• 충청수학회지
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• 제30권1호
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• pp.103-116
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• 2017

In this paper, we show that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have asymptotic property by imposing conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y).

• 대한수학회지
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• 제51권4호
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• pp.837-851
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• 2014

We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.535-543
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• 2003

A ranked set sample version of the sign test is proposed for testing hypotheses concerning the quantiles of a population characteristic by Kaur, et. al(2002). In this paper, we proposed the ranked set sample Wilcoxon signed rank test for quantiles under equal allocation. We obtain the asymptotic property and the asymptotic relative efficiencies of the proposed test statistic with respect to Wilcoxon signed rank test of simple random sample for quantiles under equal allocation. We calculate the ARE of test statistics, the proposed test statistic is more efficient than simple random sampling for all quantiles. The relative advantage of ranked set sampling is greatest at the median and tapers off in the tails.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.563-573
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• 2000

In this thesis, we propose the test statistic for ordered alternatives on c-sample ranked set samples(RSS). The proposed test statistic JRSS is Jonckheere type statistic using the median of the i-th samples in each cycle. We obtained the asymptotic property of the proposed test statistic and the asymptotic relative efficiencies of the proposed test statistic with respect to J SRS which Jonckheere type statistic on simple random samples(SRS). From the simulation works, J RSS is superior to J SRS. We compared the empirical powers of J RSS with respect to U RSS on ranked set sample and U SRS on simple random sample using all samples, which are proposed by Kim, Kim and Lee(1999). The powers of J RSS are nearly the same values when entire sample size is large. J RSS is superior to U RSS. J RSS is simpler than U RSSon calculating process.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.395-406
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• 2001

In this paper, we propose the test statistic for the umbrella alternatives on c-samples ranked set samples(RSS), where the peak of the umbrella is known. We obtain the asymptotic property of the proposed test statistic and the asymptotic relative efficiencies of the proposed test statistic with respect to U-statistic based on simple random samples(SRS). From the simulation work, we compare the empirical powers of the proposed test statistic with U-statistic based on SRS.

• International Journal of Reliability and Applications
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• 제6권1호
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• pp.1-12
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• 2005

A new test for testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential is presented based on the highly popular 'Kernel methods' of curve fitting. This new procedure is competitive with old one in the sense of Pitman's asymptotic relative efficiency, easy to compute and does not depend on the choice of either the band width or kernel. It also enjoys good power.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.345-355
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• 2018

This paper looks into phase plane behavior of the solution near the positive steady-state for the system with prey density dependent response functions. The positive invariance and boundedness property of the solution to the objective model are proved. The existence result of a positive steady-state and asymptotic analysis near the positive constant equilibrium for the objective system are of interest. The results of phase plane analysis for the system are proved by observing the asymptotic properties of the solutions. Also some numerical analysis results for the behaviors of the solutions in time are provided.

• Journal of Communications and Networks
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• 제1권3호
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• pp.182-188
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• 1999

The optimal joint maximum-likelihood sequence estima-for using an array of antennas is derived for synchronous direct sequence-code division multiple access (DS-CDMA) system. Each user employs a rate 1/n convolutional code for channel coding for the additive white Gaussian noise (AWGN) channel. The array re-ceiver structure is composed of beamformers in the users' direc-tions followed by a bank of matched filters. The decoder is imple-mented using a Viterbi algorithm whose states depend on the num-ber of users and the constraint length of the convolutional code. The asymptotic array multiuser coding gain(AAMCG)is defined to encompass the asymptotic multiuser coding gain and the spatial information on users' locations in the system. We derive the upper and lower bounds of the AAMCG. As an example, the upper and lower bounds of AAMCG are obtained for the two user case where each user employes the maximum free distance convolutional code with rate 1/2. The enar-far resistance property is also investigated considering the number of antenna elements and user separations in the space.

• 대한수학회지
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• 제61권2호
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• pp.395-408
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• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• 충청수학회지
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• 제29권4호
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• pp.651-655
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• 2016

In this paper, we show that if a quasi-Anosov diffeomorphism has the various types of shadowing property then it is Anosov.