Gauss-Manin connections for arrangements, III Formal connections

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.

     

Magnetic poly(glycidyl methacrylate) microspheres prepared by dispersion polymerization in the presence of electrostatically stabilized ferrofluids

Fine magnetite nanoparticles, both electrostatically stabilized and nonstabilized, were synthesized in situ by precipitation of Fe(II) and Fe(III) salts in alkaline medium. Magnetic poly(glycidyl methacrylate) (PGMA) microspheres with core‐shell structure, where Fe₃O₄ is the magnetic core and PGMA is the shell, were obtained by dispersion polymerization initiated with 2,2′‐azobisisobutyronitrile (AIBN), 4,4′‐azobis(4‐cyanovaleric acid) (ACVA), or ammonium persulfate (APS) in ethanol containing poly(vinylpyrrolidone) or ethylcellulose stabilizer in the presence of iron oxide ferrofluid. The average microsphere size ranged from 100 nm to 2 μm. The effects of the nature of ferrofluid, polymerization temperature, monomer, initiator, and stabilizer concentration on the PGMA particle size and polydispersity were studied. The particles contained 2–24 wt % of iron. AIBN produced larger microspheres than APS or ACVA. Polymers encapsulating electrostatically stabilized iron oxide particles contained lower amounts of oxirane groups compared with those obtained with untreated ferrofluid. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5827–5837, 2004     

Design and synthesis of labeling reagents (MS probes) for highly sensitive electrospray ionization mass spectrometry and their application to the detection of carbonyl, alcohol, carboxylic acid and primary amine samples.

Novel labeling reagents, called MS probes, which possess a positively charged quaternary amine moiety and can transform a neutral analyte into a charged compound by simply mixing with the analyte and allowing the mixture to stand from several minutes to 30 min at room temperature or while heating to 50 degrees C, were designed and synthesized for the highly sensitive detection of carbonyl, alcohol, carboxylic acid and primary amine samples by electrospray ionization mass spectrometry (ESI-MS). The positively charged products can be detected with high sensitivity in an ESI-MS system, which is the most popular liquid MS instrument. All of the labeled products showed a remarkably large increase in the molecular-ion peak abundance detection sensitivity of over 500-fold at picomolar concentration levels compared to that of unlabeled analytes in an ESI-MS system. These MS probes, used together with liquid MS detection, are widely applicable as a convenient method for the highly sensitive detection of less than picomolar levels of analytes, and therefore greatly enhance the power of ESI-MS analysis.     

The interfacial conformation of polypropylene glycols and foam behaviour

The foam behaviour of low molecular weight polypropylene glycols (PPG) was investigated as a function of concentration and molecular weight (190–2000 g mol⁻¹). For each polypropylene glycol, foam stability increases with concentration and passes through a maximum, beyond which foamability is suppressed as the solubility limit of the glycol is exceeded and droplets of glycol form. Light-scattering data as well as static and dynamic surface tension results provide the key information leading to these interpretations. A maximum in foamability was observed for the PPG molecules with increasing molecular weight (caused by a change in molecular conformation at the interface). This suppresses the Marangoni effect and leads to a decrease in foam stability.     

The Effects of a Study‐Group Process on the Implementation of Reform in Mathematics Education

In each of three consecutive years, 16 teachers were admitted to a program in which they participated in a study group to reform their teaching practices in mathematics. The 48 (total) elementary school teachers in this program were selected to ensure diversity of setting— urban and suburban, as well as public and parochial. Teachers routinely met with the study group for 1 year, engaging in follow‐up activities after that year. Surveys, interviews, and site visits showed that teachers underwent significant changes in their knowledge, beliefs, and teaching practices and were attempting to implement reform consistent with current standards. Teachers with 11 to 25 years of experience demonstrated the greatest changes. Long‐term effects of the program and its impact on colleagues within the building and district have yet to be studied.     

Oscillations of linear integro-differential equations

Sufficient conditions which guarantee that certain linear integro-differential equation cannot have a positive solution are established.