Wavelet Collocation Methods for a First Kind Boundary Integral Equation in Acoustic Scattering

In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering. The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a compressed matrix. Finally, the stiffness matrix is multiplied by diagonal preconditioners such that the resulting matrix of the system of linear equations is well conditioned and sparse. Using this matrix, the boundary integral equation can be solved effectively.     

Mean Field Behaviour of Spin Systems with Orthogonal Interaction Matrix

For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the Curie–Weiss case.     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

An explicit solution to a tandem queueing model

We consider two queues in tandem, each with an exponential server, and with deterministic arrivals to the first queue. We obtain an explicit solution for the steady state distribution of the process (N₁(t), N₂(t), Y(t)), where N_j(t) is the queue length in the jth queue and Y(t) measures the time elapsed since the last arrival. Then we obtain the marginal distributions of (N₁(t), N₂(t)) and of N₂(t). We also evaluate the solution in various limiting cases, such as heavy traffic. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

A new algorithm for fixed design regression and denoising

In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise (standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising and of compression.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

On Bahadur asymptotic efficiency in a semiparametric regression model

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Modular Breath Analyzer (MBA): Introduction of a Breath Analyzer Platform Based on an Innovative and Unique,Modular eNose Concept for Breath Diagnostics and Utilization of Calibration Transfer Methods in Breath Analysis Studies

Exhaled breath analysis for early disease detection may provide a convenient method for painless and non-invasive diagnosis. In this work, a novel, compact and easy-to-use breath analyzer platform with a modular sensing chamber and direct breath sampling unit is presented. The developed analyzer system comprises a compact, low volume, temperature-controlled sensing chamber in three modules that can host any type of resistive gas sensor arrays. Furthermore, in this study three modular breath analyzers are explicitly tested for reproducibility in a real-life breath analysis experiment with several calibration transfer (CT) techniques using transfer samples from the experiment. The experiment consists of classifying breath samples from 15 subjects before and after eating a specific meal using three instruments. We investigate the possibility to transfer calibration models across instruments using transfer samples from the experiment under study, since representative samples of human breath at some conditions are difficult to simulate in a laboratory. For example, exhaled breath from subjects suffering from a disease for which the biomarkers are mostly unknown. Results show that many transfer samples of all the classes under study (in our case meal/no meal) are needed, although some CT methods present reasonably good results with only one class.     

A mass‐fraction‐based interface‐capturing method for multi‐component flow

An interface‐capturing method based on mass fraction is developed to solve the Riemann problem in multi‐component compressible flow. Equations of mass fraction with modified form, which is derived from conservative equations of mass, are employed here to capture the interface. By introducing mass fraction into Euler equations system, as well as other conservative coefficients, a quasi‐conservative numerical model is created. Numerical examples show that the mass fraction model performs well not only in multi‐component fluids modeled by simple stiffened gas equation of state (EOS) but also in that modeled by complex Mie–Grüneisen EOS. Moreover, the mass fraction model is applied to Riemann problem with piecewise EOS; the expression of which depends on density. It is found that the mass fraction model can well adapt to the analytic change in piecewise EOS and produce accuracy solutions with fewer unknown quantities, and the model can be easily extended to m‐component fluid mixture by using only m + 4 equations with no additional conditions. Copyright © 2013 John Wiley & Sons, Ltd.