In this paper, the Shape influence of piezoelectric beams including triangle, trapezoid, rectangle, invertedtrapezoid, convex parabola, concave parabola, and comb-Shaped (a combination of two triangular beams with aconnector of 4 mm length) are addressed and analyzed by FEM. The analysis is performed for a bimorphpiezoelectric beam. The analyzed parameters include the beam length, thickness and width of the piezoelectriclayer. The study is performed using COMSOL Multiphysics software for all seven Shapes. The results show thatdue to the mechanical properties of the beams, the natural frequency of the triangular beam is more for allconsidered parameters. In addition, as the width of the beam end increases, the natural frequency reduces, too. Since natural frequency is inversely related to electric power, the inverted trapezoidal beam has the highestelectric power and the triangular beam has the lowest one.

In many water engineering studies, there is a need to fill lost rain data using mapping tools. In this research this has been done by 5 types of RBFs; the data used were extracted by 3 test functions in which the support domain varied from 0.1 by 0.1 meter net to 0.5 by 0.5 meter net with different numbers of stations in a unit area domain. The c parameter was optimized by cross validation method and the Normalized Mean Square Error (NMSE), Percent Average Estimation Error (PAEE) and Coefficient of determination (R2) were the statistical controlling tools for choosing suitable RBF function type. Compared to other works in literature, this work had a better performance in mapping. It is also shown that the c parameter that optimizes the RBF function is highly dependent on the support domain size; the finer the resolutions of support domain, the better the results achieved. The attribute was also found for an arbitrary station point, Z (0.25, 0.35) to show the model capability for an irregular domain. This work may be compared with meshless methods for further research.

In most practical cases, to increase parameter estimation accuracy, we need an estimator with the least risk. In this, contraction estimators play a critical role. Our main purpose is to evaluate the efficiency of some shrinkage estimators of the Shape parameter of the Pareto-Rayleigh distribution under two classes of shrinkage estimators. In this research, the purpose estimators’,efficiency will be compared with the unbiased estimator obtained under the quadratic loss function. The relationship between these two classes of shrinkage estimators was examined, and then the relative efficiency of the proposed estimators was discussed and concluded via doing a Monte Carlo simulation.

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable with collocation method. Then, with aid of method of lines obtained a system of ordinary differential equations according to solution function in the event of time. Methods applied for solving the nonlinear Burgers’ equation and couple Burgers’ equation. The numerical results show that the proposed method is efficient, accurate and stable.

In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in Shape parameter is considered. First the posterior distribution of Shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using various loss functions. We assumed uniform, Jeffreys, exponential, gamma and chi square distributions as prior distributions. The squared error loss function (SELF), entropy loss function (ELF), linex loss function (LLF) and precautionary loss function (PLF), are used as loss functions. We attempt to find out the best estimator for shift point under various priors and loss functions. The proposed Bayesian approach can be adapted to any similar problem for shift point detection. Simulation studies were done to investigate the performance of different loss functions. The results of simulation study denote that the Jeffrey prior distribution under PLF has the most accurate estimation of shift point for sample size of 20, and the gamma prior distribution under SELF has the most accurate estimation of shift point for sample size of 50.

The radial basis functions (RBFs) meshless method has high accuracy for the interpolation of scattered data in high dimensions. Most of the RBFs depend on a parameter, called Shape parameter which plays a significant role to specify the accuracy of the RBF method. In this paper, we present three algorithms to choose the optimal value of the Shape parameter. These are based on Rippa’, s theory to remove data points from the data set and results obtained by Fasshauer and Zhang for the iterative approximate moving least square (AMLS) method. Numerical experiments confirm stable solutions with high accuracy compared to other methods.

Accuracy of the Multiquadric method depends strongly on the choice of the Shape parameter. This research proposes a new algorithm for determining the optimal Shape parameter. It resolves some of the difficulties such as dependence on the number of computational nodes, existence of an analytical solution of the problem, high cost and low accuracy of calculations, convergence of classical optimization methods to local optimal points and so on. In this regard, the Genetic Algorithm (GA) has been used and, lower and upper bounds of the Shape parameter are suggested as minimum (when the coefficient matrix is not singular) and maximum of Euclidean radius, for speeding up the solution process. The algorithm consists of four steps: 1) producing initial Shape parameters by GA in the proposed range, 2) introducing the MQ function with a few numbers of computational points, 3) introducing the MQ function with a large number of computational points and 4) minimizing the difference of solutions of two functions obtained from the two preceding steps. In the meta-heuristic algorithm, distribution of points is uniform such that each three points are the vertices of equilateral triangles in the problem domain. For verification, examples of homogeneous, inhomogeneous and anisotropic types of the seepage phenomena were solved so that domain decomposition technique was used for inhomogeneous problems. The study shows the high capability and accuracy of the proposed algorithm. In this approach, the optimal Shape parameter can be achieved independent of the number of computational points for arbitrary geometries.