In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.  

Acanthamoeba keratitis (AK) is a sight-threating infection of the cornea that mostly affects contact lens wearers. Until now, AK treatment remains very difficult due to the existence of a highly resistant cyst stage in the life cycle of Acanthamoeba which is extremely resistant to most of the available anti-amoebic compounds. Moreover, current treatment of AK is usually based in the combination...

The main aim of this paper is to complete and improve the former results for the spectrum and …ne spectrum of the generalized di¤erence operator a;b over the sequence space c which were proved by the authors in [A.M. Akhmedov, S.R. El-Shabrawy, On the …ne spectrum of the operator a;b over the sequence space c, Comput. Math. Appl. 61 (2011) 2994-3002]. The improved results cover a wider class of...

4. Note that ‖Tx− Tnxn‖ ≤ ‖Tx− Txn‖+ ‖Txn − Tnxn‖ ≤ ‖T‖‖x− xn‖+ ‖T − Tn‖‖xn‖, and the limit as n→∞ of the right hand side is 0, so limn→∞ Tnxn = Tx. 6. (a) Clearly ‖x‖1 ≥ 0 for all x ∈ X. If ∑n k=1 akek ∈ X is non-zero then am 6= 0 for some m ∈ {1, 2, . . . , n}. This implies that ‖ ∑n k=1 akek‖1 ≥ |am| > 0. Moreover, if ∑n k=1 akek ∈ X and b ∈ K then ∥∥∥∥b n ∑ k=1 akek ∥∥∥∥ 1 = n ∑ k=1 |bak| =...

Here we will consider some simple examples which demonstrate the basic calculations underlying the Bayesian approach to survey sampling. We begin by recalling the definition of conditional probability for two events A and B, i.e. P (B | A) = P (A ∩B)/P (A) or P (A ∩B) = P (A)P (B | A) In a finite sample space let A1, . . . , AK be a set of mutually exclusive events whose union is the whole spac...

Adenylate kinase (AK) is a ubiquitous intracellular enzyme that is released into the extracellular space upon cell lysis. We have shown that AK release serves as a useful reporter of bactericidal agent activity and can be exploited for antimicrobial screening purposes. The AK assay exhibits improved sensitivity over that of growth-based assays and can detect agents that are active against bacte...

where B=(bn)n≥1 is a one-columnmatrix andX the unknown, see [2, 3, 5, 6, 7, 9]. Equation (1.2) can be written in the form AX = B, where AX = (An(X))n≥1. In this paper, we will also consider A as an operator from a sequence space into another sequence space. A Banach space E of complex sequences with the norm ‖‖E is a BK space if each projection Pn : X → PnX is continuous. A BK space E is said t...

The aim of this paper is a) if Σak2 < ∞ then Σak rk(x) is in BMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.

Let θ(a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ(a1, a2, · · · , ak) is chromatically unique if ak < a1 + a2, and find examples showing that θ(a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.

A new position-space renormalization group approach is investigated for bond directed percolation in two dimensions. The threshold value for the bond occupation probabilities is found to be pc = 0.6443. Correlation length exponents on time (parallel) and space (transverse) directions are found to be ν‖ = 1.719 and ν⊥ = 1.076, respectively, which are in very good agreement with the best known se...