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Harmanus Batkunde
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Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Unversitas Pattimura Jln. Ir. M. Putuhena, Kampus Unpatti, Poka - Ambon 97233, Provinsi Maluku, Indonesia
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Tensor: Pure and Applied Mathematics Journal
Published by Universitas Pattimura
ISSN : 27230325     EISSN : 27230333     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Tensor: Pure and Applied Mathematics Journal is an international academic open access journal that gains a foothold in the field of mathematics and its applications which is issued twice a year. The focus is to publish original research and review articles on all aspects of both pure and applied Mathematics. It Publishes original research papers of the highest Algebra Analysis Discrete Mathematics Geometry Number Theory Topology Applied Mathematics Computational Mathematics Probability Theory and Statistics
Arjuna Subject : Matematika - Matematika Terapan
Articles 72 Documents
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Some Properties of the Interval Matrix Semiring [0,a] Patty, Dyana; Tapilatu, Stevany; Leleury, Zeth Arthur
Tensor: Pure and Applied Mathematics Journal Vol 5 No 1 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss1pp49-56

Abstract

Suatu himpunan yang dilengkapi operasi penjumlahan dan pergandaan disebut semiring jika adalah monoid komutatif, adalah semigrup dan berlaku sifat distributif pada . Jika diberikan yaitu himpunan semua interval dari dan didefinisikan operasi penjumlahan dan pergandaan interval pada , maka merupakan semiring dan disebut semiring interval. Selanjutnya jika diberikan himpunan matriks yang entri-entrinya adalah koleksi interval dimana dengan dan didefinisikan operasi penjumlahan dan pergandaan matriks interval pada , maka merupakan semiring dan disebut semiring matriks interval. Dalam penelitian ini akan dibahas semiring matriks interval dan akan diperoleh struktur -semiring, -submsemiring dan -ideal semiring matriks interval. Selanjutnya akan diperoleh syarat cukup agar suatu semiring matriks interval merupakan -semiring dan dijelaskan hubungan antara -ideal matriks persegi interval dan -subsemiring matriks persegi interval.
The Modeling of Factors that Influence the Number of Death Cases of Infant and Toddler in Maluku Province using the Bivariate Poisson Regression Method Haumahu, Gabriella; Djamalullail, Syarifah Fitria Amalia; Noya Van Delsen, Marlon Stivo
Tensor: Pure and Applied Mathematics Journal Vol 5 No 1 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss1pp17-26

Abstract

The number of cases of infant mortality and under-five mortality have a significant relationship. Although there are differences in age categories, it can be a measure of quality of life early in life. In this study, a bivariate Poisson regression analysis method is used which uses a pair of count data with Poisson distribution. The number of infant deaths and the number of under-five deaths are the dependent variables, while the percentage of poor people , the percentage of married women under 19 years old , the percentage of low birth weight babies , and the percentage of exclusively breastfed babies are the independent variables. Based on the results of the modeling analysis, model 2 of the bivariate Poisson regression proved to be the best model with the lowest AIC value of 123,8951. The results of the analysis at show that variable has an influence on infant mortality cases, shows that variable has a significant effect on under-five mortality cases and at shows that variable has a significant effect simultaneously on infant and under-five mortality cases in Maluku Province in 2022
Symmetric Functions with Respect to a Point (a,b) and Its Properties that Generalized from Properties of Odd Functions Natasian, Nehemia Trianto; Lesnussa, Yopi Andry; Batkunde, Harmanus
Tensor: Pure and Applied Mathematics Journal Vol 5 No 1 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss1pp9-16

Abstract

The function f: R \to R is said to be an odd function if f (-x) = -f(x) for every x \in R. The graph of an odd function is symmetry with respect to origin, or point (0,0) . The propose of this study is to observe some properties of symmetrical functions which are generalize from some properties of odd functions. Some of the results obtained include a linear combination of two functions symmetrical with respect to the point (a,b) is a functions of symmetrical with respect to the point (a,2b). An integral functions of symmetrical with respect to the point (a,b) on a closed interval [a-c,a+c] is 2bc for any real number c. Moreover product of scalars with functions of symmetrical with respect to the point (a,b) is a functions of symmetrical with respect to the point (a,\alpha b) for every \alpha real numbers. Furthermore the addition n-symmetrical of functions with respect to the point (a,b) is a series of functions of symmetrical with respect to the point (a,nb). he function is said to be an odd function if for every . The graph of an odd function is symmetry with respect to origin, or point . The propose of this study is to observe some properties of symmetrical functions which are generalize from some properties of odd functions. Some of the results obtained include a linear combination of two functions symmetrical with respect to the point is a functions of symmetrical with respect to the point . An integral functions of symmetrical with respect to the point on a closed interval is for any real number . Moreover product of scalars with functions of symmetrical with respect to the point is a functions of symmetrical with respect to the point for every real numbers. Furthermore the addition -symmetrical of functions with respect to the point is a series of functions of symmetrical with respect to the point .
The Digital Image Compression Using Wavelet Daubechies Transform Maitimu, Meldry W; Rumlawang, Francis Y; Tilukay, Meilin I; Batkunde, Harmanus
Tensor: Pure and Applied Mathematics Journal Vol 5 No 1 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss1pp27-32

Abstract

As a form of data representation, the obstacle faced when using digital images is the large volume of data required to represent the image. For that we need a technique that can reduce the volume of data, this thechnique is called compression. In this thesis, a very well-known wavelet transform method is chosen, namely Daubechies D4 wavelet transform, with four coefficients of scaling function, and four coefficients of wavelet function. Then implemented with MATLAB 2021 software as a programming tool to see the effect of quality on the transformed image.
Mapping of the Transportation Sector in Maluku Province Using Biplot Analysis Leleury, Zeth Arthur; Radjabaycolle, Jefri Esna Thomas; ilwaru, Venn Y. I.; Sinay, Lexy Jansen; Wattimena, Abraham Z.
Tensor: Pure and Applied Mathematics Journal Vol 5 No 2 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss2pp57-66

Abstract

The transportation sector is one sector that contributes to economic development. Economic activity will develop if it has good infrastructure and transportation facilities for accessibility. This study aims to map regencies/cities in Maluku province based on the characteristics of the transportation sector. The method used is Biplot analysis. Based on the results of the study, it was found that the results of mapping 11 regencies/cities in Maluku Province if grouped according to the location of the quadrant divided into 2 clusters, namely Cluster 1 consisting of the City Ambon, West Seram Regency, Central Maluku Regency, Buru Regency, Tual City, Southeast Maluku Regency, and Tanimbar Islands Regency. The seven regencies/cities have similar characteristics of the transportation sector in the percentage of villages where public transportation is available with fixed routes, the widest type of land surface is asphalt/concrete, and the road can be passed by four wheels throughout the year. While Cluster 2 consists of Eastern Seram Regency, South Buru Regency, Southwest Maluku Regency, and Aru Islands Regency. The four regencies have similar characteristics of the transportation sector in the percentage of villages based on the availability of land and sea transportation infrastructure, the availability of sea transportation infrastructure only, public transportation is not available or available without a fixed route, the widest type of land surface is in the form of soil or hardened with gravel, the road cannot be passed by four wheels or four wheels can pass but only in the dry season. Meanwhile, based on the Euclidean distance, it can be made more specific into 4 clusters, namely Cluster 1 is Ambon City, Cluster 2 includes West Seram Regency, Central Maluku Regency, Buru Regency, Tual City, Southeast Maluku Regency, and Tanimbar Islands Regency. Meanwhile, Cluster 3 includes Eastern Seram Regency, South Buru Regency, and Southwest Maluku Regency, and Cluster 4 is Aru Islands Regency.
Prediction of Divorce Data in Pamekasan District Based on Comparison of Exponential Smoothing and Moving Average Yudistira, Ira; Romlah, Siti; Yulianto, Tony; faisol, Faisol; Mardianto, M.Fariz Fadillah
Tensor: Pure and Applied Mathematics Journal Vol 5 No 2 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss2pp67-78

Abstract

Divorce is a form of breakdown in domestic or marital relationships which is characterized by separation. Based on the Indonesian Statistics report, the number of divorce cases in Indonesia will reach 516,334 cases in 2022. This number is up 15.31% compared to the previous year of 447,743 cases. East Java is ranked second as the province with the highest divorce cases, namely 102,065 cases throughout 2022. To know the development of divorce in the future, forecasting is needed to determine when an event will occur, an increase in the divorce rate, so that we can prepare what will be done to overcome the spike. the divorce rate. In this research, the methods used to predict the number of divorce cases in Pamekasan Regency are the Exponential Smoothing and Moving Average methods. single exponential smoothing method for both divorce lawsuits and divorce divorces with MAD values ​​= 10.40539 and 15.3366868, MSE = 449.0276211 and 181.0038, MAPE = 22.1859129 and 23.84152 and SE values ​​= 21.57911661 and 13, 70064 with a value of α=0.12 for contested divorce and α=0.26 for talak divorce.
Exploring the Lazy Witness Complex for Efficient Persistent Homology in Large-Scale Data Liza, Mst Zinia Afroz; Al-Imran, Md.; Shiraj, Md. Morshed Bin; Hossain, Tozam; Murshed, Md. Masum; Akhter, Nasima
Tensor: Pure and Applied Mathematics Journal Vol 5 No 2 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss2pp79-92

Abstract

In this paper, topological data analysis (TDA) techniques have been explored, with a focus on the selection of the Witness Complex and Persistent Homology of some nested families of Lazy Witness Complex as approximations for analyzing complex datasets. The Witness Complex was chosen for its efficiency and scalability, as it constructs a simplicial complex using landmark points, reducing computational load compared to methods like the Vietoris-Rips and Čech complexes. This makes it suitable for large, high-dimensional datasets, accurately representing the dataset's intrinsic geometry even with varying data densities. Persistent Homology was then reviewed with the aim of calculating it on some nested families of the Witness Complex. Subsequently, the nested families of the Lazy Witness Complex were introduced mathematically, with an example of the entire construction process for a well-known point cloud dataset. For this purpose, 50 points were generated randomly from a circle, and persistent diagrams of the point cloud data were analyzed to understand and compare the behavior among the approximations of the Witness Complex after choosing 10 landmarks using the Maxmin method. Since the families are nested, the filtration process became faster for each successive family, thus reducing computational complexity. For all three cases , the persistent barcodes indicated the same shape of the dataset. This study may help in choosing the suitable family of the Witness Complex over Persistent Homology to balance computational feasibility with topological accuracy, enabling efficient handling of large datasets while preserving important topological features. This approach allows for extracting meaningful insights from complex data while effectively managing computational resources.
Penyelesaian Unit Commitment Problem (UCP) Menggunakan Algoritma Genetika Whardhana, Aisyah Fadhilah; Pratiwi, Asri Bekti; Winarko, Edi
Tensor: Pure and Applied Mathematics Journal Vol 5 No 2 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss2pp93-104

Abstract

The purpose of this research is to solve the Unit Commitment Problem (UCP), which is a critical task in power system optimization. The UCP involves determining the optimal scheduling of power generating units over a specified time horizon to meet the electricity demand while minimizing costs and satisfying operational constraints. In this study, a Genetic Algorithm (GA) method is proposed to solve the UCP efficiently. GA is inspired by the process of natural selection and evolution and is often used to solve complex optimization problems where traditional methods may be inefficient. The algorithm proceeds through several steps, namely parameters initialization, generating population, modification, calculating fitness function, parent selection, crossover, and mutation. The implementation of GA to solve UCP using C++ includes four different scenarios: a system with 4 units, 5 units, 10 units, and 26 units. The results obtained from the implementation of the GA on the different data sets indicate that the more iterations and the bigger initial population, the smaller the solution in the form of the total cost incurred.
The Total Disjoint Irregularity Strength of a Double and Triple Star Graphs Tilukay, Meilin Imelda; Titawanno, Tasya I.; Leleury, Zeth Arthur; Taihutu, Pranaya Dharia M.; Loves, Luvita
Tensor: Pure and Applied Mathematics Journal Vol 5 No 2 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss2pp105-110

Abstract

Application of The Naïve Bayes Algorithm Method for Classification of Families at Risk of Stunting (Case Study: Waeapo District, Buru Regency) Noya Van Delsen, Marlon Stivo; Laamena, Novita Serly; Rumanama, Siti Adnan
Tensor: Pure and Applied Mathematics Journal Vol 5 No 2 (2024): Tensor: Pure and Applied Mathematics Journal
Publisher : Department of Mathematics, Faculty of Mathematics and Natural Sciences, Pattimura University, Ambon, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/tensorvol5iss2pp111-118

Abstract

Classification is a job of assessing data objects to put them into a certain class from a number of available classes. One algorithm that can be used for classification is the Naïve Bayes Classifier. Naïve Bayes Classifier is a probability concept that can be used to determine class groups of text documents and can process large amounts of data with high accuracy results. The aim of this research is to determine the results of the classification of families at risk of stunting in Waeapo District, Buru Regency and to determine the level of accuracy of three data proportions, namely 70:30, 80:20 and 90:10. The sample in this study was 2290 families. Based on the known level of accuracy, the best accuracy value is a data proportion of 90:10 with an accuracy value of 93.9%.

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