BRST Invariant Theory of a Generalized 1 + 1 Dimensional Nonlinear Sigma Model with Topological Term

We give a generalized Lagrangian density of 1 + 1 Dimensional O(3) nonlinear σ model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear σ model, give the example of not introducing the lost constraint = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter β originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field. PACS numbers: 11.10.Lm; 11.30.Ly     

Banach空间中渐近非扩张型半群的遍历定理

对带Opial条件的Banach空间中非扩张半群的不动点理论进行推广,得到了带Opial条件的Banach空间中渐近非扩张型半群的遍历收敛定理.     

关于多项式函数的计数

Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.     

交换环上三角矩阵模间的线性保持映射(英文)

本文研究了交换环上三角矩阵模间的线性保持问题.利用矩阵计算技巧和局部化技巧,刻画了上三角矩阵T_n(R)上分别保持立方幂等,{1}逆,{1,2}逆和群逆的所有R模自同构集合中的元素,其中R是交换环.     

广义分布半群与退化发展方程的分布解

在Banach空间中引进了由有界线性算子引导的广义分布半群的新概念,并讨论了它的有关性质.在我们的方法中,广义分布半群的生成元可以不是稠定的.此外,还引进了退化发展方程在Laplace变换意义下的分布解,应用广义分布半群给出了退化发展方程分布解的构造性表达式.     

Hilbert C- 模上的半群及其应用

在Hilbert C*-模框架下建立了Co-模半群,获得了量子Stone型定理,以此为工具给出了一类量子随机过程的谱分解.     

Power Residue Symbols and the Central Sections of SL(2, A)

In TheE(2,A) sections of SL(2,A) (Ann. of Math. 134 (1991), 159–188), we locate the E(A) normalized subgroups of SL(2,A) in central sections of SL(2,A) for all subrings of Q and all commutative rings satisfying SR ₂ In solving this problem we introduced the notion of radix (see (1.1)) and the group C(P_x) = [E(2,A),E(2,A;P_x)] = [SL(2,A), SL(2,A;P_x)] for the rings considered here.The purpose of this paper is to determine SL(2,A;P_xC(P_x) for SR ₂ rings and number rings with infinitely many units.In Section 2, Mennicke symbols for Jordan ideals are defined. They are determined for number rings and shown to be connected to power residue symbols in a delicate way. This extends the work of Bass, Milnor and Serre.In Section 3, an explicit homomorphism from E(2,Al;P_x) into an additive section of A is given for all commutative rings A. If A satisfiesSR ₂ the kernel of this map is C(P_x.The main problem for number rings is solved by giving an explicit homomorphism on SL(2,A;P_x) whose kernel is C(P_x).