• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.4
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• pp.33-43
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• 2001

This paper presents a secure Linux OS in which multi-level security functions are implemented at the kernel level. Current security efforts such as firewall or intrusion detection system provided in application-space without security features of the secure OS suffer from many vulnerabilities. However the development of the secure OS in Korea lies in just an initial state, and NSA has implemented a prototype of the secure Linux but published just some parts of the technologies. Thus our commercialized secure Linux OS with multi-level security kernel functions meets the minimum requirements for TCSEC B1 level as well kernel-mode encryption, real-time audit trail with DB, and restricted use of root privileges.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.36 no.5
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• pp.335-341
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• 2018

The KDE (Kernel Density Estimation) technique in GIS (Geographic Information System) has been widely used as a method for determining whether a phenomenon occurring in space forms clusters. Most human-generated events such as traffic accidents and retail stores are distributed according to a road network. Even if events on forward and rear roads have short Euclidean distances, network distances may increase and the correlation between them may be low. Therefore, the NKDE (Network-based KDE) technique has been proposed and applied to the urban space where a road network has been developed. KDE is being studied in the field of business GIS, but there is a limit to the microscopic analysis of economic activity along a road. In this study, the NKDE technique is applied to the analysis of urban phenomena such as the density of shops rather than traffic accidents that occur on roads. The results of the NKDE technique are also compared to pedestrian networks and road centerline networks. The results show that applying NKDE to microscopic trade area analysis can yield relatively accurate results. In addition, it was found that pedestrian network data that can consider the movement of actual pedestrians are necessary for accurate trade area analysis using NKDE.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1119-1129
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• 2022

We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.939-947
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• 2012

In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.275-284
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• 2005

In the present paper we shall introduce several operators on the reproducing kernel spaces. And using them we shall find a solution of an infinite system of quadratic equations (1.1). In particular we shall convert problem for finding an approximate solution of infinite system of quadratic equations into problem for minimizing nonnegative biquadratic polynomial.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.733-745
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• 2007

We prove the $L^p(1 boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega{\in}L(log^+L)^{1/2}(S^{n-1})$. The result is an improvement and extension of some known results.

• Journal of Biomedical Engineering Research
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• v.11 no.1
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• pp.89-96
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• 1990

The numerical evaluation of Rayleigh's integral for the sound source reconstruction can be speeded up by the use of angular frequency propagation method and the FFT. However, are several source of errors involved during the reconstruction. Besides the aliasing error due to undersampling in space, the wrap around error. which is caused by undersampling the kernel functionin frequency domain, and windowing effect are present. We found that there is no replicated source problem and the windowing effect is due to the windowing the kernel function In frequency domain, and, xero padding is always required to improve the quality of reconstruction.

• The Korean Journal of Applied Statistics
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• v.33 no.5
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• pp.569-578
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• 2020

By estimating conditional quantile functions of the response, quantile regression (QR) can provide comprehensive information of the relationship between the response and the predictors. In addition, kernel quantile regression (KQR) estimates a nonlinear conditional quantile function in reproducing kernel Hilbert spaces generated by a positive definite kernel function. However, it is infeasible to use the KQR in analysing a massive data due to the limitations of computer primary memory. We propose a divide and conquer based KQR (DC-KQR) method to overcome such a limitation. The proposed DC-KQR divides the entire data into a few subsets, then applies the KQR onto each subsets and derives a final estimator by aggregating all results from subsets. Simulation studies are presented to demonstrate the satisfactory performance of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.387-396
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• 2005

In the setting of the half-plane of the complex plane, we introduce a modified reproducing kernel and we show that for $r>-1/2,\;B^{1,r}-cancellation$ property holds and the Bloch space is the dual space of $B^{1,r}$.