• Journal of the Korean Mathematical Society
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• v.40 no.1
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1111-1118
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• 2007

This paper presents our study of throughput enhancement achieved by selection diversity in a multiuser system, called multiuser diversity (MUDiv), using a new asymptotic approach. The MUDiv gain is evaluated by deriving an asymptotic formula for the throughput enhancement from the MUDiv gain as a simple closed form introducing a Puiseux series. The formula shows that the MUDiv gain is independent of the signal-to-noise ratio (SNR). This concept can be extended to analysis applicable to scheduling algorithms, such as Max C/I and proportional fair scheduling. The MUDiv gain throughput analysis is verified using Monte-Carlo simulations.

• Journal of Communications and Networks
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• v.18 no.3
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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.

• Journal of Broadcast Engineering
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• v.24 no.4
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• pp.613-622
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• 2019

A differential codebook design method using wireless channel's temporal correlation is proposed over closed loop multiple-input single-output (MISO) system. The single layer codewords in a codebook are selected among a set of phase elements. In the conventional codeword selection rule, codewords are assumed to be on a spherical cap and sine formula was used. In this paper, however, a new method using Pythagoras formula is employed to simplify computational complexity. Also, an adaptive differential codebook selection is adopted to enhance performance. Monte-Carlo simulations demonstrate that the proposed codebook is superior to the conventional ones.

• Computers and Concrete
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• v.30 no.3
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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.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.9 no.3
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• pp.80-87
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• 1995

In this paper, we design the microcontroller-based optimal lead angle control system on the basis of the presented maximum average torque formula of the permanent-type stepping motor with respect to the inductance. We confirm that optimal lead angle enlarges the operating range twice as much and increases the torque over all of the operating range in the case of presented formula as well as experimental results.

• Proceedings of the KSR Conference
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• 2004.10a
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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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• v.10 no.4
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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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• v.18 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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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.