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Zero : Jurnal Sains, Matematika, dan Terapan
Published by Universitas Islam Negeri Sumatera Utara
ISSN : 2580569X     EISSN : 25805754     DOI : 10.30829
Core Subject : Science, Education, Agriculture,
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics
Arjuna Subject : -
Articles 241 Documents
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ResNet-18 Citrus Classification with Augmentation: Peel Color Associations with pH and Vitamin C Dewi, Titin Afrina Priani; Surono, Sugiyarto; Thobirin, Aris
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.27199

Abstract

Limes and lemons are widely consumed, but field quality assessment is often subjective. This study built a ResNet-18 citrus classifier using transfer learning and data augmentation, and evaluated it with stratified 5-fold cross-validation on 80 images (40 limes, 40 lemons). All analyses were conducted per fold to reduce optimistic bias. The model reached 98.75% mean validation accuracy, misclassifying one lime image while correctly recognizing all lemons. For interpretation, peel regions were quantified using NDYI and CIELab (L*, a*, b*), and related to pH and vitamin C using Spearman correlation. Uncertainty was quantified with bootstrap-based 95% confidence intervals for each correlation. Peel color features were more consistently associated with pH (especially in limes), whereas correlations with vitamin C were weak and non-significant for both fruits. Results indicate strong performance under controlled imaging, but using peel color as a vitamin C proxy requires broader data and external validation across cameras and lighting.
Determinants of Fishermen and Fish Farmers Exchange Rate: A Panel Data Regression Approach Handayani, Vitri Aprilla; Sabarinsyah, Sabarinsyah; Arrafi, Adamsyam; Sunarsono, Hery; Anggraeni, Andini Setyo
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.26642

Abstract

This study examines the impact of key economic variables on the exchange rate of fishermen and fish farmers using monthly panel data by subsector/province for the period 2022-2024 sourced from BPS. The price index received by farmers (Y) is explicitly defined as the dependent variable. A panel data regression model was employed using three independent variables: Farmers' Paid Price Index ( ), the Fishermen and Fish Farmers Exchange Rate ( ), and the Fishermen's Business Exchange Rate ( ). The results showed that both and had a significant positive effect (α < 0.05) on Y, with exhibiting a stronger influence than . These findings suggest that policies aimed at controlling input prices and stabilizing exchange rates can effectively improve the welfare of fishermen and fish farmers. Furthermore, the regression model developed in this study provides a practical analytical framework for supporting data-driven policy decisions related to price dynamics and welfare enhancement in the fisheries sector.
Numerical Pricing of European Stock Option Based on Black-Scholes Model Using Crank-Nicolson Method Putri, Isnaini Emma Wimala; Artiono, Rudianto
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.28070

Abstract

Accurate option pricing is an important issue in quantitative finance, especially in emerging financial markets, which are generally characterized by price volatility and limited historical data. This research evaluates the numerical performance of the classical Crank–Nicolson finite difference method in determining the price of European call options based on the Black–Scholes model using Indonesian stock market data. The Black–Scholes equation is discretized on a uniform spatial and temporal grid, and the numerical solution is verified by comparison with the Black–Scholes analytical solution as a mathematical reference. The numerical results show that the Crank–Nicolson method produces stable and convergent solutions, with a relative error of less than 1% at a sufficiently fine grid resolution. Furthermore, sensitivity analysis to volatility and temporal convergence tests demonstrate the consistency of the numerical solution's behavior to variations in the model's key parameters. These findings indicate that the Crank–Nicolson method provides a reliable numerical approach for evaluating European option pricing within the classical Black–Scholes framework under the analyzed market conditions. 
Exploring the Metric Chromatic Number of Uniform, Centralized Uniform, and Cycle Uniform Theta Graphs Raventino, Raventino; Fran, Fransiskus
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.27103

Abstract

Metric coloring allows adjacent vertices of a graph to share the same color provided that their associated distance vectors are distinct, leading to the concept of the metric chromatic number. This notion is closely related to problems of vertex distinguishability and resource allocation in network-like structures. In this paper, we present the first exact determination of the metric chromatic number for three families of theta type graphs: uniform theta graphs, centralized uniform theta graphs, and a newly introduced class called the cycle uniform theta graph, obtained by cyclically arranging uniform theta subgraphs. The proposed construction enables an investigation of how cyclic configurations influence metric coloring behavior. Using a constructive metric coloring approach, exact values of the metric chromatic number are obtained. It is shown that the uniform theta graph  and the centralized uniform theta graph  both satisfy  for all positive integers  and . For the cycle uniform theta graph , the metric chromatic number equals  when  and  have the same parity or when  is odd and  is even. In contrast,  when  is even and  is odd. This latter case arises because the longest path in the cyclic structure has odd length, forcing the graph to have chromatic number three. Since the graph is connected and its chromatic number is at most three, this structural constraint directly implies that three colors are also necessary for a valid metric coloring.
Forecasting Macroeconomic Variables in Indonesia Using the Vector Autoregressive Method Amalita, Nonong; Syafriandi, Syafriandi; Kurniawati, Yenni; Meilisa, Mira; Nafandra, Bunga
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.27949

Abstract

This study aims to analyze the dynamic relationship and predict inflation, the rupiah exchange rate, oil and gas exports, and BI interest rates in Indonesia. The Vector Autoregressive (VAR) method was used with monthly data from January 2015 to September 2025, the best model obtained was VAR (2). The Granger causality test results show that most variables are dominated by their own lag effects. Impulse response analysis shows that shocks are temporary and subside in the medium term. Forecast results for October 2025–September 2026 shows relatively stable inflation in the range of 2.42–2.70%. The rupiah exchange rate is expected to depreciate moderately by around 1.4%. Meanwhile, oil and gas exports declined significantly by 3.9%, and the BI interest rate is expected to fall by 12.8% to 4.14%. These findings indicate that Indonesia's macroeconomic stability is dominated by internal dynamics, so monetary policy focuses on inflation and the exchange rate.
Bayesian Path Modeling Simulation for Stunting Analysis Sianipar, Celia; Fernandes, Adji Achmad Rinaldo; Solimun, Solimun; Zahra, Septi Nafisa Ulluya
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.26824

Abstract

This research assesses the interaction between sample size, model complexity, error variance, and their collective impact on the execution of Bayesian path modeling within the context of stunting, using Monte Carlo simulation over 100 datasets over 18 different conditions. The results indicate that the sample size positively impacts the stability of the model, but the more intricate the model and the more noise there is in the data, the greater the effect. A 0.3 error variance unpredictedly lowered the RMSE on various complex scenarios (eg. for nonlinear structures, it decreased from 0.222 to 0.079), and low error variance, combined with nonlinear pathways, led to lower CI coverage (<0.85) and lower ESS, indicating there was difficulty recovering the true parameters A unique contribution of the research is that, in Bayesian modeling, sample size is not the only driver of model complexity, noise, and stunting research. This information is beneficial in providing evidence on how to choose priors, structure models, and conclusively derive results for Bayesian causal analysis in the field of public health.
Numerical Pricing of European Options under Proportional Transaction Costs: A Semi-Discretization Approach to the Nonlinear Barles-Soner Model Noor, Dwi Maya Firanti; Artiono, Rudianto
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.28084

Abstract

The classical Black–Scholes model assumes a frictionless market, which often leads to the undervaluation of option premiums when transaction costs are present. This study prices European call options under proportional transaction costs using the nonlinear Barles–Soner framework and a semi-discretization–based numerical approach. Using historical stock data from PT XYZ (an anonymized Indonesian equity), the results show that transaction costs significantly increase effective volatility and generate systematic deviations from classical Black–Scholes prices. In particular, option premiums increase by IDR 392.33 and IDR 776.66 for transaction cost parameters of 0.015 and 0.030, respectively, compared with the frictionless benchmark. These findings confirm that ignoring transaction costs leads to substantial underpricing and that the proposed framework provides a more realistic and conservative valuation for hedging and risk management in emerging markets.
Local Stability Analysis of Leptospirosis SEITR - SI Model with the Influence of Hydroclimatic Rate and Treatment Erlangga, Ega Ananta; Prawoto, Budi Priyo
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.28376

Abstract

Leptospirosis is a zoonotic disease whose transmission is influenced by interactions between humans, vectors, and environmental conditions. This study proposes a novel SEITR–SI model that simultaneously integrates treatment dynamics and hydroclimate-dependent transmission within a single analytically tractable framework. Unlike previous SEIR–SI and SIR–SI formulations that either exclude treatment or incorporate hydroclimatic effects through explicit environmental compartments, the proposed model represents hydroclimatic influence implicitly through transmission intensity while preserving mathematical simplicity. The local stability of the disease-free and endemic equilibria is analyzed using the basic reproduction number  and the Routh–Hurwitz criterion. The analysis confirms classical threshold behavior governed by , while numerical simulations reveal that increased hydroclimatic transmission intensity elevates endemic infection levels even under higher treatment rates. These findings highlight that treatment alone may be insufficient in hydroclimate-sensitive environments and underscore the importance of integrated control strategies combining medical intervention with environmental and vector management.
A Bibliometric Analysis of Mathematics Education Research in Elementary Schools: Trends, Institutions, and Post-Pandemic Learning Integration (2020–2025) Aprianda, Lola; Dinata, Karsoni Berta
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.28108

Abstract

Research on elementary mathematics education in the post pandemic period reflects changes in publication patterns and research topics. This study aims to analyze publication trends, institutional contributions, and forms of learning integration in elementary mathematics education research published between 2020 and 2025. The method employed is a bibliometric analysis of 921 Scopus-indexed articles using RStudio. The analysis covers annual publication trends, institutional productivity, authors’ geographical distribution, keyword-based thematic clusters, and citation patterns. The results show variations in annual publication output, with an increasing trend observed since 2023. Monash University and Universitas Negeri Yogyakarta are identified as the institutions with the highest publication output. Cluster analysis identifies three main thematic groups: student-oriented and numeracy-focused research, studies related to methodological approaches and teacher development, and research concerning pedagogy and curriculum. These findings describe the characteristics and thematic distribution of post pandemic research in elementary mathematics education.
Comparative Analysis of Four Actuarial Cost Methods on Unfunded Actuarial Liability in a Pekanbaru Pension Scheme Baiti, Putri Isnaini Cahyaning; Nasrullah, Nasrullah; Saefulloh, Annisa Hevita Gustina Kumalasari; Marbun, Tika Kristin
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.27520

Abstract

Unfunded Actuarial Liability (UAL) is an important indicator in assessing the sustainability of a pension fund program, as it reflects the difference between actuarial liabilities and available assets. This study aims to compare the amount of UAL generated by four pension funding methods, namely Accrued Benefit Cost (ABC), Entry Age Normal (EAN), Unit Credit (UC), and Aggregate Cost Method (AGG). A quantitative actuarial valuation is conducted using administrative data from active civil servants of PT. TASPEN (Persero) Pekanbaru Branch Office in 2025 under uniform actuarial assumptions, including the TASPEN mortality table, interest rates, and salary growth rates. A deterministic sensitivity analysis on the discount rate and salary growth rate was conducted to examine the robustness of unfunded actuarial liability estimates. The results show that the ABC, UC, and EAN methods produce identical aggregate UAL values of approximately Rp. 16.841.220.000, - while the Aggregate Cost Method yields a higher UAL of about Rp.22.173.660.000, - due to collective liability recognition. Furthermore, the EAN and AGG methods exhibit relatively more stable contribution patterns over participants’ service periods, whereas the ABC and UC methods are more sensitive to variations in participants’ age and length of service. These findings indicate that the selection of actuarial cost methods has significant practical implications for pension fund management, particularly in terms of funding stability, contribution planning, and long-term sustainability of pension schemes.

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