• Korean Journal of Mathematics
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• 제27권2호
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• pp.525-534
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• 2019

Let $P(G,{\lambda})$ denote the number of proper vertex colorings of G with ${\lambda}$ colors. The chromatic polynomial $P(C_n,{\lambda})$ for the cycle graph $C_n$ is well-known as $$P(C_n,{\lambda})=({\lambda}-1)^n+(-1)^n({\lambda}-1)$$ for all positive integers $n{\geq}1$. Also its inductive proof is widely well-known by the deletion-contraction recurrence. In this paper, we give this inductive proof again and three other proofs of this formula of the chromatic polynomial for the cycle graph $C_n$.

• 대한수의학회지
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• 제37권4호
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• pp.917-924
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• 1997

Estrus cycle of cow, season and follicldar stimulating treatment, having an effect on the number of follicle, are investigated for the oocyte recovery rate in ovum pick-up(OPU). The number of follicle aspirated and oocyte collected on the different days of estrus cycle(D 4~5, D 9~10 and D 14~15) were not significantly different among the groups. The higher number of viable oocytes were produced on Jan-May(79.0%) than Jun-Aug(33.3%) by OPU in cow. The number of follicle and aspirated oocyte in cows treated FSH or PMSG combined with bovine somatotropin(bST) were 1.2~1.5 times higher than in cows treated alone follicular stimulating hormone(FSH) or pregnant mare serum gonadotropin(PMSG). In conclusion, OPU can be repeatedly practiced 2 or 3 times in an estrus cycle. In addition, the high environmental temperature is not good for ovarian function of cow and the bST co-treatment with FSH or PMSG is increasing the number of aspiratable follicle.

• Asian-Australasian Journal of Animal Sciences
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• 제22권8호
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• pp.1113-1116
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• 2009

The objective of this study was to compare the follicular population during spontaneous and $PGF_2{\alpha}$ induced oestrous cycles in Nili-Ravi buffaloes. In Exp.1, (n = 13 oestrous cycles) follicular population was monitored using ultrasonography on alternate days. Buffaloes were monitored for ovarian follicles from day 0 (first oestrus) until next oestrus. These animals were observed for oestrus twice daily using a teaser bull. Of 12 oestrous cycles, 9 (75%) had two waves of follicular activity and only 3 (25%) had three waves during the oestrous cycle. The mean number of small, medium and large follicles among various days of the oestrous cycle between two and three waves of follicular development were not significantly different (p>0.05). In Exp. 2, follicular population 3 days before oestrus was compared in buffaloes undergoing spontaneous (n = 12 oestrous cycles) and $PGF_2{\alpha}$ induced (n = 6) luteolysis. The mean number of small and large follicles increased (p<0.05) and the number of medium follicles decreased (p<0.05) during the 3 days before oestrus in buffaloes undergoing induced luteolysis as compared to those with spontaneous luteolysis. These results showed that the mean number of small, medium and large follicles among various days of the oestrous cycle were similar between the two and three waves of follicular development, and three days before oestrous the number of small, medium and large follicles altered due to induced luteolysis on day 9, compared to those with spontaneous luteolysis.

• 한국분무공학회지
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• 제12권1호
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• pp.65-70
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• 2007

This paper is to investigate the characteristics of exhaust emissions and nano-particle emission from diesel passenger vehicle according to using biodiesel fuel as an alternative fuel. In this work, the particulate matters (PM) of exhaust emissions in diesel engine were investigated by number of particles and mass measurement. The mass of the total PM was measured using the standard gravimetric measurement method, the total number concentrations were measured on a ECE15+EUDC driving cycle using Condensation Particle Counter (CPC). Total PM emission was reduced $2{\sim}38%$ and number concentration was reduced $1{\sim}27%$ according to increasing blended ratio of biodiesel with diesel fuel. Total PM emission was reduced more than particle number emission because volatile particles were measured in total PM but were not measured in particle number emissions.

• Korean Journal of Mathematics
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• 제21권2호
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• pp.151-159
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• 2013

An $L(j,k)$-labeling of a graph G is a vertex labeling such that the difference of the labels of any adjacent vertices is at least $j$ and that of any vertices of distance two is at least $k$ for given $j$ and $k$. The minimum span of all L(2, 1)-labelings of G is called the ${\lambda}$-number of G and is denoted by ${\lambda}(G)$. In this paper, we find a lower bound of the ${\lambda}$-number of the Cartesian product $K_m{\Box}C_n$ of the complete graph $K_m$ of order $m$ and the cycle $C_n$ of order $n$. In fact, we show that when $n{\geq}3$, ${\lambda}(K_4{\Box}C_n){\geq}7$ and the equality holds if and only if n is a multiple of 8. Moreover when $m{\geq}5$, ${\lambda}(K_m{\Box}C_n){\geq}2m-1$ and the equality holds if and only if $n$ is even.

• 열처리공학회지
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• 제31권1호
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• pp.18-23
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• 2018

In this study, low cyclic fatigue test was carried out at room temperature condition for rolled STS304 steel. The results of this study show that rolled STS304 steel has excellent static tensile strength and fatigue characteristics. The relationship between plastic strain range and fatigue life was examined using the triangular wave in order to predict the low cycle fatigue life of rolled STS304 steel by Coffin-Manson equation. Cyclic behavior of rolled STS304 steel was characterized by cyclic hardening with increasing number of cycle through the Hysteresis loop analysis and cyclic response of maximum stress versus number of cycles. It is found that the plastic deformation energy consumed per cycle is reduced by calculating the area of the hysteresis loop.

• 한국재료학회지
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• 제25권5호
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• pp.221-225
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• 2015

In-situ neutron diffraction has been employed to examine the effect of strain path on lattice strain evolution during monotonic and cyclic tension in an extruded Mg-8.5wt.%Al alloy. In the cyclic tension test, the maximum applied stress increased with cycle number. Lattice strain data were acquired for three grain orientations, characterized by the plane normal to the stress axis. The lattice strain in the hard {10.0} orientation, which is unfavorably oriented for both basal slip and {10.2} extension twinning, evolved linearly throughout both tests during loading and unloading. The {00.2} orientation exhibited significant relaxation associated with {10.2} extension twinning. Coupled with a linear lattice strain unloading behavior, this relaxation led to increasingly compressive residual strains in the {00.2} orientation with increasing cycle number. The {10.1} orientation is favorably oriented for basal slip, and thus showed a soft grain behavior. Microyielding occurred in the monotonic tension test and in all cycles of the cyclic test at an applied stress of ~50 MPa, indicating that strain hardening in this orientation was not completely stable from one cycle to the next. The lattice strain unloading behavior was linear in the {10.1} orientation, leading to a compressive residual strain after every cycle, which, however, did not increase systematically from one cycle to the next as in the {00.2} orientation.

• 산업경영시스템학회지
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• 제3권3호
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• pp.35-39
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• 1980

Although the product line produces a large volume of goods in a relatively short time, once the product line is established there are numerous problems that arise in connection with this product line. One of these problems is the problem of balancing operations or stations in terms of equal times and in terms of the times required to meet the desered rate of production. The objective of line balancing is minimizing the idle time on the line for all combinations of work stations subject to certain restrictions. In general, there are two types of line-balancing situations : (1) assembly line balancing and (2) fabrication line balancing. Two approaches to the assembly line balancing problem have been used. The first assumes a filed cycle time and find the optimum number of work stations. The second approach to the assembly line balancing problem assumes the number of work stations to be fixed and systematically coverages on a solution which minimizes the total delay time by minimizing the cycle time. Here the cycle time is determined by the longest station time. In this paper, by using the second approach method, a general mathematical model, problem solutions, and computer program for the assembly line balancing problem is presented. Data used is obtained from the company which has been confronted with many problems arising in connection with their assembly line.

• Journal of Breast Disease
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• 제6권2호
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• pp.39-45
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• 2018

Purpose: Dieckol, a phlorotannin compound isolated from Ecklonia cava, has been reported to have antioxidant, antiviral, anti-inflammatory, and anticancer properties. The purpose of this study was to investigate its anticancer effects on human breast cancer cell lines. Methods: In this study, the viability of two human breast cancer cell lines SK-BR-3 and MCF-7 was investigated after dieckol treatment using a WST-1 assay. Apoptosis and cell cycle distribution were assayed via Annexin V-fluorescein isothiocyanate and propidium iodide staining followed by flow cytometric analysis. Immunoblotting analysis was also performed using Bax/Bcl-2 to determine whether the dieckol-induced apoptosis was mediated by the intrinsic apoptotic pathway. Results: In a dose dependent manner, dieckol reduced the number of viable cells and increased the number of apoptotic cells. The effect of dieckol on the cell cycle distribution was analyzed using flow cytometry. Dieckol treatment significantly increased the percentage of MCF-7 and SK-BR-3 in the G2/M phase. Immunoblot analysis revealed that 24 hours of dieckol exposure increased the Bax/Bcl-2 ratio. Conclusion: Dieckol induced cytotoxicity in MCF-7 and SK-BR-3 human breast cancer cells inducing apoptosis and cell cycle arrest. Therefore, it is suggested that dieckol may be a potential therapeutic agent for breast cancer.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.223-237
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• 2021

Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.