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Journal of Fundamental Mathematics and Applications
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 "ARTICLES IN PRESS" : 10 Documents clear
Exploring Physics-Informed Neural Networks for Solving Boundary Layer Problems Muchamad Harry Yudha Pratama; Agus Yodi Gunawan
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
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.
THE L(2,1)-LABELING OF MONGOLIAN TENT, LOBSTER, TRIANGULAR SNAKE, AND KAYAK PADDLE GRAPH Lisa Damayanti Ningrum; Ahmad Muchlas Abrar
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
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. 
Topologi Ruang Pseudometrik Kuasi dan Operator Linear Kontinu pada Ruang Bernorma Asimetrik (Topology of Quasi-Pseudometric Spaces and Continuos Liner Operator on Asymmetric Normed Spaces) Klatenia Selawati; Christiana Rini Indrati
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.18504

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 operator on asymmetric normed spaces is focus on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.
Dualitas antara Keterkendalian Lemah dan Keterobservasian Lemah Sistem Linear atas Aljabar Max-Plus Interval Ari Suparwanto
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i2.17320

Abstract

ABSTRAK Sistem linear atas aljabar max-plus (SLMP) dengan domain kejadian mengasumsikan informasi dan pengetahuan yang pasti mengenai aktifitas di dalamnya, sementara dalam kenyataannya suatu pengukuran tidak pernah  akurat. Akibatnya nilai pengukuran pada umumnya berbeda dengan nilai sebenarnya. Setelah dilakukan pengukuran serta memperoleh hasil pengukuran, informasi yang diperoleh bahwa nilai sebenarnya dari proses pengukuran termuat pada suatu interval. Dengan dasar tersebut, dimungkinkan memberikan perkiraan tentang waktu berlangsungnya suatu proses tertentu, dalam suatu interval.Dengan dasar tersebut, aljabar maks-plus telah digeneralisasi menjadi aljabar maks-plus interval. Berdasarkan hasil-hasil pada aljabar max-plus interval, telah diteliti keterkendalian lemah dan keterobservasian lemah sistem linear atas  aljabar max-plus interval (SLMPI) dengan menggunakan konsep asticity untuk menentukan kondisi keterkendalian lemah dan keterobservasian lemah dari sistem linear atas aljabar max-plus interval. Sedangkan untuk menentukan dan membangun barisan kendali yang diinginkan digunakan konsep residuation. Demikian juga, untuk mengestimasi state digunakan konsep residuation.Diketahui pada sistem linear atas aljabar konvensional, terdapat dualitas antara sifat-sifat ketrkendalian dan keterobservasian yang dapat dikarakterisasikan melalui rank dari matriks keterkendalian dan matriks keterobservasian. Berdasarkan hasil penelitian keterkendalian lemah dan keterobservasian lemah dari sistem linear atas aljabar max-plus interval yang keduanya menggunakan konsep asticity dan residuation, maka akan diteliti dualitas antara keterkendalian lemah dan keterobservasian lemah dari sistem linear atas aljabar max-plus interval. Kata Kunci : asticity,  residuation   
The Fractional Derivative of Some Functions Louie Resti Rellon; Cymber Orvie Quevedo; Ruben Cordero, Jr.; Adrian Lupogan; Jayson Saut
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.19442

Abstract

 
A Backtracking Approach for Solving Path Puzzles Joshua Erlangga Sakti; Muhammad Arzaki; Gia Septiana Wulandari
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.18155

Abstract

We study algorithmic aspects of the Path Puzzles---a logic puzzle created in 2013 and confirmed NP-complete in 2020. This paper proposes 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. 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.
IDEMPOTENT ELEMENTS IN MATRIX RING OF ORDER 2 OVER POLYNOMIAL RING $\mathbb{Z}_{p^2q}[x]$ Muchammad Choerul Arifin; Iwan Ernanto
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
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 $M_2(\mathbb{Z}_{p^2q}[x])$.
ALTERNATIF PENENTUAN SWITCH PROBABLITY PADA FLOWER POLLINATION ALGORITHM (FPA) DENGAN MENGGUNAKAN DOUBLE EXPONENT Yuli Sri Afrianti; Fadhil Hanif Sulaiman; Sandy Vantika
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v6i2.18996

Abstract

Flower Pollination Algorithm (FPA) merupakan metode optimisasi yang mengadopsi cara kerja penyerbukan bunga dengan pemilihan switch probability untuk menentukan proses optimisasi secara global atau lokal. Pemilihan nilai switch probability ini akan mempengaruhi banyak iterasi yang diperlukan untuk mencapai nilai optimum. Pada beberapa literatur sebelumnya, nilai switch probability selalu dipilih sebesar 0.8 karena secara alami peluang optimasi global lebih besar dibandingkan lokal. Pada artikel ini akan dilakukan modifikasi dalam menentukan besar switch probability, yaitu dengan menggunakan aturan Double Exponent. Hasil yang diperoleh akan dianalisis dengan Uji Hipotesis untuk menguji apakah terdapat perbedaan signifikan antara hasil optimasi dengan switch probability 0.8 dan Double Exponent. Selain itu, ditentukan pula perlakuan yang memberi iterasi paling sedikit. Hasil ini diharapkan dapat menjadi rekomendasi untuk pengembangan Flower Pollination Algorithm (FPA) selanjutnya terutama pada tahap penentuan switch probability.
FROZEN INITIAL LIABILITY METHOD TO DETERMINE NORMAL COST OF PENSION FUND WITH VASICEK INTEREST RATE MODEL Sulma Sulma; Nur Ahniyanti Rasyid; I Nyoman Widana
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.20150

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.
PRIME LABELING OF SOME WEB GRAPHS WITHOUT CENTER Jovanco Albertha Scada; Yeni Susanti
Journal of Fundamental Mathematics and Applications (JFMA) ARTICLES IN PRESS
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.

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