and Applied Analysis 3 in the middle variable, and associative in the sense that x, y, z,w, v x, w, z, y , v x, y, z , w, v , and satisfies ‖ x, y, z ‖ ≤ ‖x‖ · ‖y‖ · ‖z‖ and ‖ x, x, x ‖ ‖x‖ see 45, 47 . Every left Hilbert C∗-module is a C∗-ternary algebra via the ternary product x, y, z : 〈x, y〉z. If a C∗-ternary algebra A, ·, ·, · has an identity, that is, an element e ∈ A such that x x, e, e ...

Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass ℘-functions in place of Riemann theta functions. An example of this approach is given.

A recently developed non-linear transform, called ‘Sign Hadamard-Haar transform’ is discussed. The transform is unique and converts ternary vectors into ternary spectral domain. New transform is extremely effective in terms of computational costs when compared with known Sign Walsh transform in application inside ternary communication system.

We introduce the notion of a generalized semi-ideal in a ternary semiring. Various examples to establish a relationship between ideals, bi-ideals, quasi-ideals and generalized semi-ideals are furnished. A criterion for a commutative ternary semiring without any divisors of zero to a ternary division semiring is given. AMS Mathematics Subject Classification (2010): 16Y60, 16Y99

The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.

Using fixed point methods, we prove the generalized Hyers–Ulam–Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen–type functional equation f( x+ y + z 3 ) + f( x− 2y + z 3 ) + f( x+ y − 2z 3 ) = f(x) .

We use exhaustive computer searches to show that there are exactly 36 codewords in an optimal ternary (11, 7) code and exactly 13 codewords in an optimal ternary (14, 10) code. We also enumerate optimal ternary (14, 10) codes and show that there are exactly 6151 inequivalent such