• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.689-700
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• 1998

We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.227-234
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• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.890-895
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• 1989

This paper discusses the regulator problem of minimizing the input energy for the multi-input linear time-invariant discrete-time system with the zero terminal state. The optimal inputs are expressed by the state feedback form and they are made up of three phases. The optimal feedback gains are independent of the initial state.

• Journal of the Korea Computer Industry Society
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• v.8 no.1
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• pp.57-64
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• 2007

In the paper, considers the design of a detection system, consisting of n identical detectors, to process the sum of spatially invariant signal fields $S_\jmath(t)$, an additive, homogeneous, spatially isotropic (in the array plane x). covariance_separable, and zero_mean Gaussian random noise field n(t, x). consisting of arrey receivers for use in optical communication through optimum turbulence atmosphers and covriance_circuit, staistical analysis through detection the maximum gain are compared with analysis theoretical analysis theoretical value and get through experimental measured value, as well the measured valus are confirmed to agreement joint Gaussian theoretical curves.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.7A
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• pp.724-729
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• 2007

In this paper, we consider a joint optimization of transmitter and receiver in additive cyclostationary noise with zero forcing criterion. We assume that the period of the cyclostationary noise is the same as the inverse of the symbol transmission rate and that the noise has a positive-definite autocorrelation function. The data sequence is modeled as a wide-sense stationary colored random process and the channel is modeled as a linear time-invariant system with a frequency selective impulse response. Under these assumptions and a constraint on the average power of the transmitted signal, we derive the optimum transmitter and receiver waveforms that jointly minimizes the mean square error with no intersymbol interference. The simulation results show that the proposed system has a better BER performance than the systems with receiver only optimization and the systems with no transmitter and receiver optimization.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1913-1925
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• 2017

Let R be a ring with identity. An ideal N of R is called ideal-symmetric (resp., ideal-reversible) if $ABC{\subseteq}N$ implies $ACB{\subseteq}N$ (resp., $AB{\subseteq}N$ implies $BA{\subseteq}N$) for any ideals A, B, C in R. A ring R is called ideal-symmetric if zero ideal of R is ideal-symmetric. Let S(R) (called the ideal-symmetric radical of R) be the intersection of all ideal-symmetric ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an ideal-symmetric ideal of a ring are obtained; (2) Ideal-symmetric property is Morita invariant; (3) For any ring R, we have $S(M_n(R))=M_n(S(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a quasi-Baer ring R, R is semiprime if and only if R is ideal-symmetric if and only if R is ideal-reversible.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.5
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• pp.444-450
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• 2004

In mobile communications environment, STBC-OFDM(Space Time Block Code-Orthogonal Frequency Division Multiplexing) system with transmit diversity obtains the MRRC(Maximal Ratio Receiver Combining) diversity gain in time-invariant channel between two received symbols. But in time-variant channel, due to the interference between received symbols, MRRC diversity gain cant be obtained. So, when the mobile device with transmit diversity moves in high speed, the scheme to reduce the performance degradation due to the interference is needed. In this paper, we propose the receiver architecture with advanced transmit diversity, which improves the performance of STBC-OFDM system. The proposed architecture obtains the diversity gain without the change of transmit bandwidth at the receiver with the interference canceller using ZF(Zero Forcing) algorithm. Simulation results show performance improvement as doppler shift is increasing.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1545-1548
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• 1991

In this note, we consider a robust linear shift-invariant feedback compensator design for discrete-time multivariable systems which have both matched and mismatched uncertainties. In order to attack the problem of designing robust compensators guaranteeing uniform ultimate boundedness of every closed-loop system response within a neighborhood of the zero state based solely on the knowledge of the upper norm-bounds of uncertainties, we use an approach which is effective on studying augmented feedback control systems with both mismatched and matched uncertainties. We draw some robust stability conditions using the approach and give an example.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2043-2051
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• 2017

Consider a sequence of compactly supported Hamiltonian diffeomorphisms ${\phi}_k$ of an exact symplectic manifold, all of which are "graphical" in the sense that their graphs are identified by a Darboux-Weinstein chart with the image of a one-form. We show by an elementary argument that if the ${\phi}_k$ $C^0$-converge to the identity, then their Calabi invariants converge to zero. This generalizes a result of Oh, in which the ambient manifold was the two-disk and an additional assumption was made on the Hamiltonians generating the ${\phi}_k$. We discuss connections to the open problem of whether the Calabi homomorphism extends to the Hamiltonian homeomorphism group. The proof is based on a relationship between the Calabi invariant of a $C^0$-small Hamiltonian diffeomorphism and the generalized phase function of its graph.