• 대한수학회지
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• 제33권3호
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• pp.481-494
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• 1996

We introduced the generalized Sobolev space $H_\omega^s$ in [4]. In this paper, we introduce the space $H_\omega^s(\Omega)$ of the generalized distributions in $H_\omega^s$ with compact supports in $\Omega$ and the local generalized Sobolev spaces $H_{\omega loc}^s(\Omega)$ of the generalized distributions on $\Omega$ which are locally in $H_\omega^s$ and study their properties.

• Current Optics and Photonics
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• 제3권3호
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• pp.243-247
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• 2019

We have developed a compact, wavelength-selectable, Q-switched Nd:YAG laser at mid ultraviolet for chemical warfare agent detection. The fundamental wave at 1064 nm is delivered by a pulsed solid state laser incorporating with a square-type Nd:YAG rod in a resonator closed by two crossed Porro prisms for environmental reliability. The output energy at 213 nm ($5{\omega}$) and 266 nm ($4{\omega}$) by ${\chi}^{(2)}$ process in the sequentially disposed BBO crystals are measured to be 6.8 mJ and 15.1 mJ, respectively. The output wavelength is selected for $5{\omega}$ and $4{\omega}$ by a motorized wavelength switch. The energy ratio of the $5{\omega}$ to the $4{\omega}$ is varied from 0.05 to 0.85 by controlling the phase matching temperature of the nonlinear crystal for sum-frequency generation without change of the output pulse parameters.

• 대한수학회지
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• 제47권5호
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• pp.899-924
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• 2010

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

• 대한수학회논문집
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• 제22권1호
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.15-25
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• 2024

In this paper, we obtain common fixed point theorems for three mappings of contractive type in the setting of generalized modular metric spaces. Our results generalize many results available in the literature including common fixed point theorems.

• 충청수학회지
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• 제24권3호
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• pp.503-515
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• 2011

Let G be a compact connected semisimple Lie group, B the Killing form of the algebra g of G, and g the invariant metric induced by B. Then, we obtain a necessary and sufficient condition for a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) to be projectively flat (resp. Einstein-Weyl). And, we also get that if a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) which has symmetric Ricci tensor $Ric^D$ is projectively flat, then the connection D is Einstein-Weyl; but the converse is not true. Moreover, we show that if a left invariant connection D with Weyl structure ($D,\;g,\;{\omega}$) on (G, g) is projectively flat (resp. Einstein-Weyl), then D is a Yang-Mills connection.

• 충청수학회지
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• 제33권2호
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• 대한수학회보
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• 제55권4호
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• pp.1137-1147
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• 2018

In this paper, we discovered a sufficient condition ensuring the weighted composition operators $C_{{\omega}_1,{\varphi}_1},{\cdots},C_{{\omega}_N,{\varphi}_N}$ were disjoint supercyclic on $H({\Omega})$ endowed with the compact open topology. Besides, we provided a condition on inducing symbols to guarantee the disjoint supercyclicity of non-constant adjoint multipliers $M^*_{{\varphi}_1},M^*_{{\varphi}_2},{\cdots},M^*_{{\varphi}_N}$ on a Hilbert space ${\mathcal{H}}$.

• 충청수학회지
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• 제27권3호
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• pp.523-530
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• 2014

In this article, we deal with the notion of ­${\Omega}$-limit sets in dynamical systems. We show that the ${\Omega}$­-limit set of a compact subset of a phase space is quasi-attracting.

• 대한수학회보
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• 제35권1호
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• pp.91-97
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• 1998

In this paper we study the Weyl spectrum of weight $\alpha, \omega_\alpha(T)$, of an operator T acting on an infinite dimensional Hilbert space. Main results are as follows. Firstly, we show that the Weyll spectrum of weight $\alpha$ of a polynomially $\alpha$-compact operator is finite, and that similarity preserves polynomial $\alpha$-compactness and the $\alpha$-Weyl's theorem both. Secondly, we give a sufficient condition for an operator to be the sum of an unitary and a $\alpha$-compact operators.