A topological aspect of Sobolev mappings

Let be a connected open set, . We give a sufficient condition for a mapping , , to have the property that sgn is almost everywhere of one sign. Following the work of Müller, Spector, and Tang [MST], we give an application of our results to the theory of non-linear elasticity. Received: 13 October 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

Tip-induced local anodic oxidation on p-GaAs surface with non-contact atomic force microscopy

Nano-sized oxide structures resulted from localized electrochemical oxidation induced by a negatively biased atomic force microscopy (AFM) tip operated with the non-contact mode were fabricated on p-GaAs(1 0 0) surface. The geometrical characteristics of the oxide patterns and their dependences on various fabrication parameters, e.g., the anodization time, the biased voltages, the tip scanning rates, as well as the formation mechanism and relevant growth kinetics are investigated. Results indicate that the height of the protruded oxide dots grow exponentially as a function of time in the initial stage of oxidation and soon reaches a maximum height depending linearly with the anodized voltages, in according with the behaviors predicted by space charge limited local oxidation mechanism. In addition, selective micro-Auger analysis of the anodized region reveals the formation of Ga(As)O_x, indicating the prominent role played by the field-induced nanometer-size water meniscus in producing the nanometer-scale oxide dots and bumps on p-GaAs(1 0 0) surface.     

Preparation,thermal properties,and flame retardance of epoxy–silica hybrid resins

A novel epoxy system was developed through the in situ curing of bisphenol A type epoxy and 4,4′‐diaminodiphenylmethane with the sol–gel reaction of a phosphorus‐containing trimethoxysilane (DOPO–GPTMS), which was prepared from the reaction of 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO) with 3‐glycidoxypropyltrimethoxysilane (GPTMS). The preparation of DOPO–GPTMS was confirmed with Fourier transform infrared, ¹H and ³¹P NMR, and elemental analysis. The resulting organic–inorganic hybrid epoxy resins exhibited a high glass‐transition temperature (167 °C), good thermal stability over 320 °C, and a high limited oxygen index of 28.5. The synergism of phosphorus and silicon on flame retardance was observed. Moreover, the kinetics of the thermal oxidative degradation of the hybrid epoxy resins were studied. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2354–2367, 2003     

Synthesis and transition temperatures of liquid crystals incorporating a 1,4-tetrafluorophenylene unit

Two homologous series of mesogenic materials which incorporate a 1,4-tetrafluorophenylene moiety and a terminal cyano- or nitro-substituent have been synthesized by using palladiumcatalysed coupling procedures. The compounds exhibit nematic and/or smectic A phases.     

Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Geometric Knowledge of Middle School Students in a Reform-based Mathematics Curriculum

National and international studies have found U.S. elementary students to be weak in their understandings and applications of geometric concepts. The University of Chicago School Mathematics Project's (UCMSP) Everyday Mathematics Program is one of the current reform-based elementary curricula incorporating geometry throughout the K-6 curriculum, with an emphasis on hands-on and problem-solving activities. In this study, the geometric knowledge of fifth and sixth graders using the UCSMP curriculum is compared to the knowledge of students using more traditional curricula. Because UCSMP students had been in the program since kindergarten, this research attempts to measure the longitudinal effects of such an approach. Along with an overall score, a subset of test items was used to assign each student a van Hiele level for geometric thinking, as well as a reasoning score. On all measures, UCSMP students substantially outperformed their counterparts, and nearly all differences were significant. Aspects of the UCSMP curriculum and the van Hiele model for learning geometry are discussed relative to these results.