• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1125-1140
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• 2018

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1443-1455
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• 2017

Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.743-755
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• 2019

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.13-22
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• 2019

We compute the second cohomology of the affine Lie algebra aff(1) on the dimensional real space with coefficients in the space ${\mathcal{D}}^n_{{\underline{\lambda}},{\mu}}$ of n-ary linear differential operators acting on weighted densities where ${\underline{\lambda}}=({\lambda}_1,{\ldots},{\lambda}_n)$. We explicitly give 2-cocycles spanning these cohomology.

• Structural Engineering and Mechanics
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• v.27 no.6
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• pp.713-739
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• 2007

Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

• Journal of Biomedical Engineering Research
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• v.27 no.5
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• pp.203-209
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• 2006

The aim of this study is to investigate the feasibility of ex vivo MR diffusion tensor imaging technique in order to observe the diffusion-contrast characteristics of human gastric tissues. On normal and pathologic gastric tissues, which have been fixed in a polycarbonate plastic tube filled with 10% formalin solution, laboratory made 3D diffusion tensor Turbo FLASH pulse sequence was used to obtain high resolution MR images with voxel size of $0.5{\times}0.5{\times}0.5mm^3\;using\;64{\times}32{\times}32mm^3$ field of view in conjunction with an acquisition matrix of $128{\times}64{\times}64$. Diffusion weighted- gradient pulses were employed with b values of 0 and $600s/mm^2$ in 6 orientations. The sequence was implemented on a clinical 3.0-T MRI scanner(Siemens, Erlangen, Germany) with a home-made quadrature-typed birdcage Tx/Rx rf coil for small specimen. Diffusion tensor values in each pixel were calculated using linear algebra and singular value decomposition(SVD) algorithm. Apparent diffusion coefficient(ADC) and fractional anisotropy(FA) map were also obtained from diffusion tensor data to compare pixel intensities between normal and abnormal gastric tissues. The processing software was developed by authors using Visual C++(Microsoft, WA, U.S.A.) and mathematical/statistical library of GNUwin32(Free Software Foundation). This study shows that 3D diffusion tensor Turbo FLASH sequence is useful to resolve fine micro-structures of gastric tissue and both ADC and FA values in normal gastric tissue are higher than those in abnormal tissue. Authors expect that this study also represents another possibility of gastric carcinoma detection by visualizing diffusion characteristics of proton spins in the gastric tissues.

• Journal of the Korean Association of Geographic Information Studies
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• v.17 no.4
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• pp.69-85
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• 2014

Carbon stocks of NFI plots can be accurately estimated using field survey information. However, an accurate estimation of carbon stocks in other unsurveyed sites is very difficult. In order to fill this gap, various spatial information can be used as an ancillary data. In South Korea, there is the 1:5,000 forest type map that was produced by digital air-photo interpretation and field survey. Because this map contains very detailed forest information, it can be used as the high-quality spatial data for estimating carbon stocks. In this study, we compared three upscaling methods based on the 1:5,000 forest type map and 5th national forest inventory data. Map algebra(method 1), RK(Regression Kriging)(method 2), and GWR(Geographically Weighted Regression)(method 3) were applied to estimate forest carbon stock in Chungcheong-nam Do and Daejeon metropolitan city. The range of carbon stocks from method 2(1.39~138.80 tonC/ha) and method 3(1.28~149.98 tonC/ha) were more similar to that of previous method(1.56~156.40 tonC/ha) than that of method 1(0.00~93.37 tonC/ha). This result shows that RK and GWR considering spatial autocorrelation can show spatial heterogeneity of carbon stocks. We carried out paired t-test for carbon stock data using 186 sample points to assess estimation accuracy. As a result, the average carbon stocks of method 2 and field survey method were not significantly different at p=0.05 using paired t-test. And the result of method 2 showed the lowest RMSE. Therefore regression kriging method is useful to consider spatial variations of carbon stocks distribution in rugged terrain and complex forest stand.