scholarly journals A harmonic mean inequality for the polygamma function

2020 ◽  
pp. 71-76
Author(s):  
Sourav Das ◽  
Anbhu Swaminathan
Keyword(s):  
Harmonic Mean ◽  
Polygamma Function

scholarly journals On Certain Differential Subordination of Harmonic Mean Related to a Linear Function

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 966
Author(s):  
Anna Dobosz ◽  
Piotr Jastrzębski ◽  
Adam Lecko
Keyword(s):  
Convex Function ◽  
Linear Function ◽  
Differential Subordination ◽  
Harmonic Mean ◽  
Best Dominant ◽  
Symmetry Properties ◽  
Differential Subordinations ◽  
Difficult Issue

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

scholarly journals Linkage disequilibrium and genetic variances under mutation-selection balance.

Genetics ◽  
1989 ◽  
Vol 121 (4) ◽  
pp. 857-860 ◽  
Author(s):  
A Hastings
Keyword(s):  
Linkage Disequilibrium ◽  
Mutation Rate ◽  
Genetic Variance ◽  
Harmonic Mean ◽  
Recombination Rates ◽  
Genetic Variances ◽  
Locus Selection

Abstract I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.

On Representing an Integer as the Harmonic Mean of Integers

1973 ◽  
Vol 46 (5) ◽  
pp. 241-244
Author(s):  
Solomon W. Golomb
Keyword(s):  
Harmonic Mean

A Neutral Model With Fluctuating Population Size and Its Effective Size

Genetics ◽  
2002 ◽  
Vol 161 (1) ◽  
pp. 381-388
Author(s):  
Masaru Iizuka ◽  
Hidenori Tachida ◽  
Hirotsugu Matsuda
Keyword(s):  
Asymptotic Behavior ◽  
Population Size ◽  
Diffusion Model ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Effective Size ◽  
Neutral Model ◽  
Average Heterozygosity ◽  
Special Case ◽  
Concrete Model

Abstract We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.

scholarly journals Some More Results on Harmonic Mean Graphs

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
S. S. Sandhya ◽  
S. Somasundaram ◽  
R. Ponraj
Keyword(s):  
Harmonic Mean

scholarly journals A New Nearest Centroid Neighbor Classifier Based on K Local Means Using Harmonic Mean Distance

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 234 ◽  
Author(s):  
Sumet Mehta ◽  
Xiangjun Shen ◽  
Jiangping Gou ◽  
Dejiao Niu
Keyword(s):  
Small Sample Size ◽  
Classification Performance ◽  
Error Rates ◽  
Small Sample ◽  
Harmonic Mean ◽  
Local Means ◽  
Local Mean ◽  
Real World Datasets ◽  
Nearest Neighbour Classifier ◽  
Query Sample

The K-nearest neighbour classifier is very effective and simple non-parametric technique in pattern classification; however, it only considers the distance closeness, but not the geometricalplacement of the k neighbors. Also, its classification performance is highly influenced by the neighborhood size k and existing outliers. In this paper, we propose a new local mean based k-harmonic nearest centroid neighbor (LMKHNCN) classifier in orderto consider both distance-based proximity, as well as spatial distribution of k neighbors. In our method, firstly the k nearest centroid neighbors in each class are found which are used to find k different local mean vectors, and then employed to compute their harmonic mean distance to the query sample. Lastly, the query sample is assigned to the class with minimum harmonic mean distance. The experimental results based on twenty-six real-world datasets shows that the proposed LMKHNCN classifier achieves lower error rates, particularly in small sample-size situations, and that it is less sensitive to parameter k when compared to therelated four KNN-based classifiers.

scholarly journals Mujeres y hombres. Desigualdades de género en el contexto mexicanoWomen and men. Gender inequalities in the Mexican context

2014 ◽  
Vol 22 (44) ◽  
Author(s):  
Francisco José Zamudio Sánchez ◽  
María Del Rosario Ayala Carrillo ◽  
Roxana Ivette Arana Ovalle
Keyword(s):  
Policy Change ◽  
Social Factors ◽  
Human Life ◽  
National Level ◽  
Living Conditions ◽  
Harmonic Mean ◽  
Gender Inequalities ◽  
Men And Women ◽  
Las Mujeres ◽  
Cultural Constructions

Las construcciones socioculturales sobre género permean todas las esferas de la vida humana generando diversas inequidades. Es necesario medirlas y proponer alternativas de solución o modificación de políticas que las atiendan. Usando una media harmónica sobre las condiciones en las que viven mujeres y hombres, se midieron atributos de once factores sociales disponibles a escala nacional. Los atributos fueron jerarquizados para cuantificar el diferencial en el cual estos factores se encuentran. No únicamente las mujeres están en condiciones de inequidad, aunque son más frecuentes y graves. Políticas públicas en seis factores deben atender, prioritariamente, a las mujeres y en cinco a los hombres. En cada factor identificamos los atributos más inequitativos para hacer posible la instrumentación de acciones pertinentes. Así, el diseño de las políticas, desde la planeación, cuenta con posibilidades de actuar en congruencia con las necesidades. Abstract Cultural constructions of gender permeate all areas of human life, generating diverse inequities. This requires knowledge of the situations in which men and women are in a particular one and, accordingly, propose solutions or policy change that pay attention to such inequities. Using a harmonic mean on the living conditions in which women and men are, attributes of eleven social factors were measured, available at national level. Such attributes were analytically nested to quantify the differential in which these factors are. Not only women are in inequity conditions, although they are more frequent and severe. Public policies in six factors should attend, mainly, to women and in five to men. We identified, inside each factor, the attributes with more inequity to make possible the implementation of appropriate actions. The corresponding design of policies has, from planning, possibilities of acting in line with the needs.

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