• 대한전기학회논문지:시스템및제어부문D
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• 제54권1호
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• pp.40-47
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• 2005

This paper concerns on Filtered-x least mean square (FXLMS) algorithm for adaptive estimation of feedforward control parameters. The conditions for convergence in ensemble mean of the FXLMS algorithm are derived and the directional convergence properties are discussed from a new geometric vector analysis. The convergence and its directionality are verified along with some computer simulations.

• 대한수학회보
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• 제58권6호
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• pp.1419-1443
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• 2021

The asymmetric Laplace distribution arises as a limiting distribution of geometric summations of independent and identically distributed random variables with finite second moments. The main purpose of this paper is to study the weak limit theorems for geometric summations of independent (not necessarily identically distributed) random variables together with convergence rates to asymmetric Laplace distributions. Using Trotter-operator method, the orders of approximations of the distributions of geometric summations by the asymmetric Laplace distributions are established in term of the "large-𝒪" and "small-o" approximation estimates. The obtained results are extensions of some known ones.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.49-57
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• 2003

In this paper, we give some sufficient conditions for convergence of geometric mean for T-related fuzzy numbers where T is an Archimedean t-norm under some mild restrictions. These results generalize earlier results of Hong and Lee [Fuzzy Sets and Systems 116 (2000) 263-267].

• 대한수학회보
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• 제55권4호
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• pp.1241-1261
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• 2018

We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order H which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.

• 대한수학회보
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• 제57권5호
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• pp.1115-1126
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• 2020

The main purpose of this paper is to establish the rates of convergence in weak limit theorems for normalized geometric sums of independent identically distributed random variables via Zolotarev's probability metric.

• 응용통계연구
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• 제22권6호
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• pp.1277-1287
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• 2009

For stratifying skewed populations, the Lavall$\acute{e}$e-Hidiroglou(LH) algorithm is often considered to have a take-all stratum with the largest units and some take-some strata with the middle-size and small units. Related to its iterative nature have been reported some numerical difficulties such as the dependency of the ultimate stratum boundaries to a choice of initial boundaries and the slow convergence to locally-optimum boundaries. The geometric stratification has been recently proposed to provide initial boundaries that can avoid such numerical difficulties in implementing the LH algorithm. Since the geometric stratification does not pursuit the optimization but the equalization of the stratum CVs, the corresponding stratum boundaries may not be (near) optimal. This paper revisits these issues concerning convergence and near-optimality of optimal stratification algorithms using artificial numerical examples. We also discuss the formation of the strata and the sample allocation under the optimization process and some aspects related to discontinuity arisen from the finiteness of both population and sample as well.

• ETRI Journal
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• 제30권6호
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• pp.774-782
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• 2008

An operational orbit determination (OD) and prediction system for the geostationary Communication, Ocean, and Meteorological Satellite (COMS) mission requires accurate satellite positioning knowledge to accomplish image navigation registration on the ground. Ranging and tracking data from a single ground station is used for COMS OD in normal operation. However, the orbital longitude of the COMS is so close to that of satellite tracking sites that geometric singularity affects observability. A method to solve the azimuth bias of a single station in singularity is to periodically apply an estimated azimuth bias using the ranging and tracking data of two stations. Velocity increments of a wheel off-loading maneuver which is performed twice a day are fixed by planned values without considering maneuver efficiency during OD. Using only single-station data with the correction of the azimuth bias, OD can achieve three-sigma position accuracy on the order of 1.5 km root-sum-square.

• 한국멀티미디어학회논문지
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• 제20권8호
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• pp.1312-1320
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• 2017

Recently, vector map data is developed and used in many domains widely. In the most cases, vector map data contains confidential information which must be kept away from unauthorized users. Moreover, the production process of vector maps is considerably complex and consumes a lot of money and human resources. Therefore, the secured storage and transmission are necessary to prevent the illegal copying and distribution from hacker. This paper presents a selective encryption algorithm using geometric objects in frequency domain for vector map data. In the proposed algorithm, polyline and polygon data in vector map is the target of the selective encryption process. Experimental results verified that proposed algorithm is effectively and adaptive the requirements of security.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.983-994
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• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• 대한수학회논문집
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• 제34권3호
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• pp.1029-1047
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• 2019

We are interested in the problem of determining the best fitted circle to a set of data points in space. This can be usually obtained by minimizing the geometric distances or various approximate algebraic distances from the fitted circle to the given data points. In this paper, we propose an algorithm in such a way that the sum of the squares of the geometric distances is minimized in ${\mathbb{R}}^3$. Our algorithm is mainly based on the steepest descent method with a view of ensuring the convergence of the corresponding objective function Q(u) to a local minimum. Numerical examples are given.