Nonparametric estimation methods for the multivariable frequency response function are experimentally evaluated using closed-loop data from an industrial robot. Three classical estimators (H1, joint input-output, arithmetic mean) and two estimators based on nonlinear averaging techniques (harmonic mean, geometric/logarithmic mean) are considered. The estimators based on nonlinear averaging give...

We propose a definition for geometric mean of k positive (semi) definite matrices. We show that our definition is the only one in the literature that has the properties that one would expect from a geometric mean, and that our geometric mean generalizes many inequalities satisfied by the geometric mean of two positive semidefinite matrices. We prove some new properties of the geometric mean of ...

Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...

Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have imp...

A study was completed of more than 170,000 records of pediatric venous blood levels and supporting demographic information collected in New York City during 1970-1976. The geometric mean (GM) blood lead level shows a consistent cyclical variation superimposed on an overall decreasing trend with time for all ages and ethnic groups studied. The GM blood lead levels for blacks are significantly gr...

This paper, in considering aspects of the geometric mean sequence, offers new results connecting Jacobsthal and Horadam numbers which are established and then proved independently.

This report presents the geometric mean blood lead levels of an 80% cross-sectional sample of children aged 1-72 months in New Haven, Connecticut. Blood lead levels were related to age, sex and race. It was found that age and race were independently important sources of variation in blood lead levels. Sex of children in this age group was not related to differences in blood lead levels. The hig...

We prove some general theorems which unify results on arithmetic-geometric mean and some other related matrix inequalities. As an application we obtain some results involving Hadamard product of matrices. Mathematics subject classification (2010): 47A30 15A60.