Group 4 initiators for the stereoselective ROP of rac-β-butyrolactone and its copolymerization with rac-lactide

In this paper we demonstrate the utility of Group 4 metals for the well-controlled and stereoselective (syndiotactic) ring opening polymerization (ROP) of rac-β-butyrolactone (BBL) and their ability to form copolymers.     

The isomorphism problem for some universal operator algebras

This paper addresses the isomorphism problem for the universal (non-self-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if and only if the defining polynomial relations are the same up to a unitary change of variables, and that this happens if and only if the associated subproduct systems are isomorphic. The proof makes use of the complex analytic structure of the character space, together with some recent results on subproduct systems. Restricting attention to commutative operator algebras defined by a radical ideal of relations yields strong resemblances with classical algebraic geometry. These commutative operator algebras turn out to be algebras of analytic functions on algebraic varieties. We prove a projective Nullstellensatz connecting closed ideals and their zero sets. Under some technical assumptions, we find that two such algebras are isomorphic as algebras if and only if they are similar, and we obtain a clear geometrical picture of when this happens. This result is obtained with tools from algebraic geometry, reproducing kernel Hilbert spaces, and some new complex-geometric rigidity results of independent interest. The C^?-envelopes of these algebras are also determined. The Banach-algebraic and the algebraic classification results are shown to hold for the wot-closures of these algebras as well.     

A six-coordinate aryl-germanium complex formed by the Kläui ligand

PhGeCl₃ reacts with Na{[OP(OEt)₂]₃CoCp} to give the six-coordinate complex PhCl₂Ge{[OP(OEt)₂]₃CoCp}, characterised spectroscopically and by an X-ray crystal structure determination which showed a firmly-attached tridentate ligand [Ge-O 1.973(2) Å].     

Ingredients and equations for making a magnetic field in the early Universe

The ingredients required to create a magnetic field in the early Universe are identified, and compared with Sakharov's conditions for baryogenesis. It is also shown that a long range coherent magnetic field is not generated by the classical rolling Higgs vacuum expectation value during the electroweak phase transition.     

Diffractive optics: Design, realization, and applications

This paper presents methods for designing and recording optimal computer-generated diffractive optical elements. The design method is based on an analytic ray-tracing procedure for minimizing aberrations. The recording involves computer-generated masks and multiple lithographic processes in order to form reflective and transmissive multilevel, surface relief-phase, diffractive elements. As a result, the elements can have high diffraction efficiencies over a broad range of incidence angles. Even generalized diffractive elements that operate with highly uniform diffraction efficiency and polychromatic radiation can be designed and recorded by optimizing the shape and height of the relief gratings. To illustrate the effectiveness of the diffractive optical elements, they have been incorporated into a number of applications, involving visible as well as infra-red radiation. Some that deal with coordinate transformation, beam shaping, and polarization control are briefly reviewed.