We formulate a linear difference equation which yields averaged semi-inclusive decay rates for arbitrary, not necessarily large, values of the masses. We show that the rates for decays M → m+M ′ of typical heavy open strings are independent of the masses M and m, and compute the “mass deffect” M−m−M ′. For closed strings we find decay rates proportional to Mm(1−D)/2 R , wheremR is the reduced m...

The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn 1 α βxn γxn−k / 1 xn−k , n ∈ N0, where the parameters α, β, γ ∈ 0,∞ , k ≥ 2 is an integer, and the initial conditions x−k, . . . , x0 ∈ 0,∞ . It is shown that the unique positive equilibrium of the equation is globally asymptotically ...

In this note, we study the general form of some rational recursive sequences. By some modification of the methods and ideas, as well as the transformation from the paper [K. The global attractivity of the rational difference equation y n = y n−k +yn−m 1+y n−k yn−m , Appl. Math. Lett. 20 (2007), 54–58], we give a new proof for the conjectures posed therein.

whenever (un) ∞ n=0 is a non-degenerate linear recurrence sequence. Mahler’s proof is not effective in the following sense. Given a positive integer m the proof does not yield a number C(m) which is effectively computable in terms of m, such that |un| > m whenever n > C(m). However, Schmidt [31, 32], Allen [1], and Amoroso and Viada [2] have given estimates in terms of t only for the number of ...

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

in this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{ax_n+x_{n-1}}{b+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $a, b$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

In this paper, using the linearized equations of an inverted pendulum, a fuzzy logic controller (FLC) is designed for stabilizing its motion. The complete closedloop control system is observed for its output response employing unit step input. Further, an approach is presented for analyzing the stability nature of fuzzy logic controller. For this, utilizing the output membership values obtained...

In this paper, some properties of all positive solutions are considered for a higher order rational difference equation, mainly for the existence of eventual prime period two solutions, the existence and asymptotic behavior of nonoscillatory solutions and the global asymptotic stability of its equilibria. Our results show that a positive equilibrium point of this equation is a global attractor ...

For any integer m let P (m) denote the greatest prime factor of m and let Q(m) denote the greatest square free factor of m with the convention that P (0) = P (±1) = 1 = Q(±1) = Q(0). Thus, if m = p1 1 · · · p hr r with p1, . . . , pr distinct primes and h1, . . . , hr positive integers, then Q(m) = p1 · · · pr. van der Poorten and Schlickewei [6] and Evertse [1] proved, by means of a p-adic ver...

This paper deals with obtaing necessary and sufficient conditions for the existence of at least one Ψ-bounded solution for the non-homogeneous matrix difference equation X(n+1) = A(n)X(n)B(n)+F (n), where F (n) is a Ψ-bounded matrix valued function on Z+. Finally, we prove a result relating to the asymptotic behavior of the Ψ-bounded solutions of this equation on Z+.