• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.475-490
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• 2019

Let C^(q) be the q-commuting arithmetic table of (x + y)ⁿ with noncommuting variables. We study sequential properties of diagonal sums of C^(q) with various q > 0. One of our results shows that each diagonal sum plays like Fibonacci number with some minor conditions.

• 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.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.1
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• pp.225-229
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• 2012

Background: Males have a higher prevalence of hepatocellular carcinoma (HCC) than females in general, but the reasons for the sex disparity are still obscure. DNA copy number alteration (CNA) is a major feature of solid tumors including HCC, but whether CNA plays a role in sex-related differences in HCC development has never been evaluated. Methods: High-resolution array comparative genomic hybridization (CGH) was used to examine 17 female and 46 male HCC patients with chronic hepatitis B virus (HBV) infection in Shanghai, China. Two-tailed Fisher's exact or ${\chi}^2$ tests was used to compare CNAs between females and males. Results: The overall frequencies and patterns of CNAs in female and male cases were similar. However, female HCC tumors presented more copy number gains compared to those in males on 1q21.3-q22 (76.5% vs. 37.0%, P = 0.009), 11q11 (35.3% vs. 0.0%, P = 0.0002) and 19q13.31-q13.32 (23.5% vs. 0.0%, P = 0.004), and loss on 16p11.2 (35.3% vs. 6.5%, P = 0.009). Relative to females, male cases had greater copy number loss on 11q11 (63.0% vs. 17.6%, P = 0.002). Further analyses showed that 11q11 gain correlated with 19q13.31-q13.32 gain (P = 0.042), 11q11 loss (P = 0.011) and 16p11.2 loss (P = 0.033), while 1q21.3-q22 gain correlated with 19q13.31-q13.32 gain (P = 0.046). Conclusions: These findings suggest that CNAs may play a role in sex-related differences in HBVassociated HCC development.

• Proceedings of the Korean Society of Crop Science Conference
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• 2017.06a
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• pp.101-101
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• 2017

This study was carried out to improve yield potential of Tongil type rice variety based on QTLs analysis associated with yield component using a total of 386 rice recombinant inbred lines (RILs) derived from a cross between Tongil type high yield variety "Hanareum2" and Japonica variety "Unkwang". 384 SNP markers were used, and 241 of them (62.6%) were polymorphic between Hanareum2 and Unkwang. One hundred forty-four QTLs in 11 traits, such as heading days, were detected. Most of them were 21 QTLs associated with 1000 grain weight and the least was 8 QTLs associated with panicle number. The QTL, qDTH3-2 associated with days to heading was identified to delay heading date for 2.4~2.6 day. Eleven QTLs were associated with culm length. The QTL, qCL1-2 on chromosome 1, was identified to decrease culm length. A total of 16 QTLs were detected for panicle length. Three QTLs, qPL3, qPL6, and qPL7-1 were increased panicle length. Seven QTLs related to panicle number except qPN7 were increased the number of panicle. Four QTLs related to grain number per panicle, qGNP2-1, qGNP6, and qGNP7, were increased the number of grains. Three QTLs associated with grain filling rate, qGFR1, qGFR2-2, and qGFR7-1 were increased grain filling rate. Twelve QTLs associated with 1,000 grain weight. were increased the grain weight. Fourteen QTLs were identified associated with grain length. 10 QTLs, such as qGL1-1, were increasing grain. Fifteen QTLs associated with grain width were detected. The 8 QTLs, such as qGW1-1, were elongated grain width. Seventeen QTLs were associated with grain thickness, and ten QTLs of them were increased grain thickness. We need further study to develop introgression lines of each QTL to improve yield potential of Tongil type rice variety.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• Journal of the Korea Society of Computer and Information
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• v.10 no.5 s.37
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• pp.87-94
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• 2005

This paper describes the method of detecting the region of vehicle number plate in colored car image with number plate. Vehicle number plate region generally shows formula colors in accordance with type of car. According to this, we use the method to combine a color ingredient H of HSI color model and a color ingredient Q of YIQ color model. However, the defect which a total operation time takes much exists if it uses such method. Therefore, in this paper, the concurrent accomplishes a candidate area extraction operation as draw a color H and Q ingredient among steps of extracting a region of vehicle number Plate. After the above step, as a next step in combination with color H and Q we can accomplish an region extraction fast by comparing to candidate regions extracted from each steps not to do a comparison operation to all of image pixel information. We also show implementation results Processed at each steps and compare with extraction time according to image resolutions.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1055-1073
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• 2018

In this paper, we define an alternative q-analogue of the $Ruci{\acute{n}}ski$-Voigt numbers. We obtain fundamental combinatorial properties such as recurrence relations, generating functions and explicit formulas which are shown to be q-deformations of similar properties for the $Ruci{\acute{n}}ski$-Voigt numbers, and are generalizations of the results obtained by other authors. A combinatorial interpretation in the context of A-tableaux is also given where convolution-type identities are consequently obtained. Lastly, we establish the matrix decompositions of the $Ruci{\acute{n}}ski$-Voigt and the q-$Ruci{\acute{n}}ski$-Voigt numbers.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.26 no.3
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• pp.245-253
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• 2000

The development and progression of oral cancer is associated with an accumulation of multiple genetic alterations through the multistep processes. Comparative genomic hybridization(CGH), newly developed cytogenetic and molecular biologic technique, has been widely accepted as a useful method to allow the detection of genetic imbalance in solid tumors and the screening for chromosome sites frequently affected by gains or losses in DNA copy number. The authors examined 19 primary oral squamous cell carcinomas using CGH to identify altered chromosome regions that might contain novel oncogenes and tumor suppressor genes. Interrelationship between these genetic aberrations detected and major oncogenes and tumor suppressor genes previously recognized in carcinogenesis of oral cancers was studied. 1. Changes in DNA copy number were detected in 14 of 19 oral cancers (78.9%, mean: 5.58, range: $3{\sim}13$). High level amplification was present in 4 cases at 9p23, $12p21.1{\sim}q13.1$, 3q and $8q24{\sim}24.3$. Fourteen cases(78.9%, mean: 3.00, range: $1{\sim}8$) showed gains of DNA copy number and 12 cases(70.5%, mean: 2.58, range: $1{\sim}9$) revealed losses of DNA copy number. 2. The most common gains were detected on 3q(52.6%), 5p(21.0%), 8q(21.0%), 9p(21.0%), and 11q(21.0%). The losses of DNA copy number were frequently occurred at 9p(36.8%), 17q(36.8%), 13q(26.3%), 4p(21.0%) and 9p(21.0%). 3. The minimal common regions of gains were repeatedly observed at $3q24{\sim}26.7$, $3q27{\sim}29$, $1q22{\sim}31$, $5p12{\sim}13.3$, $8q23{\sim}24$, and 11q13.1-13.3. The minimal common regions of losses were detected at $9q11{\sim}21.3$, 17p31, $13q22{\sim}34$, and 14p16. 4. In comparison of CGH results with tumor stages, the lower stage group showed more frequent gain at 3q, 5q, 9p, and 14q, whereas gains at 1q($1q22{\sim}31$) and 11q($11q13.1{\sim}13.3$) were mainly detected in higher stage group. The loss at $13q22{\sim}34$ was exclusively detected in higher stage. The results indicate that the most frequent genetic alterations in the development of oral cancers were gains at $3q24{\sim}26.3$, $1q22{\sim}31$, and $5p12{\sim}13.3$ and losses at $9q11{\sim}21.3$, 17p31, and 13q. It is suggested that genetic alterations manifested as gains at $3q24{\sim}26.3$, $3q27{\sim}29$, $5p12{\sim}13.3$ and 5p are associated with the early progression of oral cancer. Gains at $1q22{\sim}31$ and $11q13.1{\sim}13.3$ and loss at 13q22-34 could be involved in the late progression of oral cancers.

• The Transactions of the Korea Information Processing Society
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• v.7 no.5
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• pp.1370-1376
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• 2000

Consider the problem to updata breadth-First Spanning Tree in response to topology change of the network. The paper proposes an efficient distributed algorithm that solves such a problem after several processors and links are added and deleted. Its message complexity and its ideal-time complexity are O(p√q+q+a+n') respectively, where n' is the number fo processors in the network after the topology change, a is the number of added links, p is the total number of links in the biconnected component (of the network before the topology change) including the detected links or added links, and q is the total number of processors in the biconnected component (of the network before the topology change) including the deleted links or added links, and q is the total number of processors in the biconnected component including the deleted links or added links.