非齐次非线性扩散方程的高维不变子空间和等价变换

利用与不变子空间方法相关的等价变换和变换v=enu给出了非齐次非线性扩散方程的等价方程,并得到了等价方程的高维不变子空间.最后给出一些例子构造了非齐次非线性扩散方程的广义泛函分离变量解.     

Measure of noncompactness and semilinear nonlocal functional differential equations in Banach spaces

This paper is concerned with the measure of noncompactness in the spaces of continuous functions and semilinear functional differential equations with nonlocal conditions in Banach spaces.The relationship between the Hausdorff measure of noncompactness of intersections and the modulus of equicontinuity is studied for some subsets related to the semigroup of linear operators in Banach spaces.The existence of mild solutions is obtained for a class of nonlocal semilinear functional differential equations without the assumption of compactness or equicontinuity on the associated semigroups of linear operators.     

Investigating the effects of side chain length on the AIE properties of water-soluble TPE derivatives

The emissive properties of fluorophores in aggregated state are important for the development of bio-sensors or bio-imaging reagents. So three water-soluble TPE derivatives with different lengths of side chains have been synthesized and we investigated the effects of side chains on aggregation-induced emission (AIE) properties in the aggregated states. The results indicate that side chains on the fluorophores play a pivotal role in their emission in aggregated state mediated by heparin or solid state, because the coplanarity of these TPE derivatives was affected by side chains. The rates of radiative decay k_f and non-radiative decay k_nr have been obtained through the quantum yields and lifetime, and a larger k_f and smaller k_nr were present for compound TPE-C4N, suggesting that the aggregated TPE-C4N should posses the most remarkable fluorescent property.     

Amicoumacins from the marine-derived bacterium Bacillus sp. with the inhibition of NO production

Chemical examination of the fermentation broth of the marine-derived bacterium Bacillus sp. resulted in the isolation of seven new amicoumacin-type isocoumarin derivatives, namely bacillcoumacins A–G (1–7), together with four known analogues. Their structures were elucidated on the basis of extensive spectroscopic analysis, while the absolute configurations of the new compounds were determined by CD, Mosher’s method, and chemical conversion. Compounds 7 and 9 showed inhibitory effects against the NO production induced by lipopolysaccharide (LPS) in mouse macrophage RAW 264.7 cells.     

Crystal Structures and Photoluminescence Properties of Zinc(II) and Cadmium(II) Coordination Polymers with “Y”‐Shaped Ligands

Three Zn^II and Cd^II complexes with Y‐shaped dicarboxylate ligands, namely [Zn(L₁)(2,2′‐bpy)₂(H₂O)] · 2H₂O ( 1 ), [Zn(L₁)(bpp)(H₂O)] ( 2 ), and [Cd(L₁)(H₂O)] · H₂O ( 3 ) [H₂L₁ = N‐phenyliminodiacetic acid, 2,2′‐bpy = 2,2′‐bipyridine, bpp = 1,3‐bis(4‐pyridyl)propane] were synthesized and characterized by elemental analysis, IR spectroscopy single‐crystal X‐ray diffraction, and thermogravimetric analyses. Compound 1 shows an hydrogen‐bonded 2D network, whereas compound 2 is an infinite 1D wavy chain structure, though O–H ··· O hydrogen‐bonded to form a 2D network. Compound 3 displays a 2D uninodal 3‐connected Shubnikov plane net with the point symbol of (4.8²). Moreover, the solid‐state such as thermal stabilities and fluorescence properties of 1 – 3 were also investigated.     

Palladium‐Catalyzed C?S Activation/Aryne Insertion/Coupling Sequence: Synthesis of Functionalized 2‐Quinolinones

The insertion of an aryne into a C S bond can suppress the addition of an S nucleophile to the aryne in the presence of palladium. Catalyzed by Pd(OAc)₂, a wide range of α‐carbamoyl ketene dithioacetals readily react with arynes to selectively afford functionalized 2‐quinolinones in high yields under neutral reaction conditions by a C S activation/aryne insertion/intramolecular coupling sequence. The attractive feature of the new strategy also lies in the versatile transformations of the alkythio‐substituted quinolinone products.     

Studies of degradation behaviors of poly (3‐hexylthiophene) layers by X‐ray photoelectron spectroscopy

Degradation behaviors of poly(3‐hexylthiophene‐2,5‐diyl) (P3HT) layers on NiO in the presence of H₂O at ambient pressure and dark conditions were studied using X‐ray photoelectron spectroscopy (XPS). Upon H₂O exposure at 120 °C, partial oxidation of P3HT together with molecular water incorporation, but with the maintained local ring‐structure, were deduced by XPS. Valence band spectra of XPS evidenced that the partial oxidation of P3HT local structure could alter π‐conjugation systems of P3HT layers, forming additional electronic states close to its original highest occupied molecular orbital. For comparison, P3HT surface was also exposed to O₂, and no change in the S 2p and C 1s spectra was found by O₂ exposure at 120 °C, implying that H₂O plays a major role at the initial stage of P3HT oxidation. Copyright © 2014 John Wiley & Sons, Ltd.     

Lewis acid-catalyzed tandem acylation–Nazarov cyclization for the syntheses of fused cyclopentenones

Treatment of N-tosylpyrroles or N-tosylindoles with α-unsubstituted α,β-unsaturated carboxylic acids or unsaturated carboxylic acids having an α electron-withdrawing substituent in the presence of TFAA and a Lewis acid catalyst resulted in the formation of fused cyclopentenones via a tandem acylation–Nazarov cyclization sequence, while either the acylation product obtained or no reaction occurred in the absence of the Lewis acid catalyst.     

Cascade synthesis of 3-aza-bicyclo[3.1.0]hex-2-ene derivatives from N-allyl enamines

An efficient iodine-mediated cascade synthesis of 3-aza-bicyclo[3.1.0]hex-2-ene derivatives from easily prepared N-allyl enamines has been developed. The advantages of the reaction include facilitative preparation of substrates 3a–t, good functional group tolerance and transition-metal-free conditions.     

Tetrasubstituted pyrazinones derived from the reaction of praziquantel with N-bromosuccinimide

When praziquantel was exposed to N-bromosuccinimide in the presence of ethanol, a tricyclic 3-bromo-1-ethoxy pyrazinone was formed. From this and the analogous 1,3-dibromopyrazinone, a small library of 3-alkylamino-1-ethoxy, 1,3-dialkoxy, 3-alkoxy-1-bromo, and 3-alkylamino-1-bromo substituted pyrazinones were synthesized in high yields.