Journal of Fundamental Mathematics and Applications (JFMA)
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.
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<![CDATA[An Algorithm for Generalized Conversion to Normal Distribution for Independent and Identically Distributed Random Variables ]]>
<![CDATA[Rellon, Louie Resti Sandoval]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.20508
<![CDATA[The paper analyzes an efficient alternative to the Box-Cox and Johnson’s transformation to normality methods which operates under fairly general settings. The method hinges on two results in mathematical statistics: the fact that the cumulative distribution function F(x) of a random variable x always has a U(0,1) distribution and the Box-Mueller transformation of uniform random variables to standard normal random variables. Bounds for the Kolmogorov-Smirnov statistic between the distribution of the transformed observations and the normal distribution are provided by numerical simulation and by appealing to the Dvoretzky-Kiefer- Wolfowitz inequality.]]>
<![CDATA[COORDINATING AND OPTIMIZING TWO-WAREHOUSE INVENTORY SYSTEMS: A MATHEMATICAL PROGRAMMING APPROACH ]]>
<![CDATA[Sutrisno, Sutrisno]]>;
<![CDATA[Widowati, Widowati]]>;
<![CDATA[Azis, Moh. Ivan]]>;
<![CDATA[Aldila, Dipo]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.25758
<![CDATA[Effective supplier and carrier selection plays a pivotal role in supply chain management, ensuring maximum profitability. This study introduces an innovative decision-support system designed for supplier and carrier selection problems in static two-warehouse inventory systems. The model assumes warehouse collaboration, where warehouses consolidate efforts to fulfill overall demand. To address this, a mathematical programming approach is developed and solved using the LINGO 21.0 optimization software. Experimental results reveal that the proposed model delivers optimal decisions. Even though challenges are still available on the constraint functions and the derivation of parameters' values, the results provide positive managerial insights that offer valuable tools for stakeholders to improve supply chain efficiency.]]>
<![CDATA[Construction of the Rough Quotient Modules over the Rough Ring by Using Coset Concepts ]]>
<![CDATA[Rahma, Aira]]>;
<![CDATA[Fitriani, Fitriani]]>;
<![CDATA[Faisol, Ahmad]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.23564
<![CDATA[Given an ordered pair $(U, \theta)$ where $U$ is the set universe and $\theta$ is an equivalence relation on the set $U$ is called an approximation space. The equivalence relation $\theta$ is a relation that is reflexive, symmetric, and transitive. If the set $X \subseteq U$, then we can determine the upper approximation of the set $X$, denoted by $\overline{Apr}(X)$, and the lower approximation of the set $X$, denoted by $\underline{Apr}(X)$. The set $X$ is said to be a rough set on $(U, \theta)$ if and only if $\overline{Apr}(X)-\underline{Apr}(X) \neq \emptyset$. A rough set $X$ is a rough module if it satisfies certain axioms. This paper discusses the construction of a rough quotient module over a rough ring using the coset concept to determine its equivalence classes and discusses the properties of a rough quotient module over a rough ring related to a rough torsion module.]]>
<![CDATA[BOUNDING LINEAR-WIDTH AND DISTANCE-WIDTH USING FEEDBACK VERTEX SET AND MM-WIDTH FOR GRAPH ]]>
<![CDATA[Fujita, Takaaki]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.24222
<![CDATA[Studying the upper and lower bounds of graph parameters is crucial for understanding the complexity and tractability of computational problems, optimizing algorithms, and revealing structural properties of various graph classes. In this brief paper, we explore the upper and lower bounds of graph parameters, including path-distance-width, MM-Width, Feedback Vertex Set, and linear-width. These bounds are crucial for understanding the complexity and structure of graphs.]]>
<![CDATA[EPIDEMIC ANALYSIS, MATHEMATICAL MODELLING AND NUMERICAL SIMULATION OF COVID-19 TRANSMISSION ]]>
<![CDATA[Triyana, Eka]]>;
<![CDATA[Widowati, Widowati]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.25039
<![CDATA[This research develops a model with seven compartments SEIQDHR for the spread of COVID-19, with detected and treated individual behavior changes affecting disease transmission. The Next Generation Matrix is used to analyze local and global stability and to calculate the basic reproduction number. Then, the analysis of disease-free equilibrium and endemic equilibrium. Stability analysis shows that the equilibrium point is locally asymptotically stable when the basic reproduction number is less than one and globally asymptotically stable when it is greater than one. The results of the sensitivity analysis show that the transmission rate, the progression rate from exposure, and the detection rate are parameters that significantly influence the dynamics of disease spread. Numerical simulations were used to validate the analysis results and identify key parameters that contribute most to the spread of the disease among affected, infected, quarantined, diagnosed, and hospitalized individuals.]]>
<![CDATA[HPPCv: a Modification of HPPC Scheme with Vinegar Variables ]]>
<![CDATA[Ali, Saifullah]]>;
<![CDATA[Wijayanti, Indah Emilia]]>;
<![CDATA[Isnaini, Uha]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.23279
<![CDATA[The Hidden Product of Polynomial Composition (HPPC) Digital Signature is multivariate-based cryptography using an HFE trapdoor. The HPPC scheme provides the technique for choosing the HFE central map. Its technique utilizes the product of the composition of two linearized polynomials. In this research, we proposed the modification of the HPPC scheme. We modify the HPPC scheme such that the scheme is based on HFEv. The linearized polynomial with vinegar variables will be chosen for constructing the central map. In our modification version, the public key becomes a system of polynomials of degree 4 and a map from n+v to n-dimension vector space. For a final remark, Despite an increase in the polynomial degree, HPPCv maintains a computational cost similar to HPPC.]]>
<![CDATA[HOW TO COMBINE VAM AND DIJKSTRA’S ALGORITHM ]]>
<![CDATA[Ahmad, Mizan]]>;
<![CDATA[Aspriyani, Riski]]>;
<![CDATA[Susilowati, Eka]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.24044
<![CDATA[Solving transportation problems sometimes does not only require using one method or algorithm. Sometimes it is necessary to use several methods or algorithms at once. In this research, combining the Vogel’s Approximation Method (VAM) and Dijkstra algorithm can be carried out if three assumptions are met. These three assumptions are based on the characteristics of each VAM and Dijkstra’s algorithm, as well as the compatibility between the two.]]>
<![CDATA[ON A HIGHLY ROTUND NORM AND UNIFORMLY ROTUND NORM IN EVERY DIRECTION ON A FRECHE’T SPACE ]]>
<![CDATA[Wanjara, Amos Otieno]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.24207
<![CDATA[The word rotund comes from Latin word "rotundus" implying wheel-shaped or round (from rota wheel). Rotundity is the roundness of a 3-dimensional object. Some of the properties of rotundity include: UR-Uniformly Rotund, LUR-Locally Uniformly Rotund, MLUR-Midpoint Locally Uniformly Rotund, WUR-Weakly Uniformly Rotund, URED-Uniformly Rotund in Every Direction, HR- Highly Rotund, WLUR-Weakly Locally Uniformly Rotund and URWC-Uniformly Rotund in Weakly Compact sets of directions. Problems on Rotundity properties are still open. Smith gave a summary chart on rotundity of norms in Banach spaces. The chart left an open question whether or not a Highly Rotund norm(HR) implies Uniformly Rotund norm on Every Direction(URED). It is not clear whether if a Banach space has a Highly Rotund(HR) norm it follows that it has and equivalently URED. In this paper, we investigated the relationship between a Highly Rotund norm(HR) and a Uniformly Rotund norm in Every Direction(URED) on a Freche’t Space. The result shows that both Highly Rotund norm and Uniformly Rotund norm on Every Direction(URED) exist in Freche’t spaces. The implication of this result is that rotundity properties can be extended within spaces. This research work is very important since rotundity properties are strongly applicable in many branches of mathematics.]]>
<![CDATA[On the necessary and sufficient condition of a k-Euler pair ]]>
<![CDATA[Wijaya, Yosua Feri]]>;
<![CDATA[Isnaini, Uha]]>;
<![CDATA[Susanti, Yeni]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.24953
<![CDATA[In this paper, we discuss George Andrews’ definition of an Euler pair andSubbarao’s generalization of the Euler pair to a k-Euler pair. Let N and M be non-empty sets of natural numbers. A pair (N, M) is called a k-Euler pair if, for any natural number n, the number of partitions of n into parts from N is equal to the number of partitions of n into parts from M, with the condition that each part appears fewer than k times. We further explore several theorems concerning Euler pairs that were established by Andrews and Subbarao, and we present proofs using a method distinct from those previously utilized.]]>
<![CDATA[TWO-COMPARTMENT PHARMACOKINETIC MODELS WITH SINGLE AND DOUBLE ELIMINATION RATES FOR ORAL ADMINISTRATION OF TWO DRUGS ]]>
<![CDATA[Juwita, Rhenata]]>;
<![CDATA[Zulkarnaen, Diny]]>;
<![CDATA[Khumaeroh, Mia Siti]]>
<![CDATA[ Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025) ]]>
Publisher : <![CDATA[Diponegoro University ]]>
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DOI: 10.14710/jfma.v8i1.24852
<![CDATA[This paper presents two pharmacokinetic models with two compartments, incorporating both single and double elimination rates for the oral administration of two drugs. The models allow for the estimation of the absorption, distribution, and elimination rate constants. This estimation is performed in two phases based on the time intervals. The first phase estimates the distribution and elimination rates using concentration data from larger time data points, employing residual techniques and least squares error. In contrast, the absorption rate estimation is conducted using the Wagner-Nelson method for smaller time intervals. Prior to these estimations, an analytical solution is required, for which Laplace transformation is utilized. Finally, graphical simulations are performed to observe the dynamics of drug concentrations throughout the processes of absorption, distribution, and elimination. Additionally, these simulations facilitate a comparison between the actual data of drug concentrations in each compartment and their respective approximations.]]>
