• 대한수학회지
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• 제40권1호
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• pp.109-128
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• 2003

In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP$^{n}$ invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chen's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP$^{n}$ ; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.

• 한국통신학회논문지
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• 제32권11C호
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• pp.1111-1118
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• 2007

본 논문은 다중 사용자 시스템에서 좋은 채널을 가진 사용자를 선택함으로써 얻을 수 있는 다이버시티, 즉 다중 사용자 다이버시티로부터 증대되는 처리율 (throughput)에 대해 새로운 접근 방식을 이용하여 분석하였다. 이와 같은 다중 사용자 다이버시티 이득으로부터 도출되는 처리율의 증가를 근사적 형태의 식으로 유도하기 위하여, 본 논문에서는 Puiseux 급수를 이용하였고 이를 통해 단순화된 맺음식 (closed form)의 결과를 얻을 수 있었다. 이 결과식은 다중 사용자 다이버시티 이득이 신호 대 잡음비 (SNR)에 독립적이라는 것을 보여주고 있다. 또한 본 논문에서는 위의 결과를 Max C/I과 proportional fair scheduling과 같은 스케줄링 알고리즘에 확대 적용하였다. 그리고 제시한 결과식을 모의실험과 비교하여 검증하였다.

• Journal of Communications and Networks
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• 제18권3호
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• pp.523-530
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• 2016

We use both theoretical analysis and simulations to study the impact of crosspoint-queued (CQ) buffer size on CQ switch throughput and delay performance under different traffic models, input loads, and scheduling algorithms. In this paper, we present the following. 1) We prove the stability of CQ switch using any work-conserving scheduling algorithm. 2) We present an exact closed-form formula for the CQ switch throughput and a non-closed-form but convergent formula for its delay using static non-work-conserving random scheduling algorithms with any given buffer size under independent Bernoulli traffic. 3) We show that the above results can serve as a conservative guide on deciding the required buffer size in pure CQ switches using work-conserving algorithms such as the random scheduling, under independent Bernoulli traffic. 4) Furthermore, our simulation results under real-trace traffic show that simple round-robin and random work-conserving algorithms can achieve quite good throughput and delay performance with a feasible crosspoint buffer size. Our work reveals the impact of buffer size on the CQ switch performance and provides a theoretical guide on designing the buffer size in pure CQ switch, which is an important step toward building ultra-high-speed switch fabrics.

• 방송공학회논문지
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• 제24권4호
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• pp.613-622
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• 2019

코드북을 이용하는 폐루프 MISO 시스템에서 시간 상관성을 이용한 차분 코드북 설계 방법을 제안한다. 단일계층 코드북의 코드워드 인자들은 위상 성운의 집합 중에서 선택된다. 기존의 코드워드 선택 식에서는 코드워드들을 구면의 캡들이라 가정하고 서로의 각도를 사인 법칙을 이용하여 구하였으나, 본 논문에서는 피타고라스 법칙을 이용하는 새로운 방법을 이용하여 계산식을 간소화 시키는 식을 제안한다. 그리고 선택되는 코드워드간의 상관 계수 즉, 위상차의 변화를 추적하여 2 개의 코드북 중에 최적의 코드북을 적응적으로 선택하는 방법을 제안한다. Monte-Carlo 컴퓨터 시뮬레이션을 통해 제안하는 코드북의 성능을 검증한다.

• Computers and Concrete
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• 제30권3호
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• pp.225-236
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• 2022

In this article, Multi-Gene Genetic Programming (MGGP) is proposed for the estimation of the compressive strength of concrete. MGGP is known to be a powerful algorithm able to find a relationship between certain input space features and a desired output vector. With respect to most conventional machine learning algorithms, which are often used as "black boxes" that do not provide a mathematical formulation of the output-input relationship, MGGP is able to identify a closed-form formula for the input-output relationship. In the study presented in this article, MGPP was used to predict the compressive strength of plain concrete, concrete with fly ash, and concrete with furnace slag. A formula was extracted for each mixture and the performance and the accuracy of the predictions were compared to the results of Artificial Neural Network (ANN) and Extreme Learning Machine (ELM) algorithms, which are conventional and well-established machine learning techniques. The results of the study showed that MGGP can achieve a desirable performance, as the coefficients of determination for plain concrete, concrete with ash, and concrete with slag from the testing phase were equal to 0.928, 0.906, 0.890, respectively. In addition, it was found that MGGP outperforms ELM in all cases and its' accuracy is slightly less than ANN's accuracy. However, MGGP models are practical and easy-to-use since they extract closed-form formulas that may be implemented and used for the prediction of compressive strength.

• 한국조명전기설비학회지:조명전기설비
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• 제9권3호
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• pp.80-87
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• 1995

영구자석형 스테핑 전동기의 언덕턴스를 고려하여 최대 평균 토오크식을 제시하였으며, 제시된 토오크식에 근거하여 마이크로컨트롤러에 의해 lead angle을 전동기의 속도에 따라 최적으로 제어함으로서 최대 토오크를 발생시키는 제어시스템을 설계하여 전동기의 토오크/속도 특성 실험을 하였다. 이론식에 의하면 토오크/속도 곡선에서 최적 lead angle의 도입에 따라 발생하는 토오크가 증대되며, 운전영역이 2배이상 확대되는 바와 같이, 특성실험 결과에서도 최적 lead angle의 실현에 따라 구동모드에 관계없이 발생 토오크가 증대되며, 운전영역이 2배이상 학대됨을 확인 할 수 있다.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2004년도 추계학술대회 논문집
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• pp.1407-1412
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• 2004

Impedance calculations of electric railway traction systems is essential to define characteristics and to design it. The self impedance is defined voltage drop rate per unit length, the mutual impedance is represented as a voltage induced to transmission line from transmission line. The self and the mutual impedance are influenced by ground return currents. The earth is considered as a semi-infinitely extended non-ideal conductor. The current of transmission line produces earth current induced magnetically and it flow through a path having minimum impedance. Carson proposed the impedance calculation formula using wave equations and magnetic field equations. Though the formula have an improper equation, that is still used as a standard impedance calculation method. This paper introduced an impedance calculation method that the complex depth of earth return method assumes that the current in conductor returns through an imagined earth depth path located directly under original conductor at a depth of. In this paper, we showed that this proposed method has a closed form and is easier than Carson's.

• Journal of electromagnetic engineering and science
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• 제10권4호
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• pp.219-223
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• 2010

Based on a provided closed-form wireless power transmission (WPT) efficiency formula, which may be used for any value of load, we have analyzed the WPT efficiencies between two metamaterial-inspired loop antennas in various aspects. Due to the modeling based on low frequency circuit theory, the provided formula at the center resonant frequency has been found to be accurate until when the distance between the two loop antennas increases to 15 cm (about $\lambda_0/6$ at 300 MHz). When the two loops get closer, the resonant frequency has been found to split into two in theory, simulations, and measurements. The EM-simulated and measured efficiencies at new resonant frequencies are 60.9 % and 46.3 %, respectively, at d=15 cm. With two extra rings around the loops, the maximum efficiency is enhanced to 93.7 % at d=15 cm. The effect of the additional two rings is about 30 %.

• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• 대한수학회지
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• 제57권5호
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• pp.1167-1186
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• 2020

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possesses the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirm that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.