• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.205-209
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• 1995

Throughout this paper X is a Banach space and $\mu$ is the Lebesgue measure on [0, 1] and all operators are assumed to be bounded and linear. $L^1(\mu)$ is the Banach space of all (classes of) Lebesgue integrable functions on [0, 1] with its usual norm. Let $T : L^1(\mu) \to X$ be an operator.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.653-655
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• 2006

We give a simple proof of the statement that if T is a bounded linear operator on a complex HIlbert space then T is Fredholm if and only if ${\pi}(T)$ is not a TDZ, where ${\pi}(\cdot)$ is the Catkin homomorphism.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1365-1370
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• 1990

We have developed a new fuzzy control method for paper machine basis weight profile. The conventional linear control method has not yielded good results on some machines. This new control method, however, realizes long-term stability and convergence of the profile as good or better than that achieved under manual control by an operator.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.511-526
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• 2008

In this paper, we consider an elliptic system of three equations using the minimax theorem. We prove the existence of two solutions for suitable forcing terms, under a condition on the linear part which prevents resonance with eigenvalues of the operator.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.23-32
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• 1998

In the present paper the author studies the decomposition property ($\delta$) of the bounded linear operators.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.237-257
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• 1998

By introducing the notion of a generalized normal state space, we give a necessary and sufficient condition for that there exists a unital normal completely map from a von Neumann algebra into another, in terms of their generalized normal state spaces.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.703-711
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• 2008

Let ${{\xi}_k,k{\in}{\mathbb{Z}}}$ be an associated H-valued random variables with $E{\xi}_k$ = 0, $E{\parallel}{\xi}_k{\parallel}$ < ${\infty}$ and $E{\parallel}{\xi}_k{\parallel}^2$ < ${\infty}$ and {$a_k,k{\in}{\mathbb{Z}}$} a sequence of bounded linear operators such that ${\sum}^{\infty}_{j=0}j{\parallel}a_j{\parallel}_{L(H)}$ < ${\infty}$. We define the sationary Hilbert space process $X_k={\sum}^{\infty}_{j=0}a_j{\xi}_{k-j}$ and prove that $n^{-1}{\sum}^n_{k=1}X_k$ converges to zero.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.3
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• pp.86-92
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• 1998

This paper deals with an output feedback H control problem for linear time ivariant systems with state delay. The proposed output feedback controller is represented by the lower linear fractional transformation of alinear time invariant system and a delay operator. Sufficient conditions for the existence of the output feedback controller are given in the form of linear matrix inequalities which are less conservative than those for the existence of a rational output feedback controler. We also present a numerical example to demonstrate the efficacy of the proposed method.of the proposed method.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.393-408
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• 2024

The sparse linear discriminant analysis can be incorporated into the penalized linear regression framework, but most studies have been limited to specific convex penalties, including the least absolute selection and shrinkage operator and its variants. Within this framework, concave penalties can serve as natural counterparts of the convex penalties. Implementing the concave penalized direction vector of discrimination appears to be straightforward, but developing its theoretical properties remains challenging. In this paper, we explore a class of concave penalties that covers the smoothly clipped absolute deviation and minimax concave penalties as examples. We prove that employing concave penalties guarantees an oracle property uniformly within this penalty class, even for high-dimensional samples. Here, the oracle property implies that an ideal direction vector of discrimination can be exactly recovered through concave penalized least squares estimation. Numerical studies confirm that the theoretical results hold with finite samples.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.1129-1134
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• 1989

In this paper, we propose a neural network for learning to control semi-linear dynamical systems. The network is a composite system of four three-layer backpropagation subnetworks, and is able to control inverted pendulums better than systems based on modern control theory at least in some ranges of parameters. Three of the four subnetworks in our network system process angles, velocities, and positions of a moving inverted pendulum, respectively. The outputs from those three subnetworks are input to the remaining subnetwork that makes control decisions. Each of the four subnetworks learns connection weights independently by backpropagation algorithms. Teaching signals are given by the human operator. Also, input signals are generated by the human operator, but they are converted by preprocessors to actual input data for the three subnetworks except for the network for control decisions. The whole system is implemented on both of 16 bit personal computers and 32 bit workstations. First, we briefly provide the research background and the inverted pendulum problem itself, followed by the description of our composite neural network model. Next, some results from the simulation are given, which are subsequently compared with the results from a control system based on modern control theory. Then, some discussions and conclusion follow.