In this paper, we present a rigorous derivation of new kinetic equation describing the limiting behavior classical system particles with three particle elastic instantaneous interactions, which are modeled using non-symmetric version ternary distance. The collisional operator derive can be seen as first step towards obtaining toy model for non-ideal gas where higher order interactions taken int...

We determine the identities of degree ≤ 6 satisfied by the symmetric (Jordan) product a◦ b = ab+ ba and the associator [a, b, c] = (ab)c−a(bc) in every nonassociative algebra. In addition to the commutative identity a◦b = b◦a we obtain one new identity in degree 4 and another new identity in degree 5. We demonstrate the existence of further new identities in degree 6. These identities define a ...

We use a generalized Jordan algebra of the second kind to study the recently proposed BLG theory of multiple M2-branes. We find the restriction imposed on the ternary product from its consistency with the BLG theory. [email protected] [email protected] [email protected]

This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic structure of finite-dimensional quantum theory. The derivation relies on the Koecher-Vinberg Theorem, which sets up an equivalence between order-unit spaces having...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

In the present paper, we prove that every local and $2$-local derivation of complex finite-dimensional simple Filippov algebra is a derivation. As corollary have description all derivations semisimple algebras. All ternary Malcev $M_8$ are described. It first example admits pure derivations, i.e. which not

In this note, by means of the spectrum of the generating operator, we characterize the self-adjointness and closedness of the range of a normal and a self-adjoint Jordan *-derivation, respectively.

We show that a quaternary Jordan derivation on a quaternary Banach algebra associated with the equation f( x+ y + z 4 ) + f( 3x− y − 4z 4 ) + f( 4x+ 3z 4 ) = 2f(x) . is satisfied in generalized Hyers–Ulam stability.

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