• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.945-968
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• 2024

This study focuses on SIR model for SARS-CoV-2. The SIR model classifies a population into three compartments: susceptible S(t), infected I(t), and recovered R(t) individuals. The SARS-CoV-2 model considers various factors, such as immigration, birth rate, death rate, contact rate, recovery rate, and interactions between infected and healthy individuals to explore their impact on population dynamics during the pandemic. To analyze this model, we employed two powerful semi-analytical methods: the Laplace Adomian decomposition method (LADM) and the differential transform method (DTM). Both techniques demonstrated their efficacy by providing highly accurate approximate solutions with minimal iterations. Furthermore, to gain a comprehensive understanding of the system behavior, we conducted a comparison with the numerical simulations. This comparative analysis enabled us to validate the results and to gain valuable understanding of the responses of SARS-CoV-2 model across different scenarios.

• Fire Science and Engineering
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• v.30 no.1
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• pp.31-36
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• 2016

This study investigates the characteristics of thermal decomposition of an epoxy-based intumescent paint using thermogravimetric analysis (TGA) and numerical simulation. A mathematical and numerical model is introduced to describe mass loss profiles of the epoxy-based intumescent coating induced by the thermal decomposition process. The decomposition scheme covers a range of complexity by employing simplified 4-step sequential reactions to describe the simultaneous thermal decomposition processes. The reaction rates are expressed by the Arrhenius law, and reaction parameters are optimized to fit the degradation behavior seen during thermogravimetric (TG) experiments. The experimental results show a major 2-step degradation under nitrogen and a 3-step degradation in an air environment. The experiment also shows that oxygen takes part in the stabilization of the intumescent coating between 200 and $500^{\circ}C$. The simulation results show that the proposed model effectively predicts the experimental mass loss as a function of time except for temperatures above $800^{\circ}C$, which were intentionally not included in the model. The maximum error in the simulation was less than 3%.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.837-842
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• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

• Proceedings of the KIEE Conference
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• 2002.11b
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• pp.171-173
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• 2002

This paper presents a power system decomposition technique for digital simulation of large power system. To decompose power system, distributed transmission line model is used. But this model can be used only for long transmission lines. In this paper, capacitor compensation method is proposed to use distributed transmission line model for short transmission line. And case study shows proposed method can be used for effective power system decompositon in digital simulation of large power system.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.475-478
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• 2015

The objective of this study is to apply a hybrid model for estimating solar radiation and investigate their accuracy. A hybrid model is wavelet-based support vector machines (WSVMs). Wavelet decomposition is employed to decompose the solar radiation time series into approximation and detail components. These decomposed time series are then used as inputs of support vector machines (SVMs) modules in the WSVMs model. Results obtained indicate that WSVMs can successfully be used for the estimation of daily global solar radiation at Champaign and Springfield stations in Illinois.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.433-439
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• 2005

This paper describes a reinforced concrete crack model, which utilizes a strain decomposition technique. The strain decomposition technique enables the explicit inclusion of physical behavior across the cracked concrete surface such as aggregate interlock and dowel action rather than intuitively defining the shear retention factor. The proposed concrete crack model is integrated into the commercial finite element software ABAQUS shell elements through a user-supplied material subroutine. The FE results have been compared to experimental results reported by other researchers. The proposed bridge FE model is capable of predicting the initial cracking load level, the ultimate load capacity, and the crack pattern with good accuracy.

• Industrial Engineering and Management Systems
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• v.1 no.1
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• pp.73-78
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• 2002

In this paper, we propose a constrained optimization model for conjoint analysis (a preference decomposition technique) to improve parameter estimation by restricting the relative importance of the attributes to an extent as decided by the respondents. Quite simply, respondents are asked to provide some pairwise attribute comparisons that are then incorporated as additional constraints in a linear programming model that estimates the partial preference values. This data collection method is typical in the analytic hierarchy process. Results of a simulation study show the new model can improve the predictive accuracy in partial value estimation by ordinal east squares (OLS) regression.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.90-90
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• 2011

Long-term nonstationary oscillations (NSOs) are commonly observed in hydrological and climatological data series such as low-frequency climate oscillation indices and precipitation dataset. In this work, we present a stochastic model that captures NSOs within a given variable. The model employs a data-adaptive decomposition method named empirical mode decomposition (EMD). Irregular oscillatory processes in a given variable can be extracted into a finite number of intrinsic mode functions with the EMD approach. A unique data-adaptive algorithm is proposed in the present paper in order to study the future evolution of the NSO components extracted from EMD.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.947-961
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• 2023

This paper summarizes some research findings that show how the differential transform method (DTM) is used to resolve the Holling-Tanner model. To confirm the application, effectiveness, and correctness of the approach, a comparison between the differential transform method (DTM) and the Adomian decomposition method (ADM) is carried out, and an accurate solution representation in truncated series is discovered. The approximate solution obtain using both techniques and comparison demonstrates same outcome which remains a preferred numerical method for resolving a system of nonlinear differential equations.

• Journal of the Korea Society of Computer and Information
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• v.26 no.7
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• pp.127-132
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• 2021

This paper applies a machine learning model to forecasting freight rates in dry bulk and tanker markets with wavelet decomposition and empirical mode decomposition because they can refect both information scattered in the time and frequency domain. The decomposition with wavelet is outperformed for the dry bulk market, and EMD is the more proper model in the tanker market. This result provides market players with a practical short-term forecasting method. This study contributes to expanding a variety of predictive methodologies for one of the highly volatile markets. Furthermore, the proposed model is expected to improve the quality of decision-making in spot freight trading, which is the most frequent transaction in the shipping industry.