• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• 제5권1호
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• pp.40-45
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• 2002

The calculation of earthwork plays a major role in the planning and design phases of many civil engineering projects, such as seashore reclamation; thus, improving the accuracy of earthwork calculation has become very important. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three-dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors, especially those concerned with accuracy of volume computations. The mathematical models of the conventional methods have a common drawback: the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial is chosen as the mathematical model of the new method. In this paper, we propose an algorithm of finding a spline surface, which interpolates the given data, and an appropriate method to calculate the earthwork. We present some computational results that show the proposed method, of the Maple program, provides better accuracy than the method presented by Chen and Lin.

• 대한수학회논문집
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• 제38권4호
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• pp.1309-1320
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• 2023

Let f : X → Y be a map between simply connected CW-complexes of finite type with X finite. In this paper, we prove that the rational cohomology of mapping spaces map(X, Y ; f) contains a polynomial algebra over a generator of degree N, where N = max{i, π_i(Y)⊗ℚ ≠ 0} is an even number. Moreover, we are interested in determining the rational homotopy type of map(𝕊ⁿ, ℂP^m; f) and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.

• Journal of the Korean Wood Science and Technology
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• 제43권3호
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• pp.311-319
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• 2015

근적외선 반사율 분광분석법을 이용하여 리기다 소나무, 소나무, 잣나무, 백합나무의 섬유포화점 이하 함수율 예측모델을 개발하였다. 시편들을 다양한 평형함수율 상태로 유도한 후 1000 nm~2400 nm 파장영역의 반사율 스펙트럼을 획득하였다. 최적 함수율 예측 모델을 선정하기 위해 5가지의 수학적 전처리(moving average (smoothing point: 3), baseline, standard normal variate (SNV), mean normalization, Savitzky-Golay $2^{nd}$ derivatives (polynomial order: 3, smoothing point: 11))를 8가지 조합으로 각 시편의 반사율 스펙트럼에 적용하였다. 수학적 전처리 후, 변형된 스펙트럼을 이용하여 PLS 회귀분석을 실시하였다. 그 결과, 최적 함수율 예측 모델을 도출한 전처리 방법은 리기다 소나무와 소나무의 경우 moving average/SNV, 잣나무와 백합나무의 경우 moving average/SNV/Savitzky-Golay $2^{nd}$ derivatives이며, 모든 모델은 3개의 주성분을 포함하고 있었다.

• 한국경영과학회지
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• 제23권4호
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• pp.11-20
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• 1998

This paper deals with a mathematical model and an algorithm for the problem of determining k most vital arcs in the shortest path problem. First, we propose a 0-1 integer programming model for finding k most vital arcs in shortest path problem given the ordered set of paths with cardinality q. Next, we also propose an algorithm for finding k most vital arcs ln the shortest path problem which uses the 0-1 Integer programming model and shortest path algorithm and maximum flow algorithms repeatedly Malik et al. proposed a non-polynomial algorithm to solve the problem, but their algorithm was contradicted by Bar-Noy et al. with a counter example to the algorithm in 1995. But using our algorithm. the exact solution can be found differently from the algorithm of Malik et al.

• 대한산업공학회지
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• 제13권2호
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• pp.105-115
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• 1987

Although there are many theoretical methods for the transformation of random variables. it is difficult to find probability density functions for the new random variables because of the complexity in mathematics. The author developed a simulation model solving the above difficulties using FBI (Fortran Based Interpreter) routines. The FBI is a kind of language Interpreter analyzing the arithmetic statement in character data forms. In this paper. the FBI routines will be explained and the structure and applications of simulation model will be also demonstrated. Polynomial curve fitting method is applied to define the probability density function which can not be defined by well-known pdf. This program can also be used for instructing mathematical statistics and identifying distribution of the simulated data.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 하계학술대회 논문집 B
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• pp.1352-1354
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• 2004

The accurate analysis on railway traction power system should be carried out a load forecast preferentially. Commonly, it has been performed through Train Performance Simulator (TPS). In the study focused on velocity or location of train, however, the electric power consumption have been computed by converting mechanical power according to given velocity. Therefore, this paper presents a development of a mathematical model for electric load. The proposed load model is expressed as polynomial to reflect the influence of variance of train speed, that is, the model expresses the power as a function of train speed. in this study, method of the least squares method is used to find each coefficient and field test is performed to acquire data, electric power and speed of train in commercial running line.

• 대한원격탐사학회지
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• 제19권3호
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• pp.247-253
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• 2003

The mainly used technique to correct satellite images with geometric distortion is to develop a mathematical relationship between pixels on the image and corresponding points on the ground. Polynomial models with various transformations have been designed for defining the relationship between two coordinate systems. GCP based geometric correction has peformed overall plane to plane mapping. In the overall plane mapping, overall structure of a scene is considered, but local variation is discarded. The Region with highly variant height is rectified with distortion on overall plane mapping. To consider locally variable region in satellite image, TIN-based rectification on a satellite image is proposed in this paper. This paper describes the relationship between GCP distribution and rectification model through experimental result and analysis about each rectification model. We can choose a geometric correction model as the structural characteristic of a satellite image and the acquired GCP distribution.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2003년도 Proceedings of ACRS 2003 ISRS
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• pp.1143-1145
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• 2003

Some of satellites such as IKONOS don't provide the orbital elements so that we can’ utilize the physical sensor model. Therefore, Rational Function Model(RFM) which is one of mathematical models could be a feasible solution. In order to improve 3D geopositioning accuracy of IKONOS stereo imagery, Rational Polynomial Coefficients(RPCs) of the RFM need to be updated with Ground Control Points(GCPs). In this paper, a method to improve RPCs of RFM using GCPs and 3D cube is proposed. Firstly, the image coordinates of GCPs are observed. And then, using offset values and scale values of RPC provided, the image coordinates and ground coordinates of 3D cube are initially determined and updated RPCs are computed by the iterative least square method. The proposed method was implemented and analyzed in several cases: different numbers of 3D cube layers and GCPs. The experimental results showed that the proposed method improved the accuracy of RPCs in great amount.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.766-771
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• 1993

A mathematical model is developed to represent the batch reactor for free radical polymerization of PMMA The model is validated by comparing the simulation result with the experimental data. A computational scheme is proposed to determine the trajectory of the reactor temperature that will produce polymer product having the desired molecular weight distribution. For this instantaneous number average chain length and polydispersity are introduced to calculate the reactor temperature. The former is assumed to be a second order polynomial of the sum of the living and dead polymer concentrations. Various reactor temperature, trajectories are observed depending on the reactor conditions and prescribed molecular weight distributions. Fuzzy and PID control algorithms are applied to trace the reactor temperature trajectory. While the PID control gives rise to an overshoot when the trajectory changes its direction, the fuzzy controller yields a more satisfactory performance because it secures information on the trajectory pattern.

• Structural Engineering and Mechanics
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• 제71권6호
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• pp.657-668
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• 2019

The numerical thermal frequency responses of the skew sandwich shell panels structure are investigated via a higher-order polynomial shear deformation theory including the thickness stretching effect. A customized MATLAB code is developed using the current mathematical model for the computational purpose. The finite element solution accuracy and consistency have been checked via solving different kinds of numerical benchmark examples taken from the literature. After confirming the standardization of the model, it is further extended to show the effect of different important geometrical parameters such as span-to-thickness ratios, aspect ratios, curvature ratios, core-to-face thickness ratios, skew angles, and support conditions on the frequencies of the sandwich composite flat/curved panel structure under elevated temperature environment.