On equality of line type and variety type of real hypersurfaces in Cn

Recently McNeal proved, by analytic methods, that the D’Angelo type of a boundary point of a convex domain agrees with the maximal order of contact of the boundary with complex lines. We give an elementary geometric proof and generalization of McNeal’s theorem. Communicated by Steven Krantz     

Levi foliations in pseudoconvex boundaries and vector fields that commute approximately with

Boas and Straube proved a general sufficient condition for global regularity of the -Neumann problem in terms of families of vector fields that commute approximately with . In this paper, we study the existence of these vector fields on a compact subset of the boundary whose interior is foliated by complex manifolds. This question turns out to be closely related to properties of interest from the point of view of foliation theory.

     

Plurisubharmonic Defining Functions, Good Vector Fields, and Exactness of a Certain One Form

 We show that the approaches to global regularity of the -Neumann problem via the methods listed in the title are equivalent when the conditions involved are suitably modified. These modified conditions are also equivalent to one that is relevant in the context of Stein neighborhood bases and Mergelyan type approximation.     

Power series with integer coefficients in several variables

A classical theorem of Borel-Pólya, which concerns rationality of an analytic function whose Taylor expansion at a point has integer coefficients, is generalized to several variables. This research partially supported by an Indiana University Summer Faculty Fellowship.     

Mixing-induced global modes in open active flow

We describe how local mixing transforms a convectively unstable active field in an open flow into absolutely unstable. Presenting the mixing region as one with a locally enhanced effective diffusion allows us to find the linear transition point to an unstable global mode analytically. We derive the critical exponent that characterizes weakly nonlinear regimes beyond the instability threshold and compare it with numerical simulations of a full two-dimensional flow problem.     

Adsorption of diblock copolymers on stripe-patterned surfaces

We present the results of extensive Monte Carlo simulations of diblock copolymers adsorbed on stripe-patterned surfaces of various widths. We have found that the width of the stripe pattern is an important parameter which dictates favorable recognition on the surface. For certain stripe widths, the adsorption of diblock copolymers to striped surfaces exhibits two transitions. The process involves recognition of the surface pattern by the diblock copolymer which follows a two step process in which the first block getting adsorbed to the appropriate pattern on the surface, without any recognition of the surface pattern, followed by the adsorption of the second block, where a reorganization process happens. For small widths and also for higher widths, the chain behaves just like a homopolymer where the twofold adsorbing process changes to the typical homopolymer adsorption. We have also found that there exists an optimal width of the stripes, independent of the chain length, where the recognition on the surface pattern is most favored. The characteristic temperature of the adsorption of the second block with weaker interactions is found to be independent of the chain length at this optimal width, proving that only local rearrangements take place after the first step. Some of our results describing the thermodynamics compare very well with the recent semianalytical approach of Kriksin et al. [J. Chem. Phys. 122, 114703 (2005)] on multiblock copolymers on heterogeneous surfaces. We also present some interesting conformational properties of the copolymer chain near the stripe-patterned surface.     

A mean-field approach of the theory of topological constraints in polymer melts and networks

A new mean-field concept is discussed for the topological constraints in polymer melts and networks. The constraining potential is assumed to be determined by the dependence of the free energy of the surrounding chains on the position of the considered chain. The concept is applied to polydisperse systems, in which a new criterion is derived to describe the onset of the influence of entanglement effects.