C ϰ(X) and a property of (db)-spaces

Summary A new class of locally convex linear topological spaces, the (db)-spaees, recently defined by Robertson, Tweddle and Yeomans, interpolates the classes of Baire-like and unordered Baire-like spaces. Saxon and Narayanaswami have given convex metrizable spaces that distinguish among these classes. This paper gives a new characterization of (db)-spaces from which is extracted the class of b-spaces. This class interpolates the classes of -spaces and -spaces of Lehner. Let C(X) be the space of all real-valued continuous functions on the completely regular Sausdorf space X, supplied with the topology of uniform convergence on compact sets of X. It is shown that C(X) is a b-space if and only if it is an -space. A characterization of X for which C(X) is a (db)-space is unknown. Other open questions are stated in the paper.     

Facile Phenylphosphinidene Transfer Reactions from Carbene–Phosphinidene Zinc Complexes

Phosphinidenes [R-P] are convenient P₁ building blocks for the synthesis of a plethora of organophosphorus compounds. Thus far, transition-metal-complexed phosphinidenes have been used for their singlet ground-state reactivity to promote selective addition and insertion reactions. One disadvantage of this approach is that after transfer of the P₁ moiety to the substrate, a challenging demetallation step is required to provide the free phosphine. We report a simple method that enables the Lewis acid promoted transfer of phenylphosphinidene, [PhP], from NHC=PPh adducts (NHC=N-heterocyclic carbene) to various substrates to produce directly uncoordinated phosphorus heterocycles that are difficult to obtain otherwise.     

Convenient Method for the 3‐Functionalization of Isoindazoles

The C‐3 position of isoindazoles is readily functionalized by metalation with lithium diisopropylamide followed by reaction with a variety of electrophiles.     

Closed paths of light trapped in a closed Fermat curve

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the curve varies, including a generalization to non integer powers.     

Microsoft Excel as a supplement in a high school statistics course

This study was conducted in the spring of 2002 at Arlington High School in a Probability and Statistics course for junior and senior level students. Two sections of the class were compared with respect to the use/non-use of EXCEL in the course. The experimental group (the one using EXCEL) outperformed the control group on five of the six teacher-created unit tests and on both of the criterion referenced assessments used by the district; however, the differences were not statistically significant at the 0.05 level. Furthermore, the experimental group expressed very positive feelings towards the use of the software in a survey administered at the conclusion of the course.     

Synthetic studies towards zetekitoxin AB: preparation of 4,5-epi-11-hydroxy-saxitoxinol

A concise synthesis of 4,5-epi-11-hydroxy-saxitoxinol utilizing d-ribose to direct an asymmetric Mannich reaction. This approach allows many modes of reactivity, which can be used to access various analogs of saxitoxin.