ON THE MODULI NUMBER OF PLANE CURVE SINGULARITIES WITH ONE CHARACTERISTIC PAIR

61.IntroductionSincethepoineeringworkofZariskil1o]therehavebeenmanypaperspublishedonthemodulinumberofplanecurvesingUlaritiesl5-9].TheproblemhowtocomputethemodulinumberattractsmWattentions[3'6-1o1.Asfarastheauthors'knowledgethemostgener-aJizedalgorithmistheworkof[3]whichdependsonthedivisiontheoremin[1,2].HerewegivealinearalgebraicproofoftheBriancon-Granger-Maisonobe,stheoremlwhichavoidstheDivisiontheorem.Sincethedivisiontheoremonlyholdsindimension2,itseemsquitehopefUlthattheproofherewil1beg…     

中立型方程x(t)+cx(t-ㄒ)+ax(t)+bx(t-ㄒ)=0零解渐近稳定的代数判据

本文建立了方程ｘ（ｔ）＋ｃｔ（ｔ－ｔ）＋ａｘ（ｔ）＋ｂｘ（ｔ－ｔ）＝０零解渐近稳定的充要条件,给出了其零解渐近稳定的代数判据,同时纠正了文［２］中出现的错误．     

二维周期系数线性微分方程的特征指数

给出利用系数直接判定二维周期系数线性微分方程特征指数符号的若干结论．     

Möbius function and characteristic monomials for combinatorial enumeration

After the definitions of amplified representations and number-theoretical vectors, the markaracter table of a cyclic subgroup is converted into the corresponding Q-conjugacy character table. The conversion is shown to necessitate an interconversion matrix that contains M?bius functions as elements. Since the interconversion matrix gives characteristic monomials for cyclic groups, all the powers appearing in each of the characteristic monomials are shown to be integers. Characteristic monomials for finite groups are then built up by starting from those of cyclic groups. This procedure clarifies the fact that all the powers appearing in each characteristic monomial for finite groups are integers. The relationship between characteristic monomial tables and unit-subduced-cycle-index tables is discussed with respect to their application to isomer enumeration. Received: 15 July 1998 / Accepted: 16 December 1998 / Published online: 16 March 1999     

On extending real functions to finite dimensional algebras

In a finite dimensional real algebra, we define functional calculus for real functions. The analytic hypothesis is replaced by a differentiable hypothesis. High order differentibility is essentially necessary and sufficient to our discussions. Moreover, we give some examples. Partially supported by NSF of China The authors gratefully acknowledge the support of K. C. Wong Education Foundation, Hong Kong     

混合液体介质的特性声阻抗

本文从理想混合液的基本假设出发,由声速公式导出了混合液的特性声阻抗表达工,在此基础上对二元混液的特性声阻抗进行了讨论,对甘油和乙醇,进行了混合实验,由本文导出的公式所计算出的混合液的特性声阻抗值与由实验所测得的值符合较好。     

典型煤的近红外反射光谱特征的方向性研究

高光谱遥感是煤矿区探测的有效方法,对于煤炭资源调查、矿区环境监测等具有重要意义,其中煤、矸石、植被、水体等被遥测物各个方向的反射光谱特征是煤矿高光谱遥感的基础,为此有必要针对典型煤的方向反射光谱特征进行研究.从我国不同矿区收集了无烟煤、烟煤、褐煤三大类煤中的4种典型煤样,4种煤样按煤阶由高到低顺序包括无烟煤一号、贫煤、...     

Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy

In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.     

On the global structure and asymptotic stability of low-stretch diffusion flame: Forced convection

The present work analyzes cylindrical diffusion flames (Tsuji burner) under low stretch condition, considering fuel injection also from the backward region of the burner. To highlight the fundamental aspects of this flame, some assumptions are imposed, like constant thermodynamic and transport coefficients, unitary Lewis number and no radiative heat loss. It is also considered potential flow model and incompressible Navier–Stokes model. Despite the simplicity of the former model, results from both models show good agreement. Also, an asymptotic analysis describing the problem far from the burner is able to capture the most important mechanisms controlling the flame, then the flame shape is determined and the dependence of the characteristic length scales on Peclet number (based on the burner properties), free stream velocity and stoichiometry is revealed. The results show that the flame width is proportional to the mass stoichiometric coefficient and reciprocal to the Peclet number the 1/4 power and free stream velocity the 3/4 power, and that the flame height is proportional to the square of the mass stoichiometric coefficient and to the square root of the ratio of Peclet number to free stream velocity. In addition, an asymptotic stability analysis reveals low-stretch flame extinction to be caused by reduction in fuel and oxidizer concentrations, which provides the range of the stoichiometric coefficient for stable regime, and at the same time the range of heat released.