A general form of dynamical equations is obtained on the requirement of the superposition principle of quantum states; hence the constraints on the forms of the Lagrangians are acquired, under the assumption of correspondence between quantum states and field operators. It shows that the superposition principle requires the continuous transformation group of the Lagrangians to be compact, and th...

Saturation-based calculi such as superposition can be successfully instantiated to decision procedures for many decidable fragments of first-order logic. In case of termination without generating an empty clause, a saturated clause set implicitly represents a minimal model for all clauses, based on the underlying term ordering of the superposition calculus. In general, it is not decidable wheth...

We comment on some analytical solutions to a class of Boussinesq–like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the time variable. We derive more general results by means of travelling waves and argue that a curious superposition principle may not be of any mathematical or p...

We consider a general planar reaction diffusion equation which we hypothesize has a localized traveling wave solution. Under assumptions which are no stronger than those needed to prove the stability of a single pulse, we prove that the PDE has solutions which are roughly the linear superposition of two pulses, so long as they move along trajectories which are not parallel. In particular, we pr...

We characterize the entire functions which transform a weighted Banach space of holomorphic functions on the disc of type H∞ into another such space by superposition. We also show that all the superposition operators induced by such entire functions map bounded sets into bounded sets and are continuous. Superposition operators that map bounded sets into relatively compact sets are also considered.

A general form of the dynamical equations is obtained on the requirement of the superposition principle of quantum states; hence the constraint on the forms of the Lagrangians is acquired under an assumption of correspondence between state and field operator. It shows that the superposition principle requires the continuous transformation group of the Lagrangians to be compact, and that the Lag...

Measure Differential Equations (MDE) describe the evolution of probability measures driven by velocity fields, i.e. on tangent bundle. They are, one side, a measure-theoretic generalization ordinary differential equations; other they allow to concentration and diffusion phenomena typical kinetic equations. In this paper, we analyze some properties class equations, e...