• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.693-701
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• 2006

Using Minimax principle and Linking theorem in critical point theory, we prove the existence of two nontrivial solutions for the following second order superlinear difference systems $$(P)\{{\Delta}^2x(k-1)+g(k,y(k))=0,\;k{\in}[1,\;T],\;{\Delta}^2y(k-1)+f(k,\;x(k)=0,\;k{\in}[1,\;T],\;x(0)=y(0)=0,\;x(T+1)=y(T+1)=0$$ where T is a positive integer, [1, T] is the discrete interval {1, 2,..., T}, ${\Delat}x(k)=x(k+1)-x(k)$ is the forward difference operator and ${\Delta}^2x(k)={\Delta}({\Delta}x(k))$.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1573-1594
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• 2017

This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

• Journal of the Korean School Mathematics Society
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• v.2 no.1
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• pp.181-195
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• 1999

This research is produced as a applet of learning materials, and is made with the internet languages HTML, Java, and NamoWebeditor. It contains "Greatest Common Divisor and Least Common Multiple", "Parallel translation of function of second order", "Pythagoras Theorem", which is the current middle school mathmatics textbook for third graders. The keynote of this research is that the students can study individually through logging into the internet on their own computers; the program is made using graphics and animation on order to develop the learners′ interest in mathematics. I hope that this research can supplement our currently insufficient internet educational data.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• ETRI Journal
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• v.40 no.5
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• pp.634-642
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• 2018

Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum-product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.1-6
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• 1997

The scheduling problem of satisfying both 0/1 constraint and the timing constraint while minimizing the total error is NP-complete when the optional parts have arbitrary processing times. In this paper, we present a heuristic scheduling algorithm for 0/1 constraint imprecise systems which consist of communicating tasks running on multiple processors. The algorithm is based on the program graph which is similar to the one presented in[4]. To check the schedulability, we apply Lawler and Moore's theorem. To analyze the performance of the proposed algorithm, intensive simulation is done. The results of the simulation shows that the longest processing first selection strategy outperforms random or minimal laxity policies.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.615-621
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• 1999

In this paper, we consider the robust stability of uncertain linear systems with time-delay in the time domain. The considered uncertainties are both the unstructured uncertainty which is only Known its norm bound and the structured uncertainty which is known its structured. Based on Lyapunov stability theorem and{{{{ { H}_{$\infty$ } }}}} theory known as Strictly Bounded Real Lemma (SBRL), we present new conditions that guarantee the robust stability of system. Also, we extend this to multiple time-varying delays systems and large-scale systems, respectively. Finally, we show the usefulness of our results by numerical examples.

• 전기의세계
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• v.28 no.6
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• pp.61-77
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• 1979

This paper is concerned with minimization process of the binary logic function. This paper describes an algorithm called the SIMPLE TABLE METHOD that well suited to minimization a switching function of any number of variables. For the Simple Table construction, a theorem based upon the numerical properties of the logic function is derived from the relationships governing minterms of the given function. Finally the minimal sum of products can be obtained in terms of the Direct Method or the Indirect Method from the table and table characteristics derived from the Simple Table. The properties and table characteristics used in this paper are described. All the minterms of a switching function are manipulated only by decimal numbers, not binary numbers. Some examples are used as a vehicle to guide the readers who are familiar with the Karnaugh map and Quine-McCluskey tabular method to this New method. These examples not only treat how to handle Don't Care miterms but also show the multiple output functions.

• International Journal of Internet, Broadcasting and Communication
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• v.14 no.3
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• pp.79-84
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• 2022

Towards the sixth generation (6G) mobile networks, spectrum and energy efficiency of non-orthogonal multiple access (NOMA) transmissions in the fifth generation (5G) wireless system have been improved by intelligent reflecting surface (IRS) technologies. However, the reflecting devices of an IRS tend to be correlated because they are placed close on the surface each other. In this paper, we present an analysis on the correlated IRS in NOMA cellular networks. Specifically, we consider the bit-error rate (BER) performances for correlated-IRS in NOMA networks. First, based on the central limit theorem, we derive an approximate analytical expression of the BER for correlated-IRS NOMA systems, by using the second moment of the channel gain. Then we validate the proposed analytical BER by Monte Carlo simulations, and show that they are in good agreement. In addition, we also show numerically the BER improvement of the correlated-IRS NOMA over the conventional independent-IRS NOMA.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.37 no.1
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• pp.1-11
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• 2000

We propose a predistorter to compensate for nolinear distortion induced by a high power amplifier employed in multi carrier-code division multiple access (MC-CDMA) systems. The proposed scheme rests upon the fixed point iteration (FPI) associated with the contraction mapping theorem. Unlike the predistorter based on the FPI already presented by the authors in other literatures which operates on complex-valued modulation signals, the proposed predistorter in this paper deals with real-valued FPI on modulation signal amplitudes, resulting in less complexity. Simulation results on a BPSK-modulated, 64-subcarrier synchronous MC-CDMA baseband system with a traveling wave tube amplifier in the transmitter, indicate that the proposed predistorter achieves significant improvement in terms of bit error rate and total degradation over those without the predistorter. Moreover, the proposed predistorter outperforms the complex-valued counterpart, in particular, for small output back-off levels.