Euler Characteristics on virtually free products

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These formulas are obtained from a general result which applies to the rank gradient and the first L²?Betti number of a finitely generated group.     

交错群A_5与二面体群D_6直积的整群环的挠单位

本文利用Luthar-Passi方法,研究了五次交错群A_5与六阶二面体群D_6直积的整群环的挠单位,得到了该群的Zassenhaus猜想成立.     

Torsion simple modules over the quantum spatial ageing algebra

Various classes of simple torsion modules are classified over the quantum spatial ageing algebra (this is a Noetherian algebra of Gelfand-Kirillov dimension 4). Explicit constructions of these modules are given and for each module its annihilator is found.     

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

Stress Singularity in an Elastic Cylinder of Cylindrically Anisotropic Materials

The issue of stress singularity in an elastic cylinder of cylindrically anisotropic materials is examined in the context of generalized plane strain and generalized torsion. With a viewpoint that the singularity may be attributed to a conflicting definition of anisotropy at r=0, we study the problem through a compound cylinder in which the outer cylinder is cylindrically anisotropic and the core is transversely isotropic. By letting the radius of the core go to zero, the cylinder becomes one with the central axis showing no conflict in the radial and tangential directions. Closed-form solutions are derived for the cylinder under pressure, extension, torsion, rotation and a uniform temperature change. It is found that the stress is bounded everywhere, and singularity does not occur if the anisotropy at r=0 is defined appropriately. This revised version was published online in July 2006 with corrections to the Cover Date.     

阶跃扭矩作用下弹性圆柱壳冲击屈曲

本文首先基于Koiter初始后屈曲理论和Thompson离散坐标方法,给出了受扭圆柱壳的缺陷敏感性分析及冲击扭转屈曲渐近分析,并指出它对应于对称失稳的情形。然后通过求解受扭圆柱壳的非线性动力学方程,指出在阶跃扭矩作用下的后屈曲阶段,壳体的振动幅值剧增,周期变大。     

HOMOGENIZATION—BASED TOPOLOGY DESIGN FOR PURE TORSION OF COMPOSITE SHAFTS

In conjunction with the homogenization theory and the finite element method, the mathematical models for designing the corss-section of composite shafts by maximizing the torsion rigidity are developed in this paper. To obtain the extremal torsion rigidity, both the cross-section of the macro scale shaft and the representative microstructure of the composite material are optimized using the new models. The micro scale computational model addresses the problem of finding the periodic microstructures with extreme shear moduli. The optimal microstructure obtained with the new model and the homogenization method can be used to improve and optimize natural or artificial materials. In order to be more practical for engineering applications, cellular materials rather than ranked materials are used in the optimal process in the existence of optimal bounds for the elastic properties. Moreover, the macro scale model is proposed to optimize the cross-section of the torsional shaft based on the tailared composites. The validating optimal results show that the models are very effective in obtaining composites with extreme elastic properties, and the cross-section of the composite shaft with the extremal torsion rigidity. The project supported by the National Natural Science Foundation of China (10172078 and 10102018)     

Beschreibung des visko-elastischen Verhaltens des polymeren Mischsystems Phenolnovolakharz-Nitrilkautschuk (PF/NBR) mit Hilfe der Van-der-Poel-Gleichung

Zusammenfassung Morphologische Untersuchungen an dem polymeren Mischsystem Phenolnovolakharz-Nitrilkautschuk haben gezeigt, daß diese Mischungen eine Struktur aufweisen, in der harte kugelige PF-Teilchen in einer Kautschukmatrix bzw. weiche Kautschukteilchen in einer Harzmatrix eingebettet sind. Mit Hilfe der morphologischen und mechanisch-dynamischen Untersuchungen wird versucht, das viskoelastische Verhalten von Polyblends mit der Van-der-Poel-Gleichung zu beschreiben. Es konnte gezeigt werden, daß bis zu ModulwertenGhart/Gweich ~ 100 eine gute Übereinstimmung mit der Van-der-Poel-Gleichung gefunden wird. Hohe Modulverhältnisse der harten Einlagerungskomponente zur weichen KomponentenGhart/Gweich ~ 1000, wie sie im kautschukelastischen Bereich auftreten, zeigen eine Übereinstimmung mit der Van-der-Poel-Gleichung nur bei einer Volumenkonzentration der harten EinlagerungskomponenteV _f < 0,3. Diese Ergebnisse werden mit anderen bekannten theoretischen Überlegungen über den Zusammenhang zwischen Elastizitätsmodul und Zusammensetzung von Verbundwerkstoffen verglichen.Schlüsselwörter Phenolnovolakharz-Nitrilkautschuk-System, viskoelastisches Verhalten, Torsionspendel, Van-der-Poel-Gleichung

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Summary Morphological investigations of the polymer compound-system novolak resin-nitril rubber (PF/NBR) have shown, that these mixtures exhibit structures, in which hard spherical particles are embedded in a rubber matrix, respectively soft rubber particles in a resin matrix.An attempt was made to describe the viscoelastic behaviour of these polyblends by means of morphological and dynamic-mechanical investigations with the relation given by Van der Poel.Up to ratios of the moduliGhard/Gsoft ~ 100 a good agreement with the Van-der-Poel equation was found. In the rubber elastic region at ratiosG hard/G soft ~ 1000 this agreement was found for volume concentrations of the phenolic componentV _f ~ 0.3 only.The results are compared with other existing theories on the correlation between elastic modulus and composition of compound materials.

Mit 7 Abbildungen und 6 Tabellen