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Element free Galerkin method is one of many numerical methods which was applied to various engineering systems. Therefore, in this study two linear elastic rods having solid cross sections were investigated for different loading conditions. The problem considered in the analysis is one dimensional linear elastic cantilever rods and rods are subjected to axial loads f(x)=x and f(x)=0 [ f(l)=1]. Moving least square approximation was used as shape functions. Shape functions were applied to one and two dimensional solution domains, and plotted. In this paper, axial displacement values obtained by using element free Galerkin method which proposed and used by researchers for approximating the solution were compared with analytical solution. As a result, it was found that element free Galerkin method is an effective and trustworthy numerical solution method. [ABSTRACT FROM AUTHOR]

Fundamentals of the Research: In the presence of outlier(s), the method of Ordinary Least Squares (OLS) can be affected and gives misleading results. The common applications of OLS and the frequent existence of outliers in researches require to be tended to use resistant estimators in every statistical work. Purpose of the Research: Hence the purposes of this study are to introduce some high breakdown robust estimation techiques that are alternative to OLS, to investigate the effects of outliers on OLS and robust estimators and lastly diagnose of outliers. Main Discussion and Results: In case of having atypical and infrequent observations, OLS estimation results, standard errors and confidence intervals are affected badly. Whereas reliable results and outlier diagnosis can be attained with robust estimators. The consequences of robust and sensitive estimators on demographically structured data are analyzed within the context of this subject. These consequences are also ascertained in some of the data set which provide two-dimensional plots with a visual perception. Furthermore, diagnosed outliers in data verify the past demographic statistics' summaries. [ABSTRACT FROM AUTHOR]

In this study, recursive least squares method (RLSM) that is one of the adaptable classical methods was used. Firstly forgetting factor was adapted to RLSM. Phase information of voltage signal belonging to an electric power network that contains harmonics and spike was obtained by developed approach. Then responses of the algorithm were investigated for voltage collapse, phase shift and spike. Simulation was implemented by using MATLAB® code. Results of simulation were examined and efficiency of method was presented. [ABSTRACT FROM AUTHOR]

A new estimation concept for semiparametric regression models based on smoothing splines has been introduced in Eubank et al. (1998). The two different approaches based on smoothing splines have been compared by Schimek (2000) according to this estimation concept. In this study, the estimation of the semiparametric regression model is performed with two different approaches called partial splines of Green and Silverman and Speckman's approach and compared with the estimations of the ordinary least squares. The smoothing parameter is selected via generalized cross-validation in smoothing splines and inferences have been discussed for both the parametric and the nonparametric part of the model. For this purpose an application is performed by using a program coded in MATLAB. [ABSTRACT FROM AUTHOR]

In regression analysis, if there are some kind of relation (multicollinearity) between independent variables, the Least Squares estimation method may lead to the use of wrong models and hence to wrong findings out of the model. Various methods have been devised in order to carry out regression analysis with such independent variables which exhibit dependence on each other. One of such methods is the biased estimation methods. In this study, it has been studied on the necessary and sufficient conditions of biased estimators based on Ridge estimator to be at least efficient as much as the Least Squares estimator. [ABSTRACT FROM AUTHOR]