The push-out region of an immersed manifold

We consider immersions: and construct a subspace of which corresponds to a set of embedded manifolds which are either parallel to f, tubes around f or, in general, partial tubes around f. This space is invariant under the action of the normal holonomy group, We investigate the case where is non-trivial and obtain some results on the number of connected components of . Received 24 March 2000.     

Synthesis,characterization, and curing kinetics of novel ladder‐like polysilsesquioxanes containing side‐chain maleimide groups

Two ladder‐like polysilsesquioxanes (LPS) containing side‐chain maleimide groups have been synthesized successfully by reacting N‐(4‐hydroxyphenyl)maleimide (HPM) with LPS containing 100 mol % of chloropropyl groups (Ladder A ) and 50 mol % of each methyl and chloropropyl group (Ladder B ). HPM was synthesized by reacting maleic anhydride with 4‐aminophenol, and the resulting amic acid was imidized using p‐toluenesulfonic acid as a catalyst (Scheme 1 ). The LPSs were characterized by Fourier transform infrared (FTIR), ¹H nuclear magnetic resonance (NMR), proton‐decoupled ¹³C NMR, ²⁹Si NMR, wide‐angle X‐ray diffraction (WAXD), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). Characterization indicated that these polymers had ordered ladder‐like structures with possible defects. These polymers were soluble in common solvents at ambient temperature, which suggested that they were not crosslinked. Both the polymers and the HPM were cured, and their kinetics were followed by dynamic DSC. The Ozawa and Kissinger methods were used to calculate activation energies for curing. Curing increased the temperature at which both 5% weight loss and maximum rate of weight loss were observed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4036–4046, 2004     

Diastereoselective formation of 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines: An X-ray crystallographic and H NMR study

N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data.     

On hooks of Young diagrams

The well-known fact that there is always one more addable than removable box for a Young diagram is generalized to arbitrary hooks. As an application, this immediately implies a simple proof of a conjecture of Regev and Vershik [3] for which inductive proofs have recently been given by Regev and Zeilberger [4] and Janson [1].     

Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crust

This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.