• 대한수학회지
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• 제44권4호
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• pp.809-822
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• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.365-375
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• 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.

• 대한수학회보
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• 제59권3호
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• pp.757-780
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• 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
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• 제8권2호
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• pp.163-172
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• 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 $\mathcal{S}$.

• 충청수학회지
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• 제25권2호
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• pp.267-275
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• 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
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• 제32권1호
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• pp.117-128
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• 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.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2015년도 추계학술대회
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• pp.1121-1124
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• 2015

본 연구에서는 광대역 펄스감마선 탐지센서 최적화설계에 관한 연구를 수행하였다. 펄스감마선 탐지센서는 $1{\times}10^6{\sim}1{\times}10^8rad(Si)/s$의 방사선량에서 동작할 수 있도록 설계하였다. 에너지에 따른 펄스감마선 스펙트럼과 시간에 따른 에너지 비율을 기반으로 탐지센서 입력변수를 도출하고, 탐지감도 제어회로를 기반으로 탐지센서 출력전류를 도출하였다. N-type Epi Wafer를 이용하여 최적조건 탐지센서를 TCAD기반으로 설계하였다. 시뮬레이션 결과 인가전압 3.3V에서 최적 Epi층 두께는 45um다. 도핑농도는 N-type은 Arsenic으로 $1{\times}10^{19}/cm^3$, P-type은 Boron으로 $1{\times}10^{19}/cm^3$, Epi 층은 Phosphorus로 $3.4{\times}10^{12}/cm^3$다. 마지막으로 탐지센서는 원형으로 지름이 1.3mm 이다.

• 대한산업공학회지
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• 제29권2호
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• pp.145-149
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• 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
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• 제18권3호
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• pp.539-544
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• 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.

• 한국대기환경학회지
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• 제30권6호
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• pp.577-585
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• 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: ${\sim}355JL^{-1}$).