The harmonic index of a graph G, is defined as the sum weights 2/d(u)+d(v) all edges uv where d(u) degree vertex u in G. In this paper we find minimum bicyclic order n and diameter d. We also characterized graphs reaching bound.

A catalog record for this book is available from the British Library. Harmonic mappings in the plane / Peter Duren. Includes bibliographical references and index.

We report here on a series of tricyanovinylaniline chromophores for use as dopants in poled poly(methyl methacrylate)waveguides for anomalous dispersion phase-matched second harmonic generation. Second harmonic generation measurements as a function of mode index confirmed anomalous dispersion phase-matching efficiencies as large as 245%/Wcm over a propagation length of about 35 μm. The waveguid...

We present a new formulation of Maker fringes in parallel-surface films, using self-consistent boundary conditions for reflections and allowing for any degree of refractive-index dispersion. This treatment of the second-harmonic reflections and dispersion, unlike a number of previous derivations, leads correctly to the expected form for the effective second-harmonic d coefficients. Complete exp...

In this paper, a new non data aided estimator of the technical parameters of Continuous Phase Modulated (CPM) signals is proposed. It consists in estimating jointly the modulation index, the symbol period and the frequency offset. It is based on the following observations. Firstly, the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generat...

The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc (G) of a graph G is the mean value of eccentricities of all vertices of G. The harmonic index H (G) of a graph G is defined as the sum of 2 di+dj over all edges vivj of G, where di denotes the degree of a vertex vi in G. In this paper, we determine the unique tree with minimum average...

We present a theoretical and experimental analysis of nonlinear microwave photonic filters. Far from the conventional condition of low modulation index commonly used to neglect high-order terms, we have analyzed the harmonic distortion involved in microwave photonic structures with periodic and non-periodic frequency responses. We show that it is possible to design microwave photonic filters wi...

A discrete-time mixing architecture for software defined radio receivers is proposed. It exploits 8x RF voltage oversampling followed by charge domain weighting to achieve 40dB 3rd and 5th harmonic rejection without channel bandwidth limitations. Also noise folding is reduced by 3dB. A zero-IF downconverter chip in 65nm CMOS can receive RF signals up to 900MHz, with NFmin=12dB, IIP3=11dBm at <2...