• 호남수학학술지
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• 제30권4호
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• pp.671-676
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• 2008

We give the relation between the Riemann-Stieltjes integrals with respect to the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) distribution $H_{a,p}$ satisfying the equation a = $(1-a)^m$ and those with respect to the dual RNT distribution $H_{1-a,1-p}$, which leads to a generalization of recent results for a = $\frac{1}{2}$.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 추계종합학술대회 논문집
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• pp.724-727
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• 1999

The previous LQ-servo PI design methods have some serious design problems happened from the frequency matching of the maximum and minimum singular values of loop transfer function at both low and high frequency regions on the Bode plot. To solve these problems, this paper proposes a new design technique based on the inverse-optimal control and convex optimization.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.12-12
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• 2000

This paper consider a new weighted model reduction using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of reduced order system is quaranteed and a priori error bound is proposed. to achieve this, after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical example.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제1권1호
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• pp.29-33
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• 1994

There are various aspects of the solution of boundary-value problems for second-order linear elliptic equations in two independent variables. One useful method of solving such boundary-value problems for Laplace's equation is by means of suitable integral representations of solutions and these representations are obtained most directly in terms of particular singular solutions, termed Green's functions.(omitted)

• 해양환경안전학회지
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• 제1권2호
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• pp.61-67
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• 1995

This study examines experimentally and theoretically, the wave deformation by two large cylindrical structure in relation to the case of one structure. The wave height around the structures varies, according to the changes of the incident wave angles, the number of the structure, and the distances between the two structures. The wave deformation around the large cylindrical structures is shown to be well predicted theoretically by the diffraction theory based on the singular point distribution method using a vertical line wave source Green's function.

• 대한수학회지
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• 제56권1호
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• 호남수학학술지
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• 제43권2호
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• pp.259-267
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• 2021

Given 𝛽 > 1, we consider real numbers whose 𝛽-expansions are Sturmian words. When the slope of Sturmian words varies, their behaviors have been well studied from analytical point of view. The regularity enables us to find the Fourier series expansion, while the singularity at rational slopes yields a new kind of trigonometric series representing 𝜋.

• East Asian mathematical journal
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• 제38권1호
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• pp.13-20
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• 2022

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

• Ocean Systems Engineering
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• 제7권4호
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• pp.399-412
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• 2017

The Gauss-Legendre integral method is applied to numerically evaluate the Green function and its derivatives in finite water depth. In this method, the singular point of the function in the traditional integral equation can be avoided. Moreover, based on the improved Gauss-Laguerre integral method proposed in the previous research, a new methodology is developed through the Gauss-Legendre integral. Using this new methodology, the Green function with the field and source points near the water surface can be obtained, which is less mentioned in the previous research. The accuracy and efficiency of this new method is investigated. The numerical results using a Gauss-Legendre integral method show good agreements with other numerical results of direct calculations and series form in the far field. Furthermore, the cases with the field and source points near the water surface are also considered. Considering the computational efficiency, the method using the Gauss-Legendre integral proposed in this paper could obtain the accurate numerical results of the Green function and its derivatives in finite water depth and can be adopted in the near field.

• 천문학회보
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• 제40권1호
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• pp.77.1-77.1
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• 2015

We present our recent work published in the MNRAS (Lee and Kim, 2014). Numerical studies of the imaging and caustic properties of the singular isothermal sphere (SIS) under a wide range of external shear (from 0.0 to 2.0) are presented. Using a direct inverse mapping formula for this lensing system, we investigate various lensing properties for both low-shear (i.e. ${\gamma}$<1.0) and high-shear (i.e. ${\gamma}$ >1.0) cases. We systematically analyse the effective lensing cross-sections of double-lensing and quadruple-lensing systems, based on the radio luminosity function obtained by the Jodrell-VLA Astrometric Survey (JVAS) and the Cosmic Lens All-Sky Survey (CLASS). We find that the limit of a survey selection bias (i.e. between brighter and fainter images) preferentially reduces the effective lensing cross-sections of two-image lensing systems. By considering the effects of survey selection bias, we demonstrate that the long-standing anomaly over the high quads-to-doubles ratios (i.e. 50~70 % for JVAS and CLASS) can be explained by the moderate effective shear of 0.16~0.18, which is half that of previous estimates. The derived inverse-mapping formula could make the SIS + shear lensing model useful for galaxy-lensing simulations.