• International Journal of Contents
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• 제3권4호
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• pp.26-29
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• 2007

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria are which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. In this method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables. Future work: application area such as digital contents like animation, game graphic.

• 전자공학회논문지A
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• 제32A권1호
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• pp.45-52
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• 1995

A new Kirchhoff approximation(KA) method was proposed for microwave scttering from randomly rough surfaces. Using the spectral representation of delta function and its sifting theorem, a new KA was formulated directly without any further approximation, and this formulated was used to compute exact backscttering coefficients. The validity of the KA was verified by a numerical method, and this new KA technique was used to evaluate the existing approximated KkA methods; i.t., the zeroth-order and the first-order approximated physical optics(PO) models. It was shown that the first-order approximated PO model has small error than the zeroth-order approximated PO model at low incidence angles and the opposite happens at higher incidence angles. This new KA model can be used to compute exact scattering coefficients in the validity regions of KA and to evaluate other theoretical and numerical models for scattering from randomly rough surfaces.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• 호남수학학술지
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• 제7권1호
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• pp.7-13
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• 1985

We show that a bounded linear qperator, T, on a Banach space, X, is $C^{n}$-scalar if the sepuence {$\frac{k!}{(k+n)!}{\phi}(T^{k+n}x)$}$_{k=0}^{\infty}$ is positive-definite, for sufficiently many $\phi$ in $X^{\ast}$, x in X. We use this to show that $(T_{n}f)(t){\equiv}tf(t)+nJf(t)$, where $If(t)=\int_{0}^{1}f(s)ds$, is $C^{n}$-scalar on $L^{p}([0,1],v)$, for $1{\leq}p{\leq}\infty$, for a large class of measures, v. Other corollaries include the spectral theorem for bounded symmetric operators on a Hilbert space.

• 대한수학회보
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• 제43권4호
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• pp.715-722
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• 2006

In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.

• 한국통신학회논문지
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• 제21권3호
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• pp.753-762
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• 1996

In this paper, aperture coupled stacked microstrip array antennas are proposed and their operating characteristics are analyzed based on analytical. In order to evaluate mutual coupling between slot-coupled microstrip patches in finite array, analysis uses the reciprocity theorem and the spectral domain Green's functions for dielectric slab in a moment method solution for the unknown patches and solts current distrbution. By introducing an N-port equivalent network, the impedance matrix of an affay of N-element slot-coupled patches is evaluated directly from its network current matix of order N$^{2}$, and it can be programmed to be run on a PC. Numerical results show mutual coupling, radiation pattern, active reflection coefficient versus scan angle, radiation efficiency and active element gain pattern.

• 한국전자파학회논문지
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• 제9권2호
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• pp.238-252
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• 1998

임의의 편파로서 비스듬한 각도록 입사하는 전자파의경우에 대한 접지돈 유전체층 위에 놓여있는 주기적인 스트립격자 구조에서의 특이한 희절현상을 샘플링 정리와 파수영역 방법을 사용하여 해석하였다. 수치적 결과는 임의의 편파와 TE 및 TM편파가 입사되는 경우에 대하여 각각 Bragg 및 Off-Bragg blazing현상을 확인하고 이에 관하여 논의하였다.

• 대한수학회보
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• 제30권2호
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• 대한수학회논문집
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• 제35권3호
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• pp.855-866
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• 2020

For two essentially bounded Lebesgue measurable functions 𝜙 and ξ on unit circle 𝕋, we attempt to study properties of operators $S^k_{\mathcal{M}({\phi},{\xi})=S^k_{T_{\phi}}+S^k_{H_{\xi}}$ on H²(𝕋) (k ≥ 2), where $S^k_{T_{\phi}}$ is a k^th-order slant Toeplitz operator with symbol 𝜙 and $S^k_{H_{\xi}}$ is a k^th-order slant Hankel operator with symbol ξ. The spectral properties of operators S^k_{𝓜(𝜙,𝜙)} (or simply S^k_𝓜(𝜙)) are investigated on H²(𝕋). More precisely, it is proved that for k = 2, the Coburn's type theorem holds for S^k_𝓜(𝜙). The conditions under which operators S^k_𝓜(𝜙) commute are also explored.

• 전자공학회논문지A
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• 제33A권10호
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• pp.90-97
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• 1996

A numerical method for scattering of electromagnetic waves from a periodic strip grating over a grounded dielectric slab is considered for TE and TM polarization cases from the viewpoints of both reflection grating problem and leaky wave antenna problem. The analysis is based on a mode expansion method, floquet's theorem, and the method of moments. Numerical results involving some combinations of geometric parameters are presented in terms of complex propagation constant (kd-$\beta$d diagram), radiation pattern, and relative scattered powers of spectral modes. In particular, the relationship between complex propagatio constnat form the viewpoint of leaky wqve antenna problem and Off-bragg and bragg blazing phenomena from the viewpoint of reflecton graing problem is investigated.