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INDONESIA
Journal of the Indonesian Mathematical Society
Published by Indonesian Mathematical Society
ISSN : 20868952     EISSN : 24600245     DOI : -
Core Subject : Education,
Mathematics
Journal of the Indonesian Mathematical Society disseminates new research results in all areas of mathematics and their applications. Besides research articles, the journal also receives survey papers that stimulate research in mathematics and their applications.
Arjuna Subject : -
Articles 649 Documents
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Structural Properties and Reverse Topological Indices of Order GCD Graphs of Integers Modulo Ring Romdhini, Mamika Ujianita; Abdurahim, Abdurahim; Maharani, Andika Ellena Saufika Hakim
Journal of the Indonesian Mathematical Society Vol. 32 No. 2 (2026): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i2.2009

Abstract

The order GCD graph of a ring, having the ring elements as the vertex set, and two distinct vertices are adjacent if and only if the greatest common divisor (gcd) of the order of both vertices is equal to the order of the product of these two vertices in the ring. This paper aims to analyze the reverse Sombor, Randić, and Harmonic indices of the order GCD graph where the set of vertices is integers modulo ring elements. The results provide new insights into the mathematical properties of reverse topological indices and their potential applications.
Construction Of An n-Norm On \ell^p (R) Idris, Mochammad
Journal of the Indonesian Mathematical Society Vol. 32 No. 2 (2026): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i2.2053

Abstract

In this article, we discuss an $n$-norm, with $n \ge 2$, which is defined through bounded linear functionals on $p$-summable sequence spaces. We also introduce a new norm induced by this \( n \)-norm, which will be examined for its equivalence to the usual norm. Next, we demonstrate the relationships between various mappings, including the \( n \)-norm, \( (\!n\!\!-\!\!1\!) \)-norm, $\cdots,$ \( 2 \)-norm, and the usual norm. Finally, our results show that the \( p \)-summable sequence spaces, equipped with these mappings are complete spaces.
Coupon Coloring of Snark Graphs Remadevi, Mithra; Pandurangan, Ragukumar
Journal of the Indonesian Mathematical Society Vol. 32 No. 2 (2026): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

A k-coupon coloring of a graph $G$ is a k-coloring of G by colors [k] = {1, 2, . . ., k} such that the neighborhood of every vertex of G contains vertices of all colors from [k]. The maximum integer k for which a k-coupon coloring exists is called the coupon coloring number of G, and it is denoted by $\chi_{c}(G)$. Every d-regular graph G has $\chi_{c}(G) \geq (1 - o(1))d/ \log d$ as $d \rightarrow \infty$, and the proportion of d-regular graphs G for which $\chi_{c}(G) \leq (1 + o(1))d/ \log d$ tends to 1 as $|V(G)| \rightarrow \infty$. Coupon coloring is known to be NP-complete for k-regular graphs, even when k \geq 3. Snarks form a subclass of cubic graphs that are non-Hamiltonian. This motivated us to focus on investigating coupon coloring specifically in the context of snark graphs.
Extreme Vertices of the Psi-Divisible Graph of the Group Z_{p^n} Kumar, Amit; Kumar, Vinod; Sehgal, Amit
Journal of the Indonesian Mathematical Society Vol. 32 No. 2 (2026): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i2.2145

Abstract

The $\Psi$-divisible graph of a finite group $G$, denoted by $\Psi_G$ is a special type of simple undirected graph, in which the set of vertices contains non-trivial subgroups of $G$ and two distinct vertices $u$ and $v$ are adjacent if and only if $u$ is a proper subgroup of $v$ such that $\Psi(u)|\Psi(v)$ or $v$ is a proper subgroup of $u$ such that $\Psi(v)|\Psi(u)$. The existence of extreme vertices in the $\Psi$-divisible graph of the finite cyclic group $\mathbb{Z}_{p^n}$ is described in this article.
Smoothed Particle Hydrodynamics for Heat Transfer in Plates: Analytical Validation and Geometric Effects of Internal Heat Sources Kurniawan, Riski
Journal of the Indonesian Mathematical Society Vol. 32 No. 2 (2026): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Accurate simulation of heat transfer is essential in many engineering applications. This study investigates heat transfer on thin plates by solving two-dimensional heat equations using the Smoothed Particle Hydrodynamics (SPH) method. The accuracy of the formulation is evaluated by comparing SPH results with analytical solutions for Dirichlet and Neumann boundary conditions, where small nRMSE values confirm good agreement. The method is then applied to plates with internal heat sources of different but equal-area geometries, showing that the star-shaped source yields the fastest heat transfer. These findings highlight the flexibility of SPH for modeling heat equations under complex geometries and boundary conditions.
Analysis of Primary Resonance in Damped Duffing-Helmholtz Oscillator Excited by an Amplitude-Modulated Signal Chaudhary Anunay Kumar; Das Saureesh; Narang Pankaj; Das Mrinal Kanti
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1709

Abstract

The effect of amplitude modulated signal on the primary resonance on a Duffing-Helmholtz oscillator has been investigated using ($i$) a multiple time scale perturbation method involving two different time scales i.e., regular time ($T_0$) and a slow time, ($T_1$), to analyze the system response and ($ii$) its modified version which is valid for larger values of expansion parameter viz., asymptotic ordering parameter, incorporating Lindstedt-Poincare transformation method that allows the interaction of the amplitude and frequency of the response. The modification of the amplitude- frequency plots, exhibiting bi-stable behavior, caused by different values of modulation amplitude and damping has been obtained both analytically and numerically for various parameters of the system near the primary resonance. The peak amplitude of the response is shown to get lowered in strongly nonlinear Duffing-type system. Phase plane trajectories of stable and unstable manifolds are presented in different instances.
A New Slope Averaging Technique in Heun's Method: Combining Harmonic and Root Mean Square Means Syamsudhuha Syamsudhuha; M. Imran; Ayunda Putri; Rike Marjulisa
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1813

Abstract

This paper introduces a modified version of Heun's method for solving initial value problems (IVPs) in ordinary differential equations (ODEs). The proposed method replaces the standard arithmetic mean used for the average slope in Heun's method with a novel combination of harmonic mean and root mean square (RMS) for the slopes of the tangent lines. This alteration is designed to enhance the accuracy and performance of the method. Through theoretical analysis, we establish that the modified method retains stability and consistency properties, crucial for reliable numerical solutions. Extensive numerical experiments demonstrate that the method performs well across a range of step sizes, showing notable improvements in accuracy for both small and large step sizes when compared to the standard Heun's method. These results suggest that the new approach offers a robust alternative for solving IVPs, particularly in scenarios where adaptive step sizing or high precision is required.
A More Precise Elbow Method For Optimum K-means Clustering Indra Herdiana; Mokhamad Alfin Kamal; Triyani Triyani; Mutia Nur Estri; Renny Renny
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1862

Abstract

K-means clustering is an unsupervised clustering method that requires an initial decision of number of clusters. One method to determine the number of clusters is the elbow method, a heuristic method that relies on a graphical plot of the within-cluster sum of squares against the number of clusters. The method uses the number based on the elbow point, the point closest to $90^\circ$ that indicates the most optimum number of clusters. This research improves the elbow method such that the selection of cluster numbers is unbiased towards visual interpretation. We use the analytical geometric formula to calculate an angle between lines and real analysis principle of derivative to simplify the elbow point determination. We also consider every possibility of the elbow method graph behaviour such that the algorithm is universally applicable. The result is that the elbow point can be measured precisely with a simple algorithm that does not involve complex functions or calculations. This improved method gives an alternative of more reliable cluster determination method that contributes to more optimum k-means clustering, obtained by the fewest clusters with the lowest error.
Homomorphisms of Modules over Two Skew Generalized Power Series Rings Ahmad Faisol; Fitriani Fitriani; Muslim Ansori; Budi Surodjo
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1921

Abstract

Let R and R' be rings with identity and let S be a strictly ordered monoid equipped with twisting homomorphisms into the endomorphism rings of R and R'. Using these data, we consider two skew generalized power series rings associated with R and R'. Starting from an (R,R')-module M, we construct an induced module consisting of generalized power series with coefficients in M and show that it naturally becomes a module over the two skew generalized power series rings through a suitable trilinear action. We then study homomorphisms in this framework. In particular, we prove that every (R,R')-module homomorphism between two modules induces a corresponding homomorphism between their associated generalized power series modules. Furthermore, we provide sufficient conditions describing when a generalized power series belongs to the kernel of the induced homomorphism in terms of the coefficientwise behavior of the original map. These results extend the theory of skew generalized power series modules from the classical single-ring setting to a two-ring context and provide a foundation for further developments, including generalized isomorphism results and related algebraic applications.
SG-Lightlike Submanifolds of a Locally Bronze Semi-Riemannian Manifold Equipped With (l,m)-Type Connection Rajinder Kaur; Jasleen Kaur
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1931

Abstract

This research work introduces the geometry of the SG (Screen Generic)-lightlike submanifolds of a locally bronze semi-Riemannian manifold endowed with an (l,m)-type connection. The characterization theorems on geodesicity of such submanifolds with respect to the integrability and parallelism of the distributions are established. It is shown that there exists no coisotropic, isotropic or totally proper SG-lightlike submanifold of a locally bronze semi-Riemannian manifold. Assertions for the smooth transversal vector fields in totally umbilical proper SG-lightlike submanifold are obtained. Furthermore, the structure of a minimal SG-lightlike submanifold of a locally bronze semi-Riemannian manifold is detailed with an example.

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