Displaying similar documents to “Integrable systems via inverse integrating factor.”

A class of integrable polynomial vector fields

Javier Chavarriga (1995)

Applicationes Mathematicae

Similarity:

We study the integrability of two-dimensional autonomous systems in the plane of the form = - y + X s ( x , y ) , = x + Y s ( x , y ) , where Xs(x,y) and Ys(x,y) are homogeneous polynomials of degree s with s≥2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable ( x 2 + y 2 ) s / 2 - 1 with coefficients being functions of tan−1(y/x).

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

Similarity:

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.

Norm estimates of discrete Schrödinger operators

Ryszard Szwarc (1998)

Colloquium Mathematicae

Similarity:

Harper’s operator is defined on ℓ 2 ( Z ) by H θ ξ ( n ) = ξ ( n + 1 ) + ξ ( n - 1 ) + 2 cos n θ ξ ( n ) , where θ ∈ [ 0 , π ] . We show that the norm of ∥ H θ ∥ is less than or equal to 2 2 for π / 2 ≤ θ ≤ π . This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.