This paper proves infinite algebraic independence of the values hypergeometric

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.

This essay expounds the algebraic framework describing general physical theories, within which the phenomenon of spontaneous symmetry breaking (SSB) makes its appearance in infinite quantum systems. This is in contrast with the fact that a large class of theories both classical and quantum, finite and infinite are termed, in the conventional account of classical and quantum mechanics, as exhibi...

We study an infinite class of functions which provably achieve an optimum algebraic immunity, an optimum algebraic degree and a good nonlinearity. We checked that it has also a good behavior against fast algebraic attacks.

This paper provides the first examples of rings of algebraic numbers containing the rings of algebraic integers of the infinite algebraic extensions of Q, where Hilbert’s Tenth Problem is undecidable.

We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semiinfinite domain x ∈ 0,∞ onto a half-open interval t ∈ −1, 1 . The resulting finite-domain twopoint boundary value problem is transcribed to a system of algebraic equations using ChebyshevGauss CG collocation, wh...

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for “infinite-dimensional second-order cone...

Abstract: This paper addresses a stability analysis problem and synthesis problem for pendulum-like systems with multiple nonlinearities. A method for analysing the Lagrange stability of a pendulum-like system with multiple nonlinearities is proposed. In order to study the synthesis problem, the paper develops an Extended Strict Bounded Real Lemma for unstable systems. A sufficient condition fo...