EIGEN MATHEMATICS JOURNAL

Locating Chromatic Number for Rose Graphs and Barbell Operation

2025-07-21T05:13:48+01:00

The locating chromatic number of a graph is the minimum color required for a locating coloring. This concept is a combination of partition dimension and vertex coloring of a graph. The purpose of this paper is to determine the locating chromatic number of the Rose graph and the barbell Rose graphs. The method used to obtain the locating chromatic number of a graph is by determining its upper and lower bounds. In this paper, the locating chromatic number of the Rose graphs and its barbell operation were obtained. The locating chromatic number of Rose graph 𝑀 (𝐶𝑛) is 4 for 𝑛 ∈ {3, 4} and 5 for 𝑛 ≥ 5. Furthermore, for barbell Rose graphs, 4 for 𝑛 = 3 and 5 for 𝑛 ≥ 4

Survival Analysis Using Kaplan-Meier and Cox Regression in Hypertension Patients at Kefamenanu Regional Hospital

2025-04-14T11:15:00+01:00

Hypertension is a chronic disease with a steadily increasing global prevalence and is one of the leading causes of serious complications. Indonesia is among the countries with a high prevalence of hypertension, necessitating an understanding of the factors influencing patient treatment duration to enhance the effectiveness of healthcare services. This study aims to analyze differences in the survival rates of hypertensive patients at Kefamenanu Hospital based on gender. The Kaplan-Meier method was used to estimate patient survival rates, while Cox Proportional Hazards regression was used to evaluate the influence of gender on survival time. The Kaplan-Meier analysis results showed that female patients had a higher probability of survival than male patients during hospitalization. However, the Cox Proportional Hazards regression analysis indicated that this difference was not statistically significant. These findings suggest that while there are differences in survival patterns, gender is not the primary determinant of the duration of care for hypertensive patients. The results of this study are expected to provide input for hospitals in designing more effective care strategies that focus on other factors that may influence patient survival time.

Prediction of Rainfall in Lampung Province Using Tweedie Mixture Distribution with PCA Reduction

2025-07-25T07:04:34+01:00

Accurate rainfall prediction is crucial for supporting the agricultural sector in Lampung Province. This research employs the Exponential Dispersion Model (EDM), a special case of the Generalized Linear Model (GLM), incorporating a Tweedie mixture distribution with Principal Component Analysis (PCA) to reduce correlated variables. Rainfall data were obtained from the Meteorology, Climatology, and Geophysics Agency (BMKG) through twelve rain observation posts (2013-2022), and supplemented with precipitation data from the General Circulation Model (GCM) obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF). The Tweedie mixture distribution was selected for its ability to handle non-normally distributed rainfall data containing zero values. The results show that the Root Mean Square Error of Prediction (RMSEP) for the Tweedie mixture-PCA model at the Gisting Atas station is 163.90, while the Normal-PCA model achieved 169.11. Therefore, the Tweedie mixture-PCA approach is more effective and recommended for improving rainfall prediction in Lampung Province, offering potential benefits for agricultural planning and resource management.

Bayesian Hyperparameter Optimization Analysis for Sustainable Innovation Performance Prediction Model

2025-03-24T04:09:26+00:00

This study examines how well the Gaussian Process Regression (GPR) model performs in interpreting the optimization outcomes achieved through Bayesian Optimization (BO) with Keras Tuner, specifically in the context of Sustainable Innovation Performance (SIP). The GPR surrogate model serves to examine the outcomes of optimization and offers valuable insights into the strategies of exploration and exploitation while seeking the most effective hyperparameters. The evaluation of the effectiveness of GPR involved calculating the Mean Absolute Error (MAE), which was bootstrapped 1000 times to establish a 95\%. Confidence Interval (CI). This study's findings demonstrate the dependability of GPR in forecasting the validation loss generated by BO, characterized by minimal prediction errors and consistent confidence intervals. The results indicate that GPR serves as a dependable statistical method for assessing uncertainty in Bayesian-based optimization. Additionally, they offer valuable perspectives on how exploration and exploitation strategies can be utilized to attain optimal hyperparameter configurations. By strategically balancing exploitation and exploration, Bayesian Optimization can enhance the process of identifying optimal hyperparameter configurations within continuous innovation prediction models.

Application of Optimal Control to the SEITRS Mathematical Model of Tuberculosis Transmission with Control Variables Socialization and Therapy

2025-08-06T02:22:52+01:00

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis, which remains a serious public health concern. The objective of this study is to develop, analyze, and propose an optimal control strategy for the transmission dynamics of TB using an SEITRS mathematical model. The model consists of five population compartments: Susceptible (S), Exposed (E), Infected (I), Treatment (T), and Recovered (R). The methodology involves constructing the SEITRS model, determining the equilibrium points, and analyzing their stability under different conditions of the basic reproduction number. The model has two equilibrium points, namely the non-endemic and endemic equilibrium. If the basic reproduction number is less than one and certain conditions are satisfied, the non-endemic equilibrium is locally asymptotically stable. Conversely, if the basic reproduction number is greater than one and specific conditions are met, the endemic equilibrium becomes locally asymptotically stable. Furthermore, this study provides optimal control strategies in the SEITRS model. We use two control variables in this model, namely socialization and therapy, to reduce the number of infected individuals. The sufficient conditions for the existence of optimal controls are derived using Pontryagin’s Maximum Principle. Numerical simulations are then conducted to examine the impact of applying these controls on the system. The simulation results indicate that the simultaneous implementation of socialization and therapy controls is effective in reducing the number of TB-infected individuals.

A Novel Approach to Topological Indices of the Power Graph Associated with the Dihedral Group of a Certain Order

2025-11-14T05:30:52+00:00

Power graph of a group G, represented by \Gamma_G, is a graph where the vertex set consists of the elements of G. Two distinct vertices a, b \in G are connected by an edge if and only if there exists a positive integer m such that a^m = b or b^m = a. This study explores the utilization of a new approach to compute the topological indices of power graph associated with dihedral group with n=p^k, p is primes and k \in \mathbb{Z}. Results obtained indicate that the topological indices calculated using new approach yield the same values as those obtained with the conventional approach.

Simulation of Spring Oscillations in Second-Order Differential Equations Using the Finite Difference Method

2025-10-06T01:50:27+01:00

This study aims to simulate the motion of a damped spring oscillation, modeled by a second-order ordinary differential equation, using the Finite Difference Method (FDM). The main focus is on implementing the central finite difference scheme to discretize the equation, deriving an explicit iterative formula, and analyzing the oscillation dynamics and the accuracy of the numerical solution. The simulation was conducted with specific parameters (mass m = 1.0 kg, spring constant k = 10.0 N/m, damping coefficient c = 0.5 Ns/m) and various time steps (\Delta t = 0.5 s, 0.1 s, 0.01 s). The simulation results qualitatively show damped oscillatory behavior consistent with physical theory, where the amplitude decreases over time. The accuracy of the numerical solution, measured by the Symmetric Mean Absolute Percentage Error (SMAPE) against the analytical solution, was significantly influenced by \Delta t; the smallest time step (0.01 s) yielded the highest accuracy with a SMAPE of 0.4495%. The Finite Difference Method proved effective in analyzing the spring oscillation system, demonstrating that the proper selection of \Delta t is crucial for balancing accuracy and computational efficiency.