• Korean Journal of Radiology
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• 제22권7호
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• pp.1194-1202
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• 2021

Objective: To investigate the age-dependent changes in regional cerebral blood flow (CBF) in healthy adults by fitting mathematical models to imaging data. Materials and Methods: In this prospective study, 90 healthy adults underwent pseudo-continuous arterial spin labeling imaging of the brain. Regional CBF values were extracted from the arterial spin labeling images of each subject. Multivariable regression with the Akaike information criterion, link test, and F test (Ramsey's regression equation specification error test) was performed for 7 models in every brain region to determine the best mathematical model for fitting the relationship between CBF and age. Results: Of all 87 brain regions, 68 brain regions were best fitted by cubic models, 9 brain regions were best fitted by quadratic models, and 10 brain regions were best fitted by linear models. In most brain regions (global gray matter and the other 65 brain regions), CBF decreased nonlinearly with aging, and the rate of CBF reduction decreased with aging, gradually approaching 0 after approximately 60. CBF in some regions of the frontal, parietal, and occipital lobes increased nonlinearly with aging before age 30, approximately, and decreased nonlinearly with aging for the rest of life. Conclusion: In adults, the age-related perfusion patterns in most brain regions were best fitted by the cubic models, and age-dependent CBF changes were nonlinear.

• 대한수학회지
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• 제47권2호
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• pp.385-407
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• 2010

To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\chi^2$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.

• 대한수학교육학회지:수학교육학연구
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• 제20권1호
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• pp.73-84
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• 2010

학교수학에서 다루는 수학적 모델링의 일반적인 특성은 하나의 실제적인 문제를 해결하기 위하여 수학적 모델을 도입하고 이를 풀어서 실제적인 문제에 답을 제시하는 일회적인 경우가 많다. 그러나 실제적인 문제는 일회적인 모델링으로는 해결되지 않거나 그 해가 충분히 정밀하지 못한 경우가 있다. 본 연구는 여러 가지 변인을 가진 실제적인 문제를 해결하기 위해 수학적 모델을 구성할 경우, 구성한 수학적 모델의 해의 의미성을 분석해 보고 필요하면 더욱 정교한 해를 구할 수 있는 모델로 나아가는 수학적 모델링의 정교화 과정 모형을 구안하였다. 또한 그것을 수학교실에서 활용할 수 있는 수학적 모델링의 예를 제시함으로써 학교수학에서 수학적 모델링의 정교화를 다룰 수 있게 하였다.

• 대한토목학회논문집
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• 제2권2호
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• pp.29-38
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• 1982

유효강우량(有效降雨量), 섬체시간(暹滯時間) 및 유출(流出)의 비선형(非線型)을 포함하는 비선형(非線型) 수문학적(水文學的) 모형(模型)이 기술(記述)된다. 모형(模型)의 입력자료(入力資料)를 구성하는 유효강우량(有效降雨量)의 산정(算定)은 polynomial fitting 방법(方法)이 이용되었으며 섬체시간(暹滯時間)의 비선형성(非線型性)이 고려된 비선형섬체모형(非線型暹滯模型)을 남한강(南漢江) 상류(上流)에 위치한 섬강유역(蟾江流域)에 적용하여 상수(常數)값을 산정하고 종래의 방법인 fitting 방법(方法) 및 저류함수모형(貯溜凾數模型)에 변형(變型)을 가한 상관모형(相關模型)의 상수(常數)값들과 비교하였다. 각 모형(模型)에서 구한 상수(常數)값의 결과로부터 본연구(本硏究)의 수학적(數學的) 해법(解法)인 연속근사해법(連續近似解法)과 수치해법(數値解法)인 Newton-Rhapson 방법(方法)이 비선형(非線型) 유출과정해석(流出過程解析)에서 종전의 계산도해법(計算圖解法) 등에 비해 우수함이 밝혀졌다.

• 한국지반환경공학회 논문집
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• 제16권12호
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• pp.23-35
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• 2015

전단파괴 이전 지반의 동적비선형거동특성은 일반적으로 함수형 피팅모델과 Masing 법칙을 이용하여 수치해석프로그램에 사용된다. 그러나 대부분의 함수형 피팅모델은 특정 전단변형률 영역에서 실험결과 대비 전단탄성계수와 감쇠비의 오차를 유발하는 것이 일반적인 현상이다. 이러한 오차의 원인은 현재 피팅모델로 표현하기 어려운 지반재료의 고유 특성에 기인할 수 있다. 지금까지 상기 문제를 해결하기 위하여 몇몇 피팅모델이 제안되었으나, 오차의 영향이 지진 시 부지응답해석에 미치는 영향은 아직까지 구체적으로 검토된 바는 없다. 본 논문에서는 상기 영향 검토를 응답이력해석을 통하여 실시하였다. 세 개의 서로 다른 함수형 피팅모델을 이용하여 부지응답해석을 시행하였으며, 그 결과는 동적원심모형시험 결과의 원형 계측치를 기준으로 검증을 실시하였다. 실험과 해석 간의 오차는 입력지진 크기가 증가함에 따라 커짐을 알 수 있었다. 저-중간 강도의 입력지진 범위에서 함수형 피팅모델에 따른 해석의 정확도 차이는 실용적인 측면에 있어서 큰 차이가 나지 않음을 알 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.180-193
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• 2023

Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.103-115
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• 2004

A computational algorithm is developed for fitting given data in the plane or in 3-space by implicitly defined quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coefficients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coefficients such as to reduce the sum of those squared distances. Numerical examples are given.

• Geosystem Engineering
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• 제21권6호
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• pp.335-343
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• 2018

Alkali-surfactant polymer flooding has become an important technique to improve oil recovery following the development of oil fields while the function of emulsification in enhanced oil recovery is rarely considered in the existing mathematical model for numerical simulation. In this paper, the mechanism of improving the recovery of the emulsification was analyzed in ASP flooding, and a relatively perfect mathematical model with deep filtration-theory was established, in which oil-water volume equation, saturation equation, viscosity equation, and permeability reduction equation are included. The new model is used to simulate the actual block of an oil field; the simulated results of the new model and an old model without considering the emulsification are compared with the actual well history. It is found that new model which is easy to be realized in numerical simulation has a high precision fitting, and the effect of adding oil and decreasing water is obvious. The sensitivity of emulsification was analyzed, and the results show that the water reducing funnel becomes wider and the rate of water cut decreases rapidly with the increase of emulsifying capacity, and then the rate of recovery slows down. The effect of increasing oil and decreasing water is better, and the degree of recovery increases. The emulsification of the ASP flooding is maintained at a moderate level, which corresponds to ${\Phi}=0.2$ in the new model, and the emulsification is applied to realize the general mathematical quantitative description, so as to better guide the oilfield development.

• Elastomers and Composites
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• 제56권2호
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• pp.79-84
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• 2021

A strain energy density function is used to characterize the hyperelasticity of rubber-like materials. Conventional models, such as the Neo-Hookean, Mooney-Rivlin, and Ogden models, are widely used in automotive industries, in which the strain potential is derived from strain invariants or principal stretch ratios. A fitting procedure for experimental data is required to determine material constants for each model. However, due to the complexities of the mathematical expression, these models can only produce an accurate curve fitting in a specified strain range of the material. In this study, a hyperelastic model for Neodymium Butadiene rubber is developed by using the Artificial Neural Network. Comparing the analytical results to those obtained by conventional models revealed that the proposed model shows better agreement for both uniaxial and equibiaxial test data of the rubber.

• 한국CDE학회논문집
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• 제17권4호
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.