New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices

Using Hadamard matrices and mutually orthogonal Latin squares, we construct two new quasi-symmetric designs, with parameters 2 − (66,30,29) and 2 − (78,36,30). These are the first examples of quasi-symmetric designs with these parameters. The parameters belong to the families 2 − (2u ² − u,u ² − u,u ² − u − 1) and 2 − (2u ² + u,u ²,u ² − u), which are related to Hadamard parameters. The designs correspond to new codes meeting the Grey–Rankin bound.     

Multiblock latent root regression. Application to epidemiological data

Several papers have already stressed the interest of latent root regression and its similarities to partial least squares regression. A new formulation of this method which makes it even simpler than the original method to set up a prediction model is discussed. Furthermore, it is shown how this method can be extended not only to the case where it is desired to predict several response variables from a set of predictors but also to the multiblock setting where the aim is to predict one or several data sets from several other data sets. The interest of the method is illustrated on the basis of a data set pertaining to epidemiology.     

Approximation of the joint spectral radius using sum of squares

We provide an asymptotically tight, computationally efficient approximation of the joint spectral radius of a set of matrices using sum of squares (SOS) programming. The approach is based on a search for an SOS polynomial that proves simultaneous contractibility of a finite set of matrices. We provide a bound on the quality of the approximation that unifies several earlier results and is independent of the number of matrices. Additionally, we present a comparison between our approximation scheme and earlier techniques, including the use of common quadratic Lyapunov functions and a method based on matrix liftings. Theoretical results and numerical investigations show that our approach yields tighter approximations.     

Neumann problems for nonlinear hemivariational inequalities

In this paper we study nonlinear Neumann problems driven by the p ‐Laplacian and having a nonsmooth potential. Using techniques from the nonsmooth critical point theory, we prove two existence theorems and a multiplicity result. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficient iterative method for solving the matrix equation AXB + CYD = E

This paper presents an iterative method for solving the matrix equation AXB + CYD = E with real matrices X and Y. By this iterative method, the solvability of the matrix equation can be determined automatically. And when the matrix equation is consistent, then, for any initial matrix pair [X₀, Y₀], a solution pair can be obtained within finite iteration steps in the absence of round‐off errors, and the least norm solution pair can be obtained by choosing a special kind of initial matrix pair. Furthermore, the optimal approximation solution pair to a given matrix pair [X?, ?] in a Frobenius norm can be obtained by finding the least norm solution pair of a new matrix equation AX?B + C?D = ?, where ? = E ? AX?B ? C?D. The given numerical examples show that the iterative method is efficient. Copyright © 2005 John Wiley & Sons, Ltd.     

Estimation of parameters in nonlinear problems

In this paper, we describe two efficient methods to estimate parameters in nonlinear least squares problems: continuation and sentinels methods. When the studied system is modeled by differential equations, we have to identify both unknown parameters and initial conditions. For that, we propose to process in two steps: first identify the unknown parameters, then identify again using the found results, considering now both the parameters and the initial conditions as unknown. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Lagrangian vortex method for unbounded flows

A technique is presented for velocity calculations on the highly distorted node distributions typical of those found in Lagrangian vortex methods. The method solves the partial differential equation for streamfunction directly on the nodes, via a sparse, symmetric system of equations that can be solved using standard iterative solvers. When implemented in a triangulated vortex method, the technique gives computation times which scale as N^1.23, where N is the number of nodes. The computation scheme is derived for two‐dimensional problems and applied to the prediction of the evolution of perturbed multipolar vortices. Due to the numerical performance of the method, it has been possible to examine such evolution at higher and lower Reynolds numbers than have been considered in published numerical studies. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust weighting in least-squares fits

Spectroscopic data sets often contain a significant number of outliers due to effects such as misassignments, trial assignments, or local perturbations. Standard fitting routines can be made robust to such outliers by the method of iteratively reweighted least squares. It is proposed here that the weight of datum i in a give iteration is given by w_i=1/(σ_i²+αr_i²), where σ_i is the standard deviation for the idealized distribution without outliers, and r_i is the residual from the previous iteration. The value of α should depend on the fractional number of outliers and the size of their residuals, but a standard value of α=1/3 is suggested for spectroscopic applications.     

周期异方差时间序列的季节单位根检验

为检验带异方差的季节时间序列中的单位根,提出基于最小二乘估计的统计量.在原假设下得到检验统计量的极限分布.用M on te C arlo方法计算同方差下的经验分位数并考虑异方差对检验水平的影响.实例分析表明了用该方法检验季节单位根的有效性.     

Sturm-Liouville算子方程边值问题的最小极值解

利用 Banach空间中度量广义逆理论 ,证明了 LP(a,b)空间中 Sturm-Liouville算子方程边值问题最小极值解的存在性 ,并借助 Banach空间几何方法给出了最小极值解存在的等价条件