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Jambura Journal of Mathematics

jjom
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Published by Universitas Negeri Gorontalo

ISSN : 26545616 EISSN : 26561344 DOI : https://doi.org/10.34312/jjom

Core Subject : Education,

Mathematics

Jambura Journal of Mathematics (JJoM) is a peer-reviewed journal published by Department of Mathematics, State University of Gorontalo. This journal is available in print and online and highly respects the publication ethic and avoids any type of plagiarism. JJoM is intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. The scope of the articles published in this journal deal with a broad range of topics, including: Mathematics; Applied Mathematics; Statistics; Applied Statistics.

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Articles 99 Documents

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Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk Auliya Fithry; I Wayan Mangku; I Gusti Putu Purnaba
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Compound cyclic Poisson process have the mean and variance functions. The objective of this paper is to construct confidence intervals for respectively the mean and variance functions of a compound cyclic Poisson process with significance level 0alpha1 and to do a simulation study to observe the probabilities that parameters are contained in the confidence intervals. We do not assume any parametric form for the intensity function except that it is periodic. We consider in the observed there is only one realization of the cyclic Poisson process in a bounded interval. The main results are two theory about confidence intervals for parameters. The simulation shows that the probability values of the observed parameters contained in the confidence intervals are in accordance with the theory.

Hasil Kali Matriks (Mod 2) pada Graf Roda, Graf Pertemanan dan Graf Bunga Fransiskus Fran; Novita Indah Saputri; Mariatul Kiftiah
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKPada artikel ini dibahas sifat-sifat hasil kali matriks (mod 2) terkait graf roda, graf pertemanan, dan graf bunga yang grafikal. Beberapa hasil yang diperoleh, A(Wn)A(Wn)(Mod 2) dan A(Wn)A(Sn)(Mod 2) grafikal apabila n=2k+1 dengan Sn merupakan graf bintang. Selanjutnya, diperoleh A(Wn)A(Go)(mod 2) dan A(Wn)A(G0)(mod 2) grafikal untuk semua n=3 dengan G0 adalah subgraf dari Wn dengan degG0v0=0, degG0vl=degWnvl, untuk 1= l = n. Hasil kali matriks (mod 2) yang grafikal juga diperoleh untuk graf pertemanan dan graf bunga dengan komplemen dan subgrafnya masing- masing. Hasil lebih umum diperoleh untuk kondisi sehingga A(G)A(G)(mod 2) grafikal. ABSTRACTIn this paper, we discussed the properties of the wheel, flower and friendship graphs for which the matrix product under modulo 2 was graphical. Let Sn be a star graph and G0 be a subgraph of Wn where degG0v0=0, degG0vl=degWnvl, for 1= l = n. We proved the matrix product A(Wn)A(Wo)(mod 2) and A(Wn)A(Sn)(Mod 2) was graphical for n=2k+1 and the matrix product A(Wn)A(Go)(mod 2) and A(Wn)A(G0)(mod 2) was graphical for all n=3. For the next, a graphical matrix product (mod 2) was also obtained for the friendship graph and the flower graph with its complement and subgraph, respectively. As more general results were obtained for conditions such that A(G)A(G)(mod 2) was graphical.

Graceful Labeling and Skolem Graceful Labeling on the U-star Graph and It’s Application in Cryptography Meliana Pasaribu; Yundari Yundari; Muhammad Ilyas
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Graceful Labeling on graph G=(V, E) is an injective function f from the set of the vertex V(G) to the set of numbers {0,1,2,...,|E(G)|} which induces bijective function f from the set of edges E(G) to the set of numbers {1,2,...,|E(G)|} such that for each edge uv e E(G) with u,v e V(G) in effect f(uv)=|f(u)-f(v)|. Meanwhile, the Skolem graceful labeling is a modification of the Graceful labeling. The graph has graceful labeling or Skolem graceful labeling is called graceful graph or Skolem graceful labeling graph. The graph used in this study is the U-star graph, which is denoted by U(Sn). The purpose of this research is to determine the pattern of the graceful labeling and Skolem graceful labeling on graph U(Sn) apply it to cryptography polyalphabetic cipher. The research begins by forming a graph U(Sn) and they are labeling it with graceful labeling and Skolem graceful labeling. Then, the labeling results are applied to the cryptographic polyalphabetic cipher. In this study, it is found that the U(Sn) graph is a graceful graph and a Skolem graceful graph, and the labeling pattern is obtained. Besides, the labeling results on a graph it U(Sn) can be used to form a table U(Sn) polyalphabetic cipher. The table is used as a key to encrypt messages.

Assessing Forecasting Performance of Daily Mean Temperature at 1st and 2nd Perak Station, Surabaya Using ARIMA and VARIMA Model with Outlier Detection Taly Purwa; Barbara Ngwarati
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Air temperature is an important data for several sectors. The demand of fast, exact and accurate forecast on temperature data is getting extremely important since it is useful for planning of several important sectors. In order to forecast mean daily temperature data at 1st and 2nd Perak BMKG Station in Surabaya, this study used the univariate method, ARIMA model and multivariate method, VARIMA model with outlier detection. The best ARIMA model was selected using in-sample criteria, i.e. AIC and BIC. While for VAR model, the minimum information criterion namely AICc value was considered. The RMSE values of several forecasting horizons of out-sample data showed that the overall best model for mean daily temperature at 1st and 2nd Perak Station was the multivariate model, i.e. VARX (10,1) with four outliers incorporated in the model, indicated that it was necessary to consider the temperature from the nearest stations to improve the forecasting performance. This study recommends performing the overall best model only for short term forecasting, i.e. two weeks at maximum. By using the one week-step ahead and one day-step ahead forecasting scheme, the forecasting performance is significantly improved compared to default the k-step ahead forecasting scheme.

Studi Longitudinal Pada Analisis Data Gula Darah Pasien Diabetes melalui Principal Component Analysis Anna Islamiyati; Sitti Sahriman; Sakinah Oktoni
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Multicollinearity is a relationship or correlation between predictor variables. Multicollinearity can also occur in longitudinal data, which is a combination of cross-section data and time-series data. The impact of multicollinearity causes the influence of the predictor variable on the response variable to be insignificant, the least-squares estimator, and the error to be sensitive to changes in the data. Therefore, the procedure to overcome multicollinearity uses the principal component analysis method. This study aims to model PCA longitudinal data regression with a fixed-effect model that is applied to blood sugar data of diabetic patients with a time span of January 2019 to July 2019 at Ibnu Sina Hospital Makassar City. The results of this study indicate that there are two main components formed from PCA longitudinal data regression modelling with a fixed-effect model. Obtained variable values are systolic blood pressure of -0.007, diastolic blood pressure of -0,016, the body temperature of -0.098, and platelets of 0.005 which affect blood sugar in patients with diabetes.

Using k-Means and Self Organizing Maps in Clustering Air Pollution Distribution in Makassar City, Indonesia Suwardi Annas; Uca Uca; Irwan Irwan; Rahmat Hesha Safei; Zulkifli Rais
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Air pollution is an important environmental problem for specific areas, including Makassar City, Indonesia. The increase should be monitored and evaluated, especially in urban areas that are dense with vehicles and factories. This is a challenge for local governments in urban planning and policy-making to fulfill the information about the impact of air pollution. The clustering of starting points for the distribution areas can ease the government to determine policies and prevent the impact. The k-Means initial clustering method was used while the Self-Organizing Maps (SOM) visualized the clustering results. Furthermore, the Geographic Information System (GIS) visualized the results of regional clustering on a map of Makassar City. The air quality parameters used are Suspended Particles (TSP), Sulfur Dioxide (SO2), Nitrogen Dioxide (NO2), Carbon Monoxide (CO), Surface Ozone (O3), and Lead (Pb) which are measured during the day and at night. The results showed that the air contains more CO, and at night, the levels are reduced in some areas. Therefore, the density of traffic, industry and construction work contributes significantly to the spread of CO. Air conditions vary, such as high CO levels during the day and TSP at night. Also, there is a phenomenon at night that a group does not have SO2 and O3 simultaneously. The results also show that the integration of k-Means and SOM for regional clustering can be appropriately mapped through GIS visualization.

Ruang Fase Tereduksi Grup Lie Aff (1) Edi Kurniadi
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKDalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari melalui orbit coadjoint buka di titik tertentu pada ruang dual dari aljabar Lie . Aksi dari grup Lie pada ruang dual menggunakan representasi coadjoint. Hasil yang diperoleh adalah ruang Fase tereduksi tiada lain adalah orbit coadjoint-nya yang buka di ruang dual . Selanjutnya, ditunjukkan pula bahwa grup Lie affine tepat mempunyai dua buah orbit coadjoint buka. Hasil yang diperoleh dalam penelitian ini dapat diperluas untuk kasus grup Lie affine berdimensi dan untuk kasus grup Lie lainnya.ABSTRACTIn this paper, we study a reduced phase space for a Lie group, particularly for the 2-dimensional affine Lie group which is denoted by Aff (1). The work aims to identify the reduced phase space for Aff (1) by open coadjoint orbits at certain points in the dual space aff(1)* of the Lie algebra aff(1). The group action of Aff(1) on the dual space aff(1)* is considered using coadjoint representation. We obtained that the reduced phase space for the affine Lie group Aff(1) is nothing but its open coadjoint orbits. Furthermore, we show that the affine Lie group Aff (1) exactly has two open coadjoint orbits in aff(1)*. Our result can be generalized for the n(n+1) dimensional affine Lie group Aff(n) and for another Lie group.

Penghitungan Premi Asuransi Kendaraan Bermotor Menggunakan Generalized Linear Models dengan Distribusi Tweedie Tri Andika Julia Putra; Donny Citra Lesmana; I Gusti Putu Purnaba
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKSeorang aktuaris mempunyai tugas penting dalam menentukan harga premi yang sesuai untuk setiap nasabah dengan risiko dan karakteristik yang berbeda. Banyak variabel yang dapat mempengaruhi harga premi. Oleh karena itu, aktuaris harus mengetahui variabel-variabel yang berpengaruh signifikan terhadap premi. Tujuan dari penelitian ini adalah untuk menentukan variabel yang dapat mempengaruhi besaran premi murni menggunakan distribusi campuran dalam menentukan besarnya premi melalui Generalized Linear Models (GLM) serta menentukan model harga premi yang sesuai berdasarkan variabel-variabel yang mempengaruhinya. Salah satu analisis statistik yang dapat digunakan untuk memodelkan premi asuransi adalah Generalized Linear Models. GLM merupakan perluasan dari model regresi klasik yang dapat mengakomodasi fleksibilitas untuk menggunakan beberapa distribusi data tetapi terbatas pada distribusi keluarga eksponensial. Dalam model GLM, premi diperoleh dengan mengalikan nilai ekspektasi bersyarat dari frekuensi klaim dan biaya klaim. Berdasarkan penelitian yang telah dilakukan diketahui bahwa frekuensi klaim dan besarnya klaim mengikuti distribusi Tweedie. Dari kedua model tersebut diketahui bahwa variabel yang mempengaruhi premi murni adalah jumlah anak, pendapatan per bulan, status pernikahan, pendidikan, pekerjaan, penggunaan kendaraan, besarnya bluebook yang dibayarkan, dan jenis kendaraan nasabah. Hal ini menunjukkan bahwa model GLM merupakan model yang representatif dan berguna bagi perusahaan asuransi. ABSTRACTIt is an important task for an actuary in determining the appropriate premium price for each customer with different risks and characteristics. Many variables can affect the premium price. Therefore, actuaries must determine the variables that significantly affect the premium. The purpose of this study is to determine the variables that can affect the amount of pure premium using a mixed distribution in determining the amount of premium through Generalized Linear Models (GLM) and determine the appropriate premium price model based on the variables that influence it. One of the statistical analyzes that can be used to model insurance premiums is the Generalized Linear Models. GLM is an extension of the classic regression model that can accommodate the flexibility of its users to use multiple data distributions but is limited to the exponential family distribution. In the GLM model, the premium is obtained by multiplying the conditional expected value of the frequency of claims and the cost of claims. Based on the research that has been done, it is known that the frequency of claims and the size of claims follow the Tweedie distribution. From the two models, it is known that the variables affecting the pure premium are the number of children, monthly income, marital status, education, occupation, vehicle use, the number of bluebooks paid, and the type of vehicle from the customer. This shows that the GLM model is a representative and useful model for the insurance company business.

Penerapan Peta Kendali Neutrosophic Exponentially Weighted Moving Average (NEWMA) X dalam Monitoring Rata-Rata Proses Ketebalan Kaca Wibawati Wibawati; Widya Amalia Rahma; Muhammad Ahsan; Wilda Melia Udiatami
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

In the industrial sector, the measurement results of a quality characteristic often involve an uncertainty interval (interval indeterminacy). This causes the classical control chart to be less suitable for monitoring quality. Currently, a control chart with a neutrosophic approach has been developed. The neutrosophic control chart was developed based on the concept of neutrosophic numbers with control charts. One of the control charts that have been developed to monitor the mean process is the Neutrosophic Exponentially Weighted Moving Average (NEWMA) X control chart. This control chart is a combination of neutrosophic with classical EWMA control chart. The neutrosophic control chart consists of two control charts, namely lower and upper, each of which consists of upper and lower control limits. Therefore, NEWMA X is more sensitive to detect out-of-control observations. In this research, the NEWMA X control chart will be used to monitor the average process of the thickness of the panasap dark grey 5mm glass produced by a glass industry. Through the analysis in this research, it was found that by using weighting λN [0, 10; 0, 10] and constant value kN [2, 565; 2, 675], the average process of the thickness of panasap dark grey 5mm glass has not beet controlled statistically because 21 observations were identified that were outside the control limits (out of control). When compared with the classical EWMA control chart with the same weighting λ, 17 observations were detected out of control. This proves that the NEWMA X control chart is more sensitive in detecting observations that are out of control because the determination of the in-control state is based on two values, lower and upper, both at the lower and upper control limits.

Complexity of a Discrete-Time Predator-Prey Model Involving Prey Refuge Proportional to Predator P. K. Santra; Hasan S. Panigoro; G. S. Mahapatra
Jambura Journal of Mathematics Vol 4, No 1: January 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.

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Home Page

OAI Link

Editorial Team

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Contact Name Resmawan

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Phone +6285255230451

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Editorial Address Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

Location Kota gorontalo, Gorontalo INDONESIA

Abstract

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Contact Name
Resmawan

Contact Email
resmawan@ung.ac.id

Phone
+6285255230451

Journal Mail Official
info.jjom@ung.ac.d

Editorial Address
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia

Location
Kota gorontalo,

Gorontalo

INDONESIA