On the use of the Galerkin method for 3D numerical modelling of the general circulation: the South Atlantic eperiment

A linear three‐dimensional hydrodynamical numerical model, with the application of the Galerkin Method for the vertical dependence, is here presented. The spherical coordinate system is used, in order to allow large‐scale simulations. The equations and mathematical development of the model are shown in detail, together with the boundary and initial conditions, and the sequence of equations' solution. The model is applied to the South Atlantic Ocean, for estimating typical seasonal circulations, and the results are summarized in maps of currents at surface and 1000 m depth, and in transport values of the Brazil Current between 30°S and 40°S. Copyright © 2002 John Wiley & Sons, Ltd.     

Equivariant quantization on quotients of simple Lie groups by reductive subgroups of maximal rank

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation quantizations equivariant under the action ofG and the corresponding quantum group. We also classify Poisson brackets relating to such quantizations. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

Equivalence of Toda-Hopf invariants

In this paper it is shown that various existing constructions of ‘Hopf invariant’ are equivalent to each other. In consequence one gets that the oneToda-Hopf invariant enjoys various properties. Both authors supported in part by the NSF.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Strong, low-energy two-photon absorption in extended amine-terminated cyano-substituted phenylenevinylene oligomers

Three quadrupolar oligophenylenevinylenes with five rings in the conjugated backbone, terminal donor groups, and various acceptors and/or donors along the backbone were synthesized and their two-photon spectroscopic properties investigated. These chromophores exhibit large two-photon absorption cross sections over a wide wavelength range and two distinct peaks, the strongest of which (deltamax > 3600 GM) is observed at 960-970 nm, a wavelength close to twice the value of the linear absorption maximum (2lambda(1)max). The findings on these chromophores are compared with those for analogous molecules with shorter conjugation length, for which the main two-photon band is at significantly shorter wavelength than 2lambda(1)max.     

Synthesis and evaluation of a C8 stationary phase on a silica hydride surface by hydrosilation of 1-octyne

The silanization/hydrosilation method is used to bond an alkyne (1-octyne) to a silica hydride surface. The new bonded material is characterized by elemental analysis and diffuse reflectance infrared Fourier transform spectroscopy. The hydrophobic behavior of this material was determined by the retention characteristics of aromatic solutes and the shape selectivity as well as phase classification (monomeric or polymeric) was measured by the polycyclic aromatic hydrocarbon mixture standard reference material 869. The presence of residual silanols on the bonded phase was probed by several basic solutes at pH 7. Long-term stability studies were conducted by measuring retention and peak symmetry of basic compounds over several thousand column volumes at pH 10.     

Catalytic desulfurization of condensed thiophenes by means of methanol

Desulfurization of dibenzothiophene, two methyldibenzothiophenes, and phenanthro[4,5-bcd]-thiophene to give 60-80% yields of hydrocarbon products was effected by means of a sulfided molydena catalyst plus methanol at 450° and a pressure of ca. one atmosphere. The methanol functions both as an in situ hydrogen donor and as a methylating agent.     

Enzymatic polymerizations using surfactant microstructures and the preparation of polymer-ferrite composites

Applied Biochemistry and Biotechnology - Horseradish peroxidase has been used as a biocatalyst to synthesize a polymeric material from alkyl-substituted phenols. The synthesis is carried out in a...