On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

钟摆模型极限环的存在性研究

钟摆系统是一类典型的分段光滑系统,结合Filippov系统刻画语言,解释了当钟摆无能量补充时,钟摆最终会停止在滑动集上的原因.利用数值模拟的方法,给出钟摆系统在有能量补充时,存在极限环的条件.最后,结合环域定理证明了一般的钟摆模型存在唯一稳定的极限环.     

去乙酰毛花苷的流动注射化学发光分析研究

在碱性介质中,去乙酰毛花苷对鲁米诺-KIO4发光体系有明显的抑制作用,且抑制效果与其质量浓度呈良好的线性关系,据此建立了去乙酰毛花苷的流动注射化学发光分析方法。该方法的线性范围为1.0×10-8~1.0×10-5g/mL,检出限为3.1×10-9g/mL,对1.0×10-7g/mL的去乙酰毛花苷进行连续11次平行测定,相对标准偏差为2.3%。可用于相应注射剂分析,并与药典方法进行对照。     

抗癫痫药卡马西平的流动注射化学发光分析

在酸性条件下,卡马西平对KMnO4-Na2SO3化学发光体系具有明显的增敏作用,据此建立了流动注射化学发光测定卡马西平的新方法.该发光体系中,卡马西平质量浓度在1.0×10-9～1.0×10-6 g/mL 范围内与发光强度呈良好的线性关系,检出限为2.0×10-10g/mL,对1.0×10-7 g/mL 卡马西平进行11次平行测定,其相对标准偏差为0.9%.本方法已应用于片剂中卡马西平测定,并与药典方法进行了对照.     

聚合物费米型截面阵列波导光栅的优化设计

利用微扰理论给出"等效矩形波导法",分析了费米型截面硅基聚合物阵列波导光栅的传输特性.模拟表明,波导的费米型截面将使阵列波导光栅的传输光谱产生漂移、并使串扰增大.为了消除光谱漂移、减小串扰、实现正常的解复用功能,对阵列波导光栅的结构参量进行了重新优化.结果表明,重新设计的费米型截面聚合物阵列波导光栅的光谱响应和串扰恢复到初始设计的聚合物矩形截面阵列波导光栅的水平.     

Logistic映射三周期轨道分支值确定

运用分支函数的方法研究了Logistic映射出现稳定三周期点的参数窗口,借助软件Singular 2.0.3运用多元多项式的Grobner基并结合严格局部分析的方法给出Logistic映射出现稳定三周期点时的参数值范围,最后数值模拟方法对所得的结果进行了验证,并指出伪轨现象.     

ASYMMETRY PARAMETERS AND DIFFERENTIAL CROSS SECTIONS FOR PHOTOIONIZATION-EXCITATION OF HELIUM

Asymmetry parameter β₂ for photoionization of helium leaving the He⁺ ion in the n=2 level and differential cross sections(DCSs) in the n=2,3,4 levels with photon emission angle θ=90⁰ are provided at photon energies 69-76.8 eV employing the R-matrix method with a 20-term target representation, in which five polarization orbitals \bar{6}l are included. The asymmetry parameter β₂ and the DCS, in the n=2 level in the region of 69-73 eV, are in good agreement with available experimental and theoretical results. Above the n=3 threshold, we present new theoretical results along with measurements. No theoretical and experimental results can be used to compare with the present calculations of the DCSs for photoionization into the He⁺ ion in the n=3,4 levels.     

LASER-ASSISTED e-Ar SCATTERING IN CO2 LASER FIELD

Electron scattering from argon in a laser field is investigated empolying the second-order perturbation theory. The absolute differential cross sections of e-Ar scattering with multiphoton exchange in special scattering geometries G1 (for small-angle scattering) and G2 are calculated. Our results are found to be better than other theoretical results as compared with the experimental data.     

聚合物费米型截面阵列波导光栅的优化设计

利用微扰理论给出“等效矩形波导法”,分析了费米型截面硅基聚合物阵列波导光栅的传输特性.模拟表明,波导的费米型截面将使阵列波导光栅的传输光谱产生漂移、并使串扰增大.为了消除光谱漂移、减小串扰、实现正常的解复用功能,对阵列波导光栅的结构参量进行了重新优化.结果表明,重新设计的费米型截面聚合物阵列波导光栅的光谱响应和串扰恢复到初始设计的聚合物矩形截面阵列波导光栅的水平.     

铕-环丙沙星的稀土敏化荧光研究及应用

在pH 7.4 NH3·H2O-NH4Cl缓冲溶液中, Eu(Ⅲ)与环丙沙星反应形成1∶2的稳定缔合物, 产生稀土敏化荧光现象, 其最佳激发、发射波长分别为λex=355 nm、λem=612 nm. 在该反应体系中加入适量维生素M溶液, 使Eu(Ⅲ)与环丙沙星缔合物的荧光发生猝灭. 利用这一现象, 建立了测定维生素M的荧光分析方法. 该方法保持了维生素M结构的完整性, 维生素M浓度在1.0×10-7～7.0×10-6 mol/L范围内符合线性关系, 检出限4.4×10-8 mol/L. 该方法用于片剂及胶囊中维生素M含量的测定, 6次平行测定回收率为95.7%～103.0%, 相对标准偏差为0.99%～1.4%.