We present a new, simple proof of existence for the Lanczos spinor potential in 3+1 dimensions that introduces a potential T ABCD = T (ABC)D of the Lanczos potential together with several generalizations to other index configurations and metric signatures. The potential T ABCD can also be used to express, in a concise way, the gauge freedom left in the Lanczos potential after the differential g...

Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host–parasite dynamics through a convection–diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. Howev...

(a) Definition of a ∆-system, statement and proof of the ∆-system lemma. (b) Statement of MA (Martin’s Axiom) and MAκ, proof that MAω holds and MAc fails. (c) Definition of a club and a stationary subset of κ, of the club filter and proof that the club filter on a regular cardinal κ is κ-complete. (d) Statement and proof of the Pressing Down Lemma. i. An application: Statement and proof of Thom...

This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lin [2]. Furthermore, we can conclude that every strong solution can be approximated by many strong polynomial solutions locally in time.

Given two vectors a; 2 Rn, the Schur-Horn theorem states that a majorizes if and only if there exists a Hermitian matrix H with eigenvalues and diagonal entries a. While the theory is regarded as classical by now, the known proof is not constructive. To construct a Hermitian matrix from its diagonal entries and eigenvalues therefore becomes an interesting and challenging inverse eigenvalue prob...

Since the fundamental work of Bayen et al. [1] in the seventies, a lot of effort has been dedicated to show the existence of deformations of a Poisson manifold. Some landmarks in this way were the proof of the existence of differential star products for symplectic manifolds which was done independently by De Wilde and Lecomte [2] and Fedosov [5], using different constructions. It turned out tha...

We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies generators which are related to evolution of an open system with a tuned repeated harmonic perturbation. Our main result is the proof of existence of uniquely determined minimal trace-preserving strongly continuous dynamical semigroups on the space of density matrices. The corresponding dual W -dynamical system is shown...

In this paper we consider a free boundary problem for a nonlinear system of two ordinary differential equations, one of which is singular at some points, including the initial point r = 0. Because of the singularity at r = 0, the initial value problem has a one-parameter family of solutions. We prove that there exists a unique solution to the free boundary problem. The proof of existence employ...

We place the Thomas-Fermi model of the quantum theory of atoms, molecules, and solids on a firm mathematical footing. Our results include: (1) A proof of existence and uniqueness of solutions of the nonlinear Thomas-Fermi equations as well as the fact that these solutions minimize the Thomas-Fermi energy functional, (2) a proof that in a suitable large nuclear charge limit, the quantum mechanic...

A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincaré map.