• East Asian mathematical journal
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• 제40권1호
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• pp.95-107
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• 2024

Let K be an imaginary quadratic field with ring of integers 𝓞_K and N be a positive integer. By K_(N) we mean the ray class field of K modulo N𝓞_K. In this paper, for each prime p of K relatively prime to N𝓞_K we explicitly describe the action of the Artin symbol (${\frac{K_{(N)}/K}{p}}$) on special values of modular functions of level N. Furthermore, we extend the Kronecker congruence relation for the elliptic modular function j to some modular functions of higher level.

• 해양환경안전학회지
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• 제24권4호
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• pp.467-474
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• 2018

본 연구의 목적은 2가지 선속에서 운항하는 선박의 선형 설계 자동화에 관한 것이다. 가장 기본적인 선박의 형상을 가지는 60계열($C_B=0.6$) 선박을 대상선박으로 선택하여 연구를 수행하였다. 선박 형상의 향상 방향은 저항성능 향상의 관점이며, 특히 선박의 형상과 밀접한 관계를 가지는 조파저항성능을 향상하기 위한 선박 형상 설계 자동화를 수행하였다. 본 연구의 목적을 실현하기 위하여 최적화 기법과 저항 성능을 예측하는 기법 그리고 선형의 형상을 변경하는 기법을 접목하여 선박 형상 설계 자동화 소프트웨어를 개발하였으며, 개발된 소프트웨어를 대상선박에 적용하였다. 최적화 기법으로는 순차이차계획법(sequential quadratic programming method)를 사용하였으며, 조파저항성능을 예측하기 위하여 포텐셜기저 패널법(potential-based panel method)을 사용하였다. 선박 형상의 변경은 가우시안형 수정함수법(Gaussian-type modification function method)를 개발하여 적용하였다. 개발된 소프트웨어를 사용하여 대상선박의 서로 다른 두 가지 선속에 대하여 설계를 수행하고 그 결과를 서로 비교하였다. 그리고 개발된 프로그램의 타당성을 검증하기 위하여 모형시험을 수행하여 구한 실험값과 수치해석을 수행하여 구한 계산값을 서로 비교하였다.

• 한국항해항만학회지
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• 제29권7호
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• pp.603-609
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• 2005

This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP( sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using NURBS(Non-Uniform Rational B-Spline) surface patches. To verify the validity of the developed program the numerical calculations for Wigley hull and Series 60 Cb=0.6 hull are performed and the results obtained after the numerical calculations are compared with the initial hulls.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.542-547
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• 2003

A new approach to design of a discrete-time robust $H_{\infty}$ filter in finite horizon case is proposed. It is shown that robust $H_{\infty}$ filtering problem can be cast into the minimization problem of an indefinite quadratic form, which can be solved by implementing the Kalman filter defined in Krein space. The proposed filter is readily derived by simply augmenting the state space model and has the robustness property against the parameter uncertainties of a given system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.501-506
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• 1993

An efficient solution algorithm of the optimal load distribution problem with joint torque constraints is presented. Multiple robot system where each robot is rigidly grasping a common object is considered. The optimality criteria used is the sum of weighted norm of the joint torque vectors. The maximum and minimum bounds of each joint torque in arbitrary form are considered as constraints, and the solution that reduces the internal force to zero is obtained. The optimal load distribution problem is formulated as a quadratic optimization problem in R, where I is the number of robots. The general solution can be obtained using any efficient numerial method for quadratic programming, and for dual robot case, the optimal solution is given in a simple analytical form.

• Structural Engineering and Mechanics
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• 제32권1호
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• pp.37-53
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• 2009

In this paper the problem of calculating the probability that the responses of a wind-excited structure exceed specified thresholds within a given time interval is considered. The failure domain of the problem can be expressed as a union of elementary failure domains whose boundaries are of quadratic form. The Domain Decomposition Method (DDM) is employed, after being appropriately extended, to solve this problem. The probability estimate of the overall failure domain is given by the sum of the probabilities of the elementary failure domains multiplied by a reduction factor accounting for the overlapping degree of the different elementary failure domains. The DDM is extended with the help of Line Sampling (LS), from its original presentation where the boundary of the elementary failure domains are of linear form, to the current case involving quadratic elementary failure domains. An example involving an along-wind excited steel building shows the accuracy and efficiency of the proposed methodology as compared with that obtained using standard Monte Carlo simulations (MCS).

• 한국해양공학회지
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• 제18권3호
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• pp.32-39
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• 2004

A design procedure for a ship with minimum total resistance has been developed using a numerical optimization method called SQP(sequential quadratic programming) to search for different optimal hull forms. The frictional resistance has been estimated using the ITTC 1957 model-ship correlation line formula, and the wave resistance has been evaluated using a potential-flow panel method that is based on Rankine sources with nonlinear free surface boundary conditions. The geometry of a hull surface has been modified using B-spline surface patches, during the whole optimization process. The numerical analyses have been carried out for the modified Wilgey hull at three different speeds (Fn=0.25, 0.316, 0.408), and the calculation results were compared.

• Communications for Statistical Applications and Methods
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• 제27권5호
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2005년도 춘계학술대회 논문집
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• pp.435-440
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• 2005

This study describes a new method of constructing Reconfigurable machine tools configurations from a set of modules or components. This proposed method defines combinability vector for each module and mutual combinability coefficient matrix for adjacent two modules. All of machine configurations possible to be generated from any two adjacent modules can be determined by quadratic form of two associated combinability vectors. Furthermore, all of possible RMT configurations generating from a series of multiple modules also can be obtained by multiplying quadratic form of two adjacent conbinability vectors recursively. Our proposed RMT configuration generating method can be successfully applied to determining all of possible machine configurations from several modules or components at conceptual- or preliminary- design stage.

• Journal of the Korean Data and Information Science Society
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• 제20권3호
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• pp.577-585
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• 2009

So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.