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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 135 Documents
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ROBUST PREDICTION INTERVALS FOR INDONESIAN INFLATION: A BIAS-CORRECTED BOOTSTRAP APPROACH Mahmudah, Umi; Fatimah, Siti
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.20502

Abstract

Inflation is important to be analyzed due to its impact is felt across various aspects of the economy and individuals' lives. This research aimed to develop robust and reliable predictions concerning Indonesian inflation using the bias-corrected bootstrap method for an AR model. The data utilized spanned from January 2020 to September 2023 and was obtained from Bank Indonesia's website. The analysis provided the optimal order in the AR model, which resulted in p=2 as the best order (AIC=-1.858, BIC=-1.698, and HQ=-1.798). The number of bootstrap replications used was B=100, 250, 500, and 1000. The analysis was conducted using R Studio. The analysis results indicated that the model employed for prediction analysis was highly stable, with all point forecasts indicating result consistency. The prediction results suggested that inflation in Indonesia was expected to decrease in the upcoming 5 months. The results also revealed that the bias-corrected bootstrap approach could provide forecasting results with a higher level of accuracy. This research contributed to the understanding and forecasting of Indonesian inflation, emphasizing model stability and consistent results.
MIXTURE PURIFICATION MODEL WITH CASCADING TANK CONFIGURATION Tama, Yanuar Bhakti Wira; Robby, Robby
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.22480

Abstract

Consider mixing problems which are often found in Calculus or Differential Equation courses. Under some assumptions, this problem can be used to model the purification process in a polluted mixture. In this case, the cascading configuration will be investigated for modelling the spread of pollution from one mixture to another. There are two main problems: finding time needed so the amount of pollutant in mixture inside the certain tank does not exceed certain threshold and finding the number of tanks needed so that the amount of mixture in the last tank does not exceed certain threshold. The solution for the second problem will be simplified by using Stirling approximation, which approximates factorial into exponential term. For the first problem, the time needed depends on the number of tanks, initial value of the pollutant, the rate of flow, and the volume of solution inside the tanks. For the second problem, the number of tanks only depends on the initial value of the pollutant.
THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER Malik, Deny Putra; Husni, Muhammad Naoval; Miftahurrahman, Miftahurrahman; Wardhana, I Gede Adhitya Wisnu; Semil @ Ismail, Ghazali
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.20269

Abstract

Chemical topological graph theory constitutes a subdomain within mathematical chemistry that leverages graph theory to model chemical molecules.  In this context, a chemical graph serves as a graphical representation of molecular structures. Specifically, a chemical molecule is portrayed as a graph wherein atoms are denoted as vertices, and the interatomic bonds are represented as edges within the graph. Various molecular properties are intricately linked to the topological indices of these molecular graphs. Notably, commonly employed indices encompass the Wiener Index, the Gutman Index, and the Zagreb Index.  This study is directed towards elucidating the numerical invariance and topological indices inherent to a nilpotent graph originating from a modulo integer ring with prime order. Consequently, the investigation seeks to discern how the Wiener Index, the Zagreb Index, and other characteristics of the nilpotent graph manifest within a ring of integers modulo prime order powers.
ANALYSIS OF THE EFFECT OF STUART NUMBER AND RADIATION ON VISCOUS FLUID FLOW Anggriani, Indira; Norasia, Yolanda; Tafrikan, Mohamad; Ghani, Mohammad; Widodo, Basuki
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.22481

Abstract

Computational fluid dynamics (CFD) is a numerical solution of fluid flow problems built from applied mathematical modeling. The problem of the flow of a viscous fluid which is influenced by a magnetic field gives rise to a boundary layer, from this boundary layer a dimensional building equation is formed. The governing equation is obtained from the continuity equation, momentum equation, and energy equation, then transformed into a non-dimensional equation by substituting non-dimensional variables and transformed into a similarity equation. The numerical solution to this problem uses the Keller Box method. The numerical simulation results show that the Stuart Number increases the velocity profile, while the temperature profile decreases. The effect of radiation parameters on the velocity profile did not change significantly, but the temperature profile decreased.
OPTIMIZATION ALGORITHMS FOR PROJECTILE MOTION: MAXIMIZING RANGE AND DETERMINING OPTIMAL LAUNCH ANGLE Alridha, Ahmed Hasan
Journal of Fundamental Mathematics and Applications (JFMA) Vol 6, No 2 (2023)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i2.20750

Abstract

In this paper, we undertake an in-depth exploration of the optimization of parameters governing the trajectory of a projectile. Our primary objective is the determination of the optimal launch angle and initial velocity that yield the maximum achievable range for the projectile. To accomplish this, we leverage five distinct optimization methodologies, specifically the Nelder-Mead, Powell, L-BFGS-B, TNC, and SLSQP algorithms, in pursuit of our research goals. This paper offers a comprehensive analysis of the optimization procedures, shedding light on the impact of these diverse algorithms on the resultant outcomes. For each set of optimized parameters, the manuscript conducts extensive simulations of the projectile’s trajectory, presenting visual depictions of the paths traversed by the projectile. Additionally, our study incorporates comparative charts to emphasize the performance distinctions among various algorithms with respect to both maximum range and launch angle.
OPTIMAL CONTROL OF MATHEMATICAL MODELS IN BIOENERGY SYSTEMS AS EMPOWERMENT OF SUSTAINABLE ENERGY SOURCES Nugraheni, Kartika; Soemarsono, Annisa Rahmita; Millah, Nashrul; Anggriani, Indira; Usrotus Wakhidah, Ummi Saydatul
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.22482

Abstract

Energy has a very important role in everyday life. Dependence on non-renewable energy increases its vulnerability to supply instability, making it important to seek alternative energy sources to overcome this dependence. Bioenergy is an alternative energy produced from organic materials such as biomass. Control of renewable energy is needed to increase production and empowerment. In this research, a mathematical model of biogas production growth in the form of differential equations formed with optimal control modifications is proposed. Completion of the model is carried out by forming an objective function, as well as determining the Hamilton function and Lagrange function. Numerical simulations in the model show that providing control can increase biogas production as a sustainable energy source.
SOMBOR INDEX AND ITS GENERALIZATION OF POWER GRAPH OF SOME GROUP WITH PRIME POWER ORDER Pratama, Rendi Bahtiar; Maulana, Fariz; Hijriati, Na'imah; Wardhana, I Gede Adhitya Wisnu
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.22552

Abstract

Graphs are an intriguing topic of discussion due to their numerous applications, particularly in chemistry. Topological indices derived from graph representations of molecules enable us to predict various properties of these compounds, including their physical characteristics, chemical reactivity, biological activity, toxicity, and atom-to-atom interactions. More recently, graphs have also been utilized to depict abstract mathematical objects such as groups. A notable example of graph representation in group theory is seen in power graphs. This research explores new graph topological indices based on vertex degrees, inspired by the Euclidean metric, particularly the Sombor index, and its application to the power graph of the integer modulo group and the dihedral group. The primary outcome of this study is the derivation of a general formula for the Sombor index and its generalization.
Pythagorean Fuzzy Set and Its Application to Determining Student Concentration Using Max-Min-Max Composition Nuur, Imam Hafiidz; Munandar, Arif
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.21170

Abstract

Pythagorean fuzzy set is a generalization of intuitionistic fuzzy set. As intuitionistic fuzzy set that can be used to help in solving problems regarding decision making, pythagorean fuzzy set can also be done for the same thing.  In the pythagorean fuzzy set, a max-min-max composition relation will be formed and used it to solve decision-making problems. Through this research, decision making in determining the concentration for students of the Mathematics undergraduates program at Sunan Kalijaga State Islamic University Yogyakarta is discussed based on data on student grades in compulsory courses that have been taken by students until the 4th semester. Concentration that is in line with the interests and abilities is expected to facilitate the writing of the student's final project.
ANALYSIS OF A NON LINEAR DYNAMICS MODEL FOR TRANSMISSION TUBERCULOSIS IN NIGERIA INCORPORATING TREATMENT AND VACCINATION Fenuga, Olusegun Joseph; Yusuff, Adubi Olaoluwa; Isah, Nura
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.21608

Abstract

This work models and analyzes the transmission of tuberculosis infection with the impact of vaccination and treatment on the bacteria in Nigeria from 2010 to 2022 incorporating treatment and vaccination. The susceptible-vaccinated-Exposed-Infected-Recovered (SVEIR) model is used for the transmission of the bacteria in which the with immigrants are exposed to infection infectious individuals, and it is assumed that there is permanent immunity and homogenous mixing against the bacteria. The constant immigration of the infected individuals into the population makes it impossible for the disease to die out and so there is no disease-free equilibrium. The fraction of chemoprophylaxis Bacillus Calmette-Guerin (BCG) was incorporated into the model equation for successful vaccination. Stability analysis shows that a disease free equilibrum is locally asymptotically stable for R0<1 and endemic equilibrum which is stable for R0>1 which can wipe out the whole population. Hence, treatment and vaccination are the measures that can reduce below 1 in order to control tuberculosis.
BOUNDED TREE-DEPTH, PATH-DISTANCE-WIDTH, AND LINEAR-WIDTH OF GRAPHS Fujita, Takaaki
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.24214

Abstract

The study of width parameters and related graph parameters is an activearea of research in graph theory. In this brief paper, we explore the upper and lowerbounds of graph parameters, including path-distance-width, tree-distance-width, tree-depth, and linear-width. These bounds are crucial for understanding the complexityand structure of graphs.

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