For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, ...

Abstract: We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a ...

Abstract: In this paper, new stability conditions are obtained by designing a Lyapunov function that contains polynomials of the system states and membership functions. An iterative algorithm is ...

Bernstein polynomial estimation provides a robust nonparametric technique for approximating both density and distribution functions. Based on the properties of Bernstein polynomials, which uniformly ...

In this paper, we deduce several types of generating functions for q-2D Hermite polynomial by the method of homogeneous q-difference equations. Besides, we deduce a multilinear generating function for ...

For 𝛼, 𝛽 ∈ ℕ₀ and max{𝛼, 𝛽} > 0, it is shown that the integrals of the Jacobi polynomials∫0t(t−0) δPn(α12,β12)(cosθ)(sinθ2)2α(cosθ2)2βdθ>0for all 𝑡 ∈ (0, 𝜋] and 𝑛 ∈ ℕ if 𝛿 ≥ 𝛼 + 1 for 𝛼, 𝛽 ...