On the Perfect Matchings of Near Regular Graphs

Let k, h be positive integers with k ≤ h. A graph G is called a [k, h]-graph if k ≤ d(v) ≤ h for any v ? V(G){v \in V(G)}. Let G be a [k, h]-graph of order 2n such that k ≥ n. Hilton (J. Graph Theory 9:193–196, 1985) proved that G contains at least ?k/3?{\lfloor k/3\rfloor} disjoint perfect matchings if h = k. Hilton’s result had been improved by Zhang and Zhu (J. Combin. Theory, Series B, 56:74–89, 1992), they proved that G contains at least ?k/2?{\lfloor k/2\rfloor} disjoint perfect matchings if k = h. In this paper, we improve Hilton’s result from another direction, we prove that Hilton’s result is true for [k, k + 1]-graphs. Specifically, we prove that G contains at least ?\fracn3?+1+(k-n){\lfloor\frac{n}3\rfloor+1+(k-n)} disjoint perfect matchings if h = k + 1.     

Zygmund微分映射的正则点

该文的主要结果是: 对任意Zygmund类$C^{p,Z}$映射$f:R^{n}\rightarrow R^{m}$, 若$\frac{n-m}{2}\leq p\leq n-m-1$, 则有mes$K_{f}>0$或者mes$C_{f}>0$. 这个结果给出了Hirsch问题的部分回答.     

On Projecting Symmetries by Unbranched Regular Coverings of Riemann Surfaces

A symmetry of a Riemann surface X of genus g is an antiholomorphic involution σ of X. It is a classical result of Harnack that the set of fixed points of σ consists of k closed Jordan curves, called ovals, for some k, 0 ≤ k ≤ g + 1; when k = g or k = g+1 we say, following Natanzon [8], that σ is an (M – 1)- or an M-symmetry, respectively. Given a Riemann surface X with an M-symmetry, a Riemann surface Y and a regular covering p: X → Y, we prove that Y admits either an M- or an (M – 1)-symmetry and whenever p is unbranched we describe the groups of covering transformations of p. In the case that X is hyperelliptic we calculate as well the number of unbranched regular coverings p: X → Y in which X has an M-symmetry. The first two authors are supported by MTM2005-01637, the third by SAB2005-0049.     

Polar sets, Regular Points and Recurrent sets for the Symmetric and Increasing Stable Processes

In [8] S. J. Taylor enquired whether, or not, all stable processesof index , < 1, in R have the same polar sets. In [6] S.Orey answered this question in the affirmative. The object ofthis paper is to give a simple proof of this fact and to showthat the relationship between the stable processes of index is even stronger. We show that, with an obvious, modification,all stable processes of index , < 1, in R give rise to thesame regular points and recurrent sets.     

关于对称点的亚纯星象函数

本文给出了亚纯星象函数的某些必要与充分条件及其结构公式.     

On Real Forms of Belyi Surfaces With Symmetric Groups of Automorphisms

In virtue of the Belyi Theorem an algebraic curve can be defined over the algebraic numbers if and only if the corresponding Riemann surface can be uniformized by a subgroup of a Fuchsian triangle group. Such surfaces are known as Belyi surfaces. Here we study the actions of the symmetric groups S _n on Belyi Riemann surfaces. We show that such surfaces are symmetric and we calculate the number of connected components of the corresponding real forms.     

Symmetric Versus Non-Symmetric Spin Models for Link Invariants

We study spin models as introduced in [20]. Such a spin model can be defined as a square matrix satisfying certain equations, and can be used to compute an associated link invariant. The link invariant associated with a symmetric spin model depends only trivially on link orientation. This property also holds for quasi-symmetric spin models, which are obtained from symmetric spin models by certain gauge transformations preserving the associated link invariant. Using a recent result of [16] which asserts that every spin model belongs to some Bose-Mesner algebra with duality, we show that the transposition of a spin model can be realized by a permutation of rows. We call the order of this permutation the index of the spin model. We show that spin models of odd index are quasi-symmetric. Next, we give a general form for spin models of index 2 which implies that they are associated with a certain class of symmetric spin models. The symmetric Hadamard spin models of [21] belong to this class and this leads to the introduction of non-symmetric Hadamard spin models. These spin models give the first known example where the associated link invariant depends non-trivially on link orientation. We show that a non-symmetric Hadamard spin model belongs to a certain triply regular Bose-Mesner algebra of dimension 5 with duality, and we use this to give an explicit formula for the associated link invariant involving the Jones polynomial.     

Centroaffine First Order Invariants of Surfaces in IR4

An investigation of the centroaffine geometry of surfaces in IR⁴ leads to the centroaffine first order invariants: the vector bundle valued second fundamental form, the affine semiconformal structure, the h³-semiconformal structure and the centroaffine metric. A classification of surfaces by their semiconformal structures according to signature and rank is given. This involves the study of the orbits of two pencils of symmetric bilinear forms on IR² under a change of basis. Combined with previous results ([Nomizu-Sasaki 93]) a complete classification of the zero-degenerate surfaces is obtained and examples of the other surface types are constructed.     

Orbits and Invariants of Third-Order Cubic Matrices with Symmetric Fibers

In the note, for an action which is the tensor product of the tautological action of the unimodular group of three-dimensional space and the second symmetric power of the tautological action of the unimodular group of three-dimensional space, the orbits are classified and the generators of the algebra of invariants are described.     

A Note on Regular Near Polygons

Let be a regular near polygon of order (s,t) with s>1 and t3. Let d be the diameter of , and let r:= max{i(c_i,a_i,b_i)=(c₁,a₁,b₁)}. In this note we prove several inequalities for . In particular, we show that s is bounded from above by function in t if We also consider regular near polygons of order (s,3).This work was partly supported by the Grant-in-Aid for Scientific Research (No 14740072), the Ministry of Education, Culture, Sports, Science and Technology, JapanThis work was partly done when the author was at the Com²MaC center at the Pohang University of Science and Technology. He would like to thank the Com²MaC-KOSEF for its support     

Distance-j-Ovoids in Regular Near 2d-Gons

In [8] valuations were introduced and it was shown that these were important objects for classifying near 2n-gons. Several classes were given including one arising from so-called distance-2j-ovoids. Here we introduce pseudo-valutions and explain why these objects can be important for classifying near (2n+1)-gons. Every valuation of a near polygon gives rise to pseudo-valuations and almost all known examples of pseudo-valuations arise in this way. We show that every distance-(2j+1)-ovoid gives rise to a pseudo-valuation which does not come from a valuation. Subsequently, we study distance-j-ovoids in regular near polygons. We are able to calculate the number of elements of a distance-j-ovoid in two ways, yielding a relation between the parameters of the regular near polygon. We will discuss some cases where this relation can be solved. Postdoctoral Fellow of the Research Foundation - Flanders     

Weierstrass Points and Regular Maps

It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map.     

由交换群决定的Near环

本文讨论了加群上保持零元的映射集合对映射的加法和乘法作成的Ｎｅａｒ环，研究了它的理想特点，并构造了几类特殊的左，右理想．     

On the Existence of Focal Points near Closed Geodesics on Surfaces

We establish some criteria for the existence or nonexistence of focal points near closed geodesics on surfaces. These criteria are in terms of the curvature of the manifold along the closed geodesic and the average values of the partial derivatives of the curvature in the direction perpendicular to the geodesic. Our criteria lead to a new family of examples of surfaces with no focal points. We also show that if S is a compact surface with no focal points and an inequality relating the curvature of the surface to the curvature of the horocycles holds, then the horocycles (considered as curves in S) are uniformly C ^2+Lipschitz.     

Canonical Forms for Symmetric and Regular Structures

Matrices associated with symmetric and regular structures can be arranged into certain block patterns known as Canonical forms. Using such forms, the decomposition of structural matrices into block diagonal forms, is considerably simplified. In this paper the main canonical forms are reviewed; and symmetric/regular structural configurations that can be explained with such forms are investigated. The invariant subspaces are formulated and the closed form solutions for the block-diagonalized stiffness matrices are provided in each case. Utility and robustness of the canonical forms in the analysis of structures exhibiting decomposable matrix patterns are demonstrated by numerous examples. Furthermore, a numerical method is proposed to extend the computational advantages of the matrix canonical forms to other nonconforming regular structures.     

轨形Gromov-Witten不变量沿光滑点的加权涨开公式

本文考虑,当一个紧辛轨形群胚(X,ω)沿着光滑点作加权涨开时,它的形如<α_1,…,α_m,[pt]>_(g,A)~X的轨形Gromov-Witten不变量的变化公式,其中[pt]∈H_(dR)~(2n)(X)是生成元,dimX=2n.我们证明了对于非零A∈H_2(|X|,Z),<α_1,…,α_m,[pt]>_(g,A)~X={_(g_1,pl(A)-e’)~xdimX=4,g≥0,∑((-1)g_1·2)/(2g_1+2)!_(g_2,pl(A)-e’)~xdimX=6,g≥0,_(g_1,pl(A)-e’)~xdimX≥8,g=0其中x是X沿一光滑点的权α=(α_1,…,α_n)的加权涨开,且α_1≥α_i,2≤i≤n.