• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.479-495
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• 2013

Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $n$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1169-1183
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• 2008

In this paper, a method to find the weighted possibilistic variance and moments about the mean value of fuzzy numbers via applying a difuzzification using minimizer of the weighted distance between two fuzzy numbers is introduced. In this way, we obtain the nearest weighted point with respect to a fuzzy number, this main result is a new and interesting alternative justification to define of weighted mean of a fuzzy number. Considering this point and the weighted distance quantity, we introduce the weighted possibilistic mean (WPM) value and the weighted possibilistic variance(WPV) of fuzzy numbers. This paper shows that WPM is the nearest weighted point to fuzzy number and the WPV of fuzzy number is preserved more properties of variance in probability theory so that it can simply introduce the possibilistic moments about the mean of fuzzy numbers without problem. The moments of fuzzy numbers play an important role to estimate of parameters, skewness, kurtosis in many of fuzzy times series models.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.213-228
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• 2010

A weighted version of the geometric mean of k ($\geq\;3$) positive invertible operators is given. For operators $A_1,{\ldots},A_k$ and for nonnegative numbers ${\alpha}_1,\ldots,{\alpha}_k$ such that $\sum_\limits_{i=1}^k\;\alpha_i=1$, we define weighted geometric means of two types, the first type by a direct construction through symmetrization procedure, and the second type by an indirect construction through the non-weighted (or uniformly weighted) geometric mean. Both of them reduce to $A_1^{\alpha_1}{\cdots}A_k^{{\alpha}_k}$ if $A_1,{\ldots},A_k$ commute with each other. The first type does not have the property of permutation invariance, but satisfies a weaker one with respect to permutation invariance. The second type has the property of permutation invariance. We also show a reverse inequality for the arithmetic-geometric mean inequality of the weighted version.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.6
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• pp.1964-1981
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• 2014

An improved Mean-Shift (MS) tracker called joint CB-LBWH, which uses a combined weighted-histogram scheme of CBWH (Corrected Background-Weighted Histogram) and LBWH (likelihood-based Background-Weighted Histogram), is presented. Joint CB-LBWH is based on the notion that target representation employs both feature saliency and confidence to form a compound weighted histogram criterion. As the more prominent and confident features mean more significant for tracking the target, the tuned histogram by joint CB-LBWH can reduce the interference of background in target localization effectively. Comparative experimental results show that the proposed joint CB-LBWH scheme can significantly improve the efficiency and robustness of MS tracker when heavy occlusions and complex scenes exist.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.1
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• pp.97-105
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• 2015

Multiresponse optimization (MRO) seeks to find the setting of input variables, which optimizes the multiple responses simultaneously. The approach of weighted mean squared error (WMSE) minimization for MRO imposes a different weight on the squared bias and variance, which are the two components of the mean squared error (MSE). To date, a weighted sum-based method has been proposed for WMSE minimization. On the other hand, this method has a limitation in that it cannot find the most preferred solution located in a nonconvex region in objective function space. This paper proposes a Tchebycheff metric-based method to overcome the limitations of the weighted sum-based method.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.123-135
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• 2016

In this article, we introduce the transforms of Pythagorean and quadratic means of weighted shifts. We then explore how the transforms of weighted shifts behaves, in comparison with the Aluthge transform.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.189-197
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• 2019

In this paper we obtain some new inequalities for the weighted chaotically geometric mean of two positive operators on a complex Hilbert space.

• Survey Research
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• v.7 no.2
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• pp.53-69
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• 2006

Weights can be made and imposed in both sample design stage and analysis stage in a sample survey. While in design stage weights are related with sample data acquisition quantities such as sample selection probability and response rate, in analysis stage weights are connected with external quantities, for instance population quantities and some auxiliary information. The final weight is the product of all weights in both stage. In the present paper, we focus on the weight in analysis stage and investigate the effect of such weights imposed on the weighted mean when estimating the population mean. We consider a finite population with a pair of fixed survey value and weight in each unit, and suppose equal selection probability designs. Under the condition we derive the formulas of the bias as well as mean square error of the weighted mean and show that the weighted mean is biased and the direction and amount of the bias can be explained by the correlation between survey variate and weight: if the correlation coefficient is positive, then the weighted mein over-estimates the population mean, on the other hand, if negative, then under-estimates. Also the magnitude of bias is getting larger when the correlation coefficient is getting greater. In addition to theoretical derivation about the weighted mean, we conduct a simulation study to show quantities of the bias and mean square errors numerically. In the simulation, nine weights having correlation coefficient with survey variate from -0.2 to 0.6 are generated and four sample sizes from 100 to 400 are considered and then biases and mean square errors are calculated in each case. As a result, in the case or 400 sample size and 0.55 correlation coefficient, the amount or squared bias of the weighted mean occupies up to 82% among mean square error, which says the weighted mean might be biased very seriously in some cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.279-282
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• 2014

In this paper, we report a new sharp inequality of interpolation type in $\mathbb{R}^n$. This inequality is for controlling weighted average of a function via $L^n$ norm of the gradient of a function together with its' certain exponential norm.

• 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.