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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 10 Documents
 1 
Search results for , issue "Vol 7, No 1 (2024)" : 10 Documents clear
THE L(2,1)-LABELING OF MONGOLIAN TENT, LOBSTER, TRIANGULAR SNAKE, AND KAYAK PADDLE GRAPH Ningrum, Lisa Damayanti; Abrar, Ahmad Muchlas
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.v6i2.18228

Abstract

Let G = (V,E) be a simple graph. L(2, 1)−labeling defined as a functionf : V (G) → N0 such that, x and y are two adjacent vertices in V, then if x andy are adjacent to each other, |f(y) − f(x)| ≥ 2 and if x and y have the distance 2,|f(y) − f(x)| ≥ 1. The L(2, 1)-labeling number of G, called λ2,1(G), is the smallestnumbermof G. In this paper, we will further discuss the L(2, 1)-labeling of mongoliantent, lobster, triangular snake, and kayak paddle.Keywords: L(2,1)-Labeling, mongolian tent, lobster, triangular snake, kayak paddle. 
PRIME LABELING OF SOME WEB GRAPHS WITHOUT CENTER Scada, Jovanco Albertha; Susanti, Yeni
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.v0i0.19862

Abstract

The prime labeling of a graph  \(G\) of order \(n\) is a bijection function from the set of vertices in \(G\) to the set of the first \(n\) positive integers, such that any two adjacent points in \(G\) have labels that are coprime to each other. In this paper  we discuss the primality of the graph \(W_0(2,n)\) along with its combinations with similar graphs and various types of edges subdivisions in the graph \(W_0(2,n)\). Moreover, it is also presented the necessary and sufficient conditions for the graph to be prime.
MATHEMATICAL MODELLING OF THE SPREAD OF COVID-19 WITH FIRST, SECOND AND THIRD DOSES OF VACCINATION IN SEMARANG CITY Dewi Purnamasari, Mahardika Karunia; Fitriyah, Aini; Zulaikha, Zulaikha
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.v7i1.19750

Abstract

This research models the spread of Covid-19 by developing the  model. In this model there are seven compartments, namely the susceptible subpopulation (S), the subpopulation that has received the first dose of vaccine (V1), the subpopulation that has received the second dose of vaccine (V2), the subpopulation that has received the third dose of vaccine (V3), the exposed subpopulation (E), infected subpopulation (I), and recovered subpopulation (R). From the model that has been formed, a search for disease-free and endemic equilibrium points is carried out, then looking for the basic reproduction number (R0) as a benchmark for the presence or absence of the spread of Covid-19 in a population, then numerically simulating it using the Matlab R2017a software. The results of this numerical simulation are in accordance with the dynamic analysis carried out, namely if the condition is  then Covid-19 cannot spread, whereas if the condition is  then Covid-19 can spread in a certain area. In addition, the disease cannot spread quickly if the proportion of those who are vaccinated is increased, so that the use of vaccines can be used as an effort to prevent the spread of Covid-19.
ALGEBRAIC STRUCTURES IN HEREDITY HUMAN BLOOD GROUP SYSTEM Wasil, Moh.; Hartiansyah, Fiqih Rahman; Alifia, Istianah
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.v7i1.20552

Abstract

Marriage or in this case the researcher calls it "cross-operation" between two individuals (male and female) who have the same or different blood type has the probability to produce children (offspring) with the same blood type as one of the parents or even have a completely different blood type with both of them, whether it is the ABO blood type system or MN if it is associated with the rhesus system or not. The cross-operation between two individuals can be viewed from a mathematical perspective as an algebraic structure with one closed binary operation (OB). The cross-operation of ABO blood group system is an algebraic structure in groupoid form. The cross-operation of MN blood group system is an algebraic structure in groupoid form. And finally, the cross-operation of ABO and MN blood group systems when associated with the rhesus blood group system is an algebraic structure in groupoid form.
CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS Ramdhania, Khairunnisa Fadhilla; Sari, Rafika; Khalida, Rakhmi; Pratama, Aldira Ryan; Lestari, Nur’aini Puji
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.v7i1.19256

Abstract

This paper discusses the theory of derivatives and integrals in the form of fractions with a particular order initiated by Lioville. Specifically, regarding the correlation between fractional derivatives and integrals, by examining definitions, determining the kernel function, and applying them to several examples, so a general formula will be obtained regarding the relationship between the two. This formula is the product of the fractional derivative of an order of a polynomial function of m-degree which is equal to the (n+1) th derivative of the related order fractional integral of a polynomial function of -degree that the truth is proved by using Mathematical Induction.
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.
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.

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