Here, we point out on an intriguing mapping between the quantum harmonic oscillator ground state and zero absolute vorticity plane Couette flow of a Boltzmann-like density distributed ideal gas in thermal equilibrium. The is obtained when embedded rotating frame whose rotation rate equal to half frequency oscillator.

The millihertz gravitational-wave frequency band is expected to contain a rich symphony of signals with sources ranging from galactic white dwarf binaries extreme mass ratio inspirals. Many these will not be individually resolvable. Instead, they incoherently add produce stochastic confusion noise whose content governed by the dynamics sources. angular structure power modulated distribution acr...

We prove that a harmonic quasiconformal mapping defined on finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits extension to whole plane if its Schwarzian derivative is small. also make observation univalence criterion for mappings holds uniform domains.

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...