• 호남수학학술지
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• 제44권3호
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• pp.325-338
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• 2022

In this paper, a new identity is given. On the basis of this identity, we establish some new estimates of Milne's quadrature rule, for functions whose first derivative is s-convex. We discuss the cases where the derivatives are bounded as well as Lipschitzian. Some illustrative applications are given.

• 한국지능시스템학회논문지
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• 제13권3호
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• pp.316-321
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• 2003

최근들어, 서포트 벡터 학습은 패턴 분류, 함수 근사 및 비정상 상태 탐지 등의 분야에서 상당한 관심을 끌고 있다. 여러가지 서포트 벡터 학습 방법들 중 누-버전(nu-versions)으로 불리는 방법들은 서포트 벡터의 개수를 제어해야할 필요가 있는 경우에는 특히 유용한 것으로 알려져 있다. 본 논문에서는, $\nu-SVR$로 불리는 누-버전 서포트 벡터 학습 방법과 미리 정해진 기저함수를 모두 활용하는 함수 근사 문제를 고려한다. $\varepsilon-SVR$, $\nu-SVR$ 및 세미-파라메트릭 함수 근사 방법론등을 복습한 후에, 본 논문은 정해진 기저함수를 이용할 수 있는 방향으로 기존의 $\nu-SVR$ 방법을 확장하는 방안을 제시한다. 그리고, 제안된 방법의 적용가능성이 예제를 통하여 보여진다.

• Steel and Composite Structures
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• 제47권5호
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• 한국측량학회지
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• 제30권2호
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• pp.153-162
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• 2012

본 연구는 저니키 모멘트 서술자를 이용하여 객체 쌍의 기수성에 영향을 받지 않고 M:N 면 객체 쌍의 형상 유사도를 측정할 수 있는 방법을 제안한다. 제안된 형상 유사도는 저니키 기저함수에 객체 집합의 공간적 분포 영역을 투영하여 얻어지는 모멘트를 이용하기 때문에 형상을 구성하는 객체들의 기수성에 영향을 받지 않는다. 또한 낮은 차수의 기저함수에 대응되는 모멘트는 전역적인 형상을 표현하고, 높은 차수의 기저함수에 대응되는 모멘트는 지역적인 형상을 표현하기 때문에 원형상과 유사한 수준으로 형상을 복원할 수 있는 차수까지의 모멘트를 이용함으로써 효과적으로 형상을 서술하고 비교하는 것이 가능하다. 제안된 방법은 서울시 지역의 도로명주소 지도와 차량용 항법 지도의 건물 객체를 대상으로 적용 및 평가하였다. 기존 중첩면적비를 이용한 유사도에 비하여 제안된 유사도는 기수성의 변화에 강건함을 확인할 수 있었다.

• 대한수학회보
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• 제54권6호
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• 대한전자공학회논문지TC
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• 제49권8호
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• pp.25-32
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• 2012

본 논문에서는 고속 시변 채널 OFDM을 위한 저복잡도 LS(Least Squares) 채널 예측의 성능 개선 방안을 제안한다. 저복잡도 LS 채널 예측을 위해 사용하는 CE-BEM(Complex Exponential-Basis Expansion Model) 채널 모델의 경우 채널 모델 자체의 문제점으로 인하여 채널 예측 성능 저하가 발생한다. 본 논문에서는 우선 시간 영역 윈도우를 이용하여 데이터 심볼에 의한 ICI(Interchannel Interference)의 영향을 제거한다. LS 채널 예측 결과에서 샘플을 취하여 윈도우의 영향을 제거한 후 특성이 채널 변화의 표현에 적합한 DPSS(Discrete Prolate Spheroidal Sequences)를 기저함수(basis function)로 하는 보간 (interpolation) 방식으로 채널 응답을 복원하여 CE-BEM의 문제점을 해결한다. 컴퓨터 모의실험을 통한 성능 확인 결과 제안된 채널 예측 방식은 기존의 방식과 비교하여 특히 고속 시변 채널에서 우수한 성능 개선 효과를 보여주며, 선택된 기저함수의 형태뿐만 아니라 기저함수의 개수의 설정이 성능을 크게 좌우하는 또 다른 요소임을 확인하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.391-396
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady state heat conduction problems. The only inside of complicated domain is identified by the level set functions and taken into account in computation. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. The nucleation of holes is possible whenever and wherever necessary during the optimization using a topological derivative concept.

• 한국CDE학회논문집
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• 제21권4호
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• pp.443-452
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• 2016

This paper proposes a method for expensive black box optimization using radial basis functions (RBFs). The proposed algorithm is a computational strategy that uses a RBF model approximating the expensive black box function to predict an optimum. First, a RBF-based approximation technique is introduced and a sampling plan for estimation of the black box function is described. Then the proposed algorithm is explained, which presents the pseudo-codes for implementation and the detailed description of each step performed in the optimization process. In addition, numerical experiments will be given to analyze the performance of the proposed algorithm, by investigating computation accuracy, number of function evaluations, and convergence history. Finally, geometric distance problem as application example will be also presented for showing the algorithm applicability to different engineering problems.

• International Journal of Concrete Structures and Materials
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• 제6권3호
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• pp.135-144
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• 2012

This article reviews the tailoring of engineered cementitious composites (ECC), a type of high performance fiber reinforced cementitious composites with a theoretical design basis, for special attributes or functions. The design basis, a set of analytic tools built on micromechanics, provides guidelines for tailoring of fiber, matrix, and fiber/matrix interfaces to attain tensile ductility in ECC. If conditions for controlled multiple cracking are disturbed by the need to introduce ingredients to attain a special attribute or function, micromechanics then serve as a systematic and rational means to efficiently recover composite tensile ductility. Three examples of ECCs with attributes of lightweight, high early strength, and self-healing functions, are used to illustrate these tailoring concepts. The fundamental approach, however, is broadly applicable to a wide variety of ECCs designed for targeted fresh and/or hardened characteristics required for specific applications.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.170-175
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• 1998

Transporting a large table using multiple robotic agents requires at least two group behaviors of homing and herding which are to bo coordinated in a proper sequence. Existing GP methods for multi-agent learning are not practical enough to find an optimal solution in this domain. To evolve this kind of complex cooperative behavior we use a novel method called fitness switching. This method maintains a pool of basis fitness functions each of which corresponds to a primitive group behavior. The basis functions are then progressively combined into more complex fitness functions to co-evolve more complex behavior. The performance of the presented method is compared with that of two conventional methods. Experimental results show that coevolutionary fitness switching provides an effective mechanism for evolving complex emergent behavior which may not be solved by simple genetic programming.