• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.809-822
• /
• 2007

Certain weak type endpoint estimates are established for maximal commutators generated by $Calder\acute{o}n-Zygmund$ operators and $Osc_{exp}L^{\gamma}({\mu})$ functions for ${\gamma}{\ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calder\acute{o}n-Zygmund$ operators only satisfy the standard size condition and some $H\ddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{\gamma}({\mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{\gamma}({\mu})$ = RBMO(${\mu}$) if ${\gamma}$ = 1 and $Osc_{exp}L^{\gamma}({\mu}){\subset}RBMO({\mu})$ if ${\gamma}$ > 1.

• The Pure and Applied Mathematics
• /
• v.15 no.4
• /
• pp.365-375
• /
• 2008

We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.757-780
• /
• 2022

In this article, we study the weak and extra-weak type integral inequalities for the modified integral Hardy operators. We provide suitable conditions on the weights ω, ρ, φ and ψ to hold the following weak type modular inequality $${\mathcal{U}}^{-1}\({\int_{{\mid}{\mathcal{I}}f{\mid}>{\gamma}}}\;{\mathcal{U}}({\gamma}{\omega}){\rho}\){\leq}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}(C{\mid}f{\mid}{\phi}){\psi}\),$$ where ${\mathcal{I}}$ is the modified integral Hardy operators. We also obtain a necesary and sufficient condition for the following extra-weak type integral inequality $${\omega}\(\{{\left|{\mathcal{I}}f\right|}>{\gamma}\}\){\leq}{\mathcal{U}}{\circ}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}\(\frac{C{\mid}f{\mid}{\phi}}{{\gamma}}\){\psi}\).$$ Further, we discuss the above two inequalities for the conjugate of the modified integral Hardy operators. It will extend the existing results for the Hardy operator and its integral version.

• Korean Journal of Mathematics
• /
• v.8 no.2
• /
• pp.163-172
• /
• 2000

Let $\mathcal{S}^{\prime}(\mathbb{R})$ be the dual of the Schwartz spaces $\mathcal{S}(\mathbb{R})$), A be a self-adjoint operator in $L^2(\mathbb{R})$ and ${\Gamma}(A)^*$ be the adjoint operator of ${\Gamma}(A)$ which is the second quantization operator of A. It is proven that under a suitable condition on A there exists a nuclear subspace $\mathcal{S}$ of a fundamental space $\mathcal{S}_A$ of Hida's type on $\mathcal{S}^{\prime}(\mathbb{R})$) such that ${\Gamma}(A)\mathcal{S}{\subset}\mathcal{S}$ and $e^{-t{\Gamma}(A)}\mathcal{S}{\subset}\mathcal{S}$, which enables us to show that a stochastic differential equation: $$dX(t)=dW(t)-{\Gamma}(A)^*X(t)dt$$, arising from the central limit theorem for spatially extended neurons has an unique solution on the dual space $\mathcal{S}^{\prime}$ of $\mathcal{S}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.2
• /
• pp.267-275
• /
• 2012

We present new results for the local convergence of Newton's method to a unique solution of an equation in a Banach space setting. Under a flexible gamma-type condition [12], [13], we extend the applicability of Newton's method by enlarging the radius and decreasing the ratio of convergence. The results can compare favorably to other ones using Newton-Kantorovich and Lipschitz conditions [3]-[7], [9]-[13]. Numerical examples are also provided.

• East Asian mathematical journal
• /
• v.32 no.1
• /
• pp.117-128
• /
• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2015.10a
• /
• pp.1121-1124
• /
• 2015

In this paper, we propose and demonstrate an optimal design of wideband pulsed gamma-ray detectors. Pulsed gamma-ray detectors are designed to operate in a dose rate of $1{\times}10^6{\sim}1{\times}10^8rad(Si)/s$. The input parameter was derived based on the energy ratio of pulse gamma-ray spectrum and the time of the energy. The sensor output current was calculated based on the dose rate control circuit. Using the N-type Epi Wafer, the optimum condition detection sensor was designed based on TCAD. The simulation results show that the optimal Epi layer thickness is 45um when applied voltage 3.3V. The doping concentrations are as follows : N-type is an Arsenic as $1{\times}10^{19}/cm^3$, P-type is a Boron as $1{\times}10^{19}/cm^3$ and Epi layer is Phosphorus as $3.4{\times}10^{12}/cm^3$. Pulse gamma-ray detector diameter is the 1.3mm.

• Journal of Korean Institute of Industrial Engineers
• /
• v.29 no.2
• /
• pp.145-149
• /
• 2003

We consider the estimation of failure rate and acceleration factor under type-I censoring without using acceleration model when testing is conducted in only one highly accelerated condition. Failure times of an item are assumed to be exponentially distributed. It is also assumed that the uncertainty about the acceleration factor, the failure time contraction ratio between accelerated condition and use condition, can be modeled by the uniform or gamma prior distribution of appropriate parameters. We respectively use Bayes and maximum likelihood approaches to estimate acceleration factor and failure rate in the use condition. An example is given to show how the method can be applied.

• Journal of Microbiology and Biotechnology
• /
• v.18 no.3
• /
• pp.539-544
• /
• 2008

A mutant of Arthrospira platensis PCC 9108, strain M9108, obtained by mutagenesis with UV treatment, was able to mixotrophically grow in an SOT medium containing 40 g of glucose/l. The biomass and specific growth rate of strain M9108 (4.10 g/l and 0.70/d) were 1.9-fold and 1.4-fold higher, respectively, than those of the wild type (2.21 g/l and 0.58/d) under mixotrophic culture condition. In addition, when compared with the wild type, the content of ${\gamma}$-linolenic acid (GLA) in the mutant was increased when glucose concentration was increased. Compared with the wild type, the GLA content of the mutant was 2-fold higher in autotrophic culture and about 3-fold higher in mixotrophic culture. Thus, the mutant appears to possess more efficient facility to assimilate and metabolize glucose and to produce more GLA than its wild-type strain.

• Journal of Korean Society for Atmospheric Environment
• /
• v.30 no.6
• /
• pp.577-585
• /
• 2014

A series of experiments using atmospheric-pressure non-thermal plasma coupled with transition metal catalysts were performed to remove ethylene from agricultural storage facilities. The non-thermal plasma was created by dielectric barrier discharge, which was in direct contact with the catalyst pellets. The transition metals such as Ag and $V_2O_5$ were supported on ${\gamma}-Al_2O_3$. The effect of catalyst type, specific input energy (SIE) and oxygen content on the removal of ethylene was examined to understand the behavior of the hybrid plasma-catalytic reactor system. With the other parameters kept constant, the plasma-catalytic activity for the removal of ethylene was in order of $V_2O_5/{\gamma}-Al_2O_3$ > $Ag/{\gamma}-Al_2O_3$ > ${\gamma}-Al_2O_3$ from high to low. Interestingly, the rate of plasma-catalytic ozone generation was in order of $V_2O_5/{\gamma}-Al_2O_3$ > ${\gamma}-Al_2O_3$ > $Ag/{\gamma}-Al_2O_3$, implying that the catalyst activation mechanisms by plasma are different for different catalysts. The results obtained by varying the oxygen content indicated that nitrogen-derived reactive species dominated the removal of ethylene under oxygen-lean condition, while ozone and oxygen atoms were mainly involved in the removal under oxygen-rich condition. When the plasma was coupled with $V_2O_5/{\gamma}-Al_2O_3$, nearly complete removal of ethylene was achieved at oxygen contents higher than 5% by volume (inlet ethylene: 250 ppm; gas flow rate: $1.0Lmin^{-1}$; SIE: ${\sim}355JL^{-1}$).