• 대한수학회논문집
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• 제14권3호
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• pp.581-595
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• 1999

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

• 대한수학회보
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• 제47권1호
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• Journal of the Korean Data and Information Science Society
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• 제28권6호
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• 대한수학회보
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• 제32권2호
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• pp.221-231
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• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• 전자공학회논문지C
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• 제34C권11호
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• pp.95-103
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• 1997

A robust center estimation tecnique of n-fold engineering parts is presented, which use self-organizing neural networks with generating and merging learning for training neural units. To estimate the center of the n-fold engineering parts using neural networks, the segmented boundaries of the interested part are approximated to strainght lines, and the temporal estimated centers by thecosine theorem which formed between the approximaged straight line and the reference point, , are indexed as (.sigma.-.theta.) parameteric vecstors. Then the entries of parametric vectors are fed into self-organizing nerual network. Finally, the center of the n-fold part is extracted by mean of generating and merging learning of the neurons. To accelerate the learning process, neural network uses an adaptive learning rate function to the merging process and a self-adjusting activation to generating process. Simulation results show that the centers of n-fold engineering parts are effectively estimated by proposed technique, though not knowing the error distribution of estimated centers and having less information of boundaries.

• 한국멀티미디어학회논문지
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• 제10권10호
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• pp.1328-1337
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• 2007

본 논문에서는 P2P 네트워크에서 피어들 간에 멀티미디어 콘텐츠의 특정 구간을 구간정보를 이용하여 효율적으로 스트리밍 하는 방법에 대하여 논한다. 피어들은 콘텐츠의 관심 있는 부분만을 쉽고 편리하게 추출하려는 경향이 있기 때문에 멀티미디어 콘텐츠에서 구간정보를 색인한 파일을 만들어 검색서버에 등록한 후 피어들의 요청이 있을 때 이 구간정보를 이용하여 필요한 부분만을 스트리밍 서비스할 수 있도록 한다. 이를 위하여 피어의 PC가 필요에 따라 서버 기능을 할 수 있도록 기능을 구현하고, 검색서버에서 제공되는 구간정보에 따라 해당하는 피어가 구간별로 콘텐츠를 스트리밍 한다. 본 논문에서 제안한 스트리밍 방식의 평가는 스트리밍 요청 후 재생되는 시점까지의 최초전송지연시간에 초점을 맞추었으며, 동일 조건에서 기존의 스트리밍 방식과 비교하여 낮은 수치를 보여주고 있다.