• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.403-417
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• 2021

This note is devoted to establishing the boundedness for some classes of Littlewood-Paley square operators defined by the kernels without any regularity on the mixed radial-angular spaces. The corresponding vector-valued versions are also presented. As applications, the corresponding results for the Littlewood-Paley g∗λ function and the Littlewood-Paley function related to the area integrals are also obtained.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.719-727
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• 2006

In this paper, we study the boundedness and the com-pactness of weighted composition operator between $H^{\infty}$ and Bergman type space on the unit ball of $\mathbb{C}^n$. Also, the norm of corresponding weighted composition operator is computed.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.331-336
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• 1994

Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.221-267
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• 2019

In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and $^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on ${\mathbb{R}}^d$. By using these operators we define the hypergeometric translation operator ${\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, and its dual $^t{\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, we express them in terms of the hypergeometric Fourier transform ${\mathcal{H}}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform ${\mathcal{H}}^W$. We study also the hypergeometric convolution product on W-invariant $L^p_{\mathcal{A}k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.309-313
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• 2007

By applying ideas from [M. S. Moslehian, et al., Norms of operators in $X_{\lambda}$ spaces, Appl. Math. Lett. (2007), doi:10.1016/j.aml.2006. 11.009], we investigate the norm of the cubic operator on the function space $X_{\lambda}$.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.237-243
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• 2024

A similarity transformation of a solution of the Cauchy problem for the linear difference equation in Hilbert space has been studied. In this manuscript, we obtain necessary and sufficient conditions for linear equivalence of the discrete semigroup of operators, generated by the solution of the difference equation utilizing four Canonical semigroups.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.665-685
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• 2000

The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems ($\Phi$($\upsilon$'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T], $\Phi$: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where $\Phi$(u) is the vector p-Laplacian $\mid$u$\mid$p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.

• Korean Institute of Interior Design Journal
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• v.16 no.5
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• pp.81-88
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• 2007

Energy consumption has been increased world widely, and the energy retain is one of the most important economic alternatives. These tendencies expand the nuclear power plants not only quantitatively but also qualitatively. Despite of the increasing construction of nuclear power plants and related facilities, every system in main control room(MCR) has been designed and administered solely based on the safety-first principles because of the specificity of nuclear industry. However, recent main control rooms started with the concept that the operators' performance could be optimized though the organic interrelation between human, machine, and environments. Now, it has been recognised in the scope of Ergonomics and Space Design which acknowledge our living spaces as Man-Environment Interface and this change connotes the MCR spaces should be special spaces rather than ordinary spaces. This research investigated domestic and foreign nuclear power plants' MCRs to suggest basic alternatives which can be applied to future MCR. With the review of characteristics of MCR, an integration of interior design, lighting and Ergonomics was explored and classified as types. Futhermore, the classification of environmental characteristics within the relationships between human, machine, and environments was developed through the case analysis of nuclear power plants. The results of this study will provide a basis of space design for system environments that the high level of safety and function are extremely important.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.649-659
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• 2015

The space $BV^2_{\alpha}(I)$ of all the real functions defined on interval $I=[a,b]{\subset}\mathbb{R}$, which are of bounded second ${\alpha}$-variation (in the sense De la Vall$\acute{e}$ Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function $h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}$, and prove, in particular, that if H maps $BV^2_{\alpha}(I)$ into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

• Korean Institute of Interior Design Journal
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• v.23 no.4
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• pp.257-266
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• 2014

This study has been performed to come up with any rational way for responding to the functions of fire-fighting spaces newly required by the changing social paradigms and to seek for the approach to designing fire-fighting spaces by taking into account the psychological and behavioral factors of fire-fighters who are exposed stress of operations. In particular, it is to satisfy any physical and functional requirements as special working-spaces and to reflect the psychological and behavioral approach to the workers who are forced to be at standby for a long time, which is the characteristic of their operation, to designing. Accordingly, for fundamental appreciation of whether or not such space programs as space organization needed for operational function are being practiced actively, the fire-fighting headquarters of Incheon City has been selected for the research. First, in the process of assessing the trend of organizing the space at safety centers for the recent 20 years, those built more than 20 years ago were left out from the space selection for the research. Second, those with less than 20 operators also were excluded. Third, among those completed in the same year, only one was selected, which was to avoid overlapping, with the consideration its regional representative nature for applying the safety centers in the jurisdiction of the headquarters equally. The study was performed through the visits to and the actual inspections by surveys at the selected 119 Safety Centers as well as the reviews of literature based on case studies. And for the assessment of significance, surveys and analysis of reliability and factors were carried out. The actual users of Safety Centers were picked as objects for the assessment of significance of space factors at 119 Safety Centers, which revealed that there are five types of dimensions for factor-analyzing standard with which users estimate any significance, which are "Area of Mobilization Preparation and Return" "Area of Standby" "Area of Working Activities" "Area of Employ Welfare" and "Area of Support".