• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.13-23
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• 2013

In this present work, the authors obtain Fekete-Szeg$\ddot{o}$ inequality for certain normalized analytic function $f(z)$ defined on the open unit disk for which $$\frac{{\lambda}{\beta}z^3(L(a,c)f(z))^{{\prime}{\prime}{\prime}}+(2{\lambda}{\beta}+{\lambda}-{\beta})z^2(L(a,c)f(z))^{{\prime}{\prime}}+z(L(a,c)f(z))^{{\prime}}}{{\lambda}{\beta}z^2(L(a,c)f(z))^{{\prime}{\prime}}+({\lambda}-{\beta})z(L(a,c)f(z))^{\prime}+(1-{\lambda}+{\beta})(L(a,c)f(z))}\;(0{\leq}{\beta}{\leq}{\lambda}{\leq}1)$$ lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szeg$\ddot{o}$ inequality for a class of functions defined through fractional derivatives are obtained.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.291-297
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• 2008

In this paper, new inequalities of Ostrowski type involving two functions and their derivatives for mapping whose derivations belong to $L^p$[a, b], p>1 are established.

• 대한수학회논문집
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• 제33권2호
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• pp.495-505
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• 2018

The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_1(z)f^{(1)}(z)+a_2(z)f^{(2)}(z)+{\cdots}+a_n(z)f^{(n)}(z)$, where the coefficients $a_k(z)(k=1,2,{\ldots},n)$ are rational functions and $a_n(z){\not{\equiv}}0$.

• Wind and Structures
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• 제7권6호
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• pp.421-447
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• 2004

This paper presents a time domain approach for predicting buffeting response of long suspension bridges under skew winds. The buffeting forces on an oblique strip of the bridge deck in the mean wind direction are derived in terms of aerodynamic coefficients measured under skew winds and equivalent fluctuating wind velocities with aerodynamic impulse functions included. The time histories of equivalent fluctuating wind velocities and then buffeting forces along the bridge deck are simulated using the spectral representation method based on the Gaussian distribution assumption. The self-excited forces on an oblique strip of the bridge deck are represented by the convolution integrals involving aerodynamic impulse functions and structural motions. The aerodynamic impulse functions of self-excited forces are derived from experimentally measured flutter derivatives under skew winds using rational function approximations. The governing equation of motion of a long suspension bridge under skew winds is established using the finite element method and solved using the Newmark numerical method. The proposed time domain approach is finally applied to the Tsing Ma suspension bridge in Hong Kong. The computed buffeting responses of the bridge under skew winds during Typhoon Sam are compared with those obtained from the frequency domain approach and the field measurement. The comparisons are found satisfactory for the bridge response in the main span.

• 대한수학회보
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• 제59권1호
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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.

• 대한수학회지
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• 제38권6호
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• Journal of Microbiology and Biotechnology
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• 제33권10호
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• pp.1317-1328
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• 2023

Green tea (GT) polyphenols undergo extensive metabolism within gastrointestinal tract (GIT), where their derivatives compounds potentially modulate the gut microbiome. This biotransformation process involves a cascade of exclusive gut microbial enzymes which chemically modify the GT polyphenols influencing both their bioactivity and bioavailability in host. Herein, we examined the in vitro interactions between 37 different human gut microbiota and the GT polyphenols. UHPLC-LTQ-Orbitrap-MS/MS analysis of the culture broth extracts unravel that genera Adlercreutzia, Eggerthella and Lactiplantibacillus plantarum KACC11451 promoted C-ring opening reaction in GT catechins. In addition, L. plantarum also hydrolyzed catechin galloyl esters to produce gallic acid and pyrogallol, and also converted flavonoid glycosides to their aglycone derivatives. Biotransformation of GT polyphenols into derivative compounds enhanced their antioxidant bioactivities in culture broth extracts. Considering the effects of GT polyphenols on specific growth rates of gut bacteria, we noted that GT polyphenols and their derivate compounds inhibited most species in phylum Actinobacteria, Bacteroides, and Firmicutes except genus Lactobacillus. The present study delineates the likely mechanisms involved in the metabolism and bioavailability of GT polyphenols upon exposure to gut microbiota. Further, widening this workflow to understand the metabolism of various other dietary polyphenols can unravel their biotransformation mechanisms and associated functions in human GIT.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.105-114
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• 2005

In this paper we investigate the growth of finite order solutions of the differential equation $f^{(k)}\;+\;A_{k-1}(Z)f^{(k-l)}\;+\;{\cdots}\;+\;A_1(z)f^{\prime}\;+\;A_0(z)f\;=\;F(z)$, where $A_0(z),\;{\cdots}\;,\;A_{k-1}(Z)\;and\;F(z)\;{\neq}\;0$ are entire functions. We find conditions on the coefficients which will guarantees the existence of an asymptotic value for a transcendental entire solution of finite order and its derivatives. We also estimate the lower bounds of order of solutions if one of the coefficient is dominant in the sense that has larger order than any other coefficients.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.435-449
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• 2020

This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.

• 천문학회지
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• 제37권4호
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• pp.159-169
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• 2004

This is a proposal to probe local part of the interplanetary dust (IPD) cloud complex and retrieve mean volume emissivity of the local IPDs at mid-infrared wavelengths. This will be done by monitoring, with Infrared Camera (IRC) aboard the ASTRO-F, the annual modulation of the zodiacal emission. In pointing mode of the ASTRO-F mission the spacecraft can make attitude maneuvering over approximately ${\pm}1^{\circ}$ range centered at solar elongation $90^{\circ}$ in the ecliptic plane. The attitude maneuvering combined with high sensitivity of the IRC will provide us with a unique opportunity observationally to take derivatives of the zodiacal emission brightness with respect to the solar elongation. From the resulting differential of the brightness over the ${\pm}1^{\circ}$ range, one can directly determine the mean volume emissivity of the local IPDs with a sufficient accuracy to de-modulate the annual emissivity variations due to the Earth's elliptical motion and the dis-alignment of the maximum IPD density plane with respect to the ecliptic. The non-zero eccentricity ($e_{\oplus}$= 0.0167) of the Earth's orbit combined with the sensitive temperature dependence of the Planck function would bring modulations of amplitude at least $3.34\%$ to the zodiacal emission brightness at mid-infrared wavelengths, with which one may determine the IPD temperature T(r) and mean number density n(r) as functions of heliocentric distance r. This will in turn fix the power-law exponent $\delta$ in the relation $T(r) = T_o(r/r_o)^{-\delta}$ for the dust temperature and v in $n(r) = n_o(r/r_o)^-v$ for the density. We discuss how one may de-couple the notorious degeneracy of cross-section, density, reference temperature $T_o$ and exponent $\delta$.