• 대한수학회지
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• 제61권2호
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• 대한수학회보
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• 제56권4호
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• pp.977-992
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• 2019

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

• 대한수학회지
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• 제48권4호
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• pp.775-795
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• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

• 제어로봇시스템학회논문지
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• 제19권7호
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• pp.583-586
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• 2013

We consider discrete-time LTI (Linear Time-Invariant) systems with constant input delays. The input delay is modeled by a first-order PdE (Partial difference Equation) and a backstepping transformation is employed to design a predictor feedback controller. The backstepping approach results in the construction of an explicit Lyapunov function, with which we prove the exponential stability of the closed-loop system formed by the predictor feedback. The numerical example demonstrates the design of the predictor feedback controller, and illustrates the validity of the exponential stability.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.519-536
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• 2005

The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju [17]. The second approach is to modify the analytical methods of MacMillan [20] and Zhang [25] in a discrete time space. The third approach is to apply the simulation technique of Ibanez and Zapareto [14] to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.

• 조명전기설비학회논문지
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• 제26권2호
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• pp.34-43
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• 2012

This paper describes system modeling and controller design method in the measured signal by discrete Fourier transform. Transfer function of the second order system is estimated by the dominant parameter which is computed in the magnitude and the phase of Fourier spectrum of the measured signal. In addition, the controller was designed by the estimated transfer function, and the results were compared. The proposed estimation method of transfer function contains only a very simple mathematical process. Therefore, it is effective to design the controller in the measured signal when the output of the system contains the characteristics of complex exponential functions case. The proposed method was applied on Op-Amp system to verify the efficiency and the reliability. The results show that the proposed algorithms are highly applicable to the system modeling and controller design in the measured data.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.153-165
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• 2007

This paper deals with the empirical Bayes two-action problem of testing $H_0\;:\;{\theta}{\leq}{\theta}_0$: versus $H_1\;:\;{\theta}>{\theta}_0$ using a linear error loss for some discrete nonexponential families having probability function either $$f_1(x{\mid}{\theta})=(x{\alpha}+1-{\theta}){\theta}^x\prod\limits_{j=0}^x\;(j{\alpha}+1)$$ or $$f_2(x{\mid}{\theta})=[{\theta}\prod\limits_{j=0}^{x-1}(j{\alpha}+1-{\theta})]/[\prod\limits_{j=0}^x\;(j{\alpha}+1)]$$. Two empirical Bayes tests ${\delta}_n^*\;and\;{\delta}_n^{**}$ are constructed. We have shown that both ${\delta}_n^*\;and\;{\delta}_n^{**}$ are asymptotically optimal, and their regrets converge to zero at an exponential decay rate O(exp(-cn)) for some c>0, where n is the number of historical data available when the present decision problem is considered.

• 한국통신학회논문지
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• 제8권3호
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• pp.105-112
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• 1983

本論文은 線形空間的不變인 段損(blur)과 自色가우스性雜音에 의해 損傷된 映像에 대한 循環復元(recursive restoration)技法을 論하였다. 映像은 確率設計學的으로 그 平均과 相關函數(correlation function)에 의해 特徵지워진다. 隣接모델(neighborhood model)에 指數的自己相關函數(exponential autocorrelation function)가 사용되며 解析이 간단하고 편리하므로 映像度相關函數를 나타내는데 벡터 모델이 사용된다. 이 벡터 모델을 基本으로 한 映像表現에 있어서 離散的, 統計學的인 12點隣接모델이 開發되고 次元의 增加를 抑制하며 破損되고 雜音섞인 映像을 復元하기 위한 窓(window)移動處理技法이 使用되었다. 12點隣接모델 8點隣接모델보다 優秀한 것으로 나타나며 隣接의 많은 畵素를 요하는 精密畵像에 適合함을 보인다. 이 結果는 線形필터링을 요하는 映像處理에 널리 이용될 수 있음을 나타낸다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2000년도 춘계종합학술대회
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• pp.392-397
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• 2000

Interlace된 2차원 필드영상에 대해 병렬로 DWT를 적용하는 압축기법을 제시하였다. 그 결과 영상의 분해 및 압축율의 증가와 화상 재구성의 PSNR을 증가시키며 신호압축 처리 시간을 단축시킨다. PSNR은 2의 멱수 N의 증가에 따라 지수함수로 감소한다. DCT 기반 압축보다 이득이 30%정도 높다. 독립된 병렬처리는 초당 처리능력을 향상시키며 프레임간 압축보다 간단하다. 또한 필드 영상에서 프레임을 근사 시킬 수 있다.

• 대한수학회지
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• 제56권4호
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.