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.