• 대한수학회보
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• 제29권2호
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• 대한기계학회논문집B
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• 제31권3호
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• pp.300-305
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• 2007

Many practical flow problems are defined with the circular boundary. Fluid flows within a circular boundary are however susceptible to a singularity problem when the cylindrical coordinates are employed. To remove this singularity a method has been developed in this study which uses the local harmonic functions in discretization of derivatives as well as interpolation. This paper describes the basic reason for introducing the harmonic functions and the overall numerical methods. The numerical methods are evaluated in terms of the accuracy and the stability. The Lamb-dipole flow is selected as a test flow. We will see that the harmonic-function method indeed gives more accurate solutions than the conventional methods in which the polynomial functions are utilized.

• International Journal of Aeronautical and Space Sciences
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• 제9권1호
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• pp.1-30
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• 2008

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect; its state equation remains always valid, except, it is named in more by calorically imperfect gas. The aim of this work is to trace the profiles of the supersonic axisymmetric Minimum Length Nozzle to have a uniform and parallel flow at the exit section, when the stagnation temperature is taken into account, lower than the dissociation threshold of the molecules, and to have for each exit Mach number and stagnation temperature shape of nozzle. The method of characteristics is used with the algorithm of the second order finite differences method. The form of the nozzle has a point of deflection and an initial angle of expansion. The comparison is made with the calorically perfect gas. The application is for air.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.55-61
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• 2002

In the present study, a first order shear deformable Loop-subdivision triangular element which can handle transverse shear deformation of moderately thick shell and composite laminated or sandwich shells are developed. The developed element is more general than the previous one based on classical shell theory, since it includes the effect of transverse shell deformation and has standard five degrees of freedom per node. The quartic box spline function is employed as the interpolation basis function. Numerical examples for the benchmark static shell problems are analyzed to assess the performance of the developed subdivision shell element and locking trouble.

• 충청수학회지
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• 제26권1호
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• pp.231-242
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• 2013

In this work, we deal with $q$-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$-Genocchi polynomials and derive distribution formula for the $q$-Genocchi polynomials. In the final part, we introduce a definition of $q$-Zeta-type function which is interpolation function of the $q$-Genocchi polynomials at negative integers which we express in the present paper.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.397-410
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• 2007

Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.

• Structural Engineering and Mechanics
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• 제12권3호
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• pp.313-328
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• 2001

A multi-span bridge has the peak value of resultant girder moment or membrane stress at the interior support. In this paper, the spline finite strip method (FSM) is modified to obtain the more appropriate solution at the interior support where the peak values of solution exist. The modification has been achieved by expressing the shape function with non-periodic B-splines which have multiple knots at the boundary. The modified B-splines have the useful feature for interpolating the curve with sudden change in curvature. Moreover, the modified spline FSM is very efficient in analyzing multi-span box girder bridges, since a bridge can be modeled by an assembly of strips extended along the entire bridge length. Numerical examples of the bridge analysis have been performed to verify the efficiency and accuracy of the new spline FSM.

• 한국정밀공학회지
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• 제23권8호
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• pp.119-126
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• 2006

Kriging model is widely used as design DACE(analysis and computer experiments) model in the field of engineering design to accomplish computationally feasible design optimization. In this paper, the optimization of gate valve was performed using Kriging based approximation model. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. In addition, we describe the definition, the prediction function and the algorithm of Kriging method and examine the accuracy of Kriging by using validation method.

• 한국측량학회지
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• 제25권3호
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• pp.257-266
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• 2007

적조에 관한 조사는 육안과 샘플링에 의한 현지조사에 의해 일반적으로 진행되고 있다. 이와 같은 기존의 조사, 분석방법은 적조의 발생과 소멸까지의 경로를 정확하게 예측하기 곤란하였다. 이에 좀더 객관적이고 과학적인 방법으로 적조의 발생과 그 이동경로 등 시 공간적인 환경인자를 분석해 볼 필요성이 대두되고 있다. 본 연구에서는 지리정보시스템을 적용하여 적조의 공간특성을 분석하고자 Arc/Info를 활용하여 자료를 구축한 후 적조발생해역에서의 적조밀도분포를 추정하기 위해 IDW 보간법을 적용하였다. 그 후 GRID 모듈의 CON 및 SUM Function을 이용하여 밀도 1,000cells/ml이상 발생된 해역을 추출하였으며, 추출된 해역을 기준으로 날짜별로 밀도를 누적하였다. 본 연구를 통하여 적조가 발생되는 해역을 지리정보시스템에 의해 적조의 분포 현황을 시 공간적으로 판단할 수 있었으며, 적조발생지의 공간별 밀도와 누적빈도를 GIS를 적용하여 분석한 결과 최대밀도 발생해역과 최대 빈도 발생해역 모두 남해도 남면일대 해역으로서 최대 누적빈도는 49회임을 알 수 있었다. 이를 근거로 차 후 발생되는 적조발생해역에 대한 자료의 보완이 이뤄질 경우 적조 발생과 소멸까지의 이동경로를 예측 할 수 있으리라 판단된다.

• 한국식품위생안전성학회지
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• 제28권2호
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• pp.168-173
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• 2013

본 연구는 신선편이 식품에서 오염 가능성이 있는 병원성 식중독 균 E. coli O157:H7에 대해 파프리카에서 성장 예측 모델을 적용하고, 본 연구에서 개발된 성장 예측 모델을 내부 검증하였다. 이를 비교하여 신선편이 식품을 안전하게 관리하기 위한 적절한 모델을 제시하고자 하였다. 파프리카에 E. coli O157:H7접종하여 온도에 따라 12, 24, 30, $36^{\circ}C$에 보관하여 성장을 측정하였다. Gompertz 식을 이용하여 온도에 따른 성장곡선을 그리고 LT와 SGR을 산출하였다. 산출된 LT와 SGR은 각각 Davey model와 squareroot model를 이용하여 2차 모델을 개발하였다. 개발된 2차 모델에 대하여 LT와 SGR model의 $R^2$값은 각각 0.999, 0.994로 1에 근접하는 높은 적합성을 보였다. 또한 내부 검정 결과 LT와 SGR model의 Bf 값은 각각 1.01, 0.89, LT model은 안전하게 SGR model 위험하게 예측되었다. 파프리카의 LT와 SGR의 상대적인 오차 값은 모두 허용 가능한 오차 범위에 포함 되었다. 따라서 개발된 모델을 이용하여 온도에 따른 E. coli O157:H7성장을 추정할 수 있으며, 이를 위해평가 자료로 활용할 수 있을 것으로 보인다.