• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).

• Korean Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.20-32
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• 1996

The boundary evaluation technique for Boolean operation on non-manifold models which is regarded as the most popular and powerful method to create and modify 3-D CAD models has been developed. This technique adopted the concept of Merge and Selection in which the CSG tree for Boolean operation can be edited quickly and easily. In this method, the merged set which contains complete information about primitive models involved is created by merging primitives one by one, then the alive entities are selected following the given CSG tree. This technique can support the hybrid representation of B-rep(Boundary Representation) and CSG(Constructive Solid Geometry) tree in a unified non-manifold model data structure, and expected to be used as a basic method for many modeling problems such as data representation of form features, and the interference between them, and data representation of conceptual models in design process, etc.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.2
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• pp.344-354
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• 2009

Side scan sonar using acoustic wave plays a very important role in the underwater, sea floor, and shallow marine geologic survey. In this study, we have acquired side scan sonar data for the underwater man-made structures, artificial reefs and fishing grounds, installed and distributed in the survey area. We applied digital image processing techniques to side scan sonar data in order to improve and enhance an image quality. We carried out digital image processing with various kinds of filtering in spatial domain and frequency domain. We tested filtering parameters such as kernel size, differential operator, and statistical value. We could easily estimate the conditions, distribution and environment of artificial structures through the interpretation of side scan sonar.

• Nuclear Engineering and Technology
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• v.2 no.4
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• pp.249-254
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• 1970

A time-energy transient characteristics of pulsed neutron transport problem with an inelastic kernel in the fast domain is solved exactly with a continuous energy transfer operator. A discrete time eigenvalue is found which is asymptotically dominant. The complete solution consists of three parts: a time-energy separable mode which is asymptotically dominant and a non-separable mode which is made up by two parts； a pure energy slowing-down transient and a mixture of time and energy transient which is negligible asymptotically.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1087-1094
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• 2016

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• Journal of the Korean Chemical Society
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• v.25 no.5
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• pp.291-299
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• 1981

A test particle kinetic theory for reaction dynamics in liquids is presented at the repeated ring collision level for the hard sphere model. A kinetic equation for the equilibrium time correlation function of the reactive test particle phase space density is derived and the rate kernel expression for the reversible chemical reaction of the type A +B ${\rightleftharpoons$ C + D in the presence of inert solvent S is obtained by the projection operator method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.299-304
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• 1996

This paper studies the rational approximation of multiple input delay systems using the Hankel singular values and vectors, which are the soultion of a transcendental equation. Rational approximatants are obtained from output normal realizations which are constructed by the Hankel singular values and vectors. Consequently, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pade approximants.