Signless Laplacians of finite graphs

We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix. For regular graphs the whole existing theory of spectra of the adjacency matrix and of the Laplacian matrix transfers directly to the signless Laplacian, and so we consider arbitrary graphs with special emphasis on the non-regular case. The results which we survey (old and new) are of two types: (a) results obtained by applying to the signless Laplacian the same reasoning as for corresponding results concerning the adjacency matrix, (b) results obtained indirectly via line graphs. Among other things, we present eigenvalue bounds for several graph invariants, an interpretation of the coefficients of the characteristic polynomial, a theorem on powers of the signless Laplacian and some remarks on star complements.     

Spectral radius of graphs with given matching number

In this paper, we show that of all graphs of order n with matching number β, the graphs with maximal spectral radius are K_n if n = 2β or 2β + 1; if 2β + 2 ? n < 3β + 2; or if n = 3β + 2; if n > 3β + 2, where is the empty graph on t vertices.     

ChemInform Abstract: Molecular Structure of Chromium Tetrafluoride in the Gas Phase

is determined by electron diffraction at 195-220 °C. The diffraction patterns are completely consistent with a molecule of tetrahedral (Td) symmetry.     

ChemInform Abstract: Trends in Gas-Phase Fluoride Ion Affinities of Main-Group Oxyfluorides and Fluoride Sulfides. Generation and Characterization of the Fluoride Adducts of FAsO,FPO, FPO2, F2SiO,F4SO,FBO, F2SiS,FPS, FAsS,F2S2, and S2O by Ion Cyclotron Resonance Addition-Elimination Reactions.

Novel oxyfluoride and fluoride sulfide anions are generated by the isoelectronic replacement of F in a main-group polyfluoride by O- or S- via the reaction of either tBuO- or RS- (R: H, Me) with the polyfluorides.     

微波电子回旋共振等离子体增强化学气相沉积法沉积氟化非晶碳薄膜的研究

使用三氟甲烷和苯的混合气体,利用微波电子回旋共振等离子体增强化学气相沉积法制备了F/C比在0.11—0.62之间的α-C∶F薄膜.研究了微波功率对薄膜沉积和结构的影响,发现微波功率的升高提高了薄膜的沉积速率,降低了薄膜的F/C比,也降低了薄膜中CF和CF₃基团的密度,而使CF₂基团的密度保持不变.在高微波功率下可以获得主要由CF₂基团和C=C结构组成的α-C∶F薄膜.薄膜的介电频率关系(1×10³—1×10⁶Hz)和损耗频率关系(1×10²—1×10⁵Hz)均呈指数规律减小,是缺陷中心间简单隧穿引起的跳跃导电所致.α-C∶F薄膜的介电极化主要来源于电子极化 关键词： 氟化非晶碳薄膜 ECR等离子体沉积 键结构 介电性质     

激光金等离子体的电子离子碰撞电离速率系数

电子离子碰撞电离过程在超组态碰撞辐射(SCROLL)模型中真实模拟非局域热动力学平衡(non-LTE)高Z材料Au激光等离子体M带谱5f-3d跃迁中各种复杂离子的电离态特性,诸如离子的平均电离度和电荷态分布是一个主要过程.基于准相对论扭曲波玻恩交换近似,采用组态平均的方法,从头计算了金M带类铁金离子-类锗金离子的电子离子碰撞电离速率系数,其中电离截面的高能行为由Bethe系数决定.结果表明:在"神光Ⅱ"实验装置诊断的电子温度～2keV,电子密度～6×1021cm-3范围内,这些参数有利于使用超组态碰撞辐射模型拟Au的激光等离子体M带细致谱5f-3d跃迁的平均电离度和电荷态分布.     

On the oscillons in the signum-Gordon model

New periodic solutions of signum-Gordon equation are presented. We first find solutions φ₀(x, t) defined for (x, t) ∈ ? × [0, T ] and satisfying the condition φ₀(x, 0) = φ₀(x, T ) = 0. Then these solutions are extended to the whole spacetime by using (2.4).     

Essential and continuous spectrum of symmetric difference equations

Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation.     

Boundedness of the fbi transform on sobolev spaces and propagation of singularities

It is shown that the FBI transform of Baouendi, Chang and Treves is bounded on Sobolev spaces.Applications to the propagation of singularities are given     

Spherically Averaged Endpoint Strichartz Estimates For The Two­Dimensional Schrödinger Equation

The endpoint Strichartz estimates for the Schrödinger equation is known to be false in two dimensions[7]. However, if one averages the solution in L2 in the angular variable, we show that the homogeneous endpoint and the retarded half­endoint estimates hold, but the full retarded endpoint fails. In particular, the original verisions of these estimates hold for radial data