特征2有限域上的亏格2超椭圆曲线的同构类

研究特征2有限域F_q上的亏格2超椭圆曲线的同构类数目的计算,给出了此同构类数目N的精确公式, 即对于 q=2^m, N=2q³+q²−q (4Œm时)和N=2q³+q²−q+8 (4 Œm时). 这些结果可用于分类问题和超椭圆曲线密码体制的研究.     

关于亏格g的超椭圆曲线同构等价类数目的估计

研究了对应于椭圆曲线同构的变换类,并利用计数统计法获得了没有重根且第二项系数为常数的首一多项式的数目计算公式,在此基础上给出了奇数特征的有限域上亏格g的超椭圆曲线同构等价类的数目的估计.     

关于二阶半线性椭圆方程的Dirichlet边值问题一个注记(英文)

本文研究二阶半线性椭圆方程的Dirichlet边值问题.利用山路引理和最小作用原理,获得了在新条件下具有Dirichlet边值问题的二阶半线性椭圆方程的弱解的存在性的结果.     

关于Kumar和Mathur一文的注记

1°记T_n(x)=cosθ(x=cosθ)为多项式,x_k=cosθ_k=cos(2k-1/2n)π(k=1,…,n)是它的n个零点。以(1-x~2)T_n(x)的零点为节点的Lagrange插值多项式有如下形式:     

关于“L—Fuzzy群同态与同构及其性质”一文的注记

文（１）给出了Ｌ－Ｆｕｚｚｙ群间的同态映射，满同态映射以及Ｌ－Ｆｕｚｚｙ群的Ｌ－正规子群等概念。本文指出以上三种定义的不合理性，并给出它们的合理性定义。     

关于Arasu和Ma的一个引理的注记

通过改进Ａｒａｓｕ和Ｍａ的一个引理,在没有自共轭条件的情形下得到了一个关于西罗子群的指数界的差集存在的必要条件,作为它的一个应用,首次得到了不依赖于自共轭条件的指数界,从而对ＭｃＦａｒｌａｎｄ族与Ｓｐｅｎｃｅ族差集证明了Ｌａｎｄｅｒ猜想。     

关于某些椭圆曲线的Tate—Shafarevich群的注记

本文首先考虑某个四元代数，通过对此四元代数的算术的研究，得到某类丢番图方程的解数与某些虚二次域类数之间的关系，最后，应用Ｔｕｎｎｅｌｌ的定理，得到一簇椭圆曲线的Ｔａｔｅ－Ｓｈａｆａｒｅｖｉｃｈ群的阶的上界。     

关于AQSI随机序列的一个注记

首先建立关于AQSI随机序列的Borel-Cantelli引理,在适当的条件下,获得了同分布AQSI随机序列的M-Z型强大数定理成立的充分必要条件.     

On the isomorphism classes of Legendre elliptic curves over finite fields

In this paper,the number of isomorphism classes of Legendre elliptic curves over finite field is enumerated.     

The Semi-Arc Automorphism Group of a Graph with Application to Map Enumeration

A map is a connected topological graph cellularly embedded in a surface. For a given graph Γ, its genus distribution of rooted maps and embeddings on orientable and non-orientable surfaces are separately investigated by many researchers. By introducing the concept of a semi-arc automorphism group of a graph and classifying all its embeddings under the action of its semi-arc automorphism group, we find the relations between its genus distribution of rooted maps and genus distribution of embeddings on orientable and non-orientable surfaces, and give some new formulas for the number of rooted maps on a given orientable surface with underlying graph a bouquet of cycles B_n, a closed-end ladder L_n or a Ringel ladder R_n. A general scheme for enumerating unrooted maps on surfaces(orientable or non-orientable) with a given underlying graph is established. Using this scheme, we obtained the closed formulas for the numbers of non-isomorphic maps on orientable or non-orientable surfaces with an underlying bouquet B_n in this paper.     

A Note on a Paper by P. Amodio and F. Mazzia

In 1999 Amodio and Mazzia presented a new backward error analysis for LU factorization and introduced a new growth factor _n . Their very interesting approach allowed them to obtain sharp error bounds. In particular, they derive nice results assuming that partial pivoting is used. However, the forward error bound for the solution of a linear system whose coefficient matrix A is an M-atrix given in Theorem 4.1 of that paper is not correct. They first obtain a bound for the condition number (U) assuming that one has the LU factorization of an M-matrix and then they apply the bounds obtained when partial pivoting is used. But if P is the permutation associated with partial pivoting then PA = LU can fail to be an M-atrix and the bound for (U) can be false, as shown in our Example 1.1. We also prove that, for a pivoting strategy presented in the paper, the growth factor of an M-matrix A is _n(A) = 1 and (U) (A), where U is the upper triangular matrix obtained after applying such a pivoting strategy.This revised version was published online in October 2005 with corrections to the Cover Date.     

关于几乎等距嵌入的一个注记

本文将指出：对于足够小的ε＞ ０,不存在从无穷维“抽象 ＬＰ”空 间（０＜ ｐ＜∞）到空间（ｃ）的ε－等距线性算子．     

A Note on the Paper

In this paper, we point out a fault in Theorem B in [1], generalize Hua-Wang type inequalities given by Theorem A in [1], and prove them by using elementary mean value inequalities. It also makes the improved Theorem B its corollary.     

关于全纯映照模的Schwarz引理一点注记

记DC为单位圆盘,B~k C~k为开欧氏单位球,Ω是C~k(或C)中的域.记H_n(D,Ω)为满足一定条件的全纯映照族(或函数族)的全体.作者证明了若,∈Hn(D,D),则|f′(z)|≤(n|z|~(n-1))/(1-|z|~(2n))(1-|f|(z|~2),z∈DD同时,对Hn(D,B~k)中映照的模也得到类似的结果.该结论推广了Pavlovic的相应结果.     

A Note on a Problem of M. S. Berger

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U (?)E→ F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x)=y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.     

有关M.S.Berger问题的注记

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U 真包含 E → F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x) = y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.