A Lefschetz type result for Koszul cohomology

We study the behaviour of Koszul cohomology under restriction to a divisor, extending previous results of M. Green. Using our result we compare Greens canonical conjecture to the gonality conjecture of Green-Lazarsfeld.Revised version: 15 May 2003Acknowledgements. M. Aprodu was financed by a EC-Marie Curie Fellowship, contract no. HPMF-CT-2000-00895. We would like to thank the referee for some useful remarks on the first version of this paper.     

Intensity-related dynamics of femtosecond frequency combs

We have performed systematic studies of intensity-related dynamics of the pulse repetition and carrier-envelope offset frequencies in mode-locked Ti:sapphire lasers. We compared the results far two laser systems that have different intracavity dispersion-compensation schemes. We found that the carrier-envelope phase noise and its dynamic response depend critically on the mode-locking conditions. An intensity-related shift of the laser spectrum was found to be instrumental in interpretations.     

Conditional weak compactness in vector-valued function spaces

Let be an ideal of over a -finite measure space and let be the Köthe dual of with . Let be a real Banach space, and the topological dual of . Let be a subspace of the space of equivalence classes of strongly measurable functions and consisting of all those for which the scalar function belongs to . For a subset of for which the set is -bounded the following statement is equivalent to conditional -compactness: the set is conditionally -compact and is a conditionally weakly compact subset of for each , with . Applications to Orlicz-Bochner spaces are given.

     

Strong topologies on vector-valued function spaces

Let be a real Banach space and let E be an ideal of L ⁰ over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.     

The Conley index over a base

We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in , and the problem of continuing two periodic orbits which are not homotopic as loops.

     

Effects of electron-beam irradiation on surface oxidation of polymer composites

The aim of this article was to show the effects of an electron radiation dose and presence of a compatibilizer on the oxidation of composites made of blends of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polypropylene (PP), polystyrene (PS), and poly(ethylene terephthalate) (PET) as well as of blends of LDPE, HDPE, and PP. As the compatibilizers, the styrene-ethylene/butylene-styrene elastomer grafted with maleic anhydride (SEBS-g-MA) and trimethylol propane trimethylacrylate (TMPTA) were used; they were added in the amounts of 5, 10, and 15 wt% and 1, 2, and 3 wt%, respectively. The oxidation of the surface layer (SL) was investigated by the X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It was found that the extent of the composite oxidation increased with the increasing dose of the electron radiation. The addition of the compatibilizers enhanced the oxidation of the SL but hindered the oxidation of the bulk of the material.     

Atmospheric plasma treatment of pre‐electrospinning polymer solution: A feasible method to improve electrospinnability

The electrospinnability of polyethylene oxide (PEO) was manipulated by atmospheric plasma treatment of pre‐electrospinning solutions. Conductivity, viscosity, and surface tension of PEO solutions increased after plasma treatment, and the plasma effect remained longer when the solution concentrate increased. Both untreated and treated solutions were then electrospun, and the morphology of the resultant nanofibers was observed by SEM. Atmospheric plasma treatment improved the electrospinnability of PEO solutions and led to less beads and finer diameter distribution in the resultant nanofibers. Additionally, plasma treatment of the pre‐electrospinning solutions affected the crystal structure of resultant nanofibers. These results suggest that atmospheric plasma treatment is a feasible approach to improve the electrospinnability of polymer solutions and can used to control the structure of electrospun nanofibers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Pressure‐induced polymerization of tetraethylene glycol dimethacrylate

The polymerization and crosslinking of tetraethylene glycol dimethacrylate were induced by high pressure. The product was analyzed by both swelling experiments and broadband dielectric spectroscopy to determine the structure, with IR measurements used to follow the extent of reaction and its temperature dependence. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3795–3801, 2008