A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined. They are then related to the 1D and 2D hydrogen atoms and it is numerically found that they have continuous components, so that ionization can take place. PAC...

In this paper we continue exploring the notion of weak solution of forward–backward stochastic differential equations (FBSDEs) and associated forward–backward martingale problems (FBMPs). The main purpose of this work is to remove the constraints on the martingale integrands in the uniqueness proofs in our previous work (Ma et al. in Ann Probab 36(6):2092–2125, 2008). We consider a general clas...

The evolution of the corrosion interface separating the uncorroded concrete part and the corroded part of a partially wet concrete wall of a pipe under the innuence of hydrogen sullde can be modelled by a moving boundary problem for three coupled one-dimensional diiusion equations. We show that the problem formulated via weak solutions is well-posed. The function describing the position of the ...

The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in L∞ are obtained through the vanishing viscosity method and the compensated compactness framework. The L∞ uniform estimate and H−1 compactness are ...

We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three. We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use the cancellations that...

We present solutions of the holomorphic anomaly equations for compact two-parameter Calabi-Yau manifolds which are hypersurfaces in weighted projective space. In particular we focus on K3-fibrations where due to heterotic type II duality the topological invariants in the fibre direction are encoded in certain modular forms. The formalism employed provides holomorphic expansions of topological s...

In this article, the mathematical analysis of a model arising from biology consisting of diffusion, chemotaxis with volume filling effect and transport through an incompressible fluid, is studied. Motivated by numerical and modeling issues, the global-in-time existence of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of two-s...

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