Orthogonality or near-orthogonality is an important property in the design of experiments. Supersaturated designs are natural when we wish to investigate the main effects for a large number of factors but are restricted to a small number of runs. These supersaturated designs, by definition, cannot satisfy pairwise orthogonality of all the factor columns in the designmatrix. Hence, we need amean...

In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of con...

There are well-known examples of dynamical systems for which the Birkhoff averages with respect to a given observable along some or all of the orbits do not converge. It has been suggested that such orbits could be classified using higher order averages. In the case of a bounded observable, we show that a classical result of G.H. Hardy implies that if the Birkhoff averages do not converge, then...

where κ = 0, . . . , n, and λj is pure imaginary precisely when 1 ≤ j ≤ κ, and λ1, −λ1, . . . , λn, −λn are eigenvalues of Hzz(0)J with z = (x, y) and Jxj = yj = −J yj. One says that λ1, . . . , λn are non-resonant, if λ ·α ≡ λ1α1 + · · ·+λnαn 6= 0 for all multi-indices of integers α 6= 0. The Birkhoff normal form says that under the non-resonance condition on λ, there is a formal symplectic tr...

Abstract. In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a num...

In honor of the 100th birthday of the article, " Sur les groupes continus " Abstract. A methodical analysis of the research related to the article, " Sur les groupes continus " , of Henri Poincaré reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this article confirms the precedence of his discovery of many important concepts...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...