• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.351-355
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• 2019

We obtain two characterizations of uniform distribution based on ratios of upper record values by the properties of independence and identical distribution.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.4
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• pp.282-285
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• 2002

The magnitude of evanescent modes in terms of dynamics is investigated in case that the transformation of water waves is predicted using the linear wave theory. In other words, derivation is made of both the kinetic and potential wave energies of evanescent modes as welt as propagating modes. The evanescent modes consist of compound components of propagating and evanescent modes, those of identically equal evanescent modes, and those of identically different evanescent modes. The wave energy per a horizontal distance decreases exponentially with the distance.

• Journal of Communications and Networks
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• v.1 no.2
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• pp.111-117
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• 1999

Using a method recently reported in the literature for analyzing the bit error probability (BEP) performance of noncoherent Mary orthogonal signals with square-law combining in the presence of independent and identically distributed Nakagami-m faded paths, we are able to reformulate this method so as to apply to a generalized fading channel in which the fading in each path need not be identically distributed nor even distributed ac-cording to the same family of distribution. The method leads to exact expressions for the BEP in the form of a finite-range integral whose integrand involves the moment generating function of the combined signal-to-noise ratio and which can therefore be readily evaluated numerically. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the multipath intensity profile (MIP) as well as the fading correlation profile (FCP) on the BEP performance of M-ary orthogonal signal over Nakagami-m fading channels. Thses numerical results show that both MIP and FCP induce a non-negligible degradition in the BEP and have therefore to be taken into account for the accurate prediction of the performance of such systems.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.2
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• pp.134-140
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• 2011

Recent work in compressed sensing theory shows that $M{\times}N$ independent and identically distributed sensing matrix whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if $M{\ll}N$. In particular, it is well understood that the $L_1$-minimization algorithm is able to recover sparse signals from incomplete measurements. In this paper, we propose a novel sparse signal reconstruction method that is based on the reweighted $L_1$-minimization via support detection.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.829-842
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• 2009

Let {$X_{ni}|1\;{\le}\;i\;{\le}\;n$, $n\;{\ge}\;1$} be an array of rowwise negatively associated random variables and let $\alpha$ > 1/2, 0 < p < 2 ${\alpha}p\;{\ge}\;1$. In this paper we discuss $n^{{\alpha}p-2}h(n)$ max $_{1\;{\le}\;k{\le}n}\;|\;{\sum}^k_{i=1}\;X_{ni}|/n^{\alpha}\;{\to}\;0$ completely as $n\;{\to}\;{\infty}$ under not necessarily identically distributed with a suitable conditions and h(x) > 0 is a slowly varying function as $x\;{\to}\;{\infty}$. In addition, we obtained that $n^{{\alpha}p-2}h(n)$ max $_{1\;{\le}\;k{\le}n}\;|\;{\sum}^k_{i=1}\;X_{ni}|/n^{\alpha}\;{\to}\;0$ completely as $n\;{\to}\;{\infty}$ if and only if $E|X_{11}|^ph(|X_{11}|^{1/\alpha})\;<\;{\infty}$ and $EX_{11}\;=\;0$ under identically distributed case and some corollaries are obtained.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4623-4643
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• 2015

This paper considers physical-layer security protocols in multicast cognitive radio (CR) networks. In particular, we propose dual-hop cooperative decode-and-forward (DF) and randomize-and-forward (RF) schemes using partial relay selection method to enhance secrecy performance for secondary networks. In the DF protocol, the secondary relay would use same codebook with the secondary source to forward the source's signals to the secondary destination. Hence, the secondary eavesdropper can employ either maximal-ratio combining (MRC) or selection combining (SC) to combine signals received from the source and the selected relay. In RF protocol, different codebooks are used by the source and the relay to forward the source message secretly. For each scheme, we derive exact and asymptotic closed-form expressions of secrecy outage probability (SOP), non-zero secrecy capacity probability (NzSCP) in both independent and identically distributed (i.i.d.) and independent but non-identically distributed (i.n.i.d.) networks. Moreover, we also give a unified formula in an integral form for average secrecy capacity (ASC). Finally, our derivations are then validated by Monte-Carlo simulations.

• Journal of the Korean Statistical Society
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• v.10
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• pp.97-104
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• 1981

It is shown that a lattice distribution defined on a set of n lattice points $L(n,\delta) = {\delta,\delta+1,...,\delta+n-1}$ is a distribution induced from the distribution of convolution of independently and identically distributed (i.i.d.) uniform [0,1] random variables. Also the m-th moment of the lattice distribution is obtained in a quite different approach from Park and Chung (1978). It is verified that the distribution of the sum of n i.i.d. uniform [0,1] random variables is completely determined by the lattice distribution on $L(n,\delta)$ and the uniform distribution on [0,1]. The factorial mement generating function, factorial moments, and moments are also obtained.

• Journal of the Korean Statistical Society
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• v.13 no.2
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• pp.87-106
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• 1984

It ${X_t}$ is a sequence of independent identically distributed normal random variables, then the conditional probability density of $X_1, X_2, \cdots, X_n$ given the first p+1 sample autocovariances converges to the maximum entropy probability density satisfying the corresponding covariance constraints as the length of the sample sequence tends to infinity. This establishes that the maximum entropy probability density and the associated Gaussian autoregressive process arise naturally as the answers of conditional limit problems.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.269-273
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• 2013

We prove a characterization of the power function distribution by lower record values. We prove that $F(x)=(\frac{x}{a})^{\alpha}$ for all $x$, 0 < $x$ < $a$, ${\alpha}$ > 0 and $a$ > 0 if and only if $\frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ are independent for $1{\leq}m$ < $n$.