In this paper we study the sequences generated by a neuronal equation of the form xn " 1[!ki"1 aixn#i # Θ], where k is the size of the memory. We show that in the case where all the parameters (ai)1%i%k are strictly positive reals and k is a multiple of 6 (i.e., k " 6m), there exists a subset B " &w1, w2, . . . , wΑ( of &1, 2, . . . , m # 1( and for which there exists a neuronal equation of mem...

ArXiv : math.CO/0403017 v 1 1 March 2004 Summary Combinatorial interpretation of the fibonomial coefficients recently attampted by the present author [1,2] and presented here with suitable improvements results in a proposal of a might be combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided within the context of the classical combinat...

This paper concerns the oscillation of solutions to the second sublinear dynamic equation with damping xΔΔ t q t xΔ σ t p t x σ t 0, on an isolated time scale which is unbounded above. In 0 < α < 1, α is the quotient of odd positive integers. As an application, we get the difference equation Δ2x n n−γΔx n 1 1/n lnn β b −1 / lnn β x n 1 0, where γ > 0, β > 0, and b is any real number, is oscilla...

and then showing that bn/an converges to ζ(3) fast enough to ensure irrationality of ζ(3) (see [5]). Another remarkable discovery of Apéry is that an and bn satisfy the recursive relation (n+2)un+2− (34n+153n+231n+117)un+1+(n+1)un = 0 (un = an or bn). Thus, if we set A(t) = ∑∞ n=0 ant n and B(t) = ∑∞ n=0 bnt , then the functions A(t) and B(t) satisfy the differential equations (1) (1− 34t+ t)θA...

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented. c...

Given positive integers n, k, and m, the (n, k)-th mrestrained Stirling number of the first kind is the number of permutations of an n-set with k disjoint cycles of length ≤ m. Inverting the matrix consisting of the (n, k)-th m-restrained Stirling number of the first kind as the (n+1, k +1)-th entry, the (n, k)-th m-restrained Stirling number of the second kind is defined. In this paper, the mu...

We explore the possibility of using the method of classical integral transforms to solve a class of q-difference-differential equations. The Laplace and the Mellin transform of q-derivatives are derived. The results show that the Mellin transform of the qderivative resembles most closely the corresponding expression in classical analysis, and it could therefore be useful in solving certain q-di...

and T (r, f), which is only true for finite order meromorphic functions. We have also obtained the proximity function and pointwise estimates of f(z+η)/f(z) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations. This also allows us to solve an...

The boundedness character of positive solutions of two nonlinear fourth-order difference equations, which are particular cases of two large classes of difference equations by Stević, are studied in this paper.

We use four different methods involving recurrence relations for polynomials, orthogonal polynomials, symbolic summations and generating functions to determine a sum that originates in a calculation involving record statistics.