• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.289-305
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• 2014

In this paper we propose a new approach to the variable selection problem for a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method does not depend on the sample size and also takes into account the shape of the unknown function.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.777-786
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• 2014

We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.75-84
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• 2002

Using good properties of an optimal normal basis of type I in a finite field ${\mathbb{F}}_{2^m}$, we present a design of a bit serial multiplier of Berlekamp type, which is very effective in computing $xy^2$. It is shown that our multiplier does not need a basis conversion process and a squaring operation is a simple permutation in our basis. Therefore our multiplier provides a fast and an efficient hardware architecture for a bit serial multiplication of two elements in ${\mathbb{F}}_{2^m}$.

• Journal of the Korean Chemical Society
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• v.57 no.2
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• pp.172-175
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• 2013

We compare the relative usefulness of common basis functions and numerical integration methods in representing complex resonance state encountered in the molecular scattering problem of aluminum dimer electronic predissociation. Specifically, the basis set size and computing CPU times are monitored in order to find the minimum requirement for ensuring the modest accuracy of calculated resonance energies (0.1 $cm^{-1}$) for more than 100 resonance states. The combination of the so-called one-dimensional box eigenfunctions and energy-dependent boundary functions are found to be most efficient if integration is done using the basis set quadrature rules.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.553-561
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• 2007

In this paper we propose the concept of fuzzy basis of fuzzy submachine, which is the generalized form of crisp basis of submachine, and we extend the system of generators and free subset to fuzzy forms, from which we prove that minimal system of fuzzy generators, maximally free fuzzy subset, and fuzzy basis are equivalent forms.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.6
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• pp.391-398
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• 2023

In this paper, a penalized maximum likelihood estimation (PMLE) method that applies a penalty to increase the accuracy of a basis-screening-based Kriging model (BSKM) is introduced. The maximum order and set of basis functions used in the BSKM are determined according to their importance. In this regard, the cross-validation error (CVE) for the basis functions is employed as an indicator of importance. When constructing the Kriging model (KM), the maximum order of basis functions is determined, the importance of each basis function is evaluated according to the corresponding maximum order, and finally the optimal set of basis functions is determined. This optimal set is created by adding basis functions one by one in order of importance until the CVE of the KM is minimized. In this process, the KM must be generated repeatedly. Simultaneously, hyper-parameters representing correlations between datasets must be calculated through the maximum likelihood evaluation method. Given that the optimal set of basis functions depends on such hyper-parameters, it has a significant impact on the accuracy of the KM. The PMLE method is applied to accurately calculate hyper-parameters. It was confirmed that the accuracy of a BSKM can be improved by applying it to Branin-Hoo problem.

• Proceedings of the Korea Contents Association Conference
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• 2007.11a
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• pp.209-211
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• 2007

The computational time of Stocahstic Diagonalization (SD) calculation for 2-dimensional interacting fermion systems is reduced by using several methods including symmetry operations. First, each lattice is subdivided into spin-up and spin-down lattices separately, thus allowing a bi-partite lattice. A valid basis state is then obtained from stacking up an up-spin configuration on top of a down-spin configuration. As a consequence, the memory space to be used in saving the trial basis state reduces significantly. Secondly, the matrix elements of a Hamiltonianin are reconrded in a look-up table when making basis state set. Thus the repeated calculation of the matrix elements of the Hamiltonian are avoided during SD process. Thirdly, by applying symmetry operations to the basis state set the original basis state is transformed to a new basis state whose elements are the eigenvectors of the symmetry operations. The ground state wavefunction is constructed from the elements of symmetric - bonding state - basis state set. As a result, the total number of basis states involved in SD calculation is reduced upto 50 percentage by using symmetry operations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.20 no.5
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• pp.11-22
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• 2010

Recently, Fan and Dai introduced a Shifted Polynomial Basis and construct a non-pipeline bit-parallel multiplier for $F_{2^n}$. As the name implies, the SPB is obtained by multiplying the polynomial basis 1, ${\alpha}$, ${\cdots}$, ${\alpha}^{n-1}$ by ${\alpha}^{-\upsilon}$. Therefore, it is easy to transform the elements PB and SPB representations. After, based on the Modified Shifted Polynomial Basis(MSPB), SPB bit-parallel Mastrovito type I and type II multipliers for all irreducible trinomials are presented. In this paper, we present a bit-parallel architecture to multiply in SPB. This multiplier have a space complexity efficient than all previously presented architecture when n ${\neq}$ 2k. The proposed multiplier has more efficient space complexity than the best-result when 1 ${\leq}$ k ${\leq}$ (n+1)/3. Also, when (n+2)/3 ${\leq}$ k < n/2 the proposed multiplier has more efficient space complexity than the best-result except for some cases.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.385-394
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• 2007

An upper bound of the basis number of the semi-strong product of cycles with bipartite graphs is given. Also, an example is presented where the bound is achieved.