For a general discrete subgroup in .

These notes provide an introduction to some aspects of the analytic theory of automorphic forms on G=SL(R),or the upper half-plane X with respect to a discrete subgroupΓ of G of finite covolume.

Character of group which only have n nontrivial normal subgroups

By using algebra of fixed point class to determine the component factors and properties of normal subgroup H of the fundamental group of the covering space, the paper studies the relation of fixed point class with fixed point class H.

Based on the Rough theory, a rough subgroup with respect to a normal subgroup of a group is discussed, and some properties of the lower and the upper approximations in a group are studied.

Su Xiang Ying and Wang Pin Chao obtained some sufficient conditions of supersoluble groups by studying semi normal subgroups of finite groups[1,2,7].

Considering the subnormal subgroups,some equivalent conditions for nilpotency of finite groups are given and a sufficient condition for nilpotency of finite groups is obtained.

Optimization model of development cost based on discrete particle swarm algorithm;

Adaptive radial basis function neural network model based on discrete particle swarm optimization algorithms;

Multiple optimization strategies for improving hybrid discrete particle swarm

This paper presents a new current learning adaptive hybrid discrete particle swarm optimization algorithm for NP-hard combinatorial optimization problem and particle swarm discretization problem.