In this paper we investigate the global property of the states constructed through superposition of many states by using the concept of incomparability under LOCC as the inherent property of the states. In our work we are able to form a bridge between comparable and incomparable classes of states through linear superposition of a states and the concept of strong incomparability criterian under ...

We consider the class of integer rectifiable currents without boundary in Rn × R satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

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 pro...

We investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We also investigate the entanglement behaviour of such classes of states, specifically their monotone nature. Finally we are able to construct some counterintuitive situations, on the bounds of different measures of entanglement, emphasis on the idea of comparability and i...

Abstract We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODE...

Modularity is a highly desirable property in the development of satisfiability procedures. In this paper we are interested in using a dedicated superposition calculus to develop satisfiability procedures for (unions of) theories sharing counter arithmetic. In the first place, we are concerned with the termination of this calculus for theories representing data structures and their extensions. T...

In this note we discuss a few simple classical (as opposed to quantum) prediction problems. The thrust of this work is to examine the predictive role of probability theory and we shall see that some situations are not really paradoxical. In particular we want to separate the role of probability as a predictive tool from one of the basic sources of strangeness in quantum mechanics, namely the pr...

Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei–Norman method is applied for obtaining the associated differential equation in the group SL(2,R). The superposition principle for first order differential equation systems and Lie-Scheffers theorem are also analysed f...