• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.225-231
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• 2019

In a previous paper, the authors of this paper studied $2{\times}2$ matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1, 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the $2{\times}2$ matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such $2{\times}2$ operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.

• 대한수학회논문집
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• 제17권1호
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• pp.1-14
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• 2002

Some recent results on the distribution of zeros of real entire functions are surveyed.

• 대한수학회보
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• 제35권4호
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• pp.701-707
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• 1998

An operator $T{\in} {{\mathcal L}(H)}$ is generalized k-quasihyponormal if there exist a constant M>0 such that $T^{\ast k}[M^2(T-z)^{\ast}(T-z)-(T-z)(T-z)^{\ast}]T^k{\geq}0$ for some integer $k{\geq}0$ and all $Z{\in} {\mathbf C}$. In this paper, we show that it T is a generalized k-quasihyponormal operator with the property $0{\not\in}{\sigma}(T)$, then T is subscalar of order 2. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum has interior in C.

• 대한수학회보
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• 제30권1호
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• pp.91-97
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• 1993

In this article, we consider the case that S is a topologically complete subspace of $R^{k}$ , and that .GAMMA. is a set of monotone functions on S into S. It is obtained the sugficient condition for the existence of a unique invariant probability to which $P^{(n}$/(x,dy) converges exponentially fast in a metric stronger than the Kolmogorov's distance. This extends the earlier results of Bhattacharya and Lee (1988) who considered the case .GAMMA. a set of nondecreasing functions.tions.

• 대한수학회논문집
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• 제34권3호
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• pp.981-989
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• 2019

In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f:X{\rightarrow}X$ be a continuous map of a compact metric space X and A be an f-invariant dense subspace of X. We show that if $f{\mid}_A:A{\rightarrow}A$ has the periodic shadowing property, then f has the periodic shadowing property. Also, we show that f has the finite average shadowing property if and only if $f{\mid}_A$ has the finite average shadowing property.

• Structural Monitoring and Maintenance
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• 제4권4호
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• pp.365-379
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• 2017

This paper presents a comparison of the black-box and the physics based derived gray-box models for subspace identification for structures subjected to support-excitation. The study compares the damage detection capabilities of both these methods for linear time invariant (LTI) systems as well as linear time-varying (LTV) systems by extending the gray-box model for time-varying systems using short-time windows. The numerically simulated IASC-ASCE Phase-I benchmark building has been used to compare the two methods for different damage scenarios. The efficacy of the two methods for the identification of stiffness parameters has been studied in the presence of different levels of sensor noise to simulate on-field conditions. The proposed extension of the gray-box model for LTV systems has been shown to outperform the black-box model in capturing the variation in stiffness parameters for the benchmark building.

• 대한수학회지
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• 제33권4호
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• pp.1069-1099
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• 1996

Let X be a smooth, simply connected and oriented closed fourmanifold such that the dimension $b_{2}^{+}(X)$ of a maximal positive subspace for the intersection form is greater than or equal to 3.

• 대한수학회보
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• 제37권3호
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• pp.411-418
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• 2000

In this paper, we want to give an operator which is not unicellular. We try to prove the non-unicellularity of the operator by using the method given in [8].

• 호남수학학술지
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• 제29권4호
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• pp.523-533
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• 2007

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

• 한국정보통신학회논문지
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• 제3권4호
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• pp.895-905
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• 1999

This paper identifies a linear time-invariant mathematical model of each stand of a five-stand tandem cold mill to design a robust $H_\infty$ thickness controller by applying input and output data sets to N4SID (Numerical algorithms for Subspace State Space System Identification) method. The input-output data sets describe interstand interference in the process of tandem cold rolling and are obtained from a nonlinear simulator of the tandem cold mill. In result, it is shown that the identified model well approximates the nonlinear model than a Taylor linearized model. Furthermore, uncertainties including roll eccentricity and incoming strip variation are quantitatively analyzed from the plot of maximum singular values.