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.

Researchers in various engineering fields are increasingly interested in evaluating the influence of the microstructural properties of minerals, such as hematite, on their reactivity. Hematite behaviour and microstructural changes during mechanical activation (MA) were investigated using the shape parameter. The laser diffraction analysis indicates the occurrence of agglomeration in the mechanically activated hematite after 60 min of MA. Based on the microstructural studies, the hematite crystallinity reduced to below 16% after 240 min of MA. Microstrain and crystallite size continuously changed during MA, leading to an increase in hematite leaching efficiency by sulfuric acid. The results revealed that the microstrain variation rate is higher than other microstructural parameters. The obtained shape parameter increased from about 0.31 in the initial hematite to 0.88 and 0.66 in the hematite mechanically activated for 60 and 240 min, respectively. The shape parameter study demonstrated that most mechanical energy is stored in the hematite lattice as microstrain after 240 minutes of MA. Considering the lower impact of microstrain on promoting hematite reactivity, shorter MA times could be preferred over prolonged MA, which would reduce costs and increase capacity.

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.