On the Residual Finiteness of a Class of Infinite Soluble Groups

Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted by a rational integer m.Then Om(n)is an infinite soluble group.In this paper,the residual finiteness of Om(n)is investigated.

Residual finiteness of outer automorphism groups of certain 1-relator groups

We prove that certain 1-relator groups have Property E. Using this fact, we characterize all conjugacy separable 1-relator groups of the form a,b;(a-αbβaαbγ)t , t 1, having residually finite outer automorphism groups.

Numerical Analysis of Rolling-sliding Contact with the Frictional Heat in Rail

Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature field, but few literatures focus on wheel-rail thermal stress caused by frictional heating. However, the wheel-rail creepage is one of important influencing factors of the thermal stress In this paper, a thermo-mechanical coupling model of wheel-rail rolling-sliding contact is developed using thermo-elasto-plastic finite element method. The effect of the wheel-rail elastic creepage on the distribution of heat flux is investigated using the numerical model in which the temperature-dependent material properties are taken into consideration. The moving wheel-rail contact force and the frictional heating are used to simulate the wheel rolling on the rail. The effect of the creepage on the temperature rise, thermal strain, residual stress and residual strain under wheel-rail sliding-rolling contact are investigated. The investigation results show that the thermally affected zone exists mainly in a very thin layer of material near the rail contact surface during the rolling-sliding contact. Both the temperature and thermal strain of rail increase with increasing creepage. The residual stresses induced by the frictional heat in the surface layer of rail appear to be tensile. When the creepage is large, the frictional heat has a significant influence on the residual stresses and residual strains of rail. This paper develops a thermo-meehanical coupling model of wheel-rail rolling-sliding contact, and the obtained results can help to understand the mechanism of wheel/rail frictional thermal fatigue.

Influence of residual stresses on failure pressure of cylindrical pressure vessels

The utilization of pressure vessels in aerospace applications is manifold.In this work,fnite element analysis（FEA）has been carried out using ANSYS software package with 2D axisymmetric model to access the failure pressure of cylindrical pressure vessel made of ASTM A36 carbon steel having weld-induced residual stresses.To fnd out the effect of residual stresses on failure pressure,frst an elasto-plastic analysis is performed to fnd out the failure pressure of pressure vessel not having residual stresses.Then a thermo-mechanical fnite element analysis is performed to assess the residual stresses developed in the pressure vessel during welding.Finally one more elasto-plastic analysis is performed to assess the effect of residual stresses on failure pressure of the pressure vessel having residual stresses.This analysis indicates reduction in the failure pressure due to unfavorable residual stresses.

Polycyclic Groups Admitting a Regular Automorphism of Order Four

Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G→ G defined by g;= [g, α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C;（α;） and G/[G, α;] are both abelian-by-finite.

A unifying approach in simulating the shot peening process using a 3D random representative volume finite element model

Using a modified 3D random representative volume（RV）finite element model,the effects of model dimensions（impact region and interval between impact and representative regions）,model shapes（rectangular,square,and circular）,and peening-induced thermal softening on resultant critical quantities（residual stress,Almen intensity,coverage,and arc height）after shot peening are systematically examined.A new quantity,i.e.,the interval between impact and representative regions,is introduced and its optimal value is first determined to eliminate any boundary effect on shot peening results.Then,model dimensions are respectively assessed for all model shapes to reflect the actual shot peening process,based on which shape-independent critical shot peening quantities are obtained.Further,it is found that thermal softening of the target material due to shot peening leads to variances of the surface residual stress and arc height,demonstrating the necessity of considering the thermal effect in a constitutive material model of shot peeing.Our study clarifies some of the finite element modeling aspects and lays the ground for accurate modeling of the SP process.

Abelian Subgroup Separability of Certain Generalized Free Products of Groups

We prove that generalized free products of certain abelian subgroup separable groups are abelian subgroup separable.Applying this,we show that tree products of polycyclic-by-finite groups,amalgamating central subgroups or retracts are abelian subgroup separable.

Subgroup Separability of Certain Generalized Free Products of Nilpotent-by-finite Groups

In this paper, we show that certain generalized free products of nilpotent-by-finite groups are subgroup separable when the amalgamated subgroup is × D where D is in the center of both factors.

The Symbolic Extension Theory in Topological Dynamics

In this survey we will present the symbolic extension theory in topological dynamics,which was built over the past twenty years.

Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form<h>×D,where h has infinite order and D is finite.

Regular automorphisms of order p2

Let G be a group,and let a be a regular automorphism of order p2 of G,where p is a prime.If G is polycyclic-by-finite and the map φ:G→G defined by=g^φ,[g,a]is surjective,then G is soluble.If G is polycyclic,then CG(a^p)and G/[G,a^p]are both nilpotent-by-finite.