• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1037-1049
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• 2015

It is well-known that the spectrum of a $spin^{\mathbb{C}}$ Dirac operator on a closed Riemannian $spin^{\mathbb{C}}$ manifold $M^{2k}$ of dimension 2k for $k{\in}{\mathbb{N}}$ is symmetric. In this article, we prove that over an odd-dimensional Riemannian product $M^{2p}_1{\times}M^{2q+1}_2$ with a product $spin^{\mathbb{C}}$ structure for $p{\geq}1$, $q{\geq}0$, the spectrum of a $spin^{\mathbb{C}}$ Dirac operator given by a product connection is symmetric if and only if either the $spin^{\mathbb{C}}$ Dirac spectrum of $M^{2q+1}_2$ is symmetric or $(e^{{\frac{1}{2}}c_1(L_1)}{\hat{A}}(M_1))[M_1]=0$, where $L_1$ is the associated line bundle for the given $spin^{\mathbb{C}}$ structure of $M_1$.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.43-57
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• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.117-121
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• 2009

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

• Korean Journal of Microbiology
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• v.46 no.1
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• pp.46-51
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• 2010

Coenzyme Q10 (CoQ10) is an essential lipid-soluble component of membrane-bound electron transport chains. CoQ10 is involved in several aspects of cellular metabolism and is increasingly being used in therapeutic applications for several diseases. Despite the recent accomplishments in metabolic engineering of Escherichia coli for CoQ10 production, the production levels are not yet competitive with those by fermentation or isolation. So we tested several microorganisms obtained from the KCTC of Biological Resource Center to find novel sources of strain-development for CoQ10-production. Then we selected two strains, Paracoccus denitrificans (KCTC 2530) and Asaia siamensis (KCTC 12914), and tested to optimize the CoQ10 production conditions. Among the carbon sources tested, CoQ10 production was the highest when fructose was supplied about 4% concentration. Yeast extract produced the highest CoQ10 production about 2% concentration. The highest CoQ10 production was obtained at pH 6.0 for P. denitrificans and pH 8.0 for A. siamensis. And two strains showed the highest CoQ10 production at $30^{\circ}C$, but the highest DCW was obtained at $37^{\circ}C$. In the fed-batch culture, P. denitrificans yielded $14.34{\pm}0.473$ mg and A. siamensis yielded $12.53{\pm}0.231$ mg of final CoQ10 production.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.5
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• pp.1133-1138
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• 2010

In the anti-collision scheme proposed by EPCglobal Class-1 Gen-2 standard, the frame size for a query round is determined by Q-algorithm. In the Q-algorithm, the reader calculates a frame size without estimating the number of tags in it's identification range. It uses only the slot status. Therefore, Q-algorithm has advantage that the reader's algorithm is simpler than other algorithms. However, it cannot allocate an optimized frame size because it does not consider the number of tags. Also, the conventional Q-algorithm does not define an optimized parameter value C for adjusting the frame size. In this paper, we propose a modified Q-algorithm and evaluate the performance with computer simulations. The proposed Q-algorithm estimates the number of tags at every query round, and determines the parameter value C based on the estimated number of tags.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.167-179
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• 2023

In this paper, we investigate solutions of equations which are linear (p, q)-difference equation of higher order by using (p, q)-derivative and integral. We also derive the solution of equation in the case of second order.

• Journal of Forest and Environmental Science
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• v.8 no.1
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• pp.51-66
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• 1992

This study was carried out to investigate the micromorphology of vessel wall sculpture such as shape of perforation plate, perforation rim, steepness of perforation plate, occurrence of vestured pit, warty layer and ray-vessel pitting on 13 species of Fagaceae in Korea. The results were summarized as follows ; 1. In the species examined, all sample species except Fagus crenata var. multinervis have simple perforation plate. But Fagus crenata var. multinervis has simple and scalariform perforation plate (it was called to combination perforation plate) in a tree stem. 2. The shapes of perforation rim could be classified into five types; Type A without tail, Type B with small tail on both sides, Type C with long tail on both sides, Type D with tail only one side and Type E with the very short interval between perforations. Among five types, Type Band C have higer frequency of distribution than the others. 3. The steepness of perforation plate measured was about 20 degree on pore zone and 43 degree on outside parts of pore zone. 4. Species with vestured pit were Q. aliena, Q, dentata, Q. variabilis, Fagus crenata var. multinervis, Castanopsis cuspidata var sieboldii, Q. acuta, Q. stenophylla, and Q. glauca. But the extent of vesturing was very slight and vestured pits were observed mainly in ray-vessel pit of some vessel elements. 5. Species with warty layer on the inner surface wall of all vessel elements were Q. acuta, Q. stenophylla, Q. glauca, Fagus crenata var. multinervis and species with warty layer of some vessel elements were Q. aliena, Q, dentata, Q. variabilis, Castanopsis cuspidata var. sieboldii. 6. Species with palisade ray-vessel pit were Q. acuta, Q. stenophylla, Q. glauca, Castanea crenata, Castanea bungeana, Q. aliena, Q. serrata, Q. mongolica, and species with scalariform ray-vessel pit was Fagus crenata var. multinervis and species with oval ray-vessel pit were Q, dentata, Castanopsis cuspidata var sieboldii.

• Magazine of the Korean Society of Agricultural Engineers
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• v.22 no.4
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• pp.96-107
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• 1980

This study is carried out to estimate the rate of sediment transportation both to measure the amount of suspended and bedload sediment that moves on or near the river bed and passes through the cross section of a river in unit time, with suspended and bed load samplers used for the Milyang river and to determine the most satisfactory and convenient formula of some formulas for sediment discharge by comparing the measured rate with the calculated rate. The results of this study are summarized as follows; 1) The interrelationship (1) between the total discharge and the total sediment discharge (2) between discharge and suspended sediment load and (3) between discharge and bed load in the Milyang river are (1) i) 4$\leq$Q$\leq$100 C.M.S. Qr=0. 00272 Q0.70 (kg/sec) ii) 150$\leq$Q$\leq$800 C.M.S. Qr=0. 4807 Q0.46 (kg/sec) (2) Qs~=0. 07576 Q1.02 (kg/sec) (3) QB=0. 00957 Q0.44 (kg/sec) 2) The rate of suspended sediment load to total sediment discharge is found to be about; 99%. The suspended load is shown to be almost wash load which consists of silt and clay. 3) The relation between the total discharge and the suspended sediment load that are measured at three medium and small rivers in Korea is Qs=0. 13831 Q0.97 (kg/sec) 4) Brown's formula is determined to be the most convenient formula for application and comparison with observed data obtained for the Milyang river.

• The Korean Journal of Ecology
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• v.16 no.3
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• pp.353-364
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• 1993

To elucidate ecophysiological factors affecting nutural distribution of evergreen broad-leabed trees in Danohad National Marine Park, water potential, relative water content and photosynthetic activities of 4 species, Cammellia japonica, Machilus thunbergii, Castanopsis cuspidata var.sieboldii and Quercus acuta, were potential began to decrease from 07:00h to its minimum value at 13:00h for C. cuspidata var. sieboldii (-14.3bar) and Q. acuta (-19.4bar) at 16:00 h for M. thunbergii(-17.0bar) and at 19:00 h for C. japonica (-14.5bar), and these showed similar trends to relative water content. Photosynthetic activities of 4 species began to increase from 7:00 h and reached maximum values before their minimum values of water potential occureed. Optimum temperature renges of photosynthetic activities was $18~20^{\circ}C$ for C. japonica - M. thunbergii and $14~16^{\circ}C$ for C. cuspidata var. sieboldii Quercus acuta.Q.acuta had the highest light saturation point of $0.4mM/m^2/s$ and C. japonica the lowest of $0.15mM/m^2/s$. Water potential of 4 species subjected to water stress, began to decrease after 1st day of drought and after 21th day of drought, those of C. japonica, M. thunbergii, C. cuspidata var. sieboldii and Q. acuta decreased to species began to decrease after 7th day of drought and after 21th day, those of M. thunbergii, C. cuspidata var. sieboldii and Q. acuta were dropped to about 50% and C. japonica 83.5%. Photosynthetic activity of 4 specie began to decline in the order of C. cuspidata var. sieboldii, Q.acuta, C. japonica and M. thunbergii after 10th day of drought. These results suggest that the segregated disributions of C. japonica - M. thunbergii on vally positions and C. cuspidata var. sieboldii - Q. acuta on slopes were associated with different responses of water status and photosyntheties to their environment.

• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.77-94
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• 2016

Purpose: This paper reviews Type 1 Gage study, Gage R&R study, and procedure of ISO 22514-7 for assessing a measurement system, and discusses some relationships between the measurement capability indices. Methods: The gage capability index $C_g$ of Type 1 Gage study, precision-to-tolerance ratio PTR of Gage R&R study, and measurement performance ratio $Q_{MS}$ and $Q_{MP}$ of ISO 22514-7 are considered in this paper. Results: This paper derives the relationships between $C_g$ and $Q_{MS}$, PTR and $Q_{MP}$, and $Q_{MS}$ and $Q_{MP}$, respectively, and discusses the acceptance conditions for each procedures. Conclusion: The measurement capability analysis is the first step for the quality improvement of the manufacturing processes. Therefore the result of this study provides a helpful guidelines for assessing the measurement system, enabling proper evaluation of manufacturing processes.