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Journal of Fundamental Mathematics and Applications (JFMA)
Published by Universitas Diponegoro
ISSN : 26216019     EISSN : 26216035     DOI : https://doi.org/10.14710
Core Subject : Science,
Decision Sciences, Operations Research & Management
Journal of Fundamental Mathematics and Applications (JFMA) is an Indonesian journal published by the Department of Mathematics, Diponegoro University, Semarang, Indonesia. JFMA has been published regularly in 2 scheduled times (June and November) every year. JFMA is established to highlight the latest update of mathematical researches in both theoretical and applied works. The scope in JFMA is pure mathematics and applied mathematics. All accepted papers will be published both in print and online versions. The online version can be accessed via the DOI link of each article. The print version can be ordered to the journal administrator. JFMA welcomes both theoretical and applied research work to be published in the journal. The topics include but are not limited to: (1) Mathematical analysis and geometry (2) Algebra and combinatorics (3) Discrete Mathematics (4) Mathematical physics (5) Statistics (6) Numerical method and computation (7) Operation research and optimization (8) Mathematical modeling (9) Mathematical Logic in Computer Science, Informatics, etc.
Arjuna Subject : Matematika - Matematika Terapan
Articles 151 Documents
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BOILING POINT MODELING OF EUGENOL COMPOUNDS AND ITS DERIVATIVES USING THE SOMBOR INDEX AND REDUCED SOMBOR INDEX APPROACHES Alfian Putra Ardana; Syaftirridho Putri; Dia Lestari; I Gede Adhitya Wisnu Wardhana; Ni Komang Tri Dharmayani
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i2.25725

Abstract

Eugenol and its derivatives, phenylpropanoid compounds derived from plants like Syzygium aromaticum, exhibit significant biological activities, including antimicrobial, antifungal, anti-inflammatory, antioxidant, analgesic, and anticancer properties. These attributes make them valuable in drug development and medical applications. In mathematical chemistry, chemical topology graphs are used to determine the topological indices of molecules, which to help predict physical and chemical properties. Here, atoms are represented as nodes and bonds as edges. This study explores the relationship between the Sombor index, the reduced Sombor index, and the boiling points of eugenol and its derivatives. The methodology includes literature review and computational analysis of the indices, followed by correlation analysis with the boiling points. The findings reveal that the Sombor index negatively correlates with the boiling point, explains 84.8% of the boiling point variance. This implies that an increase in the Sombor index results in a lower boiling point. Conversely, the reduced Sombor index demonstrates a positive correlation, influencing 36.1% of the boiling point variations, indicating that higher reduced Sombor indices correspond to higher boiling points. When combined, the Sombor and reduced Sombor indices explain 86.4% of the boiling point variance, highlighting their significance as predictive parameters. These results provide insights into the thermal properties of eugenol-based compounds and their potential applications in material and pharmaceutical sciences. By leveraging these indices, researchers can better predict and tailor the physical properties of eugenol derivatives for specific purposes.
PMC-Labeling of Certain Classes of Graphs R Ponraj; S Prabhu; A M S Ramasamy
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.26263

Abstract

In this paper, we investigate the PMC-labeling behavior of some new graphs such as the double fan graph, triple fan graph, $m$--enriched fan graph,  C_{n}--snake, stripe blade graph, G_{n}, Sf_{n} + K_{1}, armed helm graph, alternate armed helm graph and spectrum graph.
Regression Analysis for Multistate Models Using Time Discretization with Applications to Patients’ Health Status Rianti Siswi Utami; Adhitya Ronnie Effendie; Danardono Danardono
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.28439

Abstract

This paper addresses the estimation of multistate models in discrete time, which are widely used to describe complex event histories involving transitions between multiple health states. Accurate estimation of transition intensities and probabilities is essential for understanding disease progression and evaluating the impact of covariates. However, conventional estimators such as the Nelson–Aalen estimator often produce rough estimates, especially in sparse data settings. To improve estimation, we apply kernel smoothing to Nelson–Aalen estimators of transition intensities. Transition probabilities are then derived via product-integrals of the smoothed intensities. Covariate effects on transition intensities are modeled using the Cox proportional hazards model. Rather than modeling covariate effects on transition probabilities indirectly through their influence on transition intensities, we model them directly using pseudo-values of state occupation probabilities obtained through a jackknife procedure. These pseudo-values are treated as outcome variables in a Generalized Estimating Equation (GEE) framework. The proposed methodology is applied to patient visit data from a clinic in West Java, Indonesia, where it successfully captures both the progression dynamics across health states and the influence of key covariates.
STABILITY ANALYSIS OF THE MODEL SVEI_a I_sR ON COVID-19 SPREAD Tiara Adinda Permatasari; Redemtus Heru Tjahjana; Widowati Widowati
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.29819

Abstract

 The COVID-19 pandemic has presented a major challenge in understanding the dynamics of disease transmission in a region. DKI Jakarta is the province with the highest number of COVID-19 cases in Indonesia. In this article, the SVEIₐIₛR model (Susceptible, Vaccinated, Exposed, Asymptomatic, Symptomatic, and Recovered) is examined to model the spread of COVID-19 in DKI Jakarta Province. The basic reproduction number is obtained through the Next Generation Matrix (NGM) approach, whereas the local stability analysis is carried out using the Routh–Hurwitz criterion. Furthermore, there are two equilibrium points obtained, which are the disease-free equilibrium and the endemic equilibrium. The stability of the equilibrium point is analyzed based on the value of the basic reproduction number. The endemic equilibrium point is considered asymptotically stable if the basic reproduction number is less than one. To demonstrate the behavior of the COVID-19 transmission model, numerical simulations are conducted using data obtained from DKI Jakarta Province. The results of the analysis indicate that, the COVID-19 transmission model is asymptotically stable at the diseas-free equilibrium point with R0=0.001897843854. This indicates that, over time, the COVID-19 disease will eventually disappear from the population.  
HIERARCHICAL BAYESIAN SMALL AREA ESTIMATION ON OVERDISPERSED DATA: WORKERS WITH DISABILITIES IN INDONESIA Danardana Muhammad; Halim Nur Jamaluddin; Mira Octavia; Rohimma Arisanti; Nofita Istiana
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.28526

Abstract

Persons with disabilities encounterdifficulties in accessing essentialservices, including employment, healthcare, information, and political participation. In line with the target 8.5 of the SDGs, efforts have been made to promotefull, productive, and decent employment for all, including for persons with disabilities. However, the majority ofworkers with disabilities in Indonesia remain concentrated in the informal sector during the period of 2022–2023. Unfortunately, data on workers with disabilities is currently only available at the national level. This limitation arises because the sample size of workers with disabilities is insufficient to meet the minimum requirements for direct estimation at the provincial level. Therefore, a Small Area Estimation approach is necessary to assess the participationof persons with disabilities in the workforce at more granular level, such as provinces. In this study, auxiliary variables such as the sex ratio, the number of residents who are shackled, and the availability of computer skills infrastructure were incorporated to the Small Area Estimation (SAE) framework. The Hierarchical Bayesian Poisson-Gamma was employed to improve the precision of direct estimation. The research results show that the HB Poisson-gamma estimator has better precision compared to the direct estimator.
ON CONDITIONS FOR WHICH A FRE’CHET SPACE NOT CONTAINING ADMITS THE GELFAND-PHILLIPS PROPERTY Amos Otieno Wanjara
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v9i1.30583

Abstract

If X is a Gelfand-Phillips space, then every sequence  which is equivalent to  contains an infinite subsequence  such that  is complemented in X.  is the space of all sequences  such that  as . The norm is  It is known that if every limited set of X is relatively weakly compact, then every copy of  in X contains a subspace still isomorphic to  which is complemented in X. A Banach space is said to have the Gelfand-Phillips property if every limited subset is relatively norm compact. The question whether if a Fre’chet space does not contain   implies it can admit or have the Gelfand-Phillips property is still open. The purpose of this study was to establish the conditions for which  a Fre’chet Space can admit the Gelfand-Phillips property without . We investigated the conditions on which a Fre’chet space not containing   admits the Gelfand-Phillips property. The methodology involved the use of literature study related to Fre’chet spaces and Gelfand-Phillips property. The conditions which imply that a Fre’chet space  has the Gelfand-Phillips property in spite  of it not containing   were given.  It was established that if a Fre’chet space  has a compact subspace , then it admits the Gelfand-Phillips property even if it doesn’t contain  . The results in this study have a momentous contribution in the field of Mathematical Analysis.
Mathematical Modeling of Leachate in Landfills: Overview and Application Achmad Fahrurozi; Kartono Kartono; Sunarsih Sunarsih
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.27693

Abstract

The Jatibarang Final Processing Site (TPA) plays a crucial role as a domestic waste treatment unit for the Semarang City area. Accumulated domestic waste generates leachate, which typically contains toxic chemicals, pathogenic bacteria, as well as organic and inorganic compounds. Uncontrolled management of domestic waste can lead to severe environmental impacts, such as the spread of diseases and the degradation of water quality, which may hinder potential reuse. It is essential for TPA management to monitor leachate concentration distribution to facilitate effective mitigation efforts. The phenomena and challenges associated with TPAs can be examined through mathematical modeling particularly dynamic models to study the behavior of leachate dispersion. Numerical approaches, especially the finite difference method, play a significant role in solving the complexity of models that are otherwise analytically intractable. This article presents a study based on field observations and a review of relevant scientific literature to identify the various potentials and challenges related to leachate dispersion, analyzed through mathematical modeling and numerical techniques.
PARAMETERS ESTIMATION OF DISCRETE TIME MARKOV CHAIN SUSCEPTIBLE INFECTED RECOVERED (DTMC SIR) EPIDEMIC MODEL CASE STUDY : THE SPREAD OF TUBERCULOSIS IN INDONESIA Adityo Wahyu Saputro; Nanang Susyanto
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v9i1.30140

Abstract

An epidemic is the rapid spread of disease that arises in several individuals in region at a certain time. A susceptible infected recovered (SIR) epidemic model describes the pattern of spread of disease with characteristics susceptible individuals who interact with infected individuals can be infected by a particular disease, and after recovery they will have permanent immunity. A SIR epidemic model that studies changes in the number of infected individuals in discrete time is called a discrete time Markov chain susceptible infected recovered (DTMC SIR) epidemic model. This study aims to estimate the parameters of the discrete time Markov chain susceptible infected recovered (DTMC SIR) epidemic model using the maximum likelihood method and to apply to the case of tuberculosis transmission in Indonesia. The method used in this research is estimate the parameters of the discrete time Markov chain susceptible infected recovered (DTMC SIR) epidemic model by study theoretical references that is relevant then to apply to the case of tuberculosis transmission in Indonesia. The result of this study describes that tuberculosis in Indonesia has contact rate β = 0, 1614 and recovery rate γ = 0, 1377. Based on result tuberculosis will continue to exist and epidemic has not over until 2039.
Stability Analysis Of The Bullying Model With The Factor Of Changing The Nature Of The Victim To Become A Bullies Marshellino Marshellino; Abyan Daffa Akbar
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v9i1.29059

Abstract

Bullying cases in Indonesia have increased over time. One of the places where the most bullying cases occur is in the educational environment, namely a form of abusive behaviour when students show aggressive behaviour that lasts a long time and is carried out repeatedly against their peers. In 2024, 527 cases of bullying occurred in educational environments in Indonesia. In this article, a mathematical model of a bullying case is formulated in non-dimensional form, taking into account the possibility that bullying victims can become bullies. Based on the model analysis, we obtained an equilibrium point. The equilibrium point is locally asymptotically stable according to the Routh-Hurwitz criterion. Next, the numerical simulation of the model is demonstrated to support the analytical results.
SPATIAL PANEL REGRESSION AND GEOGRAPHICALLY WEIGHTED PANEL REGRESSION MODELING OF DENGUE HEMORRHAGIC FEVER CASES IN WEST JAVA PROVINCE Fatsa Vidyaningtyas Sabila; Yekti Widyaningsih
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v9i1.29949

Abstract

Dengue Hemorrhagic Fever (DHF) is an infectious disease caused by the dengue virus, transmitted through the bites of Aedes aegypti and Aedes albopictus mosquitoes. DHF case data containing spatial and temporal information is a form of spatial panel data that can be analyzed using spatial panel modeling. Spatial panel regression is a regression approach used to assess spatial autocorrelation in the data. Geographically Weighted Panel Regression (GWPR) is a local regression method capable of capturing spatial heterogeneity effects. This study aims to develop spatial panel regression and GWPR models to estimate the number of DHF cases and their associated factors at the regency/city level in West Java Province from 2021 to 2023. The results of the spatial panel lag regression model show that the number of hospitals and the percentage of households using safely managed sanitation services are statistically significant in explaining DHF cases. In contrast, the GWPR model with an adaptive bisquare kernel reveals variations in the local influence of variables. Significant variables in several regions include population density, number of hospitals, number of health centers, percentage of households with safely managed sanitation services, access to improved sanitation, poverty rate, and average number of elementary school students. Both models complement each other in the spatio-temporal analysis of DHF cases distribution.

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