Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.     

General Method for the Synthesis of Salicylic Acids from Phenols through Palladium‐Catalyzed Silanol‐Directed C?H Carboxylation

A silanol‐directed, palladium‐catalyzed C H carboxylation reaction of phenols to give salicylic acids has been developed. This method features high efficiency and selectivity, and excellent functional‐group tolerance. The generality of this method was demonstrated by the carboxylation of estrone and by the synthesis of an unsymmetrically o,o′‐disubstituted phenolic compound through two sequential C H functionalization processes.     

Thermal Conversion of Methane to Formaldehyde Promoted by Gold in AuNbO3+ Cluster Cations

In addition to generation of a methyl radical, formation of a formaldehyde molecule was observed in the thermal reaction of methane with AuNbO₃⁺ heteronuclear oxide cluster cations. The clusters were prepared by laser ablation and mass‐selected to react with CH₄ in an ion‐trap reactor under thermal collision conditions. The reaction was studied by mass spectrometry and DFT calculations. The latter indicated that the gold atom promotes formaldehyde formation through transformation of an Au?O bond into an Au?Nb bond during the reaction.     

Travelling waves in dilatant non-Newtonian thin films

We prove the existence of a travelling wave solution for a gravity-driven thin film of a viscous and incompressible dilatant fluid coated with an insoluble surfactant. The governing system of second order partial differential equations for the film's height h and the surfactant's concentration γ are derived by means of lubrication theory applied to the non-Newtonian Navier–Stokes equations.     

Fused-Pentagon Isomers of C60 Fullerene Isolated as Chloro and Trifluoromethyl Derivatives

The carbon cage of buckminsterfullerene I_h-C₆₀, which obeys the Isolated-Pentagon Rule (IPR), can be transformed to non-IPR cages in the course of high-temperature chlorination of C₆₀ or C₆₀Cl₃₀ with SbCl₅. The non-IPR chloro derivatives were isolated chromatographically (HPLC) and characterized crystallographically as ¹⁸⁰⁹C₆₀Cl₁₆, ¹⁸¹⁰C₆₀Cl₂₄, and ¹⁸⁰⁵C₆₀Cl₂₄, which contain, respectively two, four, and four pairs of fused pentagons in the carbon cage. High-temperature trifluoromethylation of the chlorination products with CF₃I afforded a non-IPR CF₃ derivative, ¹⁸⁰⁷C₆₀(CF₃)₁₂, which contains four pairs of fused pentagons in the carbon cage. Addition patterns of non-IPR chloro and CF₃ derivatives were compared and discussed in terms of the formation of stabilizing local substructures on fullerene cages. A detailed scheme of the experimentally confirmed non-IPR C₆₀ isomers obtained by Stone–Wales cage transformations is presented.     

Transition-Metal-Free Multiple Functionalization of Piperidines to 4-Substituted and 3,4-Disubstituted 2-Piperidinones

Remote and multiple functionalization of piperidines without the use of transition-metal catalysts and elaborate directing groups is one of the major challenges in organic synthesis. Herein is reported an unprecedented two-step protocol that enables the multiple functionalization of piperidines to either 4-substituted or trans-3,4-disubstituted 2-piperidones. First, by exploiting the duality of TEMPO reactivity, which under oxidative and thermal conditions fluctuates between cationic and persistent-radical form, a novel multiple C(sp³)-H oxidation of piperidines to α,β-unsaturated 2-piperidones was developed. Second, the intrinsic low reactivity of the unsaturated piperidones toward conjugated Grignard additions was overcome by using trimethylsilyl chloride (TMSCl) as Lewis acid. Subsequently, conjugated Grignard addition/electrophilic trapping protocol provided substituted 2-piperidone intermediates, some of which were then transformed into pharmaceutical alkaloids.     

Hantzsch Ester as a Visible-Light Photoredox Catalyst for Transition-Metal-Free Coupling of Arylhalides and Arylsulfinates

Diethyl 2,6-dimethyl-1,4-dihydropyridine-3,5-dicarboxylate (HEH) has been utilized as a visible-light photoredox catalyst for the cross coupling of arylhalides and arylsulfinates without transition metal, sacrificial agent, and mediator. This method is compatible with various functional groups and provides diaryl sulfones in good to high yields. Mechanistic studies indicate that this reaction undergoes the stepwise light irradiation of HE⁻, single electron transfer (SET) in donor–acceptor complex (DAC) from *HE⁻ to arylhalide, trapping of aryl radical with sulfinate, and SET oxidation of sulfone radical anion by HE^. to sulfone by the DAC method.