• Honam Mathematical Journal
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• v.30 no.3
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• pp.479-486
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• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.39-50
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• 2004

In [25] Taskinen shows that if $\{E_n\}_n\;and\;\{F_n\}_n$ are two sequences of Frechet spaces such that ($E_m,\;F_n$) has the BB-property for all m and n then (${\Pi}_m\;E_m,\;{\Pi}_n\;F_n$) also has the ΒΒ-property. Here we investigate when this result extends to (i) arbitrary products of Frechet spaces, (ii) countable products of DFN spaces, (iii) countable direct sums of Frechet nuclear spaces. We also look at topologies properties of ($H(U),\;\tau$) for U balanced open in a product of Frechet spaces and $\tau\;=\;{\tau}_o,\;{\tau}_{\omega}\;or\;{\tau}_{\delta}$.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.11
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• pp.1-8
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• 1999

In this paper, new polyphase sequences and a sequence generation method are suggested. These sequences are found to have good correlation properties. Since the suggested generation method consists only of integer sums and modular techniques, sequence generation is also easy. The performance of the sequences is investigated when used in QS-CDMA systems under frequency selective, time nonselective, slow Nakagami fading channel with additive white Gaussian noise.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.441-460
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• 2017

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\mathfrak{F}$-independent random variables sequences, the convergence of sums of $\mathfrak{F}$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.149-156
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• 1994

For an r > 2 and a finite B, $E\mid max \;1\leq k\leq n \;\sum\limits_{j=m+1}^{m+k}X_j\mid^r\leq Bn^ {\frac{r}{2}}$ (all $n\geq 1$) is obtained for a negatively associated sequence $\{X_j \;:\; j\in N\}$. We also derive the maximal inequelity for a negatively associated sequence. Stationarity is not required.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.57-72
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• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.658-662
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• 2004

This paper proposes an orthogonal reception structure for OS/SS communication with time-shifted m-sequences, and compares the performances of the proposed and conventional receiver. This structure provides two important characteristics to reference user signal with not only increment of auto-correlation value but also cancel of the cross-correlation value out to zero between the reference user and other user signals. In addition, the structure can be easily implemented with the conventional receiver adding an additional integrator path in parallel and an adder that sums the conventional path output and the new path output signal. Hence, the proposed structure can be applied for channel impulse response measurement, and efficiently used for multi-user interference signal cancellation and channel capacity increment by flexible structural inter-working operation, connection or disconnection, of the new path to conventional receiver structure.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.879-895
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• 2022

This paper establishes the Baum-Katz type theorem and the Marcinkiewicz-Zymund type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors {X, X_n, n ≥ 1} taking values in a Hilbert space H with general normalizing constants $b_n=n^{\alpha}{\tilde{L}}(n^{\alpha})$, where ${\tilde{L}}({\cdot})$ is the de Bruijn conjugate of a slowly varying function L(·). The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.