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Perspectives in Mathematics and Applications (PERMATA)
Published by PT. Kreasi Pustaka Mandiri (Krestama)
ISSN : -     EISSN : 31103847     DOI : -
Core Subject : Economy, Science, Engineering,
Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Engineering Physics
Perspectives in Mathematics and Applications (PERMATA) is a high-quality, peer-reviewed, open-access journal published by Kreasi Pustaka Mandiri (Krestama), with biannual issues in June and December, and has a registration number e-ISSN 3110-3847 (media online). PERMATA provides a dedicated platform for researchers, academics, and practitioners to publish rigorous theoretical and applied mathematical research. The journal covers: Pure Mathematics, including algebra, analysis, geometry, topology, and number theory. Applied Mathematics, spanning computational mathematics, mathematical modeling, optimization, statistics, and operations research. Interdisciplinary Applications, integrating mathematics with science, engineering, economics, and education advancements. PERMATA aims to bridge theory and real-world applications by fostering the exchange of ideas across disciplines, contributing to the ongoing development of mathematical sciences.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 10 Documents
 1 
Penentuan strategi pemasaran aplikasi e-commerce menggunakan game Theory Syifa Fijri Arrofilah; Herlinda Nur’afwa Sofhya
Perspectives in Mathematics and Applications Vol 1 No 1 (2025): Juni
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

Online shopping activities have recently increased significantly, resulting in consumers who initially shopped at offline stores switching to online stores through e-commerce applications, which are currently experiencing intense competition. In the face of fierce competition in the global business world, every company needs to develop a strategic marketing plan to enhance business quality and achieve its goals. This study aims to identify the attributes that are most important to consumers in each e-commerce application, determine the value of the game, and identify the optimal e-commerce marketing strategy using game Theory. This study utilises two e-commerce applications, namely Tokopedia and Shopee, and employs eight strategies: product, place, price, delivery speed, promotion, practicality, website appearance, and security. The marketing strategy used is a mixed approach, utilising POM QM Software for Windows V4 for support. The results obtained from the competition between Tokopedia and Shopee indicate that the optimal strategy for Tokopedia is a combination of price and promotion. In contrast, the optimal strategy for Shopee is a combination of promotion and security. According to the research results above, the attribute that is emphasised in each e-commerce application is the promotion strategy.
Mengoptimalkan Kebutuhan Gizi Balita dengan Metode Simpleks Menggunakan POM-QM untuk Pencegahan Stunting Nurrochmah Sri Rahayu Nurrochmah; Saluky
Perspectives in Mathematics and Applications Vol 1 No 1 (2025): Juni
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

This research aims to develop an optimization mathematical model to help meet toddlers' daily nutritional intake needs to prevent stunting. The Simplex method is applied in this model to determine food combinations that meet the standards of nutritional needs at minimal cost, considering budget constraints and the availability of foodstuffs so that they can be adapted to diverse socioeconomic conditions. The POM-QM application is used as a calculation tool to apply the Simplex method, making the optimization process more practical and accurate. Mathematical modeling is carried out by compiling a function of objectives by minimizing the cost of consuming foodstuffs that meet the daily nutritional needs of toddlers, including protein, fat, carbohydrates, iron, vitamin A, and vitamin C. The optimization results showed that nutritional needs could be optimally met with a combination of vegetable soup consumption of 22.5 grams, Tempe 8.476 g, and banana 4.5 g, with a total minimum cost of IDR 146,928. The nutrient content of the combination exceeds daily needs, such as protein (241.41 g), fat (274.06 g), Fe (82.93 mg), as well as vitamin A (450 RE) and vitamin C (45 mg), while carbohydrates are fulfilled exactly as much as 220 grams. These results show that the optimization approach can be used to design a balanced, nutritious diet that is cost-efficient as an effort to prevent stunting in toddlers.
Penerapan Algoritma K-Means dalam Pengelompokan Capaian Belajar Siswa dalam Matematika di MAN 1 Cirebon Hani Tarkasih
Perspectives in Mathematics and Applications Vol 1 No 1 (2025): Juni
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

This study aims to apply the K-means Algorithm in grouping students' mathematics learning outcomes at MAN 1 Cirebon and measure its accuracy using the Davies-Bouldin Index. This type of research employs an experimental design with a quantitative approach. The research population consists of all students at MAN 1 Cirebon, with a sample of class X students majoring in Mathematics and Natural Sciences. The data used came from daily test scores and odd semester end-of-semester assessments. The results showed that the K-Means Algorithm successfully grouped student learning outcomes into three categories: Cluster 1 (high category), comprising 83 students; Cluster 2 (medium category), containing 64 students; and Cluster 3 (low category), comprising 27 students. The Davies-Bouldin Index value of 0.30 indicates that the grouping results are good quality. This research contributes to the application of data mining methods in supporting the objective and systematic evaluation of student learning outcomes.
Analisis implementasi matriks Leslie pada model laju pertumbuhan populasi perempuan Siti Musyarofah; Herlinda Nur’afwa Sofhya
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

Demographic problems in Indonesia are important because Indonesia is ranked fourth as the country with the largest population. One way to determine future population growth is to predict female population growth. The Leslie matrix is a model used to predict and determine female population growth. The general form of the Leslie matrix is a square matrix in which the first row entries are the female fertility rates, the subdiagonal entries are the female survival rates, and the remaining entries are zero. The purpose of the study was to predict the rate of female population growth in Indonesia. The results showed that the Leslie matrix, influenced by the initial population, female fertility rate, and female survival rate, had a dominant eigenvalue of 1.001, indicating that the rate of female population growth in Indonesia tends to increase.
Optimasi biaya distribusi talenan menggunakan algoritma heuristik penghematan Clark dan Wright (studi kasus di PT Titan) Lutpi Abdul Latip
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

One of the main challenges in PT Titan’s distribution process is the inaccurate determination of vehicle routes and improper selection of vehicle types and capacities, which leads to inefficient distribution costs. Although PT Titan already has a distribution route, the author proposed a more cost-effective alternative using the Clark and Wright Saving Heuristic, which efficiently solves vehicle routing problems by allowing a single vehicle to serve multiple agents in a single trip. The research aimed to identify the current distribution routes for cutting board products, apply the algorithm to improve them, and determine the most optimal routes after optimization. Graphs were used to visualize the revised distribution plan. The results showed two significant optimizations in mileage and cost. For the L300 and Ankle Box vehicles, mileage was reduced by 9 km, and distribution costs were reduced by 2.8% (Rp 250,000 per trip). Meanwhile, the Double ankle and L300 vehicles achieved a mileage reduction of 55.13%, corresponding to 1,386 km. They cost savings of 28.1% or Rp2.500,000 The final optimized routes consist of Route 1 (Depot–Klaten–Boyolali–Depot) and Route 2 (Depot–Bogor–Tangerang–Depot) using Doubel ankle vehicle, and Route 3 (Depot–Kuningan–Cikijing–Depot) using an L300 vehicle, resulting in a more efficient and cost-effective distribution system for PT Titan.
Analisis Indeks ABC pada Invers dan Graf Non-Commuting Grup hingga Sefti Fajriatul Musyarrofah; Rio Satriyantara
Perspectives in Mathematics and Applications Vol 1 No 1 (2025): Juni
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

This study investigates the Atom Bond Connectivity (ABC) index applied to inverse and non-commuting graphs of finite groups. The research focuses on two distinct structures: inverse graphs formed from generalized quaternion groups and non-commuting graphs derived from non-abelian finite groups. By utilizing topological index Theory, particularly the ABC index introduced by Estrada, the study aims to characterize the graph structures based on vertex degrees. The ABC index is determined using known group properties and edge classifications for the inverse graphs of generalized quaternion groups. Similarly, the ABC index of non-commuting graphs is explored by analyzing group centers and the connectivity patterns among non-central elements. The results reveal that the ABC index quantifies group connectivity, enhancing the understanding of structural properties in algebraic graph representations. This analysis contributes to the broader application of graph Theory in abstract algebra and theoretical chemistry.
Analisis teoritis indeks Hyper-Wiener dalam graf yang diturunkan dari struktur aljabar Ashadul Umam; Abdurahim
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

The Hyper-Wiener index is a widely used topological descriptor that quantifies the structural complexity of graphs, particularly those arising from algebraic structures. This paper presents a structured synthesis of key theorems related to the Hyper-Wiener index in coprime graphs, non-coprime graphs, and power graphs constructed from the integer modulo group and the dihedral group. Adopting a systematic literature review approach, we compile and restate formal results, including explicit formulas and proven properties. Each theorem is analyzed in relation to the algebraic structure of its underlying group and the resulting graph topology. Our findings highlight how group-theoretic properties—such as order, operation, and element interactions—directly impact the Hyper-Wiener index. This paper is intended to support researchers by providing a conceptual bridge between group theory and topological graph theory, and by identifying potential directions for future work.
Solusi persamaan adveksi menggunakan metode variasi iterasi Azis Chaerul Bisri; Mashuri; Najmah Istikaanah
Perspectives in Mathematics and Applications Vol 1 No 1 (2025): Juni
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

Partial differential equations, particularly one-dimensional advection equations, frequently arise in various physics and engineering problems, including heat transfer and fluid flow. This study used the Iteration Variation method to solve the one-dimensional advection equation. The Iteration Variation method was chosen for its advantages in providing a solution that converges quickly without requiring complex linearisation. This study aims to analyse the effectiveness of the Iteration Variation method in producing analytical solutions and compare them with exact solutions for specific cases. The results show that the solutions obtained by the Iteration Variation method are close to the exact solution, with a relatively small error rate. Therefore, this method can be an efficient alternative for solving one-dimensional advection problems. The results of this study demonstrate that the Iteration Variation method can simplify the completion process and provide accurate results in the initial iteration, requiring only four iterations. The form of the solution is visualised using the MAPLE computer program. Although the complexity of the algebra increases with the number of iterations, it can be achieved with the help of the MaPLE program, which allows for the visualisation of the solution both in its algebraic formula and in its graphical representation.
Penerapan integral tentu terhadap pengaruh lebar cakram dan bentuk kaliper pada pengereman sepeda motor di jurusan otomotif SMK Muhammad Maskur
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

The application of mathematical material in everyday life is part of the expected curriculum achievement in contextual mathematics learning. One of them is integral learning. The benefits of learning materials for solving everyday life problems can help calculate the area or volume needed. One area where mathematical concepts can be applied is the modification of a motorcycle's braking system. Modifying the braking system is important in maintaining driving safety. In this study, the aim is to determine the effectiveness of the brake system by applying definite integrals to changes in the disc and caliper widths. In addition, to determine the performance results of each change in the width of the disc and changes in the shape of the caliper. In this study, researchers used a qualitative approach. Considering the operational enhancements observed in motorcycle disc brake systems, alterations to the caliper, independent of disc plate modifications, prove more efficacious than adjustments to disc plate width while maintaining the original caliper piston configuration.
Peta Penelitian SEIRS-Vaksin COVID-19: Analisis Tren, Temuan, dan Tantangan Model Matematika Muhamad Fahri Fauzan; Alya Ramadhani; Dara Maywanti; Aban Subanul Fahmi; Bayu Sukmaangara
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

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Abstract

The control of the COVID-19 pandemic requires mathematical models that are able to accommodate complex immune dynamics, especially waning immunity phenomena and vaccination interventions. This study conducted a Systematic Literature Review using the PRISMA protocol to map trends, findings, and methodological challenges in SEIRS-Vaccination modeling. Of the 80 articles identified in the initial stage, 56 articles met the inclusion criteria and were analyzed. Furthermore, 11 articles were selected through purposive sampling techniques as representative samples for in-depth comparative analysis of five main methodology categories: Deterministic (ODE), Optimal Control, Fractional Order, Data Assimilation/Stochastic, and Spatial. The results of the literature synthesis reveal a significant paradigm shift from classical deterministic models that focused on stability analysis  static towards a more adaptive model. Specifically, this study identifies the use of the Ensemble Kalman Filter for estimation of dynamic parameters and Optimal Control Theory for resource allocation strategies as the dominant methodological trends. The model's findings consistently validate that vaccination rate is the most sensitive intervention parameter, but its long-term effectiveness is highly dependent on the duration of immunity. The study concludes the need to develop a hybrid model that integrates stochastic approaches and optimal control to generate more precise policy recommendations in the future.

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