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...

The grand partition function for a long linear system of alternating alpha and beta sequences with the restraint of a fixed number, N(alphabeta), of alphabeta boundaries depends in an extremely simple way on the alpha-sequence and beta-sequence grand partition functions, xi(alpha) and xi(beta). When the restraint is removed, we have mualphabeta = 0, where mualphabeta is the chemical potential c...

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...

It is known that host cells can produce type I IFNs (IFN-alphabeta) after exposure to conserved bacterial products, but the functional consequences of such responses on the outcome of bacterial infections are incompletely understood. We show in this study that IFN-alphabeta signaling is crucial for host defenses against different bacteria, including group B streptococci (GBS), pneumococci, and ...

Cytokines that are induced by infection may contribute to the initiation of immune responses through their ability to stimulate dendritic cells (DCs). In this paper, we have addressed the role of IL-15 in DC activation, investigating its expression by DCs in response to three different signals of infection and examining its ability to stimulate DCs. We report that the expression of both IL-15 a...