• Journal of the Korean Mathematical Society
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• v.61 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.7
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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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• v.17 no.1_2_3
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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.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.26 no.2
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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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• v.23 no.1_2
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.8 no.3
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• pp.105-112
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• 1983

This paper discribes technique of the recursive restoration for the images degraded by linear space invariant blur and additive white Gaussian noise. The image is characterized statistically by tis mean and correlation function. An exponential autocorrelation function has been used to model neighborhood model. The vector model was used because of analytical simplicitly and capability to implement brightness correlation function. Base on the vector model, a two-dimensional discrete stochastic a 12 point neighborhood model for represeting images was developme and used the technique of moving window processing to restore blurred and noisy images without dimensionality increesing, It has been shown a 12 point neighborhood model was found to be more adequate than a 8 point pixel model to obtain optimum pixel estimated. If the image is highly correlated, it is necessary to use a large number of points in the neighborhood in order to have improvements in restoring image. It is believed that these result could be applied to a wide range of image processing problem. Because image processing thchniques normally required a 2-D linear filtering.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2000.05a
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• pp.392-397
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• 2000

An Interlaced 2D field images compression technique by Discrete Wavelet Transform is proposed. The result has a good image resolution and compression rate, PSNR, and reduces processing time of compression. PSNR depends on the exponential function corresponding to 2 power N has higher 30% than DCT. And It is easier to process the inter-frame and fast to work a second with each parallel field processing, and more be able to approximate a frame on the field.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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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.