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ARITHMETICGEOMETRICHARMONIC MEAN OF THREE POSITIVE OPERATORS
, 2009
"... ABSTRACT. In this paper, we introduce the geometric mean of several positive operators defined from a simple and practical recursive algorithm. This approach allows us to construct the arithmeticgeometricharmonic mean of three positive operators which has many of the properties of the standard one ..."
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ABSTRACT. In this paper, we introduce the geometric mean of several positive operators defined from a simple and practical recursive algorithm. This approach allows us to construct the arithmeticgeometricharmonic mean of three positive operators which has many of the properties of the standard
Some Inequalities Involving Geometric and Harmonic Means
, 2016
"... Abstract Using a forwardbackward induction method, we proved that n 1+β is a lower bound of the series , where a i is a positive integer greater than 1, and β is the geometric mean from a 1 to a n . We also proved that n 1+γ is an upper bound of the series, where γ is the harmonic mean from a 1 to ..."
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Abstract Using a forwardbackward induction method, we proved that n 1+β is a lower bound of the series , where a i is a positive integer greater than 1, and β is the geometric mean from a 1 to a n . We also proved that n 1+γ is an upper bound of the series, where γ is the harmonic mean from a 1
KHarmonic Means  A Data Clustering Algorithm
, 1999
"... Data clustering is one of the common techniques used in data mining. A popular performance function for measuring goodness of data clustering is the total withincluster variance, or the total meansquare quantization error (MSE). The KMeans (KM) algorithm is a popular algorithm which attempts to f ..."
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lesser extent. In this paper, we propose a new clustering method called the KHarmonic Means algorithm (KHM). KHM is a centerbased clustering algorithm which uses the Harmonic Averages of the distances from each data point to the centers as components to its performance function. It is demonstrated
Highly Degenerate Harmonic Mean Curvature Flow
, 2006
"... Abstract. We study the evolution of a weakly convex surface Σ0 in R 3 with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the boundaries of the flat sides evolve by the curve shortening flow. It ..."
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Abstract. We study the evolution of a weakly convex surface Σ0 in R 3 with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the boundaries of the flat sides evolve by the curve shortening flow
Estimating the integrated likelihood via posterior simulation using the harmonic mean identity
 Bayesian Statistics
, 2007
"... The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison a ..."
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the posterior simulation iterations. The key is the harmonic mean identity, which says that the reciprocal of the integrated likelihood is equal to the posterior harmonic mean of the likelihood. The simplest estimator based on the identity is thus the harmonic mean of the likelihoods. While this is an unbiased
Some more inequalities for arithmetic mean, harmonic mean and variance
 J. Math. Inequal
, 2008
"... (communicated by R. Bhatia) Abstract. We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds for t ..."
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Cited by 5 (1 self)
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(communicated by R. Bhatia) Abstract. We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds
Generalized Fuzzy Bonferroni Harmonic Mean Operators and Their Applications in Group Decision Making
"... The Bonferroni mean (BM) operator is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the BM and harmonic mean operators, H. Sun and M. Sun (2012) developed the fuzzy Bonferroni harmonic mean (FBHM) and fuzzy ordered Bonferroni harmonic mean (FOBH ..."
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The Bonferroni mean (BM) operator is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the BM and harmonic mean operators, H. Sun and M. Sun (2012) developed the fuzzy Bonferroni harmonic mean (FBHM) and fuzzy ordered Bonferroni harmonic mean
A SIMPLE GOEMETRIC CONSTRUCTION OF THE HARMONIC MEAN OF n VARIABLES
"... nn a a a a h ". The harmonic mean is the reciprocal of the mean of the reciprocals of the numbers 1 2 3, , , na a a a ". In this short note we show a simple way to geometrically construct the harmonic mean of n positive numbers and give an application to finding the resistance of n resisto ..."
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nn a a a a h ". The harmonic mean is the reciprocal of the mean of the reciprocals of the numbers 1 2 3, , , na a a a ". In this short note we show a simple way to geometrically construct the harmonic mean of n positive numbers and give an application to finding the resistance of n
GENERALIZED ULAMHYERS STABILITY OF THE HARMONIC MEAN FUNCTIONAL EQUATION IN TWO VARIABLES
"... Abstract. In this paper, we find the solution and prove the generalized UlamHyers stability of the harmonic mean functional equation in two variables. We also provide counterexamples for singular cases. 1. ..."
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Abstract. In this paper, we find the solution and prove the generalized UlamHyers stability of the harmonic mean functional equation in two variables. We also provide counterexamples for singular cases. 1.
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