In this paper we study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the following systems of two difference equations of exponential form: x nþ1 ¼

We obtain Willett-Wong-type oscillation and nonoscillation theorems for second order linear dynamic equations with integrable coefficients on a time scale. The results obtained extend and are motivated by oscillation and nonoscillation results due to Willett [20] and Wong [21] for the second order linear differential equation. As applications of the new results obtained, we give the complete cl...

In this paper we give some recurrence relations satisfied by single and product moments of generalized order statistics from doubly truncated generalized exponential distribution. These relations are deduced for moments of record values and order statistics. Further, using a recurrence relation for single moments we obtain a characterization of generalized exponential distribution.

In this paper, we extend the oscillation criteria that have been established by Hille [15] and Nehari [21] for second-order differential equations to third order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third order differential and difference equations, i.e. when T = R and T = N. We consider several examples to illustrate...

We investigate the oscillatory behavior of the second order nonlinear dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = 0, the forced dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = e(t) and the forced-perturbed dynamic equation ` a(x) ́∆ (t) + q(t)x(t) = e(t) + p(t)x (t). The obtained results are new and not only extend the known results appeared in the literature, but they also improve and unify the kn...

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For ...

S. Chowla conjectured that every prime p has the property that there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. Gauss’ genus theory guarantees the existence of infinitely many such fields when p = 2, and the work of Davenport and Heilbronn [D-H] suffices for the prime p = 3. In addition, the DavenportHeilbronn result demonstrates that a positive pr...

We study the structure of the Fourier coefficients of low degree multivariate polynomials over finite fields. We consider three properties: (i) the number of nonzero Fourier coefficients; (ii) the sum of the absolute value of the Fourier coefficients; and (iii) the size of the linear subspace spanned by the nonzero Fourier coefficients. For quadratic polynomials, tight relations are known betwe...

“FIBONACCI” directly implements the recurrence relation of the Fibonacci sequence. Each number in the sequence is the sum of the two previous numbers in the sequence. The running time is clearly O(n). The subproblem graph consists of n+ 1 vertices, v0, v1, ..., vn. For i = 2, 3, ..., n, vertex i has two leaving edges: to vertex vi−1 and to vertex vi−2. No edges leave vertices v0 or v1. Thus, th...

This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation r t xΔ t γ Δ p t x g t 0 on an arbitrary time scale T with sup T ∞, where g t ≥ t and ∫∞ to Δs/ r1/γ s < ∞. Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify th...