依状态独立的随机环境中的马氏链

本主要讨论了依状态独立的随机环境中的马氏链，并严格地证明了依状态独立的随机环境中的马氏链，如果在环境不退化的一般情形下，不是时齐马氏链，而环境退化必然是马氏链这个结论。     

The p-Harmonic Heat Flow with Potential into Homogeneous Spaces

In this paper we prove the existence of global weak solutions of the p-harmonic flow with potential between Riemannian manifolds M and N for arbitrary initial data having finite p-energy in the case when the target N is a homogeneous space with a left invariant metric. Received March 17, 1999, Revised September 22, 1999, Accepted October 15, 1999     

Bifurcation and resonance in a fractional Mathieu-Duffing oscillator

The bifurcation and resonance phenomena are investigated in a fractional Mathieu-Duffing oscillator which contains a fast parametric excitation and a slow external excitation. We extend the method of direct partition of motions to evaluate the response for the parametrically excited system. Besides, we propose a numerical method to simulate different types of local bifurcation of the equilibria. For the nonlinear dynamical behaviors of the considered system, the linear stiffness coefficient is a key factor which influences the resonance phenomenon directly. Moreover, the fractional-order damping brings some new results that are different from the corresponding results in the ordinary Mathieu-Duffing oscillator. Especially, the resonance pattern, the resonance frequency and the resonance magnitude depend on the value of the fractional-order closely.     

高功率氙灯脉冲放电过程中石英管壁热损伤机理

基于高功率激光装置对脉冲氙灯工程运行可靠性的要求,利用现有的能源模块开展了氙灯放电考核实验。实验结果表明：虽然氙灯运行在安全的能量负载水平,当能源模块单个放电回路的峰值功率超过300 MW时,氙灯石英玻璃管壁存在热损伤风险。肉眼观察到管壁损伤后在反射器对侧的灯管内壁出现乳白色沉积层。经扫描电镜和X射线光电子能谱测试分析,证实热损伤形成的乳白色沉积物为二氧化硅。为探究管壁热损伤机制,采用高速摄影观测了氙灯放电等离子体沟道发展过程。图像显示放大器内金属反射器的几何形状对放电沟道的分布产生了显著影响,尤其是在侧灯箱,灯内电弧沟道会靠近反射器一侧集中分布,因此,导致等离子体对灯管的偏烧。当放电峰值功率超过石英热负载极限时,管壁表面二氧化硅材料会被烧蚀至蒸发、气化,并随后沉积在灯管较冷部位。研究结果表明放电回路的放电峰值功率过高、放大器内金属反射器均会对氙灯造成热损伤。     

ORTHOGONAL (g,f)-FACTORIZAFIONS OF BIPARTITE GRAPHS

1 IntroductionIn this paper we con8ider finite undirected simple graphs. Let G be a graph with vertexset V(G) and edge set E(G). Let g and f be two po8itive iuteger-valued functions defined onV(G) such that g(x) 5 f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanningsubgraph H of G satisfying g(x) 5 dH(x) 5 f(x) for each x E V(H). In particular, if G itselfis a (g, f)-factor, then G is called a (g, f)-grapl1. A subgrapl1 H of G is called an rmsubgraphif H has m edg…     

Can Dirac quantization of constrained systems be fulfilled within the intrinsic geometry?

For particles constrained on a curved surface, how to perform quantization within Dirac’s canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance in passing from the classical Hamiltonian to its quantum mechanical form while preserving the classical algebraic structure between positions, momenta and Hamiltonian to the extent possible. On the other, on the curved surface, we have no exact Cartesian coordinate system within intrinsic geometry. These two facts imply that the three-dimensional Euclidean space in which the curved surface is embedded must be invoked otherwise no proper canonical quantization is attainable. In this paper, we take a minimum surface, helicoid, on which the motion is constrained, to explore whether the intrinsic geometry offers a proper framework in which the quantum theory can be established in a self-consistent way. Results show that not only an inconsistency within Dirac theory occurs, but also an incompatibility with Schrödinger theory happens. In contrast, in three-dimensional Euclidean space, the Dirac quantization turns out to be satisfactory all around, and the resultant geometric momentum and potential are then in agreement with those given by the Schrödinger theory.     

Crystal structure,dielectric and piezoelectric properties of Ta/W codoped Bi3TiNbO9 Aurivillius phase ceramics

Aurivillius phase Bi₃Ti_1−xTa_xNb_1−xW_xO₁₂ high temperature piezoceramics were prepared by a conventional solid state reaction method. The crystal structure, dielectric, electrical conduction and piezoelectric properties were systematically studied. Pure or modified Bi₃TiNbO₉ ceramics revealed the presence of only two-layered Aurivillius phase, indicating that Ta/W doping entered into the B-site of pseudo-perovskite structure and formed solid solutions. The Curie temperature had a strong reliance on the structural distortion. Furthermore, Ta/W dopants act as a donor doping, decrease the number of oxygen vacancies and facilitate the domain wall motion. As a result, Ta/W modifications significantly increase the DC resistivity and piezoelectric properties. Bi₃Ti_0.98Ta_0.02Nb_0.98W_0.02O₁₂ ceramics possess the optimum d₃₃ value (∼12.5 pC/N) together with a high T_C point (∼893 °C). Moreover, the resonance–antiresonance spectra demonstrate that the Ta/W-BTN ceramics are indeed piezoelectric in nature at 600 °C. The d₃₃ value of BTTNW-2 ceramic remains ∼12.2 pC/N after annealing at 700 °C. These factors suggest that the BTTNW-based ceramic is a promising candidate for ultra-high temperature sensor applications.     

Preparation,Morphology and Properties of Poly(Trimethylene Terephthalate)/Thermoplastic Polyester Elastomer Blends

Poly(trimethylene terephthalate)(PTT)/thermoplastic polyester elastomer (TPEE) blends were prepared and their miscibility, crystallization and melting behaviors, phase morphology, dynamic mechanical behavior, rheology behavior, spherulites morphology, and mechanical properties were investigated by differential scanning calorimetry (DSC), scanning electron microscopy (SEM), dynamic mechanical analysis (DMA), parallel-plate rotational rheometry, polarized optical microscopy (POM), wide angle X-ray diffraction (WAXD), universal tensile tester and impact tester, respectively. The results suggested that PTT and TPEE were partially miscible in the amorphous state, the TPEE rich phase was dispersed uniformly in the solid matrix with a size smaller than 2 μm, and the glass transition temperatures of the blends decreased with increasing TPEE content. The TPEE component had a good effect on toughening the PTT without depressing the tensile strength. The blends had improved melt viscosities for processing. When the blends crystallized from the melt state, the onset crystallization temperature decreased, but they had a faster crystallization rate at low temperatures. All the blends’ melts exhibited a predominantly viscous behavior rather than an elastic behavior, but the melt elasticity increased with increasing TPEE content. When the blends crystallized from the melt, the PTT component could form spherulites but their morphology was imperfect with a small size. The blends had larger storage moduli at low temperatures than that of pure PTT.     

半群代数中理想FA良序基的构造

讨论了在半群代数k[A]中,如何利用Gause-Jordan消元法去构造半群代数的理想的良序基,进而得到理想的良性基-Groedner-基。