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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 9 Documents
 1 
Search results for , issue "Vol 6, No 2 (2023)" : 9 Documents clear
EXPLORING PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING BOUNDARY LAYER PROBLEMS Pratama, Muchamad Harry Yudha; Gunawan, Agus Yodi
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.v6i2.20084

Abstract

In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN) to tackle boundary layer problems. We here examine four different cases of boundary layers of second-order ODE: a linear ODEwith constant coefficients, a nonlinear ODE with homogeneous boundary conditions, an ODE with non-constant coefficients, and an ODE featuring multiple boundary layers. We adapt the line of PINN technique for handling those problems, and our results show that the accuracy of the resulted solutions depends on how we choose the most reliable and robust activation functions when designing the architecture of the PINN. Beside that, through our explorations, we aim to improve our understanding on how the PINN technique works better for boundary layer problems. Especially, the use of the SiLU (Sigmoid-Weighted Linear Unit) activation function in PINN has proven to be particularly remarkable in handling our boundary layer problems.
TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES Selawati, Klatenia; Indrati, Christiana Rini
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.v6i2.18504

Abstract

In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operators on asymmetric normed spaces is focused on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.
A BACKTRACKING APPROACH FOR SOLVING PATH PUZZLES Sakti, Joshua Erlangga; Arzaki, Muhammad; Wulandari, Gia Septiana
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.v6i2.18155

Abstract

We study algorithmic aspects of the Path puzzle--a logic puzzle created in 2013 and confirmed NP-complete (Non-deterministic Polynomial-time-complete) in 2020. We propose a polynomial time algorithm for verifying an arbitrary Path puzzle solution and a backtracking-based method for finding a solution to an arbitrary Path puzzle instance.To our knowledge, our study is the first rigorous investigation of an imperative algorithmic approach for solving Path puzzles. We prove that the asymptotic running time of our proposed method in solving an arbitrary Path puzzle instance of size $m \times n$ is $O(3^{mn})$. Despite this exponential upper bound, experimental results imply that a C++ implementation of our algorithm can quickly solve $6 \times 6$ Path puzzle instances in less than 30 milliseconds with an average of 3.02 milliseconds for 26 test cases. We finally prove that an $m \times n$ Path puzzle instance without row and column constraints is polynomially solvable in $O(\max\{m,n\})$ time.
IDEMPOTENT ELEMENTS IN MATRIX RING OF ORDER 2 OVER POLYNOMIAL RING $\mathbb{Z}_{p^2q}[x]$ Arifin, Muchammad Choerul; Ernanto, Iwan
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.v6i2.19307

Abstract

An idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements, 0 and 1, these particular idempotent elements are commonly referred to as the trivial idempotent elements However, in the case of rings $\mathbb{Z}_n$ and $\mathbb{Z}_n[x]$ it is possible to have non-trivial idempotent elements. In this paper, we will investigate the idempotent elements in the polynomial ring $\mathbb{Z}_{p^2q}[x]$ with $p,q$ different primes. Furthermore, the form and characteristics of non-trivial idempotent elements in $M_2(\mathbb{Z}_{p^2q}[x])$ will be investigated. The results showed that there are 4 idempotent elements in $\mathbb{Z}_{p^2q}[x]$ and 7 idempotent elements in $M_2(\mathbb{Z}_{p^2q}[x])$.
FLOWER POLLINATION ALGORITHM (FPA): COMPARING SWITCH PROBABILITY BETWEEN CONSTANT 0.8 AND DOUBLE EXPONENTGUNAKAN DOUBLE EXPONENT Afrianti, Yuli Sri; Sulaiman, Fadhil Hanif; Vantika, Sandy
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.v6i2.18996

Abstract

Flower Pollination Algorithm (FPA) is an optimization method that adopts the way flower pollination works by selecting switch probabilities to determine the global or local optimization process. The choice of switch probability value will influence the number of iterations required to reach the optimum value. In several previous literatures, the switch probability value was always chosen as 0.8 because naturally the global probability is greater than local. In this article, comparison is studied to determine the switch probability by using the Double Exponent rule. The results are analyzed using Hypothesis Testing to test whether there is a significant difference between the optimization results. The study involved ten testing functions, and results showed that the 0.8 treatment is significantly different from the Double Exponent. However, in general no treatment is better than the other.
FROZEN INITIAL LIABILITY METHOD TO DETERMINE NORMAL COST OF PENSION FUND WITH VASICEK INTEREST RATE MODEL Sulma, Sulma; Rasyid, Nur Ahniyanti; Widana, I Nyoman
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.v6i2.20150

Abstract

Civil servants have an important role in national development, so increasing their productivity is needed. The pension fund program is given as a form of effort by government agencies to ensure employee welfare when entering retirement. This research discusses the normal cost of the defined benefit pension program using one of the actuarial valuation methods, namely Frozen Initial Liability (FIL), by taking into account the stochastic interest rate following the Vasicek model. The data used in this study are lecturers majoring in MIPA, Faculty of Science and Technology, Universitas Jambi, consisting of 8 people of female gender with the status of being a participant since 2022. Based on the calculation results obtained that in the period 0-30 years, the normal cost for each group member is constant, namely  per year or  per month. When the working period entered 31 years, one by one the participants began to enter their retirement period, which resulted in a change in the normal cost value. At 38 years of service, there was only one participant with a normal cost of  per year or by  per month. Changes in normal cost tend to decrease when retirement program participants also decrease. In the period of more than 38 years, all participants have retired so that normal cost payments are stopped.
MODIFIED HOUSEHOLDER METHOD OF FIFTH ORDER OF CONVERGENCE AND ITS DYNAMICS ON COMPLEX PLANE Putri, Ayunda; Imran, M; Marjulisa, Rike
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.v6i2.20554

Abstract

In this paper, a modified Householder method of fifth order is proposed for solving nonlinear equations. The modification is done by adapting a cubic interpolation polynomial to approximate the second derivative in the Householder method. Weprovide a theorem to prove the order of convergence of the proposed method. The simulations reveal that the proposed method needs fewer iterations, even with challenging initial guesses, and excels in sending a large portion of initial points to convergence and exhibits rapid convergence.
MATHEMATICAL MODEL OF MEASLES DISEASE SPREAD WITH TWO-DOSE VACCINATION AND TREATMENT Manaqib, Muhammad; Yuliawati, Ayu Kinasih; Zulkifli, Dhea Urfina
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.v6i2.20091

Abstract

This study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C<R_0. Numerical simulations of disease-free and endemic equilibrium points are carried out to provide an overview of the results analyzed with parameter values from several sources. The results of the numerical simulation are in line with the analysis carried out. From the model analysis, the disease will disappear more quickly when the level of vaccine used and individuals who carry out treatment are enlarged.
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.

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