• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.227-234
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• 2022

Let 𝔽_q be a finite field with odd q elements. In this article, we prove that if E ⊆ 𝔽^d_q, d ≥ 2, and |E| ≥ q, then there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d such that for all y ∈ Y, the number of distances between the point y and the set E is ~ q. As a corollary, we obtain that for each set E ⊆ 𝔽^d_q with |E| ≥ q, there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d so that any set E ∪ {y} with y ∈ Y determines a positive proportion of all possible distances. The averaging argument and the pigeonhole principle play a crucial role in proving our results.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.393-396
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• 2002

In this paper, we give the definitions of the q-Haar and q-Gabor wavelet. Instead of using the conventional Gaussian distribution as a kernel of the Gabor wavelet, if the q-normal distribution is used, we can get the q-Gabor wavelet as a possible generalization of the Gabor wavelet. The q-normal distribution, which is given by the author, is one of the generalized Gaussian distribution. On the other hand, if two sets of the q-normal distribution are connected anti-symmetrically, we can get the q-Haar wavelet as a possible generalization of the Haiw wavelet. We give experiments on the q-eabor and q-Haar wavelet and discuss about the q-Gabor and q-Haar wavelet.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.411-421
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• 2016

In this paper, we investigate the problem of transcendental entire functions that share two values with one of their derivative. Let f be a transcendental entire function, n and k be two positive integers. If $f^n-Q_1$ and $(f^n)^{(k)}-Q_2$ share 0 CM, and $n{\geq}k+1$, then $(f^n)^{(k)}{\equiv}{\frac{Q_2}{Q_1}}f^n$. Furthermore, if $Q_1=Q_2$, then $f=ce^{\frac{\lambda}{n}z}$, where $Q_1$, $Q_2$ are polynomials with $Q_1Q_2{\not\equiv}0$, and c, ${\lambda}$ are non-zero constants such that ${\lambda}^k=1$. This result shows that the Conjecture given by W. $L{\ddot{u}}$, Q. Li and C. Yang [On the transcendental entire solutions of a class of differential equations, Bull. Korean Math. Soc. 51 (2014), no. 5, 1281-1289.] is true. Also we exhibit some examples to show that the conditions of our result are the best possible.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.11
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• pp.66-70
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• 2016

This paper presents an 24 GHz I/Q LO generator for a heartbeat measurement radar system. In order to improve the mismatch performance between I and Q LO signals against process variation, a 24 GHz I/Q LO generator employing a low-pass phase shifter and a high-pass phase shifter composed of inductors and capacitors is proposed. The proposed 24 GHz I/Q LO generator consists of an LO buffer, a low-pass phase shifter and a high-pass phase shifter. It was designed using a 65 nm CMOS technology and draws 8 mA from a 1 V supply voltage. The proposed 24 GHz I/Q LO generator shows a gain of 7.5 dB, a noise figure of 2.3 dB, 0.1 dB gain mismatch and $4.3^{\circ}$ phase mismatch between I and Q-path against process and temperature variations for the operating frequencies from 24.05 GHz to 24.25 GHz.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.83-98
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• 2014

During the last decade, several papers have focused on linear q-difference equations of the form ${\sum}^n_{j=0}a_j(z)f(q^jz)=a_{n+1}(z)$ with entire or meromorphic coefficients. A tool for studying these equations is a q-difference analogue of the lemma on the logarithmic derivative, valid for meromorphic functions of finite logarithmic order ${\rho}_{log}$. It is shown, under certain assumptions, that ${\rho}_{log}(f)$ = max${{\rho}_{log}(a_j)}$ + 1. Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations. As a consequence of the main results, it follows that the q-gamma function and the q-exponential functions all have logarithmic order two.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.35-43
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• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• Korean Journal of Breeding Science
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• v.41 no.3
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• pp.236-243
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• 2009

This study was conducted to develop a japonica-type rice cultivar with brown planthopper (BPH) resistance using DNA markers. A doubled haploid (DH) population consisting of 120 pure-lines was established by anther culture of $F_1$ hybrids between 'Samgang', a Tongil type BPH resistance cultivar, and 'Nagdong', a japonica cultivar. To determine the map position of genes responsible for BPH resistance in rice, a genetic map was constructed based on 120 DH lines. A total of 162 molecular markers were classified into 12 linkage groups, covering 1,884 Kosami centimorgan (cM) with an average of 11.6 cM. Five QTLs (qBPR3, qBPR6, qBPR7, qBPR8, and qBPR12) associated with BPH resistance were identified and mapped on chromosomes 3, 6, 7, 8, and 12, respectively, using the genetic map constructed in this study. To analyze the relationship between BPH resistance and agronomic traits, a total of eight QTLs related to the agronomic traits were detected on 12 rice chromosomes. In an analysis of relationships, three QTLs (qBPR3, qBPR7, and qBPR8) showed a linkage with tested agronomic traits. A QTL (qBPR3) located on chromosome 3 (RM282-3023) was closely linked to culm length (qCL3). The QTL (qBPR8) for BPH resistance on the short arm of chromosome 8 also overlapped the region detected in culm length (qCL8).

• Clinical and Experimental Pediatrics
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• v.59 no.sup1
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• pp.19-24
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• 2016

Constitutional interstitial deletions of the long arm of chromosome 5 (5q) are quite rare, and the corresponding phenotype is not yet clearly delineated. Severe mental retardation has been described in most patients who present 5q deletions. Specifically, the interstitial deletion of chromosome 5q33.3q35.1, an extremely rare chromosomal aberration, is characterized by mental retardation, developmental delay, and facial dysmorphism. Although the severity of mental retardation varies across cases, it is the most common feature described in patients who present the 5q33.3q35.1 deletion. Here, we report a case of a de novo deletion of 5q33.3q35.1, 46,XY,del(5)(q33.3q35.1) in an 11-year-old boy with mental retardation; to the best of our knowledge this is the first case in Korea to be reported. He was diagnosed with severe mental retardation, developmental delay, facial dysmorphisms, dental anomalies, and epilepsy. Chromosomal microarray analysis using the comparative genomic hybridization array method revealed a 16-Mb-long deletion of 5q33. 3q35.1(156,409,412-172,584,708)x1. Understanding this deletion may help draw a rough phenotypic map of 5q and correlate the phenotypes with specific chromosomal regions. The 5q33.3q35.1 deletion is a rare condition; however, accurate diagnosis of the associated mental retardation is important to ensure proper genetic counseling and to guide patients as part of long-term management.

• Explosives and Blasting
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• v.35 no.4
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• pp.27-35
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• 2017

A total of 22 sites around openings of limestone mine are chosen to assess rock mass classification schemes such as RMR, Q-system, and GSI. RMR and Q are modified to estimate the relationship with GSI. Q' is the modified Q with SRF=1.0 and $J_w=1.0$. Rock mass is assumed to be completely dry and very favorable discontinuity orientations are assumed to estimate ${RMR_{89}}^{\prime}$. Relationships of Q-Basic RMR, Q-Total RMR, ${GSI-RMR_{89}}^{\prime}$, and GSI-Q' are analyzed, in which a correlation of ${GSI-RMR_{89}}^{\prime}$ is found to be the highest. Failure strains are calculated using the modulus ratios and most measuring sites appear to be stable with low failure strain class.