is the DFT of the zero-padded wavelet filter. Similarly let {G(k)} denote the DFT of the zero-padded scaling filter. Further, suppose we attach to each pair (j, n) in the wavelet packet tree a sequence of ones and zeros according to the following rule. Let {c1,0} = {0} and {c1,1} = {1} and let {cj,n} = {cj,n,0, . . . , cj,n,j−1} where cj,n,k ∈ {0, 1} for k = 0, . . . , j − 1. Define, for n = 0,...

Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr -convergence of Laguerre series ∑ cj a j . Then, we prove aHardy-Littlewood type inequality ∫∞ 0 |f(t)|r dt≤ C ∑∞ j=0 |cj| j̄1−r/2 for certain r ≤ 1, where f is the limit function of ∑ cj a j . Moreover, we show that if f(x) ∼ ∑cj a j is ...

Editorial CJ 4(2)

Editorial de CLIL Journal of Innovation and Research in Plurilingual Pluricultural Education, 4(1)

What is a language? Something which assigns meanings to certain strings of types of sounds or of marks. It could therefore be a function, a set of ordered pairs of strings and meanings. The entities in the domain of the function are certain finite sequences of types of vocal sounds, or of types of inscribable marks; if CJ is in the domain of a language£, let us call CJ a sentence of£. The entit...

Cj(S): The total completion time of schedule S. Finally, for convenience, for each order constructed from aj (bj , cj), we simply call it order aj (respectively, bj , cj). Also, we assume that the subscripts of the orders in a schedule are labelled in such a way that, aj (bj , or cj) (j = 1, 2, . . . , n): means that there are (j − 1) orders of type a scheduled before aj (respectively, bj , or ...

ing momentum p from ζ(q, ω) in equation (14) results to a relation 〈〈c†p+q,↑cp,↓;S (0, 0)〉〉 = cJ 2 〈c†p,↓cp,↓〉 − 〈c † p+q,↑cp+q,↑〉 ω − εp + εp+q − cJ〈Sz〉 ×G(q, ω). (15) Combining equations (10) and (14) results to a closed form of Green’s function equation G(q, ω), (ω − cJ〈σ〉 + cJ 2 〈S〉 ∑ p 〈c†p,↓cp,↓〉 − 〈c † p+q,↑cp+q,↑〉 ω − εp + εp+q − cJ〈Sz〉 )