具渐近线性无共振p(x)-Laplace方程的多解性

研究了如下p(x)-Laplace方程(?)多解的存在性问题,其中Ω是R~N上具有光滑边界的有界区域.我们以改进的山路引理为工具,获得了在给予f(x,u)某些条件的基础上,该问题具有多解性结果的结论.     

矩阵多项式空间的进一步研究

设A为数域F上的n级矩阵,记F[A]={f(A)|f(x)∈F[x]},它显然是F~(n×n)的子空间.讨论了F[A]的基和维数,引入了f(A)的坐标和F[A]的因式子空间的概念,给出了用因式子空间表示F[A]的几个定理,刻画了F[A]的结构.     

Manganese(III) Acetate Catalyzed Oxidative Radical Additions of α‐Dicarbonyl Compounds to 1‐ and 2‐Phenylcyclohepta‐1,3,5‐triene

Manganese(III) acetate catalyzed oxidative radical‐addition reactions of α‐dicarbonyl compounds such as methyl acetoacetate ( 6 ), acetylacetone ( 7 ), and dimedone ( 8 ) to the mixture of 1‐ and 2‐phenylcyclohepta‐1,3,5‐triene ( 4 and 5 ) were investigated (Scheme 1). The 1‐phenylcyclohepta‐1,3,5‐triene ( 4 ) formed mainly [2+3] and [4+3] dihydrofuran addition products derived from cycloheptatriene and [2+3] dihydrofuran addition products derived from the norcaradiene structure. The 2‐phenylcyclohepta‐1,3,5‐triene ( 5 ) formed mainly [6+3] dihydrofuran addition products derived from cycloheptatriene and [4+3] dihydrofuran addition products derived from the norcaradiene structure. The structures of isolated products were established by their spectroscopic data (IR, ¹H‐ and ¹³C‐NMR, MS, and elemental analysis) and comparison with literature data. The formation mechanism of the products is discussed.     

The study for the incipient solvation process of NaCl in water: the observation of the NaCl-(H2O)n (n = 1, 2, and 3) complexes using Fourier-transform microwave spectroscopy

Pure rotational spectra of the sodium chloride-water complexes, NaCl-(H(2)O)(n) (n = 1, 2, and 3), in the vibronic ground state have been observed by a Fourier- transform microwave spectrometer coupled with a laser ablation source. The (37)Cl-isotopic species and a few deuterated species have also been observed. From the analyses of the spectra, the rotational constants, the centrifugal distortion constants, and the nuclear quadrupole coupling constants of the Na and Cl nuclei were determined precisely for all the species. The molecular structures of NaCl-(H(2)O)(n) were determined using the rotational constants and the molecular symmetry. The charge distributions around Na and Cl nuclei in NaCl are dramatically changed by the complex formation with H(2)O. Prominent dependences of the bond lengths r(Na-Cl) on the number of H(2)O were also observed. By a comparison with results of theoretical studies, it is shown that the structure of NaCl-(H(2)O)(3) is approaching to that of the contact ion-pair, which is considered to be an intermediate species in the incipient solvation process.     

Butylene linked palladium N-heterocyclic carbene complexes: Synthesis and catalytic properties

New bis(NHC)-Pd complexes were synthesized and characterized by elemental analysis, ¹H NMR, ¹³C NMR, and IR spectroscopy. The reaction of Pd(OAc)₂ and bis(benzimidazolium) salts in DMSO gave the monomeric palladium complex in which the N-heterocyclic carbene was bound to the metal centre. The crystal and molecular structure of the cis-dibromo{1,1′-di[2,3,4,5,6-pentamethylbenzyl]-3,3′-butylenedibenzimidazol-2,2′-diylidene}-palladium(II) complex was determined by single-crystal X-ray diffraction. The activity of the Pd(II) complexes in the direct arylation of benzothiazole with arylbromides was investigated. A preliminary catalytic study showed that these bis(NHC)-Pd complexes were highly active in the direct arylation of benzothiazole with arylbromides.     

Quantum chemical computations of 1,3-phenylenediacetic acid

Molecular geometry, vibrational wavenumbers and gauge including atomic orbital (GIAO) 13C NMR and 1H NMR chemical shift values of 1,3-phenylenediacetic acid (C10H10O4), in the ground state have been calculated by using ab initio Hartree-Fock (HF) and density functional theory (DFT/B3LYP) methods with 6-311++G(d,p) basis set for the first time. Comparison of the observed fundamental vibrational modes of 1,3-phenylenediacetic acid and calculated results by density functional B3LYP and Hartree-Fock methods indicate that B3LYP is superior to the scaled Hartree-Fock approach for quantum chemical studies. Geometric parameters (bond lengths and bond angles) and vibrational wavenumbers obtained by the HF and DFT/B3LYP methods are in good agreement with the experimental data. Furthermore, this is the first time the results of the calculated JCH and JCC coupling constants of the C10H10O4 molecule are presented in this study.     

EPR and optical studies of vanadium doped potassium dihydrogen citrate (C6H7KO7) single crystal

An EPR and optical studies of VO2+ doped potassium dihydrogen citrate (PDHC) single crystals have been carried out at room temperature. It crystallizes in triclinic symmetry with the unit cell dimensions: a=11.343?, b=13.078?, c=6.272?, α=89.79°, β=94.36°, γ=104.2°. The angular variation of EPR spectra have shown that two different VO2+ complexes are located in different chemical environments and each environment contains one magnetically VO2+ site occupying substitutional position in the lattice and show very high angular dependence.     

Vibrational spectroscopic study on some Hofmann type clathrates: M(2-(1-cyclohexenyl)ethylamine)2Ni(CN)4·2benzene (M=Ni and Cd)

New Hofmann type benzene clathrates in the form of M(CyHEA)2Ni(CN)4·2benzene (where CyHEA=2-(1-cyclohexenyl)ethylamine and M=Ni or Cd) have been prepared in powder form and FT-IR and Raman spectra have been reported. The results suggest that title compounds are similar in structure to Hofmann type clathrates and their structures consist of polymeric layers of |M-Ni(CN)4|∞ with the CyHEA molecule bounded to the metal atoms (M).