• Journal of the Korean Statistical Society
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• v.26 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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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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• v.36 no.1
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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.

• Journal of Integrative Natural Science
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• v.1 no.3
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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 $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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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 $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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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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• v.25 no.7
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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.

• Journal of KIISE:Software and Applications
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• v.37 no.10
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• pp.745-750
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• 2010

To effectively retrieve mathematical documents including various equations, mathaware search engines are needed. In this paper, we propose a equation retrieval system which helps users effectively search structurally similar equations. The proposed system disassembles MathML equations into three types of heterogeneous indexing terms; operators, variables, and partial structures of equations. Then, it independently indexes the disassembled terms. When a user inputs a MathML equation, the proposed system searches and ranks equations using weighted sums of three language models for the heterogeneous indexing terms. In the experiments with 244,744 MathML equations, three proposed system showed reliable performances (a P@1 of 53% in the closed test and a P@1 of 63% in the open test).

• Journal of IKEEE
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• v.24 no.3
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• pp.895-900
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• 2020

In this paper, BSPE replaced the existing multiplication algorithm that consumes a lot of power. Hardware resources are reduced by using a bit-serial multiplier, and variable integer data is used to reduce memory usage. In addition, MOA resource usage and power usage were reduced by applying LOA (Lower-part OR Approximation) to MOA (Multi Operand Adder) used to add partial sums. Therefore, compared to the existing MBS (Multiplication by Barrel Shifter), hardware resource reduction of 44% and power consumption of 42% were reduced. Also, we propose a hardware architecture design for BSPE Core.

• The Transactions of the Korea Information Processing Society
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• v.7 no.1
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• pp.266-272
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• 2000

The square-based multiplication using look-up table simplifies the process and speeds-up the operating speed. However, the look-up table size increases exponentially as bit size increases. Recently, Wey and Shieh introduced a noble design of square generator circuit using a folding approach for high-speed performance applications. The design uses the ones complement values of ROM addresses to fold the huge look-up ROM table repeatedly such that a much smaller table can be sufficient to store the squares. We present new folding techniques that do not require a ones complement part, one of three major parts in the Wey and Shiehs method. Also the proposed techniques reduce the bit size of partial sums such that the hardware implementation be simplified and the performance be enhanced.