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All Journal Jurnal Matematika JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Amir Kamal Amir
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Mathematics

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Partition Dimension of Dutch Windmill Graph: Dimensi Partisi Graf Kincir Angin Belanda untuk siklus orde besar Hasmawati Hasmawati; Budi Nurwahyu; Ahmad Syukur Daming; Amir Kamal Amir
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 3 (2021): May, 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v17i3.13596

Abstract

Let be a connected graph G and -partition of end . The coordinat to is definition . If every twovertex is distinct applies, then is a called partition of . The minimum k for which k-resolving partition of is the partition dimension and denoted with . In this paper, we investigates the partition dimensionfor a large Dutch windmill graph for and . We show that if for some, forany.
Beberapa Sifat dari Modul dan Gelanggang dengan Dimensi Goldie Berhingga (Suatu Kajian Pustaka) Amir Kamal Amir
Jurnal Matematika Vol 1 No 2 (2011)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2011.v01.i02.p17

Abstract

Suatu modul M dikatakan mempunyai demensi Goldie berhingga jika modul tersebuttidak memuat suatu jumlahan langsung dari takberhingga banyak submodul-submodultaknol. Sedangkan, suatu gelanggang R dikatakan mempunyai dimensi Goldie kanan berhinggajika gelanggang tersebut mempunyai dimensi Goldie berhingga sebagai suatu modul kanan.Tulisan ini akan menyajikan beberapa sifat dari modul dan gelanggang yang mempunyai dimensiGoldie berhingga. Sifat-sifat tersebut bukanlah merupakan sifat-sifat yang baru. Namundemikian, tulisan ini akan menyajikan pembuktian dari sifat-sifat tersebut dengan cara yanglebih terperinci dan lengkap sehingga lebih mudah dimengerti, terutama bagi pembaca pemuladalam bidang aljabar.
BEBERAPA SIFAT IDEAL GELANGGANG POLINOM MIRING: SUATU KAJIAN PUSTAKA AMIR KAMAL AMIR
Jurnal Matematika Vol 1 No 1 (2010)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2010.v01.i01.p09

Abstract

Let R be a ring with identity 1 and s be an endomorphism of R and d be a left s - derivation . Theskew polynomial ring over R in an indeterminate x is: R[x;s ,d ] = { f (x) = anxn +L+ a0 | ai Î R}with xa =s (a)x +d (a) The aim of this research is to investigate the ideals in the above skewpolynomial ring in case of d = 0 . Precisely, we will investigate the following: (1) the ideal of skewpolynomial ring D[x;s ] ; (2) the ideal prim of skew polynomial ring K[x;s ] ; and (3) the s - primideal of skew polynomial ring D[x;s ] .
Dimensi Metrik dari Hasil Operasi Shackle Graf Siklus C_3 St. Munieroh Fachrunnisa; Hasmawati Hasmawati; Amir Kamal Amir
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 2 (2023): JANUARY 2023
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i2.22957

Abstract

Let G be a connected graph and W be a ordered vertices subset on a connected graph . The set W is called resolving set for G if every vertex on graph G has distinct representation of W. A resolving set containing a minimum number of vertices is called resolving set minimum or basis for G and the cardinality of resolving set is the metric dimension on graph G, denoted by dim(G). In the thesis discusses about metric dimensions of shackle operation C3 cycle graph, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 for k>=2 . To proof this results, we was used mathematical induction method.
Konstruksi Gelanggang Armendariz menggunakan Gelanggang Matriks Segitiga Formal Aidah Nabilah Anwar; Amir Kamal Amir; Nurdin Hinding
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 2 (2023): JANUARY 2023
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i2.23263

Abstract

Trinion and Quaternion numbers are one of the hypercomplex numbers which is an extensions of the complex number. From Trinion and Quaternion numbers, a bimodule can be formed which is an ordered pair of Trinion and Quaternion. Furthermore, Trinion number, Quaternion number, and their bimodule can be formed into a  Formal Triangle Matrix. The Formal Triangle Matrix is better known as the Upper Triangle Matrix. Since Trinion number, Quaternion number and their bimodule are rings, then the Formal Triangle Matrix can be called as the Formal Triangular Matrix Ring. The purpose of this study is to construct the Armendariz Ring using the Formal Triangular Matrix Ring. The obtained results will show that the Formal Triangular Matrix Rings are the -Skew Armendariz Ring and the -Skew -Armendariz Ring, where  is a Ring Endomorphism and  is -derivation.
English Language English Language Jeki Saputra; Amir Kamal Amir; Andi Muhammad Anwar
Jurnal Matematika, Statistika dan Komputasi Vol. 19 No. 2 (2023): JANUARY 2023
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v19i2.24141

Abstract

The Sylvester-Kac matrix is also known as the Clement matrix The Sylvester-Kac matrix is widely used and applied both in processing, graphs and other fields. The Sylvester-Kac matrix developed in the paper is the T-Sequence-Sylvester-Kac matrix The calculation of the determinant, and inverse has always been a challenge for mathematicians to find. In this paper will be given the formulation of determinant, and inverse of the T-Sequence-Sylvester-Kac matrix
Co-Authors Afriani Afriani Ahmad Syukur Daming Aidah Nabilah Anwar Andi Muhammad Anwar Budi Nurwahyu Hasmawati Basir Hasmawati Hasmawati Hasmawati Hasmawati Jeki Saputra Nur Erawati Nurdin Hinding Qharnida Khariani St. Munieroh Fachrunnisa