the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...

Abstract Autonomous quantum thermal machines do not require an external coherent drive or work input to perform the desired tasks, making them a promising candidate for management in systems. Here, we propose autonomous machine which two uncoupled macroscopic mechanical resonators microwave achieve considerable entanglement via hot bath. This becomes possible by coupling common two-level system...

this paper presents a new control methodology for active power filters that provide an adaptive online harmonic estimation with partial and selective harmonic reduction schemes, which has been implemented within an integrated controller. the proposed approach is to provide partial and selective reduction of those individual harmonics which exceed the recommended levels as set by regulatory bodi...

High-repetition-rate ultrafast lasers are needed for diverse applications. Harmonic modelocking, where multiple identical, equidistant pulses circulate in the cavity, reaches beyond practical limitations of reducing cavity length. However, it suffers from stochastic deviations that manifest as supermodes radio-frequency spectrum and difficulties maintaining same harmonic state, often coupled wi...

This paper presents an adaptive time-domain post-filtering technique based on the modified Yule-Walker filter. Conventionally, post-filtering is derived from an original LPC spectrum [1]. In general, this time-domain technique produces unpredictable spectral tilt that is hard to control by the modified LPC synthesis, inverse and high pass filtering and causes unnecessary attenuation or amplific...

High harmonic generation in gases is developing rapidly as a soft X-ray femtosecond light-source for applications. This requires control over all the harmonics characteristics and in particular, spatial properties have to be kept very good. In previous literature, measurements have always included several harmonics contrary to applications, especially spectroscopic applications, which usually r...