• 대한수학회논문집
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• 제38권3호
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• 대한전기학회논문지:전력기술부문A
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• 제52권12호
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• pp.691-697
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• 2003

This paper proposes a current differential relay for transformer protection that operates in accordance with a blocking method based on the difference-function of a differential current. For magnetic inrush and over-excitation, discontinuities in the first-difference function of the differential current arise at the points of inflection, which correspond to the start and end of each saturation period of the core. These discontinuities are converted into the pulses in the second- and third-difference functions of the differential current. The magnitudes of the pulses are large enough to detect saturation of the core. A blocking signal is issued if the magnitude of the third-difference function exceeds the threshold and is maintained for three quarters of a cycle. The performance of the relay is assessed under various conditions with magnetic inrush, internal faults and external faults. The proposed blocking method can improve significantly the operating time of a relay and achieve high sensitivity of a relay.

• 한국미생물생명공학회:학술대회논문집
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• 한국미생물생명공학회 2000년도 추계 학술대회
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• pp.125-139
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• 2000

The differential enhanced degradation of cis- and trans-1,3-D was observed in the previous two studies performed by Ou et al. (1995) and especially Chung et al. (1999). This study was initiated to investigate the involvement of microorganisms in the differential enhanced degradation of the chemicals. As expected, microorganisms were responsible for the enhanced degradation of the chemicals. A mixed bacterial culture capable of degrading 1,3-D was isolated from an enhanced soil sample collected from a site treated with 1,3-D. Similar to the enhanced soil, the mixed culture degraded trans-1,3-D faster than cis-1,3-D. This mixed culture could not utilize cis- and trans-1,3-D as a sole source of carbon for growth. Rather, a variety of second substrates were evaluated to stimulate the differential enhanced degradation of the two isomers. As a result, the mixed culture degraded cis- and trans-1,3-D only in the presence of a suitable second substrate. Second substrates that had the capacity to stimulate the degradation included soil leachate, tryptone, tryptophan, and alanine. Other substrates tested, including soil extract, glucose, yeast extract, and indole (ailed to stimulate the degradation of the two isomers. Therefore, it appeared that the degradation of cis- and trans-1,3-D was a cometabolic process. The mixed culture was composed of four morphologically distinctive bacterial colonies.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.245-253
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• 2007

In this paper, the existence of bounded positive solution of the second-order nonlinear neutral differential equations are studied. Some new sufficient conditions are given. Furthermore, examples given show that the results here are almost sharp.

• ETRI Journal
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• 제38권2호
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• pp.387-396
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• 2016

This paper introduces a new type of collision attack on first-order masked Advanced Encryption Standards. This attack is a known-plaintext attack, while the existing collision attacks are chosen-plaintext attacks. In addition, our method requires significantly fewer power measurements than any second-order differential power analysis or existing collision attacks.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• 대한수학회보
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• 제33권1호
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• pp.135-170
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• 1996

Recently many people have studied the Sobolev orthogonal polynomials, that is, polynomials which are orthogonal relative to a symmetric bilinear form $\phi(\cdot,\cdot)$ defined by $$ (1.1) $\phi(p,q) := (p,q)_N = \sum_{k=0}^{N} \int_{R}p^(k) (x)q^(k) (x) d\mu_k, $$ where each $d\mu_k$ is a signed Borel measure on the real line $R$ with finite moments of all orders. For the brief history on this subject, we refer to the survey article Ronveaux [13] and Marcellan and et al [10].

• 한국항해항만학회지
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• 제30권2호
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• pp.167-172
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• 2006

In this paper, the issue of blind detection of Alamouti-type differential space-time (ST) ${\pi}/2$-shifted BPSK modulation in static Rayleigh fading channels is considered. We introduce a novel transformation to the received signal from each receiver antenna such that this binary ST modulation, which has a second-order transmit-diversity, is equivalent to QPSK modulation with second-order receive-diversity. The pre-detection combining of the result of transformation allows us to apply a low complexity detection technique specifically designed for receive-diversity, namely, scalar multiple-symbol differential detection (MSDD). With receiver complexity proportional to the observation window length, our receiver can achieve the performance 1.5dB better than that of conventional differential detection ST and 0.5dB worse than that qf a coherent maximum ratio combining receiver (with differential decoding) approximately.

• 한국정보통신학회논문지
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• 제25권4호
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• pp.501-507
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• 2021

신경망은 미분가능한 활성화 함수를 사용하는 경우에는 입력변수에 대하여 미분가능하다. 본 연구에서는 신경망의 근사 능력을 향상시키기 위하여 신경망의 그래디언트와 헤시안이 블랙-숄즈 미분방정식을 만족하도록 한다. 본 논문은 확률 미분방정식과 블랙-숄즈 편미분 방정식이 옵션 가격과 기초자산의 미분관계를 표현하는 옵션 가격결정에 제안한 방법을 사용한다. 이는 옵션 가격의 일차와 이차미분은 금융공학에서 중요한 역할을 하므로 미분 값을 쉽게 얻을 수 있는 제안한 방법을 적용할 수 있기 때문이다. 제안한 신경망은 (1) 확률 미분방정식이 생성하는 옵션가격의 샘플 경로와 (2) 각 시간과 기초자산 가격에서 블랙-숄즈 방정식을 만족하도록 학습한다. 실험을 통하여 제안한 방법이 옵션가격과 일차와 이차 미분 값을 정확히 예측함을 보인다.

• 대한수학회지
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• 제34권4호
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.