In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary conditions. The fractional derivative is described in the Caputo sense. The shifted Jacobi-Gauss-Lobatto points are used as collocation nodes. The main characteristic behind the Jacobi-Gauss-Lobatto collocation approach is that it reduces such a pr...

A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...

We give an elementary proof of the development of Macdonald polynomials in terms of “modified complete” and elementary symmetric functions.

The image of Abel–Jacobi embedding of a hyperelliptic Riemann surface of genus less than 5 to its Jacobian is the intersection of several shifted theta divisors with carefully chosen shifts. c ⃝ 2014 Elsevier Inc. All rights reserved.

We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.

We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L2 expansion coefficients between a polynomial family and a modified family by a sparse transformation. Accuracy and conditioning of the connection and its inverse are explored. The connection and recurrence coefficient...

Abstract We prove the existence of quasi-Jacobi form solutions for an analogue Kaneko–Zagier differential equation Jacobi forms. The transformation properties under group are derived. A special feature is polynomial dependence index parameter. results yield explicit conjectural description all double ramification cycle integrals in Gromov–Witten theory K3 surfaces.

We consider the three-dimensional Schrödinger equation simulating nanoscale semiconductor quantum dots with non-parabolic effective mass approximation. To discretize the equation, we use non-uniform meshes with half-shifted grid points in the radial direction. The discretization yields a very large eigenproblem that only several eigenpairs embedded in the spectrum are interested. The eigenvalue...