These observations were quantified using: (i) an entropic analysis of texts [16]; (ii) the variance of the sequence of recurrence times [17]; (iii) the recurrence time distribution [19], [42]; and (iv) the related distribution of the number of occurrences of words per document [14], [15].
Hence, we can ensure that the recurrence sequence of the parameter vector ({mathbf{p} _{K}}_{Kgeq1}) obtained as solution of (4) is bounded if (B_{K}) is also bounded.
The fact that endothelial cells undergoing apoptosis release interleukin -1 β (IL-1 β) that via a paracrine loop in turn stimulates the expression of adhesion molecules on the endothelial cells (Hebert et al, 1998a; Chandra et al, 2003b) suggests that the following sequence of events for the recurrence of tumour cells at distant sites occur.
In the Solomon randomized controlled trial (NTR1245), the Solomon technique was associated with a significant reduction in twin-anemia polycythemia sequence and recurrence of twin-twin transfusion syndrome when compared with the standard laser surgery technique.
To investigate the solution of the parameterized boundary value problem (6) let us introduce the sequence of functions defined by the recurrence relation x m + 1 ( t, z, λ ) : = z + ∫ 0 t f ( s, x m ( s, z, λ ) ) d s - t T ∫ 0 T f ( s, x m ( s, z, λ ) ) d s + t T [ C - 1 d - ( C - 1 A + I 2 ) z ], (14).
Given an arbitrary vector ξ, consider the sequence of functions defined by the recurrence relation u m ( t, ξ ) : = ξ + ∫ 0 t f ( s, u m − 1 ( s, ξ ) ) d s − t p ∫ 0 p f ( s, u m − 1 ( s, ξ ) ) d s, t ∈ [ 0, p ], (4).
Since x = 0 is an ordinary point of (1), we remark that p 0 ≠ 0. Theorem 3.2 Let { c m } be a sequence of complex numbers satisfying the recurrence relation (3) for all m ∈ N 0, where (b) is referred for the value of a m, and let ρ 2 be the radius of convergence of the power series ∑ m = 0 ∞ c m x m.
As a result, we obtain a system of recurrences that if solved successfully gives a sequence of generalized AW densities with more and more parameters.
Sequences were interrogated with respect to alignment, frequency of sequence recurrence and the presence of any Alu sequences.
end{aligned} Next, one shows several recurrences for the sequence of poly-Cauchy polynomials with a q parameter of the first kind and of the second kind.
