-matrices. Z-matrices are usually only employed for small molecules because there is no easy way to glue two Z-matrices together to get the Z-matrix of a larger molecule. It is shown that Z-matrices are simply Z-systems together with additional extraneous structures and that the Z-systems for any two molecules can be naturally glued together to obtain a Z-system for the combined molecule. A general mathematical framework suitable for the detailed study of molecular geometry is introduced and applied to five and six-membered molecular rings. A classification of shapes of hexagons with opposite sides and angles congruent is given with explicit parameterizations of the flexible and rigid solutions. The entire mathematical formalism generalizes to a theory of polyspherical coordinate systems on orbit spaces of the group of -dimensional rigid motions acting on finite collections of points in -dimensional Euclidean space. The -dimensional Z-system is a new discrete structure related to abstract simplicial complexes, graded posets, and iterated line graphs. Complete proofs of all the -dimensional results are given, and connections to other areas of mathematics are noted.     

分配格上矩阵的特征向量

设(L,≤,∨,∧)为一分配格。满足Ax=x的向量x称为方阵A的特征向量。本文的主工目的是通过矩阵的伴随有向图来刻画矩阵的特征向量并给出矩阵特征向量的界。同时我们将定义矩阵A的上基本特征向量并讨论它的性质。     

On S-Barrelled Spaces

Locally convex spaces E for which every linear map of E into an arbitrary Frechet space with sequentially closed graph is continuous are studied.     

ON LKUR SPACES

In this paper it is proved that if X is an LKUR space,then X has(H)property andif X is an LKUR space,then X has RNP.Also,if M is a Chebyshev subspace of LKURspace,then P(M) is continuous.     

关于sn-度量空间

本文利用ｓｎ－度量空间的一些等价刻划及ｓｎ－度量空间与ｇ－度量空间、度量空间之间的关系，研究了ｓｎ－度量空间的一些映射性质，证明了ｓｎ－度量空间的闭象是ｓｎ－度量空间当且仅当它是ｓｎ－第一可数的，利用这一结果证明了有限到一闭映射和开闭映射均保持ｓｎ－度量空间，并给出反例说明完备映射不保持ｓｎ－度量空间，本文还证明了ｓｎ－变量空问满足完备逆象Ｇδ－对角线定理．