强symmetric环

为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x~(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环.     

Global regularity of the elastic fields of a power‐law model on Lipschitz domains

In this paper, we study the global regularity of the displacement and stress fields of a nonlinear elastic model of power‐law type. It is assumed that the underlying domains are Lipschitz domains which satisfy an additional geometric condition near those points, where the type of the boundary conditions changes. The proof of the global regularity result relies on a difference quotient technique. Finally, a global regularity result for the stress fields of the elastic, perfect plastic Hencky model is derived. This model appears as a limit model of the power‐law model. Copyright © 2006 John Wiley & Sons, Ltd.     

Using cross-product matrices to compute the SVD

This paper concerns accurate computation of the singular value decomposition (SVD) of an matrix . As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD method is proposed: (a) Use a backward stable algorithm to compute the eigenpairs of and take the square roots of the large eigenvalues of it as the large singular values of ; (b) form the Rayleigh quotient of with respect to the matrix consisting of the computed eigenvectors associated with the computed small eigenvalues of ; (c) compute the eigenvalues of the Rayleigh quotient and take the square roots of them as the small singular values of . A detailed quantitative error analysis is conducted on the method. It is proved that if small singular values are well separated from the large ones then the method can compute the small ones accurately up to the order of the unit roundoff . An algorithm is developed that is not only cheaper than the standard Golub–Reinsch and Chan SVD algorithms but also can update or downdate a new SVD by adding or deleting a row and compute certain refined Ritz vectors for large matrix eigenproblems at very low cost. Several variants of the algorithm are proposed that compute some or all parts of the SVD. Typical numerical examples confirm the high accuracy of our algorithm.Supported in part by the National Science Foundation of China (No. 10471074).     

直觉模糊正规子群与直觉模糊商群

在直觉模糊子群的基础上 ,引入直觉模糊正规子群与直觉模糊商群概念 ,并讨论了它们的一些性质 ,最后研究了群同态下 ,直觉模糊正规子群的对应关系     

Generalized Rayleigh quotient and finite element two-grid discretization schemes

This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of fin...     

Global stress regularity of convex and some nonconvex variational problems

We derive a global regularity theorem for stress fields which correspond to minimizers of convex and some special nonconvex variational problems with mixed boundary conditions on admissible domains. These are Lipschitz domains satisfying additional geometric conditions near those points, where the type of the boundary conditions changes. In the first part it is assumed that the energy densities defining the variational problem are convex but not necessarily strictly convex and satisfy a convexity inequality. The regularity result for this case is derived with a difference quotient technique. In the second part the regularity results are carried over from the convex case to special nonconvex variational problems taking advantage of the relation between nonconvex variational problems and the corresponding (quasi-) convexified problems. The results are applied amongst others to the variational problems for linear elasticity, the p-Laplace operator, Hencky elasto-plasticity with linear hardening and for scalar and vectorial two-well potentials (compatible case).      

Tuned preconditioners for inexact two‐sided inverse and Rayleigh quotient iteration

Convergence results are provided for inexact two‐sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized non‐Hermitian eigenproblem and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two‐sided methods is considered, and the successful tuning strategy for preconditioners is extended to two‐sided methods, creating a novel way of preconditioning two‐sided algorithms. Furthermore, it is shown that inexact two‐sided Rayleigh quotient iteration and the inexact two‐sided Jacobi‐Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov–Galerkin–Krylov method is used and when this specific tuning strategy is applied. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed Boundary Value Problems for Nonlinear Elliptic Systems with p‐Structure in Polyhedral Domains

The nonlinear elliptic system is investigated on a non‐smooth domain. Mixed boundary value conditions are given. The left‐hand side of the system has p‐structure (e.g., it is the p‐Laplacian and 1 < p < ∞). Global regularity results of u and |∇u|^p/2 in fractional order Sobolev spaces are proven.     

Compact Clifford–Klein Forms of Homogeneous Spaces of SO(2, n)

A homogeneous space G/H is said to have a compact Clifford–Klein form if there exists a discrete subgroup of G that acts properly discontinuously on G/H, such that the quotient space \G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford–Klein form, but our classification is not quite complete when n is odd. The work reveals new examples of homogeneous spaces of SO(2, n) that have compact Clifford–Klein forms, if n is even. Furthermore, we show that if H is a closed, connected subgroup of G = SL(3, R), and neither H nor G/H is compact, then G/H does not have a compact Clifford–Klein form, and we also study noncompact Clifford–Klein forms of finite volume.     

Vocal Intensity Characteristics inNormal and Elderly Speakers

The relationship of lung pressure, fundamental frequency, peak airflow, open quotient, and maximal flow declination rate to vocal intensity for a normal speaking, young male control group and an elderly male group was investigated. The control group consisted of 17 healthy male subjects with a mean age of 30 years and the elderly group consisted of 11 healthy male subjects with a mean age of 77 years. Data were collected at three levels of vocal intensity: soft, comfortable, and loud, corresponding to 25%, 50%, and 75% of dynamic range, respectively. Phonational threshold pressure and lung pressure were obtained using the intraoral technique. The oral airflow waveform was inverse filtered to provide an approximation to the glottal airflow waveform from which measures of fundamental frequency, peak airflow, open quotient, and maximal flow declination rate were determined. Excess lung pressure was calculated as lung pressure minus estimated phonational threshold pressure. The results show for both groups an increase in sound pressure level across the conditions, with corresponding increases in lung pressure, excess lung pressure, fundamental frequency, peak airflow, and maximal flow declination rate. Open quotient decreased with increasing vocal intensity. Lung pressure, sound pressure level, and peak airflow were all found to be significantly greater for the control group than for the elderly group at each condition. Open quotient was found to be significantly lower in the control group than in the elderly group at each condition. No significant difference was observed for excess lung pressure, phonational threshold pressure, fundamental frequency, or maximal flow declination rate between the two groups. These results show that a difference in vocal intensity does exist between young and elderly voices and that this difference is the result of differences in lung pressure, peak airflow, and open quotient.