East West Math

SEMIGROUP OF 2 × 2 TROPICAL CIRCULANT MATRICES AND THE BIORDER STRUCTURE OF THEIR IDEMPOTENTS

Ardra T. Joy, Prakash G. N. Shenoi, A. R. Rajan — Tue, 12 May 2026 11:36:46 +0800

Tropical circulant matrix is a circulant matrix which operates within the tropical algebra framework where addition is replaced by the minimum and multiplication by the ordinary addition. These matrices have found applications in areas like cryptography and graph theory. In this paper we are dealing with C2(R), the multiplicative semigroup of 2 × 2 circulant matrices over tropical semiring R = (R [ f1g; min; +). The semigroup M2(R) of all 2×2 tropical matrices are known to be a regular semigroup. We show that the subsemigroup C2(R) of circulant matrices is an inverse semigroup, that is, a regular semigroup in which every element has a unique inverse. It is known that the set of idempotents of an inverse semigroup is a semi-lattice and this semi-lattice of idempotents provides a way to understand and analyze the structure and behavior of inverse semigroups. So the semi-lattice E(C2) of idempotents of C2(R) plays a crucial role in the structure of C2(R). Also we determine the biorder structure of the set of idempotents and describe the sandwich sets associated with the idempotents. A description of the associated inductive groupoid is also given.

CATEGORY OF PRESHEAVES OF A LIE GROUPOID AND REPRESENTATION OF LIE GROUPOIDS

P. G. Romeo — Tue, 12 May 2026 11:41:16 +0800

A representation of a Lie groupoid G := G ⇒ M is a Lie groupoid morphism of G to a Lie groupoid of manifolds. In this article, we provide a representation of a Lie groupoid G via the functor category of presheaves of G and their equivalence to ManG, the Lie groupoid of right G-manifolds and right G-manifold morphisms.

RELATIONS BETWEEN THE INDEPENDENCE POLYNOMIAL OF STAR GRAPHS AND THEIR ASSOCIATED JULIA SETS

K U Sreeja — Tue, 12 May 2026 11:49:11 +0800

Independence polynomials of star graphs are used to investigate their dynamic behavior. The analysis covers structural aspects, examines polynomial stability, and studies the symmetry and rotational attributes of the corresponding Julia sets. The results offer insight into the interaction between graph theory and complex dynamics.

AN ALGORITHM FOR DETERMINING LIE ALGEBRA TYPES

Tu T. C. Nguyen, Tuan A. Nguyen, Vu A. Le — Tue, 12 May 2026 00:00:00 +0800

This paper investigates the Jordan{Kronecker invariant of finite dimensional complex Lie algebras. We present an explicit algorithm for determining the type of a given Lie algebra from its Jordan{Kronecker invariant. The algorithm is implemented in a specific Matlab program.

MODELING CHEATING BEHAVIOR IN ONLINE EXAMS: A THEORY OF PLANNED BEHAVIOR (TPB) BASED APPROACH

Duong Quang Hoa, Ha Van Hieu, Do Ba Khang, Do Ba Khang — Tue, 12 May 2026 11:58:06 +0800

Cheating in higher education has been widely studied, yet findings on its prevalence across traditional and online learning environments remain inconsistent. The COVID-19 pandemic triggered a sudden global shift to online education and examinations, amplifying concerns over academic integrity. Empirical evidence from this period suggests a surge in cheating behaviors; however, most studies lacked a robust theoretical framework to explain this trend. This paper develops and validates a theoretical model of online cheating, grounded in Ajzen’s Theory of Planned Behavior (TPB) and enhanced by Bandura’s concept of moral disengagement. To capture the unique dynamics of online exams, we refine the traditional TPB construct of Perceived Behavioral Control into two distinct dimensions: Regulations (REG), encompassing institutional policies and monitoring technologies, and Enabling Technology (TEC), referring to digital tools and platforms that facilitate misconduct. Using Structural Equation Modeling (SEM) with survey data from students at three Vietnamese universities in 2022, our findings confirm the model’s explanatory power in identifying factors that contributed to the surge of online cheating during the pandemic-driven transition.

POSITIVE WEAK SOLUTIONS OF THE STEKLOV PROBLEM FOR A CLASS OF QUASI LINEAR ELLIPTIC OPERATORS CONTAINING THE p(·)- LAPLACIAN AND THE MEAN CURVATURE OPERATOR

Junichi Aramaki — Tue, 12 May 2026 12:05:55 +0800

In this paper, we consider the existence of positive weak solutions for a class of quasilinear elliptic operators containing p(·)-Laplacian and mean curvature operator with the Steklov boundary condition. The results for p(·)-Laplacian are known, however, we attempt in this paper to extend the results for a class of quasilinear elliptic operators containing not only p(·)-Laplacian but also the mean curvature operator.