THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Dimethylzinc-mediated addition of alkenylzirconocenes to alpha-keto and alpha-imino esters

[reaction: see text] Hydrozirconation of alkynes followed by in situ transmetalation to dimethylzinc and 1,2-addition to activated ketones and N-diphenylphosphinoylimines leads to tertiary allylic alcohols and amines in high overall yield. With 8-phenylmenthol as the chiral auxiliary, si-face attack proceeds in good to excellent diastereoselectivities.     

Application of divergent multi-component reactions in the synthesis of a library of peptidomimetics based on γ-amino-α,β-cyclopropyl acids

The multi-component condensation of organozirconocene, aldimine and zinc carbenoid was applied to the stereoselective synthesis of cyclopropane amino acid derivatives. These compounds served as scaffolds for the preparation of a 46-member library. The C- and N-termini of the cyclopropane amino acid derivatives were diversified by condensations with ten amines and ten acylating agents, respectively. To improve yields and accelerate library synthesis, most products were prepared under microwave irradiation and purified by polymer-bound scavengers and SPE methodology. All compounds were analyzed by LC-MS and a representative selection was fully characterized.     

A New Synthetic Route to (±)-Perhydrohistrionicotoxin

Starting from ethyl 2-cyclohexen-1-carboxylate ( 3 ) the total synthesis of the perhydrohistrionicotoxin intermediate 23 was achieved in 25% overall-yield. The two key steps involve a positionally specific addition of HOBr to the oxime-olefin 7 and the alkylation of bromooxime 17 with 1-lithio-1-butyne. The latter represents a novel method for stereospecific and position-specific introduction of a nucleophilic butyl equivalent in α-position to a ketonic carbonyl group.     

Total synthesis of natural (levo) and enantiomeric (dextro) forms of prostaglandin El

1 newly-discovered method of synthesizing PGE1 (prostaglandin E1) is explained and diagrammed chemically. Recrystallization of the synthetic product produced material identical in all respects with natural PGE1. The synthetic product showed the same infrared spectrum and chromatographic values as racemic and natural forms of PGE1. The biological activity of the synthetic product was found to be .1% of that of the naturally-occurring PGE1 in the stimulation of smooth muscle contraction. This is the 1st report of a total synthesis of PGE1. Research continues on improvements in this synthesizing method and on discovering other synthetic approaches to PGs.     

A mechanistically guided design leads to the synthesis of an efficient and practical new reagent for the highly enantioselective,catalytic dihydroxylation of olefins

[structure: see text] The catalytic asymmetric dihydroxylation of olefins has been accomplished with high enantioselectivities using a proline-based catalyst. The pre-transition-state assembly for styrene is shown.     

A short and efficient enantioselective route to a key intermediate for the total synthesis of forskolin

A simple route for the enantioselective synthesis of key intermediates (11 and 12) for the total synthesis of forskolin has been developed starting from acid 6 and (S)-alcohol 5. The latter is prepared by enantioselective catalytic CBS reduction of dienone 3, and is converted by an intramolecular Diels-Alder reaction to tricyclic lactone 9.     

Microwave-assisted "libraries from libraries" approach toward the synthesis of allyl- and C-cyclopropylalkylamides

Cascade reactions of internal and terminal alkynes, zirconocene hydrochloride, dimethylzinc, and phosphinoyl imines (prepared in one step from aldehydes and diphenylphosphinoyl amide) lead to allylic phosphinoyl amides after aqueous workup. Microwave acceleration allows the completion of this one-pot reaction sequence in 10 min. These allylic amides can be converted into a variety of derivatives, including carbamates and sulfonamides, or reacted prior to workup with diiodomethane to give novel C-cyclopropylalkylamides. A solution-phase "libraries from libraries" approach was used to generate an intermediate 20-member library which was subsequently expanded to a 100-member library by a series of N-functionalizations. The biological activity was evaluated in an assay for competitive binding to the estrogen receptor (ERalpha), revealing three potent lead compounds of a new structural type.     

Synthesis of 6,7-disubstituted-5H-pyrrolo[2,3-b]pyrazines via palladium-catalyzed heteroannulation

A concise and efficient method for the preparation of 6,7-disubstituted-5H-pyrrolo[2,3-b]pyrazines via a palladium-catalyzed heteroannulation is reported. Both conventional and microwave heating were used to perform the reactions, with the latter showing dramatically improved results.