• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.261-267
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• 2006

A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the $Fr\'{e}chet$-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.313-336
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• 1996

In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

• KDI Journal of Economic Policy
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• v.39 no.1
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• pp.19-40
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• 2017

This paper analyzes the interaction between monetary and macroprudential policies mainly in the context of the non-cooperation among policy authorities. Each policy authority's optimal response is to tighten its policy measures when other authorities' policy measures are loosened. This indicates that the two policies are substitutes for each other. This result still holds when an additional financial stability mandate is assigned to the central bank. The condition for the response functions to converge to a Nash equilibrium state is analyzed along with the speed of convergence, showing that they depend on the authorities' preferences and the number of mandates assigned to policy authorities. If the financial supervisory authority (FSA) assigns greater importance to the output gap or a stronger financial stability mandate is assigned to the central bank (CB), the probability of non-convergence increases and the speed of convergence declines even when the condition of convergence is satisfied. Meanwhile, if the CB considers output stability as an important task, the probability of convergence and the speed of converging to a state of equilibrium are high. Finally, when a single mandate or small number of mandates is/are assigned to each authority, stability is more quickly restored as compared to when many mandates are assigned.

• Journal of the Institute of Convergence Signal Processing
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• v.5 no.1
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• pp.32-39
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• 2004

Biological neurons generally have chaotic characteristics for permanent or transient period. The effects of chaotic response of biological neuron have not yet been verified by using analytical methods. Even though the transient chaos of neuron could be beneficial to overcoming the local minimum problem, the permanent chaotic response gives adverse effect on optimization problems in general. To solve optimization problems, which are needed in almost all neural network applications such as pattern recognition, identification or prediction, and control, the neuron should have one stable fixed point. In this paper, the dynamic characteristics of the chaotic dynamic neuron and the condition that produces the chaotic response are analyzed, and the convergence conditions are presented.

• Journal of the Korea Convergence Society
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• v.8 no.7
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• pp.295-304
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• 2017

The purpose of this study was to identify the immediate effect of the joint mobilization with an elastic taping on standing balance in patients with knee osteoarthritis. Thirty patients with knee osteoarthritis were randomly divided into three groups: a taping group, a joint mobilization group, and a joint mobilization with taping group. A foot pressure platform (Zebris) was used to evaluate standing balance ability, and the sway area, path length and average velocity were measured during eyes open condition and eyes closed condition. All the groups showed a significant improvement in the sway area during eyes closed condition after intervention, and the joint mobilization with taping group revealed significant improvements in the path length and average velocity. There was no significant difference in the standing balance ability among all the groups. Both the joint mobilization and taping method were effective methods for standing balance during eyes closed condition, and it has been found that the convergence of the two interventions had an effect on diverse balance variables. Thus, it is recommended to apply the convergence of the two interventions for patients with knee osteoarthritis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.3
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• pp.151-157
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• 2021

This paper is devoted to a convergence study of the nonlocal integral operator in peridynamics. The implicit formulation can be an efficient approach to obtain the static/quasi-static solution of crack propagation problems. Implicit methods require constly large-matrix operations. Therefore, convergence is important for improving computational efficiency. When the radial influence function is utilized in the nonlocal integral equation, the fractional Laplacian integral equation is obtained. It has been mathematically proved that the condition number of the system matrix is affected by the order of the radial influence function and nonlocal horizon size. We formulate the static crack problem with peridynamics and utilize Newton-Raphson methods with a preconditioned conjugate gradient scheme to solve this nonlinear stationary system. The convergence behavior and the computational time for solving the implicit algebraic system have been studied with respect to the order of the radial influence function and nonlocal horizon size.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.581-592
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• 1999

Let M be a properly immersed timelike hypersurface of $\overline{M}$. If M is a diagonal type, M satisfies the generic condition under the certain conditions of the eigenvalues of the shape operator. Moreover, applying them to Raychaudhuri equation, we can show that M satisfies the generic condition. Thus, by these results, we establish the singularity theorem for M in $\overline{M}$.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.383-395
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• 2016

The convergence rate of a numerical procedure based on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [8], one formulated the twolayer multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. Two-dimensional implementation was presented in [10]. In this paper, we present an implementation for threedimensional problem.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.33-44
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• 2015

The convergence rate of a numerical procedure based on Schwarz Alternating Method(SAM) for solving elliptic boundary value problems depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that the Robin condition (mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. In [7], one formulated the multi-parameterized SAM and determined the optimal values of the multi-parameters to produce the best convergence rate for one-dimensional elliptic boundary value problems. Two-dimensional implementation was presented in [8]. In this paper, we present an implementation for three-dimensional problem.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.10
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• pp.740-747
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• 1988

This paper describes the parameter convergence property for an adaptive identifier and deals with the stability of the adaptive system in terms of the general error model. The Persistent Excitation (PE) condition to guarantee parameter convergence is derived using the Power Spectrum Analysis. In the adaptive identifier designed under the assumptions that the plant has not unmodelled dynamics, it can be shown that the equilibrium points of adjustable parameters are independent on the position or the number of input spectrums, if the adaptive signal is PE. When the plant contains unmodelled dynamics and the same controller is used, the PE condition can still hold but the parameter tuned values are changed with the spectrum.