• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.31-46
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• 1997

Let $X_{t}$ = .beta. $X_{{t-1}}$ + .epsilon.$_{t}$ be an autoregressive process where $\mid$.beta.$\mid$ < 1 and {.epsilon.$_{t}$} is independent and identically distriubted with regularly varying tail probabilities. This process is called the asymptotically stationary first-order autoregressive process (AR(1)) with infinite variance. In this paper, we obtain a host of weak convergences of some point processes based on bootstrapping of { $X_{t}$}. These kinds of results can be generalized under the infinite variance assumption to ensure the asymptotic validity of the bootstrap method for various functionals of { $X_{t}$} such as partial sums, sample covariance and sample correlation functions, etc.ions, etc.

• 대한수학회논문집
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• 제26권1호
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

• East Asian mathematical journal
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• 제36권1호
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• pp.25-34
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• 2020

The classical limit theorems like strong law of large numbers, central limit theorems and law of iterated logarithms are fundamental theories in probability and statistics. These limit theorems are proved under additivity of probabilities and expectations. In this paper, we investigate strong law of large numbers under sub-linear expectation which generalize the classical ones. We give strong law of large numbers under sub-linear expectation with respect to the partial sums and some conditions similar to Petrov's. It is an extension of the classical Chung type strong law of large numbers of Jardas et al.'s result. As an application, we obtain Chung's strong law of large number and Marcinkiewicz's strong law of large number for independent and identically distributed random variables under the sub-linear expectation. Here the sub-linear expectation and its related capacity are not additive.

• 통합자연과학논문집
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• 제1권3호
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• pp.216-220
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• 2008

In general the Banach space $L^1(T^1)$ doesn't admit convergence in norm. Thus the convergence in norm of the partial sums can not be characterized in terms of Fourier coefficients without additional assumptions about the sequence$\{^{\^}f(\xi)\}$. The problem of $L^1(T^1)$-convergence consists of finding the properties of Fourier coefficients such that the necessary and sufficient condition for (1.2) and (1.3). This paper showed that let $\{{\alpha}_{\kappa}\}{\in}BV$ and ${\xi}{\Delta}a_{\xi}=o(1),\;{\xi}{\rightarrow}{\infty}$. Then (1.1) is a Fourier series if and only if $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• 대한수학회지
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• 제43권3호
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• pp.529-538
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• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.49-54
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• 2002

For arbitrary random variables {$X_{n},n{\geq}1$}, the order of growth of the series. $S_{n}\;=\;{\sum}_{j=1}^n\;X_{j}$ is studied in this paper. More specifically, when the series S_{n}$ diverges almost surely, the strong law of large numbers $S_{n}/g_{n}^{-1}$($A_{n}{\psi}(A_{n}))\;{\rightarrow}\;0$ a.s. is constructed by extending the results of Petrov (1973). On the other hand, if the series $S_{n}$ converges almost surely to a random variable S, then the tail series $T_{n}\;=\;S\;-\;S_{n-1}\;=\;{\sum}_{j=n}^{\infty}\;X_{j}$ is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series $S_{n}$, a tail series strong law of large numbers $T_{n}/g_{n}^{-1}(B_{n}{\psi}^{\ast}(B_{n}^{-1}))\;{\rightarrow}\;0$ a.s., which generalizes the result of Klesov (1984), is also established by investigating the duality between the limiting behavior of partial sums and that of tail series. In particular, an example is provided showing that the current work can prevail despite the fact that previous tail series strong law of large numbers does not work.

• Bulletin of the Korean Chemical Society
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• 제25권7호
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• pp.1061-1064
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• 2004

Molecular visualization software has the common objective of manipulation and interpretation of data from numerical simulations. They visualize many complicated molecular structures with personal computer and workstation, to help analyze a large quantity of data produced by various computational methods. However, users are often discouraged from using these tools for visualization and analysis due to the difficult and complicated user interface. In this regard, we have developed an easy-to-use three-dimensional molecular visualization and analysis program named POSMOL. This has been developed on the Microsoft Windows platform for the easy and convenient user environment, as a compact program which reads outputs from various computational chemistry software without editing or changing data. The program animates vibration modes which are needed for locating minima and transition states in computational chemistry, draws two and three dimensional (2D and 3D) views of molecular orbitals (including their atomic orbital components and these partial sums) together with molecular systems, measures various geometrical parameters, and edits molecules and molecular structures.

• 한국정보과학회논문지:소프트웨어및응용
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• 제37권10호
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• pp.745-750
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• 2010

다양한 수식을 포함하는 수학 문서들을 효과적으로 검색하기 위해서는 수식 인지 검색 엔진이 필요하다. 본 논문에서는 구조적으로 유사한 수식들을 효과적으로 찾아주는 수식 검색 시스템을 제안한다. 제안 시스템은 MathML 수식들을 연산자, 변수, 그리고 수식 구조와 같은 3가지 형태의 이질적 색인어로 분리하고 독립적으로 색인한다. 사용자가 MathML 수식을 입력하면 제안 시스템은 이질적인 색인어들을 위한 3가지 언어모델들의 가중치 합을 이용하여 수식들을 검색하고 순위화한다. 244,824개의 MathML 수식을 대상으로 한 실험에서 제안 시스템은 비공개 테스트에서 53%의 1순위 정확률, 공개 테스트에서 63%의 1순위 정확률을 보였다.

• 전기전자학회논문지
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• 제24권3호
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• pp.895-900
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• 2020

본 논문에서 BSPE는 전력이 많이 소모되는 기존의 곱셈 알고리즘을 대체했다. Bit-serial Multiplier를 이용해 하드웨어 자원을 줄였으며, 메모리 사용량을 줄이기 위해 가변적인 정수 형태의 데이터를 사용한다. 또한, 부분 합을 더하는 MOA(Multi Operand Adder)에 LOA(Lower-part OR Approximation)를 적용해서 MOA의 자원 사용량 및 전력사용량을 줄였다. 따라서 기존 MBS(Multiplication by Barrel Shifter)보다 하드웨어 자원과 전력이 각각 44%와 42%가 감소했다. 또한, BSPE Core를 위한 hardware architecture design을 제안한다.

• 한국정보처리학회논문지
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• 제7권1호
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• pp.266-272
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• 2000

제곱 테이블을 이용한 곱셈 방법은 처리과정을 간단히 하고 속도도 향상시킨다. 그러나, 비트 길이가 증가함에 따라 테이블 크기는 지수 승으로 증가하게 된다. 최근에 Wey와 Shieh는 고속 곱셈이 요구되는 응용분야에 적합한 폴딩 기법을 이용한 우수한 제곱 발생기를 제안하였다. 이 기법은 ROM 주소에 대한 1의 보수 값을 이용하여 제곱 값을 위한 거대한 테이블을 계속 폴딩함으로써 필요한 테이블의 크기를 작게 만들어 ROM의 크기를 줄일 수 있도록 한다. 본 논문에서는 Wey와 Shieh의 기법에서 1의 보수 부분이 필요 없는 개선된 폴딩 기법을 제안한다. 그리고 제안된 방법은 중간 과정에서 필요한 부분 합의 비트 길이를 줄임으로써 하드웨어 구현을 쉽게 하고 성능을 더욱 향상시킨다.