For Schrödinger maps from R ×R+ to the 2-sphere S, it is not known if finite energy solutions can form singularities (“blowup”) in finite time. We consider equivariant solutions with energy near the energy of the two-parameter family of equivariant harmonic maps. We prove that if the topological degree of the map is at least four, blowup does not occur, and global solutions converge (in a dispe...

where vg is the volume form on (M,g) and e( f )(x) := (1/2)‖df (x)‖T∗M⊗ f −1TN is the energy density of f at the point x ∈M. In local coordinates (x)i=1 on M and (y)a=1 on N , the energy density is given by e( f )(x)= (1/2)gi (x)hab( f (x))(∂ f a/∂xi)(∂ f b/∂x j). Critical points of the energy functional are called harmonic maps. The first variational formula of the energy gives the following c...

In recent years, renewable energy sources have been considered the most encouraging resources for grid and off-grid power generation. This paper presents an improved current control strategy for a three-phase photovoltaic grid-connected inverter (GCI) under unbalanced and nonlinear load conditions. It is challenging to suppress the harmonic content in the output current below a pre-set value in...

For Schrödinger maps fromR2×R+ to the 2-sphere S2, it is not known if finite energy solutions can form singularities (blow up) in finite time. We consider equivariant solutions with energy near the energy of the two-parameter family of equivariant harmonic maps. We prove that if the topological degree of the map is at least four, blowup does not occur, and global solutions converge (in a disper...

We examine a scheme for a Free Electron Laser (FEL) harmonic amplifier seeded by a 30-nm wavelength signal produced using a process of High-order Harmonic Generation (HHG). The seed is first amplified in an optical klystron from 100 kW to 30 MW using a 1 GeV electron beam and then is used for an energy modulation of electrons in the downstream undulator. Subsequently, a 100MW level of radiation...

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...

An earlier exact result (Phys. Rev. Lerf. 55 (1985). 2273) for the free energy of an oscillatordipole interacting with the radiation field is obtained using the fluctuation-dissipation theorem. A key feature of the earlier calculation, a remarkable formula for the free energy of the oscillator, is obtained in the form of a corresponding formula for the oscillator energy. This confirms, by a lon...

The proposed system presents power-control strategies of a grid-connected hybrid generation system with versatile power transfer. This hybrid system allows maximum utilization of freely available renewable energy sources like wind and photovoltaic energies. For this, an adaptive MPPT algorithm along with standard perturbs and observes method will be used for the system. Also, this configuration...

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the...