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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 145 Documents
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HPPCv: a Modification of HPPC Scheme with Vinegar Variables Ali, Saifullah; Wijayanti, Indah Emilia; Isnaini, Uha
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.23279

Abstract

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.
HOW TO COMBINE VAM AND DIJKSTRA’S ALGORITHM Ahmad, Mizan; Aspriyani, Riski; Susilowati, Eka
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.24044

Abstract

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.
ON A HIGHLY ROTUND NORM AND UNIFORMLY ROTUND NORM IN EVERY DIRECTION ON A FRECHE’T SPACE Wanjara, Amos Otieno
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.24207

Abstract

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.
On the necessary and sufficient condition of a k-Euler pair Wijaya, Yosua Feri; Isnaini, Uha; Susanti, Yeni
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.24953

Abstract

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.
TWO-COMPARTMENT PHARMACOKINETIC MODELS WITH SINGLE AND DOUBLE ELIMINATION RATES FOR ORAL ADMINISTRATION OF TWO DRUGS Juwita, Rhenata; Zulkarnaen, Diny; Khumaeroh, Mia Siti
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 1 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i1.24852

Abstract

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.
ON PROPERTIES OF PROJECTIVE SPACE DETERMINED BY QUOTIENT MAP Kurniadi, Edi; Badrulfalah, Badrulfalah
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.v0i0.27702

Abstract

The state of a system in quantum theory is not always described by an element of a Hilbert space but by an element of projective space. The research aims to prove that the real projective space consisting of one-dimensional linear subspaces is a smooth manifold which is constructed by a quotient map. It is shown that a projective space is a Hausdorff space, second countable, and -dimensional locally Euclidean. It is also proved that the -dimensional real a projective space is homeomorphic to the quotient topology . The proof involves a quotient map which is defined by a quotient topology.
A note on outer-connected hop Roman dominating function in graphs Casinillo, Leomarich F
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.v0i0.28547

Abstract

Let $G=(V(G), E(G))$ be a simple, connected, and finite graph with vertex set $V(G)$ and edge set $E(G)$.  Let $\phi: V(G) \rightarrow \{0, 1, 2\}$  be an HRDF on $G$, and for each $i\in \{0, 1, 2\}$, let  $V_i=\{u\in V(G): \phi(u)=i\}$. A function $\phi=(V_0, V_1, V_2)$ is an outer-connected hop Roman dominating function (OcHRDF) on $G$ if, for every $v\in V_0$, there exists $u\in V_2$ such that $d_G(u, v)=2$ and either $V_1=V(G)$ or the sub-graph $\langle V_0 \rangle$ is connected. The weigth of OcHRDF $\phi$ denoted by $\widetilde{\omega}_G^{chR}(\phi)$ and defined by $\widetilde{\omega}_G^{chR}(\phi)=\sum_{v\in V(G)}\phi(v)$=|V_1|+2|V_2|$. The outer-connected hop Roman domination number of $G$ is denoted by $\widetilde{\gamma}_{chR}(G)$ and defined by $\widetilde{\gamma}_{chR}(G)=min\{$\widetilde{\omega}_G^{chR}(\phi): \phi is an OcHRDF  on G\}$. Moreover, any OcHRDF $\phi$ on $(G)$ with $\widetilde{\gamma}_{chR}(G)=$\widetilde{\omega}_G^{chR}(\phi)$ is called $\overline{\gamma}_{chR}$-function on $G$. In this paper, a new restricted parameter of a hop Roman domination in graphs is introduced, and some combinatorial properties are discussed.
SOME PROPERTIES OF MODULAR TOPOLOGY IN THE ORLICZ SEQUENCE SPACE Haryadi, Haryadi; Solikhin, Solikhin
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.v0i0.26542

Abstract

In this article, we examined some properties of modular topology on the Orlicz sequence space. Discussions were conducted by constructing the topology on the sequence space using a modular neighborhood of zero. The neighborhood forms a local base that is balanced, absorbing, and symmetrical. Furthermore, if the Orlicz function that grows not soo rapidly, the modular neighborhood induces a topological vector space. We also characterize the modular boundedness, modular convergence, and modular closed set on the sequence space.
Corrected Trapezoidal Rule For The Riemann-Stieltjes Integral Marjulisa, Rike; Imran, M; Putri, Ayunda
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.v0i0.26475

Abstract

This study investigates the derivation of a corrected trapezoidal rule for approximating the Riemann-Stieltjes integral. The corrected trapezoidal rule is derived by approximating certain monomial functions to obtain optimal method coefficients.  The proposed method has an accuracy of order three. Furthermore, an error analysis is conducted to assess the accuracy of the obtained approximation. In the final section, numerical computations are presented to compare the performance of the proposed method with existing methods. The results demonstrate that the proposed method produces smaller errors compared to previously developed approaches.
Sharper Upper Bounds for Roots of Polynomials Generated by Positive Sequences Farokhi, Jamal
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.v0i0.25669

Abstract

Finding sharp and easily computable upper bounds for the moduli of the roots of polynomials with real coefficients is a long-standing problem with applications in numerical analysis, control theory, and the study of linear recurrence relations. The classical bounds of Cauchy and Lagrange, despite their age, remain the most frequently used estimates because of their extreme simplicity. This paper introduces a new family of upper bounds specifically designed for polynomials whose coefficients are the initial terms of a positive real sequence a_n that does not grow too rapidly. For each such polynomial we construct an explicit number by taking the two largest values appearing among the (i+1)-th roots of the successive absolute differences of the sequence together with the simple quantity a_1+1, and adding them. We prove that the resulting value rigorously bounds the modulus of every root. A companion bound based on second differences is obtained as an immediate corollary. Extensive numerical tests on constant, arithmetic, harmonic, and exponential sequences show that the new estimates are often several times tighter than Cauchy’s bound and, in many cases, also outperform recently published refinements. The contribution is twofold: (i) a new, fully explicit bound using first differences, and (ii) an even sharper variant using second differences presented as a corollary.

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