• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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• pp.867-876
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• 2003

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Four points Hermite interpolation in the homogeneous direction and Chebyshev polynomials in the inhomogeneous direction is adopted to simulate the fluid particle dispersion. An inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersions and Lagrangian structure functions of velocity are scaled by the Kolmogorov similarity. The auto-correlations of velocity and acceleration are shown at the different releasing locations. Effect of initial particle location on the dispersion is analyzed by the probability density function at the several downstreams and time instants.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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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).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.3 s.258
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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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• v.9 no.1
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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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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• v.23 no.1_2
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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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• v.12 no.3
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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.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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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.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.25 no.3
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• pp.257-266
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• 2007

The research on red tide is generally in progress through field work, such as the naked eye and sampling. It was difficult to forecast exactly the course, from appearance of red tide to disappearance. with the established ways of investigation and analysis. Accordingly it is need to analyze environmental factors in time and space, the appearance of red tide and the path of its migration by more objective and scientific methods. In this study, GIS is applied to analyse the space character of red tide and the interpolation of IDW(Inverse Distance Weight) is applied to assume the density distribution of red tide after gather data by using Arc/Info. After IDW interpolation, the sea area occurred over 1,000 cells/ml of red tide density is extracted with CON and SUM Function of Grid Module, and the density of the sea area is accumulated daily. As a result of this study, the distribution condition of red tide is found timely and spacially by applying GIS to the sea area of red tide, the results indicated that the spatial density and the cumulative frequency about the origin of red tide using GIS, the sea area demonstrated that the maximum density and the maximum frequency varied significantly over the Nammyun of Namhae-Is. with the maximum frequency being 49 times. accordingly if data about the areas of red tide will occur from the present are accumulated, the shifting route of red tide occurrence and extinction can be predicted.