Extension of β-chloroenals to ethyl 5-chloro-2,4-pentadienoates using Wadsworth-Emmons reactions: subsequent conversions to 5-aryl-5-chloro-2,4-pentadienoic acids and 5-aryl-2-penten-4-ynoic acids

Convenient routes from (Z)-3-aryl-3-chloroenals to (2E,4Z)-5-aryl-5-chloro-2,4-pentadienoates and (2E)-5-aryl-2-penten-4-ynoates are described. The stereochemical assignments are based on NMR spectral data.     

Evaluation of AM1-calculated radical cation ion-neutral complexes

AM1 semiempirical molecular orbital calculations are reported for 20 ion-neutral complexes, including hydrogen-bonded complexes, presumably involved in the gas-phase unimolecular decomposition of simple organic radical cations. The systems investigated are [C₂H₄O₂]^˙+, [C₂H₅NO]^˙+, [C₂H₆O]^˙+, [C₂H₆O₂]^˙+, [C₃H₆O]^˙+, [C₃H₆O₂]^˙+, [C₃H₈O]^˙+, and [C₃H₈O₂]^˙+. The AM1 results are compared with ab initio molecular orbital calculations at different levels of theory up to MP3/6-31G(d, p)//SCF/6-31G(d) + ZPVE and the available experimental data. AM1 fails to predict some local minima and the equilibrium geometries calculated for several complexes are found to be qualitatively different from those predicted by the ab initio calculations. However, reasonable agreement is generally found for the stabilization energies of the complexes toward dissociation into their loosely bound components. © John Wiley & Sons, Inc.     

Polyhedral polarity defined by a general bilinear inequality

LetX andY be finite dimensional vector spaces over the real numbers. Let be a binary relation betweenX andY given by a bilinear inequality. The-polar of a subsetP ofX is the set of all elements ofY which are related by to all elements ofP. The-polar of a subset ofY is defined similarly. The-polar of the-polar ofP is called the-closure ofP andP is called-closed ifP equals its-closure. We describe the-polar of any finitely generated setP as the solution set of a finite system of linear inequalities and describe the-closure ofP as a finitely generated set. The-closed polyhedra are characterized in terms of defining systems of linear inequalities and also in terms of the relationship of the polyhedronP with its recessional cone and with certain subsets ofX andY determined by the relation. Six classes of bilinear inequalities are distinguished in the characterization of-closed polyhedra.     

A Note on Random Sums with Nonrandom Centering

Let X ₁, X ₂,... be a sequence ofi.i.d. random variables and N _n a sequence ofnon-negative integer valued random variables, independent of{X _i }. The main results concern tightnessand weak convergence of under the natural condition that thesample mean is a consistent estimator of .     

A dual-polarization InSb receiver for 461/492 GHz

A dual-polarization InSb hot-electron bolometer-mixer receiver has been built for the James Clerk Maxwell Telescope, for operation at 461 and 492 GHz (the frequencies of theJ=43 rotational transition of CO and of the³ P ₁³ P ₀ transition of neutral carbon). Receiver noise temperatures of 500K have been obtained at 461 GHz, in observing bandwidths of 3 MHz. The receiver was designed as a common-user or facility instrument. Here we describe those aspects of the design and construction which enabled this goal to be realized.