Analysis on the Crown Domain

This paper is a further development of complex methods in harmonic analysis on semi-simple Lie groups [AG], [BeR], [KrS1,2]. We study the growth behaviour of the holomorphic extension of the orbit map of the spherical vector of an irreducible spherical representation of a real reductive group G when approaching the boundary of the crown domain of the Riemannian symmetric space G/K. As an application, we prove that Maa? cusp forms have exponential decay. Received: August 2006, Revision: June 2007, Accepted: June 2007     

Eigenfunction Statistics in the Localized Anderson Model

We consider the localized region of the Anderson model and study the distribution of eigenfunctions simultaneously in space and energy. In a natural scaling limit, we prove convergence to a Poisson process. This provides a counterpoint to recent work, [9], which proves repulsion of the localization centres in a subtly different regime. Submitted: December 12, 2005; Revised: April 22, 2006; Accepted: May 3, 2006     

On strong convergence in real Banach spaces obtained by dropping the Lipshitz condition

We consider an implicit iterative process for two finite families of mappings in a real Banach space and prove strong convergence results without using the Lipschitz condition on mappings. Our results mainly improve and extend the recent results of Chang et al. (2001, 2009, 2007) [1], [2], [3], Cho et al. (2005) [4], Gu (2008) [14], Ofoedu (2006) [9], Schu (1991) [13], Zeng (2003, 2005) [20], [21], and Qin et al. (2008) [11], [12].     

Application of generalized diagonal dominance in wireless sensor network optimization problems

The recent application of the diagonal dominance in the development of the optimization algorithms in the wireless sensor networks design, has been done by Yuan and Yu (2006) [14], extended in Yu et al. (2006) [9], and surveyed in Machado and Tekinay [11]. In this paper, we will use the concept of generalized diagonal dominance, to improve the obtained results regarding the power control game, in three directions. We also discuss the applicability of such improvements.     

Some new Gronwall-Bellman-Bihari type integral inequalities with delay

Some new linear and nonlinear delay integral inequalities of G-B-B type are obtained which generalize some results of O. Akinyele [1], P. Ch. Tsamatos and S. K. Ntouyas [16]. Application examples are also given. This revised version was published online in June 2006 with corrections to the Cover Date.     

Overflow and loss probabilities in a finite ATM buffer fed by self-similar traffic

In [13], real-time measurements from LANs, variable-bit-rate video sources, ISDN control-channels, the World Wide Web and other communication systems have shown that traffic exhibits a behaviour of self-similar nature. In this paper, we give new lower bounds to buffer-overflow and cell-loss probabilities for an ATM queue system with a self-similar cell input traffic and finite buffer. The bounds are better than those obtained in [20], in an important region of parameters. As in [20], they decay hyperbolically with buffer size, when the latter goes to infinity. However, in some region, a factor which accompanies the decay is higher in this paper than in [20]. This revised version was published online in June 2006 with corrections to the Cover Date.     

Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space

In this paper, we establish strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Our results extend and improve the recent ones announced by Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257-266], Matinez-yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411], and many others.     

More results on overlapping squares

Three recent papers (Fan et al., 2006; Simpson, 2007; Kopylova and Smyth, 2012) [5], [11], [8] have considered in complementary ways the combinatorial consequences of assuming that three squares overlap in a string. In this paper we provide a unifying framework for these results: we show that in 12 of 14 subcases that arise the postulated occurrence of three neighboring squares forces a breakdown into highly periodic behavior, thus essentially trivial and easily recognizable. In particular, we provide a proof of Subcase 4 for the first time, and we simplify and refine the previously established results for Subcases 11–14.     

Ingham-Beurling type theorems with weakened gap conditions

Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition. Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in [2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system of vibrating strings. This revised version was published online in June 2006 with corrections to the Cover Date.     

Parallel linear multigrid by agglomeration for the acceleration of 3D compressible flow calculations on unstructured meshes

In this paper, we report on our recent efforts concerning the design of parallel linear multigrid algorithms for the acceleration of 3-dimensional compressible flow calculations. The multigrid strategy adopted in this study relies on a volume agglomeration principle for the construction of the coarse grids starting from a fine discretization of the computational domain. In the past, this strategy has mainly been studied in the 2-dimensional case for the solution of the Euler equations (see Lallemand et al. [6]), the laminar Navier–Stokes equations (see Mavriplis and Venkatakrishnan [12]) and the turbulent Navier–Stokes equations (see Carré [1], Mavriplis [10] and Francescatto and Dervieux [4]). A first extension to the 3-dimensional case is presented by Mavriplis and Venkatakrishnan in [13] and more recently in Mavriplis and Pirzadeh [11]. The main contribution of the present work is twofold: on the one hand, we demonstrate the successful extension and application of the multigrid by a volume agglomeration principle to the acceleration of complex 3-dimensional flow calculations on unstructured tetrahedral meshes and, on the other hand, we enhance further the efficiency of the methodology through its adaptation to parallel architectures. Moreover, a nontrivial aspect of this work is that the corresponding software developments are taking place in an existing industrial flow solver. This revised version was published online in June 2006 with corrections to the Cover Date.     

An Erdős type convergence process in weighted interpolation. II

The aim of this paper is to continue the investigation of the second author started in [14], where a weighted version of a classical result of P. Erdős was proved using Freud type weights. We shall show that an analogous statement is true for weighted interpolation if we consider exponential weights on [-1,1]. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on the split common fixed-point problem for quasi-nonexpansive operators

Based on the very recent work by Censor and Segal (2009) [1], and inspired by Xu (2006) [9], Zhao and Yang (2005) [10], and Bauschke and Combettes (2001) [2], we introduce and analyze an algorithm for solving the split common fixed-point problem for the wide class of quasi-nonexpansive operators in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related algorithms.     

Existence of a dense orbit and topological transitivity: When are they equivalent?

Topological transitivity and existence of a dense orbit are two notions which play an important role in every definition of chaos [2], [4]. Unfortunately, in the literature there are often misunderstandings (or even false statements) about their relationship. In this note we show that generally neither condition implies the other and then we give two propositions (Propositions1 and 2) for implication in either direction. This revised version was published online in June 2006 with corrections to the Cover Date.     

非线性差分方程的多重周期解

用变分方法得到一类非线性差分方程多重周期解的存在性．我们的结果推广了Cai，Yu和Guo[Comput．Math．Appl．，52（2006），1630-1647]的结果，并且这里给出的证明显著地简化了．     

Stability of two families of queueing networks and a discussion of fluid limits

We investigate the stability of two families of queueing networks. The first family consists of a general class of networks, where service is allotted to the lead customer at each buffer. The other generalizes networks considered by Humes [18], and is related to the insertion of “leaky buckets” into the system. The arguments for the stability of the networks in each case rely on the corresponding behavior for the associated fluid models. This connection is employed using the framework established by Dai [10], with some modifications. It is discussed here in a somewhat more general setting, with future applications in mind. This revised version was published online in June 2006 with corrections to the Cover Date.     

Gronwall-Bellman type nonlinear delay integral inequalities on time scales

In this paper, some Gronwall-Bellman type nonlinear delay integral inequalities on time scales are established, which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales. Our results generalize some of the main results in Lipovan (2006) [1], Pachpatte (2000) [2], Ferreira and Torres (2009) [3], Zhang and Meng (2008) [4], Cheung and Ren (2006) [5], Kim (2009) [6], and some of our results unify continuous and discrete analysis in the literature.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces

The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of variational inequality for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend the recent results of Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515], Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43–52], Combettes and Hirstoaga [P.L. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 486–491], Iiduka and Takahashi, [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and many others.     

The relationship among the solutions of two auxiliary ordinary differential equations

In a recent article [Phys. Lett. A 356 (2006) 124], Sirendaoreji extended their auxiliary equation method by introducing a new auxiliary ordinary differential equation (NAODE) and its 14 solutions. Then the author studied some nonlinear evolution equations (NLEEs) and got more exact travelling wave solutions. In this paper, we will show that the 14 solutions of the NAODE are actually the same as the solutions obtained by original auxiliary equation method, and they are only different in the form.     

On the peripheral spectrum of bounded positive semigroups on atomic Banach lattices

Generalizing a recent result of E.B. Davies [4], we show that generators of bounded positive C₀-semigroups on atomic Banach lattices with order continuous norm have trivial peripheral point spectrum. Moreover, we give examples that the peripheral spectrum can be any closed cyclic subset of . Received: 20 September 2005; revised: 23 January 2006