Search results for "Inverse function"
showing 4 items of 4 documents
Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields
2003
Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ Ising lattices with nearest neighbor ferromagnetic exchange and four free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces, at which antisymmetric surface fields $\ifmmode\pm\else\textpm\fi{}{H}_{s}$ act, are studied for a wide range of linear dimensions $(4l~Ll~320,30l~{L}_{y}l~1000),$ in an attempt to clarify finite size effects on the wedge filling transition in this ``double-wedge'' geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a li…
Some Nonlinear Methods in Fréchet Operator Rings and Ψ*-Algebras
1995
Two different inverse function theorems, one of Nash-Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo-convex Frechet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo-convex Frechet algebra with unit e and T+ : Ψ Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation where T- = IΨ- T, has a solution x ∈ Ψ for every y ∈ U?
Infinite Dimensional Banach spaces of functions with nonlinear properties
2010
The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on R(n) failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.
Invertibility of Sobolev mappings under minimal hypotheses
2010
Abstract We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W 1 , n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.