The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

The amplitude distribution in a SAR image can present a heavy tail. Indeed, very high–valued outliers can be observed. In this paper, we propose the usage of the Harmonic, Geometric and Arithmetic temporal means for amplitude statistical studies along time. In general, the arithmetic mean is used to compute the mean amplitude of time series. In this study, we will show that comparing the behavi...

The Anderson–Hubbard Hamiltonian at half–filling is investigated within dynamical mean–field theory at zero temperature. The local density of states is calculated by taking the geometric and arithmetic mean, respectively. The non–magnetic ground state phase diagrams obtained within the different averaging schemes are compared.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy”. Upper and lower error bars on the accuracy are provided by the...

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.

The arithmetic mean is the mean for addition and the geometric mean is that for multiplication. Then what kind of binary operation is associated with the arithmetic-geometric mean (AGM) due to C. F. Gauss? If it is possible to construct an arithmetic operation such that AGM is the mean for this operation, it can be regarded as an intermediate operation between addition and multiplication in vie...

A singular value inequality for sums and products of Hilbert space operators is given. This inequality generalizes several recent singular value inequalities, and includes that if A, B, and X are positive operators on a complex Hilbert space H, then sj ( A 1/2 XB 1/2 ) ≤ 1 2 ‖X‖ sj (A+B) , j = 1, 2, · · · , which is equivalent to sj ( A 1/2 XA 1/2 −B 1/2 XB 1/2 ) ≤ ‖X‖ sj (A⊕B) , j = 1, 2, · · ...