Banach空间中半线性混合型发展方程的解

在不要求C0-半群为紧半群的前提下．利用函数e^-λt（其中λ〉0是常数）和Monch不动点定理,在更广泛的条件下,得到了Banach空间中一类半线性混合型发展方程初值问题的整体mild解和正mild解,本质上改进和推广了已有相关结果．     

Effect of topology on the multiplicity of solutions for some semilinear elliptic systems with critical Sobolev exponent

In this paper, we are concerned with the effect of the domain topology on the multiplicity of solutions for some semilinear elliptic systems involving critical Sobolev exponent. We show that if the interaction term is sufficiently small, then the number of solutions of the system is estimated from below by 2 catΩ. The proof of this fact requires analysis of the structure of the Nehari manifold associated with the system. This research was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.     

A matricial computation of rational quadrature formulas on the unit circle

A matricial computation of quadrature formulas for orthogonal rational functions on the unit circle, is presented in this paper. The nodes of these quadrature formulas are the zeros of the para-orthogonal rational functions with poles in the exterior of the unit circle and the weights are given by the corresponding Christoffel numbers. We show how these nodes can be obtained as the eigenvalues of the operator Möbius transformations of Hessenberg matrices and also as the eigenvalues of the operator Möbius transformations of five-diagonal matrices, recently obtained. We illustrate the preceding results with some numerical examples.     

A D’Alembert Formula for Flat Surfaces in the 3-Sphere

We find all the flat surfaces in the unit 3-sphere $\mathbb{S}^{3}We find all the flat surfaces in the unit 3-sphere that pass through a given regular curve of with a prescribed tangent plane distribution along this curve. The formula that solves this problem may be seen as a geometric analogue of the classical D’Alembert formula that solves the Cauchy problem for the homogeneous wave equation. We also provide several applications of this geometric D’Alembert formula, including a classification of the flat M?bius strips of  .      

Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds

We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.     

Stability of an encapsulated bubble shell

The stability of an encapsulated bubble filled with gas is studied where gas is allowed to diffuse out of the bubble. A mechanistic model that takes into account shell stiffness and surface tension is considered. A critical shell radius for loss of mechanical stability is derived based on a technique adapted for small radius, where surface tension effects become substantial. A new parameter is defined that determines the relative importance of surface tension forces and shell stiffness for shell stability. The developed technique allows to predict, for a given bubble population and gas saturation level of the surrounding liquid, a range of bubble sizes which may collapse in time. Surface tension effects are dominant in determining the critical radius but have a negligible effect on the minimal radius for collapse. The influence of the surface tension on the stability of the shell is illustrated for Optison, a typical ultrasound contrast agent.     

Critical behavior of La0.67−y (Sr, Ba, Ca)0.33+y Mn1−x Sn x O3 (x = 0.01, 0.02, y = 0, 0.07) perovskites

The magnetic critical behavior of the manganese perovskite series $ {\text{La}}_{{0.67 - y}} {\left( {{\text{Sr,}}\,\,{\text{Ba,}}\,\,{\text{Ca}}} \right)}_{{0.33 + y}} {\text{Mn}}_{{1 - x}} {\text{Sn}}_{x} {\text{O}}_{3} The magnetic critical behavior of the manganese perovskite series (x = 0.01, 0.02, y = 0, 0.07) is studied by means of dc magnetic measurements and ¹¹⁹Sn M?ssbauer spectroscopy. The structure can be described by a rhombohedral unit cell (space group R–3C) for the samples where the A-site is occupied by La and Sr or La and Ba ions and orthorhombic unit cell (space group Pnma) for the samples where the A-site is occupied by La and Ca ions. Arrott and scaling plots show that the samples, where the A-site is occupied by La and Sr or La and Ba ions, follow the behavior of a conventional second-order ferromagnetic transition. In contrast, the samples that contain La and Ca ions in the A-site show anomalous behavior around Curie point. M?ssbauer measurements show two magnetic phases below T _c. One of them exhibits stronger exchange interactions with more rapid electron transfer between Mn³⁺/Mn⁴⁺, compared to the other.     

Synthesis and Antiviral Activity of N-Adamantyl-2-amino(or 2-phenoxy)-acylamides

New N-adamantyl-2-amino-acylamides(3a―3f) and N-adamantyl-2-phenoxy-acetamides(6a―6d) were designed and synthesized by the modification of the amino group of amantadine 1 and the structures were confirmed by mass spectra(MS) and ¹H NMR spectra. The antiviral potencies of the synthesized compounds were evaluated against the replication of influenza virus A/H₃N₂ subtype in Madin-Darby canine kidney(MDCK) cells. Among the amantadine derivatives, compound 3a had the strongest antiviral potency and showed activity similar to that of amantadine. Interestingly, the bulky and extended lipophilic moieties on the α-position of the carbonyl group resulted in decreases in potency.     

γ-Fe2O3纳米纤维的丙酮敏感特性

采用静电纺丝法制备了PVP/FeC₆H₅O₇复合纳米纤维, 并将复合纤维在500 ℃高温烧结3 h, X射线衍射分析(XRD)表明, 烧结后的产物为正尖晶石结构的γ-Fe₂O₃晶体. 扫描电子显微镜(SEM)观测结果表明, 制得了直径均匀、 连续的复合纳米纤维, 其平均直径约为1000 nm; 烧结后的γ-Fe₂O₃纳米纤维保持了其连续性, 但纤维发生了收缩, 直径较烧结前小, 平均约为600 nm. 比表面积分析表明, γ-Fe₂O₃纳米纤维比表面积为57.18 m²/g. 气敏性能测试结果表明, 230 ℃为γ-Fe₂O₃纳米纤维检测丙酮气体的最佳工作温度. 在此温度下, γ-Fe₂O₃纳米纤维对丙酮气体表现出高响应度[S=6.9, c(Acetone)=7.88×10⁴ mg/m³]和线性度(7.88×10²~1.58×10⁵ mg/m³浓度范围内). 同时, γ-Fe₂O₃纳米纤维气体传感器件还表现出良好的长期稳定性.     

基于H_∞滤波的主/子惯导组合中挠曲变形补偿算法

针对舰载环境下,主/子惯导组合中主、子惯导间的挠曲变形问题,设计了H?滤波算法。算法将主、子惯导间的挠曲变形作为一种能量有限的量测噪声,通过H?滤波对不确定噪声的鲁棒性来保证滤波精度。在经典的"速度+姿态"匹配方法的基础上,仿真比较了:1)方案一,已知挠曲变形时的标准Kalman滤波算法;2)方案二,未知挠曲变形时的标准Kalman滤波算法;3)方案三,未知挠曲变形时的H?滤波算法。仿真误差曲线直观表明:基于H?滤波算法可以在未知挠曲变形时有效提高组合精度;统计结果表明:滤波方案三得到的姿态与速度的系统误差、随机误差均与理想条件下的方案一相当;相较于方案二,滤波方案三得到的姿态与速度的系统误差至少可减小40%,随机误差至少可减少15%。