Properties of ternary semigroups, groups and algebras are briefly reviewed. It is shown that there exist three types of ternary units. A ternary analog of deformation is shortly discussed. Ternary coalgebras are defined in the most general manner, their classification with respect to the property “to be derived” is made. Three types of coassociativity and three kinds of counits are given. Terna...

We devise a ternary operation for combining three quantum states: it consists of permuting the input systems in a continuous fashion and then discarding all but one of them. This generalizes a binary operation recently studied by Audenaert et al. [ADO16] in the context of entropy power inequalities. Our ternary operation continuously interpolates between all such nested binary operations. Our c...

We investigate the use of NVIDIA’s Compute Unified Device Architecture (CUDA) to speed up matching in classifier systems. We compare CUDA-based matching and CPU-based matching on (i) real inputs using interval-based conditions and on (ii) binary inputs using ternary conditions. Our results show that on small problems, due to the memory transfer overhead introduced by CUDA, matching is faster wh...

The Bi–In–Sn–Zn system is an important alloy system in lead-free soldering. Thermodynamic descriptions for the ternary systems Bi–In–Sn, Bi–In–Zn, Bi–Sn–Zn and In–Sn–Zn are optimized, using the CALPHAD method and combined to obtain a description of the quaternary Bi–In–Sn–Zn. All available experimental data from the literature are taken into consideration in the optimization. Calculated liquidi...

In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as the main parameter to assess the efficiency of the representation, in terms of information compactness and estimated implementation cost in hardware. Using pr...

Galois Field Sum of Products (GFSOP) leads to efficient multi-valued reversible circuit synthesis using quantum gates. In this paper, we propose a new generalization of ternary Toffoli gate and another new generalized reversible ternary gate with discussion of their quantum realizations. Algorithms for synthesizing ternary GFSOP using quantum cascades of these gates are proposed. In both the sy...

Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. [1,12] Multivalued quantum systems have also been used in the framework of quantum cryptography, [4] and the concept of a qudit cluster state has been proposed by generalizing the qubit cluster state. [5] An evolutionary algorithm based synthesizer for ternary quantum ci...

in this work, artificial neural network (ann) has been employed to propose a practical model forpredicting the surface tension of multi-component mixtures. in order to develop a reliable modelbased on the ann, a comprehensive experimental data set including 15 ternary liquid mixtures atdifferent temperatures was employed. these systems consist of 777 data points generally containinghydrocarbon ...

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...