Articles
<![CDATA[Ekivalensi Ideal Hampir Prima dan Ideal Prima pada Bilangan Bulat Gauss ]]>
<![CDATA[Fariz Maulana]]>;
<![CDATA[I Gede Adhitya Wisnu Wardhana]]>;
<![CDATA[Ni Wayan Switrayni]]>
<![CDATA[ Eigen Mathematics Journal Vol. 2 No. 1 Juni 2019 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v1i1.29
<![CDATA[Kriptografi adalah salah satu cabang ilmu matematika yang banyak digunakan pada sistem keamanan digital. Kriptografi itu sendiri berkaitan dengan bilangan bulat dan sifat-sifatnya, terutama bilangan prima. Lebih spesifik, beberapa algoritma penting seperti RSA, sangat bergantung pada faktorisasi prima dari bilangan bulat. Abstraksi bilangan prima diperkenalkan oleh Dedekind pada tahun 1871, dikenal dengan nama ideal prima. Ideal prima diperumum oleh Bhatwadekar pada tahun 2009 dan dinamakan ideal hampir prima. Paper ini akan membuktikan bahwa ideal hampir prima dan ideal prima di bilangan bulat Gasuss adalah ekivalen]]>
<![CDATA[Analisis Masalah Heteroskedastisitas Menggunakan Generalized Least Square dalam Analisis Regresi ]]>
<![CDATA[Aditya Setyawan R]]>;
<![CDATA[Mustika Hadijati]]>;
<![CDATA[Ni Wayan Switrayni]]>
<![CDATA[ Eigen Mathematics Journal Vol. 2 No. 2 Desember 2019 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v1i2.43
<![CDATA[Regression analysis is one statistical method that allows users to analyze the influence of one or more independent variables (X) on a dependent variable (Y).The most commonly used method for estimating linear regression parameters is Ordinary Least Square (OLS). But in reality, there is often a problem with heteroscedasticity, namely the variance of the error is not constant or variable for all values of the independent variable X. This results in the OLS method being less effective. To overcome this, a parameter estimation method can be used by adding weight to each parameter, namely the Generalized Least Square (GLS) method. This study aims to examine the use of the GLS method in overcoming heteroscedasticity in regression analysis and examine the comparison of estimation results using the OLS method with the GLS method in the case of heteroscedasticity.The results show that the GLS method was able to maintain the nature of the estimator that is not biased and consistent and able to overcome the problem of heteroscedasticity, so that the GLS method is more effective than the OLS method.]]>
<![CDATA[Banyak Pohon Pembangun pada Graf Barbell ]]>
<![CDATA[Muklas Maulana]]>;
<![CDATA[Ni Wayan Switrayni]]>
<![CDATA[ Eigen Mathematics Journal Vol. 2 No. 2 Desember 2019 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v1i2.46
<![CDATA[Teori graf merupakan salah satu bidang ilmu yang memiliki berbagai kegunaan dalam kehidupan sehari-hari. Salah satu topik yang dibahas dalam teori graf yaitu terkait banyak pohon pembangun (Spanning Trees). Pohon (Tree) dalam teori graf merupakan suatu graf terhubung yang tidak memuat cycle. Kemudian banyak pohon pembangun (spanning trees) dari suatu graf terhubung didefinisikan sebagai banyaknya pohon yang dapat dibentuk dari suatu graf yang melewati semua simpul pada graf tersebut. Pada penelitian ini, akan dibahas terkait spanning trees atau pohon pembangun dari graf barbell. Graf Barbell merupakan graf yang diperoleh dengan menghubungkan buah graf lengkap oleh sebuah bridge. Berdasarkan hasil penelitian dari artikel ini diperoleh suatu fakta bahwa graf barbell memiliki spanning trees sebanyak . Selanjutnya pada artikel ini juga akan dibahas terkait beberapa sifat dari spanning trees dan graf barbell.]]>
<![CDATA[Sifat-Sifat Graf Pembagi Nol pada Gelanggang Polinom Kuosien (Z_p [x])/〈x^(n+1) 〉 ×(Z_q [x])/〈x^(n+1) 〉 ]]>
<![CDATA[Dais Alifian Fatahillah]]>;
<![CDATA[Ni Wayan Switrayni]]>
<![CDATA[ Eigen Mathematics Journal Vol. 3 No. 1 Juni 2020 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v3i1.51
<![CDATA[Zero-divisor graph is an undirectedgraphwhose vertices are zero-divisors of a commutative ring and edges defined as if and only if .Wicaksono (2013) gave some characteristics of graph zero-divisor in the modulary integer ring. This research aims to represent the zero-divisor elements of the polynomial kuosien ring where are prime numbers and into a graph called the zero-divisor graph The method used in this research is a deduktive method. The result shows that the zero divisor graph obtained from polynomial kuosien ring is complete bipartit graph with some characteristics related to its girth, ecccentricity, radius and diameter.]]>
<![CDATA[Analisis Rotasi Ortogonal pada Teknik Analisis Faktor Menggunakan Metode Procrustes ]]>
<![CDATA[Himayati Himayati]]>;
<![CDATA[Ni Wayan Switrayni]]>;
<![CDATA[Desy Komalasari]]>;
<![CDATA[Nurul Fitriyani]]>
<![CDATA[ Eigen Mathematics Journal Vol. 3 No. 1 Juni 2020 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v3i1.66
<![CDATA[Factor analysis is a multivariate statistical method that tries to explain the relationship between a number of independent variables by grouping these variables into factors. With this grouping, the existing variables will be easier to interpret. In increasing the power of factor interpretation, a matrix loading factor transformation must be performed. The transformation can be done by choosing the method that is in orthogonal rotation, the varimax or quartimax or equamax method. In order to find out which rotation techniques is the most appropriate, the minimum square distance values () generated from the procrustes method used. In this study three data were used from the results of the questionnaire, for data I obtain the value of the minimum distance squared with a varimax rotation that is with ; for data II obtain the value of the minimum distance squared with a quartimax rotation that is with ; for data III obtain the value of the minimum distance squared with a varimax rotation that is with .]]>
<![CDATA[Modifikasi Algoritma Kriptografi Hill Chiper dengan Matriks Generalisasi Bilanga Fibonacci dalam Penyandian Pesan ]]>
<![CDATA[Husni Fitroti]]>;
<![CDATA[Mamika Ujianita Romdhini]]>;
<![CDATA[Ni Wayan Switrayni]]>
<![CDATA[ Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v4i2.107
<![CDATA[Hill Cipher algorithm is a technique of message encoding by implementing a matrix of order as a key matrix. The key matrix is a matrix that has a multiplicative inverse. The security of message is measured by the number of processes in encoding. The more processes in encoding the longer time it takes. Consequently, the massage will be more secure. The purpose of this research is to modify the Hill Cipher algorithm by using generalized Fibonacci matrix whose degree-p and rank-n . This research showed that for any non-negative integer p and positive integer n, matrix can be used as a key matrix in Hill Cipher algorithm. The modification of the Hill Cipher algorithm has been done by modifying the former key by making the degree and rank of as the key used in the encryption and decryption process of data (message).]]>
<![CDATA[The Power Graph of a Dihedral Group ]]>
<![CDATA[Evi Yunartika Asmarani]]>;
<![CDATA[Abdul Gazir Syarifudin]]>;
<![CDATA[I Gede Adhitya Wisnu Wardhana]]>;
<![CDATA[Ni Wayan Switrayni]]>
<![CDATA[ Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v4i2.117
<![CDATA[Graph theory is one of the topics in mathematics that is quite interesting to study because it is applicable and can be combined with other mathematical topics such as group theory. The combination of graph theory and group theory is that graphs can be used to represent a group. An example of a graph is a power graph. A power graph of the group is defined as a graph whose vertex set is all elements of and two distinct vertices and are connected if and only if or for a positive integer x and y. In this study, the author discusses the power graph of the dihedral group The results obtained from this study are the power graph of the dihedral group where with prime numbers and an natural number is a graph consisting of two non-disjoint subgraphs, namely complete subgraphs and star subgraphs. And we find that its radius and diameter are 1 and 2.]]>
<![CDATA[Prime submodul of an integer over itself ]]>
<![CDATA[Muhammad Rijal Alfian]]>;
<![CDATA[Fariz Maulana]]>;
<![CDATA[Ni Wayan Switrayni]]>;
<![CDATA[Qurratul Aini]]>;
<![CDATA[Dwi Noorma Putri]]>;
<![CDATA[I Gede Adhitya Wisnu Wardhana]]>
<![CDATA[ Eigen Mathematics Journal Vol. 5 No. 1 Juni 2022 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v5i1.132
<![CDATA[One of the sciences used in digital security systems is cryptography. Cryptography is closely related to the integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. One form of abstraction of prime numbers is the prime ideal. Previous studies have proven that an Ideal is said to be a prime ideal on if and only if I is constructed by a prime element. Other studies have also shown how the prime ideal develops. One of them is the research result of Dauns, where the prime ideal form is developed in the form of a prime submodule. A prime submodule is one of the objects in the module, which is an abstraction of prime numbers. Based on these things, it is exciting if the properties of the prime submodule are applied to other module forms, one of which is the integer module.]]>
<![CDATA[Submodul Prima Lemah dan Submodul Hampir Prima Pada Z‐modul M_2x2 (Z_9) ]]>
<![CDATA[Wardhana, I Gede Adhitya Wisnu]]>;
<![CDATA[Switrayni, Ni Wayan]]>;
<![CDATA[Aini, Qurratul]]>
<![CDATA[ Eigen Mathematics Journal Vol 1 No 1: Vol 1 No 1 Juni 2018 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v1i1.6
<![CDATA[Prime submodule is the abstraction to module theory of prime ideal in ring theory. A proper submodule N of an R-module M is called prime submodule if for all r in R and m in M such that rm in N implies r in (N:M) or m in N. Prime submodule also generalized into weakly prime submodule and almost prime submodule. This study deal with particular cases of both of them in Z-module M_2x2(Z_9), the three submodules are equivalent in case of non-zero submodule.]]>
<![CDATA[Analisis Keberhinggaan Matriks Representasi atas Grup Berhingga ]]>
<![CDATA[Taufan, Muhammad]]>;
<![CDATA[Romdhini, Mamika Ujianita]]>;
<![CDATA[Switrayni, Ni Wayan]]>
<![CDATA[ Eigen Mathematics Journal Vol 1 No 1: Vol 1 No 1 Juni 2018 ]]>
Publisher : <![CDATA[University of Mataram ]]>
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DOI: 10.29303/emj.v1i1.10
<![CDATA[Representation of a finite group G over generator linear non singular mxm matrix with entries of field K defined by group homomorphismA : G → GLm(K)Basically, the non singular mxm matrix A(x) which representing the finite group G divided into two, that are the unitary matrix and non unitary matrix . If A(x) is a non unitary matrix, then there exist a unitary matrix which similar to A(x). This research deals to analyze the numbers of one example of a unitary matrix representation over arbitrary finite group G with order n that is permutation matrix, and the number of unitary matrix which is similar to real non unitary matrix representation of arbitrary finite group G order 2. The results showed the numbers of permutation matrix representation is n! and unitary matrix which is similar to non unitary matrix representation is 2.]]>
