• International Journal of Naval Architecture and Ocean Engineering
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• 제12권1호
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• pp.468-478
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• 2020

The wave interaction problem with a vertical slotted breakwater, consisting of impermeable upper, lower parts and a permeable middle part, has been studied theoretically. An analytical model was presented for the estimation of reflection and transmission of monochromatic waves by a slotted breakwater. The far-field solution of the wave scattering involving nonlinear porous boundary condition was obtained using eigenfunction expansion method. The empirical formula for drag coefficient in the near-field, representing energy dissipation across the slotted barrier, was determined by curve fitting of the numerical solutions of 2-D channel flow using CFD code StarCCM+. The theoretical model was validated with laboratory experiments for various configurations of a slotted barrier. It showed that the developed analytical model can correctly predict the energy dissipation caused by turbulent eddies due to sudden contraction and expansion of a slotted barrier. The present paper provides a synergetic approach of the analytical and numerical modelling with minimum CPU time, for better estimation of the hydrodynamic performance of slotted breakwater.

• 한국수학사학회지
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• 제23권3호
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• pp.121-140
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• 2010

본 논문은 속도, 온도, 농도, 밀도, 단가, 일인당 국민소득 등의 내포량의 평균을 구할 때, 내포량마다 다른 공식을 적용하여 구해야 하는 불편함을 해소하기 위하여, 지레의 원리를 이용하여 두 내포량의 평균 공식 $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$를 유도하였고, 이 공식의 관계적 이해를 돕기 위해 지레의 원리를 이용한 조작적 학습법을 제시하였다. 비의 의미의 분수는 그 수치만으로 덧셈을 할 수가 없어 비가법적이라고 한 것을 비중을 적용하여 계산할 수 있음을 보인 것이다. 또한 두 양에서뿐만 아니라 여러 양의 덧셈도 단 한번의 공식에의 적용으로 해결할 수 있도록 확장 적용시킨 $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$ (단, $f_1+f_2+{\cdots}+f_n=N$) 은 새로운 공식이 가중평균을 구하는 공식이었다는 것을 밝혔다. 또한 통계학에서 의문거리였던 하위 제표의 방향성과 다른 모습을 보이는 상위제표의 통계자료에 대한 심프슨의 파라독스의 의문점을 가중평균의 원리를 이용하여 밝혔다.

• 천문학회보
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• 제41권1호
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• pp.38.2-38.2
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• 2016

The mapping of dark matter clustering from real to redshift spaces introduces the anisotropic property to the measured density power spectrum in redshift space, known as the Redshift Space Distortion (hereafter RSD) effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to the indefinite cross correlations between the density and velocity fields, and the Finger-of-God (hereafter FoG) effect due to the randomness of the peculiar velocity field. Furthermore, the rigorous test of this mapping formula is contaminated by the unknown non-linearity of the density and velocity fields, including their auto- and cross-correlations, for calculating which our theoretical calculation breaks down beyond some scales. Whilst the full higher order polynomials remains unknown, the other systematics can be controlled consistently within the same order truncation in the expansion of the mapping formula, as shown in this paper. The systematic due to the unknown non-linear density and velocity fields is removed by separately measuring all terms in the expansion using simulations. The uncertainty caused by the velocity randomness is controlled by splitting the FoG term into two pieces, 1) the non-local FoG term being independent of the separation vector between two different points, and 2) the local FoG term appearing as an indefinite polynomials which is expanded in the same order as all other perturbative polynomials. Using 100 realizations of simulations, we find that the best fitted non-local FoG function is Gaussian, with only one scale-independent free parameter, and that our new mapping formulation accurately reproduces the observed power spectrum in redshift space at the smallest scales by far, up to k ~ 0.3 h/Mpc, considering the resolution of future experiments.

• Journal of the Korean Statistical Society
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• 제7권1호
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• 한국공작기계학회논문집
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• 제14권1호
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• pp.81-88
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• 2005

There have been many studies on generation equipment and plant piping, but there is no significant study result on the heat transportation pipe. As such, this study established basic theory on the compensated method among buried pipe for regional heating, and further obtained the following results by applying the conditions of AGFW and NCHPP respectively in calculation of friction and maximum installation distance for the buried pipe. Friction coefficient according to the types and physical properties of soil, friction and maximum installation distance were compared to set the application value of friction coefficient according to the location of works. Calculation formula of clay load to be applied for calculation of friction was introduced to the formula of AGFW and the formula of NCHPP that has been used in Nowon district since 1997 to determine the difference and applicability. $120^{\circ}C$ and $95^{\circ}C$ were applied in temperature difference for expansion volume to compare the arm length at the curve pipe so thai it can be reflected in the design in the future. Maximum installation distance according to thickness of pipe was compared to present the necessity of unified specification so that same kinds of pipe materials can be used for same kinds of works.

• 대한화학회지
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• 제16권4호
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• pp.214-218
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• 1972

The quadratic force constants of heteronuclear diatomic molecules, LiH, BeH, BH, CH, NH and OH are evaluated by use of the one center function of Bishop et. al. The master formula on which the computation is based was suggested by the previous work of one of the present authors. The results are in good agreement with the experimental values. It is found that around the nucleus of the atom located in the close vicinity of the expansion center of the one center function, the electronic distribution is relatively unrealistic, and the suggested formula would lead an erroneous result when one takes the origin of variables of $P_2(cos{\theta})/r_3$ at the atomic nucleus.

• 한국조명전기설비학회지:조명전기설비
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• 제9권3호
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• pp.80-87
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• 1995

영구자석형 스테핑 전동기의 언덕턴스를 고려하여 최대 평균 토오크식을 제시하였으며, 제시된 토오크식에 근거하여 마이크로컨트롤러에 의해 lead angle을 전동기의 속도에 따라 최적으로 제어함으로서 최대 토오크를 발생시키는 제어시스템을 설계하여 전동기의 토오크/속도 특성 실험을 하였다. 이론식에 의하면 토오크/속도 곡선에서 최적 lead angle의 도입에 따라 발생하는 토오크가 증대되며, 운전영역이 2배이상 확대되는 바와 같이, 특성실험 결과에서도 최적 lead angle의 실현에 따라 구동모드에 관계없이 발생 토오크가 증대되며, 운전영역이 2배이상 학대됨을 확인 할 수 있다.

• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권4호
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• pp.275-287
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• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• 한국정밀공학회지
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• 제27권9호
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• pp.94-102
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• 2010

The spindle is the main component in machine tools. To develop high speed machine tools, a lot of studies have been carried out for high speed spindle. Bearing is very important part in spindle. The bearing clearance is influenced by shrink fit and thermal expansion during operation. The designer must take into account the reduction of shrink fits. The aims of this study are to grasp the shrink fits and behavior of a bearing which is a deeply connected with fatigue life of bearing and performance of spindle through FEM(Finite Element Method). This paper proposed optimum value of shrink fit considering deformation of spindle and stress of fitting area using design of experiments. Thus, the proposed formula can be used to obtain bearing internal clearance.