• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.877-888
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• 1998

We show that if dialation operator $\parallel\sigma_r\parallel\; E=\Psi(r)$ of E, then $\Lambda_\subset_{\Psi1}E\subset\;M_\Psi$, We also show that there are lattice-isomorphic copies of $l_\rho \; and \;l_\infty$ in $M \Psi$ under some condition.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.579-591
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• 2006

In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for $f(z)\;=\;{\sum}^{\infty}_{k=1}\;P_{nk}(z)$ (the homogeneous polynomial expansion of f) satisfying $n_{k+1}/n_{k}{\ge}{\lambda}>1$ for all $k\;{\in}\;N$, to belong to the weighted Bergman space $$A^p_{\alpha}(B)\;=\;\{f{\mid}{\int}_{B}{\mid}f(z){\mid}^{p}(1-{\mid}z{\mid}^2)^{\alpha}dV(z) < {\infty},\;f{\in}H(B)\}$$. We find a growth estimate for the integral mean $$\({\int}_{{\partial}B}{\mid}f(r{\zeta}){\mid}^pd{\sigma}({\zeta})\)^{1/p}$$, and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space $H_{p,q,{\alpha}$(B) and weighted Bergman space on polydisc $A^p_{^{\to}_{\alpha}}(U^n)$ are also given.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.43-51
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• 2018

The manifold $^{\ast}g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to derive a new set of powerful recurrence relations and to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 5-dimensional $^{\ast}g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the second class.

• Journal of the Korean Magnetic Resonance Society
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• v.6 no.2
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• pp.103-112
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• 2002

The photoproduced cation radical of N-methylphenothiazine $(PC_1)$ doped into phenyltriehtoxysilane (PhiTEOS), vinyltriethoxysilane (VTEOS) and methyltriethoxysilane (METOS) was studied with electron spin resonance (ESR) and electron nuclear double resonance (ENDOR). The photoinduced charge separation efficiency was determined by integration of ESR spectra which correspond to the amount of photoproduced cation radical in the matrices. This was correlatively studied with the polarity and pore size of the gel matrices. The relative polarity of the matrices was determined by measuring ${\lambda}_{max}$ values of $PC_1$ in the different matrices. The relative pore size among the matrices was determined by measuring relative proton matrix ENDOR line widths of the photoproduced cation of $PC_1$. The decay kinetic constants of the cation radical of $PC_1$ in the different matrices with relatively studied with fitting the biexponential decay curves after exposure at the ambient condition. This is correlatively interpreted with the polarity and pore size of the matrices.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.173-180
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• 2000

Let $k$ be a real abelian field such that the conductor of every nontrivial character belonging to $k$ agrees with the conductor of $k$. Note that real quadratic fields satisfy this condition. For a prime $p$, let $k_{\infty}$ be the $\mathbb{Z}_p$-extension of $k$. The aim of this paper is to produce a set of generators of the Tate cohomology group $\hat{H}^{-1}$ of the circular units of $k_n$, the $nth$ layer of the $\mathbb{Z}_p$-extension of $k$, where $p$ is an odd prime. This result generalizes some earlier works which treated the case when $k$ is real quadratic field and used them to study ${\lambda}$-invariants of $k$.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.28 no.2
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• pp.194-201
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• 1995

In order to make clear the resistance of bag nets, the resistance R of bag nets with wall area S designed in pyramid shape was measured in a circulating water tank with control of flow velocity v and the coefficient k in $R=kSv^2$ was investigated. The coefficient k showed no change In the nets designed in regular pyramid shape when their mouths were attached alternately to the circular and square frames, because their shape in water became a circular cone in the circular frame and equal to the cone with the exception of the vicinity of frame in the square one. On the other hand, a net designed in right pyramid shape and then attached to a rectangular frame showed an elliptic cone with the exception of the vicinity of frame in water, but produced no significant difference in value of k in comparison with that making a circular cone in water. In the nets making a circular cone in water, k was higher in nets with larger d/l, ratio of diameter d to length I of bars, and decreased as the ratio S/S_m$ of S to the area $S_m$ of net mouth was increased or as the attack angle 9 of net to the water flow was decreased. But the value of ks15m was almost constant in the region of S/S_m=1-4$ or $\theta=15-90^{\circ}$ and in creased linearly in S/S_m>4 or in $\theta<15^{\circ}$ However, these variation of k could be summarized by the equation obtained in the previous paper. That is, the coefficient $k(kg\;\cdot\;sec^2/m^4)$ of bag nets was expressed as $$k=160R_e\;^{-01}(\frac{S_n}{S_m})^{1.2}\;(\frac{S_m}{S})^{1.6}$$ for the condition of $R_e<100$ and $$k=100(\frac{S_n}{S_m})^{1.2}\;(\frac{S_m}{S})^{1.6}$$ for $R_e\geq100$, where $S_n$ is their total area projected to the plane perpendicular to the water flow and $R_e$ the Reynolds' number on which the representative size was taken by the value of $\lambda$ defined as $$\lambda={\frac{\pi d^2}{21\;sin\;2\varphi}$$ where If is the angle between two adjacent bars, d the diameter of bars, and 21 the mesh size. Conclusively, it is clarified that the coefficient k obtained in the previous paper agrees with the experimental results for bag nets.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.08a
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• pp.130.1-130.1
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• 2013

We made attempts to improve photocatalytic activity of $TiO_2$ nanoparticles under visible light exposure by combining two additional treatments. N-doping of $TiO_2$ by ammonia gas treatment at $600^{\circ}C$ increased absorbance of visible light. By coating thin film of polydimethylsiloxane (PDMS), and subsequent vacuum-annealing at $800^{\circ}C$, $TiO_2$, became more hydrophilic, thereby enhancing photocatalytic activity of $TiO_2$. Four types of $TiO_2$ samples were prepared, bare-$TiO_2$, hydrophilic-modified $TiO_2$ ($h-PDMS/TiO_2$), N-doped $TiO_2$ ($N/TiO_2$) and hydrophilic-modified and N-doped $TiO_2$ ($h-PDMS/N/TiO_2$). Adsorption capability was evaluated under dark condition and photocatalytic activity of $TiO_2$ was evaluated by photodegradation of MB under blue LED (400 nm< ${\lambda}$) irradiation. N-doping on $TiO_2$ was characterized using XPS and hydrophilic modification of $TiO_2$ surface was analyzed by FT-IR spectrometer. It was found that N-doping and hydrophilic modification both had positive effect on enhancing adsorption capability and photocatalytic activity of $TiO_2$ at the same time. Particularly, N-doping enhanced visible light absorption of $TiO_2$, whereas hydrophilic surface modification increased MB adsorption capacity. By combining these two strategies, photocatalytic acitivity under visible light irradiation became the sum of individual effects of N-doping and hydrophilic modification.

• Applied Chemistry for Engineering
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• v.23 no.5
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• pp.462-466
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• 2012

$\beta$-cyclodextrin ($\beta$-CD) polymers were prepared in a strong alkali condition solution (NaOH solution 30% (w/v)) using epichlorohydrin (EPI) as a cross-linker, and the molar ratio of EPI to $\beta$-CD was 10 : 1. The $\beta$-CD content in $\beta$-CD polymers is about 52%. In order to get the photo-responsible and pH-responsible, cinnamic acid was added to be inserted into the cavities of $\beta$-CD due to the hydrophobic interaction. The complex formation was confirmed using transmission electron microscope. The dimerization degree of complexes increased under UV irradiation at $\lambda$ = 365 nm but decreased under the UV irradiation at $\lambda$ = 254 nm. Dynamic light scattering analysis of particle sizes showed that the sizes of complexes did not change with different UV wavelength. Moreover, the complexes were pH-responsible because of the carboxyl group of cinnamic acid, but the size and zeta potential of the complex did not change in strong acid and alkali conditions.

• 한국생물공학회:학술대회논문집
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• 2000.11a
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• pp.575-578
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• 2000

The N-acetylneuraminate lyase(NALase) from Escherichia coli was cloned and it was compared to that from Haemophilus influenzae and Clostridium perfringens. NALase from E. coli was expressed in very high level(about 6U/mg). The ManNAc Km value of three enzymes was almost the same. Pyruvate inhibited from H. influenzae was inhibited by GlcNAc in lower level than the others. The crude extract has about 30 times more activity than the cell for the substrate and product diffusion limit problem. The pH stability of three enzymes at pH 11 was also checked for its importance in the direct synthesis of Neu5Ac from GlcNAc and pyruvate at high alkaline condition.