This paper deals with Lavrentiev regularization for solving linear ill-posed problems, mostly with respect to accretive operators on Hilbert spaces. We present converse and saturation results which are an important part in regularization theory. As a byproduct we obtain a new result on the quasi-optimality of a posteriori parameter choices. Results in this paper are formulated in Banach spaces ...

Then Γ acts cocompactly on X and X , and the orbit spaces X/Γ and X /Γ are closed manifolds with contractible universal covers. The only nontrivial homotopy groups are thus the fundamental groups, π1(X/Γ) ∼= Γ ∼= π1(X /Γ). It follows that there is a homotopy equivalence X/Γ X /Γ which can be lifted to a map f : X X . This map f can then be shown to be a quasi-isometry. Recall that a (not necess...

The appropriate general completeness notion for topological vector spaces is quasi-completeness. There is a stronger general notion of completeness, which proves to be too strong in general. For example, the appendix shows that weak-star duals of infinite-dimensional Hilbert spaces are quasi-complete, but never complete in the stronger sense. Quasi-completeness for Fréchet spaces is ordinary me...

We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables we systematically look for uncorrelated quantities and find three of them which are highly c...

We study the dynamic structure factor S(q, ω) of superfluid 4 He at zero temperature in the roton momentum region and beyond using field-theoretical Green's function techniques. We start from the Gavoret-Nozì eres two-particle propagator and introduce the concept of quasi-particles. We treat the residual (weak) interaction between quasiparticles as being local in coordinate space and weakly ene...

The well-known self-similar solution for the two-point correlation function of the density field is valid only in an Einstein – de Sitter universe. We attempt to extend the solution for non – Einstein – de Sitter universes. For this purpose we introduce an idea of quasi-self-similar evolution; this approach is based on the assumption that the evolution of the two-point correlation is a successi...

The dynamics of a bright matter wave soliton in a quasi 1D Bose-Einstein condensate with periodically rapidly varying trap is considered. The governing equation is derived based on averaging over fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of GP equation with effective potential of more complicated structure than unperturbed trap. For the case of inverted ...

UST about a hundred years ago, Albert Einstein began writing a paper that secured his place in the pantheon of humankind's greatest thinkers. With his discovery of special relativity, Einstein upended the familiar, thousands-yearold conception of space and time. To be sure, even a century later, not everyone has fully embraced Einstein's discovery. Nevertheless, say "Einstein" and most everyone...

We discuss a toy model for an emergent non-relativistic gravitational theory. Within a certain class of Bose–Einstein condensates, it is possible to show that, in a suitable regime, a modified version of non-relativistic Newtonian gravity does effectively describes the low energy dynamics of the coupled system condensate/quasi-particles.