• 대한수학회보
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• 제38권4호
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• pp.663-668
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• 2001

X and Y are Banach spaces for which K(X, Y), the space of compact operators from X to Y, is an M-ideal in L(X, Y), the space of bounded linear operators form X to Y. If Z is a closed subspace of Y such that L(X, Z) has property SU in L(X, Y) and d(T, K(X, Z)) = d(T, K(X, Y)) for all $T \in L(X, Z)$, then K(X, Z) is an M-ideal in L(X, Z) if and only if it has property SU is L(X, Z).

• Coupled systems mechanics
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• 제1권2호
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• pp.183-204
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• 2012

A method for the analysis of wave scattering in 3-D elastic full space is developed by means of the coupled boundary-volume integral equation, which takes into account the effects of both the boundary of inclusions and the uctuation of the wave field. The wavenumber domain formulation is used to construct the Krylov subspace by means of FFT. In order to achieve the wavenumber domain formulation, the boundary-volume integral equation is transformed into the volume integral equation. The formulation is also focused on this transform and its numerical implementation. Several numerical results clarify the accuracy and effectiveness of the present method for scattering analysis.

• 호남수학학술지
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• 제34권3호
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• pp.409-422
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• 2012

Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$. And let X and Y be operators acting on a Hilbert space $\mathcal{H}$. Let $sp(x)=\{{\alpha}x\;:\;{\alpha}{\in}\mathcal{C}\}$ $x{\in}\mathcal{H}$. Assume that $\mathcal{H}=\overline{range\;X}{\oplus}sp(h)$ for some $h{\in}\mathcal{H}$ and < $h$, $E^{\bot}Xf$ >= 0 for each $f{\in}\mathcal{H}$ and $E{\in}\mathcal{L}$. Then there exists an operator A in Alg$\mathcal{L}$ such that AX = Y if and only if $sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\parallel}E^{\bot}Yf{\parallel}}\;:\;f{\in}H,\;E{\in}\mathcal{L}\}$ = K < ${\infty}$. Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}||A{\parallel}=K$.

• 충청수학회지
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• 제25권4호
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• pp.731-738
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• 2012

Let L(M) be the bundle of all linear frames over $M,\;u$ an arbitrarily given point of L(M), and ${\nabla}\;:\;\mathfrak{X}(M)\;{\times}\;\mathfrak{X}(M)\;\rightarrow\;\mathfrak{X}(M)$ a linear connection on L(M). Then the following results are well known: the horizontal subspace and the connection form at the point $u$ may be written in terms of local coordinates of $u\;{\epsilon}\;L(M)$ and Christoffel's symbols defined by $\nabla$. These results are very fundamental on the study of the theory of connections. In this paper we show that the local expressions of those at the point $u$ do not depend on the choice of a local coordinate system around the point $u\;{\epsilon}\;L(M)$, which is rarely seen. Moreover we give full explanations for the following fact: the covariant derivative on M which is defined by the parallelism on L(M), determined from the connection form above, coincides with $\nabla$.

• 대한수학회지
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• 제45권4호
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• pp.903-921
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• 2008

A continuous linear operator $T\;:\;X{\rightarrow}X$ is called hypercyclic if there exists an $x\;{\in}\;X$ such that the orbit ${T^nx}_{n{\geq}0}$ is dense. We consider the problem: given an operator $T\;:\;X{\rightarrow}X$, hypercyclic or not, is the restriction $T|y$ to some closed invariant subspace $y{\subset}X$ hypercyclic? In particular, it is well-known that any non-constant partial differential operator p(D) on $H({\mathbb{C}}^d)$ (entire functions) is hypercyclic. Now, if q(D) is another such operator, p(D) maps ker q(D) invariantly (by commutativity), and we obtain a necessary and sufficient condition on p and q in order that the restriction p(D) : ker q(D) $\rightarrow$ ker q(D) is hypercyclic. We also study hypercyclicity for other types of operators on subspaces of $H({\mathbb{C}}^d)$.

• 전자공학회논문지S
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• 제34S권12호
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• pp.30-40
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• 1997

This paper presents a design method of fuzzy control systems by clustering the data in the subspace of the input-output produyct space. In the case of servo control, most input-outputdata are concentrated in thye steady-state region, and the the clustering will result in only steady-state fuzzy rules. To overcome this problem, we divide the input-output product space into some subspaces according to the state of input variables. The fuzzy control system designed by the subspace clustering showed good transient response and smaller steady-state error, which is comparable with the reference fuzzy system.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.29-36
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• 2004

Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and ｙ be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

• 대한기계학회논문집A
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• 제24권2호
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• pp.290-302
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• 2000

In this paper, we study on the identification of discrete-time state-space model for robust control of tandem cold mill, using a MOESP(MIMO output-error state-space model identification) algorithm based on subspace method. It is shown that the identified model is well adapted to input-output data sets, which are obtained from nonlinear mathematical equations of tandem cold mill. Furthermore, deterministic H$\infty$ norm bounds on uncertainties including modeling errors and disturbances are quantitatively identified in the frequency domain. Finally, the results give a basic idea to determine weighting functions included in formulating some robust control problems of tandem cold mill.

• 대한수학회논문집
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• 제18권3호
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.677-680
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• 2004

This study investigates the buckling evaluation of connecting rods used in the diesel engine through finite element analysis. The Rankine formula, which is modified from classical Euler‘s formula, has been widely accepted in automotive industry to evaluate the buckling of connecting rods. Apparently, this formula is most suitable for the straight and idealized rod shape, and over-simplifies the geometric complexity associated with connecting rods. The subspace iteration method in FEA is used to predict the critical buckling stress of a connecting rod with certain slenderness ratio. To create models with various slenderness ratios for shank portion in the rod, the automatic meshing preprocessor was implemented. Results from FEA were verified by the experiments, in which the embedded strain gages measured for the connecting rod running at 4000rpm. The result indicates that the buckling prediction curve through FEA and experiment is effectively different from the curve of classical Rankine formula.