On the estimation of the Bernoulli regression function using Bernstein polynomials for group observations

The estimate for the Bernoulli regression function is constructed using the Bernstein polynomial for group observations. The question of its consistency and asymptotic normality is studied. A testing hypothesis is constructed on the form of the Bernoulli regression function. The consistency of the constructed tests is investigated.

A New Algorithm Based on Bernstein Polynomials Multiwavelets for the Solution of Differential Equations Governing AC Circuits

We extend the application of multiwavelet-based Bernstein polynomials for the numerical solution of differential equations governing AC circuits (LCR and LC). The operational matrix of integration is obtained from the orthonormal Bernstein polynomial wavelet bases, which diminishes differential equations into the system of linear algebraic equations for easy computation. It appeared that fewer wavelet bases gave better results. The convergence and exactness were examined by comparing the calculated numerical solution and the known analytical solution. The error function was calculated and illustrated graphically for the reliability and accuracy of the proposed method. The proposed method examined several physical issues that lead to differential equations. HIGHLIGHTS Differential equations governing AC circuits are converted into the system of linear algebraic equations using Bernstein polynomial multiwavelets operational matrix of integration for easy computation The convergence and exactness were examined by comparing the calculated numerical solution and the known analytical solution The error function is calculated and shown graphically GRAPHICAL ABSTRACT

Optimal design of piezoelectric cantilever velocity sensor based on PVDF

The response charge of piezoelectric speed sensors using a conventional rectangular cantilever is low, which also causes a low sensitivity in speed measurement. To improve the sensor sensitivity, a piezoelectric speed sensor based on a streamlined piezoelectric cantilever is employed in this paper. Furthermore, a theoretical optimization model of the sensor based on Bernstein polynomial equation is established, and a simulation optimization flow work is also proposed. With method of moving asymptotes (MMA) algorithm, more charge output can be obtained than before. The simulation results show that the optimized sensor can output a voltage of 416 mV and obtain a sensitivity of 52 mV/m⋅s−1 when the input speed is 8 m/s. As compared with the values of 300 mV and 37.5 mV/m⋅s−1 in the un-optimized case, the improvement in the sensor sensitivity is up to 38%, which confirms the effectiveness of the proposed method.

A new approach for Volterra functional integral equations with non-vanishing delays and fractional Bagley-Torvik equationss

A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delays and fractional Bagley-Torvik equation is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are utilized to evaluate the accurate results. The findings for examples figs and tables show that the technique is accurate and simple to use.

Bernstein polynomial induced two step hybrid numerical scheme for solution of second order initial value problems

This paper presents a two-step hybrid numerical scheme with one off-grid point for the numerical solution of general second-order initial value problems without reducing to two systems of the first order. The scheme is developed using the collocation and interpolation technique invoked on Bernstein polynomial. The proposed scheme is consistent, zero stable, and is of order four($4$). The developed scheme can estimate the approximate solutions at both steps and off-step points simultaneously using variable step size. Numerical results obtained in this paper show the efficiency of the proposed scheme over some existing methods of the same and higher orders.