复Banach空间上推广的Roper-Suffridge算子

从定义出发证明复Banach空间特定域上推广的Roper-Suffridge算子保持α次强β型螺形性及ρ次抛物型β型螺形性,由此得到推广后的算子在复Banach空间特定域上保持α次强星形性、ρ次抛物星形性及抛物星形性,为由复平面C中单位圆盘D上的α次强β型螺形映照及ρ次抛物β型螺形映照来构造复Banach空间特定域上相应的映照提供了一种新的途径,充实了对Roper-Suffridge算子的研究.     

A class of discontinuous Petrov–Galerkin methods. II. Optimal test functions

We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes having test function spaces that are automatically computable to guarantee stability. Given a trial space, a DPG discretization using its optimal test space counterpart inherits stability from the well posedness of the undiscretized problem. Although the question of stable test space choice had attracted the attention of many previous authors, the novelty in our approach lies in the fact we identify a discontinuous Galerkin (DG) framework wherein test functions, arbitrarily close to the optimal ones, can be locally computed. The idea is presented abstractly and its feasibility illustrated through several theoretical and numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Application of penalty methods to non-stationary variational inequalities

We solve a general variational inequality problem in a finite-dimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We suggest to utilize a sequence of solutions of auxiliary problems based on a penalty method. Its convergence is attained without concordance of penalty and approximation parameters under mild coercivity type conditions. We also show that the regularized version of the penalty method enables us to further weaken the coercivity condition.     

Banach空间中一类映像的三重迭代法

利用赋范线性空间X的凸性模定义,以及凸性模的单调性及半紧性条件,研究了渐近非扩张映射不动点的三步迭代法.减弱了许多条件,从而推广了同类问题的某些结果.     

On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings

In this note, we speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorithms for Non-expansive Mappings and Some of Their Generalizations, in: Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, vol. 1, 2, Kluwer Acad. Publ, Dordrecht, 2003, pp. 383–429], and Liu [L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 125 (2) (1997) 1363–1366], and some other known results. The technique of the proof, presented in this paper, is different from the technique used by Chidume.     

On functional identities in left ideals of prime rings

In the present paper we describe surjective Lie and Jordan maps onto left ideals of prime noncommutative rings. Further, we describe bijective linear maps of left ideals of centrally closed prime algebras preserving commutativity.     

Coupled fluid–solid interaction under shock wave loading

This paper considers the treatment of fluid–solid interaction problems under shock wave loading, where the solid experiences large bulk Lagrangian displacements. This work addresses the issues associated with using a level set as a generalized interface for fluid–solid coupling where the fluid–solid interface is embedded in an unstructured fluid grid. We outline the formulation used for the edge‐based unstructured‐grid Euler solver. The identification of the fluid–solid interface on the unstructured fluid mesh uses a super‐sampled ??² projection technique, which in conjunction with a Lagrangian interface position, permits fast identification of the interface and the concomitant imposition of boundary conditions. The use of a narrow‐band approach for the identification of the wetted interface is presented with the details of the construction of interface conditions. A series of two and three‐dimensional shock‐body computations are presented to demonstrate the validity of the current approach on problems with static and dynamic interfaces, including projectile/shock interaction simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings

For quasianalytic Denjoy-Carleman differentiable function classes CQ where the weight sequence Q=(Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of CQ-mappings is cartesian closed in the sense that CQ(E,CQ(F,G))≅CQ(E×F,G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of CQ-diffeomorphisms is a regular CQ-Lie group but not better.     

Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations

An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high‐order piecewise divergence‐free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.     

An eigenvector‐based linear reconstruction approach for time stepping in discontinuous Galerkin scheme used to solve shallow water equations

Discontinuous Galerkin (DG) methods have shown promising results for solving the two‐dimensional shallow water equations. In this paper, the classical Runge–Kutta (RK) time discretisation is replaced by the eigenvector‐based reconstruction (EVR) that allows the second‐order time accuracy to be achieved within a single time‐stepping procedure. Moreover, the EVRDG approach yields stable solutions near drying and wetting fronts, whereas the classical RKDG approach yields instabilities. The proposed EVRDG technique is compared with the original RKDG approach on various test cases with analytical solutions. The EVRDG solutions are shown to be as accurate as those obtained with the RKDG scheme. Besides, the EVRDG scheme is 1.6 times faster than the RKDG method. Simulating dambreaks involving dry beds confirms that EVRDG scheme gives correct solutions, whereas the RKDG method yields instabilities. Copyright © 2012 John Wiley & Sons, Ltd.