Let E be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let P = (x1/z 2 1 , y1/z 3 1) be a rational point of infinite order on E, where x1, y1, z1 are coprime integers. We show that the integer sequence (zn)n>1 defined by nP = (xn/z 2 n, yn/z 3 n) for all n > 1 does not eventually coincide with (un2)n>1 for any choice of linear recurrence sequence (un)n>1 with...

This paper studies global asymptotic stability for positive solutions to the equation yn = yn−kyn−lyn−m + yn−k + yn−l + yn−m 1 + yn−kyn−l + yn−kyn−m + yn−lyn−m , n = 0, 1, . . . , with y−m, y−m+1, . . . , y−1 ∈ (0,∞) and 1 ≤ k < l < m. The paper also includes a listing of possible semi-cycle structures for various (k, l, m). The results generalize several others in the recent literature.

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability convergence are proved with aids discrete Gronwall inequality, numerical examples presented to support theoretical analysis.

This paper presents a general approach for the stability analysis of the time-domain finite-element method (TDFEM) for electromagnetic simulations. Derived from the discrete system analysis, the approach determines the stability by analyzing the root-locus map of a characteristic equation and evaluating the spectral radius of the finite element system matrix. The approach is applicable to the T...

This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number of colored compositions for any coloration. The interesting consequences arising from this relationship also give an immediate and simple criterion to determ...