This paper discusses Penrose spin networks in relation to the bracket polynomial.

A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...

1. Let (a, b) and [a, b] be the greatest common divisor and the least common multiple of a and b, respectively . p„ denotes the n'th prime ; p, q, q1 , q2 , . . . are prime numbers. A sum Z and a product f f denote a summation and a multiplication, respectively, over primes indicated . The symbol # { . . .} denotes the number of elements indicated in the bracket 11. Pμ is the product of the fir...

We show that based on the mathematics of Markow processes and in particular based on the definition of Kramers-Moyal coefficients it is possible to estimate the deterministic part of the dynamics for a broad class of nonlinear noisy systems. In particular we show that for different kinds of noise perturbations, including non Langevin force with finite correlation time and independent measuremen...

A class of new nonabelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional YangMills theory featuring a novel nonlinear gauge symmetry and field equations for Lie-algebra valued vector potential fields. The nonlinear form of the gauge symmetry and field equations relies on the vector cross-product and vector curl opera...

We define Leibniz triple systems in a functorial manner using the algorithm of Kolesnikov and Pozhidaev which converts identities for algebras into identities for dialgebras; this algorithm is a concrete realization of the white Manin product introduced by Vallette by the permutad Perm introduced by Chapoton. We verify that Leibniz triple systems are natural analogues of Lie triple systems by s...

An infinite dimensional algebra which is a non-decomposable reducible representation of su(2) is given. This algebra is defined with respect to two real parameters. If one of these parameters is zero the algebra is the commutative algebra of functions on the sphere, otherwise it is a noncommutative analogue. This is an extension of the algebra normally refered to as the (Berezin) quantum sphere...

OBJECTIVES To investigate the static frictional resistance at the bracket/archwire interface in two recently introduced bracket systems and compare them to conventional ceramic and conventional metal bracket systems. Three variables were considered including the bracket system, archwire type and archwire angulation. MATERIAL AND METHODS Four bracket systems were tested in vitro: Self ligating...

different techniques have been introduced for the removal of ceramic brackets. since the early 1990s, lasers have been used experimentally for debonding ceramic brackets. the goal of this study is to give a comprehensive literature review on laser-aided ceramic bracket debonding. pubmed and google scholar databases were used to identify dental articles with the following combination of key word...

The Schlesinger equations S(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we address the problem of reduction of particular solutions of “more com...