• Journal of the Korean Statistical Society
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• 제26권2호
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• pp.231-243
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• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• 대한수학회지
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• 제53권4호
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• pp.781-793
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• 2016

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• 대한수학회보
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• 제43권3호
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• pp.543-549
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• 2006

Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.

• 대한수학회보
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• 제36권2호
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• pp.273-285
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• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

• 한국멀티미디어학회논문지
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• 제23권12호
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• pp.1507-1518
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• 2020

Recently, as the proportion of the elderly population in Korea has increased rapidly, it has entered an aging society. As the scope of social activities of the elderly increases, the risk of safety accidents is also increasing. The traffic accident rate of elderly pedestrians is higher than ordinary people. Although various smart devices for the elderly are researched and developed, electronic components are often used. Electronic devices may not be able to be used if charging is not regularly. In this paper, a smart hat, a smart system for the elderly and the weak, was implemented using solar panels. The system uses solar energy to provide reliable use of smart devices. It is believed to be helpful not only for the elderly but also for the weak people by easy to wear the hat.

• 디지털융복합연구
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• 제12권5호
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• pp.69-78
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• 2014

본고의 연구는 SNG 서비스의 이용에 있어 사용자간의 약한 유대관계의 힘과 감성적 상호작용이 만족과 구전에 이르는 경로모형을 검증하고, SNS가 지닌 감성적 실명효과가 서비스 확산에 미치는 영향 및 정책적 함의를 확인하고자 하였다, 연구결과 모바일 SNG 사용자의 약한 유대관계의 힘이 사용자간의 감성적 상호작용성과 만족에 영향을 미치는 것으로 확인되었다. 또한 SNS의 감성적 실명효과로 인해 사용자들은 신뢰관계가 형성되어 약한 유대관계임에도 불구하고 감성적인 상호작용을 하는 것으로 판단된다. 그리고 구전에 영향을 미치는 변인은 선행한 유대관계나 상호작용이 아닌 만족인 것으로 나타났다. 선행변인들이 실명SNS 효과가 있지만 궁극적으로 서비스를 구전하게 하는 것은 만족이라는 요소에 의해 좌우된다는 것이다. 따라서 서비스 제공사업자들은 구전으로 전달되는 서비스의 만족을 이끌어 낼 수 있도록 고객 중심의 정책으로 SNG 서비스를 개선시키는 등의 실무적 제언이 가능 할 것으로 기대된다.

• 대한수학회지
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• 제51권5호
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• pp.955-970
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• 2014

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.763-771
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• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

• 대한수학회보
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• 제56권3호
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.