Related papers: Interesting system of $3$ first-order recursions
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
We are studying fractional linear recursions of second and third orders and finding periodic recursions with periods of eight and twelve, which, apparently, were not known before.
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…
Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.
Nested recurrence relations are highly sensitive to their initial conditions. The best-known nested recurrence, the Hofstadter $Q$-recurrence, generates sequences displaying a wide variety of behaviors. Most famous among these is the…
We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…
In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…
This paper studies the iterates of the third order Lyness' recurrence $x_{k+3}=(a+x_{k+1}+x_{k+2})/x_k,$ with positive initial conditions, being $a$ also a positive parameter. It is known that for $a=1$ all the sequences generated by this…
In this paper we consider the first order discrete Hamiltonian system $$\begin{cases} x_1(n+1)-x_1(n)& =- H_{x_2}(n,x(n)), x_2(n)-x_2(n-1)& =\ \ H_{x_1}(n,x(n)). \end{cases} $$ Where $n\in \mathbb{Z}$, $x(n)=$ $x_1 (n) \choose x_2 (n)$$ \in…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…