• 충청수학회지
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• 제22권3호
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• pp.507-517
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• 2009

We prove a functional central limit theorem for a linear random field generated by negatively associated multi-dimensional random variables. Under finite second moment condition we extend the result in Kim, Ko and Choi[Kim,T.S, Ko,M.H and Choi, Y.K.,2008. The invariance principle for linear multi-parameter stochastic processes generated by associated fields. Statist. Probab. Lett. 78, 3298-3303] to the negatively associated case.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.959-967
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• 2008

In this paper we show the weak convergence of the linear random(multistochastic process) field generated by identically distributed 2-parameter array of associated random variables. Our result extends the result in Newman and Wright (1982) to the linear 2-parameter processes as well as the result in Kim and Ko (2003) to the 2-parameter case.

• 호남수학학술지
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• 제33권4호
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• pp.591-602
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• 2011

In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on $\mathbb{Z}^2$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권2호
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• pp.714-727
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• 2015

The hierarchical structure in networks is widely applied in many practical scenarios especially in some emergency cases. In this paper, we focus on a tree network with and without packet loss where one source sends data to n destinations, through m relay nodes employing random linear network coding (RLNC) over a Galois field in parallel transmission systems. We derive closed-form probability expressions of successful decoding at a destination node and at all destination nodes in this multicast scenario. For the convenience of computing, we also propose an upper bound for the failure probability. We then investigate the impact of the major parameters, i.e., the size of finite fields, the number of internal nodes, the number of sink nodes and the channel failure probability, on the decoding performance with simulation results. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized. When failure decoding probabilities are given, the operation is simple and its complexity is low in a small finite field.

• 한국통신학회논문지
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• 제40권9호
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• pp.1786-1792
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• 2015

랜덤 선형 네트워크 코딩(Random Linear Network Coding, RLNC)은 멀티캐스트의 신뢰성을 높이는 방법으로 널리 사용되고 있다. RLNC 구현에 있어서 효율적인 연산을 위해 Galois Field (GF)를 사용한다. 상용 컴퓨터에서의 연산을 고려하였을 때 GF($2^m$)의 크기 m이 32보다 작을 경우, 곱셈과 나눗셈에 대해 사전에 계산된 table을 사용하면 모든 사칙 연산이 m에 관계없이 상수 복잡도를 가진다. 이로부터 RLNC의 연산 복잡도는 m에 반비례하는 것을 보인다. 추가적으로, m이 커짐에 따라 발생하는 헤더 길이 증가, 메모리 사용량 증가 등의 추가적인 오버헤드를 고려하여 실용적인 GF의 크기를 선택한다. 이를 바탕으로 상용 컴퓨터에 RLNC를 구현하고 곱셈/나눗셈 연산 시에 사용되는 table의 종류와 한 번에 인코딩 되는 원본 패킷의 개수에 따른 성능을 실측한다.

• Journal of the Korean Statistical Society
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• 제11권2호
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• pp.118-130
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• 1982

Random walks as specia Markov stochastic processes have received particular attention in recent years. Not only the applicability of the theory already developed but also its extension within the frame work of probability measures on algebraic-topological structures such as semigroups, groups and linear spaces became a new challenge for research work in the field. At the same time new insights into classical problems were obtained which in various cases lead to a more efficient presentation of the subject. Consequently the teaching of random walks at all levels should profit from the recent development.

• 한국연소학회:학술대회논문집
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• 한국연소학회 2004년도 제28회 KOSCO SYMPOSIUM 논문집
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• pp.133-137
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• 2004

The present study is focused on the small scale turbulent mixing processes in the scalar field. In order to deal with molecular mixing in turbulent flow, the linear eddy model is addressed. In each realization, the molecular mixing term is implemented deterministically, and turbulent stirring is represented by a sequence of instantaneous, statistically independent rearrangement event called by triplet map. The LEM approach is applied with relatively simple conditions. The characteristics of scalar mixing and PDF profiles are addressed in detail.

• 호남수학학술지
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• 제31권4호
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• pp.505-513
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• 2009

Let {$X_k;k{\in}N^d$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $p{\alpha}$ > 1 and ${\alpha}$ > ${\frac{1}{2}}$ $E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})$ < ${\infty}$ if and only if ${\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P$($max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}$ > ${\epsilon}{\mid}n{\mid}$) < ${\infty}$ for all ${\epsilon}$ > 0, where log$^+$x = max{1,log x}.

• 한국수학사학회지
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• 제29권6호
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• pp.353-363
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• 2016

In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.

• Structural Engineering and Mechanics
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• 제3권3호
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• pp.273-287
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• 1995

Stochastic response of systems to random excitation can be estimated by direct integration methods in the time domain such as the stochastic central difference method (SCDM). In this paper, the SCDM is applied to compute the variance and covariance in response of linear and nonlinear structures subjected to random excitation. The accuracy of the SCDM is assessed using two-DOF systems with both deterministic and random material properties excited by white noise. For the former case, closed-form solutions can be obtained. Numerical results also are presented for a simply supported geometrically nonlinear beam. The stiffness of this beam is modeled as a random field, and the beam is idealized by the stochastic finite element method. A perturbation technique is applied to formulate the equations of motion of the system, and the dynamic structural response statistics are obtained in a time domain analysis. The effect of variations in structural parameters and the numerical stability of the SCDM also are examined.