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All Journal Natural Science: Journal of Science and Technology Kubik JURNAL PENGABDIAN KEPADA MASYARAKAT Journal of Mathematics and Mathematics Education (JMME) BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) KUBIK: Jurnal Publikasi Ilmiah Matematika Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya
Vika Yugi Kurniawan
Prodi Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Sebelas Maret Jl. Ir. Sutami No.36, Kentingan, Kec. Jebres, Kota Surakarta, Jawa Tengah 57126
Arts Humanities Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Social Sciences Transportation

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ANALYSIS OF THE COOPERATIVE LOTKA-VOLTERRA MODEL IN THE CASE OF TWO AUTOMOTIVE INDUSTRIES IN INDONESIA Rachmawati, Zahra Febrilia; Sutrima, Sutrima; Setiyowati, Ririn; Kurniawan, Vika Yugi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0295-0302

Abstract

The automotive industry sector is one of the main sectors contributing to the national economy. Companies in the automotive industry work together to increase productivity and win the market competition. This research aims to construct the cooperative interaction between two companies into the cooperative Lotka-Volterra model. The cooperative Lotka-Volterra model was analyzed for stability at the equilibrium point and bifurcation analysis was performed. Sales data for the Calya 1.2 G product from PT Toyota Motor Manufacturing Indonesia and sales data for the New Sigra 1.2 R MT product from PT Astra Daihatsu Motor are applied to the model. The results of the study show that there is a model that explains the cooperative interaction of the two companies, namely the cooperative Lotka-Volterra model. Four equilibrium points are obtained with three equilibrium points being unstable and the fourth equilibrium point being stable with conditions. The Hopf bifurcation analysis of the model shows that there are no parameters that cause a change in stability from initially stable to unstable. The data simulation shows that the cooperation of the two companies is mutually beneficial because it increases the number of sales and creates balanced market conditions.
CONSTRUCT THE TRIPLE ZERO GRAPH OF RING Z_n USING PYTHON Wulandari, Putri; Kurniawan, Vika Yugi; Kurdhi, Nughthoh Arfawi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0507-0516

Abstract

Let be a commutative ring with nonzero identity and there exists such that , , , denotes the set of all triple zero elements of . The triple zero graph of , denoted by , is an undirected graph with vertex set where two distinct vertices and are adjacent if and only if , and there exists a nonzero element of such that , , and . Python is a programming language with simple and easy-to-learn code that can be used to solve problems in algebra and graphs. In this paper, we construct the triple zero graph of ring using Python. Based on the output of the program, several properties of are obtained, such as if and , then is a planar graph, if with is prime numbers, then is a complete graph , and if with is prime numbers and , then is a connected graph.
CRAMER’S RULE IN MIN-PLUS ALGEBRA Putri, Zakia Nur Ramadhani; Siswanto, Siswanto; Kurniawan, Vika Yugi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp1147-1154

Abstract

Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation can be solved using Cramer’s rule if . Max-plus algebra is a set where is a set of real numbers, equipped with biner operations and where and . Min-plus Algebra is a set where is a set of real numbers, equipped with biner operations and where and . In max-plus algebra has been formulated Cramer’s rule to solve a system of linear equations. Because max-plus algebra is isomorphic to min-plus algebra, Cramer’s rule can be formulated into min-plus algebra. The purpose of this research is to determine the sufficient conditions for a system of linear equations can be solved using Cramer’s rule. The method used in this research is a literature study that reviews previous research related to min-plus algebra, max-plus algebra, and Cramer’s rule in max-plus algebra. By using the appropriate analogy in max-plus algebra, we can determine the sufficient conditions so that a system of linear equations in min-plus algebra can be solved using Cramer’s rule. Based on the research, the sufficient conditions for a system of linear equations can be solved using Cramer’s rule are for and with the Cramer’s rule is . For an invertible matrix A, Cramer’s rule can be written as .
ALGORITHM FOR CONSTRUCTING TRIPLE IDENTITY GRAPH OF RING Z_n USING PYTHON Kurniawan, Vika Yugi; Ekasiwi, Chessa Fanny
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1629-1638

Abstract

Let R be a commutative ring. The triple identity graph of ring R is denoted by TE(R) with sets of vertices Two different vertices and are adjacent if and only if there is an element in such that and . To easily visualize the triple identity graph, a program is needed to represent it briefly. Python can easily manipulate, analyze, and visualize data. Therefore, this study uses Python to construct the algorithm for In this research, some examples will be given and then be observed for new characteristics of the triple identity graph of ring such as the connectedness, the diameter, and the girth. And we find the characterize for which graph is empty, connected, or Hamiltonian.
ALGORITHM FOR CONSTRUCTING THE TRIPLE UNIT GRAPH OF TYPE II OF RING Z_n USING PYTHON Fitriani, Ika Nur; Kurniawan, Vika Yugi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1639-1648

Abstract

Let be a commutative ring with as the set of all unit elements in . This paper introduces a new graph associated with the ring , called the triple unit graph of type II, denoted by with the vertex set is − {0,1}. In TU2(R), two distinct vertices, and , are adjacent if there exists with and such that . This paper focuses on the algorithm for constructing using Python. This research uses the literature study research method. The Python programming language can be used to observe the characteristic result of the graph. From the patterns generated by the algorithm, some characteristics of are obtained. For example, if is a prime and , then is a connected graph, a complete graph, a regular graph, and a Hamiltonian graph
PERMANENT AND DOMINANT OF MATRIX OVER INTERVAL MIN-PLUS ALGEBRA Septiany, Ade Safira; Siswanto, Siswanto; Kurniawan, Vika Yugi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp2029-2034

Abstract

A min-plus algebra is a set , where is the set of all real numbers equipped with two binary operations, namely minimum and addition . Every square matrix in min-plus algebra can always be calculated as a permanent and dominant matrix. The min-plus algebra can be extended to an interval min-plus algebra, where the elements are closed intervals denoted with two binary operations, minimum and addition . Min-plus interval algebra can be defined in a square matrix. This research will discuss the permanent and dominant a matrix over min-plus interval algebra, the relationship between permanent and dominant matrix, and bideterminant matrix over min-plus interval algebra. From the research results obtained, permanent and dominant formulas, it found that the dominant is greater than or equal to the permanent and the bideterminant formulas.
THE TRIPLE IDENTITY GRAPH OF THE RING Z_n Kurniawan, Vika Yugi; Ekasiwi, Chessa Fanny; Wiyono, Santoso Budi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2521-2530

Abstract

Let be a commutative ring with identity and is an identity element of . The triple identity graph of the ring , represented by ), is an undirected simple graph with the vertex set . In , two different vertices and is called adjacent if there is an element such that and . The triple identity graph of the ring of integers modulo , represented by , is the subject of this study. We obtain several results regarding the properties of the graph , which are summarized as follows. The graph is a connected graph if and only if is prime and . If is connected, then diam and gr. Furthermore, is a Hamiltonian graph if is a prime number and .
Algorithm for Constructing Total Graph of Commutative Ring Meinawati, Rima; Kurniawan, Vika Yugi; Kurdhi, Nughthoh Arfawi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19850

Abstract

Let R be a commutative ring. The total graph of R, denoted by TΓ(R) is a graph whose vertices are all elements of the ring R and every i,j∈R with i≠j, then i and j vertices are connected by edges if and only if i+j∈Z(R), where Z(R) is the set of zero-divisors in R with 0∈Z(R). Python programming is code that is easy to learn, read, understand, and helpful in explaining problems regarding graphs and algebra. In this paper, we determine an algorithm to construct the total graph of ring Z_n using Python. The research methods in this paper is a literature studies. The results generated by the algorithm can be utilized to observe the characteristic patterns displayed by the graph. Based on the algorithm’s constructed graph pattern, several properties of TΓ(Z_n ) can be inferred. For instance, if n is a prime number, then TΓ(Z_n ) is a disconnected graph. On the other hand, if n is a prime number and n≥3, then TΓ(Z_2n ) and TΓ(Z_4n ) is a connected graph, regular graph, Hamiltonian graph, and has a girth gr(TΓ(〖Z〗_n ))=3. In this paper we creating an algorithm to construct total graphs from commutative rings streamlines the construction process, enhances accessibility and utilization of total graphs, and supports parameter variation exploration and application in problem-solving. 
MENINGKATKAN KUALITAS KARYA ILMIAH SISWA SMA TRENSAINS MUHAMMADIYAH SRAGEN MELALUI PELATIHAN PERANGKAT LUNAK MATHEMATICA Kurniawan, Vika Yugi; Sutrima, Sutrima; Siswanto, Siswanto; Wibowo, Supriyadi; Wiyono, Santoso Budi
JURNAL PENGABDIAN KEPADA MASYARAKAT Vol. 29 No. 4 (2023): OKTOBER-DESEMBER
Publisher : Universitas Negeri Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24114/jpkm.v29i4.50513

Abstract

Karya ilmiah adalah hasil penelitian yang disajikan dalam bentuk tertulis dan disusun secara sistematis berdasarkan kaidah ilmiah yang berlaku. Dunia akademik seperti sekolah dan perguruan tinggi adalah tempat yang sangat potensial untuk menghasilkan karya ilmiah. Beberapa sekolah menengah tingkat atas atau SMA saat ini sudah mulai memasukkan pembelajaran menulis karya ilmiah di dalam kurikulum pendidikannya. Salah satu sekolah yang sudah melakukannya adalah SMA Trensains Muhammadiyah Sragen. Trensains mengambil kekhususan pada pemahaman ilmu agama, sains kealaman dan interaksinya terbukti dengan adanya beberapa program dan fasilitas yang cukup lengkap dan memadai untuk melakukan riset. Akan tetapi, banyak siswa yang masih mengalami kesulitan dalam menuangkan ide ke dalam tulisan karya, menemukan literatur sebagai bahan kajian, serta lemahnya kemampuan siswa dalam pengolahan data penelitian. Sebagai bentuk kepedulian kepada masyarakat sekaligus menjalankan salah satu dari Tri Dharma Perguruan Tinggi, maka tim pengabdi dari Riset Grup Pure Mathematics & Application Prodi Matematika FMIPA UNS melaksanakan kegiatan pengabdian kepada masyarakat dengan SMA Trensains Muhammadiyah Sragen. Kegiatan ini dilaksanakan dalam bentuk pelatihan perangkat lunak Mathematica kepada guru dan siswa. Dengan diselenggarakannya pelatihan ini diharapkan siswa dan guru dapat menggunakan perangkat lunak Mathematica untuk membantu melakukan riset dan penulisan karya ilmiah yang ada di SMA Trensains Muhammadiyah Sragen.
Syarat Regularitas dan Eulerian Graf Unit dari Ring Z_n Kurniawan, Vika Yugi; Nisa, Lailatul Chairul
KUBIK Vol 9 No 1 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i1.33693

Abstract

Let be a ring of integers modulo and denote the set of all unit elements of the ring. The unit graph of which is denoted by is a simple graph, where the vertices of are all elements of, where two different vertices and are connected by an edge if and only if is the unit of. In this article, we will examine the properties of the unit graph of the ring. The results of this study show that is an Euler graph if where is even, and is a regular graph if is even.
Co-Authors Ashidiqi, Muhammad Rofi' Diari Indriati Ekasiwi, Chessa Fanny Ika Nur Fitriani Mariiaa, Haniiam Meinawati, Rima Muhammad Bilal Nisa, Lailatul Chairul Nughthoh Arfawi Kurdhi, Nughthoh Arfawi Purboutomo, Bayu Putranto Hadi Utomo PUTRI WULANDARI Putri, Oktaviana Putri, Zakia Nur Ramadhani Rachmawati, Zahra Febrilia S Siswanto Santoso Budi Wiyono Septiany, Ade Safira Setiyowati, Ririn Siswanto Siswanto Siswanto Supriyadi Wibowo Sutrima Sutrima Sutrima, S Sutrima, Sutrima Sutrima Wibowo, Supriyadi Wibowo