• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.57-68
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• 2016

In this work, we shall give the degree of approximation for functions belonging to $H{\ddot{o}}lder$ class by matrix summability method of multiple Fourier series in the $H{\ddot{o}}lder$ metric.

• Communications for Statistical Applications and Methods
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• 제29권1호
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• 한국전자파학회논문지
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• 제7권5호
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• pp.440-446
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• 1996

다중 ridge 원형 도파관을 퓨리에 급수 전개와 모드 정합법을 이용하여 정확하게 해석하였다. 경계 조건을 이용하여 두 급수식을 전개하고 이를 풀어 모드를 정확하게 구하였다. 다중 ridge 원형 도파관의 ridge의 수, 길이, 폭에 따른 차단 파수(cutoff wavenumber)의 변화를 살펴보았다. 구한 해는 정확하고 수렴성이 뛰어나며 dominant mode에 대해서는 간단한 근사식을 제시하였다.

• Smart Structures and Systems
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• 제23권6호
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• pp.641-651
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• 2019

The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

• Journal of Mechanical Science and Technology
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• 제14권10호
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• pp.1051-1060
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• 2000

Linear cyclic systems (LCS's) are a class of systems whose dynamic behavior changes cyclically. Such cyclic behavior is ubiquitous in systems with fundamentally repetitive motions (e. g. all rotating machinery). Yet, the knowledge of the noise and vibration transmission paths in LCS's is quite limited due to the time-varying nature of their dynamics. The first part of this two-part paper derives a generic expression that describes how the noise and/or vibration are transmitted between two (or multiple) locations in the LCS's. An analysis via the Fourier series and Fourier transform (FT) plays a major role in deriving this expression that turns out to be transfer function dependent upon the cycle position of the system. The cyclic nature of the LCS' transfer functions is shown to generate a series of amplitude modulated input signals whose carrier frequencies are harmonic multiples of the LCS' fundamental frequency. Applicability of signal processing techniques used in the linear time-invariant systems (LTIS's to the general LCSs is also discussed. Then, a criterion is proposed to determine how well a LCS can be approximated as a LTIS. In Part II, experimental validation of the analyses carried out in Part I is provided.

• International Journal of Computer Science & Network Security
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• 제24권9호
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• pp.21-29
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• 2024

Precoding of the orthogonal frequency division multiplexing (OFDM) with Walsh Hadamard transform (WHT) is known in the literature. Instead of performing WHT precoding and inverse discrete Fourier transform separately, a product of two matrix can yield a new matrix that can be applied with lower complexity. This resultant transform, T-transform, results in T-OFDM. This paper extends the limited existing work on T-OFDM significantly by presenting detailed account of its computational complexity, a lower complexity receiver design, an expression for PAPR and its cumulative distribution function (cdf), sensitivity of T-OFDM to timing synchronization errors, and novel analytical expressions signal to noise ratio (SNR) for multiple equalization techniques. Simulation results are presented to show significant improvements in PAPR performance, as well improvement in bit error rate (BER) in Rayleigh fading channel. This paper is Part II of a three-paper series on alternative transforms and many of the concepts and result refer to and stem from results in generalized multicarrier communication (GMC) system presented in Part I of this series.

• 정보학연구
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• 제5권4호
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• pp.1-8
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• 2002

본 연구는 저압 전력선에서의 데이터 통신에 적합한 변조 방식으로 주목받고 있는 다중 반송 변조의 일종인 OFDM(Orthogonal Frequency Division Multiplexing)의 변조를 실험하고, 이들 데이터를 전달 할 매체인 전력선을 채널 모델링 하였다. 전력선은 각종 전자기기에 의해 분기 연결되어 지연 전파의 경우와 임펄스성 잡음원이 존재하는 것으로 알려져 있다. 반송 주파수와 전력선의 길이에 의해 주파수 선택적 페이딩이 발생함을 알 수 있다.

• 정보학연구
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• 제6권2호
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• pp.1-8
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• 2003

본 연구는 최근 새로운 통신 방식으로 제안되고 있는 저압 전력선 통신에 대해서 검토한다. 저압 전력선 통신을 위한 지연, 감쇠, 주파수 선택적 페이딩의 특성을 갖는 전력선채널의 모델링과 함께 이 채널 특성에 다중 반송파 변조의 일종인 OFDM(Orthogonal Frequency Division Multiplexing)방식을 적용해 봄으로써 전력선 통신에 OFDM변조 방식이 적합한지 분석한다

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1583-1602
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• 2011

A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.

• 대한기계학회논문집A
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• 제26권12호
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).