Generalized holonomies

We study some issues related to the notion of generalized holonomies, providing a rigorous mathematical framework where we discuss early heuristic ideas from the physics literature, mainly due to R. Gambini and his collaborators, who have tried to formulate an “extended loop representation” of quantum gravity in Ashtekar variables. We also define a BACH (Baker-Campbell-Hausdorff) series for the formal generalized holonomy and prove its convergence in some particular cases. Finally, we discuss the issue of covariance of generalized holonomies, and prove the covariance for nilpotent connections.     

The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations. III

In the canonical smooth fiber bundles endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups (1, n) and construct (1, n)-invariant generalized differential-geometric connections. In both regular and special cases of the representations of the considered groups (1, n), we find all affine nonholonomic , and _1,2-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations (1, n) and also describe the corresponding (1, n)invariant planar connections.     

Formal and Analytic Deformations of the Witt Algebra

When studying gauge theories (e.g. with finite energy conditions), attention is traditionally restricted to the subset of irreducible connections, which is open and dense in the full space of connections. We point out that generally the residual set of reducible connections contains critical points of the gauge functionals which, moreover, are the only ones common to all theories with a given symmetry, i.e. those determined by the symmetry and geometry of the problem alone, and not by the specific choice of functional.     

Stability and non-linear second-order elastic analyses of beam and framed structures with semi-rigid connections using the cross method

The main objective of this publication is to present an extended version of the Moment Distribution Method (MDM) for the stability and non-linear second-order analysis of indeterminate beams and framed structures made of beam-columns of symmetrical cross-section including the combined effects of shear and bending deformations, axial loads, and semi-rigid connections. The proposed method along each member has the following advantages: (1) it can be utilized in the first- and second-order analyses (including buckling analysis) of indeterminate beams and framed structures made of beam-columns with rigid, semi-rigid, and simple end connections; (2) the effects of semi-rigid connections are condensed into the bending stiffness and fixed-end moments without introducing additional degrees of freedom and equations of equilibrium; and (3) it is accurate, powerful, practical, versatile, and an excellent teaching tool. Analytical studies indicate that shear deformations, semi-rigid connections, and axial loads increase the lateral deflections and affect the internal moments and reactions of continuous beams and framed structures. These effects must be taken into account particularly in slender structures and when they are made of beam or columns with relatively low effective shear areas (like laced columns, columns with batten plates or with perforated cover plates, and columns with open webs) or with low shear stiffness (like short columns made of laminated composites with low shear modulus G when compared to their elastic modulus E) making the shear stiffness GA_s of the same order of magnitude as EI/L². These effects become even more significant when the external supports are not perfectly clamped. Three comprehensive examples are included that show the effectiveness of the proposed method.     

Homogeneous spaces with invariant projectively flat affine connections

We characterize invariant projectively flat affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively flat affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras.

     

Picture change and calculations of expectation values in approximate relativistic theories

The effect of the so-called picture change on expectation values of one-electron operators in approximate two(one)-component relativistic theories is discussed. This effect is expected to be particularly large for operators which assume large values in the vicinity of heavy nuclei. The numerical results illustrating the picture change effect on electric field gradients at nuclei have been obtained in the spin-free Pauli and Douglas–Kroll approximations. It has been found that the picture change effect lowers the electric field gradient at I in HI by about 1 a.u. Very large picture change effect (−8 a.u.) has been calculated for HAt. It is concluded that in accurate calculations of expectation values of operators involving high inverse powers of the electron–nucleus distance the picture change, which accompanies the transformation of the Dirac (Dirac–Coulomb) equation to approximate two(one)-component relativistic Hamiltonians, must be taken into account. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 159–174, 1998     

斜向梁柱外伸端板连接节点的恢复力模型研究

为简化实际工程结构中斜向梁柱外伸端板连接节点的分析与设计，利用欧洲规范EC3的组件法提出了斜向梁柱外伸端板连接节点的恢复力模型。首先，采用组件法计算了斜向梁柱外伸端板连接节点的初始转动刚度和屈服承载力，提出了外伸端板连接节点考虑钢梁倾角影响的初始转动刚度计算公式。通过对试验试件骨架曲线的无量纲化拟合了此类节点的三折线骨架曲线模型。通过回归分析确定了斜向梁柱外伸端板连接节点的卸载刚度计算公式。在此基础上，建立了斜向梁柱外伸端板连接节点的三线型恢复力模型。通过与试验及参数有限元分析结果的对比，验证了斜向梁柱外伸端板连接节点恢复力模型的准确性，研究成果可为斜向外伸端板连接节点的工程分析提供参考。     

Distinguished Connections on Finsler Algebroids

Considering the prolongation of a Lie algebroid,the authors introduce Finsler algebroids and present important geometric objects on these spaces.Important endomorphisms like conservative and Barthel,Cartan tensor and some distinguished connections like Berwald,Cartan,Chern-Rund and Hashiguchi are introduced and studied.