Ternary DNA computing using 3 × 3 multiplication matrices.

Ternary DNA computing using 3 × 3 multiplication matrices† †Electronic supplementary information (ESI) available: Gel electrophoresis analysis, the stepwise treatment of H1, the individual 3 × 3 multiplication matrices operation of H2 and H3 and examples of fluorescence spectra corresponding to the parallel computation of three multiplication tables. See DOI: 10.1039/c4sc02930e

Further results on ternary complementary sequences, orthogonal designs and weighing matrices

A set of sequences is complementary, if the sum of their periodic or nonperiodic autocorrelation function is zero. Infinite families of orthogonal designs, based on some weighing matrices of order 2n, weight 2n− k and spread σ, are constructed from two circulants matrices by using complementary sequences of zero non-periodic autocorrelation function, i.e. ternary complementary pairs. Moreover, ...

2-Digit Summary

where and , and , are integers we will refer to as binary and ternary exponents. If we extend the exponents within an arbitrary signed integer space, then it is possible to represent any real number, with arbitrary precision, using a single non-zero digit, [1]. For simplicity, we will drop the subscripts and thus represent h by the 3-tuple . This provides a logarithmic type representation in th...

Algebras with ternary law of composition and their realization by cubic matrices

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial vector bundle over a ternary algebra and show that a triple product induces a structure of binary algebra in each fiber of this vector bundle. We find the suffi...

Balanced Ternary Vector-Matrix Multiplication on a Ternary Optical Computer

This paper proposes an optical method to perform a balanced ternary vector-matrix multiplication. Inspired by ternary optical computer‘s ability to process ternary information, we study techniques to realize ternary vector-matrix multiplication (VMM) based on the work of manipulating binary VMM computation. The principle and specific working flow is described in detail and the correctness of th...