The Mixed LEAST SQUARES Meshfree (MDLSM) method has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) governing the engineering problems. The method is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving LEAST SQUARES (MLS) is usually applied in the MDLSM method for constructing the shape functions. Although the required consistency and compatibility for the approximation function is satisfied by the MLS, the method loss its appropriate efficiency when the nodal points cluster too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving LEAST SQUARES (MMLS). In this approach, the cluster of closed nodal points maps to standard nodal distribution. Then the approximation function and its derivatives compute noting the some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS is evaluated by approximating the mathematical function. The obtained results show the ability of suggested MMLS method to solve the drawback. The suggested approximation function is applied in MDLSM method, and used for solving the Burgers equations. Obtained results approve the efficiency of suggested method.

Localization by the received signal Strength (RSS) measurement is inexpensive and has low computational complexity, thus extending the lifetime of the sensors in the wireless sensor network. The conventional propagation MODEL for RSS has a log-normal distribution and since the probability density function is known, the best estimator for localization is Maximum Likelihood Estimator (MLE). The ML estimator is nonlinear and nonconvex and Gauss-Newton and convex optimization methods are presented in the papers. These methods impose a lot of complexity on the system and reduce the energy of the battery. In this paper, a two-step linear estimator is employed to solve the nonlinear ML estimator. In the first step, a new DRSS MODEL is presented and nonlinear terms of ML cost function are replaced with linear variables. Also, in contrast to the estimators based on the conventional DRSS MODEL, the performance of this estimator doesn't reduce by the random selection of the number 1 reference node. In the second step, the error of approximation of the first step is minimized, thus increasing the accuracy of the location estimation. Simulations show that in both the first and second steps, the accuracy is improved and the average error root error is reduced by up to 13% compared to the existing estimators.

In this paper, a new approach is presented to fit a robust fuzzy regression MODEL based on some fuzzy quantities. In this approach, we first introduce a new distance between two fuzzy numbers using the kernel function, and then, based on the LEAST SQUARES method, the parameters of fuzzy regression MODEL is estimated. The proposed approach has a suitable performance to present the robust fuzzy MODEL in the presence of different types of outliers. Using some simulated data sets and some real data sets, the application of the proposed approach in MODELing some characteristics with outliers, is studied.

Summary Global and regional geomagnetic field MODELs give the components of the geomagnetic field as functions of place and time. Most of these MODELs utilize polynomials or Fourier series to map the input variables to the geomagnetic field values. The only temporal variation in these MODELs is the long term secular variation. However, there is an increasing need amongst certain users for the MODELs that can provide shorter term temporal variations, such as the geomagnetic daily variation. In this research, we have constructed an empirical MODEL of the quiet daily geomagnetic field variation based on functional fitting...

One of the most important procedures in the water sources studies is the estimation of the local distribution of precipitation in different time scales. The study of precipitation is a basic element in the water balance studies and is an important factor in the natural sources programs of each country. Also, because of the rain-evaluation stations deficiency and their discreteness, it is necessary to use a special MODEL. Besides the interpolation of precipitation amounts of stations, this MODEL should interpolate topography, moisture and the slope direction of precipitation. In this work, at first, some data were gathered, in one year. These data were connected with the precipitation and moisture of 9 synoptic stations and 31 rain evaluation stations. These stations were located in the Lorestan province. Second, using the LEAST square method and with the help of Maple software, the relations between precipitation and moisture was extracted. Third, by using the Python programming language, these relations were linked into the GIS. Finally, by so doing, the digital precipitation modal was achieved. The results obtained from the digital precipitation MODEL show that, the precipitation amounts are different from the measured data in the stations, from 0.02 to 11.6mm. Also, to investigate the efficiency of the considered MODEL, the data obtained from this MODEL were compared with the precipitation data achieved from TRMM radar at 21 April 2010. The concluded result show that, the determination coefficients are 79 and 86% for the TRMM data and for the digital precipitation MODEL, respectively.

Geodetic data processing usually is performed using the LEAST-SQUARES method. To achieve the best linear unbiased estimation, it is necessary to use the proper and realistic stochastic MODEL of the observables. The estimation of the unknown (co) variance components of the observables is referred to as variance component estimation (VCE). In geodetic applications, VCE is also known as the observables weights estimation. In this paper, LEAST-SQUARES variance component estimation is applied in a straightforward manner to GPS observables for determination of the realistic stochastic MODEL. For this purpose, the functional MODEL used in the analysis is the GPS geometry-based observation MODEL (GFOM). The numerical results for two receivers, namely Trimble 4000 SSi and Trimble R7, are presented. The results indicate that the correlation between observation types is significant. A positive correlation of 0.55 is observed between the code observations on CA and P2 for Trimble 4000 SSi. Also, a significant positive correlation of 0.64 is observed between the phase observations on L1 and L2 for Trimble R7.

In this paper, we propose a nonparametric rank-based alternative to the LEAST-SQUARES independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.

Image magnification is one of the current issues of image processing in which keeping the quality and structure of images is the main concern. In image magnification, it is necessary to insert information in extra pixels. Adding information to an image should be compatible with the image structure with- out making artificial blocks. In this research, extra pixels are estimated using the surface of LEAST SQUARES, and all the pixels are reviewed according to the suggested edge-improving algorithm. The suggested ethod keeps the edges and minimizes the magnified image opacity and the artificial blocks. Numerical results are presented by using PSNR and SSIM fidelity measures and compared to some other methods. The average PSNR of the original image and image zooming is 32.79 which it shows that image zooming is very similar to the original image. Experimental results show that the proposed method has a better performance than others and provides good image quality.

Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the LEAST-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the heat fundamental solution.