Journal of the Indonesian Mathematical Society

The Lieb and Nazarov Inequalities for Quaternion Linear Canonical S-Transform

Dahnial Danang — 2026-01-05

This research introduces the quaternion linear canonical S-transform. This transform is an extension of the linear canonical S-transform within quaternion algebra. We recall the properties and present the natural link between the quaternion linear canonical transform and the quaternion linear canonical S-transform. We exploit these properties and relation to establish the Lieb and Nazarov inequalities to the quaternion linear canonical S-transform.

Utilizing Trajectory Matrices and Singular Value Decomposition (SVD) for Multivariate Transformation in Time Series Analysis

Dina Prariesa — 2026-01-05

The trajectory matrix transforms univariate time series data into multivariate form using the structural properties of the Hankel Matrix (HM). Research on data matrices within Time Series Analysis (TSA) remains limited. This study examines AR models with stationary properties and applies Singular Value Decomposition (SVD) to HM in the Box-Jenkins framework. It focuses on HM properties, matrix dimension considerations in SVD, and order identification. Numerical simulations of the AR(1) and AR(2) models reveal that the PACF and SVD scree plots exhibit similar patterns. This indicates that applying SVD to HM could serve as an alternative to PACF for AR order selection. The findings highlight potential future research directions by refining, adapting, and generalizing previous studies to advance the TSA methodology.

Analysis of Earthquake Potential along the Coastal Region of South Java using Semi-Markov Models as a Tsunami Mitigation

Athaya Rahma Puteri — 2026-01-05

This study applies a semi-Markov model to assess earthquake occurrence in the South Java coastal region. The main objective is to forecast earthquakes in this area, considering three key factors: geographic location, timing, and seismic magnitude. The South Java coastal region is chosen for this study due to its proximity to the island of Java, the economic hub of Indonesia. The study divides the South Java coastal region into five distinct zones and categorizes earthquakes into three magnitude groups. The results predict that earthquakes will occur in the South Coast regions of East Java, Central Java, or West Java between December 26, 2022, and November 20, 2023. Additionally, projections suggest that earthquakes are likely to occur in East Java, West Java, or Banten between November 21, 2023, and December 31, 2030. The estimated magnitudes range from 5 to 6 Mw. The findings also indicate that no tsunamis are expected along the South Java coast until 2030. Model validation using the Mean Absolute Percentage Error (MAPE) results in a value of 4.224\%. This confirms the high accuracy of the predictions. Although no tsunamis are forecasted, the public must remain alert and prepared for the anticipated earthquakes. These findings provide important insights for disaster mitigation and emphasize the need for ongoing monitoring, early warning systems, and community preparedness to minimize potential risks

Solutions of a Generalization of Linear Volterra Integro-Differential Equations

Phaisatcha Inpoonjai — 2026-01-05

In this paper, we combine linear Volterra integro-differential equations of first and second kinds to be a generalization. Then, we use Laplace transform to solve an analytical solution on a convolution kernel and apply Laguerre polynomials to approximate a solution on a non-convolution kernel of this generalization.

Generalized Implicit Function Theorem and General Fundamental Theorem of Calculus

Ashish Dhara — 2026-01-14

We present the notion of Henstock-Kurzweil integral for mappings assuming values in Hausdorff topological vector spaces using the direct set of gauges and derive a version of Mean Value Theorem. We use the definition of Frechet derivative and obtain a general version of Implicit Function Theorem for mappings from X \times Y \rightarrow Z where, for existence and continuity of the function, X needs to be merely a topological space and for differentiability, X can be a Topological Vector Space (TVS) while Z is a Hausdorff topological vector space and Y is a Banach space. The implicit function theorem is proved in 3 parts as existence, continuity of the partial derivative and invertibility of the partial derivative. The proof is very similar to the classical proof.

The strong 3-rainbow index of graphs containing some cycles

Zata Yumni Awanis — 2026-02-02

A tree of minimum size in an edge-colored connected graph G is a rainbow Steiner tree if no two edges of G are colored the same. For an integer k, the strong k-rainbow index $srx_k(G)$ of G is the smallest number of colors required in an edge-coloring of G so that there exists a rainbow Steiner tree connecting every k-subset S of V(G). We focus on k=3. It is obvious that $srx_3(G)\leq\lVert G\rVert$ where $\lVert G\rVert$ denotes the size of G. It has been proven that $srx_3(T_n)=\lVert T_n\rVert$. In this paper, we study how the $srx_3(T_n)$ changes when we add at least one edge to $T_n$. We provide a sharp upper bound and exact values of $srx_3(G)$ where G is a graph containing at most two cycles. We obtain that $srx_3(G)=\lVert G\rVert$ where G is a unicyclic graph of girth 7 or at least 9. Otherwise, $srx_3(G)<\lVert G\rVert$.

Some Results on Inclusive Distance Antimagic Labeling of Graphs

Christyan Tamaro Nadeak — 2026-02-02

Let $G=(V,E)$ be a graph of order $n$. A bijection $f:V(G)\rightarrow \{1,2,\cdots,n\}$ is called inclusive distance antimagic labeling if $w(u)\ne w(v)$ for any two distinct vertices $u,v\in V(G)$, where $w(v) = \displaystyle \sum_{x\in N[v]} f(x)$. We start our discussion with the connection between distance magic labeling and inclusive distance antimagic labeling. Then, we investigate the existence of an inclusive distance antimagic labeling for circulant graphs, disjoint union graphs, and join graphs.

Nonlocal-Adjacency Metric Dimension of Graphs

Rinurwati Rinurwati — 2026-02-02

Let $ T = \{t_1, t_2, \ldots, t_k\} \subseteq V(G)$ be an ordered subset of the vertex set of a graph G, and let $u \in V(G)$ be a vertex in G. The adjacency metric representation of vertex u with respect to the set T is the k-vector $r_A(u \mid T ) = (d_A(u, t_1), d_A(u, t_2), \ldots, d_A(u, t_k))$. The set T is called a nonlocal-adjacency metric resolving set of the graph G if $r_A(u \mid T ) \ne r_A(w \mid T )$ for every pair of vertices $u, v \in G$ with u not adjacent to v. The minimum cardinality of a nonlocal-adjacency metric resolving set of G is called the nonlocal-adjacency metric dimension of G, denoted by $dim_{Anl}(G)$. In this paper, we present graphs obtained from the degree corona product of two graphs. The degree corona product of graphs G and H, denoted by $G \odot_{\deg} H$, is the graph constructed by taking a graph G and $\sum_{i=1}^{|V(G)|} \deg(v_i)$ copies $H_{ij}$ of graph H, and then connecting every vertex $v_i \in V(G)$ to all vertices in $H_{ij}$ for every $j \in \{1, 2, \ldots, \deg(v_i)\}$ and $i \in \{1, 2, \ldots, |V(G)|\}$. Furthermore, we determine and analyze the nonlocal-adjacency metric dimension of basic graphs $G_b \in \{P_n, C_n\}$, centered graphs $G_c \in \{K_n, S_n, K_1 + P_n, K_1 + C_n, K_m + \overline{K_n}\}$, and the degree corona product graphs $G_c \odot_{\deg} K_1$. In addition, we provide upper bounds, characterizations of the nonlocal-adjacency metric dimension of graphs, and examples of applications of this concept.

Extended Fuzzy Binary Soft Sets and Their Applications in Multi Parameter Decision Making Problems

P. G. Patil — 2026-02-03

Multi-criteria decision-making (MCDM) problems involve evaluating and selecting alternatives based on multiple criteria. This article aims to solve MCDM problems by extending the definition of fuzzy binary soft sets to two parameter sets, which are called extended fuzzy binary soft sets. Operations such as "AND" and "MaxMin" are defined and illustrated with examples. Additionally, an algorithm is presented to solve MCDM problems using extended fuzzy binary soft sets. Finally, an application of the proposed algorithm for decision-making is discussed.

An An SQP Regularization with Double Conjugate Gradient Implementation for Solving Nonlinear Complementarity Problems

Ali Ou-yassine — 2026-02-15

Building upon the works proposed in [1] and [2], we introduce an advanced version of regularized proximal point methods to solve nonlinear complementarity problems (NCP). Our contribution is characterized by two key innovations. Firstly, we introduce an innovative square root quadratic term as part of the regularized subproblem framework, replacing the commonly used logarithmic quadratic term. Secondly, we implement the conjugate gradient algorithm in two stages: the intermediate step and the correction step. This dual approach employs two optimal descent directions with two step lengths to achieve multiplicative progress in each iteration, significantly accelerating convergence. We establish the global convergence of our innovative algorithm, under the condition that F exhibits monotonicity. Initial numerical experiments are presented to confirm the algorithm’s practical effectiveness.

On the Locating-Chromatic Number of the Sunflower Graph

Des Welyyanti — 2026-02-15

Let c be vertex coloring of a connected graph. Define $c: V \rightarrow {1, 2, ...,k}$ such that $c(u) \neq c(v)$ for adjacent vertices u and $v$ in G. Let S_i be a set of vertices assigned by color i where $1 \leq i \leq k$, defined as color class. Let $Pi ={S_1, S_2, ..., S_k}$ be an ordered partition of V(G) that is induced by colo-ring c, then the representation of vertex v with respect to Pi is called a color code of v, denoted as $c_\Pi(v)$, defined as $c_\Pi(v)=(d(v,S_1),d(v,S_2),\ldots,d(v,S_k))$, where d(v, S_i ) =min{d(v,x) | x \in S_i } for $1 \leq i \leq k$. If all distinct vertices of G have distinct color codes, then c is called a k-locating coloring of G. The locating-chromatic number is defined as the minimum k such that graph G admits a k-locating coloring, denoted by $\chi_L(G)$. In this paper, we determine the locating-chromatic number of the sunflower graph SF_n for $n \geq 3$