一类联图的距离谱半径以及盖理论（英文）

令X=(n₁,n₂,…,n_t),Y=(m₁,m₂,…,m_t)是两个t维递减序列.如果对所有的j,1≤j≤t,都有∑_i=1~j、n_i≥∑_i=1~j m_i以及∑_i=1~t n_i=∑_i=1~t m_i,则称X可盖Y,记作X■Y.如果X≠Y,则记作X■Y.本文考虑联图G(n₁,n₂,…,n_t;a)=(K_n1∪_n2∪…∪K_nt)∨K_a的谱半径,这里n₁+n₂+…+n_t+a=n,(n₁,n     

Spectra of graphs and fractal dimensions II

This paper continues the study of exponentsd(x), d (x), d _R (x) andd (x) for graphG; and the nearest neighbor random walk {X _n } _nN onG, if the starting pointX ₀=x is fixed. These exponents are responsible for the geometric, resistance, diffusion and spectral properties of the graph. The main concern of this paper is the relation of these exponents to the spectral density of the transition matrix. A series of new exponentse, e ,e _R ,e are introduced by allowingx to vary along the vertices. The results suggest that the geometric and resistance properties of the graph are responsible for the diffusion speed on the graph.     

Estimates of logarithmic Sobolev constat for finite-volume continuous spin systems

LetM be a compact, connected Riemannian manifold (with or without boundary); we study the logarithmic Sobolev constant for stochastic Ising models on . Let {} be a sequence of cubes inZ ^d ; we show that the logarithmic Sobolev constant for the finite systems onM ^A shrinks at most exponentially fast in ||^(d-1)/d (d2), which is sharp in order for the classical Ising models withM=[–1, 1]. Moreover, a geometrical lemma proved by L. E. Thomas is also improved.     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.     

Spectrum of positive entropy multidimensional dynamical systems with a mixed time

It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

硅灰石矿物发光原料中Fe2+的去除与CaSiO3∶Eu3+的光谱特性

提出了用草酸．邻菲哕啉去除硅灰石中Fe^2 的方法，研究了浸取剂的浓度、浸取时间和温度等条件对Fe^2 的去除率的影响，在最佳的浸取条件下，Fe^2 的去除率达到98．35％。在去除猝灭剂后的硅灰石矿物中，掺加适量的稀土激活剂Eu^3 ，通过高温固相法制成荧光发光材料，发光强度明显提高，接近于化学试剂合成的发光材料。     

Phenolic Compounds of Plants of the Scutellaria L. Genus. Distribution, Structure, and Properties

Information on flavones, flavanones, flavanonols, flavonols, chalcones, isoflavones, biflavonoids, lignoflavonoids, and lignane glycosides and stilbenes isolated from plants of the Scutellaria L. genus was systematized and reviewed. A list of 208 phenolic compounds was given according to flavonoid type with an indication of the plant sources, structures, and physicochemical properties and citations of the original articles.     

Hole Burning and Fluorescence Spectra of Sol-Gel Derived Sm2+-Doped Glasses

Sm2+-doped glasses in the system of Al2O3-SiO2 were prepared by sol-gel processing of metal alkoxides and reacting with H2 gas at 800°C. The hole burning properties of these glasses were investigated. The holes were burned in the 7F0 5D0 line of the Sm2+ ions using a DCM dye laser at 77 K. The hole depth increased with increasing the laser irradiation time, reaching up to 15% of the total intensity within a few hundred seconds. The hole width was 3 cm–1 full width at half maximum. Fluorescence line narrowing spectra of the 5D0 7 F1 transition were analyzed to study the local structure surrounding the Sm2+ ion. It is concluded that the Sm2+ ions are closely coordinated with nine oxygens of the AlO6 group in aluminosilicate glasses and that the addition of Al3+ ions into glass induces an increase in the coordination number of the Sm2+.     

Laser irradiation induced spectral evolution of the Laser irradiation induced spectral evolution of the surface-enhanced Raman scattering(SERS)of 4-tert-butylbenzylmercaptan on gold nanoparticles assembly

The spectral evolution of the surface-enhanced Raman scattering (SERS) of 4-tert-butylbenzylmer-captan(4-tBBM)on gold nanopanlcles assembly under laser irradiation is reported.The reIative intensities of typical peaks in the spectrum of 4-tBBM gradually change with irradiation time.Comparison of the rate of spectral changes under several experimental conditions indicates that the surface plasmon resonance(SPR)induced heat in the gold nanoparticles assembly is the origin of the spectraI evolution.During the process of self-assembly,4-tBBM molecules do not form a compact ordered monolayer because of the spatial hindrance of the 4-tert-butyl end group.The heat induced by laser irradiation drives the 4-tBBM molecules to rearrange to a more stable orientation.