• Korean Journal of Mathematics
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• v.28 no.4
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• pp.931-942
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• 2020

For a polynomial $P(z)={\sum_{{\nu}=0}^{n}}\;a_{\nu}z^{\nu}$ of degree n having all its zeros in |z| ≤ k, k ≥ 1, it was shown by Rather and Dar [13] that ${\max_{{\mid}z{\mid}=1}}{\mid}P^{\prime}(z){\mid}{\geq}{\frac{1}{1+k^n}}\(n+{\frac{k^n{\mid}a_n{\mid}-{\mid}a_0{\mid}}{k^n{\mid}a_n{\mid}+{\mid}a_0{\mid}}}\){\max_{{\mid}z{\mid}=1}}{\mid}P(z){\mid}$. In this paper, we shall obtain some sharp estimates, which not only refine the above inequality but also generalize some well known Turán-type inequalities.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.5
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• pp.460-471
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• 1992

By setting a new model to describe the time-discontinuous operation of PLL loop which used tri-state and sample-hold method, the stability analysis of nonlinear PLL has been performed in z-domain and the state equations for the transient response has been introduced. Until now, the lin-ear analysis by approximation of time-discontinuous to time-continuous operation had not found then stable region of time-discontinuous digital PLL exactly. However, the analysis In z-domain by the new model has been found the unstable region where the time-continuous analysis had have not. 1'herefore the limit of loop coefficient has been computed to design digital PLL optimally.

• Natural Product Sciences
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• v.21 no.4
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• pp.282-288
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• 2015

Viriditoxin is a fungal metabolite isolated from Paecilomyces variotii, which was derived from the giant jellyfish Nemopilema nomurai. Viriditoxin was reported to inhibit polymerization of FtsZ, which is a key protein for bacterial cell division and a structural homologue of eukaryotic tubulin. Both tubulin and FtsZ contain a GTP-binding domain, have GTPase activity, assemble into protofilaments, two-dimensional sheets, and protofilament rings, and share substantial structural identities. Accordingly, we hypothesized that viriditoxin may inhibit eukaryotic cell division by inhibiting tubulin polymerization as in the case of bacterial FtsZ inhibition. Docking simulation of viriditoxin to ${\beta}-tubulin$ indicated that it binds to the paclitaxel-binding domain and makes hydrogen bonds with Thr276 and Gly370 in the same manner as paclitaxel. Viriditoxin suppressed growth of A549 human lung cancer cells, and inhibited cell division with G2/M cell cycle arrest, leading to apoptotic cell death.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.231-247
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• 2010

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-Jensen functional equation $4f(\frac{x\;+\;y}{2},\;\frac{z\;+\;w}{2})$ = f(x, z) + f(x, w) + f(y, z) + f(y, w). Also, we establish improved results for the stability of a bi-Jensen equation on the punctured domain.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.383-398
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• 2009

In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.349-355
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• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.127-134
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• 2000

Let $\Omega$ be a bounded pseudoconvex domain in$C^{n}$ with smooth defining function r and let$z_0\; {\in}\; b{\Omega}$ be a point of finite type. We also assume that $\Omega$ is convex in a neighborhood of $z_0$. Then we prove that all the holomorphic sectional curvatures of the Bergman metric of $\Omega$ are bounded below by a negative constant near $z_0$.

• BMB Reports
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• v.32 no.4
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• pp.405-408
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• 1999

The transactivation potential of HIV-1 Vpu was identified from the yeast two-hybrid screening process. The helix II domain of HIV-1 Vpu protein and mutant Vpu protein lacking the transmembrane domain exhibited transactivation of the LacZ and Leu2 reporter genes carrying LexA upstream activating sequences, but full-length HIV-1 Vpu and the helix I domain of HIV-1 Vpu did not. The helix II domain of HIV-1 Vpu consists of a number of acidic amino acids, and is especially rich in glutamic acid, a characteristic of many transcription factors. This result suggests that protein-protein interaction may occur through the acidic helix II domain of HIV-1 Vpu.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1783-1789
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• 2018

This paper treats the class of normalized logharmonic mappings $f(z)=zh(z){\overline{g(z)}}$ in the unit disk satisfying ${\varphi}(z)=zh(z)g(z)$ is analytically typically real. Every such mapping f admits an integral representation in terms of its second dilatation function and a function of positive real part with real coefficients. The radius of starlikeness and an upper estimate for arclength are obtained. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when its second dilatation has real coefficients.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.593-605
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• 2017

In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain D. Let k be a positive integer and ${\psi}(z){\not\equiv}0$, ${\infty}$ be a meromorphic function in D. If, for each $f{\in}\mathcal{F}$ and $z{\in}D$, (1) $f(z){\neq}0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-{\psi}(z)$ have multiplicities at least k + 3 in D; (3) all poles of ${\psi}(z)$ have multiplicities at most k in D, then $\mathcal{F}$ is normal in D.