On the analysis of stochastic divide and conquer algorithms

This paper develops general tools for the analysis of stochastic divide and conquer algorithms. We concentrate on the average performance and the distribution of the running time of the algorithm. As a special example we analyse the average performance and the running time distribution of the (2k + 1)-median version of Quicksort. Online publication October 13, 2000.     

Transport properties of nonelectrolyte liquid mixtures—IV. Viscosity coefficients for benzene,perdeuterobenzene, hexafluorobenzene,and an equimolar mixture of benzene + hexafluorobenzene from 25 to 100°c at pressures up to the freezing pressure

Viscosity coefficient measurements made with an estimated accuracy of ±2% using a self-centering falling body viscometer are reported for benzene, perdeuterobenzene, hexafluorobenzene and an equimolar mixture of benzene + hexafluorobenzene at 25, 50, 75 and 100°C at pressures up to the freezing pressure. The data for each liquid at different temperatures and pressures are correlated very satisfactorily by a graphical method based on plots of 9.118×10⁷ V ^2/3/(MRT)^1/2 versus logV, and are reproduced to within the experimental uncertainty by a free-volume form of equation. Application of the empirical Grunberg and Nissan equation to the mixture viscosity coefficient data shows that the characteristic constant G is practically temperature- and pressure-independent for this system.     

A socioeconomic model for managing water resources in Alicante,southeast Spain

The study analyzes variables that influence the water management model based on a simultaneous relationship between competing demands in the Marina Baja of Alicante, using a methodology that directly links together urban and irrigation demands, making them relevant to each other from a socioeconomic point of view. The paper identifies the relevant variables of this model and the agent behaviour in a closed and joint system. It also aims to demonstrate that by considering water demands for different yet simultaneous uses and regarding clean and reclaimed waters as integrated resources, the system could remain in equilibrium without external water supplies.     

A regularization method for a Cauchy problem of Laplace's equation in an annular domain

In this paper, we propose a new regularization method based on a finite-dimensional subspace generated from fundamental solutions for solving a Cauchy problem of Laplace's equation in an annular domain. Based on a conditional stability for the Cauchy problem of Laplace's equation, we obtain a convergence estimate under the suitable choice of a regularization parameter and an a-priori bound assumption on the solution. A numerical example is provided to show the effectiveness of the proposed method from both accuracy and stability.     

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+A T X −2 A=I

Necessary and sufficient conditions for the matrix equation X+A ^T X ^?2 A=I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.     

Fourth-order accurate BLAGE iterative method for the solution of two-dimensional elliptic equations in polar co-ordinates

In this article, we report on the block alternating group explicit (BLAGE) iterative method for solving the block symmetric linear system derived from the fourth-order accurate nine-point discretisation of a two-dimensional elliptic equation in cylindrical polar co-ordinates. The error analysis of the BLAGE method is discussed briefly. The performance of this more accurate BLAGE method is compared with the corresponding block successive over relaxation (BSOR) method by considering two test problems, wherein the significance of the role played by two parameters ω₁ and ω₂ of the BLAGE method becomes evident in providing both convergence and accuracy of the computed solution.     

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

High-accuracy quadrature methods for solving boundary integral equations of steady-state anisotropic heat conduction problems with Dirichlet conditions

This paper presents the mechanical quadrature methods (MQMs) for solving the boundary integral equations of steady-state anisotropic heat conduction equation on the smooth domains and polygons, respectively. The costless and high-accurate Sidi–Israeli quadrature formula are applied to deal with the integrals in which the kernels have a logarithmic singularity. Especially, the Sidi transformation is used for the polygon cases in order to obtain a rapid convergence by degrading the singularity at the corners on the boundary. The convergence and stability of the MQMs solution are proved based on Anselone's collective compact theory. In addition, asymptotic error expansion of the MQMs shows that the approximation order is of O(h³), where h is the partition size of the boundary. Finally, numerical examples are tested and results verify the theoretical analysis.