Experimental determination of solubility and ternary phase diagram of chiral compound are of tedious and time consuming tasks, and in many cases, there is not enough experimental data for different enantiomeric compositions to access the experimental ternary phase diagram. Using thermodynamic models with predictive capability, having less dependency on experimental data, affords a great advanta...

We consider two analogues of associativity for ternary algebras: total and partial associativity. Using the corresponding ternary associators, we define ternary analogues of alternative and assosymmetric algebras. On any ternary algebra the alternating sum [a, b, c] = abc − acb − bac + bca + cab − cba (the ternary analogue of the Lie bracket) defines a structure of an anticommutative ternary al...

In the context of MultiCriteria Decision Aid, we present new properties of a 2-additive bi-capacity by using a bipolar Möbius transform. We use these properties in the identification of a 2-additive bi-capacity when we represent a cardinal information by a Choquet integral with respect to a 2-additive bi-capacity.

We consider straight-line drawings of trees on a hexagonal grid. The hexagonal grid is an extension of the common grid with inner nodes of degree six. We restrict the number of directions used for the edges from each node to its children from one to five, and to five patterns: straight, Y , ψ, X, and full. The ψ–drawings generalize hvor strictly upward drawings to ternary trees. We show that co...

It is known that under certain conditions the incidence matrix of a balanced incomplete block design (v, b, r, k, λ) gives a binary code of length b and size 2(v + 1). Here we investigate the conditions where a balanced ternary design gives a similar ternary code.

Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic function is expressed in terms of projection operations including a new one. A method to realize new multi-qutrit ternary gates in terms of generalized ternary gat...

In 1963, the Dutch mathemetician F.J.M. Barning described an infinite, planar, ternary tree whose nodes are just the set of Primitive Pythagorean triples. Seven years later, A. Hall independently discovered the same tree. Both used the method of uni-modular matrices to transform one triple to another. A number of rediscoveries have occurred more recently. The purpose of this article is to annou...

In this paper we propose an efficient and regular ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic three. This method is based on full signed ternary expansion of a scalar to be multiplied. The cost per bit of this algorithm is lower than that of all previous ones.

We investigate the key management problem for broadcasting applications. Previous work showed that batch rekeying can be more cost-effective than individual rekeying. Under the assumption that every user has probability p of being replaced by a new user during a batch rekeying period, we study the structure of the optimal key trees. Constant bounds on both the branching degree and the subtree s...