• Honam Mathematical Journal
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• v.32 no.4
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• pp.769-776
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• 2010

A pebbling move on a connected graph G is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. For a connected graph G, $G^p$ (p > 1) is the graph obtained from G by adding the edges (u, v) to G whenever 2 $\leq$ dist(u, v) $\leq$ p in G. And the pebbling exponent of a graph G to be the least power of p such that the pebbling number of $G^p$ is equal to the number of vertices of G. We compute the pebbling number of fourth power of paths so that the pebbling exponents of some paths are calculated.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.283-295
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• 2015

The atom-bond connectivity index of a graph G (ABC index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of G. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the ABC index among all n vertex cactus graphs.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1131-1138
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• 2010

In the present paper, we evaluate an analytic formula as a solution of Susceptible Infective (SI) model problem for communicable disease in which the daily contact rate (C(N)) is supposed to be varied linearly with population size N(t) that is large so that it is considered as a continuous variable of time t. Again, we introduce some Lie group of operators to make an extension of above analytic formula of the determin-istic epidemics model problem. Finally, we discuss some of its particular cases.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.401-408
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• 2015

The first and second Zagreb indices of a graph G are defined as $M_1(G)={\sum}_{{\nu}{\in}V}d_G({\nu})^2$ and $M_2(G)={\sum}_{u{\nu}{\in}E(G)}d_G(u)d_G({\nu})$. where $d_G({\nu})$ is the degree of the vertex ${\nu}$. G is called a k-apex tree if k is the smallest integer for which there exists a subset X of V (G) such that ${\mid}X{\mid}$ = k and G-X is a tree. In this paper, we determine the maximum Zagreb indices in the class of all k-apex trees of order n and characterize the corresponding extremal graphs.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.899-910
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• 2016

It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts $W_{\alpha}$ with first two weights equal. Let ${\alpha}$ : 1, 1, ${\sqrt{x}}$(${\sqrt{u}}$, ${\sqrt{v}}$, ${\sqrt{w}}$)^ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let $W_{\alpha}$ be the associated weighted shift. In this paper we characterize completely the semi-cubical hyponormal $W_{\alpha}$ satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.591-591
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• 2006

• Journal of Applied Biological Chemistry
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• v.55 no.3
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• pp.149-156
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• 2012

The effects of solvent type and concentration, solid/liquid ratio, extraction time and repeated extraction on recovery of keratinase from solid-state fermentation (SSF) of chicken feather by a local Streptomyces sp. NRC 13S were investigated in order to establish the experimental conditions for keratinase yield. Among solvents tested, 0.5% (v/v) glycerol was the best. Box-Behnken design was used to investigate the effect of relevant variables on keratinase recovery. The factors investigated were solid/liquid ratio (1:1.66-1:6.66 g/mL), glycerol concentration (0.5-5% v/v) and repeated extraction (1-5 cycle). The results showed that the maximum recovery of keratinase (6933.3 U/gfs) was obtained using 0.5 (v/v) glycerol as extracting solvent, in a solid/liquid ratio of 1:5 and three extraction cycles.

• Journal of Radiopharmaceuticals and Molecular Probes
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• v.6 no.2
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• pp.92-101
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• 2020

The cyclic Arg-Gly-Asp (cRGD) peptide is well-known as a binding molecule to the integrin α_vβ₃ receptor which is highly expressed on activated endothelial cells and new blood vessels in tumors. Although numerous results have been reported by the usage of cRGD peptide-based ligands for cancer diagnosis and therapy, the distinct mechanisms, and functions of cRGD-integrin binding to cancer cells are still being investigated. In this study, we evaluated the internalization efficacy of different types of cRGD peptides (monomer, dimer and tetramer form) in integrin α_vβ₃ overexpressing cancer cells. Western blot and flow cytometric analysis showed U87MG expresses highly integrin α_vβ₃, whereas CT-26 does not show integrin α_vβ₃ expression. Cytotoxicity assay indicated that all cRGD peptides (0-200 µM) had at least 70-80% of viability in U87MG cells. Fluorescence images showed cRGD dimer peptides have the highest cellular internalization compare to cRGD monomer and cRGD tetramer peptides. Additionally, transmission electron microscope results clearly visualized the endocytic internalization of integrin α_vβ₃ receptors and correlated with confocal microscopic results. These results support the rationale for the use of cRGD dimer peptides for imaging, diagnosis, or therapy of integrin α_vβ₃-rich glioblastoma.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.29-44
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• 2021

The set D of column vectors of a generator matrix of a linear code is called a defining set of the linear code. In this paper we consider the problem of constructing few-weight (mainly two- or three-weight) linear codes from defining sets. It can be easily seen that we obtain an one-weight code when we take a defining set to be the nonzero codewords of a linear code. Therefore we have to choose a defining set from a non-linear code to obtain two- or three-weight codes, and we face the problem that the constructed code contains many weights. To overcome this difficulty, we employ the linear codes of the following form: Let D be a subset of ��2n, and W (resp. V ) be a subspace of ��2 (resp. ��2n). We define the linear code ��D(W; V ) with defining set D and restricted to W, V by $${\mathcal{C}}_D(W;V )=\{(s+u{\cdot}x)_{x{\in}D^{\ast}}|s{\in}W,u{\in}V\}$$. We obtain two- or three-weight codes by taking D to be a Vasil'ev code of length n = 2m - 1(m ≥ 3) and a suitable choices of W. We do the same job for D being the complement of a Vasil'ev code. The constructed few-weight codes share some nice properties. Some of them are optimal in the sense that they attain either the Griesmer bound or the Grey-Rankin bound. Most of them are minimal codes which, in turn, have an application in secret sharing schemes. Finally we obtain an infinite family of minimal codes for which the sufficient condition of Ashikhmin and Barg does not hold.

• Korean Journal of Materials Research
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• v.7 no.1
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• pp.81-88
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• 1997

Vanadate glasses using $B_2O_3$ as a network former and with CuO additive were mainly investigated in relation to electrical properties. Crystalline phases formed by heat-treatment in each composition were examined and dc electrical conductivity changes of the glasses were analyzed. Crystalline phases were identified as $V_3O_5,\;a-CuV_2O_6\;and\;{\beta}-CuV_2O_6$ by XRD analysis. Crystallization degrees of $V_2O_5$ and ${\beta}-CuV_2O_6$ were little changed with heat-treatment time, but those of ${\alpha}u-CuV_2O_6$ were changed sharply with heat-treatment time. The more crystallization of ${\alpha}u-CuV_2O_6$ occurred, the higher electrical conductivity was observed. Electrical conductivities with $10^{-2}~10^{-4}/{\Omega}/cm$ at room temperature(303K) could be obtained by controlling the glass compositions. The electrical conductivities were increased with increasing of $V_20_5$ content and decreasing of alkality($CuO/B_2O_3$). In this study, electron was proved to be charge carrier by seebeck coefficient measurement. Accordingly, the glasses are believed to be n-type semiconductor. Calculated activation energies for the conduction were in the range 0.098-0.124 eV. Electrical conduction mechanism was small polaron hopping without showing variable range hopping in the temperature range $30~200^{\circ}C$.