this paper presents a simple yet powerful original approach for approximating dispersivity in porous media. the key to this approach is both use of least-squares criterion and image processing technique. two dimensional transparent models, including horizontal and vertical configurations, under different combinations of grain sizes and pore velocities, experimented. concentration data were obta...

We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado’s characterisation a regular remains valid over set positive kth powers provided has at least (1+o(1))k log k thus completely describe which diagonal forms are and not, given sufficiently many In addition, prove supersaturated version theorem for linear restricted e...

recently, in order to increase the efficiency of least squares method in numerical solution of ill-posed problems, the chain least squares method is presented in a recurrent process by babolian et al. despite the fact that the given method has many advantages in terms of accuracy and stability, it does not have any stopping criterion and has high computational cost. in this article, the attempt...

In this article, a new approach to tidal harmonic analysis is introduced. This approach incorporates more constituents in the least squares method for a fixed duration of noise-free tidal record and results in a more accurate tidal prediction. Moreover, it is demonstrated that 135 days of hourly data, which is significantly less than 369 days data in the Rayleigh criterion, is sufficient for th...

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods h...

We consider two regularization approaches, the LASSO and the threshold-gradient-directed regularization, for estimation and variable selection in the accelerated failure time model with multiple covariates based on Stute's weighted least squares method. The Stute estimator uses Kaplan-Meier weights to account for censoring in the least squares criterion. The weighted least squares objective fun...

We consider a local least-squares criterion for aligning multiple time series fragments differing by locations and show the consistency of the time-lag estimator and the asymptotic normality of the location estimator. We apply the criterion to the problem of aligning 50 glacial varve fragments and construct a 3000-year surrogate for global temperature. Some key words: Aligning time series; Asym...

During the last decades, the use of information theoretic criteria (ITC) for selecting the order of autoregressive (AR) models has increased constantly. Because the ITC are derived under the strong assumption that the measured signals are stationary, it is not straightforward to employ them in combination with the forgetting factor least-squares algorithms. In the previous literature, the attem...