Phase separation in blends of two homopolymers and a diblock copolymer during film casting

Demixing during film casting of blends of polystyrene, polymethylmethacrylate, and a symmetric diblock copolymer of styrene and methylmethacrylate is discussed. The concentration fluctuations in the homogeneous solutions were calculated in mean field approximation. The structures in the homogeneous and demixed solutions and in the dry films were measured by small-angle x-ray scattering, and the morphologies of the dry films were characterized by transmission electron microscopy. The structure of the dry blends is evidently already pre-formed in solution.     

A Unified Constructive Approach to the Topological Degree in Rn

The paper gives an approach to the topological degree in Rⁿ which takes into account numerical requirements and permits derivation of the known degree computation formulas in a simple way. The new approach subsumes several earlier approaches and represents a general principle of construction of degree computation formulas. The basic idea consists of computing the degree of a continuous function relative to a bounded open subset Ω of Rⁿ by means of an auxiliary function which is defined on a polyhedron approximating Ω and maps into a known fixed convex polyhedron containing the origin of Rⁿ. It is further shown that the topological degree of a continuous function relative to an n-dimensional polyhedron P can be computed alone by means of a subset of the boundary of P .     

Onset of crater formation during short pulse laser ablation

We report morphologic changes of metallic surfaces at the onset of ablation, starting from gentle ablation to the emergence of ablation craters. The evolution of both observed melting zones and of ablation craters therein are investigated in dependence of the ablation laser fluence for nanosecond ultraviolet laser pulses. Further, consequences of crater formation for cluster synthesis within the released atomic vapor are pointed out. PACS 52.38.Mf; 79.20.Ds; 65.40.De     

Stability testing in an integrated scheme

ISO Guide 35 deals with RM stability issues and scrutinizes the evaluation of stability testing results under the assumption that either there is no trend at all (a rather rare situation), or any observed deterministic change is insignificant and thus can be neglected. However, market demands for reliable reference materials are obviously not limited to stable or at least seemingly stable materials. In many analytical applications, analytes and measurands under consideration are known, or at least suspected, to be unstable on time scales that may vary widely from measurand to measurand. The Federal Institute for Materials Research and Testing (BAM) has developed (and successfully uses) an integrated approach in its certification practice. The approach is based on an initial stability study and subsequent post-certification monitoring. Data evaluation is model-based and takes advantage of all information collected in the stability testing scheme(s). It thus allows one to deal with any kind of instability observed, to assess limiting time intervals at any stress condition in the range tested, to estimate a final expiry date for materials with detected instabilities or the maximum admissible re-testing interval for seemingly stable materials, and to assess maximum admissible stress loads during delivery of the material to the customer. The article describes (and exemplifies) typical study layout, the model selection, and the integrated data assessment.     

Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002