• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.823-855
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• 1996

We study Dirichlet forms and the associated diffusion processes for the Gibbs measures related to the quantum unbounded spin systems (lattice boson systems) interacting via superstable and regular potentials. This work is a continuation of the author's previous study on the classical systems [LPY] to the quantum cases. In [LPY], we constructed Dirichlet forms and the associated diffusion processes for the Gibbs measures of classical unbounded spin systems. Furthermore, we also showed the essential self-adjointness of the Dirichlet operator and the log-Sobolev inequality for any Gibbs measure under appropriate conditions on the potentials. In this atudy we try to extend the results of the classical systems to the quantum cases. Because of some technical difficulties, we are only able to construct a Dirichlet form and the associated diffusion process for any Gibbs measure of the quantum systems. We utilize the general scheme of the previous work on the theory in infinite dimensional spaces [AH-K1-2, AKR, AR1-2, Kus, MR, Ro, Sch] and the ideas we employed in our study of the calssical systems ]LPY].

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.779-786
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• 2006

Let $\mathbb{X}_t$ be an m-dimensional linear process defined by $\mathbb{X}_t=\sum{_{j=0}^\infty}\;A_j\;\mathbb{Z}_{t-j}$, t = 1, 2, $\ldots$, where $\mathbb{Z}_t$ is a sequence of m-dimensional random vectors with mean 0 : $m\times1$ and positive definite covariance matrix $\Gamma:m{\times}m$ and $\{A_j\}$ is a sequence of coefficient matrices. In this paper we give sufficient conditions so that $\sum{_{t=1}^{[ns]}\mathbb{X}_t$ (properly normalized) converges weakly to Wiener measure if the corresponding result for $\sum{_{t=1}^{[ns]}\mathbb{Z}_t$ is true.

• Journal of ILASS-Korea
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• v.15 no.2
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• pp.53-60
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• 2010

This study presents development of digital particle holographic system and its application to spray field to measure three-dimensional velocities and sizes of spray droplets. A double exposure hologram recording system with synchronization system for time control was established and digital holograms can be recorded in a short time interval. To process recorded holograms, the correlation coefficient method was used for focal plane determination of particles. To remove noises and improve the quality of holograms and reconstructed images, the Wiener filter was adopted. The two-threshold and image segmentation methods were used in binary image transformation. For particle pairing, the match probability method was adopted. The developed system was applied to spray field and three-dimensional velocities and sizes of spray droplets were measured. The measurement results of digital holographic system were compared with those made by laser instruments, PDPA(Phase Doppler Particle Analyzer), which proved the feasibility of in-line digital particle holographic system as a good measurement tool for spray droplets.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.245-257
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• 2007

We showed in [2] that if $r\leq2$, then the average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is proportional to $h^{2r+3}$ using zero mean Gaussian distribution under the assumption that we have subintervals (for simplicity equal length) partitioning and that each subinterval has the length. In this paper, if $r\geq3$, we show that zero mean Gaussian distribution of average error between simple Trapezoidal rule and the composite Trapezoidal rule on two consecutive subintervals is bounded by $Ch^8$.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.353-363
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• 2003

In [2], if ${\gamma}$ $\leq$ 2, the average error of the composite Trapezoidal rule on two consecutive intervals turned out to be proportional to h$\^$2r+3/ where ${\gamma}$ is the number of differentiablity and h is the length of each uniform subinterval of the interval [0, 1] In this paper, we show that if ${\gamma}$ $\geq$ 3, the average error of the composite Trapezoidal rule on two consecutive intervals is bounded by Ch$\^$8/.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.581-587
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• 2008

In this paper, to have a better a posteriori error bound of the average case error between the true value of I(f) and the Trapezoidal rule on subintervals using zero mean-Gaussian, we prove that a new average error between the difference of the true value of I(f) from the composite Trapezoidal rule and that of the composite Trapezoidal rule from the simple Trapezoidal rule is bounded by $c_rH^{2r+3}$ through direct computation of constants $c_r$ for r ${\leq}$ 2 under the assumption that we have subintervals (for simplicity equal length h) partitioning [0, 1].

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.2
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• pp.104-111
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• 2008

The ECG is biomedical electrical signal occurring on the surface of the body due to the contraction and relaxation of the heart. This signal represents an extremely important measure for health monitoring, as it provides vital information about a patient's cardiac condition and general health. ECG signals are contaminated with high frequency noise such as power line interference, muscle artifact and low frequency nose such as motion artifact. But it is difficult to filter nose from ECG signal, and errors resulting from filtering can distort a ECG signal. The present study implemented a small-size and low-power ECG measurement system that can remove motion artifact for convenient health monitoring during daily life. The implemented ECG monitoring system consists of ECG amplifier, a low power microprocessor, bluetooth module and monitoring program. Amplifier was designed and implemented using low power instrumentation amplifier, and microprocessor was interfaced to the ECG amplifier to collect the data, process, store and feed to a transmitter. And bluetooth module used to wirelessly transmit and receive the vital sign data from the microprocessor to an PC at the receiving site. In order to evaluate the performance of the implemented system, we assessed motion artifact rejection performance in each situation with artificially set condition using adaptive filter.

• Journal of Energy Engineering
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• v.23 no.2
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• pp.93-101
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• 2014

How to determine the extent of national energy security? In this paper, we estimate it by comparative analysis of South Korea and other OECD countries in terms of energy diversity (fuel diversity). Energy security consists of 4 key factors such as availability, accessibility, acceptability, affordability. Especially the importance of accessibility can grow as local imbalance of supply and demand increases. As a proxy of the accessibility, fuel diversity can be a significant indicator to estimate a measure of energy security. In this paper, we use Shannon-Wiener index to measure energy diversity. If fuel diversity increases, the stability of energy security also should increase, because of the smoothing effect to lessen dependence on key energy sources. In 2012 Korean growth rate of H-index (energy diversity) is 18.38%, which is higher than other OECD countries. However, Korean H-index itself is 1.93, lesser than other countries. Shift from oil to coals/gas within fossil fuels has more impact on H-index than weight transition from fossil fuels to renewable energies in Korea. We conclude that more renewable energy is an effective solution to achieve higher energy diversity and ultimately higher energy security as the same as the German case.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.317-334
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• 1997

The existence of an operator-valued function space integral as an operator on $L_p(R) (1 \leq p \leq 2)$ was established for certain functionals which involved the Labesgue measure [1,2,6,7]. Johnson and Lapidus showed the existence of the integral as an operator on $L_2(R)$ for certain functionals which involved any Borel measures [5]. J. S. Chang and Johnson proved the existence of the integral as an operator from L_1(R)$ to $C_0(R)$ for certain functionals involving some Borel measures [3]. K. S. Chang and K. S. Ryu showed the existence of the integral as an operator from $L_p(R) to L_p'(R)$ for certain functionals involving some Borel measures [4].

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.8A
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• pp.739-752
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• 2002

Recently, to utilize the limited bandwidth effectively, the concept of partial response (PR) signaling has widely been adopted in both the high-speed data transmission and high-density digital recording/playback systems such as digital microwave, digital subscriber loops, hard disk drives, digital VCR's and digital versatile recordable disks and so on. This paper is concerned with adaptive equalization of partial response channels particularly for the magnetic recording channels. Specifically we study how the PR channel equalizers work for different choices of desired or reference signals used for adjusting the equalizer weights. In doing so, we consider three different configurations that are actually implemented in the commercial products mentioned above. First of all, we show how to compute the theoretical values of the optimum Wiener solutions derived by minimizing the mean-squared error (MSE) at the equalizer output. Noting that this equalizer MSE measure cannot be used to fairly compare the three configurations, we propose to use the data MSE that is computer just before the final detector for the underlying PR system. We also express the data MSE in terms of the channel impulse response values, source data power and additive noise power, thereby making it possible to compare the performance of the configurations under study. The results of extensive computer simulation indicate that our theoretical derivation is correct with high precision. Comparing the three configurations, it also turns out that one of the three configurations needs to be further improved in performance although it has an apparent advantage over the others in terms of memory size when implemented using RAM's for the decision feedback part.