We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121–132, 2016). We adapt the variational framework developed by Friesecke and Wattis (Comm. Math Phys. 161:391–418, 1994) for the FermiPasta-Ulam-Tsingou lattice equations to treat a truncated problem which cuts off short-range intera...

We present a semantical proof of existence of normal forms for system F including -equality. A reduction-free normalisation function can be obtained from this. The proof uses the method of glueing (a variant of) the term model along the global sections functor, carried out in the internal language of a category of presheaves. As a by-product we obtain an semantical explanation of higherorder ab...

We have seen that the proof of existence of inverses for elements of Ext(X) can be based on a lifting theorem for (completely) positive maps of C(X) into a quotient C∗-algebra of the form E/K, where E ⊆ B(H) is a C∗-algebra containing the compact operators K. That argument works equally well for arbitrary C∗-algebras in place of C(X) whenever a completely positive lifting exists. Thus we are le...

We analyse how a learner modelling engine that uses belief functions for evidence and belief representation, called XLM, reacts to different input information about the learner in terms of changes in the state of its beliefs and the decisions that it derives from them. The paper covers XLM induction of evidence with different strengths from the qualitative and quantitative properties of the inp...

We propose a proof of existence of solutions which is conceptually simpler than the previous proof in [1]. Indeed, our proof is based on a direct parabolic regularization of the problem, whereas previous proofs involved a change of unknowns rendering the problem to a parabolic-hyperbolic formulation. Moreover, we believe that our approach also gives a way to select a unique natural solution of ...

This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schrödinger equation. In this part we study the diffraction managed discrete nonlinear Schrödinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management geometries. We show that, for vanishing averag...

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and drift of the set of particles. Each particle carries a number of internal coordinates which may evolve continuously in time, determined by what we will refer to ...

  In this article, Non radial method of dynamic DEA with the parallel network structure is presented and is used for calculation of relative efficiency measures when inputs and outputs do not change equally. In this model, DMU divisions under evaluation have been put together in parallel. But its dynamic structure is assumed in series. Since in real applications there are undesirable inputs an...

We consider the dynamics of semiflows of patterns on unbounded domains that are equivariant under a noncompact group action. We exploit the unbounded nature of the domain in a setting where there is a strong ‘global’ norm and a weak ‘local’ norm. Relative equilibria whose group orbits are closed manifolds for a compact group action need not be closed in a noncompact setting; the closure of a gr...

We establish the existence of smooth transfer between absolute Kloosterman integrals and Kloosterman integrals relative to a quadratic extension.