The general Randić index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randić index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randić in 1975. The paper outlines the results known for the (general) Randić inde...

The equations of parallel transport for a non-linear connection on phase space are examined. It is shown that, for a free-particle Lagrangian, the connection term first-order in momentum reproduces the geodesic equation of General Relativity and the term zeroth-order in the momentum reproduces the Lorentz electromagnetic force law. Hence from one mathematical expression, a non-linear parallel t...

This letter presents an almost sure convergence of the zeroth-order mirror descent (ZOMD) algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate subgradient objective using Nesterov’s Gaussian Approximation (NGA) with certain alternations suggested by some practical applications. prove iterate...

Design and performance of a coplanar waveguide (CPW) bandpass filter (BPF) using Composite Right/Left-handed (CRLH) Zeroth-order Resonators have been studied. The Bloch analysis is applied based on the S parameters to derive the characteristics of the eigenmodes (Bloch modes), from which the right/left-handed frequency band and the zeroth-order resonant frequency are clearly determined. Then, t...

In this work the usage of a composite right/lefthanded (CRLH) metamaterial transmission line resonator as a transmit/receive coil for 7 Tesla magnetic resonance imaging (MRI) is investigated. On the basis of zeroth-order resonant antennas (ZORAs) a zeroth-order resonant coil (ZORC) was designed. Due to a constant current distribution along the element, a homogenous magnetic field is achieved in...

We study string propagation in an anisotropic, cosmological background. We solve the equations of motion and the constraints by performing a perturbative expansion of the string coordinates in powers of c, the world-sheet speed of light. To zeroth order the string is approximated by a tensionless string (since c is proportional to the string tension T ). We obtain exact, analytical expressions ...