Displaying similar documents to “On a certain map of a triangle”

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

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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.

A class of integrable polynomial vector fields

Javier Chavarriga (1995)

Applicationes Mathematicae

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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).