Abstract There is no single canonical polynomial-time version of the Axiom Choice (AC); several statements AC that are equivalent in Zermelo-Fraenkel (ZF) set theory already inequivalent from a constructive point view, and similarly complexity-theoretic view. In this paper we show many classical formulations AC, when restricted to polynomial time natural ways, standard hypotheses, including wer...

We consider real trigonometric polynomial Bernoulli equations of the form A(θ)y′=B1(θ)+Bn(θ)yn where n≥2, with A,B1,Bn being polynomials degree at most μ≥1 in variables θ and Bn(θ)≢0. also A(θ)yn−1y′=B0(θ)+Bn(θ)yn A,B0,Bn variable For first equation, we show that when n≥4, it has 3 solutions n is even 5 odd. second n≥3, odd even. provide two types mentioned above maximum number achieved. The pr...

System identification uses measurements of a dynamic system's input and output to reconstruct mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most the systems around us exhibit some form nonlinear behavior, system techniques are tools will help gain better understanding our surroundings potentially let improve their performance. One is...

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...

This paper presents a static analysis of laminated composite doubly-curved shells using refined kinematic models with polynomial and non-polynomial functions recently introduced in the literature. To be specific, Maclaurin, trigonometric, exponential and zig-zag functions are employed. The employed refined models are based on the equivalent single layer theories. A simply supported shell is sub...