Skew Schubert polynomials

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schubert polynomials with nonnegative integer coefficients that are precisely the structure constants of the cohomology of the complex flag variety with respect to its basis of Schubert classes. We rederive the construction of Bergeron and Sottile in a purely combinatorial way, relating it to the construction of Schubert polynomials in terms of rc-graphs.

     

On a first-order hyperbolic system including Bean's model for superconductors with displacement current

This paper deals with a class of first-order systems with generally multivalued damping terms including Bean's model for superconductors with displacement current. The main goal is to prove the convergence of solutions to stationary states as t→∞.     

Vibration analysis by means of digital shearography

Digital shearography, also called digital speckle pattern shearing interferometry, is described as a robust measuring method due to its simple optical setup and the relative insensitivity against ambient noise. It has been applied for nondestructive testing and strain measuring. This paper explores its possibilities for vibration analysis. The measuring device performing both continuous (time-average method) and stroboscopic illuminations is described. The selection of the illumination mode is made by adjusting a controller and performed simply by a computer. The real-time observation with refreshing reference frame technique and the quantitative evaluation with the phase shift technique are presented. The results show this measuring device is well suited for both qualitative and quantitative vibration analysis.     

Synthesis of phenylquinoxaline oligomers containing pendant electron‐donating and electron‐withdrawing groups

A series of extended 6‐substituted quinoxaline AB monomer mixtures, 2‐(4‐fluorophenyl)‐3‐[4‐(4‐hydroxyphenoxy)phenyl]‐6‐substituted quinoxaline and 3‐(4‐fluorophenyl)‐2‐[4‐(4‐hydroxyphenoxy)phenyl]‐6‐substituted quinoxaline, were prepared and polymerized to afford phenylquinoxaline oligomers. High‐molecular‐weight polymers could not be obtained because of the formation of cyclic oligomers. On the basis of matrix‐assisted laser desorption/ionization time‐of‐flight analysis and molecular modeling results, the formation of a cyclic dimer could be a favorable process resulting in low‐molecular‐weight oligomers. They were completely soluble and amorphous, with glass‐transition temperatures varying from 165 to 266 °C, and they had thermooxidative stability, with samples displaying 5% weight loss temperatures of 419–511 °C in nitrogen. The thermal properties of the monomers and resultant polymers dramatically depended on the polarity of the substituents. The monomers and resultant oligomers displayed high fluorescence in tetrahydrofuran solutions and N‐methyl‐2‐pyrrolidinone solutions, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6465–6479, 2005     

ABA triblock copolymers with a ring‐opening metathesis polymerization/macromolecular chain‐transfer agent approach

Block copolymers containing polystyrene and polycyclooctene were synthesized with a ring‐opening metathesis polymerization/chain‐transfer approach. Polystyrene, containing appropriately placed olefins, was prepared by anionic polymerization and served as a macromolecular chain‐transfer agent for the ring‐opening metathesis polymerization of cyclooctene. These unsaturated polymers were subsequently converted to the corresponding saturated triblock copolymers with a simple heterogeneous catalytic hydrogenation step. The molecular and morphological characterization of the block copolymers was consistent with the absence of significant branching in the central polycyclooctene and polyethylene blocks [high melting temperatures (114–127 °C) and levels of crystallinity (17–42%)]. A dramatic improvement in both the long‐range order and the mechanical properties of a microphase‐separated, symmetric polystyrene–polycyclooctene–polystyrene block copolymer sample was observed after fractionation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 361–373, 2007     

Algorithms for extraction of spacing information from a head/tape interface

Various algorithms for the extraction of spacing information from an interferometric fringe pattern of the head/tape interface have been proposed. In this paper, a comparison of three algorithms is presented: tape unloading, polynomial fitting and Fourier transform. The relative merits of each method are discussed, together with implementation details. In an experiment with a transparent head and CrO₂ tape, it was found that all methods give a similar result to within ±5 nm, with none unilaterally preferable to the others. The Fourier transform method, which has not been used for this application before, gives smooth spacing data for high fringe orders, and is less sensitive to fringe order errors, but produces noisier spacing data in the contact region.