Synthesis of 2,2-Disubstituted 2H-Chromenes through Carbon-Carbon Bond Formation Utilizing a [1,2]-Phospha-Brook Rearrangement under Brønsted Base Catalysis

A new methodology for the synthesis of 2,2-disubstituted 2H-chromenes was developed by utilizing the [1,2]-phospha-Brook rearrangement under Brønsted base catalysis. Phosphazene P2-tBu efficiently catalyzed the addition reaction of 4H-chromen-4-ols containing a diethoxyphosphoryl group with α,β-unsaturated ketones, which involved the catalytic generation of a carbanion through the [1,2]-phospha-Brook rearrangement and subsequent conjugate addition at the 2-position to afford adducts possessing an alkenylphosphate moiety in a highly diastereoselective manner. Further transformation of the adducts based on a nickel-catalyzed cross-coupling reaction with arylzinc reagents provided densely functionalized 2,2-disubstituted 2H-chromenes.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Convergence rates of the blocked Gibbs sampler with random scan in the Wasserstein metric

ABSTRACT

This paper establishes explicit estimates of convergence rates for the blocked Gibbs sampler with random scan under the Dobrushin conditions. The estimates of convergence in the Wasserstein metric are obtained by taking purely analytic approaches.     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

An Improved Composite Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

Motor Imagery Electroencephalography (MI-EEG) has shown good prospects in neurorehabilitation, and the entropy-based nonlinear dynamic methods have been successfully applied to feature extraction of MI-EEG. Especially based on Multiscale Fuzzy Entropy (MFE), the fuzzy entropies of the τ coarse-grained sequences in τ scale are calculated and averaged to develop the Composite MFE (CMFE) with more feature information. However, the coarse-grained process fails to match the nonstationary characteristic of MI-EEG by a mean filtering algorithm. In this paper, CMFE is improved by assigning the different weight factors to the different sample points in the coarse-grained process, i.e., using the weighted mean filters instead of the original mean filters, which is conductive to signal filtering and feature extraction, and the resulting personalized Weighted CMFE (WCMFE) is more suitable to represent the nonstationary MI-EEG for different subjects. All the WCMFEs of multi-channel MI-EEG are fused in serial to construct the feature vector, which is evaluated by a back-propagation neural network. Based on a public dataset, extensive experiments are conducted, yielding a relatively higher classification accuracy by WCMFE, and the statistical significance is examined by two-sample t-test. The results suggest that WCMFE is superior to the other entropy-based and traditional feature extraction methods.     

Comparison of monomethoxy‐, dimethoxy‐, and trimethoxysilane anchor groups for surface‐initiated RAFT polymerization from silica surfaces

The immobilization of reversible addition–fragmentation chain transfer (RAFT) agents on silica for surface‐initiated RAFT polymerizations (SI‐RAFT) via the Z‐group approach was studied systematically in dependence of the functionality of the RAFT‐agent anchor group. Monoalkoxy‐, dialkoxy‐, and trialkoxy silyl ether groups were incorporated into trithiocarbonate‐type RAFT agents and bound to planar silica surfaces as well as to silica nanoparticles. The immobilization efficiency and the structure of the bound RAFT‐agent film varied strongly in dependence of the used solvent (toluene vs. 1,2‐dimethoxyethane) and the anchor group functionality, as evidenced by atomic force microscopy, transmission electron microscopy, dynamic light scattering, and UV/Vis spectroscopy. Surface‐initiated RAFT polymerizations using functionalized silica nanoparticles revealed that grafted oligomers, which often occur in SI‐RAFT, are not formed within the crosslinked structures that originate from the immobilization, and that RAFT‐agent films that show less aggregation during the immobilization are more efficient during SI‐RAFT in terms of polymer grafting density. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 103–113     

Synthesis and liquid crystalline behavior of bulky poly(methacrylamide)s

N‐(Bis(4‐(2‐ethylhexyloxy)phenyl)(phenyl)‐methyl)methacrylamide was synthesized and polymerized via reversible addition‐fragmentation chain‐transfer (RAFT) polymerization. The chain‐transfer agent (4‐cyano‐4‐(phenylcarbonothioylthio) pentanoic acid (CPADB)), combined with a chiral additive, and a radical initiator yielded polymers with dispersities between 1.2 and 1.4. At low concentrations, the polymers are soluble in hexanes and chloroform while at higher concentrations they swell in these solvents. Characterization of the polymers by wide‐angle X‐ray scattering (WAXS) revealed an interplanar distance of 19.0 Å. The WAXS data combined with polarized optical microscopy support a lamellar crystallization and lyotropic liquid crystalline behavior in hexanes and chloroform. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2563–2568     

Novel hyperbranched polymers synthesized via A3 + B(B′) approach by radical addition‐coupling polymerization

In this study, a novel application of radical addition‐coupling polymerization (RACP) for synthesis of hyperbranched polymers is reported. By Cu/PMDETA‐mediated RACP of 2‐methyl‐2‐nitrosopropane with trimethylolpropane tris(2‐bromopropionate) or a bromo‐ended 3‐arm PS macromonomer, two types of hyperbranched polymers with high degree of polymerization are synthesized under mild conditions, respectively. The chemical structures of the hyperbranched polymers are carefully characterized. By selective degradations of the ester groups and weak bonds of NO? C in the polymers, high degree of alternative connection of the two monomers in the synthesized polymers have been identified. Based on the experimental results, mechanism of formation of the hyperbranched polymer is proposed, which includes formation of carbon radicals from the tribromo monomer through single electron transfer, its capture by 2‐methyl‐2‐nitrosopropane that results in nitroxide radical, and cross‐coupling reaction of the nitroxide radical with other carbon radicals. Hyperbranched polymer can be formed in a step‐growth mode after multiple steps of such reactions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 904–913     

Synthesis of tertiary amine‐based pH‐responsive polymers by RAFT Polymerization

Well‐defined tertiary amine‐based pH‐responsive homopolymers and block copolymers were synthesized via reversible addition‐fragmentation chain transfer (RAFT) polymerization using 4‐cyanopentanoic acid dithiobenzoate (CPAD) as the RAFT agent for homopolymers and a poly(ethylene glycol) (PEG) macro‐RAFT agent for the block copolymers. ¹H NMR and gel permeation chromatography results confirmed the successful synthesis of these homopolymers and block copolymers. Kinetics studies indicated that the formation of both the homopolymers and the block copolymers were well defined. The pKa titration experiments suggested that the homopolymers and the related block copolymers have a similar pKa. The dynamic light scattering investigation showed that all of the block copolymers underwent a sharp transition from unimers to micelles around their pKa and the hydrodynamic diameter (D_h) was not only dependent on the molecular weight but also on the composition of the block copolymers. The polymer solution of PEG‐b‐PPPDEMA formed the largest micelle compare to the PEG‐b‐PDPAEMA and PEG‐b‐PDBAEMA with a similar molecular weight. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1010–1022