This paper introduces a Hopf algebra structure on family of reduced pipe dreams. We show that this is free and cofree, construct surjection onto commutative permutations. The dream contains subalgebras with interesting sets generators Hilbert series related to subsequences Catalan numbers. Three other relevant include the Loday–Ronco complete binary trees, special lattice walks quarter plane, ν...

Current and voltage waveforms of a distribution or a transmission system are not pure sinusoids. There are distortions in these waveforms that consist of a combination of the fundamental frequency, harmonics and high frequency transients. This paper presents an enhanced measurement scheme for identification and tracking of harmonics in power system. The proposed technique is not limited to stat...

High harmonic spectrum of a quasi-monochromatic pump that interacts with isotropic media consists of only odd-order harmonics. Addition of a secondary pump, e.g. a static field or the second harmonic of the primary pump, can results with generation of both odd and even harmonics of the primary pump. We propose a method for quasi-phase matching of only the even-order harmonics of the primary pum...

We report on the temporal pulse characteristics of individual harmonics in an attosecond pulse train by means of photoelectron streaking in a strong low-frequency transient. The scheme allows one to retrieve the pulse durations and first-order chirp of individual harmonics without the need for temporal scanning. The measurements were performed using an intense THz field generated by a tilted ph...

This paper proposes an improved control method based on modified Delta-Sigma Modulator (DSM) to enhance transient response and improve harmonic contents of buck DC-DC converter. The main advantages of the proposed method are improving the output voltage frequency spectrum, correction of the output voltage harmonic contents and sideband harmonics, reduction of switching noise peaks at the output...

In this work, the ratchet dynamics of Brownian particles driven by an external sinusoidal (harmonic) force is investigated. The gating ratchet effect is observed when another harmonic is used to modulate the spatially symmetric potential in which the particles move. For small amplitudes of the harmonics, it is shown that the current (average velocity) of particles exhibits a sinusoidal shape as...