Concentration controlled multilevel self‐assembly of 3‐armed poly(ethylene glycol)‐b‐poly(ε‐caprolactone) block copolymers investigated by AFM

Concentration dependent morphology of 3‐armed poly(ethylene glycol)‐b‐poly(ε‐caprolactone) copolymer aggregates in aqueous system was investigated by atomic force microscopy (AFM). The AFM results show that, at a low concentration, 4 × 10^?5 g/mL, spherical micelles occur, and unmicellized molecules are not distributed homogeneously in the copolymer aqueous solution. Unequal outspread clusters composed of wormlike aggregates are formed at a moderate copolymer concentration, 4 × 10^?4 g/mL, those wormlike aggregates are orderly packed in the clusters. At a high concentration of 0.05 g/mL, the copolymer aqueous system is indeed a gel at room temperature, outspread clusters of wormlike aggregates join together to forma network structure. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1412–1418, 2008     

Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres

We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The complete information on the numbers of faces and chains of faces in these spheres can be obtained from the defining lattices in a manner analogous to the relation between arrangements of hyperplanes and their underlying geometric intersection lattices.     

Mathematics of Philosophy or Philosophy of Mathematics?

This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics.     

物理实验教学应该重视的三个方面

实施素质教育的物理实验教学，是科学性与技术性的统一，本文从技术的角度立意，阐明了当今中学物理实验教学改革中应该重视的三个方面：操作技术，故障排除与反思心理。     

Identities of arithmetic type between values of the theta function associated to a lattice in ℝ d and its derivatives

In this paper, we introduce a notion of similarly self dual lattice in a d-dimensional Euclidean space and a classical Jacobi theta function is associated to such a lattice. We establish identities of arithmetic type between values of this theta function and its successive derivatives. This work can be related to the spectral theory of the Landau operators.      

SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

The authors establish some inequalities about the dual mixed volumes of star bodies in R^n. These inequalities are the analogue in the Brunn-Minkowski theory of the inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.