Pre-Jordan algebras were introduced recently in analogy with preLie algebras. A pre-Jordan algebra is a vector space A with a bilinear multiplication x · y such that the product x ◦ y = x · y + y · x endows A with the structure of a Jordan algebra, and the left multiplications L·(x) : y 7→ x · y define a representation of this Jordan algebra on A. Equivalently, x ·y satisfies these multilinear ...

In this paper we introduce the concepts of generalized higher left centralizer and Jordan Γ-rings M as well proved that every certain Γ-ring is prove triple M.

We define four families of word-rewriting systems: the prefix/suffix systems and the left/right systems. The rewriting of prefix systems generalizes the prefix rewriting of systems: a system is prefix (suffix) if a left hand side and a right hand side are overlapping only by prefix (suffix). The rewriting of right systems generalizes the mechanism of transducers: a system is right (left) if a l...

In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The ...

In this paper the problem of estimating a covariance matrix parametrized by an irreducible symmetric cone in a decision-theoretic set-up is considered. By making use of some results developed in a theory of finite-dimensional Euclidean simple Jordan algebras, Bartlett’s decomposition and an unbiased risk estimate formula for a general family of Wishart distributions on the irreducible symmetric...

The derivation of conservation laws and invariant functions is an essential procedure for the investigation nonlinear dynamical systems. In this study we consider a two-field cosmological model with scalar fields defined in Jordan frame. particular Brans-Dicke field theory second quintessence minimally coupled to gravity. For apply first time new technique without application variational symmet...

We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n×n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n+d)× (n+d) linear system, where d is the order of the zero of detA(λ) at λ ...

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.