We show that any non-degenerate vector field u in L∞(Ω,RN), where Ω is a bounded domain in RN , can be written as u(x) = ∇1H(S(x),x) for a.e. x ∈Ω, where S is a measure preserving point transformation on Ω such that S2 = I a.e (an involution), and H : RN ×RN → R is a globally Lipschitz anti-symmetric convex-concave Hamiltonian. Moreover, u is a monotone map if and only if S can be taken to be t...

The algebra su 2 is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators J + and J − of the group SU 2 (with J + = J † − = HUr where H is Hermitean and Ur unitary). The Wigner-Racah algebra of SU 2 is developed in a new basis arising from the simultanenous diagonalization of the commuting operators J 2 ...

we present observation of polar coronal hole plumes with foot point jets that shows evidence of longitudinal acceleration. the series of event, occurring in the north coronal hole on 10 july 2010, was observed by the aia telescopes of the solar dynamic observatory (sdo mission) in the euv lines, with unprecedented details. the structures along the plume show a propagating outward velocity of ab...

The sign function of a square matrix was introduced by Roberts in 1971. We show that it is useful to regard S = sign(A) as being part of a matrix sign decomposition A = SN, where N = (A ) ’ 1/z This decomposition leads to . the new representation sign(A) = A(A2)-‘i2. Most results for the matrix sign decomposition have a counterpart for the polar decomposition A = UH, and vice versa. To illustra...

A real, square matrix Q is J-orthogonal if Q JQ = J , where the signature matrix J = diag(±1). J-orthogonal matrices arise in the analysis and numerical solution of various matrix problems involving indefinite inner products, including, in particular, the downdating of Cholesky factorizations. We present techniques and tools useful in the analysis, application and construction of these matrices...

We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type decomposition that was obtained from the Baker–Campbell–Hausdorff formula in our study of the Hopf algebra approach of Connes and Kreimer to renormalization ...