Let dα be a measure on R and let σ = (m1,m2, ..., mn), where mk ≥ 1, k = 1, 2, ..., n, are arbitrary real numbers. A polynomial ωn(x) := (x − x1)(x − x2)...(x − xn) with x1 ≤ x2 ≤ ... ≤ xn is said to be the n-th σ-orthogonal polynomial with respect to dα if the vector of zeros (x1, x2, ..., xn) is a solution of the extremal problem ∫

We study a noncommutative generalization of Jordan algebras called Leibniz— Jordan algebras. These algebras satisfy the identities [x1x2]x3 = 0, (x 2 1 , x2, x3) = 2(x1, x2, x1x3), x1(x 2 1 x2) = x 2 1 (x1x2); they are related with Jordan algebras in the same way as Leibniz algebras are related to Lie algebras. We present an analogue of the Tits— Kantor—Koecher construction for Leibniz—Jordan a...

In the last decade, vine copulas emerged as a new efficient techniques for describing and analyzing multi-variate dependence in econometrics; see, e.g., [1–3, 7, 9–11, 13, 14, 21]. Our experience has shown, however, that while these techniques have been successfully applied to many practical problems of econometrics, there is still a lot of confusion and misunderstanding related to vine copulas...