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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 78 Documents
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Pemodelan Sistem Antrian Pelayanan BPJS (Badan Penyelenggara Jaminan Sosial) Menggunakan Petri Net dan Aljabar Max-Plus Simbolon, Yohana L.; Rumlawang, Francis Y.; Dahoklory, Novita; Patty, Henry W. M.; Taihuttu, Pranaya D. M.; Wattimena, Abraham Z. Wattimena
Tensor: Pure and Applied Mathematics Journal Vol 6 No 2 (2025): Vol 6 No 2 (2025): 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/tensorvol6iss2pp75-86

Abstract

Hospitals are one of the health facilities that serve patients with various types of services, including BPJS patients. Like other hospitals, the queue system is a challenge in service management, especially in outpatient services. The imbalance between the number of patients coming and the service capacity can cause long waiting times. In this study, outpatient queue modeling was carried out at Leimena General Hospital, Ambon, using Petri Net to describe the service flow, and Max-Plus algebraic analysis was applied to estimate patient waiting times more accurately. The simulation results showed that increasing the number of resources, such as adding registration counters and doctors in the laboratory, was able to significantly reduce patient waiting times at various stages of service, especially in the pharmacy. This modeling shows that the Petri Net and Max-Plus approaches are not only effective in mapping the queue system, but can also be used as a basis for decision making in optimizing hospital services. This study is expected to be a reference for hospitals in improving service efficiency and for further researchers to develop more complex models by considering additional relevant variables.
Reduksi Noise Pada Citra Digital Menggunakan Metode Arithmatic Mean Filter Ciptoadi, Rayhan Khalid; Sersian, Sintia Sara; Allu, Rifaldi; Wattimena, Abraham Z.; Tilukay, Meilin Imelda
Tensor: Pure and Applied Mathematics Journal Vol 6 No 2 (2025): Vol 6 No 2 (2025): 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/tensorvol6iss2pp87-94

Abstract

Citra merupakan suatu bentuk informasi yang memiliki peranan yang cukup penting. Citra dapat berbentuk 2 dimensi seperti gambar, foto, ataupun lukisan. Citra sendiri sering digunakan oleh masyarakat untuk keperluan sehari-hari, mulai dari untuk hiburan sampai untuk pekerjaan. Citra dapat digunakan sebagai hiasan atau juga dapat digunakan sebagai sumber mata pencaharian, seperti contohnya foto, video, iklan, dan lain-lain. Kamera digital, CCTV, ataupun dashboard merupakan tools atau alat yang biasa digunakan untuk menangkap citra atau gambar. Namun, dalam proses akuisisi, transmisi, dan penyimpanan, citra digital sering kali terkontaminasi oleh noise. Noise adalah gangguan acak yang mempengaruhi nilai piksel dalam citra, menyebabkan distorsi visual dan mengurangi kualitas citra secara keseluruhan. Beberapa jenis noise yang umum ditemukan dalam citra digital termasuk Gaussian noise, salt-and-pepper noise, dan speckle noise. Noise atau kebisingan yang melekat pada gambar perlu ditangani dengan cara mereduksinya agar lebih jelas dengan metode filter mean arithmatic yang dapat mengurangi noise pada gambar gambar digital jauh lebih jelas setelah dikurangi. Penelitian ini bertujuan untuk menguji keefektifan metode ini dalam mereduksi noise pada citra sehingga menghasilkan citra atau gambar dengan kualitas yang lebih baik. Pada penilitian ini digunakan dua ukuran filter pada Arithmetic Mean Filter, yaitu ukuran 3x3 dan 5x5. Hasil yang diperoleh bahwa bahwa hasil denoising menggunakan filter 3x3 lebih baik dibandingkan dengan menggunakan filter 5x5. Dimana pada filter 5x5, gambar hasil denoise menjadi blur atau kabur dibandingkan pada gambar hasil denoise menggunakan filter 3x3.
Performance Analysis of Grey Wolf Optimizer for Solving Nonlinear Systems with Complex Roots Merysa Puspita Sari; Dewi Ika Ainurrofiqoh; Agustina Pradjaningsih; Sailah Ar Rizka; Nadia Kholifia
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): 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/tensorvol7iss1pp1-8

Abstract

Nonlinear systems of equations consist of multiple equations that must be solved simultaneously, and analytical solutions are often difficult to obtain, particularly for complex cases. For this reason, numerical and metaheuristic approaches are frequently employed as practical alternatives. This study investigates the performance of the Grey Wolf Optimizer (GWO) in solving nonlinear systems involving both real and complex roots. The problem is reformulated as an optimization task by minimizing a modulus based objective function derived from the given system. The implementation is carried out in MATLAB using several test cases, and a parameter sensitivity analysis is conducted with respect to the number of search agents, search boundaries, and maximum iterations. To evaluate its performance, the results obtained using GWO are compared with those of the Particle Swarm Optimization (PSO) algorithm reported in previous studies. The findings indicate that GWO is able to produce stable solutions with objective function values close to zero across different cases. However, PSO tends to achieve higher accuracy and faster convergence in certain scenarios. Despite this, GWO demonstrates strong exploration capability, which contributes to its robustness and makes it a viable alternative for solving complex nonlinear systems.
Application of the Spatial Durbin Model (SDM) to Analyze the Factors Affecting Poverty in Maluku Province in 2024 Najla Attamimi; Ronald John Djami; Novita Serly Laamena
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): 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/tensorvol7iss1pp27-42

Abstract

Poverty is defined as a condition in which individuals are unable to meet the minimum basic needs necessary for a dignified life. In Indonesia, particularly in Maluku, poverty remains a critical problem, exacerbated by the low quality of human resources and limited access to education, health care, and employment opportunities. This study aims to analyze the factors that significantly influence poverty in Maluku Province in 2024 and to build a poverty model using the Spatial Durbin Model (SDM). This research applies a statistical method known as the Spatial Durbin Model (SDM), which is a development of the Spatial Autoregressive Model (SAR). Thus, this model not only includes spatial lag on dependent variables, but also includes spatial lag on independent variables. Based on the calculations, it was found that the factors that significantly influence poverty are the average length of schooling and the labor force participation rate . An value of 96.46% and an AIC of 54.831 indicate that the model SDM provides good results in explaining the poverty variations in Maluku Province.
Implementation of the Generalized Regression Neural Network (GRNN) Algorithm in Predicting the Level of People’s Welfare in Maluku Province Marlon Stivo Noya van Delsen; Mei Anista Ririmasse; Rosalina Salhuteru
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): 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/tensorvol7iss1pp9-16

Abstract

Permasalahan kesejahteraan rakyat di Provinsi Maluku masih menjadi isu utama yang ditandai dengan tingginya tingkat kemiskinan, rendahnya pengeluaran per kapita, serta keterbatasan akses terhadap pendidikan dan kesehatan. Penelitian ini bertujuan untuk mengidentifikasi faktor-faktor yang mempengaruhi tingkat kesejahteraan rakyat serta mengukur akurasi algoritma Generalized Regression Neural Network (GRNN) dalam memprediksi tingkat kesejahteraan rakyat di Provinsi Maluku. Penelitian yang digunakan adalah penelitian kuantitatif dengan menerapkan GRNN pada delapan variabel sosial ekonomi yang diperoleh dari data Badan Pusat Statistik (BPS) Maluku tahun 2020–2024. Analisis korelasi Pearson digunakan untuk seleksi variabel, dilanjutkan dengan optimasi parameter sigma menggunakan grid search. Hasil penelitian menunjukkan enam variabel berpengaruh signifikan dan dilanjutkan sebagai input pemodelan. Model GRNN dengan sigma optimal 0,3 menghasilkan nilai Mean Absolute Percentage Error (MAPE) sebesar 6,15%, yang termasuk kategori “sangat baik.” Oleh karena itu GRNN efektif digunakan untuk memprediksi tingkat kesejahteraan rakyat di Provinsi Maluku serta dapat menjadi dasar bagi pemerintah daerah dalam merumuskan kebijakan sosial-ekonomi yang lebih tepat sasaran.
Penerapan Aljabar Max-Plus dalam Penentuan Rute Terpendek Distribusi Barang pada Jaringan J&T Express di Kota Ambon Elvira Salelatu; Mozart Winston Talakua; Novita Dahoklory; Henry Willyam Michel Patty
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): 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/tensorvol7iss1pp43-58

Abstract

Penentuan rute terpendek merupakan suatu solusi yang diperlukan bagi perusahaan yang bergerak di bidang distribusi barang, karena rute terpendek dapat membantu perusahaan mengoptimalkan jarak yang ditempuh dan mengefisienkan waktu yang dibutuhkan. Oleh karena itu, penelitian ini bertujuan untuk menerapkan aljabar max-plus untuk menentukan jalur terpendek distribusi barang di jalur Jet Lee & Tony Chen (J&T) Express di Kota Ambon. Hasil analisis menunjukkan bahwa pendekatan ini efektif dalam meminimalkan bobot lintasan, sehingga mendukung efisiensi pengiriman barang dan meningkatkan kepuasan pelanggan melalui ketepatan waktu distribusi. Namun, hasil pemetaan juga mengungkapkan bahwa sebaran titik distribusi J&T Express di Kota Ambon belum merata di seluruh wilayah kecamatan. Beberapa desa di Kecamatan Nusaniwe dan Leitimur Selatan tidak memiliki titik distribusi yang berada dalam kecamatan yang sama, sehingga proses distribusi ke wilayah tersebut dilakukan melalui simpul transit di kecamatan lain, seperti J&T DP Galala ( ), J&T Sirimau ( ), dan J&T Teluk Ambon ( ). Selain itu, terdapat desa-desa yang secara administratif berada dalam satu kecamatan, namun dilayani oleh titik distribusi yang berada di luar wilayah tersebut. Meskipun demikian, hasil penelitian membuktikan bahwa proses distribusi tetap dapat berjalan secara optimal dengan memanfaatkan simpul distribusi terdekat sebagai titik transit. Dengan demikian, efisiensi jalur pengiriman tetap dapat dicapai melalui perencanaan rute yang tepat menggunakan analisis aljabar max-plus.
Hierarchical Cluster Analysis Based on Stunting-Related Indicators in Maluku and North Maluku Sanlly Joanne Latupeirissa; Gildo Tentua
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): 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/tensorvol7iss1pp17-26

Abstract

Stunting remains one of the major public health challenges in Indonesia because it affects children's physical growth, cognitive development, and future productivity. Identifying regional characteristics based on stunting-related indicators is important to support more targeted intervention policies. This study aims to classify regions in Maluku and North Maluku Provinces based on stunting-related indicators using Hierarchical Cluster Analysis. The study employed secondary data from 21 districts/cities in 2023 obtained from the Ministry of Health of the Republic of Indonesia, the National Socio-Economic Survey (SUSENAS), Statistics Indonesia (BPS), and the National Food Agency. The variables analyzed were expected years of schooling, food security index, households with access to proper sanitation, poverty rate, access to safe drinking water, complete basic immunization coverage, and the percentage of children under two years who received breastfeeding. Prior to clustering, all variables were standardized using Z-scores. Hierarchical Cluster Analysis was performed using Ward’s linkage method and Squared Euclidean Distance. The results indicated that the regions could be classified into two clusters. The agglomeration schedule and dendrogram supported a two-cluster solution, which was further confirmed by K-Means validation. The first cluster consisted of four regions characterized by higher expected years of schooling, food security, sanitation coverage, access to safe drinking water, and complete basic immunization coverage. The second cluster consisted of seventeen regions with relatively less favorable characteristics. Although the average prevalence of stunting was relatively similar between the two clusters, the results suggest that regions with comparable stunting prevalence may possess different socioeconomic, environmental, and health-related profiles. These findings provide useful information for identifying regional characteristics and may support the formulation of more targeted stunting prevention and control strategies.
Klasifikasi Citra Tekstur Daging Sapi, Kambing, dan Babi Menggunakan Ekstraksi Fitur Wavelet Haar dan Symlet Berbasis Support Vector Machine Green Kenny Sarimanella; Francis Yunito Rumlawang; Harmanus Batkunde; Meilin Imelda Tilukay; A. Z. Wattimena
Tensor: Pure and Applied Mathematics Journal Vol 7 No 1 (2026): 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/tensorvol7iss1pp59-66

Abstract

Meat is one of the animal protein sources widely consumed by the public; however, distinguishing different types of meat visually is often difficult because they have very similar textures. This study applies the Support Vector Machine (SVM) method with feature extraction based on Haar Wavelet and Symlet Wavelet (Sym4) to classify texture images of beef, goat meat, and pork. The dataset consisted of 1200 digital images processed through resizing, grayscale conversion, and normalization stages. Feature extraction was performed using the Discrete Wavelet Transform (DWT) to obtain statistical texture features. The classification process employed the Radial Basis Function (RBF) kernel with a multiclass classification approach. The results showed that the Haar Wavelet achieved an accuracy of 96.67%, while the Symlet Wavelet (Sym4) achieved 94.17%. These findings indicate that the combination of wavelet methods and SVM is effective for automatic and objective meat type identification

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