Localizing combinatorial properties of partitions

The purpose of this paper is to develop a framework for the analysis of combinatorial properties of partitions. Our focus is on the relation between global properties of partitions and their localization to subpartitions. First, we study properties that are characterized by their local behavior. Second, we determine sufficient conditions for classes of partitions to have a member that has a given property. These conditions entail the possibility of being able to move from an arbitrary partition in the class to one that satisfies the given property by sequentially satisfying local variants of the property. We apply our approach to several properties of partitions that include consecutiveness, nestedness, order-consecutiveness, full nestedness and balancedness, and we demonstrate its usefulness in determining the existence of optimal partitions that satisfy such properties.     

Light scattering from spherulitic materials

The azimuthal angular dependence of the depolarized component of the light scattered from spherulitic materials is derived by an algebraic method that avoids the difficult angular integrations of the usual approach. The result appears as a sum of products of two factors, a molecular factor, that depends only on the structure and the scattering angle θ, and a geometrical factor that depends only on the azimuthal angle ? and the scattering angle θ. The molecular factors are evaluated for models of spherulitic structure that assume a constant tilt of the optical polarizability tensor. The radial distribution, in principle, is arbitrary, and an evaluation for the layered spherulite is made. If the tilt angle is ω when the azimuthal patterns depend only on a linear combination of P₂(cos ω) and P₄(cos ω), where P_n(x) is the Legendre polynomial of order n. In our theory the V_H scattering pattern is a four-leaf clover whose axes are restricted by the theory to be at either 0 or 45° to the polarization directions.     

Theorie der Str?mungsmethode bei der Messung spezifischer Oberfl?chen und Mikroporosit?ten

Ohne Zusammenfassung The online version of the original article can be found at     

Synthesis and characterization of semi- and full-interpenetrating polymer networks of poly(2,6-dimethyl-1,4-phenylene oxide) and polydimethylsiloxane

The synthesis and characterization of pseudo or semi- and full-interpenetrating polymer networks (IPNs) of poly(2,6-dimethyl-1,4-phenylene oxide) and polydimethylsiloxane were performed. We observed that in full IPNs, the elasticity of the IPN samples increased very drastically, as the composition of polydimethylsiloxane increased (i.e. 0–60%) while the tensile strength (TS) and the glass transition temperature (T_g) decreases. The pseudo IPNs appeared to consist of two phases while the full IPNs of lower siloxane content were miscible.     

Prolongement de faisceaux analytiques coherents

Sans résumé     

On the inverse problem in statistical mechanics

We review briefly the status of some inverse problems in classical equilibrium statistical mechanics.This paper is dedicated to Professor P. G. Bergmann on the occasion of his sixtieth birthday.Supported by NSF grant No. GP42614X.