Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

Order of approximation by an operator involving biorthogonal polynomials

Abstract: The goal of this paper is to estimate the rate of convergence of a linear positive operator involving Konhauser polynomials to bounded variation functions on $[0,1]$ . To prove our main result, we have used some methods and techniques of probability theory.

Projected Iterations of Fixed-Point Type to Solve Nonlinear Partial Volterra Integro-Differential Equations

Abstract: In this paper, we propose a method to approximate the fixed point of an operator in a Banach space. Using biorthogonal systems, this method is applied to build an approximation of the solution of a class of nonlinear partial integro-differential equations. The theoretical findings are illustrated with several numerical examples, confirming the reliability, validity and precision of the proposed method.

Novel orthogonalization and biorthogonalization algorithms Towards multistate multiconfiguration perturbation theory

Abstract: Orthogonalization with the prerequisite of keeping several vectors fixed is examined. Explicit formulae are derived both for orthogonal and biorthogonal vector sets. Calculation of the inverse or square root of the entire overlap matrix is eliminated, allowing computational time reduction. In this special situation, it is found sufficient to evaluate the functions of matrices of the dimension matching the number of fixed vectors. The (bi)orthogonal sets find direct application in extending multiconfigurational perturbation theory to deal with multiple reference vectors.

Non-Hermitian Model for Asymmetrical Tunneling

Abstract: We present a simple non-hermitian model to describe the phenomenon of asymmetric tunneling between two energy-degenerate sites coupled by a non-reciprocal interaction without dissipation. The system was described using a biorthogonal family of energy eigenvectors, the dynamics of the system was determined by the Schrodinger equation, and unitarity was effectively restored by proper normalization of the state vectors. The results show that the tunneling rates are indeed asymmetrical in this model, leading to an equilibrium that displays unequal occupation of the degenerate systems even in the absence of external interactions.

Four-dimensional manifolds with positive biorthogonal curvature

Abstract: We classify, up to homeomorphisms, the closed simply-connected 4-manifolds that admit a Riemannian metric for which averages of pairs of sectional curvatures of orthogonal planes are positive.