On the characteristic polynomial of a special class of graphs and spectra of balanced trees

Let H be a simple graph with n vertices and G be a sequence of n rooted graphs G₁,G₂,…,G_n. Godsil and McKay [C.D. Godsil, B.D. McKay, A new graph product and its spectrum, Bull. Austral. Math. Soc. 18 (1978) 21-28] defined the rooted product H(G), of H by G by identifying the root vertex of G_i with the ith vertex of H, and determined the characteristic polynomial of H(G). In this paper we prove a general result on the determinants of some special matrices and, as a corollary, determine the characteristic polynomials of adjacency and Laplacian matrices of H(G).Rojo and Soto [O. Rojo, R. Soto, The spectra of the adjacency matrix and Laplacian matrix for some balanced trees, Linear Algebra Appl. 403 (2005) 97-117] computed the characteristic polynomials and the spectrum of adjacency and Laplacian matrices of a class of balanced trees. As an application of our results, we obtain their conclusions by a simple method.     

Darstellung und Charakterisierung von Iodoplatinaten MexNH4–xPtI4 (x = 2 − 4), gemischtvalenten Octaiododiplatinaten(II,IV) mit Pt2I8-Baugruppen

Preparation and Characterization of Iodoplatinates Me_xNH_4–xPtI₄ (x = 2–4), Mixed Valence Octaiododiplatinates(II,IV) with Pt₂I₈ Groups Iodoplatinates APtI₄ (A = Me_xNH_4–x with x = 2–4) have been prepared by partial oxidation of the correspondent hexaiododiplatinates(II) A₂Pt₂I₆ with I₂ in methanolic solutions. X-ray structure analyses of the bronze-coloured needle-shaped crystals of the compounds showed rows of dinuclear anions Pt₂I₈^2?, built up by edgesharing planar PtI₄ groups with Pt^II und octahedral PtI₆ groups with Pt^IV. The different space requirement of the cations leads to the formation of three different structures. Within the anion stacks weak intermolecular Pt^IV? I …? Pt^II interactions are detectable by Raman spectroscopy.     

铕激活的铝酸锶镁的合成及发光特性

研究了二价铕激活的Sr1-nMgnAl2O4的合成、发光性质以及基质组分Sr/Mg摩尔比与荧光性质的关系，并对其余辉及衰减进行了测定。     

有机掺杂溶胶-凝胶法制备pH敏感膜及其光谱响应的研究

使用四甲氧基硅烷（TMOS）和二甲基二甲氧基硅烷（DiMe-DMOS)为共先驱体，采用溶胶－凝胶的有机掺杂，制备对pH具有宽程响应的敏感膜。详细考察了包埋溴酚蓝和溴酚绿的敏感膜对pH的响应值、响应时间、泄漏和可逆性等响应性能指标，并进行了溴酚蓝和溴酚绿在水相与膜内吸收光谱的研究。     

查尔酮类共轭体系电子光谱及线性关系的MHMO法计算

对查尔酮类共轭体系的电子光谱,CNDO/2计算及线性关系文献中已作了全面报道。本文用林惠心等在徐光宪改进的HMO法基础上提出的改进HMO法(即MHMO法),对查尔酮类共轭体系进行了计算,结果λ_计和λ_实基本一致,线性关系良好。     

Bergman空间上Toeplitz算子的局部化

Bergman空间上Toeplitz算子的局部化@孙善利@卢玉峰...     

Raman Study of InCl3

Abstract

The Raman spectra of a crystalline powder of InCl₃ and of a de-ionized water solution show the presence of four bands at 300.0, 289.2, 115.6 and 87.1 cm^?1, thus suggesting that InCl₃ is not a perfectly planar molecule.     

A High Resolution Study of the Shock Excited Spectrum of Yttrium Oxide

Abstract

The blue-green (B²? X²?) and orange (A²? –X²?) systems of yttrium oxide have been shock excited at temperatures of about 4000°K and photographed at high dispersion (～ 1.2Å/mm) in the first order of a 21 ft. grating spectrograph. The high dispersion shock excited spectra were recorded using multiple exposures and latensification of extremely high speed film. Over 50 new bands have been observed and assigned to specific vibrational transitions for the systems. New molecular constants have been derived from the A, B and X states. Provisional calculations have been made of Franck-Condon factors and r-centroids for the systems appropriate to new constants.     

Spectral Assignments and Structural Consequences Arising from the C-H Stretching Region of Norbornadiene

Preliminary vibrational analysis of this bicyclic moiety clearly shows the presence of Fermi Resonance phenomena. The alternative to this assignment is shown to be contradictory to both electron diffraction results and to the vibrational data, presented in this paper. Of primary interest is the implications that these spectral results could have for further studies involving classical and non-classical carbonium ion structures.     

Synthesis, Crystal Structure and Properties of the Binuclear Complex [Sm2(C10H9N2O4)2(C10H8N2O4)2(H2O)4]

Abstract  A novel binuclear Smarium (III) complex with N-(2-propionic acid)-salicyloyl hydrazone (C₁₀H₁₀N₂O₄, H₃L) was prepared and characterized. The crystal structure of [Sm₂(H₂L)₂(HL)₂(H₂O)₄] (1) was determined by X-ray single crystal diffractometry. 1 crystallizes in the monoclinic systerm, space group P2(1)/c, with a = 0.10229(2), c = 31.549(7), b = 0.70599(15) nm, and Z = 4. In the structure, Sm(III) is nine-coordinated by carboxyl O and acyl O atoms and imido N atoms of two ligands (H₂L and HL forms) and O atoms from two water molecules. H₂L and HL act as tridentate ligands which form two stable five-numbered chelating rings sharing one edge in the keto form for each ligand, and the carboxyl groups of two ligands were coordinated via bidentated bridging form. The coordination polyhedron around Sm (III) was described as a monocapped square antiprism. The inter- and intramolecular hydrogen bonds resulted in a three-dimensional network and provided extra stability for the structure. The complex was researched the interaction with calf thymus DNA by electronic absorption titration and emission titration. The results show that the complex is bound to calf thymus DNA mainly by intercalation .The complex also shows good fluorescence property. Index Abstract  The title compound, [Sm₂(H₂L)₂(HL)₂(H₂O)₄] was synthesized by the treatment of N-(2-propionic acid)-salicyloyl hydrazone (C₁₀H₁₀N₂O₄, H₃L) and Sm(NO₃) · 4H₂O and its crystal structure determined. Single crystal X-ray diffraction analysis reveals that Sm (III) is nine-coordinated by carboxyl O and acyl O atoms and imido N atoms of two ligands (H₂L and HL forms) and O atoms from two water molecules. The carboxyl groups of two ligands were coordinated via bidentated bridging form. The coordination polyhedron around Sm (III) was described as a monocapped square antiprism. The inter- and intramolecular hydrogen bonds resulted in a three-dimensional network and provided extra stability for the structure.