• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.41-53
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• 2023

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ and L = {±1, ±2, ±3, … , ±ρ} called the set of labels. Consider a mapping f : V ⟶ L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.1-14
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• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

• Journal of the Korean Society for information Management
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• v.6 no.1
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• pp.15-36
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• 1989

The r a p i d i n c r e a s e o f microcomputer technology has r e s u l t e d i n t h e broad a p p l i c a t i o n t o various f i e l d s . The purpose of t h l s paper 1s to design a computerized r e t r i e v a l system f o r nuclear information m a t e r i a l s using a microcomputer.

• Microbiology and Biotechnology Letters
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• v.20 no.1
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• pp.6-13
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• 1992

- Protoplast fusion between lincomycin resistant Lactobacillus casei KCTC 1121 and rifarnpicin resistant Lactobacillus delbrueckii JK-414 was attempted to obtain the improved strains. Protoplasts of L. casei and L. delbrueckii were produced by mutanolysin digestion at $42^{\circ}C$ for 15 min. L. casei cells were converted to protoplasts by treating with 5 $\mu g$ / m l of mutanolysin in 20 mM HEPES buffer (pH 7.0) containing 0.75 M sucrose at the middle logarithmic growth phase. In case of L. delbrueckii 1.0 M sucrose was used osmotic stabilizer. Regeneration of protoplast in both strains was efficiently accomplished on the regeneration medium containing 10% sucrose, 6 mM $MgC1_2, 6 mM CaC1_2$, and 2.5% gelatin. Protoplast fusion between L. casei and L. delbrueckii was carried out in the presence of 40% of PEG 4,000. The frequency of protoplast fusion was found to be about $3.2\times 10^4$. Acid production of L. casei was better than that of L. delbrueckii. Among fusants, F23 and F35 exhibited excellent lactic acid production. F23 and F24 exhibited the improved proteolysis compared to that of the parent strains and they had twice as much as DNA content of the parents.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.155-166
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• 2022

In this paper, the paired Hayman conjecture of different types are considered, namely, the zeros distribution of f(z)ⁿL(g) - a(z) and g(z)ⁿL(f) - a(z), where L(h) takes the derivatives h^(k)(z) or the shift h(z+c) or the difference h(z+c)-h(z) or the delay-differential h^(k)(z+c), where k is a positive integer, c is a non-zero constant and a(z) is a nonzero small function with respect to f(z) and g(z). The related uniqueness problems of complex delay-differential polynomials are also considered.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.251-259
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• 2015

Let $\mathbb{F}^d_q$ be a d-dimensional vector space over a finite field $\mathbb{F}^d_q$ with q elements. We endow the space $\mathbb{F}^d_q$ with a normalized counting measure dx. Let ${\sigma}$ be a normalized surface measure on an algebraic variety V contained in the space ($\mathbb{F}^d_q$, dx). We define the restricted averaging operator AV by $A_Vf(X)=f*{\sigma}(x)$ for $x{\in}V$, where $f:(\mathbb{F}^d_q,dx){\rightarrow}\mathbb{C}$: In this paper, we initially investigate $L^p{\rightarrow}L^r$ estimates of the restricted averaging operator AV. As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on $\mathbb{F}^2_q$ play a crucial role in proving our results.

• Korean Journal of Plant Resources
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• v.34 no.5
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• pp.433-442
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• 2021

The fermented red ginseng by microorganism is known to increase pharmacological activity in vivo. To evaluate the bioavailablity of red ginseng fermented by probiotics, we conducted the pharmacokinetic study of ginsenoside Rb1, Rd and total ginsenosides (TG, ginsenosides Rb1 + Rd + Rg1 + F2 + Rg3 + compound K) in BALB/C mice. The AUC value of ginsenoside Rb1 in mice serum administered with 600mg/kg drugs showed 21.93 ± 14.68 ng·h/mL (RGw, water extract), 275.211 ± 110.04 ng·h/mL (RGe, 50% ethanol extract) and 404.91 ± 162.57 ng·h/mL (fRGe, fermented red ginseng extract). Analysis of ginsenoside Rd also showed a higher ACU value in fRGe than in RGw or RGe. And the AUC value of total ginsenosides in mice serum treated with 600 mg/kg were observed 42.12 ± 23.44 ng·h/mL (RGw), 321.44 ± 133.5 ng·h/mL (RGe) and 537.33 ± 229.01 ng·h/mL (fRGe), respectively. C_max value of ginsenoside Rb1 in mice administered with 600mg/kg were observed 3.67 ± 3.34 ng/mL (RGw), 23.27 ± 8.81 ng/mL (RGe) and 25.52 ± 7.29 ng/mL (fRGe). These results can be considered that the fermented red ginseng has more bioavailability than that of unfermented red ginseng. In quantitative analysis of the inflammation-related cytokines IL-1β and TNF, no significant difference was found between the fermented red ginseng (fRGe) and the red ginseng (RGe).

• Nuclear Medicine and Molecular Imaging
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• v.40 no.5
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• pp.263-270
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• 2006

Purpose: Several radioisotope-labeled thymidine derivatives such as $[^{11}C]$thymidine was developed to demonstrate cell proliferation in tumor. But it is difficult to track metabolism with $[^{11}C]$thymidine due to rapid in vivo degradation and its short physical half-life. 3'-$[^{18}F]$fluoro-3'-deoxythymidine ($[^{18}F]$FLT) was reported to have the longer half life of fluorine-18 and the lack of metabolic degradation in vivo. Here, we described the synthesis of the 3'-$[^{18}F]$fluoro-3'-deoxythymidine ($[^{18}F]$FLT) and compared with $([^{18}F]FET)\;and\;([^{18}F]FDG)$ in cultured 9L cell and obtained the biodistribution and PET image in 9L tumor hearing rats. Material and Methods: For the synthesis of $[^{18}F]$FLT, 3-N-tert-butoxycarbonyl-(5'-O-(4,4'-dimet hoxytriphenylmethyl)-2'-deoxy-3'-O-(4-nitrobenzenesulfonyl)-${\beta}$-D-threopentofuranosyl)thymine was used as a FLT precursor, on which the tert-butyloxycarbonyl group was introduced to protect N3-position and nitrobenzenesulfonyl group. Radiolabeling of nosyl substitued precursor with $^{18}F$ was performed in acetonitrile at $120^{\circ}C$ and deproteced with 0.5 N HCI. The cell uptake was measured in cultured 9L glioma cell. The biodistribution was evaluated in 9L tumor bearing rats after intravenous injection at 10 min, 30 min, 60 min and 120 min and obtained PET image 60 minutes after injection. Results: The radiochemical yield was about 20-30% and radiochemical purity was more than 95% after HPLC purification. Cellular uptake of $[^{18}F]$FLT was increased as time elapsed. At 120 min post-injection, the ratios of tumor/blood, tumor/muscle and tumor/brain were $1.61{\pm}0.34,\;1.70{\pm}0.30\;and\;9.33{\pm}2.22$, respectively. The 9L tumor was well visualized at 60 min post injection in PET image. Conclusion: The uptake of $[^{18}F]$FLT in tumor was higher than in normal brain and PET image of $[^{18}F]$FLT was acceptable. These results suggest the possibility of $[^{18}F]$FLT at an imaging agent for brain tumor.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.77-83
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• 2004

The aim of this work is to generalize parametric approximation in order to apply them to an one-sided $L_1$-approximation. A natural question now arises : when is the parameter map $$P:f{\rightarrow}P_{K(f)}(f)$$ continuous on $C_1(X)$ ? We find some results with a monotone decreasing sequence about above question.

• Journal of the Korean Chemical Society
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• v.43 no.1
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• pp.52-57
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• 1999

The anionic complexes, [ln($C_6F_5)_4$]-, which are thermal and moisture sensitive, have been prepared by the reaction of In($C_6F_5)_3{\cdot}D(D=CH_3CN$, O($C_2H_5)_2$) with the system ($CH_3)_3SiC_6F_5$/CsF, $C_6F_5$MgBr or Cd($C_6F_5)_2$. The stable anionic indium(III) complexes are obtained through cation exchange with PNPCI ([PNP]= bis(triphenylphosphino)ammonium). The pure substance is obtained by column chromatography. These new anionic complexes are unambiguously identifed by NMR-spectroscopy, IR spectroscopy, molecular weight, DTA/TG and elemental analysis.