We consider the question of existence of “bell-shaped” (i.e. non-increasing for x > 0 and non-decreasing for x < 0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p = 3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formul...

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...

Treating games of incomplete information with countable sets of actions and types and finite but large player sets we demonstrate that for every mixed strategy profile there is a pure strategy profile that is ‘εequivalent’. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functi...