In §1 the authors define the notion of harmonic map between two generalized Lagrange spaces. In §2 it is proved that for certain systems of differential or partial differential equations, the solutions belong to a class of harmonic maps between two generalized Lagrange spaces. §3 describes the main properties of the generalized Lagrange spaces constructed in §2. These spaces, being convenient r...

The Hodgkin-Huxley treatment of the dynamics of a nerve impulse on a cell membrane is combined with a phenomenological description of molecular hyperpolarizabilities to develop a closed-form model of an action-potential-sensitive second-harmonic response of membrane-bound chromophores. This model is employed to understand the key properties of the map between the action potential and modulation...

The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. turns into a harmonic oscillator form under suitable transformations. Thereby, relation between geometrical entropy and mean geodesic deviation established. This has connection to chaos theory where the trajectories diverge exponentially. We discuss its application cosmology black holes. Thus, we ...

The technique of complex scaling for time harmonic wave-type equations relies on a coordinate stretching to generate exponentially decaying solutions. In this work, we use Galerkin method with ansatz functions infinite support discretize complex-scaled scalar Helmholtz-type resonance problems inhomogeneous exterior domains. We show super-algebraic convergence the respect number unknowns in radi...

The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. In this work, we formulate Lieb-Robinson bounds for general harmonic systems on g...

Abstract We establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 4, respectively, obtaining criteria smooth extensibility these flows. As a corollary, we obtain characterisations singularity formation use this to estimate Hausdorff measure singular sets at first time. Finally, show that blow-ups rapidly forming...