• Korean Journal of Mathematics
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• 제7권2호
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• pp.219-226
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• 1999

In this paper, we discuss convergence theorem for exponentially bounded C-semigroups. We establish the convergence of the sequence of generators of exponentially bounded C-semigroups in some sense implies the convergence of the sequence of the corresponding exponentially bounded C-semigroups. Under the assumption that R(C) is dense, we show the equivalence between the convergence of generators and exponentially bounded C-semigroups.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.117-125
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• 2004

We investigate some properties of functions of ${\Phi}{\Lambda}$-bound variation on a closed bounded interval, which is the generalization of bounded variation.

• Smart Structures and Systems
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• 제19권1호
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• 한국수학사학회지
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• 제19권2호
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• pp.115-124
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• 2006

유계변동(bounded variation)과 관련된 Daniel Waterman의 30여 년간의 연구에 대하여 조사를 하였다.

• 호남수학학술지
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• 제32권2호
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• pp.227-237
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• 2010

For a discrete group G, the kernel of a homomorphism from bounded cohomology $\hat{H}^*(G)$ of G to the ordinary cohomology $H^*(G)$ of G is called the singular part of $\hat{H}^*(G)$. We give some results on the space of the singular part of the second bounded cohomology of G. Also some results on the second bounded cohomology of a uniformly perfect group are given.

• 대한수학회보
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• 제50권2호
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• pp.675-685
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• 2013

We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.81-90
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• 2013

We investigate the bounded weak solutions for the Hamiltonian system with bounded nonlinearity decaying at the origin and periodic condition. We get a theorem which shows the existence of the bounded weak periodic solution for this system. We obtain this result by using variational method, critical point theory for indefinite functional.

• 대한수학회보
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• 제43권1호
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• pp.1-7
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• 2006

In this paper, we investigate bounded matrices over regular rings. We observe that every bounded matrix over a regular ring can be described by idempotent matrices and invertible matrices. Let A, $B{in}M_n(R)$ be bounded matrices over a regular ring R. We prove that $(AB)^d = U(BA)^dU^{-1}$ for some $U{\in}GL_n(R)$.

• 대한수학회보
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• 제44권3호
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• pp.523-536
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• 2007

Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.545-553
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• 1997

By using the decreasing rearrangement of nonoverlapping subintervals of a closed bounded intervals and L.C.young's series for two ø-sequences we obtain some results concerning Riemann-Stieltijes integrals of functions of $\textsc{k}{\phi}-bounded$ variations.