We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.

In this paper Refinement of Generalized Jacobi (RGJ) method for solving systems of linear algebraic equations is proposed and its convergence is discussed. Few numerical examples are considered to show the efficiency of the Refinement of Generalized Jacobi method over generalized Jacobi method. Mathematics Subject Classification: 65F10, 65F50

We study spaces of reflectionless Jacobi matrices. The main theme is the following type of question: Given a reflectionless Jacobi matrix, is it possible to approximate it by other reflectionless and, typically, simpler Jacobi matrices of a special type? For example, can we approximate by periodic operators?

Contents 1. Introduction 1 2. Geometrical setting near a dilated catenoid 6 3. Jacobi-Toda system on the Catenoid 9 4. Jacobi operator and the linear Jacobi-Toda operator on the catenoid. 16 5. Approximation of the solution of the theorem 1 23 6. Proof of theorem 1. 30 7. gluing reduction and solution to the projected problem.

We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.

We introduce a family of generalized Jacobi polynomials/functions with indexes α,β ∈ R which are mutually orthogonal with respect to the corresponding Jacobi weights and which inherit selected important properties of the classical Jacobi polynomials. We establish their basic approximation properties in suitably weighted Sobolev spaces. As an example of their applications, we show that the gener...

Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces are investigated. Some results on orthogonal projections and interpolations are established. Explicit expressions describing the dependence of approximation results on the parameters of Jacobi polynomials are given. These results serve as an important tool in the analysis of numerous quadratures and numerical methods for diff...

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

We consider congruences and filtrations of Jacobi forms. More specifically, we extend Tate’s theory of theta cycles to Jacobi forms, which allows us to prove a criterion for an analog of Atkin’s U-operator applied to a Jacobi form to be nonzero modulo a prime.

Jacobi-like forms of one variable are formal power series with holomorphic coefficients satisfying a certain transformation formula with respect to the action of a discrete subgroup Γ of SL(2,R), and they are related to modular forms for Γ, which of course play a major role in number theory. Indeed, by using this transformation formula, it can be shown that that there is a one-to-one correspond...