拉回Dirac结构

引入了关于李双代数胚态射的运算，讨论了它的运算性质，并利用极大迷向子丛的对偶特征对对拉回Dira。结构做了新的描述，推广了已有的结论。     

关于表代数的特征性质

给出C—代数与表代数的特征性质,并利用表代数的特征性质讨论了二个表代数的例子.     

Geometric Formulation of Higher-Order Lagrangian Systems in Supermechanics

Using supervector fields along a morphism of graded manifolds, we study both the geometry of the tangent supermanifolds of an arbitrary order and k th-order ordinary differential superequations, in order to develop the higher-order Lagrangian formalism of supermechanics. In particular, we obtain, in this formalism, a generalization of Noether's theorem and its converse.     

Morphism spaces in stable categories of Frobenius algebras

We present an explicit formula computing morphism spaces in the stable category of a Frobenius algebra.     

Quotient morphisms, compositions, and Fredholm index

In this paper we define a composition between two quotient morphisms and prove a multiplication formula for the index of the composition of two Fredholm quotient morphisms. Using this formula and the fact that any linear relation can be seen as a quotient morphism, we obtain a multiplication formula for the index of the composition of two Fredholm linear relations.     

关于具有泛分解态射的广义Moore-

本文讨论预加法范畴中态射的广义Moore-Perurose逆．给出了具有泛分解态射的广义Moore-Penrose逆存在的几个充要条件,并把结果应用到环上的矩阵中．     

The Ker-Coker-sequence and its generalization in some classes of additive categories

We study the validity of the Snake Lemma (the existence and exactness of the Ker-Cokersequence) in a P-semi-abelian category. We also obtain a generalization of the Snake Lemma in a quasiabelian category.     

(i,p) -同伦逆和群同伦逆

该文在点标拓扑空间范畴中引进了(i,p)-同伦逆和群同伦逆的概念,并讨论了它们存在的条件和性质.     

The relation between the Jacobi morphism and the Hessian in gauge-natural field theories

We generalize a classic result, due to Goldschmidt and Sternberg, relating the Jacobi morphism and the Hessian for first-order field theories to higher-order gauge-natural field theories. In particular, we define a generalized gauge-natural Jacobi morphism where the variation vector fields are Lie derivatives of sections of the gauge-natural bundle with respect to gauge-natural lifts of infinitesimal principal automorphisms, and we relate it to the Hessian. The Hessian is also very simply related to the generalized Bergmann-Bianchi morphism, whose kernel provides necessary and sufficient conditions for the existence of global canonical superpotentials. We find that the Hamilton equations for the Hamiltonian connection associated with a suitably defined covariant strongly conserved current are satisfied identically and can be interpreted as generalized Bergmann-Bianchi identities and thus characterized in terms of the Hessian vanishing. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 377–389, August, 2007.     

范畴中态射集减序的刻划

本文研究了范畴中态射集减序的刻划问题，其主要结果是：（１）证得一般范畴情形减序的十四种刻划；（２）将Ｍｉｔｒａ、Ｂａｋｓａｌａｒｙ等人的利用（１）－逆、（１，２）－逆的包含关系及平行和来刻划复矩阵减序的结果推广到素性预加法范畴与带对合的正性预加法范畴中；（３）给出了１９８０年Ｈａｒｔｗｉｇ关于半群减序刻划的一个反例，因此否定了这个刻画．