Dichotomic maps for delayed equations

The aim of this work is to apply the method of “dichotomic maps” to study stability of the null solutions of delayed functional differential equations. Preliminaries are presented followed by proofs of main theorems on simple and asymptotic stability. Some particular cases which have been studied by others authors with more restrictive hypotheses and more elaborated methods are showed as illustrative examples enhancing the advantages of the dichotomic maps approach.     

Transition between extinction and blow-up in a generalized Fisher–KPP model

Stationary solutions of the Fisher–KPP equation with general nonlinear diffusion and arbitrary reactional kinetic orders terms are characterized. Such stationary (separatrix-like) solutions disjoint the blow-up solutions from those showing extinction. In addition a criterion for general parameter values is presented, which allows determining the blow-up or vanishing character of the solutions.     

Adaptation of the Experimental Background (ATEB) Method in Voltammetric Determination of Thujone in Herbal Matrices

In this work, a new baseline correction method, named the Adaptation of The Experimental Background (ATEB), based on the subtraction of the blank sample signal (registered for solution without an analyte, for example a supporting electrolyte), was introduced. However, the method was something more than the simple subtraction of the blank sample signal. An innovation of the algorithm consisted in improving of the blank sample signal through application of the polynomials. Operation of the algorithm was demonstrated in determination of thujone in the synthetic and real samples. The synthetic samples were composed of two different mixtures of the quasi‐absinthe herbal matrices spiked with 0.7–14 mg L⁻¹ of thujone. The measurements were conducted with or without presence of Cu²⁺, which is an interfering agent originating from production of absinthe like alcoholic beverages. The real sample was Rodnik's absinthe, likewise spiked with thujone. Application of the ATEB method enabled calculation of the calibration lines with very good correlation (not lower than 0.997).     

Effective results on a fixed point algorithm for families of nonlinear mappings

We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by López-Acedo and Xu to find common fixed points of finite families of k-strict pseudocontractive self-mappings of convex subsets of Hilbert spaces. We show that these results are guaranteed by a number of logical metatheorems for classical and semi-intuitionistic systems.     

A review of normalization techniques in analytical atomic spectrometry with laser sampling: From single to multivariate correction

Despite many advantages of laser sampling in analytical atomic spectrometry, the signal intensity of these hyphenated methods suffers from the specific influences resulting from the laser ablation process of a sample. The problems that arise affect the accuracy and precision of analytical results. Different techniques of analytical signal normalization which improve figures-of-merit for atomic spectrometry with laser sampling are considered in this review. The characteristics and application of these approaches including the use of internal standards, single or several reference signals and multivariate correction of analytical signal are discussed.     

Asymptotic Behavior of Forced Nonlinear Delay Differential Equations with Impulses

The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations, improve and generalize the known results recently obtained in [8]. Received September 7, 1997, Revised May 26, 1998, Accepted July 15, 1998     

Comparison of two screening corrections to the additivity rule for the calculation of electron scattering from polyatomic molecules

The SCAR and EGAR procedures have been proposed in order to extend to lower energies the applicability of the additivity rule for calculation of electron-molecule total cross sections. Both those approximate treatments arise after considering geometrical screening corrections due to partial overlapping of atoms in the molecule, as seen by the incident electrons. The main features, results and limitations of both treatments are put here in comparison by means of their application to some different sized species.     

The semigroup approach to transport processes in networks

We explain how operator semigroups can be used to study transport processes in networks. This method is applied to a linear Boltzmann equation on a finite as well as on an infinite network and yields well-posedness and information on the long term behavior of the solutions to the presented problems.     

A robust and efficient estimation method for single-index varying-coefficient models

A new estimation procedure based on modal regression is proposed for single-index varying-coefficient models. The proposed method achieves better robustness and efficiency than that of Xue and Pang (2013). We establish the asymptotic normalities of proposed estimators and evaluate the performance of the proposed method by a numerical simulation.     

Numerical simulation of free‐surface flow using the level‐set method with global mass correction

A new numerical method that couples the incompressible Navier–Stokes equations with the global mass correction level‐set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier–Stokes equations with the two‐step projection method on a staggered Cartesian grid. The free‐surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third‐order essentially non‐oscillatory schemes and a five stage Runge–Kutta method, to accomplish advection and re‐distancing of the level‐set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS‐VOF method. The simulations reveal some interesting free‐surface phenomena such as the free‐surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd.