• Communications for Statistical Applications and Methods
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• 제13권2호
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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.

• 대한수학회지
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• 제41권1호
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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.

• 통합자연과학논문집
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• 제10권1호
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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.

• 대한수학회지
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• 제42권5호
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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.

• 대한전자공학회논문지TC
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• 제47권7호
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• pp.36-44
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• 2010

다중 사용자 MIMO (multiple-input multiple-output) 시스템에서 사용자의 합 전송률을 최대화시키는 SRM (sum-rate maximization) 스케쥴러를 적용하는 경우, 셀 경계에 위치하거나 채널 환경이 좋지 않은 사용자는 선택받지 못하게 되는 공평성 문제를 발생시킬 수 있다. 본 논문에서는 사용자 간의 공평성을 향상시키기 위해 각 사용자 별 평균 전송률의 가중치를 고려한 합 전송률을 최대화하는 WSRM (weighted sum-rate maximization) 스케쥴러를 사용한다. 이를 활용하여 6-섹터 협력전송 시스템에서 WSRM을 위한 최적 전송 전력과 시스템의 WSR (weighted sum-rate)의 닫힌 형태 표현 수식을 유도하며, 유도한 수식을 기반으로 3-섹터 협력 전송 시스템에서 WSRM을 위한 최적 전송 전력을 찾는 알고리듬을 제안한다. 닫힌 형태 표현으로 유도한 수식과 제안한 알고리듬를 바탕으로 컴퓨터 시뮬레이션을 통해 분산 MIMO 시스템에서 SRM 스케쥴러와 WSRM 스케쥴러의 합 전송률 및 평균 전송률의 로그 합 성능을 비교한다. 또한 WSRM 스케쥴러 방식이 하위 사용자 성능을 향상시킴을 보임으로써 사용자 간의 공평성 문제를 개선할 수 있는 방식임을 검증한다.

• 대한수학회보
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• 제59권1호
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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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• 제33권3호
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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.

• 호남수학학술지
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• 제44권4호
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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.

• 자원ㆍ환경경제연구
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• 제9권3호
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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.

• 호남수학학술지
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• 제36권1호
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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.