We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.

In 1931, Jesse Douglas showed that in Rn, every set of k rectifiable Jordan curves, with k ≥ 2, bounds an area-minimizing minimal surface with prescribed topological type if a “condition of cohesion” is satisfied. In this paper, it is established that under similar conditions, this result can be extended to non-Jordan curves.

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

I review the relationship between AdS/CFT ( anti-de Sitter / conformal field theory) dualities and the general theory of positive energy unitary representations of non-compact space-time groups and supergroups. I show , in particular, how one can go from the manifestly unitary compact basis of the lowest weight ( positive energy) representations of the conformal group ( Wigner picture) to the m...

In the paper “Is there a Jordan geometry underlying quantum physics?” [Be08], generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum Theory. In the present note, we refine this proposition by discussing further structural features of Quantum Theory: the link with associative involutive algebras A and with Jordan-Lie and Lie-Jordan algebas. The...

The purpose of this paper is to establish a connection between semisimple Jordan algebras and certain invariant differential operators on symmetric spaces; and to prove an identity for such operators which generalizes the classical Capelli identity. The norm function on a simple real Jordan algebra gives rise to invariant differential operators Dm on a certain symmetric space which is a natural...

We construct a closed Jordan curve γ ⊂ R so that γ∩S is uncountable whenever S is a line segment whose endpoints are contained in different connected components of R \ γ. We say that a Jordan arc σ ⊂ R crosses a compact set K ⊂ R if the two endpoints of σ are in different connected components of R \ K. Clearly any arc crossing K must intersect K in at least one point of K. If the intersection c...

In this paper, we define new families of Generalized Fibonacci polynomials and Lucas develop some elegant properties these families. We also find the relationships between family generalized k-Fibonacci known polynomials. Furthermore, generalizations in matrix representation. Then establish Cassini’s Identities for their Finally, suggest avenues further research.