Statistics of resonance width shifts as a signature of eigenfunction nonorthogonality

We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the nonorthogonality of resonance wave functions, being zero only if those were orthogonal. Focusing further on chaotic systems, we employ random matrix theory to introduce a new type of parametric statistics in open systems and derive the distribution of the resonance width shifts in the regime of weak coupling to the continuum.     

Construction of the velocity potential of a semiinfinite liquid column excited by a spherical calotte oscillating inside a cylindrical cavity

A semiinfinite liquid column excited by a spherical calotte oscillating inside a rigid cylindrical cavity is considered. The solution of the Laplace equation is searched for under boundary conditions on spherical, cylindrical, and flat surfaces bounding the liquid. The possibility of decomposing a spherical harmonic function in terms of cylindrical harmonic functions and vice versa is considered. The potential constructed is used to evaluate the pressure and the velocity of the liquid. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 81–89, March, 2000.     

The possibility of using screened coulomb potentials in calculating asymptotic normalization coefficients

The dependence of asymptotic normalization coefficients of nuclear wave functions on methods for taking Coulomb interaction into account is studied. Calculations are performed both with the total Coulomb potential and with the Coulomb potential truncated at large distances. Both sharp and smooth truncation is used.     

The center of the category of -modules

Let be a semi-simple connected Lie group. Let be a maximal compact subgroup of and the complexified Lie algebra of . In this paper we describe the center of the category of -modules.

     

Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

Synthesis,self‐assembly and adsorption of PEO–PLA block copolymers onto colloidal polystyrene

A series of amphiphilic block copolymers composed of poly(ethylene oxide) and poly(lactide) were synthesized and their solution properties studied using static and dynamic light scattering. These materials self‐assemble in aqueous media with the hydrodynamic radius increasing with increasing hydrophobic fraction in the copolymer. To ascertain the potential for use of these materials as degradable coatings in delivery applications, block copolymers of varying compositions were adsorbed onto a series of colloidal polystyrene particles with varying radii, and the thickness of the adsorbed layer was determined from changes in the hydrodynamic size. The adlayer thicknesses ranged from 3 to 14 nm with varying block copolymer compositions, and colloid radii. The trends fit well with theoretical models for adlayer thickness, with the exception of the smallest colloids. In these systems, we propose that the colloids may become encapsulated into the block copolymer assembly. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 244–252, 2008     

Optimal Distributed Dynamic Advertising

We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem. The first author gratefully acknowledges financial support by the NSF, the DAAD, the SFB 611 (Bonn), and the Max-Planck-Institut für Mathematik (Leipzig) through an IPDE fellowship.     

On minimal representations of Chevalley groups of type D n , E n and G 2

Let G be a simply connected Chevalley group of type D _n , E _n or G₂. In this paper, we show that the minimal representation of G is unique for types D _n and E _n and it does not exist for the type G₂.     

Tannaka duality on quotient stacks

Let = [X/G] be the quotient stack of a scheme X by an affine group scheme G over a field k. Assume that there is a line bundle on whose underlying line bundle on X is very ample. Let VB() be the category of vector bundles on .We show that is canonically isomorphic to the stack of fiber functors on VB(). This is an analogue of the Tannaka duality for affine groups. Partially supported by CNCSIS contract no. 33079/2004