A New Existence and Uniqueness Theorem for Continuous Games

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mapping from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence of a unique equilibrium in the general game can be shown by proving the existence of a unique equilibrium in an iterative sequence of games involving such R-to-R mappings. Finally, we show how a general condition for this to occur is that a matrix derived from the Jacobean matrix of best-response functions be have positive leading principal minors, and how this condition generalises some existing uniqueness theorems for particular games.Existence; Uniqueness; Continuous Games; Contraction Mapping Theorem

The cycle contraction mapping theorem

This report lays the foundation for a theory of total correctness for programs not based upon termination. The Cycle Contraction Mapping Theorem is both an extension of Wadge's cycle sum theorem for Kahn data flow and a generalisation of Banach's contraction mapping theorem to a class of quasi metric spaces definable using the symmetric Partial Metric distance function. This work provides considerable evidence that it is possible after all to construct a metric theory for Scott style partial order domains

An iterative method derived from existence and uniqueness theorems for systems of second-order, nonlinear, two-point-boundary- value differential equations

Iterative method for systems of two-point boundary value differential equations based on contraction mapping principl

Finding matched rms envelopes in rf linacs: A Hamiltonian approach

We present a new method for obtaining matched solutions of the rms envelope equations. In this approach, the envelope equations are first expressed in Hamiltonian form. The Hamiltonian defines a nonlinear mapping, $\cal M$, and for periodic transport systems the fixed points of the one-period map are the matched envelopes. Expanding the Hamiltonian around a fiducial trajectory one obtains a linear map, $M$, that describes trajectories (rms envelopes) near the fiducial trajectory. Using $\cal M$ and $M$ we construct a contraction mapping that can be used to obtain the matched envelopes. The algorithm is quadratically convergent. Using the zero-current matched parameters as starting values, the contraction mapping typically converges in a few to several iterations. Since our approach uses numerical integration to obtain all the mappings, it includes the effects of nonidealized, $z$-dependent transverse and longitudinal focusing fields. We present numerical examples including finding a matched beam in a quadrupole channel with rf bunchers.Comment: 10 pages, uuencoded gzipped PostScript (88K

Local Well-Posedness for Relaxational Fluid Vesicle Dynamics

We prove the local well-posedness of a basic model for relaxational fluid vesicle dynamics by a contraction mapping argument. Our approach is based on the maximal $L_p$-regularity of the model's linearization.Comment: 29 page

Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation

We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle