• Journal of electromagnetic engineering and science
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• 제12권1호
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• pp.128-134
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• 2012

In this manuscript, we consider electromagnetic imaging of perfectly conducting cracks completely hidden in a homogeneous material via boundary measurements. For this purpose, we carefully derive a topological derivative formula based on the asymptotic expansion formula for the existence of a perfectly conducting inclusion with a small radius. With this, we introduce a topological derivative based imaging algorithm and discuss its properties. Various numerical examples with noisy data show the effectiveness and limitations of the imaging algorithm.

• 대한수학회지
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• 제52권2호
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• pp.333-347
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• 2015

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.

• Journal of electromagnetic engineering and science
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• 제11권1호
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• pp.56-61
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• 2011

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

• 전기전자학회논문지
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• 제23권3호
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• pp.817-825
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• 2019

마이크로프로세서를 이용한 제어알고리즘 구현에서 차분방정식이 매우 유용하게 사용된다. 샘플링 데이터로부터 미분 값을 추정하기 위해 전향, 후향 및 중심 차분 방식이 사용되어왔다. 차분 값을 계산하기 위해서는 차분계수가 매우 중요하다. 본 논문에서는 유한 차분 계수를 계산하기 위한 새로운 방식을 제시하고자 한다. 제안된 방식의 유효성을 입증하기 위해 RLS 알고리즘을 적용한 파라미터 추정에 대하여 적용하였다.

• 대한수학회논문집
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• 제34권2호
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• pp.383-390
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• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• 대한수학회논문집
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• 제32권2호
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• pp.287-304
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• 2017

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.656-661
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• 2005

An optimization formulation of unconstrained damping treatment on beams is proposed to minimize vibration responses using a numerical search method. The fractional derivative model is combined with RUK's equivalent stiffness approach in order to represent nonlinearity of complex modulus of damping materials with frequency and temperature. The loss factors of partially covered unconstrained beam are calculated by the modal strain energy method. Vibration responses are calculated by using the modal superposition method, and of which design sensitivity formula with respect to damping layout is derived analytically. Plugging the sensitivity formula into optimization software, we can determine optimally damping treatment region that gives minimum forced response under a given boundary condition. A numerical example shows that the proposed method is very effective in minimizing vibration responses with unconstrained damping layer treatment.

• 한국소음진동공학회논문집
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• 제15권7호
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• pp.829-835
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• 2005

An optimization formulation of unconstrained damping treatment on beam is proposed to minimize vibration responses using a numerical search method. The fractional derivative model is combined with RUK's equivalent stiffness approach in order to represent nonlinearity of complex modulus of damping materials with frequency and temperature. Vibration responses are calculated by using the modal superposition principle, and of which design sensitivity formula with respect to damping layout is derived analytically. Plugging the sensitivity formula into optimization software, we can determine optimally damping treatment region that gives minimum forced response under a given boundary condition. A numerical example shows that the proposed method is very effective in suppressing nitration responses by means of unconstrained damping layer treatment.

• 대한수학회지
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• 제45권2호
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• pp.455-466
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• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

• 호남수학학술지
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• 제34권2호
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• pp.191-198
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• 2012

Minimal surfaces with given boundaries are the solutions of Plateau's problem. In studying the calculus of variations for the minimal surfaces, the functional ${\varepsilon}$, corresponding to the energy of surfaces, is introduced in [Ki09]. In this paper we derive a formula for the second derivative of ${\varepsilon}$, which is necessary for further theories of the calculus of variations.