Related papers: Catalan Numbers, Riccati Equations and Convergence
In this paper, we study Catalan numbers which can be represented by the p-adic integral on Zp and we investigate some properties and formulae related to Catalan numbers and special numbers.
We present an algorithmic mapping from permutations of length dn to labeled n-node d-ary trees and back again. Given such a bijection, one can interpret each of the factorials in the formula for the Catalan numbers as a count of…
We explore Fourier transforms of the reciprocal of the Riemann zeta function that have connections to the RH. A partial answer to a recently posed problem is explored by exploiting the fact that $\zeta(s)\neq0$ when $\Re(s)=1.$
In "Square partitions and Catalan numbers" (arXiv0912.4983), Bennett et al. presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a…
We develop the Stienstra-Beukers theory of supercongruences in the setting of the Catalan-Larcombe-French sequence. We also give some applications to other sequences.
Catalan numbers and their interpretations in terms of Dyck paths are widely used in different topics of applied mathematics and computer science. Here, we consider a general approach for constrained Dyck paths. In particular, we study Dyck…
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general…
We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of…
In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012--4024, with respect to the convergence of the accelerated Riccati iteration method for solving the…
We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of consecutive generalized Catalan numbers and find their values in the closed form.
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
In this paper we obtain bounds for integer solutions of quadratic polynomials in two variables that represent a natural number. Also we get some results on twin prime numbers. In addition, we use linear functionals to prove some results of…
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms…
Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integrals, Fourier-Legendre (FL) series expansions, and ${}_p F_q$…
In this paper, our goal is to study fundamental foundations of linear quadratic Gaussian (LQG) control problems for stochastic linear time-invariant systems via Lagrangian duality of semidefinite programming (SDP) problems. In particular,…
We describe how the reversion of a series is related to convolutional recurrence relations for the series, and we place this relationship in the context of Riordan arrays. As an example of the approach, we give new recurrence relations for…
We prove a new generalization of Davenport's Fourier expansion of the infinite series involving the fractional part function over arithmetic functions. A new Mellin transform related to the Riemann zeta function is also established.
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…