This paper explores the relationship between n-valued propositional logic connectives and modular polynomials. Namely the representing of logic connectives using modular polynomials. The case for n = 2 is explored and a method is developed for finding the coefficients of the unique polynomial that represents any given binary logic connective. Examples are then given for using the modular polyno...

In an earlier version of this paper written by the second named author, we showed that the jumping coefficients of a hyperplane arrangement depend only on the combinatorial data of the arrangement as conjectured by Mustaţǎ. For this we proved a similar assertion on the spectrum. After this first proof was written, the first named author found a more conceptual proof using the Hirzebruch-Riemann...

In this article, the new multi-polarity helix transform for ternary logic functions has been introduced. In addition, an extended dual polarity property that had been used to optimize Kronecker and quaternary Fixed-Polarity Reed-Muller (FPRM) expressions has been applied to generate efficiently the multi-polarity helix transform over GF(3). The experimental results for the transform are compare...

Fusion hierarchies of A–D–E face models are constructed. The fused critical D, E and elliptic D models yield new solutions of the YangBaxter equations with bond variables on the edges of faces in addition to the spin variables on the corners. It is shown directly that the row transfer matrices of the fused models satisfy special functional equations. Intertwiners between the fused A–D–E models ...

The role of the Lambert-Beer law in ocean optics is critically examined. The Lambert-Beer law and the three-parameter model of the submarine light field are used to construct an optical energy budget for any hydrosol. It is further applied to the analytical exponential decay coefficient of the light field and used to estimate the optical properties and effects of the dissolved/suspended compone...

The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system’s dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed loop system need not be guaranteed...

The aim of this study was to develop a method for automated discrimination of three honeybee subspecies used for breeding in Poland: A. mellifera carnica, A. m. caucasica and A. m. mellifera. The method developed exploits characteristic venation of forewings. Samples of bees were collected from 1042 bee colonies of the three subspecies. From each of the colonies 20 right forewings were dissecte...

Two of the geomorphic Laws of Drainage Net Composition are discussed and it is shown that they are essentially abstract mathematical relationships that hold for any bifurcating system. Some of the geomorphic factors that determine the value of the characteristic coefficients that are obtained by application of the Laws to single nets are also discussed.

This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that th...