Boyle’s conjecture and perfect localizations

ABSTRACT

In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle’s conjecture is true for left QI-rings with finite Gabriel dimension such that every hereditary torsion theory in the Gabriel filtration is perfect. As corollary, we get that Boyle’s conjecture is true for left QI-rings which satisfy the restricted left socle condition, a result proved by Faith in [6 Faith, C. (1976). On hereditary rings and Boyle’s conjecture. Arch. Math. 27(1):113–119.[Crossref] , [Google Scholar]].     

一种新的计算Timoshenko梁截面剪切系数的方法

Timoshenko梁理论中考虑了截面剪切变形的影响,推导了一种新的计算剪切系数的方法,首先采用悬臂梁纯弯曲变形条件下截面剪应力分布的精确解,基于能量原理得到了各种梁截面剪切系数新的表达式,然后推导了弯扭耦合变形条件下截面剪应力分布的精确解,进一步获得了该条件下截面的剪切系数.结果表明,悬臂梁端面作用力偏离截面的弯曲中心将使剪切系数变小,通过与Cowper计算结果的对比发现结果偏小,其原因是Cowper没有考虑与外力垂直的剪应力的影响,因此新的计算结果更优越.     

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.     

High-pressure torsion applied to nickel single crystals

Nickel single crystals with different crystallographic orientations were deformed by high-pressure torsion. Special attention is devoted to examining the evolution of the micro-texture and microstructure. The initial crystal orientation was found to have a significant effect on the mechanical hardening and evolution of micro-texture at low and medium equivalent strains, whereas at very high strains no effect of the initial orientation was observed and the behaviour was very similar to a polycrystal. The evolution of micro-texture is in good qualitative agreement with the full constrained Taylor model. At very high equivalent strains the initial crystal orientation has no influence on micro-texture. At such strains, the hardening, the refinement of the structure and the texture reaches a saturation. The final micro-texture is explained by the change from one preferred crystallographic orientation to another.     

The Elastic–Plastic Torsion Problem: A Posteriori Error Estimates for Approximate Solutions

We consider the variational inequality that describes the torsion problem for a long elasto-plastic bar. Using duality methods of the variational calculus, we derive a posteriori estimates of functional type that provide computable and guaranteed upper bounds of the energy norm of the difference between the exact solution and any function from the corresponding energy space that satisfies the Dirichlet boundary condition.     

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.     

The Ziegler Spectrum of a Locally Coherent Grothendieck Category

The general theory of locally coherent Grothendieck categoriesis presented. To each locally coherent Grothendieck categoryC a topological space, the Ziegler spectrum of C, is associated.It is proved that the open subsets of the Ziegler spectrum ofC are in bijective correspondence with the Serre subcategoriesof coh C the subcategory of coherent objects of C. This is aNullstellensatz for locally coherent Grothendieck categories.If R is a ring, there is a canonical locally coherent Grothendieckcategory RC (respectively, CR) used for the study of left (respectively,right) R-modules. This category contains the category of R-modulesand its Ziegler spectrum is quasi-compact, a property used toconstruct large (not finitely generated) indecomposable modulesover an artin algebra. Two kinds of examples of locally coherentGrothendieck categories are given: the abstract category theoreticexamples arising from torsion and localization and the examplesthat arise from particular modules over the ring R. The dualitybetween coh-(RC) and coh-CR is shown to give an isomorphismbetween the topologies of the left and right Ziegler spectraof a ring R. The Nullstellensatz is used to give a proof ofthe result of Crawley-Boevey that every character : K₀(coh-C) Z is uniquely expressible as a Z-linear combination of irreduciblecharacters. 1991 Mathematics Subject Classification: 16D90,18E15.