球面中具有平行平均曲率向量的2—调和等距浸入

本文讨论了单位球面中具平行平均曲率向量的２－调和等距浸入，获得其成为极小浸入的充分条件和关于第二基本形式的Ｐｉｎｃｈｉｎｇ定理．     

Rigidity of spheres in Riemannian manifolds and a non-embedding theorem

Letf:M be an isometric immersion between Riemannian manifolds. The purpose of this paper is to find the minimum possible conditions onM and (in the terms of curvatures and external diameter) in order to the image off be contained in a sphere. Our results generalize the other authors work in three major steps, domain, range and the codimension of immersions. As a byproduct, we obtain the non-embedding theorems Chern-Kuiper, Moore and Jacobowitz. The proofs are based on the maximum (comparison) principle.The author was supported by FAPEMIG Grant CEX-946/98.     

On local automorphisms of group algebras of compact groups

We show that with few exceptions every local isometric automorphism of the group algebra of a compact metric group is an isometric automorphism.

     

如何在教学中让学生觉得《抽象代数》不再"抽象"

主要从近世代数的一些定义和定理的导入着手,讨论了如何在教学中让学生觉得它的内容不再抽象,从而激发学生学习该课程的积极性,进而更好地学习它.     

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.     

A characterization of ∗-isomorphism on factor von Neumann algebras北大核心CSCD

Let H and K be complex Hilbert spaces. Let A and B be two factor von Neumann algebras acting on H and K respectively. A characterization of ∗-isomorphism between A and B is given. Let Φ: A → B be a bijection. If Φ(A∗B + B∗A) = Φ(A)∗Φ(B) + Φ(B)∗Φ(A) for all A,B ∈ A, then Φ is a linear or a conjugate linear ∗-isomorphism. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Common vertex matrix: A novel characterization of molecular graphs by counting

We present a novel matrix representation of graphs based on the count of equal‐distance common vertices to each pair of vertices in a graph. The element (i, j) of this matrix is defined as the number of vertices at the same distance from vertices (i, j). As illustrated on smaller alkanes, these novel matrices are very sensitive to molecular branching and the distribution of vertices in a graph. In particular, we show that ordered row sums of these novel matrices can facilitate solving graph isomorphism for acyclic graphs. This has been illustrated on all undecane isomers C₁₁H₂₄ having the same path counts (total of 25 molecules), on pair of graphs on 18 vertices having the same distance degree sequences (Slater's graphs), as well as two graphs on 21 vertices having identical several topological indices derived from information on distances between vertices. © 2013 Wiley Periodicals, Inc.     

超格

引入了超格、子超格等概念,并研究了超格的直积以及超格的同态和同构.     

Weyl families of transformed boundary pairs

Let $(\mathfrak{L},\mathrm{\Gamma })$ be an isometric boundary pair associated with a closed symmetric linear relation T in a Krein space $\mathfrak{H}$. Let $M_{\mathrm{\Gamma }}$ be the Weyl family corresponding to $(\mathfrak{L},\mathrm{\Gamma })$. We cope with two main topics. First, since $M_{\mathrm{\Gamma }}$ need not be (generalized) Nevanlinna, the characterization of the closure and the adjoint of a linear relation $M_{\mathrm{\Gamma }}(z)$, for some $z\in \mathbb{C}\setminus \mathbb{R}$, becomes a nontrivial task. Regarding $M_{\mathrm{\Gamma }}(z)$ as the (Shmul'yan) transform of $zI$ induced by Γ, we give conditions for the equality in $\overline{M_{\mathrm{\Gamma }}(z)}\subseteq \overline{M_{\overline{\mathrm{\Gamma }}}(z)}$ to hold and we compute the adjoint $M_{\overline{\mathrm{\Gamma }}}{(z)}^{\ast }$. As an application, we ask when the resolvent set of the main transform associated with a unitary boundary pair for $T^{+}$ is nonempty. Based on the criterion for the closeness of $M_{\mathrm{\Gamma }}(z)$, we give a sufficient condition for the answer. From this result it follows, for example, that, if T is a standard linear relation in a Pontryagin space, then the Weyl family $M_{\mathrm{\Gamma }}$ corresponding to a boundary relation Γ for $T^{+}$ is a generalized Nevanlinna family; a similar conclusion is already known if T is an operator. In the second topic, we characterize the transformed boundary pair $({\mathfrak{L}}^{\prime },{\mathrm{\Gamma }}^{\prime })$ with its Weyl family $M_{{\mathrm{\Gamma }}^{\prime }}$. The transformation scheme is either ${\mathrm{\Gamma }}^{\prime }=\mathrm{\Gamma }{V}^{-1}$ or ${\mathrm{\Gamma }}^{\prime }=V\mathrm{\Gamma }$ with suitable linear relations V. Results in this direction include but are not limited to: a 1-1 correspondence between $(\mathfrak{L},\mathrm{\Gamma })$ and $({\mathfrak{L}}^{\prime },{\mathrm{\Gamma }}^{\prime })$; the formula for $M_{{\mathrm{\Gamma }}^{\prime }}-M_{\mathrm{\Gamma }}$, for an ordinary boundary triple and a standard unitary operator V (first scheme); construction of a quasi boundary triple from an isometric boundary triple $(\mathfrak{L},{\mathrm{\Gamma }}_0,{\mathrm{\Gamma }}_1)$ with $ker\mathrm{\Gamma }=T$ and $T_0=T_0^{\ast }$ (second scheme, Hilbert space case).