Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids

The chromatic polynomial P_G(q) of a loopless graph G is known to be non-zero (with explicitly known sign) on the intervals (−∞,0), (0,1) and (1,32/27]. Analogous theorems hold for the flow polynomial of bridgeless graphs and for the characteristic polynomial of loopless matroids. Here we exhibit all these results as special cases of more general theorems on real zero-free regions of the multivariate Tutte polynomial Z_G(q,v). The proofs are quite simple, and employ deletion–contraction together with parallel and series reduction. In particular, they shed light on the origin of the curious number 32/27.     

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.     

A1.3 μm strained quantum well laser on a graded InGaAs buffer with a GaAs substrate

We grew a 1.3 μm strained-layer quantum well (SL-QW) laser with InGaP cladding layers on a lattice-relaxation buffer layer by metalorganic vapor phase epitaxy. For the lattice-relaxation buffer, we used a compositionally graded InGaAs/GaAs structure. The significantly reduced surface roughness of the InGaP cladding layers achieved by supplying a large amount of H₂Se enables CW operation of our 1.3 μm SL-QW laser. We achieved a low threshold current of less than 10 mA and a high characteristic temperature of 100K around room temperature.     

PECVD法低温形成新型SiO_xN_y薄膜的界面特性研究

研究了等离子体增强化学气相淀积（PECVD）方法低温形成新型SIOxNy薄膜的界面特性。研究侧重于PECVDSiOxNy薄膜良好界面特性的控制，探索出界面特性与微观组份、衬底工作温度、反应室气压、退火致密、金属化后退火的相互关系。同时给出了获取界面等特性优良的PECVDSiOxNy薄膜的最优化工艺条件，并对实验结果进行了理论分析与讨论。     

An easy applicable method for the design of asymmetrical finline and slotline tapers

In this paper, some utilities for the developement of asymmetrical circular arc tapes are described. Basing on a polygon-approximation of characteristic impedance a method for to determine the geometrical parameters of the taper is explained. The applicability of the method presented here is proved by extensive measurements.     

液体介质中厚度切变石英晶体传感器的特征阻尼研究

本文提出一个新概念：特征阻尼系数ｋｃ。用来区分液体中振荡的厚度切变石英晶体传感器由质量负载和液体阻尼分别引起的频率偏移。理论推导表明，当石英晶体表面附着的质量没有变化时，特征阻尼系数Ｋｃ０的大小与附着的液体或固体性质无关，只取决于晶体谐振器自身的参数，如基频、电极面积和谐波次数等。     

EXPLICITLY SOLVABLE CHARACTERISTIC METHOD FOR CONVECTION DIFFUSION PROBLEMS

In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished and solved in spaces posscssing reproducing kernel functions. At each time step, the exact solution of the approximate problem is given by explicit expression. The computational advantage of this method is that the schemes are absolutely stable, and are explicitly solvable as well. The stability and error estimates are derived. Some numerical results are given.     

几种复合传输线特性阻抗的计算

本文就高速光电器件微波封装提出了有希望的几种复合传输线（微带＋共面线，屏蔽微带＋共面线，微带＋不对称共面线），采用边界元法计算了它们的特性阻抗，给出了几组有工程价值的计算曲线，并讨论了实验结果。     

EMBEDDED 2-SPHERES IN INDEFINITE 4-MANIFOLDS

51.IntroductionOne0ftheinterestingproblemsneartheheartof4dimensionaltopologyistodecidewhich2-dimensionalhomology/homotoPyclasscanberepresentedbyasmo0thlyembedded2-sphereinagivensmooth4-dimensionalmanifold.ItwasRohlin[19]wh0pointed0utintheearly195Ostousthatnotevery2-dimensionalhthmology/hom0topyclasscanbesorepresented.TheimportanceoftheproblemwasexplainedbyKervaireandMilnorl11].Onedecadelater,theystartedthestudyin1961,followedbyBoardm..I1]?Wall[25]5Tri.t..m[23]tHsiangandSzczarba[1o],andRoh…     

开端同轴线应用于无损检测的理论分析

基于测量待测物质在开端波导处的反射以确定其介电特性，由于无需制作样品而成为一种简便的无损检测方法，其关键是要确定反向系数与待测物质介电常数之间的对应关系。在本文中，应用并矢格林函数和特征模理论研究了同轴线开端处的电磁场。利用矩量法进行数值计算，得出介电常数与反射系数的数值对应关系。数值结果与有关文献的比较分析证实了理论分析的可靠性。