Harmonic balance (HB) methods are frequency-domain algorithms used for high accuracy computation of the periodic steady-state of circuits. Matrix-implicit Krylov-subspace techniques have made it possible for these methods to simulate large circuits more efficiently. However, the harmonic balance methods are not so efficient in computing steady-state solutions of strongly nonlinear circuits with...

In this note, we characterize the $f$-harmonic maps and bi-$f$-harmonic with potential. We prove that every map potential from complete Riemannian manifold, satisfying some conditions is a More, study case of conformal between equidimensional manifolds.

We prove that a weakly Dirac-harmonic map from a Riemann spin surface to a compact hypersurface N ⊂ R is smooth. 2000 Mathematics Subject Classification: 58J05, 53C27.

An almost contact metric structure is parametrized by a section σ of an associated homogeneous fibre bundle, and conditions for σ to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field ξ, and the almost complex structure in the contact subbundle. Several examples are given where the harmonic section equations for σ reduce to those for ξ, regarde...

The advent of high-harmonic generation in gases 30 years ago set the foundation for attosecond science and facilitated ultrafast spectroscopy in atoms, molecules, and solids. We explore high-harmonic generation in the solid state by means of nanostructured and ion-implanted semiconductors. We use wavelength-selective microscopic imaging to map enhanced harmonic emission and show that the genera...