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.

We used a combination of in situ attenuated total reflectance Fourier transform infrared (ATRFTIR) spectroscopy and X-ray absorption fine structure (XAFS) spectroscopy to conduct molecular scale studies on Pb(II)-sulfate interactions at the solid-water interface of goethite at pH 4.5, 5.0, and 6.0. Both the ATR-FTIR studies (probing sorbed SO4 in a flow cell setup as a function of the Pb concen...

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.

The solubility of sodium acetate in ternary solvent mixtures of water + methanol (MeOH) + acetonitrile (ACN), water + MeOH + 1-propanol (PrOH), water + PrOH + ACN, and MeOH + PrOH + ACN at 298.2 K is reported and mathematically represented using two numerical analyses (based on measured solubility data in 54 ternary mixtures containing the particular solvents in the mass fraction ranges between...

A new realization of non-recursive digital filters using operation on ternary delta modulated signal is proposed. Direct operation on ternary delta modulated signal will be derived mathematically and a hardware implementation of ternary arithmetic operation will be shown. The primary advantage of the ternary scheme is the simplicity of the hardware and reduction in connections and interconnecti...