Abstract:
We prove a general theorem on |N¯,pn;δ|k summability factors, which generalizes a theorem of Bor (1994) on |N¯,pn|k summability factors, under weaker conditions by using an almost increasing sequence.

Abstract:
We extended a theorem of Mishra and Srivastava (1983–1984) on |C,1|k summability factors, using almost increasing sequences,to |N¯,pn|k summability under weaker conditions.

Abstract:
Using an almost increasing sequence, a result of Mazhar (1977) on |C,1|k summability factors has been generalized for |C,α;β|k and |N¯,pn;β|k summability factors under weaker conditions.

Abstract:
A general result concerning absolute summability of infinite series by quasi-power increasing sequence is proved. Our result gives correction and improvement to the result of Savas and Sevli [2].

Abstract:
In this article we define the concept of weighted pseudo almost automorphic sequence, and establish some basic properties of these sequences. Further, as an application, we show the existence, uniqueness and global attractivity of weighted pseudo almost automorphic sequence solutions of a neural network model.

Abstract:
In the work of Bor (2008), we have proved a result dealingwith summability factors by using a quasi--power increasing sequence. In this paper, we prove that result under less and more weaker conditions. Some new resultshave also been obtained.

Abstract:
It was proved by Rubey that the number of fillings with zeros and ones of a given moon polyomino that do not contain a northeast chain of size $k$ depends only on the set of columns of the polyomino, but not the shape of the polyomino. Rubey's proof is an adaption of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. In this paper we present a bijective proof for this result by considering fillings of almost-moon polyominoes, which are moon polyominoes after removing one of the rows. Explicitly, we construct a bijection which preserves the size of the largest northeast chains of the fillings when two adjacent rows of the polyomino are exchanged. This bijection also preserves the column sum of the fillings. We also present a bijection that preserves the size of the largest northeast chains, the row sum and the column sum if every row of the fillings has at most one 1.

Abstract:
Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence in A induces an almost split sequence in an exact subcategory C of A. In case A has almost split sequences and C is Hom-finite Krull-Schmidt, this provides a necessary and sufficient condition for C to have almost split sequences. Finally, we show two applications of these results.

Abstract:
The new concepts are introduced of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such sequences is relatively norm-compact and we obtain several applications of this fact.

Abstract:
We prove a theorem of Mazhar (1999) on |N¯,pn|k summability factors under weaker conditions by using a quasi β-power increasing sequence instead of an almost increasing sequence.