Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel–Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler [16], using a different approach.     

A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.     

Conditional expectation values in quantum mechanics

The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Introduction of bis-discotic and bis-calamitic mesogenic addends to C 60

The synthesis and characterization of four C 60 Bingel cyclopropanation adducts incorporating bis-biphenylene (three adducts) and bis-triphenylene (one adduct) moieties are described. The thermal analysis (POM and DSC) of these materials reveals that they are not liquid crystalline. However, two of the precursor bis-biphenylene malonate esters possess monotropic mesophases. Furthermore, each of the corresponding C 60 adducts is miscible in the melts of the precursor malonate ester, and at low dopings, retains the liquid crystalline monotropic mesophases of the precursor.     

Mathematical modelling of influence functions in computer-controlled polishing: Part I

Computer-controlled polishing (CCP) is commonly used to finish high-quality surfaces, such as optical lenses. Based on magnetorheological finishing (MRF), a mathematical model to calculate the polishing tool characteristic (influence function) was developed and verified experimentally. The first part of this paper introduces the model to predict the size and shape of an influence function. The second part of this paper describes the calculation of the distribution of material removal within the size of an influence function. The model supersedes the current cumbersome procedure for determining an influence function and thus results in considerably improved and more economical manufacture. Furthermore, the model enables the quality of the final surface to be enhanced when polishing complex, for example aspherical or free-form, workpiece geometries and provides the first step in the application of time-variant influence functions.