• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.127-133
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• 1997

In order to study the limits of sequences appearing in, for example, stochastic process, A. V. Skorokhod has defined new function space topologies. We compare these topologies with the topology of compact convergence, the topology of pointwise convergence and others.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.115-118
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• 2000

In this paper we establish limit results on the increments of (N, d)-Gaussian processes with independent components, via estimating upper bounds of large deviation probabilities on the suprema of (N, d)-Gaussian processes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.307-314
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• 2009

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2053-2059
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• 2013

In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.1105-1106
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• 2009

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.6
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• pp.706-713
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• 1985

It is clear that when the amplitude of grinding chatter increases enough the contact between grinding wheel and workpiece cannot be sustained and the loss of contact occurs during a period of grinding chatter. In this paper the behavior of nonlinear grinding chatter due to the loss of contact has been studied. A nonlinear grinding chatter loop is developed where the loss of contact is considered as a nonlinear element of asymmetrical gain. The analysis is carried out in the time domain by numerical simulation and also in the complex domain by use of describing function method. The results show that two typical patterns of nonlinear grinding chatter can originate from the nonlinearity. One is an irregular chatter frequency at starting stage decreases to the natural frequency of grinding structure while the chatter amplitude increases and decreases repeatedly. The other is a limit cycle chatter of which the amplitude and frequency converge to constant and remain. This nonlinear behavior of grinding chatter has been well analyzed by the describing function method and confirmed by the numerical simulation.

• Korean Journal of Optics and Photonics
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• v.5 no.3
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• pp.349-355
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• 1994

Superrsolution of an optical imaging system, which resolves $\epsilon_O$ (half width of the square top amplitude impulse function) less than the Rayleigh's resolution limit $\epsilon_R$, is theoretically treated by using the diffraction theory, and an experimental system is proposed. Initially superresolution is stated as an inverse problem, and an integral equation is derived as a function of parameter $\beta$, which is positive. The integration is numerically carried out for the given aperture and those given values of $\beta$, which is 1, 5, 10, 15, and 20. 1/2$\times$FWHM's of the amplitude impulse functions are meassured for the cases of diffrent value of {J and in the case of $\beta=5$, the half-width already approaches to $\epsilon_O=0.1$,urn, which is, in the case of the present work, one fifth of the Rayleigh's resolution limit. It is found both the pupil function and the phase of the Huygens wave are to be modified, and theories of the pupil function modulation plate and the phase modulation hologram plate are also presented. The result obtained may be useful in ultrafine optical lithography.graphy.

• Journal of the Korean Geotechnical Society
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• v.34 no.12
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• pp.83-92
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• 2018

The lapse of time may cause in the slope structure various deterioration phenomenon progresses in the ground of slope, and collapse due to deterioration of strength, resulting in a decrease in the service life. The approach to slope stability due to the ground deterioration is a different concept from the existing limit equilibrium analysis, which is limited to the physical characteristics and geometrical structure of ground. In this study, we conducted a comparative analysis of various literature studies related to the slope failure characteristics and behaviors to presented the optimal formulas for shear strength reduction, such as the exponential function, the logarithmic function and the inverse hyperbolic function. And then a case study was performed on cut slope of Gyeongbu High Speed Rail construction site along the Yangsan fault zone, where the slope failure of shale layer vulnerable to deterioration occurred. As a result, it was confirmed that landslide occurred due to reduction of shear strength by deterioration, as safety factor is approx. 1.0 at the time when the slope failure occurred. Based on the comprehensive case study, as a quantitative approach to the evaluation of slope stability due to deterioration of ground, finally we propose a method for evaluating slope stability with optimal strength reduction curves.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.644-650
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• 1998

In this paper , a state space model for flexible beam is presented using the assumed-modes approach. The state space equation is derived for a flexible beam in which one end is connected to a motor and is driven by a torque equation and the other end is free. Many of the transfer function proposed thus far use the torque to the flexible beam as the input and the tip deflection of the flexible beam as the output. The Technique for the analysis and synthesis of the dual-input describing function(DIDF) is introduced here and the construction of a non-linear compensator, based on this technique, is proposed. This non-linear compensator, properly connected in the direct path of a closed-loop linear or non-linear control system. The above non-linear network is used to compensate linear and non-linear systems for instability, limit cycles, low speed of response and static accuracy. The effectiveness of the proposed scheme is demonstrated through computer simulation and experimental results.