球面上等收敛算子的有界性

设Rⁿ 是n-维欧氏空间n≥3.用Ω_n表示Rⁿ 上的单位球面,对于函数f∈L（Ω_n）,E_N^δ（f）表示其Fourier-Laplace级数的δ阶Cesaro平均所决定的等收敛算子,其中,λ:=（n-2）/2,δ是熟知的临界指标.对于0<δ≤λ,令p₀:=(2λ)/（λ+δ）,本文主要证明了如下结果:     

基于6-羟基-2-吡啶基膦酸配体的铜配合物的合成、结构及磁性

在水热条件下, 以6-羟基-2-吡啶基膦酸为主配体, 4, 4′-联吡啶(bpy)及1, 2-二(4-吡啶基)乙烯(bpe)为桥联配体, 合成了2个铜膦酸配位聚合物[Cu₃(L)₂(bpy)₂(H₂O)₂]· 2H₂O (1), [Cu₃(L)₂(bpy)₂(H₂O)₃]· 2H₂O (2)。配合物1中, Cu²⁺离子由膦酸配体连接成一条链, 该链由bpy桥联成二维层, 层与层之间通过氢键作用构成三维结构。配合物2与配合物1是同构的, 桥联配体是bpe。磁性研究表明, 配合物1与2中铜离子之间存在反铁磁性耦合。     

GS型包合物G2PEDS·MeOH·2(H2O)和G2PEDS·naphthalene的合成与晶体结构

合成了两个由胍盐(G)和4，4’—苯醚二磺酸(PEDS)为主体框架所形成的主— 客体包合物，分别为[(CH6N3)]2[(C12H8O7S2)]·MeOH·2(H20)(1)和[(CH6N3)]2[ (C12H8O7S2)]·(C10H8)(2)．两个化合物都是以P—1空间群结晶，晶胞参数分别为 ：1a＝0．7509(4)nm，b＝1．2113(6)nm，c＝1．5936(8)nm，a＝102．636(10)° ，β＝102．703(11)°,γ＝91．318(10)°；2a＝0．75409(3)nm，b＝1．21584 (5)nm，c＝3．09376(14)nm，a＝81．506(2)°，β＝89．669(2)°，γ＝88． 890(2)°。在这两个晶体结构中，G和PEDS通过氢键形成了双夹层—双柱子的主体 框架，客体分子被包合在平行于a轴方向的晶格空间．这种双夹层—双柱子的主体 框架在由胍盐(G)和有机二磺酸(S)体系所形成的、具有通道结构的主体框架中是较 为少见的．     

ZnTPP Axially Coordinated with a Novel Dipyridylamine Ligand: Hydrothermal Synthesis and Crystal Structure

A novel complex ZnTPPL1·3DMF 1(TPP = tetraphenylporphyrin,L1 = N-(4-(9-carbazolyl) phenyl)-N,N-di(4-pyridyl)amine) was prepared by a hydrothermal method and characterized by elemental analysis,IR,and single-crystal X-ray diffraction analysis.Compound 1 crystallizes in triclinic,space group P1 with a = 13.3082(2),b = 14.3276(2),c = 18.6120(3) ,α = 109.853(1),β = 95.054(1),γ = 98.832(1)°,V = 3260.57(9) 3,Z = 2,Dc = 1.334 g/cm3,C81H69N11O3Zn,Mr = 1309.84,μ(MoKα) = 0.438 mm-1,F(000) = 1372,GOF = 1.159,the final R = 0.0482 and wR = 0.1479 for 12091 observed reflections(Ⅰ 2σ(Ⅰ)).Crystal structure analyses revealed that L1 utilizes one pyridyl N atom to bind Zn via axial coordination,affording a 1:1 complex.The binding constant was estimated to be 1.74(7) × 104 M-1 from electronic spectra measurements.     

KLn Dielectronic Recombination Process of B- Through He-like Cu Ions

The KLn dielectronic recombination processes of trapped highly charged B-like through He-like Cu ions are studied theoretically, and the theoretical results are used to analyse our previous experimental data at Heidelberg electron beam ion trap （EBIT）. The theoretical resonant positions agree with the experimental resonant positions to a precision of 0.4%, in comparison with the resonant positions of those highest peaks between theory and experiment. The experimental spectra are then fitted using a formula with the theoretical resonant energies and strengths, the result shows good overall agreement between theory and experiment over a wide electron energy range. The distribution of highly charged states is obtained from the fitting parameters.     

The effect of the size,shape, and structure of metal nanoparticles on the dependence of their optical properties on the refractive index of a disperse medium

The effect of the size, shape, and structure of gold and silver nanoparticles on the dependence of their extinction and integral scattering spectra on the dielectric environment has been investigated. Calculations were performed using the Mie theory for spheres and nanoshells and the T-matrix method for chaotically oriented bispheres, spheroids, and s cylinders with hemispherical ends. The sensitivity of plasmon resonances to variations in the refractive index of the environment in the range 1.3–1.7 for particles of different equivolume size, as well as to variations in the thickness of the metal layer of nanoshells, was studied. For nanoparticles with an equivolume diameter of 15 nm, the maximal shifts of plasmon resonances due to variation in the refractive index of the environment are observed for bispheres and the shifts decrease in the series nanoshells, s cylinders or spheroids, and spheres. For particles 60 nm in diameter, the largest shifts of plasmon resonances occur for nanoshells and the shifts decrease in the series bispheres, s cylinders or spheroids, and spheres. All other conditions being the same, silver nanoparticles are more sensitive to the resonance tuning due to a change in the dielectric environment.     

‘Whole-molecule Disorder’ Refinement of 4-（4-Hydroxybenzylideneiminio）phenol Hemichloride Hemihydroxide

The two independent cations of the salt, [HO-C6H4-CH=NH-C6H4-OH]·1/2OH·1/2Cl, are both disordered about an axis connecting the two oxygen atoms at the para-positions of the aromatic rings, the disorder being in a 83:17 ratio in one cation and 91:9 in the other. The hydroxide and chloride anions are ordered. The treatment of the nearly ‘whole-molecule disorder’ by employing a small number of restraints is described. Crystal data: C13H12.5Cl0.5NO2.5, triclinic, P , a = 9.1731(4), b = 9.2048(4), c = 15.9144(7) , α = 104.822(1), β = 90.077(1), γ = 118.641(1)o and V = 1127.86(9) 3 at –173 K.     

Synthesis and optical properties of poly(N-isopropylacrylamide) nanogel containing silver nanoparticles

Composite nanoparticles representing silver nanoparticle-containing polymer gels have been synthesized. The synthesis comprises two main stages. Initially, monodisperse hydrogel particles with a controlled diameter of approximately 500 nm are obtained by N-isopropylacrylamide polymerization. Then, silver ions are reduced on the surface of the polymer network. Variations in the concentration ratio between reductants and silver nitrate make it possible to produce silver nanoparticles with sizes in a range of 10–30 nm and different packing densities on the gel particle surface. The resultant nanocomposites have been studied by transmission electron microscopy, spectrophotometry, and dynamic light scattering. Depending on the size and packing density of the silver nanoparticles on the polymer particle surface, the plasmon resonance of the nanocomposites varies in a range of 420–750 nm, which determines variations in the color of the colloid from yellow, orange, and red to blue and blue-green. After the inclusion of silver nanoparticles, nanogels of poly(N-isopropylacrylamide) retain their capability for thermosensitive phase transition with a lower critical mixing temperature of 31°C.     

Gold nanorods as a perspective technology platform for SERS analytics

We discuss the application of gold nanorods for forming SERS substrates for chemical and biological sensing. Two approaches are considered: (1) formation of planar arrays on silicon wafers by using suspensions of gold nanorods; and (2) a new approach based on gold nanorod powders that can be easily dissolved in aqueous media. Both SERS platforms are characterized and their SERS enhancement factors are compared.     

Effect of the size of colloidal gold nanoparticles on the physical parameters of nanocomposite microcapsule shells

Polyelectrolyte shells of nanocomposite microcapsules containing colloidal gold nanoparticles of different diameters (5, 10, or 20 nm) are formed by the polyion assembly procedure. Microcapsules with different numbers of layers and structures are studied by transmission electron microscopy, atomic force microscopy, and confocal microscopy. The values of the thickness and roughness of microcapsule shells are determined and the dependence of these parameters on the size of gold nanoparticles constituting shells is investigated. It is established that the concentration of nanoparticles in polyelectrolyte shells of microcapsules decreases with an increase in particle diameter.