• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.51-60
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• 2014

In this paper, we construct a complex reproducing kernel space for singular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then, we transform the problem into an equivalent operator equation, and give a numerical algorithm to provide the approximate solution. The uniform convergence of this algorithm is proved, and complexity analysis is done. Lastly, we show the validity and feasibility of the numerical algorithm by two numerical examples.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.59-63
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• 2010

In this paper, we introduce the concept of weakly-ultra-${\alpha}{\psi}$-separation of two sets in a topological space using ${\alpha}{\psi}$-open sets. The ${\alpha}{\psi}$-closure and the ${\alpha}{\psi}$-kernel are defined in terms of this weakly ultra-${\alpha}{\psi}$-separation. We also investigate some of the properties of the ${\alpha}{\psi}$-kernel and the ${\alpha}{\psi}$-closure.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.2
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• pp.337-344
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• 2023

Modern OSs, including Linux, show high scalability by adopting a monolithic kernel design, but have weak security because they share all memory space. This study presents a kernel module that are isolated inside the kernel using WebAssembly. WebAssembly provides a high-performance virtual machine by defining a low-level instruction set while guaranteeing memory safety. In this paper, the WebAssembly execution environment is implemented inside the kernel, allowing developers to control the operation of kernel modules and achieving higher security.

• ETRI Journal
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• v.36 no.3
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• pp.333-342
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• 2014

Most hyper-ellipsoidal clustering (HEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that HEC with a modified Gaussian kernel metric can be interpreted as a problem of finding condensed ellipsoidal clusters (with respect to the volumes and densities of the clusters) and propose a practical HEC algorithm that is able to efficiently handle clusters that are ellipsoidal in shape and that are of different size and density. We then try to refine the HEC algorithm by utilizing ellipsoids defined on the kernel feature space to deal with more complex-shaped clusters. The proposed methods lead to a significant improvement in the clustering results over K-means algorithm, fuzzy C-means algorithm, GMM-EM algorithm, and HEC algorithm based on minimum-volume ellipsoids using Mahalanobis distance.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.19-34
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• 2008

A new algorithm for the solution of an inverse problem of determining unknown source parameter in a parabolic equation in reproducing kernel space is considered. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed algorithm.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-483
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• 2001

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

• Journal for History of Mathematics
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• v.12 no.1
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• pp.65-72
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• 1999

In this article, we give a historical referencing overview and compressed illuminating procedure of deriving the repersentors R$_y$(x) in Reproducing Kernel space W$^2_2$(R), being needed to find the solutions of integral equations, which construct the wavelets in L$^2$(1R).

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.471-478
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• 2007

In this article we shall introduce several operators on the reproducing kernel spaces and investigate quadratic forms on the $\mathcal{l}^2$ space. Using these operators we shall obtain a particular solution of a system of quadratic equations(1.5). Finally we can find an approximate solution of(1.5) by optimization of a nonnegative biquadratic polynomial.

• Journal of Radiation Industry
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• v.17 no.3
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• pp.275-282
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• 2023

Workers in nuclear power plants are likely to be exposed to radiation from various geometrical sources. In order to evaluate the exposure level, the point-kernel method can be utilized. In order to perform a dose assessment based on this method, the radiation source should be divided into point sources, and the number of divisions should be set by the evaluator. However, for the general public, there may be difficulties in selecting the appropriate number of divisions and performing an evaluation. Therefore, the purpose of this study is to develop an algorithm for dose assessment for arbitrary shaped sources based on the point-kernel method. For this purpose, the point-kernel method was analyzed and the main factors for the dose assessment were selected. Subsequently, based on the analyzed methodology, a dose assessment algorithm for arbitrary shaped sources was developed. Lastly, the developed algorithm was verified using Microshield. The dose assessment procedure of the developed algorithm consisted of 1) boundary space setting step, 2) source grid division step, 3) the set of point sources generation step, and 4) dose assessment step. In the boundary space setting step, the boundaries of the space occupied by the sources are set. In the grid division step, the boundary space is divided into several grids. In the set of point sources generation step, the coordinates of the point sources are set by considering the proportion of sources occupying each grid. Finally, in the dose assessment step, the results of the dose assessments for each point source are summed up to derive the dose rate. In order to verify the developed algorithm, the exposure scenario was established based on the standard exposure scenario presented by the American National Standards Institute. The results of the evaluation with the developed algorithm and Microshield were compare. The results of the evaluation with the developed algorithm showed a range of 1.99×10^-1~9.74×10^-1 μSv hr^-1, depending on the distance and the error between the results of the developed algorithm and Microshield was about 0.48~6.93%. The error was attributed to the difference in the number of point sources and point source distribution between the developed algorithm and the Microshield. The results of this study can be utilized for external exposure radiation dose assessments based on the point-kernel method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.2B
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• pp.129-137
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• 2003

Multimedia streams, like MPEG continuously retrieve multimedia data because of their incessant playback. While these streams need an efficient support of kernel, the current buffer cache mechanism of Linux kernel such as Unix operating system was designed apt for small files, which is aperiodically requested as well as time uncritical. But, in case of continuous media, the CPU must enormously copy memory from kernel address space to user address space. This must lead to a large CPU overhead. This overhead both degrades system throughput and cannot guarantee QOS. In this paper, we have designed and implemented two memory copy reduction schemes in Linux kernel, direct I/O and one copy. The direct I/O skips the buffer cache layer of Linux kernel and results in dramatic reduction of CPU memory copy overhead. And, the one copy provides a fast disk-to-network data path without copying to user address space. The experimental results show considerable reduction of CPU overhead and throughput improvements.