Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

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.     

Erbium:YAG (2.94 mum) laser effects on dental tissues

Past trials with soft and calcified tissues have demonstrated that long pulse train (2.5 mus) Er:YAG (2.94 mum) laser may be used to ablate tooth structure of human teeth. Determination of physical and thermal damage to surrounding tissue during removal of enamel and dentin is a primary objective of this study. Extracted human teeth with thermal probes imbedded in the pulp chambers were submitted to cavity preparation using an Erbium YAG laser with water mist. Wavelength selection as well as use of a water mist during the procedure resulted in efficient tissue removal without significant surrounding damage. Ground sections and SEM sections of teeth showed little or no melting or ash formation in adjacent dentin and enamel and no visible change in the pulp chamber. The surfaces produced by laser ablation were rough and irregular with craters and grooves. Average temperature change in the pulp chamber monitored during tooth preparation was 2.2 degrees Centigrade. These findings suggest that constantly available water aids vaporization and microexplosions, increasing the efficiency of tooth structure removal, and aids in cooling of the tooth structures. The long pulse Er:YAG (2.94 mum) laser may be an effective method for tooth reduction applications when used with a water mist.     

Fundamental role of the fostriecin unsaturated lactone and implications for selective protein phosphatase inhibition

Key derivatives and analogues of fostriecin were prepared and examined that revealed a fundamental role for the unsaturated lactone and confirmed the essential nature of the phosphate monoester. Thus, an identical 200-fold reduction in protein phosphatase 2A (PP2A) inhibition is observed with either the saturated lactone (7) or with an analogue that lacks the entire lactone (15). This 200-fold increase in PP2A inhibition attributable to the unsaturated lactone potentially may be due to reversible C269 alkylation within the PP beta12-beta13 active site loop accounting for PP2A/4 potency and selectivity.     

Preparation and polymerization of some N-(dialkylaminoalkyl)acrylamides

A series of N-(dialkylaminoalkyl)acrylamides was synthesized by reductive amination of N-(1,1-dimethyl-3-oxobutyl)acrylamide (diacetone acrylamide) and by the reaction of either an alkenylamine or an amino alcohol with acrylonitrile. These monomers homopolymerize and copolymerize readily to form high molecular weight products. The solubility of the monomers and their homopolymers in water ranges from soluble to insoluble at room temperature. The insoluble materials can be quaternized readily to produce water-soluble products. The solubility of the homopolymers in water decreases with increasing temperature. Glass transition and decomposition temperatures of the homopolymers are reported.     

An alternative preparation of the 2-dimethylaminomethylene-1,3-bis(dimethylimmonio)propane salt from phosphonoacetic acids and some applications in heterocyclic synthesis

An alternative preparation of a 2-iminovinamidinium salt from phosphonoacetic acids is described along with its application to the synthesis of 5-formylpyrimidines and masked 4-formylpyrazoles.     

A simple and efficient one step synthesis of benzoxazoles and benzimidazoles from carboxylic acids

Benzoxazoles or benzimidazoles can be rapidly and efficiently synthesized from a variety of carboxylic acids with 2-aminophenols or 1,2-phenylenediamines in one simple step, respectively. The use of commercially available PS-PPh₃ resin combined with microwave heating delivered a variety of benzoxazoles and benzimidazoles in high yields and purities.     

Contribution to the quantitative x-ray analysis of individual submicrometre particles: Asbestos fibres

Summary A procedure for the analysis of individual asbestos fibres in the submicrometre diameter range, based on the ratio method of thin film analysis, is presented. The reliability of this method has been tested in a study of identification of asbestos fibres. The systematic and statistical errors were investigated.

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Beitrag zur quantitativen Röntgenmikroanalyse einzelner Submikrometerteilchen: Asbestfasern

Zusammenfassung Es wurde versucht, eine Quantifizierungsmethode analog der Verhältnismethode zur Analyse dünner Schichten für die Analyse von Asbestfasern mit Durchmessern im Submikrometerbereich zu entwickeln. Die Zuverlässigkeit der Methode wurde mit einem Anwendungsbeispiel überprüft, und alle systematischen und statistischen Fehler wurden dargelegt.

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Presented at the 8th International Microchemical Symposium, Graz, August 25–30, 1980.     

Syntheses and Crystal Structures of Some CCo3 Clusters Containing PPh3 or dppm Ligands

Molecular structural determinations are reported for six Co₃C carbonyl cluster complexes containing tertiary phosphines, which have been isolated as by-products from a variety of reactions. Structural features are similar to those of related complexes already reported. Some discussion of apparent orientational preferences of the CH₂ group of dppm ligands, which appear to enter into H-bonding interactions with amido or carboxylate substituents, is given. Appropriate comparisons are made with unsubstituted analogues.     

Liquid chromatographic determination of sulindac and metabolites in serum

An improved liquid chromatographic procedure is described for the quantitative determination of sulindac, sulindac sulfone, and sulindac sulfide from serum. The procedure makes use of acetonitrile extraction of the compounds of interest from acidified serum samples. Under these conditions extraction efficiencies in the 85 percent range are obtained for each of the compounds. The liquid chromatographic separation of the compounds of interest and the internal standard (indomethacin) is accomplished in an isocratic elution procedure using a nitrile (CN) stationary phase. The HPLC separation procedure is completed in less than 10 minutes, giving excellent resolution and peak shape.