• The Bulletin of The Korean Astronomical Society
• /
• v.37 no.1
• /
• pp.86.1-86.1
• /
• 2012

The MHD virial theorem applied for observed photospheric field may be the one of way to estimate magnetic energy of generally invisible coronal magnetic structure. However, the photospheric field is not in a force-free state, so the application of virial theory needs some care. Here we use a series of MHD simulations of emerging field to investigate how we can apply the virial theorem to the emerging field. In early emerging phase, virial energy has a minus value although positive area at the photosphere is continuously generated toward a late emerging phase. We discuss why this tendency occurs. Then we derive the critical height where the actual emerging magnetic energy is almost comparable to the virial energy. If the difference between virial energy and magnetic energy becomes 10 percentage of the magnetic energy, we define this is the critical height, and assume the emerging field is close to force-free. We also discuss how the critical height changes with the initial twist of an emerging flux tube.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2008.10a
• /
• pp.508-518
• /
• 2008

Reliability and sensitivity analysis of the design parameters for a section of caisson type quaywall which is the most applicable in Korea were performed. It was tried to estimate probabilities of failure for the system of the multiple failure modes and to analyze LCC in the quaywall structure. The reliability analysis was performed by FORM. Also, sensitivity indices were estimated using the reliability indices, which may be used inferring effects of each design parameter on the reliability indices. As a result, the coefficient of friction between caisson and rubble, the moment by self weight and the moment of resistance mostly affected on the reliability indices in the sliding, overturning and foundation failure, respectively. System reliability theorem was applied in order to estimate the probabilities of failure for the system of the multiple failure modes. As the results of estimation of the probabilities of failure for the system, all cases were more conservative than those for the elements, according to both failure mode and load combination applied to series system. It entirely exceeded the target reliability index, but it was consistent with the theorem. According to the optimum LCC with the width of the caisson, the probability of failure exceeded the target probability of failure at then time. Therefore, it was judged to be insufficient to the practical application.

• Geomechanics and Engineering
• /
• v.13 no.3
• /
• pp.505-515
• /
• 2017

Based on the collapse characteristics of a shallow rectangular cavity, a three-dimensional failure mechanism which can be used to study the collapsing region of the rock mass above a shallow cavity roof is constructed. Considering the effects of surcharge pressure and surface bolt on the collapsing block, the external rate of works produced by surcharge pressure and surface bolt are included in the energy dissipation calculation. Using variational approach, an analytic expression of surface equation for the collapsing block, which can be used to study the collapsing region of the rock mass above a shallow cavity roof, is derived in the framework of upper bound theorem. Based on the analytic expression of surface equation, the shape of the collapsing block for shallow cavity is drawn. Moreover, the changing law of the collapsing region for different parameters indicates that the collapsing region of rock mass decreases with the increase of the density of surface bolt. This conclusion can provide reference for practicing geotechnical engineers to achieve an optimal design of supporting structure for a shallow cavity.

• School Mathematics
• /
• v.12 no.3
• /
• pp.371-388
• /
• 2010

The goals of this study are to inquire middle school students' understanding about prime number and to propose pedagogical implications for school mathematics. Written questionnaire were given to 198 Korean seventh graders who had just finished learning about prime number and prime factorization and then 20 students participated in individual interviews for member checks. In defining prime and composite numbers, the students focused on distinguishing one from another by numbering of factors of agiven natural number. However, they hardly recognize the mathematical connection between prime and composite numbers related on the multiplicative structure of natural number. This study suggests that it is needed to emphasize the conceptual relationship between divisibility and prime decomposition and the prime numbers as the multiplicative building blocks of natural numbers based on the Fundamental Theorem of Arithmetic.

• Journal of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.363-447
• /
• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• Structural Engineering and Mechanics
• /
• v.52 no.2
• /
• pp.239-260
• /
• 2014

Non-stationary random vibration of linear structures with uncertain parameters is investigated in this paper. A time-domain explicit formulation method is first presented for dynamic response analysis of deterministic structures subjected to non-stationary random excitations. The method is then employed to predict the random responses of a structure with given values of structural parameters, which are used to fit the conditional expectations of responses with relation to the structural random parameters by the response surface technique. Based on the total expectation theorem, the known conditional expectations are averaged to yield the random responses of stochastic structures as the total expectations. A numerical example involving a frame structure is investigated to illustrate the effectiveness of the present approach by comparison with the power spectrum method and the Monte Carlo simulation method. The proposed method is also applied to non-stationary random seismic analysis of a practical arch bridge with structural uncertainties, indicating the feasibility of the present approach for analysis of complex structures.

• Journal of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.959-972
• /
• 2013

Rege-Chhawchharia, and Nielsen introduced the concept of right McCoy ring, based on the McCoy's theorem in 1942 for the annihilators in polynomial rings over commutative rings. In the present note we concentrate on a natural generalization of a right McCoy ring that is called a right nilpotent coefficient McCoy ring (simply, a right NC-McCoy ring). The structure and several kinds of extensions of right NC-McCoy rings are investigated, and the structure of minimal right NC-McCoy rings is also examined.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.12 no.20
• /
• pp.47-53
• /
• 1989

This paper presents an algorithm CAPFACT to evaluate the reliability of a capacitated two terminal network such as a communication network, a power distribution network, and a pipeline network. The network is good(working) if and only if it is possible to transmit successfully the required system capacity from one specified terminal to the other. This paper defines new Capacitated series-parallel reduction to be applied to a series-parallel structure of the network. New Capacitated factoring method is applied to a non-series-parallel structure. The method is based on the factoring theorem given by Agrawal and Barlow. According to the existing studies on the reliability evaluation of the network that the capacity is not considered, the factoring method using reduction is efficient. The CAPFACT is more efficient than Aggarwal algorithm which enumerated and combined the paths. The efficiency is proved by the result of testing the number of operations and cpu time on FORTRAN compiler of VAX-11/780 at Hanyang University.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.2319-2324
• /
• 2005

This paper proposes a intelligent gain and boundary layer based sliding mode control (SMC) method for robotic systems with unknown model uncertainties. For intelligent gain and boundary layer, we employ the self recurrent wavelet neural network (SRWNN) which has the properties such as a simple structure and fast convergence. In our control structure, the SRWNNs are used for estimating the width of boundary layer, uncertainty bound, and nonlinear terms of robotic systems. The adaptation laws for all parameters of SRWNNs and reconstruction error bounds are derived from the Lyapunov stability theorem, which are used for an on-line control of robotic systems with unknown uncertainties. Accordingly, the proposed method can overcome the chattering phenomena in the control effort and has the robustness regardless of unknown uncertainties. Finally, simulation results for the three-link manipulator, one of the robotic systems, are included to illustrate the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.433-448
• /
• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.