• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.659-668
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• 2001

Let S(z) be a power series with operator coefficients such that multiplication by S(z) is an everywhere defined transformation in the square summable power series C(z). In this paper we show that there exists a reproducing kernel Krein space which is state space of extended canonical linear system with transfer function S(z). Also we characterize the reproducing kernel function of the state space of a linear system.

• 한국공작기계학회논문집
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• 제12권5호
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• pp.67-72
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• 2003

For the analysis of Kirchhoff plate bending problems, a new meshless method is implemented. For the satisfaction of the $C^1$ continuity condition in which the first derivative is treated an another primary variable, Hermite interpolation is enforced on standard reproducing kernel particle method. In order to impose essential boundary conditions on solving $C^1$ continuity problems, shape function modifications are adopted. Through numerical tests, the characteristics and accuracy of the HRKPM are investigated and compared with the finite element analysis. By this implementatioa it is shown that high accuracy is achieved by using HRKPM for solving Kirchhoff plate bending problems.

• Interaction and multiscale mechanics
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• 제3권3호
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• pp.277-298
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• 2010

The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

• Korean Journal of Mathematics
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• 제31권1호
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.12-18
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• 2002

For the analysis of Kirchhoff plate bending problems, a new meshless method is implemented. For the satisfaction of the C¹ continuity condition in which the first derivative is treated as another primary variable, Hermite interpolation is enforced on standard reproducing kernel particle method. In order to impose essential boundary conditions on solving C¹ continuity problems, shape function modifications are adopted. Through numerical tests, the characteristics and accuracy of the HRKPM are investigated and compared with the finite element analysis. By this implementation, it is shown that high accuracy is achieved by using HRKPM fur solving Kirchhoff plate bending problems.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.939-946
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• 2008

In this paper the support vector method is presented for the probability density function estimation when the sample observations are contaminated with random noise. The performance of the procedure is compared to kernel density estimates by the simulation study.

• 호남수학학술지
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• 제44권3호
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• pp.447-460
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• 2022

We consider a closed subspace ${\tilde{A}}^{{\alpha},m}_q$ (ℂ) of the Fock space A^α,m_q (ℂ) of q-analytic functions with the weight ϕ(z) = -α log |z|²+|z|^2m for any positive integer m. We obtain the corresponding reproducing kernel K^ℂ_α,q,m(z, w) using the weighted Laguerre polynomials and the Mittag-Leffler functions. Finally, we investigate the necessary and sufficient condition on (α, q, m) such that K^ℂ_α,q,m(z, w) is zero-free.

• 응용통계연구
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• 제33권5호
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• pp.569-578
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• 2020

분위수 회귀모형은 반응변수의 조건부 분위수 함수를 추정함으로써 반응변수와 예측변수의 관계에 대한 포괄적인 정보를 제공한다. 특히 커널 분위수 회귀모형은 비선형 관계식을 고려하기 위하여 양정치 커널함수(kernel function)에 의해 만들어지는 재생 커널 힐버트 공간(reproducing kernel Hilbert space)에서 비선형 조건부 분위수 함수를 추정한다. 그러나 KQR은 이차계획법으로 공식화되어 많은 계산비용을 필요로 하므로 컴퓨터 메모리 능력의 제한으로 대용량 자료의 분석은 불가능하다. 이러한 문제점을 해결하기 위하여 본 논문에서는 분할정복(divide and conquer) 알고리즘을 활용한 KQR 추정법(DC-KQR)을 제안한다. DC-KQR은 먼저 전체 훈련자료를 몇 개의 부분집합으로 무작위로 분할(divide)한 후, 각각의 부분집합에 대하여 KQR 분위수 함수를 추정하고 이들의 산술 평균을 이용하여 최종적인 추정량으로 통합(conquer)하는 기법이다. 본 논문에서는 모의실험과 실제자료 분석을 통해 제안한 DC-KQR의 효율적인 성능과 활용 가능성을 확인하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 가을 학술발표회 논문집
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• pp.16-23
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• 1997

The Reproducing Kernel Particle Method (RKPM), one of the popular meshless methods, is developed and applied to stress concentration problems. Since the meshless methods require only a set of particles (or nodes) and the description of boundaries in their formulation, the adaptivity can be implemented with much more ease than finite element method. In addition, due to its intrinsic property of multiresolution, the shape function of RKPM provides us a new criterion for adaptivity. Recently, this multiple scale Reproducing Kernel Particle Method and its adaptive procedure have been formulated for large deformation problems by the authors. They are also under development for damage materials and localization problems. In this paper the multiple scale RKPM for linear elasticity is presented and the adaptive procedure is applied to stress concentration problems. Therefore, this work may be regarded as the edition of linear elasticity in the complete framework of multiple scale RKPM and the associated adaptivity.

• 대한수학회보
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• 제38권4호
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).