Eigen Mathematics Journal
Not a member yet
116 research outputs found
Sort by
The Intersection Graph of a Dihedral Group
Get PDFThe intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i \cap H_j \neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \gamma(\Gamma_{D_{2n}})=p.
Comparison of Hierarchical and Non-Hierarchical Methods in Clustering Cities in Java Island using the Human Development Index Indicators year 2018
Get PDFThe Human Development Index (HDI) is a composite index to assess the developmental level of life quality in a particular region. In 2018, Java Island, which geographically has the most regencies/ municipalities in Indonesia, achieved human development with “high” status and was followed by all its regencies which have also achieved human development with “high” status. Therefore, research was carried out on how the characteristics inherent in the high HDI have been achieved in regencies on Java Island and grouping them so that it is easy to interpret regencies/ municipalities with homogeneous characteristics. This study used the hierarchical cluster method (single linkage, average linkage, and ward) and non-hierarchical cluster methods (K-Means and FCM). The results show that the best hierarchical cluster method is the average linkage method which forms four clusters where the regencies/ municipalities with the best characteristics (dimensions of education, health, and high purchasing power) are Kepulauan Seribu, Bogor, and 78 other regencies/ municipalities. Then, the best non-hierarchical method is the FCM method which forms two clusters, with a prominent characteristic is those city areas have better characteristics than district areas
Comparison of Fuzzy Time Series Methods and Autoregressive Integrated Moving Average (ARIMA) for Inflation Data
Get PDFThis study compares the Fuzzy Time Series (FTS) method with the Autoregressive Integrated Moving Average (ARIMA) method on time series data. These two methods are often used in predicting future data. Forecasting or time-series data analysis is used to analyze data in the form of time series. In this study, Indonesian inflation data was used to be analyzed in comparing the FTS and ARIMA methods. Inflation is one of the economic indicators used to measure the success of a country's economy. If the inflation rate is low and stable, it will stimulate economic growth. This inflation value is calculated every month where the value can decrease and increase from one period to another. Comparison of the FTS and ARIMA methods is seen in the error value generated by the two methods. A method can be better than other methods if the value of the resulting forecast error is smaller. In this study, Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) were used to see the magnitude of the error value of the two methods on the fives data testing used. The results obtained in this study are the results of Indonesia's inflation forecast for the period January to May 2021 using the FTS method, respectively, at 0.57%, 0.375%, 0.2%, 0.2%, and 0.1125%, while the forecast results using the ARIMA method, respectively. Of 0.3715848%, 0.2362817%, 0.1508295%, 0.1731906%, and 0.2432851% and the results of calculating the size of error using MSE and MAPE indicate that the ARIMA method with the model ARIMA(3,0,0) is better at predicting inflation data in Indonesia with a value of MSE of 0.009 and MAPE of 64.987% compared to the FTS method resulted in MSE values of 0.047 and MAPE of 132.548%.
Some Special Graphs of Quaternion Group
Get PDFResearch on an algebraic structure represented in graph theory opens the way for new research in recent years. Several types of new graphs continue to be developed, such as coprime and non-coprime graphs. This article will represent the quaternion group in several graphs, such as coprime graphs, non-coprime graphs, commuting graphs, non-commuting graphs, and identity graphs. We obtained several theorems about unique graphs. One of the results is that non-coprime graphs from the quaternion group are complete and regular graphs
Modifikasi Algoritma Kriptografi Hill Chiper dengan Matriks Generalisasi Bilanga Fibonacci dalam Penyandian Pesan
No full textHill 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).Hill Cipher cryptographic algorithm is a technique of massage encoding by implementing a matrix of order n*n as a key matrix. The key matrix is a matrix that has a multiplicative inverse. The security of messages measured by the number of processes in encoding. More and more processes in the encoding will lead to the longer time required. So that the massage will be safer. The purpose of this research is to modify the Hill Cipher cryptographic algorithm by using the matrix of Fibonacci numbers generalization whose degree-p and rank-n Qn,p. The Matrix Qn,p is a matrix of order(p+1)*(p+1) and it will be the key matrix in the Hill Cipher cryptographic algorithm.This research showed that any matrix of Fibonacci number generalization Qn,p with p and n are positive integers that be used as a key matrix in the Hill Cipher algorithm. The modification of the Hill Cipher cryptographic algorithm has done with modifying the keys by making the degree (p) and rank (n) of Qn,p as the keys that used in the encryption and decryption process of data (message)
Application of the Floyd Warshall Algorithm in Determining the Shortest Route for Distribution of UD Nadira Cinta Rasa Bread to Praya, Central Lombok
Get PDFOptimizing the shortest route is needed by a company in the process of distributing goods to consumers. This optimization can help companies optimize the mileage and costs from source to destination. In this study, the shortest route method used is the Floyd-Warshall algorithm to determine the shortest route. Floyd-Warshall algorithm can compare all the possible paths in the graph for each side of all vertices it passes with the minimum number. Based on the calculation results of this study, the shortest route was obtained from Mataram as the source and Praya as the destination was 31 km
Panel Data Regression Analysis of Human Development Index in West Nusa Tenggara Province with Fixed Effect Model
Get PDFHumans are the true wealth of the nation. It is appropriate if humans become the main goal in development. Then the United Nations Development Program (UNDP) initiated the Human Development Index (HDI) as an indicator in measuring the progress of human development. Indonesia took part in applying the HDI calculation. Increasing the value of HDI from various provinces in Indonesia continues to be carried out, including in the Province of West Nusa Tenggara. Improving human development is based on an increase in all dimensions of the HDI itself. West Nusa Tenggara Province consists of 10 regencies/ cities. With different geographical, social, and economic backgrounds, the achievement of HDI in each region will vary. The purpose of this study was to determine the model of the HDI in West Nusa Tenggara Province in 2010-2017 using a fixed-effect model, which was used to see the influence of dimensions on the HDI and explain the differences in intercepts in each district/ city in West Nusa Tenggara Province. Based on the research conducted, a fixed effect panel data model on HDI was obtained for each district/ city in NTB in 2010-2017. From the HDI model obtained, it is known that the slope coefficient is constant, but the intercept varies throughout the district/ city. The slope coefficient value shows the magnitude of the influence of life expectancy, school duration, the average length of schooling, and expenditure per capita adjusted to the HDI of each district/ city
Penerapan Model Vector Autoregressive Integrate Moving Average dalam Peramalan Laju Inflasi dan Suku Bunga di Indonesia
Get PDFThe inflation and interest rates in Indonesia have a significant impact on the country's economic development. Indonesian inflation and interest rates data are multivariate time series data that show activity over a certain period of time. Vector Autoregressive Integrated Moving Average (VARIMA) is a method for analyzing multivariate time series data. This method is a simultaneous equation modeling that has several endogenous variables simultaneously. This study aimed to model the inflation and interest rates data, from January 2009 to December 2016 and predict inflation and interest rates by using VARIMA method. The model obtained was the VARIMA(0,2,2) model, with estimated parameters using the maximum likelihood method. The choice of the VARIMA(0,2,2) model was based on the smallest AIC value of -4,2891, with a MAPE value for the inflation and interest rates forecasting were 6,04% and 1,84%, respectively, which indicates a very good forecast results
Perbandingan Metode Classification and Regression Trees (CART) dengan Naïve Bayes Classification (NBC) dalam Klasifikasi Status Gizi Balita di Kelurahan Pagesangan Barat
Get PDFThis study aims to compare the Classification and Regression Trees (CART) and Naïve Bayes Classification (NBC) methods in classifying the nutritional status of toddlers in West Pagesangan by looking at their accuracy and also knowing the variables that influence the classification of toddler nutritional status. The data used in this study were toddlers who come to the posyandu in May 2019, with predictor variables used namely gender, ages, weight, mother’s employment status, mother’s education level, number of children and parents income. The result showed that Naïve Bayes Classification (NBC) is better in classifying the nutritional status of toddlers in West Pagesangan than Classification and Regression Trees (CART). This can be seen from the accuracy values obtained with three comparisons of training data and testing data. In the comparison of 90% of training data: 10% of testing data, obtained an accuracy value of 90% for NBC and 85% for CART, in the comparison of 80% of training data: 20% of testing data, obtained an accuracy value 0f 82.5% for NBC and 80% for CART, while in comparison 70% traing data : 30% testing data, obtained an accuracy value 72% for NBC and 70%for CART. This study also showed that significant variables the classification of nutritional status of toddlers in West Pagesangan village are age, gender, weight and parents income
Peramalan Indeks Harga Konsumen Kota Mataram Menggunakan Vector Autoregressive Integrated Moving Average
Get PDFPenelitian ini bertujuan untuk meramalkan data Indeks Harga Konsumen (IHK) sub-kelompok padi-padian, umbi-umbian dan hasilnya serta sub-kelompok bumbu-bumbuan di Kota Mataram. Data yang digunakan adalah data tahun 2014 sampai dengan tahun 2017, yang digunakan untuk meramalkan nilai IHK pada tahun 2018. Metode yang digunakan dalam penelitian ini adalah metode Vector Autoregressive Integrated Moving Averageatau disebut VARIMA. Hasil penelitian menunjukkan bahwa model terbaik yang diperoleh adalah model VARIMA (1,1,0) dengan akurasi model untuk IHK padi-padian, umbi-umbian dan hasilnya berdasarkan nilai MAPE sebesar 0,7359% yang menyatakan bahwa hasil peramalan dapat dikategorikan sangat baik, sedangkan akurasi model untuk IHK bumbu-bumbuan berdasarkan nilai MAPE sebesar 10,6736% yang menyatakan bahwa hasil peramalan dapat dikategorikan baik