New Pointwise Biprojectivity as an Extension of Banach Algebras

M Ghorbani, D.E. Bagha, Department of Mathematics, Central Tehran Branch, Islamic Azad university, Tehran, Iran

ABSTRACT

In the present paper, we study the Pointwise Biprojectibility of Banach Algebras. We indicate that a Pointwise Biprojective Banach Algebra is a super-amenable if and only if it has an identity. In addition, we investigate other Pointwise Biprojective properties including, the relationship between Pointwise Biprojectibility and amenability for Banach Algebras.We also maintain what kind of relationship is between Pointwise Biprojectibility L1(G) and G. Finally,we define the concept of Pointwise projecttibility and investigate the relationship between Pointwise Projevtibility and Pointwise Biprojectibility.we consider any conditions for proof that biprojective and projective are two definition similar to pointwise projective and pointwise biprojective in extension of banach algebras.the srveral instructures, we proof that almost every where, banach algebras satisfyes another situations. In Future we will find that we can develop all theorems and lemmas of this paper for Pointwise amenability. We Recommend authors show that there is a Banach algebra that it dos not apply to the conditions mentioned in this article.

Keywords

Banach Algebra,Pointwise Biprojective, Pointwise Projective, Pointwise Amenable.

On Ideals via Generalized Reverse Derivation on Factor Rings

Zakia Z. Al-Amery, Department of Mathematics, Aden University, Aden, Yemen

ABSTRACT

In current article, for a prime ideal P of any ring R, we study the commutativity of the factor ring R/P , whenever R equipped with generalized reverse derivations F and G associated with reverse derivations d and g, respectively. That satisfies certain differential identities involving in P that connected to an ideal of R. Additionally, we show that, for some cases, the range of the generalized reverse derivation F or G repose in the prime ideal P . Moreover, we explore several consequences and special cases. Throughout, we provide examples to demonstrate that various restrictions in the assumptions of our outcomes are essential.

Keywords

Prime Ideal; Integral Domain; Generalized Reverse Derivation; Factor ring.

Adaptive Search: A Hybrid Approach Using Binary, Interpolation, and Exponential Search Algorithms

Femi Ojo, Kennesaw State University

ABSTRACT

Efficient searching is a core component of numerous computing applications. However, no single search algorithm universally performs best across all data distributions and structures. This paper presents Adaptive Search, a hybrid and dynamic framework that selects among binary search, interpolation search, and exponential search based on real-time analysis of data characteristics. A decision engine evaluates the distribution, size, and bounds of the data to determine the most appropriate algorithm. Extensive experiments on synthetic and real-world datasets demonstrate that Adaptive Search outperforms individual strategies in terms of accuracy, search time, and scalability.

Keywords

Search Algorithms, Binary Search, Interpolation Search, Exponential Search, Adaptive Systems, Hybrid Algorithms.