Sign Tests for Long-memory Time Series

This paper proposes sign-based tests for simple and composite hypotheses on the long-memory parameter of a time series process. The tests allow for nonstationary hypothesis, such as unit root, as well as for stationary hypotheses, such as weak dependence or no integration. The proposed generalized Lagrange multiplier sign tests for simple hypotheses on the long-memory parameter are exact and locally optimal among those in their class. We also propose tests for composite hypotheses on the parameters of ARFIMA processes. The resulting tests statistics have a standard normal limiting distribution under the null hypothesis.Publicad

Boosting Estimation of RBF Neural Networks for Dependent Data

This paper develops theoretical results for the estimation of radial basis function neural network specifications, for dependent data, that do not require iterative estimation techniques. Use of the properties of regression based boosting algorithms is made. Both consistency and rate results are derived. An application to nonparametric specification testing illustrates the usefulness of the results.Neural Networks, Boosting

An approximate homogenization scheme for nonperiodic materials

AbstractRecently in [1], Briane announced a new homogenization method for certain nonperiodic materials in which the H-limit of a highly oscillatory but nonperiodic matrix Aε is obtained by comparing to a locally-periodic matrix Bε in domains whose size α(ε) → 0 as ε → 0 but slower than ϵ. The H-limit of Bε is a function of every point in the material, and so theoretically, in order to homogenize Aε, the solution to the usual periodic cell problem must be obtained for every point in the material. Computationally this is not feasible, so we approximate the homogenization method by keeping α fixed. We show that this approximation is O(α) by proving that the difference of two nearby cell solutions (within a cube of side length α) is O(α) in the H1-norm. This result requires that we show a uniform bound exists for the gradients of the periodic cell solutions in Lp. We then apply our approximate homogenization theory to the analysis of certain defects in fiber-reinforced composites. In particular, we show that when unexpected local spreading of the fibers occurs in a small region of the material, constituent stress concentrations of nearly three can arise

Radial functions on compact support

In this paper, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices for scattered data are discussed. They are related to the well-known thin plate spline radial functions which are highly useful in applications for gridfree approximation methods. Also, encouraging approximation results for the compactly supported radial functions are show

Analysis of a reaction-diffusion system of ƛ -w type

The author studies two coupled reaction-diffusion equations of 'ƛ - w' type, on an open, bounded, convex domain Ω C R(^d) (d ≤ 3), with a boundary of class C(^2), and homogeneous Neumann boundary conditions. The equations are close to a supercritical Hopf bifurcation in the reaction kinetics, and are model equations for oscillatory reaction-diffusion equations. Global existence, uniqueness and continuous dependence on initial data of strong and weak solutions are proved using the classical Faedo-Galerkin method of Lions and compactness arguments. The work provides a complete case study for the application of this method to systems of nonlinear reaction-diffusion equations. The author also undertook the numerical analysis of the reaction-diffusion system. Results are presented for a fully-practical piecewise linear finite element method by mimicking results in the continuous case. Semi-discrete and fully-discrete error estimates are proved after establishing a priori bounds for various norms of the approximate solutions. Finally, the theoretical results are illustrated and verified via the numerical simulation of periodic plane waves in one space dimension, and preliminary results representing target patterns and spiral solutions presented in two space dimensions

Numerical analysis of the aerodynamic noise prediction in Direct Numerical Simulation and Large Eddy Simulation

This thesis presents the rigorous numerical analysis of the aerodynamic noise generation viaLighthill acoustic analogy, which is a non-homogeneous wave equation describing thesound waves. Over more than five decades, the Lighthill analogy was extensively used as oneof the major tools in engineering applications in acoustics. However, the first mathematicalresearch of the Finite Element approximation for it is introduced here. Specifically, we focuson both Direct Numerical and Large Eddy Simulations. The more or less intuitive derivationof the Lighthill analogy is reviewed in section 1.3.First, the semidiscrete and fully discrete Finite Element methods in DNS are presentedand the effect of the computational error in the right-hand side of the wave equation ispointed out. The convergence of this error to zero is studied in the semidiscrete case. Thecomputational results support obtained theoretical predictions.Second, the numerical analysis, using the negative norms of the error, is presented in thesemidiscrete case. The negative norms help obtain better convergence rate and require lessregularity of the data than positive norms.Third, the sound power is defined as a non-linear functional of acoustic variables andthree independent ways of computing it in the semidiscrete case in DNS are presented. Allof these methods are based on the Finite Element scheme presented earlier. The methodsare compared from the point of view of computational cost, accuracy and simplicity. Again,the computational experiments are presented.Finally, the concept of Large Eddy Simulation is introduced for aeroacoustic researchvia Lighthill analogy. Two subgrid scale models, these are van Cittert deconvolution andBardina, are presented for the filtered acoustic analogy. The semidiscrete Finite ElemetMethod is analyzed for both of them. We present the numerical experiments for this researchas well