Microwave accelerated aza-Claisen rearrangements

The microwave-assisted thermal aza-Claisen rearrangement of allylic imidates and thiocyanates to the corresponding amides and isothiocyanates is investigated. Significant accelerations of the rearrangement of allylic imidates to amides and of allylic thiocyanates to isothiocyanates in comparison with standard thermal reactions is observed.     

Tandem asymmetric conjugate addition--silylation of enantiomerically enriched zinc enolates. Synthetic importance and mechanistic implications

[formula: see text] The zinc enolates, resulting from the copper-catalyzed enantioselective conjugate addition of dialkyl zinc reagents to cyclic and acyclic enones, could be trapped, quantitatively, as silyl enol ethers with TMSOTf in apolar solvents or with TMSCI and NEt3. These enantiomerically enriched silyl enol ethers were submitted to four synthetic transformations to show their synthetic utility. The zinc enolates obtained from acyclic enones were found to be configurationally stable, as shown by the stereochemistry of the silyl enol ethers.     

Rapid parallel synthesis of polymer-bound enones utilizing microwave-assisted solid-phase chemistry

A microwave-assisted parallel solid-phase synthesis of a collection of 21 polymer-bound enones has been developed. The two-step protocol involves initial high-speed acetoacetylation of polystyrene Wang resin with a selection of seven common beta-ketoesters. When microwave flash heating at 170 degreesC was employed, complete conversions were achieved within 1-10 min, a significant improvement over the conventional thermal method, which takes several hours for completion. Significant rate enhancements were also observed for the subsequent microwave-heated Knoevenagel condensations with a second set of 13 different aldehydes. Reaction times were reduced to 30-60 min at 125 degreesC in the microwave protocol compared to 1-2 days using conventional thermal conditions. Kinetic comparison studies indicate that the observed rate enhancements can be attributed to the rapid direct heating of the solvent (1,2-dichlorobenzene) by microwaves rather than to any specific microwave effect. All reactions have been carried out in commercially available parallel reactors with on-line temperature measurement, designed specifically for use in multimode microwave cavities.     

Adaptive Filtering Revisited

This paper shows that the adaptive filtering and forecasting techniques proposed by Makridakis and Wheelwright can be viewed as approximations to a more precise filtering method in which the Kalman filter is applied to a dynamic autoregressive model which is a special case of the models of Harrison and Stevens. The correct "learning" or "training factors" are shown to be data-dependent matrices rather than scalar constants.     

The ϕ 2 4 quantum field as a limit of Sine-Gordon fields

We exhibit the λ? ₂ ⁴ quantum field theory as the limit of Sine-Gordon fields as suggested by the identity $$\varphi ^4 /4! = \mathop {\lim }\limits_{\varepsilon \to 0} (\varepsilon ^{ - 4} \cos \varepsilon \varphi - \varepsilon ^{ - 4} + \tfrac{1}{2}\varepsilon ^{ - 2} \varphi ^2 ).$$ The proofs of finite volume stability for the two models, due to Nelson and Fröhlich respectively, are unrelated. We find a generalized stability argument that incorporates ideas from both of the simpler cases. The above limit, for the Schwinger functions, then proceeds uniformly in ?. As a by-product, let (?,dμ) be a Gaussian random field, ? _K (1≦κ<∞) a regularization of ?, andV a function satisfying:

1. V(? _K )≧?ak ^α
2. ∥V(?) ?V(? _K )∥ _p≦bp ^β k ^?γ, 2≦p < ∞

Thene ^?V(?)∈L ¹(dμ) provided α(β?1)<γ.     

The Robertson-Walker metric and the symmetries belong to the family of contracted Ricci collineations

It is shown that the general form of the Robertson-Walker cosmological metric admits symmetry properties that are members of the symmetry family of contracted Ricci collineations. A particular form for the conservation law generator given by _j [(–g)^1/2(T _i ^j –1/2 _i ^jT ) ⁱ ] = 0 following in consequence of these symmetries is obtained and interpreted.     

On the decay of correlations inSO(n)-symmetric ferromagnets

We prove that for low temperaturesT the spin-spin correlation function of the two-dimensional classicalSO(n)-symmetric Ising ferromagnet decays faster than |x|^–constT providedn2. We also discuss a nearest neighbor continuous spin model, with spins restricted to a finite interval, where we show that the spin-spin correlation function decays exponentially in any number of dimensions.Work supported in part by NSF, Grant PHY76-17191A Sloan Fellow     

RNAi: running interference for the cell

RNA interference or RNAi is a recently characterized mechanism of eukaryotic gene regulation in which a short sequence of double-stranded RNA (dsRNA) specifically down-regulates expression of the associated gene. Preliminary characterization of this phenomenon has revealed a set of inter-related cellular pathways which appear to represent both a response to foreign RNA and a mechanism of endogenous gene regulation. Introduction of dsRNA into cells by a variety of means, including transfection of synthetic RNA duplexes, triggers the RNAi response resulting in specific suppression of target gene expression. Recent efforts on a genome wide scale have involved application of RNAi as an important new tool in cell biology to elucidate gene function in living cells.     

Orbital contributions to the molecular charge and energy density distributions in Co2(CO)8

For Co2(CO)8, the representative of a whole class of bridged cobalt complexes, the 18-electron rule predicts a direct metal-metal bond in addition to the metal-bridge bonds. By intuition, this bond should have bent-bond character. However, it is well-known from charge density analyses that no bond critical point exists in the corresponding spatial region. Otherwise, the energy density distribution points to a certain stabilizing contribution of this local area to the total molecular energy. It is shown that a partitioning of the total charge and energy densities into orbital contributions can lead to a deeper insight into complex bonding properties.     

A systematic study of ligand intermolecular interactions in crystals of copper(II) complexes of bidentate guanidino derivatives

The synthesis and X-ray structures of four neutral copper(II) complexes and one cationic complex incorporating bidentate alkyl N-(4-oxo-5,5-diphenyl-4,5-dihydro-1H-imidazol-2-yl)imidocarbamate ligands are reported. The neutral complexes, which possess potential doublet (DA) hydrogen bonding motifs, form supramolecular structures based on synthons involving hydrogen bonding or phenyl embraces. The formation of sheets within the crystal through combination of these synthons, and the occurrence of guest molecules trapped in cavities between the sheets, are described. The cationic complex forms an extended hydrogen-bonded structure that incorporates nitrate ions. The structures of the five complexes are compared with others reported previously for complexes of related ligands.