iosr-Jm   Volume-6 ~ Issue-6

Abstract: The sequence spaces 𝑙∞(𝑢,𝑣,Δ), 𝑐0(𝑢,𝑣,Δ) and 𝑐(𝑢,𝑣,Δ) were recently introduced. The matrix classes (𝑐 𝑢,𝑣,Δ :𝑐) and (𝑐 𝑢,𝑣,Δ :𝑙∞) were characterized. The object of this paper is to further determine the necessary and sufficient conditions on an infinite matrix to characterize the matrix classes (𝑐 𝑢,𝑣,Δ ∶𝑏𝑠) and (𝑐 𝑢,𝑣,Δ ∶ 𝑙𝑝). It is observed that the later characterizations are additions to the existing ones.

Keywords- Difference operators, Duals, Generalized weighted mean, Matrix transformations

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Abstract: Let 𝑅 be a ring and 𝜎,𝜏 be an endomorphisms of 𝑅, in this paper we will present and study the concepts of higher (𝜎,𝜏)-centralizer, Jordan higher(𝜎,𝜏)-centralizer and Jordan triple higher (𝜎,𝜏)-centralizer and their generalization on the ring. The main results are prove that every Jordan higher (𝜎,𝜏)-centralizer of prime ring 𝑅 is higher (𝜎,𝜏)-centralizer of 𝑅 and we prove let 𝑅 be a 2-torsion free ring,𝜎 𝑎𝑛𝑑 𝜏 are commutative endomorphism then every Jordan higher (𝜎,𝜏)-centralizer is Jordan triple higher (𝜎,𝜏)-centralizer. Mathematics Subject Classification: 16A12,16N60,16W25,16Y99.

Keywords: higher (𝜎,𝜏)-centralizer, Jordan higher (𝜎,𝜏)-cenralizer, Jordan triple higher (𝜎,𝜏)-centralizr

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Abstract:New conjecture about prime numbers is proposed for solving the criterion of Goldback's puzzle about natural numbers. It is found that Goldback's puzzle is a corollary of that new conjecture.

Keywords – Goldback's Puzzle, Prime Numbers Distribution, Remarks.𝜏)-centralizr

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Abstract: In this paper we introduce and study the concept of a new class of closed sets called (𝜏𝑖, 𝜏𝑗)− regular generalized b- closed sets (briefly(𝜏𝑖, 𝜏𝑗)− rgb-closed) in bitopological spaces.Further we define and study new neighborhood namely (𝜏𝑖, 𝜏𝑗)− rgb- neighbourhood (briefly(𝜏𝑖, 𝜏𝑗)− rgb-nhd) and discuss some of their properties in bitopological spaces. Also, we give some characterizations and applications of it.)-centralizr

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