Journal of the Indonesian Mathematical Society

Pointwise Multipliers of Orlicz-Morrey Spaces

2025-03-05T13:09:32+00:00

We investigate the space of pointwise multipliers of Orlicz-Morrey spaces. Using the H\"older inequality in Orlicz-Morrey spaces, we prove that the space of pointwise multipliers of Orlicz-Morrey spaces contains an Orlicz-Morrey space. We also prove a partial reverse inclusion of this result. In addition, we des\-cribe the space of pointwise multipliers of Orlicz-Morrey spaces by adding some growth conditions on Young functions. Our results can be viewed as an extension of the results on pointwise multipliers of Morrey spaces.

The Structure of Cayley Graph of Dihedral Groups of Valency 4

2024-01-01T07:34:19+00:00

Let G be a group and S be a subset of G in which e /∈ S and S−1 ⊆ S. The Cayley graph of group G with respect to subset S, denoted by Cay(G, S), is an undirected simple graph whose vertices are all elements of G, and two vertices x and y are adjacent if and only if xy−1 ∈ S. If |S| = k, then Cay(G, S) is called a Cayley graph of valency k. The aim of this paper is to determine the structure of Cayley graph of dihedral groups D2n of order 2n when n = p or 2p2, where p is an odd prime number. The graph structures are based on circulant graphs with suitable jumps.

Necessary Condition for Boundedness of Stein-Weiss Operator on Orlicz-Morrey Spaces

2025-03-05T02:29:41+00:00

This study aims to find necessary conditions for the boundedness of Stein-Weiss Operator on Orlicz-Morrey spaces. It is well known that the Orlicz-Morrey space is the generalization of the Lebesque space. In particular, by considering power function as Young’s function and zero as Morrey Space index, the Orlicz-Morrey space is a Lebesgue space itself. Orlicz-Morrey space and several operators in the space have been studied intensively by several researchers. In this study, we find a necessary condition for the boundedness of the Stein-Weiss operator on Orlicz-Morrey spaces. The technique to achieve our purpose is by substituting dilation of a radial function on a ball into inequality of boundedness assumption, and some basic properties of Young’s function. {Due to the properties of the dilation, the result will be presented as an inequality involving suitable parameters}. As a result we get the necessary condition. As a discussion, we try to find several examples that satisfy the inequalities. The most important, the result shows that there is a significant factor to see the boundedness of the Stein-Weiss operator on Orlicz-Morrey spaces. Since { Stein-Weiss operator is a generalization of fractional integral operator, the result shows that it generalize the boundedness of fractional integral on Orlicz space.

The Locating Chromatic Number For Corona Operation Of Path And Cycle With Python Programming

2025-01-19T12:12:26+00:00

Locating chromatic number of a graph is a concept that is still interesting today because there is no theorem or algorithm that can determine the locating chromatic number of any graph. In this research, an algorithm was created to determine the locating chromatic number for corona operation of path and cycle with Python programming.

On Generalized Bourbaki Theorem in the Category (S,Q)-Cat

2025-03-02T15:40:28+00:00

Bourbaki developed the concept of a proper map in topological spaces and proved that a continuous map between topological spaces is proper if and only if it is perfect, known as Bourbaki theorem. Clementino and Tholen extended this concept to lax algebras, formulating a generalized Bourbaki theorem applicable to a special type of category called a $(\S,\Q)$-category. Their theorem states that, under certain conditions, a $(\S,\Q)$-functor is proper if and only if both pullbacks of the functor are closed and a specific transformation is closed. They also provide an equivalent characterization using compactness of fibers. Clementino and Tholen then posed a question: If we slightly modify the conditions in their generalized theorem, do the equivalences still hold? This paper aims to answer this question, investigating the impact of these modifications on the relationship between properness and closure properties.

Jacobsthal Trigonometric Functions

2025-06-14T06:01:09+00:00

Jacobsthal numbers satisfy a second order homogeneous recurrence relation $J_{n}=J_{n-1}+2J_{n-2}$ where $J_{n}$ denotes the $n^{th}$ Jacobsthal number. In this paper, the Jacobsthal sine, cosine, tangent and cotangent are defined, and some identities of Jacobsthal trigonometric functions are provided.

Optimal Control of HIV/AIDS Epidemics: Integrating Media Awareness and Antiviral Treatment

2025-08-27T02:38:58+00:00

This paper investigates an optimal control strategy to mitigate the spread of HIV/AIDS by integrating media awareness campaigns and antiviral treatment efforts. A modified SI-type model is developed, dividing the population into five subgroups: unaware susceptible individuals, aware susceptible individuals, unaware infected individuals, aware infected individuals, and individuals undergoing treatment. Additionally, a separate compartment representing the level of media awareness is included to model the dynamics of awareness campaigns over time. Three control variables are introduced: the success of media awareness programs aimed at reducing contact between susceptible and infected individuals and encouraging infected individuals to seek and receive treatment; the effort to provide antiretroviral treatment; and the effort to strengthen the intensity of media awareness programs. The objective is to minimize the number of unaware susceptible and infected individuals while maximizing the number of individuals receiving treatment, and to reduce implementation costs. The model employs optimal control theory to identify the best combination of strategies by minimizing a cost functional. Numerical simulations explore seven control strategy combinations, ranging from single to multiple controls. The results indicate that combining all control variables yields the most significant reduction in unaware and infected individuals, a substantial increase in the number of individuals receiving treatment, and effective minimization of costs.

On Spectrum and Energy of Non-Commuting Graph for Group U_{6n}

2025-01-27T12:01:43+00:00

Let $G$ be a group and $Z(G)$ be the center of $G$. In this paper, we discuss a specific type of graph known as the non-commuting graph, denoted by $\Gamma_G$, whose vertex set contains all group elements excluding central elements, $G\backslash Z(G)$. This graph has to satisfy a condition in which $v_p,v_q \in G\backslash Z(G)$ where $v_p \neq v_q$, are adjacent whenever $v_p v_q\neq v_q v_p$. This paper presents the spectrum and energy of the non-commuting graph for $U_{6n}$, $\Gamma_{U_{6n}}$ associated with the adjacency, degree sum, and degree sum adjacency matrices and their energy relationship.

Some Properties of Cartesian Product of Non-Coprime Graph Associated with Finite Group

2025-06-27T21:36:34+00:00

This paper investigates several properties of the Cartesian product of two non-coprime graphs associated with finite groups. Specifically, we focus on key numerical invariants, namely the domination number, independence number, and diameter. The non-coprime graph associated with finite group $G$ is constructed with the vertex set $G\setminus \{e\}$ and connects two distinct vertices if and only if their orders are not coprime. Using this construction, we investigate the Cartesian products of non-coprime graphs associated with various types of groups, including nilpotent groups, dihedral groups, and $p$-groups. We derive several new results, including exact expressions for the domination number, independence number, and diameter of these Cartesian products.

On \Lambda e^-Open and \Lambda e^-Closed Sets in Topological Spaces and Their Use in Financial Risk Assessment

2025-06-28T03:04:05+00:00

In this paper, the notions of \Lambda e^*-open and \Lambda e^*-closed sets are introduced and studied within the framework of general topology. Several fundamental results and characterizations are established, including their relationships with e^*-open sets, regular closed sets, and various separation axioms. The interplay between \Lambda e^*-sets and classical topological structures is examined through a sequence of lemmas and theorems. Furthermore, the developed concepts are applied to construct a mathematical model for low-risk stock selection. Specifically, the properties of \Lambda e^*-sets are utilized to filter stocks that maintain topological stability under uncertainty, providing a novel approach to identifying financially stable investment options within a given market.