Synthesis of 2-indanones via [4 + 1] annulation reactions of (trialkylsilyl)arylketenes

[reaction: see text] (Trialkylsilyl)arylketenes combine with (trimethylsilyl)diazomethane in a new [4 + 1] annulation process leading to 2-indanone derivatives. The (trialkylsilyl)arylketene annulation substrates are available via the photochemical Wolff rearrangement of alpha-silyl-alpha-diazo ketones, which are themselves prepared by silylation of the corresponding diazo ketones. The mechanism of the annulation reaction is proposed to involve the formation of a 2,3-bis(silyl)cyclopropanone, which is in equilibrium with an oxyallylic cation. Electrocyclic closure of this intermediate forms the new cyclopentenone ring.     

Investigating Why Teachers Reported Continued Use and Sharing of an Educational Innovation After the Research Has Ended

We investigated prospects for reported sustainable adoption and sharing of an educational innovation through survey research including online questionnaires and telephone interviews. This investigation is part of the Scaling-Up SimCalc experimental program, which combines dynamic representational algebra software (SimCalc MathWorlds) with integrated curriculum and small professional development workshops focused on how to use the software and how to integrate this intervention into the larger year-long curriculum. Teachers who (1) perceived the usefulness of the SimCalc professional development as being consistent with personal aims and (2) perceived specific affordances of the software/curriculum to be valuable were more likely to report continued use of the innovation after the research had ended and that they had shared it with colleagues over time.     

The electoral system for the Italian Senate: an analogy with deterministic chaos?

The electoral system adopted for the allocation of seats in the Italian Senate utilizes a complex mechanism of awards at a regional level with the aim of strengthening, when necessary, the winning coalition and so improve overall government stability. The results presented here demonstrate that in a significant number of cases, the effect of the mechanism is opposite to that desired, to wit, weakening the resultant government by awarding more seats to the minority coalition. Indeed the award to the minority can even be such that the minority coalition becomes the majority and wins the election. The application of the award mechanism is strongly unpredictable as it depends crucially on the precise number of seats independently obtained in each region, and that each adjustment thereof can be positive, zero or negative; a characteristic that closely resembles the behaviour of a chaotic dynamical system whose trajectory, although purely deterministic, depends on infinitely precise details and is therefore unpredictable. To perform the systematic numerical analysis of the award effectiveness, we introduce characteristic polynomials, one for each electoral district, which carry information about all possible outcomes and award applications. Their product yields a polynomial containing the dependence of the result at national level on each of the regional awards.     

Electrodynamics: A consequence of nonlinear realizations of the Lorentz group

Extensions from the representations of the Lorentz group to include local nonlinear diagonal transformations is sufficient to generate, via the covariant derivative, the interaction of minimal coupling. These diagonal realizations are characterized by six functions φ which must satisfy a system of transformation equations. Inequivalent categories of solutions for the φ give rise to different electromagnetic fields. The Dirac monopole and Coulomb potentials follow directly from two different categories of these nonlinear realizations. Within this theory, charge becomes simply the nonlinear counterpart of intrinsic spin for aparticular nonlinear realization of the Lorentz group. Charge is thus placed on equal footing with intrinsic spin in the sense that both phenomena can be described as consequences of our space-time symmetry. Other solutions for the six φ exist, including a spinor. We briefly discuss the possibility that with these other solutions, these realizations could represent some other basic properties of elementary particles.     

Identification of a 4H-benz[f]indole by-product from the friedel-crafts-based synthesis of benzoylpyrrole calcium channel activators

9,9a-Dihydro-2,9a-dimethyl-4-oxo-4H-benz[f]indole-3-carboxylic acid, methyl ester was formed in varying amounts from the Friedel-Crafts-based synthesis of benzoylpyrrole calcium channel activators. The structure of this by-product was determined using two-dimensional long-range ¹H-¹³C heteronuclear correlated and INADEQUATE nmr techniques.