Stability of the Lipschitz extension property under metric transforms

We show that the linear and nonlinear Lipschitz extension properties of a metric space are not changed when the original metric is replaced by a new metric obtained by composition with an arbitrary concave function. Submitted: January 2001, Revised: February 2001.     

Free Algebras of Automorphic Forms on the Upper Half-Plane

We find all pairs (,a) consisting of a cocompact Fuchsian group of genus zero and an automorphy factor a of for which the graded algebra of a--automorphic forms is free.     

Whitney's extension problem for multivariate -functions

We prove that the trace of the space to an arbitrary closed subset is characterized by the following ``finiteness' property. A function belongs to the trace space if and only if the restriction to an arbitrary subset consisting of at most can be extended to a function such that

The constant is sharp.

The proof is based on a Lipschitz selection result which is interesting in its own right.

     

Modeling the Behavior of Heat-Shrinkable Thin Films

We describe an asymptotic model for the behavior of PET-like heat-shrinkable thin films that includes both membrane and bending energies when the thickness of the film is positive. We compare the model to Koiter’s shell model and to models in which a membrane energy or a bending energy are obtained by Γ-convergence techniques. We also provide computational results for various temperature distributions applied to the films.     

A class of differential-delay systems with hysteresis: Asymptotic behaviour of solutions

A class of differential-delay systems with hysteresis is considered. Conditions ensuring boundedness of solutions and related asymptotic and integrability properties are expressed in terms of data associated with the linear component of the overall system and a Lipschitz constant associated with the hysteretic component.     

A Study of the Behavior of Cobalt in Carbonylation of Copper-Nickel Metallurgical Half-Products at Medium Pressure of the Reaction Gas

Dependences of the cobalt recovery into the carbonyl gas phase on the content of sulfur and carbon in sulfidized copper-nickel metallurgical half-products subjected to carbonylation were studied at a medium pressure of the reaction gas (70 gage atm). The behavior of cobalt was examined by means of metallographic analysis of the residue formed in carbonylation. A mechanism of solid-phase interaction of cobalt with copper sulfide and a method for calculation of the volume self-diffusion coefficient of cobalt in the crystal lattice of metallic copper deformed after removal of nickel were suggested.     

Completeness and orthogonality of the null plane of one class of solutions of the relativistic wave equations

Possible redefinitions of the scalar product are analyzed for relativistic wave fields of the Klein-Gordon and Dirac types. It is shown that for an entire class of new exact solutions, for which it was previously not possible to define the usual scalar product on the x⁰=const plane, it is possible to find a correct scalar product on the null plane x⁰?x³=const. Orthogonality and completeness relations are proved for this scalar product. Possible applications of the results are discussed.