Gamma,delta-unsaturated beta-diketones by acylation of ketones

[reaction: see text] Gamma,delta-unsaturated beta-diketones have been prepared by the acylation of ketones with N-acylbenzotriazoles of various aliphatic and aromatic alpha,beta-unsaturated carboxylic acids.     

Quantitative estimations of bivariate summation‐integral–type operators

In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0],∞)(×[0],∞) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.     

Copper(I)-promoted dechlorinative Surzur-Tanner rearrangement of 2,2,2-trichloroethyl carboxylates

[reaction: see text] 2,2,2-Trichloroethyl carboxylates undergo highly efficient dechlorinative Surzur-Tanner rearrangement with 2 equiv of a 1:1 molar mixture of CuCl and bpy in boiling DCE to give 1-chloroethenyl carboxylates in which copper appears to play an important role, probably by coordinating the initial radical or as a Lewis acid catalyst.     

Preparation and characterization of 1,2,3‐triazole‐cured polymers from endcapped azides and alkynes

Fourteen commercial polyols have been characterized by GPC, NMR spectroscopy, and elemental analysis. From these, eight corresponding tosylates, six nitrate esters, seven mesylates, 13 alkynes, and 14 azides have been prepared and all these derivatives have been fully characterized. Five alkyne monomers and eight azide monomers were also prepared. Twelve alkynes and 13 azides (functionality 2–4) were combined in 1,3‐dipolar cycloaddition reactions under neat conditions to prepare triazole‐cured polymers, avoiding any heavy metal catalyst. Characterization by NMR spectroscopy, elemental analysis, and gel permeation chromatography indicated triazole polymers 14 , 22 , 23 , 28 , and 30 with degrees of polymerization of 17–28 to be the best candidates for future work. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 238–256, 2008     

Synthesis of Boltorn 1,2,3‐triazole dendrimers by click chemistry

Second‐, third‐, and fourth‐generation hyperbranched aliphatic polyols namely Boltorn® H20, Boltorn H30, and Boltorn H40 were endcapped with azido and activated acetylenic groups in good to excellent yields (75–95%) following an acid catalyzed procedure. The resultant terminally functionalized dendritic azido and acetylenic groups undergo 1,3‐dipolar cycloaddition using methyl (or ethyl) propiolate and benzyl azide, respectively, under catalytic or noncatalytic conditions below 40 °C to yield 1,2,3‐triazole dendrimeric polymers in 82–95% yield, under extremely mild conditions that could be applied for compounds sensitive to acid, base, or heat. The dendritic azido and activated acetylenic derivatives may act as novel scaffolds to tune the mechanical properties of different polymers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3748–3756, 2009     

Some remarks on the <Emphasis Type="Italic">q</Emphasis>-exponents of generalized modular functions

We discuss some properties of exponents of q-product expansions of specific generalized modular functions on the congruence subgroup Γ₀(N).     

Polar modes with elastic restoring forces, “bose condensation” and the possibility of a metastable “ferroelectric” state

The system consists of an electric polarisation field coupled on the one hand to an elastic field and on the other to a thermal reservoir. When the polarisation modes are pumped, Bose condensation in the lowest mode occurs, for energy inflow above a certain critical amount. It is shown that elastic forces, called into play to stabilise the excitation of the polar modes, lowers the threshold for Bose condensation. With further increase in the pumping rate the possibility exists for the softening of the polarisation oscillations leading, in the presence of quartic self-interaction of the polarisation field (inserted for stability), to a metastable ferroelectric state. The work represents an attempt to develop a microscopic approach to the Fröhlich model for the dynamics of macromolecules (such as proteins and enzymes) of biological significance.     

Imidazolium-based polymer supported gadolinium triflate as a heterogeneous recyclable Lewis acid catalyst for Michael additions

A heterogeneous Lewis acid catalytic system has been developed by incorporating gadolinium triflate on to poly[styrene-co-(1-((4-vinylphenyl)methyl)-3-methylimidazolium) tetrafluoroborate] (1-Gd(OTf)₃), and the catalytic activity of this system has been examined for Michael additions of amines and thiols to α,β-unsaturated esters and acrylonitrile. The reactions proceed in moderate to excellent yields in the presence of catalytic system 1-Gd(OTf)₃. The catalytic system could be efficiently recycled and reused.     

Oxatriquinane and oxatriquinacene: extraordinary oxonium ions

Oxatriquinane, a fused, tricyclic alkyl oxonium ion of unprecented stability, was synthesized in five steps from 1,4,7-cyclononatriene. It survives reflux in H2O, chromatography, and attack by alcohols, alkyl thiols, halide ions, and hindered amine bases. The X-ray crystal structure shows longer C-O bond distances and more acute C-O-C bond angles than any reported alkyloxonium salt. The corresponding oxatriquinene and oxatriquinacene were also synthesized and represent the first examples of stable allyl oxonium species.     

Computer simulation of proton channelling in silicon

The channelling of 3 MeV protons in the 〈110〉 direction of silicon has been simulated using Vineyard model taking into account thermally vibrating nuclei and energy loss due to ion-electron interactions. A beam made up of constant energy particles but with spatial divergence has been simulated for the purpose. The values of the minimum scattering yield and half width of the channelling dip are shown to be depth sensitive and agree well with the measured values. The dependence of yield on the angle of incidence has been found to give information of all three types of channelling. The critical angles for the three types of channelling and wavelength of planar oscillations are consistent with the previous calculations.