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Journal of Fundamental Mathematics and Applications

jfma
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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 105 Documents

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SOME CARTESIAN PRODUCTS OF A PATH AND PRISM RELATED GRAPHS THAT ARE EDGE ODD GRACEFUL Yeni Susanti; Iwan Ernanto; Aluysius Sutjijana; Sufyan Sidiq
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 2 (2021)
Publisher : Diponegoro University

Let $G$ be a connected undirected simple graph of size $q$ and let $k$ be the maximum number of its order and its size. Let $f$ be a bijective edge labeling which codomain is the set of odd integers from 1 up to $2q-1$. Then $f$ is called an edge odd graceful on $G$ if the weights of all vertices are distinct, where the weight of a vertex $v$ is defined as the sum $mod(2k)$ of all labels of edges incident to $v$. Any graph that admits an edge odd graceful labeling is called an edge odd graceful graph. In this paper, some new graph classes that are edge odd graceful are presented, namely some cartesian products of path of length two and some circular related graphs.

HASIL PERBANDINGAN METODE IMPROVED NEWTON-RAPHSON BERBASIS DEKOMPOSISI ADOMIAN DAN BEBERAPA METODE KLASIK PADA MASALAH PERSAMAAN NON-LINIER Indah Jumawanti; Sutrisno Sutrisno; Bayu Surarso
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 1 (2018)
Publisher : Diponegoro University

In this paper, we work with ten nonlinear equations to compare a new method in nonlinear equation solving, Improved Newton-Raphson based on Adomian Decomposition method (INR-ADM) that consisting of two types called INR-ADM 1 and INR-ADM 2. The difference between INR-ADM 1 and INR-ADM 2 is on the iteration formula form. From our results, it was showed that INR-ADM 1 and INR-ADM 2 are not always better than classic Newton-Raphson method in term of the iteration number. However, if INR-ADM 1 and INR-ADM 2 are compared to Regula False method and Secant method, they are always better i.e. they had fewer number of iteration. The INR-ADM 1 and INR-ADM 2 had shorter computational time than Regula False method. Furthermore, the computational time of INR-ADM 1 and INR-ADM 2 cannot be claimed that they had shorter or longer if they are compared to Newton-Raphson method and Secant method.

SEMINORM PADA RUANG FUNGSI TERINTEGRAL DUNFORD Solikhin Solikhin; Y.D. Sumanto; Abdul Aziz
Journal of Fundamental Mathematics and Applications (JFMA) Vol 2, No 1 (2019)
Publisher : Diponegoro University

This article discussed the seminorm on Dunford integrable functional space. We show that the set of all Dunford integrable functions is linear space. The results were shown that $\left( D[a,b],\ \left\| \ \cdot \ \right\| \right)$ is a seminorm space with function defined by $\left\| f \right\|=\underset{\begin{smallmatrix} {{x}^{*}}\in {{X}^{*}} \\ \left\| {{x}^{*}} \right\|\le 1 \end{smallmatrix}}{\mathop{\sup }}\,\ \left\{ \underset{E\subset [a,b]}{\mathop{\sup }}\,\,\left| \left( L \right)\int\limits_{E}{{{x}^{*}}f} \right| \right\}$. Furthermore, $\left( D[a,b],\ d \right)$ is a pseudomatrix space with function defined by $d\left( f,g \right)=\left\| f-g \right\|=\underset{\begin{smallmatrix} {{x}^{*}}\in {{X}^{*}} \\ \left\| {{x}^{*}} \right\|\le 1 \end{smallmatrix}}{\mathop{\sup }}\,\ \left\{ \underset{E\subset [a,b]}{\mathop{\sup }}\,\,\left| \left( L \right)\int\limits_{E}{{{x}^{*}}\left( f-g \right)} \right| \right\}$.

ANALISIS TARIF PREMI DAN ASUMSI LOADING PADA PRODUK ASURANSI DWIGUNA BEASISWA Ira Rosianal Hikmah; Yulial Hikmah
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 1 (2020)
Publisher : Diponegoro University

Based on data from Badan Pusat Statistik (BPS), the number of Indonesia's population has consistently increased every year. This will cause several problems, one of them is public health. Health problems that occur cause some risks that cause losses. Therefore, one way to reduce the impact of these risks is insurance. This study analyzes how the process of forming premium prices with loading assumptions that are in accordance with existing assumptions in order to meet the criteria of equitable to the client, deliverable by the agent, and profitable to the company. This research uses a quantitative research approach. The population in this study was all Sum Insured (SI) while the sample was 1000 SI male sex. The data used in this study are secondary data that is data from an ABC insurance company in Indonesia, literature study through books, journal references, and previous research. The results of this study are the calculation of premiums by the methods used by the company more efficiently when compared with formulas in accordance with the theory. Although the price of a premium is more expensive using the company method, it is not significantly different. If using the company method, the sum insured used is the sum insured from death benefit whereas the theory is the average of claims incurred at that age. The fees charged are still fairly reasonable in accordance with the rules of setting the price of insurance premiums. In addition, the use of CSO 80 tables and Reinsurance Rates that have been adjusted to the company's interest rate of 5% in accordance with the expected cash value desired by the company.

BEBERAPA SIFAT (R,S)-SUBMODUL PRIMA-α GABUNGAN Dian Ariesta Yuwaningsih; Rusmining Rusmining; Puguh Wahyu Prasetyo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 2 (2021)
Publisher : Diponegoro University

Diberikan dan merupakan ring komutatif. Keprimaan pada suatu ring telah mengalami perkembangan ke dalam struktur modul. Namun, definisi keprimaan yang ada selama ini hanya berfokus pada operasi pergandaan skalar di dalam modul. Submodul prima-α merupakan salah satu perumuman dari submodul prima yang melibatkan operasi aditif dan pergandaan skalar di dalam modul. Pada artikel ini disajikan generalisasi dari submodul prima-α ke dalam struktur (R,S)-modul, yang selanjutnya disebut (R,S)-submodul prima-α gabungan. Selanjutnya, disajikan beberapa sifat dari (R,S)-submodul prima-α gabungan. Beberapa sifat tersebut diantaranya adalah syarat perlu dan syarat cukup suatu (R,S)-submodul membentuk (R,S)-submodul prima-α gabungan; sifat (R,S)-submodul prima-α gabungan yang berkaitan dengan homomorfisma (R,S)-modul; serta syarat perlu dan syarat cukup suatu (R,S)-submodul faktor membentuk (R,S)-submodul prima-α gabungan. Beberapa sifat (R,S)-submodul prima-α gabungan tersebut diperoleh dari pengembangan sifat keprimaan dalam struktur modul.

IMPLEMENTASI LOGIKA FUZZY MAMDANI UNTUK MENENTUKAN KOMPOSISI OPTIMAL PUPUK ORGANIK DAN ANORGANIK NPK PADA TANAMAN MENTIMUN Fajar Ridwan Analistyawan; Sutrisno Sutrisno; Solichin Zaki
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 2 (2018)
Publisher : Diponegoro University

In this article, we have determined the optimal composition of organic fertilizer and NPK inorganic fertilizer for cucumber plants. We have formulated two fuzzy systems which are fuzzy system 1 and fuzzy system 2. The inputs for fuzzy system 1 are plants’ height and the number of leaves where the output is the growth rate. Fuzzy system 2 had input of growth rate and NPK concentration and output of organic fertilizer concentration. By processing the data using fuzzy system, we have compared the cucumber plant with organic fertilizer and NPK to cucumber plant that was used only NPK fertilizer. The result had shown that the cucumber plant with organic fertilizer and NPK was produced the better outcome than the cucumber plants with NPK only.

COPRIME GRAPH OF INTEGERS MODULO n GROUP AND ITS SUBGROUPS Rina Juliana; Masriani Masriani; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni; Irwansyah Irwansyah
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 1 (2020)
Publisher : Diponegoro University

Coprime Graph is a geometric representation of a group in the form of undirectedgraph. The coprime graph of a group G, denoted by $\Gamma_G$ is a graph whose vertices are all elements of group G; and two distinct vertices a and b are adjacent if and only if $(|a|,|b|)=1$. In this paper, we study coprime graph of integers modulo n group and its subgroups. One of the results is if n is a prime number, then coprime graph of integers modulo n group is a bipartite graph.

NEW COUNTING FORMULA FOR DOMINATING SETS IN PATH AND CYCLE GRAPHS Leomarich F Casinillo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020)
Publisher : Diponegoro University

Let G=(V(G), E(G)) be a path or cycle graph. A subset D of V(G) is a dominating set of G if for every u element of V(G)\D, there exists v element of D such that uv element of E(G), that is, N[D]=V(G). The domination number of G, denoted by gamma(G), is the smallest cardinality of a dominating set of G. A set D_1 subset of V(G) is a set containing dominating vertices of degree 2, that is, each vertex is internally stable. A set D_2 subset of V(G) is a set containing dominating vertices where one of the element say a element of D_2, and the rest are of degree 2. A set D_3 subset of V(G) is a set containing dominating vertices in which two of the elements say b, c element of D_3, deg(b)=deg(c)=1. This paper developed a new combinatorial formula that determines the number of ways of putting a dominating set in a path and cycle graphs of order n>=1 and n>=3, respectively. Further, a combinatorial function P^1_G(n), P^2_G(n) and P^3_G(n) that determines the probability of getting the set D_1, D_2, and D_3, respectively in graph G of order n were constructed.

A SHORT NOTE ON FIBONACCI NUMBERS IN A GENERALIZED PYTHAGOREAN TRIPLES Emily L Casinillo; Leomarich F Casinillo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 1 (2021)
Publisher : Diponegoro University

This paper aims to construct a new formula that generates a Fibonacci numbers in a generalized Pythagorean triples. In addition, the paper formulates some Fibonacci identities and discuss some important findings.

IMPLEMENTATION OF EXTENDED FINITE ELEMENT METHOD IN CRACK PROPAGATION OF CONCRETE Muhammad Rafi Purba; Tulus Tulus; M.R. Syahputra; Sawaluddin Sawaluddin
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 1 (2022)
Publisher : Diponegoro University

The Extended Finite Element Method is a numerical solution based on the Finite Element Method (FEM) XFEM has really become a very important generalization of classical finite element techniques, by establishing a mesh independent generalization of classical finite elements to reduce the mesh-dependent shortcomings of the solution. The application of XFEM in crack simulation should improve the modeling of the crack tip environment and also apply to generalized advanced global failure criteria, which is specifically designed to deal with problems in the engineering field Such as the fracture behaviour model. The purpose of this paper is to identify the application of the Extended Finite Element Method to a technical problem, namely fracture behaviour model. The media used is pure boneless concrete modelled with COMSOL Multiphysics 5.6 software by combining stress ratio, lateral strain due to axial loading, concrete density, and crack growth rate. The crack growth process provides initial prolonged growth along with the increase in crack size. In the end, the growth is faster. The reason for this accelerated growth is the stress intensity factor at the crack tip. As the crack grows, the stress intensity factor increases, leading to faster growth. The crack grows until it reaches a critical value, and fracture occurs. The test results obtained the cause of failure: the critical stress intensity is exceeded. See a comparison of crack size and stress cycle as the crack size increases. This accelerated growth is because the growth rate depends on the stress intensity factor at the crack tip, and the stress intensity factor depends on the crack size. As the crack grows, the stress intensity factor increases, leading to faster growth. The crack grows to a critical size, and failure occurs. The results show a relatively strong relationship between increasing crack size and increasing crack growth rate.

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Journal Mail Official admin.math@live.undip.ac.id

Editorial Address Jl. Prof Soedarto, SH, Tembalang, Semarang, Indonesia 50275

Location Kota semarang, Jawa tengah INDONESIA

Abstract

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Abstract

Contact Name
Sutrisno Sutrisno

Contact Email
s.sutrisno@live.undip.ac.id

Phone
+62247474754

Journal Mail Official
admin.math@live.undip.ac.id

Editorial Address
Jl. Prof Soedarto, SH, Tembalang, Semarang, Indonesia 50275

Location
Kota semarang,

Jawa tengah

INDONESIA