Classification theory guarantees the existence of an isomorphism between any two E8’s, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠ 2,3 an explicit isomorphism between the algebra obtained from J by Faulkner’s construction and the algebra obtained from the split ...

Using combined resonance and ultrasonic methods, a full set of material constants has been measured for morphotropic phase boundary (MPB) composition xPb(In(12)Nb(12))O(3)-(1-x-y)Pb(Mg(13)Nb(23))O(3)-yPbTiO(3) (PIN-PMN-PT) single crystals poled along [001](c). Compared with the MPB composition (1-x)Pb(Mg(13)Nb(23))O(3)-xPbTiO(3) (PMN-PT) single crystals, the PIN-PMN-PT single crystals have smal...

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc − acb − bac + bca + cab − cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation ...

and Applied Analysis 3 for x, y, z ∈ A. A Banach non-Archimedean ternary algebra is a normed non-Archimedean ternary algebra such that the normed non-Archimedean vector space with norm ‖ · ‖ is complete. The ternary algebras have been studied in nineteenth century. Their structures appeared more or less naturally in various domains of mathematical physics and data processing. The discovery of t...

In this study, different derivative spectrophotometric methods are proposed for the simultaneous determination of chlorpheniramine maleate (CP), phenylephrine HCl (PE) and phenylpropanolamine HCl (PP) in their ternary mixtures and in pharmaceutical dosage forms. Spectra of single component and ternary mixtures of various concentrations and combinations from zero- to fourth-derivation were obtai...

In this study, different derivative spectrophotometric methods are proposed for the simultaneous determination of chlorpheniramine maleate (CP), phenylephrine HCl (PE) and phenylpropanolamine HCl (PP) in their ternary mixtures and in pharmaceutical dosage forms. Spectra of single component and ternary mixtures of various concentrations and combinations from zero- to fourth-derivation were obtai...

Let A be a non-commutative prime ring with involution ∗, of characteristic ≠2(and3), Z as the center and Π mapping Π:A→A such that [Π(x),x]∈Z for all (skew) symmetric elements x∈A. If is non-zero CE-Jordan derivation A, then satisfies s4, standard polynomial degree 4. ∗-derivation s4 or Π(y)=λ(y−y*) y∈A, some λ∈C, extended centroid A. Furthermore, we give an example to demonstrate importance re...

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In case of S3-symmetry, the Lie algebras are coordinatized by some nonassociative systems, which are termed generalized Malcev algebras, as they extend the classical Malcev algebras. These s...