O− and OH− chemical ionization of some fatty acid methyl esters and triacylglycerols

O^? and OH^? react with fatty acid methyl esters (FAMES) under chemical ionization conditions both as Bronsted bases to form [M - H]^? and as nucleophiles to form the carboxylate ion RCOO^?. O^? shows a much greater tendency to react as a nucleophile than does OH^?. The [M - H]^? ions fragment by elimination of CH³OH, with unsaturation in certain positions in the fatty acid hydrocarbon chain promoting this elimination for unknown reasons. The reaction of O^? and OH^? with triacylglycerols leads to [M - H]^?, characteristic of the molecular mass, and to carboxylate ions characteristic of the fatty acid(s) present in the lipid. The presence of the three ester functions in the lipids greatly enhances the formation of carboxylate ions compared to the FAMES.     

On error bounds for lower semicontinuous functions

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f. In a reflexive Banach space X, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini derivative of f. Received: April 27, 2001 / Accepted: November 6, 2001?Published online April 12, 2002     

Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Superconvergence of recovered gradients of discrete time/piecewise linear Galerkin approximations for linear and nonlinear parabolic problems

Superconvergent error estimates in l₂(H¹) and l∞(H¹) norms are derived for recovered gradients of finite difference in time/piecewise linear Galerkin approximations in space for linear and quasinonlinear parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context, and covers problems in regions with nonsmooth boundaries under certain assumptions on the regularity of the solutions. © 1994 John Wiley & Sons, Inc.     

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.     

Chemistry of biureas—I: Cyclisation of ethoxycarbonyl derivatives of thiobiureas and bithioureas

The interaction of ethoxycarbonyl isothiocyanate with semicarbazides or thiosemicarbazides produces 1-ethoxycarbonyl-2-thiobiureas or bithioureas, respectively. The former are cyclisable to 2-ethoxycarbonamido-5-hydroxy-l,3,4-thiadiazole in acid, or to 2(H)-carbamoyl-3-hydroxy-5-alkylthio-1,2,4-triazoles, and thence to 3-hydroxy-5-mercapto-1,2,4-triazole in alkaline media. The ring-closure of the 1-ethoxycarbonylbithioureas proceeds similarly affording, under the influence of acids, 5-amino (or mercapto)-2-ethoxycarbonamido-1,3,4-thiadiazoles. The action of alkali produces compounds derived from 3-hydroxy-5-mercapto-1,2,4-triazole; the isolation, in a selected example, of the 2(H)-phenylthiocarbamoyl-derivative, elucidates the course of this reaction. Hydrazinolysis of 1-ethoxycarbonylbithiourea yields 4-amino-3-hydrazino-5-mercapto-1,2,4-triazole.     

CAROTENOID TRIPLET STATES IN PHOTOSYNTHETIC BACTERIA

Abstract— The triplet state spectra of anaerobically grown cells of Rhodopseudomonas sphaeroides GIC and R. sphaeroides wild type and aerobically grown cells of R. sphaeroides wild type were examined under reducing and non-reducing conditions at 100 K. by electron paramagnetic resonance (EPR). Large differences in the zero field splitting parameters, |D| and |E| of the triplets are seen to arise in the different preparations. The spectra are assigned to the triplet states of carotenoids, some of which are closely associated with the reaction center and others are contained in the light harvesting complex. Taken together with the triplet state data on Rhodospirillum rubrum wild type previously published the trends in the zero field splitting parameters can be understood in terms of the extent of electron derealization in carotenoids of varying length.