非齐次树上m重非齐次马氏链的一类强偏差定理

研究给出了非齐次树上m重非齐次马氏链的一类强偏差定理.     

GAMLSS模型在车险定价中的应用

在系统梳理国内外非寿险产品费率厘定方法的基础上,详细介绍了GAMLSS模型,证明了在位置参数和尺度参数的预测中均引入随机效应的GAMLSS模型可更有效地解释纵向数据中个体间的异质性.最后将GAMLSS模型应用于一组纵向车辆保险数据,计算了先验保费、后验保费、后验风险保费和奖惩因子.实证结果表明,GAMLSS模型不仅可为非寿险产品的定价提供依据,而且使风险分类更加稳定、合理.     

Evaluation of the Hamming weights of a class of linear codes based on Gauss sums

Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of q-ary linear codes under some certain conditions, where q is a power of a prime. The lower bound of its minimum Hamming distance is obtained. In some special cases, we evaluate the weight distributions of the linear codes by semi-primitive Gauss sums and obtain some one-weight, two-weight linear codes. It is quite interesting that we find new optimal codes achieving some bounds on linear codes. The linear codes in this paper can be used in secret sharing schemes, authentication codes and data storage systems.     

激光脉冲放大器增益通量耦合系统解

研究了一个激光脉冲放大器增益通量系统解的问题.首先讨论了较一般的系统, 然后引入一个同伦映射.再利用映射的性质, 引进一个人工参数, 将求解非线性问题转化为求解一系列线性问题.再逐次地求出对应的线性问题的解, 最后得到了原模型解的近似展开式.可以看出, 同伦映射方法是一个解析的方法.它是通过函数的解析运算并用初等函数来表达近似解,其不同于用离散数值运算的数值计算方法.因此通过同伦映射解, 还可以对它继续进行解析运算, 从而可以进行微分和积分等运算来得到与激光脉冲放大器增益通量相关的其他物理量的性态.     

On the criterion vectors of lines of portfolio selection with multiple quadratic and multiple linear objectives

As the research for portfolio selection evolves, traditional models and models with one quadratic objective and multiple linear objectives are being solved. In this paper, I propose models with multiple quadratic and multiple linear objectives. Due to the difficulty involved, I study the new models by lines in decision space, analyze the criterion vectors of the lines by projection, and approximate the nondominated sets by the criterion vectors. As an illustration, I extend Merton’s portfolio selection model, propose algorithms to approximate the nondominated sets by the criterion vectors of portfolios with cardinality 3 and then K, and demonstrate the number of the criterion vectors.     

凝胶渗透色谱-气相色谱-离子阱质谱法测定桔梗原药和当归提取物中101种农药残留

建立了凝胶渗透色谱（GPC）-气相色谱-离子阱质谱同时检测桔梗原药和当归提取物中101种农药残留的分析方法。方法采用乙腈超声辅助提取桔梗原药和当归提取物,浓缩提取液至近干后用乙酸乙酯-环己烷（1∶1, v/v）复溶,采用凝胶渗透色谱法（选取40 cm长、内径20 mm的凝胶渗透色谱柱）对样品进行净化,弃去前段含脂类、色素等杂质的流出液,收集17~30 min洗脱液并旋转蒸发浓缩至近干,甲苯1 mL定容上机。选用DB-5MS毛细管色谱柱分离待测物,通过离子阱质谱实现对101种农药残留的高效检测。方法通过优化前处理条件和离子阱二级质谱参数,有效降低了复杂中药基质对待测化合物的干扰,最大限度提高了样品中农药的定量准确性和回收率,101种农药3水平添加的平均回收率为58.3%~108.9%,每个添加水平10次独立重复测定的相对标准偏差为0.4%~16.5%,检出限（LOD）范围为0.2~40.0 μg/kg,可满足当前韩国、日本、欧洲规定的最大残留限量（maximum residue limits, MRLs）要求。方法具有操作简单快速、灵敏度高、重复性好等特点,凝胶渗透色谱技术的应用克服了固相萃取小柱净化容量不足的弊端,离子阱技术的应用可以进一步排除共流出基体杂质的干扰,提高定量和定性的准确性,检测效果优于常用的气相色谱-质谱法,是对中药中同时分析多种农药残留检测方法的有益补充。     

发光颜色可调的白磷钙矿结构Ca8MgBi(PO4)7∶Ce3+，Tb3+荧光粉的制备、发光性能及能量传递

采用具有白磷钙矿结构的磷酸盐作为目标产物,通过高温固相法制备了发光颜色可调的Ca₈MgBi(PO₄)₇∶Ce³⁺,Tb³⁺荧光粉。利用X射线粉末衍射(XRD)、扫描电子显微镜(SEM)和荧光光谱等表征手段对其物相组成、微观形貌及发光性能进行了详细研究。结果表明：掺杂少量的Ce³⁺、Tb³⁺并没有改变Ca₈MgBi(PO₄)₇基质的晶体结构。荧光光谱和荧光寿命曲线确定了Ce³⁺-Tb³⁺之间存在能量传递,其能量传递机制为四极-四极相互作用,能量传递效率可达81%。固定Ce³⁺浓度而逐渐增加Tb³⁺的掺杂量时,系列Ca₈MgBi(PO₄)₇∶0.08Ce³⁺,yTb³⁺荧光粉的发...     

GdPO4∶Sm3+荧光粉的焙烧温度和掺杂浓度的优化及发光和磁性能

以GdPO₄为基质,Sm³⁺为激活剂,采用水热法合成了纳米荧光粉前驱体,分别在800、900、1 000、1 100和1 200℃下焙烧,得到一系列GdPO₄∶Sm³⁺荧光粉。首先探究了GdPO₄∶Sm³⁺的最佳焙烧温度;其次研究了Sm³⁺掺杂浓度对GdPO₄∶Sm³⁺荧光性能的影响;最后研究了GdPO₄∶2% Sm³⁺的高温荧光性能和磁性能。使用X射线衍射仪(XRD)、扫描电子显微镜(SEM)、磁强计和荧光分光光度计(FL)对荧光粉的晶体结构、形貌、发光和磁性能进行了表征。结果表明：荧光粉的晶体结构由前驱体六方晶系GdPO₄·H₂O∶Sm³⁺变为单斜晶系的GdPO₄∶Sm³⁺,形貌由纳米棒变为无规则块体。当焙烧温度为1 000℃,Sm³⁺掺杂浓度为2%时,荧光粉的发光强度和荧光寿命达到最大值。GdPO₄∶2% Sm³⁺中Sm³⁺之间能量传递类型为电偶极-电偶极相互作用,能量传递的临界距离为1.646~1.884 nm。最佳样品GdPO₄∶2% Sm³⁺有优异的热稳定性,热猝灭活化能为-0.157 eV,且具有良好的顺磁性,质量磁化率值为1.22×10^-4 emu·g^-1·Oe^-1。     

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C₉₆H₂₄Ar₆)₂ (Ar=2,6-dimethylphenyl) ( 1 ₂) was transformed to a triply negatively charged species 1 ₂^3.−, which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 1 ₂^3.− features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp² carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 1 ₂^3.−, which indicates graphene upon reduction doping may behave as a quantum spin liquid.