• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.191-204
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• 2017

A new fifth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary differential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge-Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge-Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specified very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.

• Research in Mathematical Education
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• v.18 no.1
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• pp.31-40
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• 2014

Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.3
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• pp.434-440
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• 2010

In this paper, we define generalized induced linguistic aggregation operator called generalized induced linguistic ordered weighted harmonic mean(GILOWHM) operator. Each object processed by this operator consists of three components, where the first component represents the importance degree or character of the second component, and the second component isused to induce an ordering, through the first component, over the third components which are linguistic variables and then aggregated. It is shown that the induced linguistic ordered weighted harmonic mean(ILOWHM) operator and linguistic ordered weighted harmonic mean(LOWHM) operator are the special cases of the GILOWHM operator. Based on the GILOWHM and LWHM operators, we develop an approach to group decision making with linguistic preference relations. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.2
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• pp.186-200
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• 2010

In order to render global illumination realistically, we need to accurately compute the direct and indirect illumination that represents the light information incoming through complex light paths. In this process, the indirect illumination at given point is greatly affected by surrounding geometries. Harmonic mean distance is a mathematical tool which is often used as a metric indicating the distance from a surface point to its visible objects in 3D space, and plays a key role in such advanced global illumination algorithms as irradiance/radiance caching and ambient occlusion. In this paper, we analyze the accuracy of harmonic mean distance estimated against various environments in the final gathering and photon mapping methods. Based on the experimental results, we discuss our experiences and future directions that may help develop an effective harmonic mean distance computation method in the future.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.481-484
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• 2003

We will show that if U is a Bergman ball E($\alpha;\;\delta$) in $B_n\;\subset\;{\mathbb{C}_n}$ and if U has M-harmonic volume mean value property at a for all M-harmonic functions f on $\={U} $, then U must be a ball centered at the origin with $\alpha\;=\;0$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.559-572
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• 2021

It is well known that every invariant harmonic function on the unit ball of the multi-dimensional complex space has the volume version of the invariant mean value property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space. Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space. In this paper we obtain the half-space analogues of the results of Liu and Shi.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.541-553
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• 2012

In this paper, we study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain on the generalized gambling system indexed by a tree by constructing a nonnegative martingale. As corollary, we obtain the property of the harmonic mean and the arithmetic mean of random transition probability for a second-order nonhomogeneous Markov chain indexed by a double root tree.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.4
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• pp.1961-1974
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• 2019

In this letter, a harmonic-mean-based dual-antenna selection scheme at relay node is proposed in two-way relaying networks (TWRNs). With well-designed distributed orthogonal concatenated Alamouti space-time block code (STBC), a dual-antenna selection problem based on the instantaneous achievable sum-rate criterion is formulated. We propose a low-complexity selection algorithm based on the harmonic-mean criterion with linearly complexity $O(N_R)$ rather than the directly exhaustive search with complexity $O(N^2_R)$. From the analysis of network outage performance, we show that the asymptotic diversity gain function of the proposed scheme achieves as $1/{\rho}{^{N_R-1}}$, which demonstrates one degree loss of diversity order compared with the full diversity. This slight performance gap is mainly caused by sacrificing some dual-antenna selection freedom to reduce the algorithm complexity. In addition, our proposed scheme can obtain an extra coding gain because of the combination of the well-designed orthogonal concatenated Alamouti STBC and the corresponding dual-antenna selection algorithm. Compared with the common-used selection algorithms in the state of the art, the proposed scheme can achieve the best performance, which is validated by numerical simulations.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.521-533
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• 2019

In this paper, we define a mean of two positive numbers called the k-golden mean and study some properties of it. Especially, we show that the 2-golden mean refines the harmonic and the geometric means. As an application, we define the k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

• Proceedings of the KIEE Conference
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• 2005.07a
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• pp.214-216
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• 2005

A magnitude of generated harmonic currents along with the operation of traction has nonlinear characteristics. The harmonic currents generated along with the operating speed of electrical railroad traction is to analyze very difficulty. This paper therefore presents probabilistic approach for the harmonic currents evaluation about the operating speed of the arbitrary single traction. To use probabilistic method for railroad system, probability density function(PDF) using measuring data based on the realistic harmonic currents per operating speed is calculated. Mean and variance of harmonic currents of single traction also are obtained the PDF of the operating speed and electrical railroad traction model. Uncertainty of harmonic currents expects to results through mean and variance with PDF. The probability of harmonic currents generated with the operating of arbitrary many tractions is calculated by the convolution of functions. The harmonics of different number of tractions are systematically investigated. It is assessed by the total demand distortion(TDD) for the railroad system.