• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권3호
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• pp.133-137
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• 2008

We prove an extended version of asymptotic behavior of the orthonormal cardinal refinable functions from Blaschke products introduced by Contronei et al [2]. In fact, we show the orthonormal cardinal refinable function ${\varphi}_{k,q}$ converges in $L^p(\mathbb{R})$ ($2{\leq}p{\leq}{\infty}$) to the Shannon refinable function as ${\kappa}{\rightarrow}{\infty}$ uniforml on a class $\mathcal{Q}_{A,B}$ of real symmetric polynomials determined by positive constants $A{\leq}B$.

• 한국광학회:학술대회논문집
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• 한국광학회 2009년도 창립 20주년기념 특별학술발표회
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• pp.50-51
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• 2009

• 대한수학회지
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• 제36권3호
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• pp.489-507
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• 1999

We investigate the asymptotic behavior of the extreme zeros of orthogonal polynomials with respect to a positive measure d$\alpha$(x) in terms of the three term recurrence coefficients. We then show that the asymptotic behavior of extreme zeros of orthogonal polynomials with respect to g(x)d$\alpha$(x) is the same as that of extreme zeros of orthogonal polynomials with respect to d$\alpha$(x) when g(x) is a polynomial with all zeros in a certain interval determined by d$\alpha$(x). several illustrating examples are also given.

• 대한수학회보
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• 제36권1호
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• pp.63-78
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• 1999

Let $\mu$(x) be an increasing function on the real line with finite moments of all oeders. We show that for any linear operator T on the space of polynomials and any interger n $\geq$ 0, there is a constant $\gamma n(T)\geq0$, independent of p(x), such that $\parallel T_p\parallel\leq\gamma n(T)\parallel P\parallel$, for any polynomial p(x) of degree $\leq$ n, where We find a formular for the best possible value $\Gamma_n(T)\;of\;\gamma n(T)$ and estimations for $\Gamma_n(T)$. We also give several illustrating examples when T is a differentiation or a difference operator and $d\mu$(x) is an orthogonalizing measure for classical or discrete orthogonal polynomials.

• 대한수학회지
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• 제55권1호
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• pp.101-129
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• 2018

From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

• Structural Engineering and Mechanics
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• 제55권2호
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 추계학술대회 논문집 전기물성,응용부문
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• pp.266-269
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• 2003

In this work, a new formulation is presented for analyzing the transient electromagnetic response from wire antennas using the time-domain integral equation. The solution method is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Piecewise triangle basis functions have been used for spatial expansion functions for arbitrarily shaped wire structures. The time-domain variation is approximated by a set of orthonormal basis functions that are derived from the Laguerre polynomials. The method presented in this paper results in very stable transient responses from wire antennas.

• 한국지능시스템학회논문지
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• 제22권6호
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• pp.793-798
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• 2012

In this paper, we explored the new method for extracting feature from the electroencephalography (EEG) signal based on linear regression technique with the orthonormal polynomial bases. At first, EEG signals from electrodes around motor cortex were selected and were filtered in both spatial and temporal filter using band pass filter for alpha and beta rhymic band which considered related to the synchronization and desynchonization of firing neurons population during motor imagery task. Signal from epoch length 1s were fitted into linear regression with Legendre polynomials bases and extract the linear regression weight as final features. We compared our feature to the state of art feature, power band feature in binary classification using support vector machine (SVM) with 5-fold cross validations for comparing the classification accuracy. The result showed that our proposed method improved the classification accuracy 5.44% in average of all subject over power band features in individual subject study and 84.5% of classification accuracy with forward feature selection improvement.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 추계학술대회 논문집 전기물성,응용부문
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• pp.78-81
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• 2003

In this paper, we analyze the transient electromagnetic response from three-dimensional dielectric bodies using a time-domain PMCHW (Poggio, Miller, Chang, Harrington, Wu) formulation. The time-domain unknown coefficients of the equivalent currents are approximated by a set of orthonormal basis functions that are derived from the Laguerre polynomials. Numerical results computed by the proposed method are presented.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제52권9호
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• pp.412-417
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• 2003

In this Paper, we propose a time-domain magnetic field integral equation (TD-MFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated tv a set of orthonormal basis function that is derived from the Laguerre polynomials. These basis functions are also used for the temporal testing. Numerical results computed by the proposed method are presented and compared.