• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.429-440
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• 2006

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-105
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• 2004

In this paper we will consider the weighted composition operators W = $uC_{\tau}$ between $L^{p}$$(X,\sum,\mu$) spaces and Orlicz spaces $L^{\phi}$$(X,\sum,\mu$) generated by measurable and non-singular transformations $\tau$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\tau$ that induce weighted composition operators between $L^{p}$ -spaces by using some properties of conditional expectation operator, pair (u,${\gamma}$) and the measure space $(X,\sum,\mu$). Also, some other properties of these types of operators will be investigated.

• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.40-42
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• 2017

In this note, we study a generalization of a certain polynomial $z^n-{\sum\limits_{k=0}^{n-1}}a_kz^k$, where $\sum\limits_{k=0}^{n-1}a_k=1$, $a_k{\geq}0$ for each k, whose all zeros except for z=1 lie on the circle of radius 1/2 with center at the origin.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.949-957
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• 2005

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.7
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• pp.36-44
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• 2010

When multi-user MIMO (Multiple-Input Multiple-Output) systems utilize a sum-rate maximization (SRM) scheduler, the throughput of the systems can be enhanced. However, fairness problems may arise because users located near cell edge or experiencing poor channel conditions are less likely to be selected by the SRM scheduler. In this paper, a weighted sum-rate maximization (WSRM) scheduler is used to enhance the fairness performance of the MIMO systems. Closed-form expressions for the optimal transmit power allocation of WSRM and corresponding weighted sum-rate (WSR) are derived in the 6-sector collaborative transmission system. Using the derived results, we propose an algorithm which searches the optimal power allocation for WSRM in the 3-sector collaborative transmission system. Based on the derived closed-form expressions and the proposed algorithm, we perform computer simulations to compare performance of the WSRM scheduler and the SRM scheduler with respect to the sum-rate and the log-sum-of-average rates. We further verify that the WSRM scheduler efficiently improves fairness performance by showing the enhanced performance of average transmission rates in low percentile region.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.1-13
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• 2022

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.3
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• pp.395-402
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• 2009

This paper presents the newly developed Pareto-based multi-objective Bees Algorithm with weighted sum technique for solving a power system multi-objective nonlinear optimization problem. Specifically, the Pareto-based Bees Algorithm with memorized zone has been developed to alleviate both difficulties from classical techniques and intelligent techniques for multi-objective problems (MOP) and successfully applied to an Environmental/Economic (electric power) dispatch (EED) problem. This multi-objective Bees Algorithm has been examined and applied to the standard IEEE 30-bus six-generator test system. Simulation results have been compared to those obtained using other approaches. The comparison shows the potential and effectiveness of the proposed Bees Algorithm for solving the multi-objective EED problem.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.618-627
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• 2022

On the setting of the orthogonal complement of the weighted Bergman space, we study the problem of when a finite sum of dual Toeplitz products is compact or zero. Our results extend several known results on the unweighted space to the weighted spaces.

• Environmental and Resource Economics Review
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• v.9 no.3
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• pp.461-487
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• 2000

Kang et al. (1999) computed a composite environmental index in Korea by practicing the survey for environmental experts. They used the weighted sum form among feasible aggregation forms. In this study, we carry out the survey for both experts and non-experts to see the degree of differences of the weights for nine types of environmental problems between two groups. In addition, we apply different aggregation forms such as linear sum, weighted sum, root-sum-power, root-mean-square forms and compare these four outcomes. We found no significant discrepancy in the trends of composite indices. In case we rely on the weights provided by the experts, the composite index, on average, has been increased annually by about 7.2% over the 1986~1997 period, which informs us that overall environmental quality in 1997 has been worse than in 1986 by about 1.8 times.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.33-41
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• 2014

Ko(2013, JIA 2013:473) discussed complete convergence for weighted sum of martingale difference field when all indices have the same powers in the normalization. In this paper we generalize this law to the case where different indices have different powers in the normalization.