• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.57-66
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• 2009

In this paper, we characterize the boundedness and compactness of the extended $Ces{\grave{a}}ro$ operators from general function spaces F(p, q, s) to Bloch-type spaces ${\mathcal{B}}_{\mu}$ where $\mu$ is normal function on [0,1).

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.141-151
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• 2002

Let X and Y be real Banach spaces and $\varepsilon$, p $\geq$ 0. A mapping T between X and Y is called an ($\varepsilon$, p)-isometry if ｜∥T(x)-T(y)∥-∥x-y∥｜$\leq$ $\varepsilon$∥x-y∥$^{p}$ for x, y$\in$X. Let H be a real Hilbert space and T : H longrightarrow H an ($\varepsilon$, p)-isometry with T(0) = 0. If p$\neq$1 is a nonnegative number, then there exists a unique isometry I : H longrightarrow H such that ∥T(x)-I(y)∥$\leq$ C($\varepsilon$)(∥x∥$^{ 1+p)/2}$+∥x∥$^{p}$ ) for all x$\in$H, where C($\varepsilon$) longrightarrow 0 as $\varepsilon$ longrightarrow 0.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.589-597
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• 1999

Let G be a closed subspace of a Banach space X and let (S,$\Omega$,$\mu$) be a $\sigma$-finite measure space. It was known that $L_1$(S,G) is proximinal in $L_1$(S,X) if and only if $L_p$(S,G) is proximinal in $L_p$(S,X) for 1$\infty$. In this article we show that this result remains true when "proximinal" is replaced by "Chebyshev". In addition, it is shown that if G is a proximinal subspace of X such that either G or the kernel of the metric projection $P_G$ is separable then, for 0 < p $\leq$ $\infty$. $L_p$(S,G) is proximinal in $L_p$(S,X)

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.259-262
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• 2003

A efficient P2P (peer to peer) networking for sharing multimedia contents is proposed to overcome the limitations of unstructured approaches. The proposed approach is attempting to organize the participating P2P nodes by modifying a n-dimensional cartesian-coordinate space DHT (distributed hash table), CAN (content addressable network). The network identifiers (e.g., network prefix of IP address) of participating nodes are mapped into the CAN virtual coordinate space (in 2-d) and nodes with similar identifiers are grouped into the same zone. The proposed scheme is expected to show some level of concentration reflecting the network identifiers. Network simulator-based evaluation is performed to verify the effectiveness of the proposed scheme.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.2
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• pp.93-97
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• 1990

Interfacil charge approximations and structures at doped semiconductor interfaces were proposed. Rectifying phenomena at the III-V compound semiconductor (p-GaP, p-InP, n-GaAs)/$CsNO_3$ aqueous electrolyte interfaces were qualitatively analyzed in terms of their cyclic current-voltage characteristics. The current-voltage characteristic curves, the ion adsorption and potential barrier processes at the semiconductor interfaces were verified using continuous cyclic voltammetric methods. The pn or np junction structures and the related rectifying types at the doped semi-condudtor-electrolyte inferfaces are determined by the space charges.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.271-287
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• 2022

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d^*) satisfying the following ξ-weakly expansive condition: d^*(𝒫c, 𝒫d) ≥ d^* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.959-968
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• 2024

Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = sup_z∈ⅅ(1 - |z|²)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where f_r(z) = f(rz) and ||·||ʙ_q is the Besov seminorm given by ║f║ʙ_q = (∫_𝔻 |f'(z)|^q(1-|z|²)^q-2dA(z)). These results improve previous results of Clunie and MacGregor.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.133-147
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• 2001

In this paper, we introduce the concepts of multiple $L_p$ analytic Fourier-Feynman transform ($1{\leq}p$ < ${\infty})$ and a convolution product of functionals on abstract Wiener space and verify the existence of the multiple $L_p$ analytic Fourier-Feynman transform for functionls in the Fresnel class. Moreover, we verify that the Fresnel class is closed under the $L_p$ analytic Fourier-Feynman transformation and the convolution product, respectively. And we establish some relationships among the multiple $L_p$ analytic Fourier-Feynman transform and the convolution product on the Fresnel class.

• Korean Journal of Optics and Photonics
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• v.2 no.2
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• pp.83-88
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• 1991

Studies on space-invariant pattern recognition have been carried out from various approaches. Pattern recognition system using SDF filter, from weighted linear summation of tranining images, has been the focus of research since its first appearence. In this thesis, off-axis pSDF spatial matched filter has been constructed by combining angular multiplexing of off-axis reference plane wave with pSDF filter made from pseudo-inverse algorithm, and transformed to phase only filter. From observation of the correlation responses in the correlation plane, it is shown that proposed off-axis pSDF spatial matched filter is available to pattern classification and can be used for optical correlator.

• Korean Journal of Crystallography
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• v.15 no.1
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• pp.9-17
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• 2004

There are 25 space groups in the trigonal system. Eighteen out of them have a lattice letter P displaying only hexagonal axes, wherease the remaining seven rhombohedral space groups R3(146), $R\={3}$(148), R32(155), R3m(160), R3c(161), $R\={3}m$(166) and $R\={3}c$(167) are described with two corrdinate systems, first with hexagonal axes having three lattice points (0, 0, 0), (2/3, 1/3, 1/3), (1/3, 2/3, 2/3) and second with primitive rhombohedral axes. In this paper, the space group $R\={3}c$ is discussed and the crystal structure of a compound, tris(1,2,3,4-tetraphenylbuta-1,3-dienyl)cyclotriphosphazene, $C_{84}H_{60}N_3P_3$, belonging to the space group $R\={3}c$ is elucidated with both hexagonal and rhombohedral cells.