East West Math

STRUCTURES OF POWER DIGRAPHS ASSOCIATED WITH xpk ≡ y (mod n) WHERE p IS AN ODD PRIME

Ratinan Boonklurb — 2024-02-27

Let k and n be positive integers and p be an odd prime. A power digraph G(pk; n) for which the vertex set is f0; 1; 2; : : : ; n - 1g and (u; v) is a directed edge from a vertex u to a vertex v if upk ≡ v (mod n). We study the structures of this power digraphs. Moreover, we provide some interesting results when p is 3; 5 or 7.

EXISTENCE OF THREE WEAK SOLUTIONS FOR THE KIRCHHOFF-TYPE PROBLEM WITH MIXED BOUNDARY CONDITION IN A VARIABLE SOBOLEV SPACE

Junichi Aramaki — 2024-02-27

In this paper, we consider the Kirchhoff-type problem for a class of nonlinear operators containing p(·)-Laplacian and mean curvature operator with mixed boundary conditions. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions according to hypotheses on given functions and values of parameters.

ON THE COFINITENESS OF IN DIMENSION < 2 LOCAL COHOMOLOGY MODULES FOR A PAIR OF IDEALS

Ngo Thi Ngoan — 2024-02-27

In this note, we prove the cofiniteness of local cohomology modules Hi I;J(N) with respect to a pair of ideals (I; J) for all i < t and the finiteness of (0 :Ht I;J (N) I) and Ext1 R(R=I; HI;J t (N)) provided that

Exti R(R=I; N) is finitely generated for all i ≤ t + 1 and HI;J i (N) is in dimension < 2 for all i < t, where t ≥ 1 is an integer (here, N is not necessarily finitely generated over R). This extends the results of Bahmanpour-Naghipour [5, Thm 2.6], Bahmanpour-Naghipour-Sedghi [4, Thm 2.8] and H-N [16, Thm 1.1].

PICARD OPERATORS IN STRONG b-TVS CONE METRIC SPACES

Bui The Hung — 2024-02-27

Let X be a topological space. A mapping T : X ! X is called a Picard operator if T has a unique fixed point ¯ x 2 X and for any x 2 X, the sequence of iterates fT nxg converge to ¯ x. In this paper, we give new results concerning the existence of Picard operators in strong b-TVS cone metric space. Our result is an extension of Sh. Rezapuor and R. Hamlbarani [19]

MATHEMATICAL LITERACY FOR DIGITAL ERA: REVIEW OF MATHEMATICAL THINKING AND COMPUTATIONAL THINKING FOR CURRICULUM DEVELOPMENT

Maitree Inprasitha — 2024-02-27

In the Era of AI and Data Science under the fourth industrial revolution, Mathematical Capitalism (Ministry of Economy, Trade and Industry, Japan., 2019 [32]) becomes a key issue in Education up to higher education in this changing society. Mathematical Thinking provides the grand for Informatics as a school subject that develops computational thinking. This article confirmed mathematics as the key literacy subject in school and re-viewed it as universal literacy in the era through the confirmation of mathematical thinking and value are a necessary component of general competency in the era. This claim is illustrated by the historical meaning of mathematics, the current aims of mathematics education, and re-viewed the meaning of mathematics education for the digital society