On Wavelet Decomposition of the Singular Splines

In this paper, we study inextensible flows of spacelike curves lying fully on a spacelike surface Ω according to equiform frame in 4-dimensional Minkowski space ℝ1 4 . We give necessary and sufficient conditions for this inextensible flows which are expressed as a partial differential equation involving the equiform curvature functions in 4-dimensional Minkowski space ℝ1 4 . Finally we give an application of inextensible flows of spacelike curves in ℝ1 4 .

Inextensible Flows of Spacelike Curves According to Equiform Frame in 4-dimensional Minkowski Space R41

Mahmoud

Noreldeen

2021

Pairwise Strongly Lindelöf, Pairwise Nearly, Almost and Weakly Lindelöf Bitopological Spaces

Almuhur

Al-Labadi

2021

The main purposes of this article is to introduce new generalizations of the notion of pairwise Lindelöf spaces in bitopological spaces where new notions: pairwise strongly Lindelöf, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelöf bitopological spaces depend on the new notion pairwise preopen countable covers. These covers where we focused on their importance in topology consist of countable subfamilies whose closures cover the bitopological spaces and we clarified how pairwise preopen countable covers effect on pairwise strongly Lindelöf spaces. The new concepts of pairwise strongly Lindelöf, pairwise nearly, pairwise almost and pairwise weakly strongly Lindelöf bitopological spaces are introduced and many definitions, propositions, characterizations and remarks concerning those notions are initiated, discussed and explored. Furthermore, the relationships between those bitopological spaces are examined and investigated. We illustrated the implications hold by these new bitopological spaces. We put some queries and claims, then we struggle to provide their proofs.

On Factorization of Functional Operators with Reflection on the Real Axis

Karelin

Tarasenko

2021

Problems of factorization of matrix functions are closely connected with the solution of matrix Riemann boundary value problems and with the solution of vector singular integral equations. In this article, we study functional operators with orientation-reversing shift reflection on the real axes. We introduce the concept of multiplicative representation of functional operators with shift and its partial indices. Based on the classical notion of matrix factorization, the correctness of the definitions is shown. A theorem on the relationship between factorization of functional operators with reflection and factorization of the corresponding matrix functions is proven.