A Method for Solving a Class of Multiple-Criteria Analysis Problems

AMS subject classification: 90C29.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.

A class of domain decomposition preconditioners for hp-discontinuous Galerkin finite element methods

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.

Prevalence and characteristics of spontaneous tinnitus in 11-year-old children

OBJECTIVE: To estimate the prevalence of spontaneous tinnitus in 11-year-old children. DESIGN: A prospective UK population-based study. STUDY SAMPLE: A total of 7092 children from the Avon longitudinal study of parents and children (ALSPAC) who attended the hearing session at age 11 years and answered questions about tinnitus. RESULTS: We estimated the prevalence of any spontaneous tinnitus as 28.1% (95% CI 27.1, 29.2%), and the prevalence of 'clinically significant' tinnitus as 3.1% (95% CI 2.7, 3.5%). Children were less likely to have clinically significant tinnitus if the tinnitus was 'soft' rather than 'loud' and if continuous rather than intermittent. Clinical significance was more likely if the tinnitus occurred more than once a week. Neither pitch nor length of history were important determinants of clinical significance. Small increases in mean hearing threshold (of up to 2.3 dB HL) were associated with clinically significant tinnitus. CONCLUSIONS: Although the prevalence of any tinnitus in 11-year-old children appears high, the small proportion in which this was found to be clinically significant implies that this does not necessarily indicate a large unmet clinical demand. We would expect approximately one child per class of 30 to have clinically significant tinnitus which is, by definition, problematic.

Age and growth, mortality, reproduction and relative yield per recruit of the bogue, Boops boops Linne, 1758 (Sparidae), from the Algarve (south of Portugal) longline fishery

Samples of Boops boops ranging from 7.4 to 30.5 cm were obtained mainly by longline, supplemented by beach seining in the Ria Formosa lagoon, and by market sampling in the Algarve (southern Portugal). The macroscopic analyses of the gonads and the gonad somatic index showed that the south coast of Portugal B. boops spawn mainly from late winter to spring, between February and May. The length at first maturity was similar for males and females and the value for both sexes combined was estimated to be 15.22 cm, corresponding to an age range of 1-3. Age was determined by reading growth bands on otoliths. Age determination was validated by marginal increment analysis. The estimated parameters were L-infinity = 28.06, K = 0.22 and t(0) = -1.42. Mortality rates were calculated for fish captured with longlines, and the estimated parameters were M = 0.33, Z = 1.04 and F = 0.71. Relative yield per recruit analysis and sensitivity analysis showed that the resource is moderately exploited. From the perspective of sustainability, these results provide support for the use of longlines as a gear that is among the least harmful for species such as the bogue.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.