• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
• /
• pp.416-419
• /
• 1995

A finite-dimensional approximation technique is developed for a class of spectral systems with input and output operators which are unbounded. A corresponding bounding technique on the frequency-response error is also established for control system design. Our goal is to construct an uncertainty model including a nominal plant and its error bounds so that the results from robust linear control theory can be applied to guarantee a closed loop control performance. We demonstrate by numerical example that these techniques are applicable, with a modest computational burden, to a wide class of distributed parameter system plants.

• 대한수학회논문집
• /
• 제9권3호
• /
• pp.593-598
• /
• 1994

In this note we give some results on the jump (due to Kato [5] and West [7]) of a semi-Fredholm operator. Throughout this note, suppose X is an Banach space and write L(X) for the set of all bounded linear operators on X. A operator $T \in L(x)$ is called upper semi-Fredholm if it has closed range with finite dimensional null space, and lower semi-Fredholm if it has closed range with its range of finite co-dimension. It T is either upper or lower semi-Fredholm we shall call it semi-Fredholm and Fredholm it is both. The index of a (semi-) Fredholm operator T is given by $$ index(T) = n(T) = d(T),$$ where $n(T) = dim T^{-1}(0)$ and d(T) = codim T(X).

• 대한수학회논문집
• /
• 제27권1호
• /
• pp.77-95
• /
• 2012

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.

• 대한수학회지
• /
• 제57권3호
• /
• pp.655-668
• /
• 2020

In this paper, we establish the generalized Cameron-Storvick type theorem on function space. We then give relationships involving the generalized Cameron-Storvick type theorem, modified generalized integral transform and modified convolution product. A motivation of studying the generalized Cameron-Storvick type theorem is to generalize formulas and results with respect to the modified generalized integral transform on function space. From the some theories and formulas in the functional analysis, we can obtain some formulas with respect to the translation theorem of exponential functionals.

• International Journal of Reliability and Applications
• /
• 제5권1호
• /
• pp.25-36
• /
• 2004

Ultrasonic inspection system consist of the examination procedures, equipment, and operators. The reliability of nondestructive testing is influenced by the inspection environment, materials and types of defect. It is very difficult to estimate the reliability of NDT due to the various factors. Piping inspection round robin was conducted to quantify the capability of ultrasonic inspection during in-service. In this study, the models for predicting the ultrasonic NDE reliability by logistic model and linear regression model are discussed. The utility of the NDT reliability assessment is verified by the analysis of the data from round robin test with these models.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2000년도 하계학술대회 논문집 D
• /
• pp.2849-2850
• /
• 2000

We developed an automatic 3D inspection system. The system consists of two parts one includes hardwares such as actuators. linear scales and a probe. etc. the other involves softwares for management and control of the system. Compared with existing 3D measurement systems. this system achieved automatically the inspection. This automatic inspection makes the system have some advantages to reduce a measurement time and to be easily used by operators.

• Structural Engineering and Mechanics
• /
• 제39권5호
• /
• pp.669-682
• /
• 2011

A Chebyshev spectral method (CSM) for the dynamic analysis of non-uniform Timoshenko beams under various boundary conditions and concentrated masses at their ends is proposed. The matrix-based Chebyshev spectral approach was used to construct the spectral differentiation matrix of the governing differential operator and its boundary conditions. A matrix condensation approach is crucially presented to impose boundary conditions involving the homogeneous Cauchy conditions and boundary conditions containing eigenvalues. By taking advantage of the standard powerful algorithms for solving matrix eigenvalue and generalized eigenvalue problems that are embodied in the MATLAB commands, chebfun and eigs, the modal parameters of non-uniform Timoshenko beams under various boundary conditions can be obtained from the eigensolutions of the corresponding linear differential operators. Some numerical examples are presented to compare the results herein with those obtained elsewhere, and to illustrate the accuracy and effectiveness of this method.

• Structural Engineering and Mechanics
• /
• 제61권1호
• /
• pp.143-160
• /
• 2017

The paper studies the attenuation of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder made of linear viscoelastic materials. Investigations are made by utilizing the exact equations of motion of the theory of viscoelasticity. The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the attenuation of the waves under consideration. Specific numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov. In particular, how the rheological parameters influence the attenuation of the axisymmetric longitudinal waves propagating in the cylinder under consideration, is established.

• 통합자연과학논문집
• /
• 제11권1호
• /
• pp.51-56
• /
• 2018

For topological vector spaces X and Y, let $F_0(X,Y)=\{f{\in}Y^X:f(0)=0\}$. Then it is an extremely large family and the family of linear operators is a very small subfamily of $F_0(X,Y)$. In this paper, we establish the characterizations of $F_0(X,Y)$-matrix families (${l^{\infty}(X)$, ${l^{\infty}(Y)$), ($c_0(X)$, $l^{\infty}(Y)$) and ($c_0(X)$, $l^{\infty}(Y)$).

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제18권1호
• /
• pp.31-39
• /
• 2011

Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$-group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$-modules.