• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.855-868
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• 2021

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≤ 1, then for 𝜌R ≥ k² and 𝜌 ≤ R, Aziz and Zargar [4] proved that $${\max_{{\mid}z{\mid}=1}}{\mid}p^{\prime}(z){\mid}{\geq}n{\frac{(R+k)^{n-1}}{({\rho}+k)^n}}\{{\max_{{\mid}z{\mid}=1}}{\mid}p(z){\mid}+{\min_{{\mid}z{\mid}=k}}{\mid}p(z){\mid}\}$$. We prove a generalized L^r extension of the above result for a more general class of polynomials $p(z)=a_nz^n+\sum\limits_{{\nu}={\mu}}^{n}a_n-_{\nu}z^{n-\nu}$, $1{\leq}{\mu}{\leq}n$. We also obtain another L^r analogue of a result for the above general class of polynomials proved by Chanam and Dewan [6].

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.323-329
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• 2022

Let $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ be a polynomial of degree n and $p^{\prime}(z)$ its derivative. If $\max\limits_{{\mid}z{\mid}=r}{\mid}p(z){\mid}$ is denoted by M(p, r). If p(z) has all its zeros on |z| = k, k ≤ 1, then it was shown by Govil [3] that $$M(p^{\prime},\;1){\leq}\frac{n}{k^n+k^{n-1}}M(p,\;1)$$. In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

• Korean Journal of Ichthyology
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• v.18 no.4
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• pp.339-346
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• 2006

In this study we conducted artificial hybridization between two sibling species, Rhodeus uyekii and R. notatus, and observed the morphological characteristics in early developmental stage. The two species showed difference in egg shape having rhombus and club respectively. The morphology of yolk of larva just hatched also showed well specific characteristics, that is the bean chaff type for R. uyekii (U type) and anchor type for R. notatus (N type). The rate of fertilization between female R. uyekii and male R. notatus (UN type) and between female R. notatus and male R. uyekii (NU type) were complete and its hatching rate were very high, 71.6% for UN type and 97.5% for NU type. The differences occurred in the yolk shape of hatched larvae for each combination of hybrids. In the group of UN, U type of larvae were found very rarely, but almost all the larvae showed intermediate shape polarized to NN type. Similar phenomenon was observed in the NU having intermediate polarized to UU, but without any NN type. These hybrids will be analyzed for their external morphology, sex ratio, the function of sexual organ and karyology after they grown up to adult.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.809-817
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• 2012

The resonance structure of the preionization spectrum of $H_2$ in the region immediately above its ionization threshold, ($^2{\sum}_{g}^{+}$, $\nu^+=0$, $N^+=0$) converging toward its rotationally excited ($\nu^+=0$, $N^+=2$) limit, is complicated due to perturbation by the vibrationally excited levels $7_{p\pi}\;v=1$ and $57_{p\pi}\;v=2$. The spectra of interlopers are separated from the rotationally preionizing Rydberg series to allow analysis of this complex resonance structure. Although only two vibrationally excited levels perturb the rotational preionization spectrum, at least 6 interloper Rydberg series participate in the complex spectrum over most of its energy range and more interloper series participate at a narrow range around $124500cm^{-1}$ in the spectrum. To allow handling of an arbitrary number of interloper series, MATLAB$^{(R)}$'s symbolic operation is used to perform on-the-fly formulation.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1055-1072
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• 2022

Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F_p,𝜈(a, b; c; z) and Fox-Wright function _rΨ_s(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z).

• Korean Journal of Fisheries and Aquatic Sciences
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• v.30 no.4
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• pp.543-549
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• 1997

The problems in the existing modeling rules for fishing nets, especially in the Tauti's rule which had been used most commonly, were investigated and it was found that the rules could not give a good similarity between the prototype and model nets because they din neither analyze the flow resistance of nets accurately nor decide the ratio of flow velocity between the two nets properly. Thus, the modeling rule was newly derived by regarding the nets as holey structures sucking water into their mouth and then filtering water through their meshes as in the previous paper. The similarity conditions obtained, between the two nets distinguished by subscript 1 and 2, are as follows; $$\frac{d_2}{d_1}=\sqrt{\frac{l_2}{l_1}},\;\frac{N_2}{N_1}=(\frac{d_1}{d_2})^{1.5}\frac{L_2}{L_1},\;\varphi_1=\varphi_2,\;\frac{d_{r2}}{d_{r1}}=\sqrt{\frac{L_2{(\rho_{r1}-\rho_{w1})}}{{L_1{(\rho_{r2}-\rho_{w2})}}$$ $$\frac{N_{a2}}{N_{a1}}=\frac{W_{a1}}{W_{a2}}(\frac{L_2}{L_1})^2,\;\nu_1=\nu_2\;and\;\frac{R_2}{R_1}=(\frac{L_2}{L_1})^2$$, where L is the length of nettings, d the diameter of netting twines, 2l the mesh size, $2\varphi$ the angle between two adjacent bars, N the number of meshes at the sides of nettings, $d_r$, the diameter of ropes, $\rho_r$, the specific gravity of ropes, $W_a$ the weight in water of one piece of float or sinker, $N_a$ the number of floats or sinkers, $\nu$ the flow velocity, and R the flow resistance of net. In the case where the model experiments aim at investigating the influence of weight in water of nettings on their shapes in nets subjected to the water flow of very low velocity, however, the following condition is added; $$\frac{\rho_2-\rho_{w2}}{\rho_1-\rho_{w1}}=\frac{d_1}{d_2}$$ where $\rho$ is the specific gravity of netting twines.

• Korean Journal of Plant Taxonomy
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• v.49 no.4
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• pp.282-293
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• 2019

Broussonetia × kazinoki Siebold has long been utilized as a major component in the manufacturing of Korean traditional paper, hanji, and has been suggested as a hybrid species of B. papyrifera and B. monoica. By applying three molecular markers, chloroplast (cp) ndhF-rpl32 IGS, a nuclear ribosomal internal transcribed spacer, and the TOPO6 gene, the hybrid origin of B. × kazinoki is tested. As a result, B. × kazinoki in Korea is demonstrated to be a hybrid of B. monoica × B. papyrifera, most likely formed naturally in Korea. The cp haplotypes detected provided information about the origins and genetic diversity of the maternal lineage B. monoica and paternal lineage B. papyrifera. The two nuclear markers were supplemented to each other, leading to the discovery of introgression in Broussonetia.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.1138-1149
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• 1988

Experiments have been conducted to investigate mean thermal structure in unstable turbulent thermal convection between two horizontal flat plates. The upper plate was kept at a constant cold temperature and the bottom plate at a constant hot temperature. Both air and water were used as its working fluids. Chamber aspect ratios were 3.80 and 6.17, the mean temperature differences between two plates were 2.6-9.3.deg. C, whose Rayleigh numbers in a range 6.13*10$^{5}$ -1, 07*10$^{8}$ . The heat transfer correlations obtained through the experiments are Nu=0.139R $a^{0.285}$ for air and Nu=0.087 R $a^{0.319}$ for water. Profiles of the mean temperature gradient clearly show the -2 and 1 4/3 power law regions.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.975-979
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• 2012

Structure and Dynamics of dilute two-dimensional (2D) ring polymer solutions are investigated by using discontinuous molecular dynamics simulations. A ring polymer and solvent molecules are modeled as a tangent-hard disc chain and hard discs, respectively. Some of solvent molecules are confined inside the 2D ring polymer unlike in 2D linear polymer solutions or three-dimensional polymer solutions. The structure and the dynamics of the 2D ring polymers change significantly with the number ($N_{in}$) of such solvent molecules inside the 2D ring polymers. The mean-squared radius of gyration ($R^2$) increases with $N_{in}$ and scales as $R{\sim}N^{\nu}$ with the scaling exponent $\nu$ that depends on $N_{in}$. When $N_{in}$ is large enough, ${\nu}{\approx}1$, which is consistent with experiments. Meanwhile, for a small $N_{in}{\approx}0.66$ and the 2D ring polymers show unexpected structure. The diffusion coefficient (D) and the rotational relaxation time ($\tau_{rot}$) are also sensitive to $N_{in}$: D decreases and $\tau$ increases sharply with $N_{in}$. D of 2D ring polymers shows a strong size-dependency, i.e., D ~ ln(L), where L is the simulation cell dimension. But the rotational diffusion and its relaxation time ($\tau_{rot}$) are not-size dependent. More interestingly, the scaling behavior of $\tau_{rot}$ also changes with $N_{in}$; for a large $N_{in}$ $\tau_{rot}{\sim}N^{2.46}$ but for a small $N_{in}$ $\tau_{rot}{\sim}N^{1.43}$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.1
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• pp.132-141
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• 1992

The critical condition for onset of Benard convection with variable viscosity .nu.=.nu.$_{0}$exp(-CT) has been obtained using a linear stability theory. The bottom wall is rigid while the upper surface may be either free or rigid. The two boundaries are subject to convective heat transfer. The critical Rayleigh numbers are presented up to maximum viscosity ratio of 3000. It is greater for smaller upper and/or lower surface Biot numbers. Its dependence on the viscosity ratio is complicated. However, a simple sublayer theory is found to be applicable for extremely large viscosity ratio. In such cases, the critical Rayleigh number and the critical wave number are functions of viscosity ratio and lower surface Biot number.r.