FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON－STRICTLY HYPERBOLIC SYSTEM

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.     

Jacobi形式的奇异性猜想

建立了Jacobi形式空间J_k ,m(Γ_n)和半整权Siegel模形式空间[Γ_n,k-12 之间的一个对应关系 ,当指标m等于1时 ,证明了关于Jacobi形式的奇异性猜想.     

ANALYSIS OF STRONG SINGULARITIES FOR NONLINEAR HYPERBOLIC EQUATIONS

In this paper we review our some results about the strongly singular (discontinuous,measure, or delta function) problems for nonlinear hyperbolic equations.     

δ掺杂的赝形高电子迁移率晶体管AlGaAs／InGaAs／GaAs结构中的费密…

报道δ掺杂赝形高电子迁移率晶体管结构Ａｌ０．３０Ｇａ０．７０Ａｓ／Ｉｎ０．１５Ｇａ０．８５Ａｓ／ＧａＡｓ的光致发光光谱研究的实验结果，除了观察到ｎ＝１电子子带到ｍ＝１重空穴子带，ｎ＝２电子子带到ｎ＝１重空穴子带间的强发光峰，还观察到了ｎ＝１电子子带到ｎ＝１轻空穴子带的弱发光峰，通过变化掺杂浓度来改变费密能级的位置，在这种δ掺杂的ＨＥＭＴｓ的系统中观察了费密边奇异性，并把它归结为费密海与费密边附近未     

顶端受集中力偶或表面受均匀载荷的圆柱型正交各向异性楔:佯谬的解决

对楔顶角为２α的圆柱型正交各向异性楔，其顶端受集中力偶的经典解当α满足ｔｇλα＝λα（λ＝（ａ６６＋２ａ１２＋２ａ１１）／ａ１１，ａ６６、ａ１２、ａ１１为弹性常数）时，应力成为无穷大；其表面受均匀载荷的经典解当α满足ｓｉｎλα＝０（对称变形）或ｔｇλα＝λα（反对称变形）时，也有同样问题。这二个佯谬均由文中利用叠加齐次解的方法解决     

Analysis of Hysteretic Strongly Nonlinearity for Quad Iced Bundle Conductors

A new hysteretic nonlinear model of quad iced bundle conductors is constructed. The bifurcation equation is obtained by applying the undetermined fundamental frequency method of the complex normal form. The transition set and bifurcation diagrams for the singularity are presented. Then the corresponding relations between the unfolding parameters and the system parameters are given, and the sensitivity parameters and its range of values are obtained to analyze and to control the galloping of the quad iced bundle conductor.     

耦合相对转动非线性动力系统的稳定性与近似解

研究了一类含三次非线性耦合项的相对转动非线性动力系统的动力学行为. 建立了具有非线性弹性力、广义摩阻力耦合项的系统动力学方程. 运用多尺度法求解谐波激励下耦合非自治系统的近似解,通过讨论系统的主共振和内共振特性,分析了耦合项对系统响应的影响. 应用奇异性理论研究了主振稳态响应分岔方程的稳定性,得到了系统的转迁集和分岔曲线的拓扑结构. 关键词： 相对转动 非线性耦合动力系统 奇异性理论 稳定性     

南开大学奇异性核物理的理论研究

简要介绍了南开大学核物理组在奇异性核物理方面的理论研究工作. 已经完成的工作有核介质内超子平均自由程的理论计算, 奇异性核物理方面已完成的其他4个理论研究课题是, 不同重子杂质对原子核的影响、重味重子超核、核物质内的eta-介子以及K介子原子核的性质.     

Homoclinic Bifurcations in Symmetric Unfoldings of a Singularity with Three-fold Zero Eigenvalue

In this paper we study the singularity at the origin with three-fold zero eigenvalue forsymmetric vector fields with nilpotent linear part and 3-jet C^∞-equivalent to y δ/δx zδ/δy ax^2yδ/δz with a≠0. We first obtain several subfamilies of the symmetric versal unfoldings of this singularityby using the normal form and blow-up methods under some conditions, and derive the local and global bifurcation behavior, then prove analytically the existence of the Sil‘nikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of this singularity, by using the generalized Mel‘nikov methods of a homoclinic orbit to a hyperbolic or non-hyperbolic equilibrium in a highdimensional space.     

Positive Solution of Multi-Point Boundary Value Problems for the One-Dimensional p-Laplacian with Singularities

In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{（ φp（u＇））＇＋q（t）f（t,u,u＇）=0,0〈t〈1,u（0）=∑i=1^nαiu（ξi）,u＇（1）=∑i=1^nβiu＇（ξi）,whereφp（s）=｜s｜^p-2s,p≥2;ξi∈（0,1）（i=1,2,…,n）,0≤αi,βi〈1（i=1,2,…n）,0≤∑i=1^nαi,∑i=1^nβi〈1,and q（t） may be singular at t=0,1,f（t,u,u＇）may be singular at u＇=0