Hybrid organosilazane/organosilylamine telechelic oligomers—I. Two-dimensional NMR spectroscopy characterization of dimethylsilylethylenediamine oligomers

The detailed characterization of multifunctional hybrid organosilazane/organosilylamine telechelic oligomers by IR and ¹H, ¹³C and ²⁹Si NMR spectroscopy in one and two dimenions has been undertaken. The specific multifunctional oligomers, comprising NH/NH₂ or SiCl functionalities depending on the monomer feed-ratio, were prepared from mono- and di-functionally reacted dichlorodimethylsilane (DDS) and mono-, di-, tri- and tetra-functionally reacted ethylenediamine (EDA). Varying the feed-ratio afforded control of the microstructures of the oligomers and the preparation of oligomers with, in some cases, conterminously located silicon–chlorine (SiCl) groups. The combination of the NMR methods with the IR technique has enabled the detailed microstructural characterization of the oligomers and the identification of the functionalities therein. This approach and the knowledge gained from the DDS/EDA system has been applied to the microstructural characterization of other hybrid organosilazane/silylamine preceramic telechelic oligomers.     

深紫外无机非线性光学晶体硼铍酸锶及其分子工程学探索方法

阐述了紫外无机非线性光学晶体分子工程学探索方法的基本特点，具体分析深紫外无机非线性光学晶体硼铍酸锶（ＳＢＢＯ）以氟硼铍酸钾（ＫＢＢＦ）为主要参考晶体的分子设计方法，随后根据晶体结构研究、单晶培养、和非线性光学性能测定等实验结果讨论ＳＢＢＯ作为新型深紫外无机晶体的主要优点，即它既具有更短的紫外吸收边（接近１５５ｎｍ）和较大的非线性光学系数（ｄ２２（ＳＢＢＯ）＝０６×ｄ２２（ＢＢＯ）＝１３８ｐｍ／Ｖ），同时晶体无明显层状习性，并肯有良好的化学稳定性和机械性能     

Asymptotics in the random assignment problem

Summary We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.Research supported by NSF Grant MCS90-01710     

Radical copolymerization of 2‐trifluoromethylacrylic monomers. II. Kinetics,monomer reactivities,and penultimate effect in their copolymerization with norbornenes and vinyl ethers

Radical copolymerizations of electron‐deficient 2‐trifluoromethylacrylic (TFMA) monomers, such as 2‐trifluoromethylacrylic acid and t‐butyl 2‐trifluoromethylacrylate (TBTFMA), with electron‐rich norbornene derivatives and vinyl ethers with 2,2′‐azobisisobutyronitrile as the initiator were investigated in detail through the analysis of the kinetics in situ with ¹H NMR and through the determination of the monomer reactivity ratios. The norbornene derivatives used in this study included bicyclo[2.2.1]hept‐2‐ene (norbornene) and 5‐(2‐trifluoromethyl‐1,1,1‐trifluoro‐2‐hydroxylpropyl)‐2‐norbornene. The vinyl ether monomers were ethyl vinyl ether, t‐butyl vinyl ether, and 3,4‐dihydro‐2‐H‐pyran. Vinylene carbonate was found to copolymerize with TBTFMA. Although none of the monomers underwent radical homopolymerization under normal conditions, they copolymerized readily, producing a copolymer containing 60–70 mol % TFMA. The copolymerization of the TFMA monomer with norbornenes and vinyl ethers deviated from the terminal model and could be described by the penultimate model. The copolymers of TFMA reported in this article were evaluated as chemical amplification resist polymers for the emerging field of 157‐nm lithography. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1478–1505, 2004     

The σ<Emphasis Type="Italic">g</Emphasis>-Drazin Inverse and the Generalized Mbekhta Decomposition

In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended Mbekhta decomposition gives a characterization of circularly isolated spectral sets.     

Remarks on a theorem of Taskinen on spaces of continuous functions

We clarify and prove in a simpler way a result of Taskinen about symmetric operators on C(Kⁿ), K an uncountable metrizable compact space. To do this we prove that, for any compact space K and any n ∈ ?, the symmetric injective n–tensor product of C(K), , is complemented in C(B_C(K)*), a result of independent interest. The techniques we develop allow us to extend the result in several directions. We also show that the hypothesis of metrizability and uncountability cannot be removed.     

Classification of real moduli spaces over genus 2 curves

We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri.     

Skin-Depth Theory Explaining Anomalous Picosecond-Terawatt Laser Plasma Interaction II

The anomaly of ion emission at laser irradiation of targets measured by Badziak et al. was analyzed on the background of the extensive research in the past. In contrast to the irradiation with lasers of longer than 100 ps pulse duration, a drastic decrease of the maximum ion energies was measured with ps pulses. Very strange was the observation that the number of emitted fast ions was intensity independent. The usual ponderomotive or relativistic self-focusing theory and related processes could not explain the results. Instead a direct interaction within the skin depth of the irradiated target was concluded. This model confirms the plane geometry nonlinear force interaction in the ps range producing fast plasma blocks moving perpendicular off or into the target. The block moving into the target opens a new scheme of laser fusion by modifying the experiments of Norreys et al. The use of relatively low subrelativistic laser intensities for the new scheme of laser fusion is evaluated on the background of the long years studies of nonlinear force driven plasma blocks and earlier interpenetration fusion reactions for providing the parameters for expected fusion gains much higher than the experiment of Norreys et al. for a fusion power scheme.     

A model for the interaction of near-infrared laser pulses with metal powders in selective laser sintering

A thermal model of the interaction of pulsed near-infrared laser radiation from a Nd:YAG laser was made, taking the measured powder properties such as reflectance, optical penetration depth and thermal conductivity into account. It allows an estimation of the evolution of two different temperatures: the average temperature of the powder (taken over the grains in a volume given by the laser beam diameter and the optical penetration depth) and the temperature distinction within a single grain. It showed that in pulsed mode consolidation can be achieved at much lower average power as the surface of the powder particles are molten but their cores remain at nearly room temperature. This leads to a much lower average temperature and therefore a dramatic decrease in residual thermal stresses in the finished piece. The results of the model were experimentally tested and confirmed. Received: 26 July 2001 / Accepted: 23 November 2001 / Published online: 23 January 2002     

Bidendriform bialgebras, trees, and free quasi-symmetric functions

We introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the Malvenuto-Reutenauer Hopf algebra and the non-commutative Connes-Kreimer Hopf algebras of planar decorated rooted trees are bidendriform bialgebras. We prove that all connected bidendriform bialgebras are generated by their primitive elements as a dendriform algebra (bidendriform Milnor-Moore theorem) and then is isomorphic to a Connes-Kreimer Hopf algebra. As a corollary, the Hopf algebra of Malvenuto-Reutenauer is isomorphic to the Connes-Kreimer Hopf algebra of planar rooted trees decorated by a certain set. We deduce that the Lie algebra of its primitive elements is free in characteristic zero (G. Duchamp, F. Hivert and J.-Y. Thibon conjecture).