随机微分方程高阶分裂步(θ_1,θ_2,θ_3)方法的强收敛性

本文首先提出一类高阶分裂步(θ_1,θ_2,θ_3)方法求解由非交换噪声驱动的非自治随机微分方程.其次在漂移项系数满足多项式增长和单边Lipschitz条件下,证明了当1/2≤θ_2≤1时该方法是1阶强收敛的.此类方法包含很多经典的方法:如随机θ-Milstein方法,向后分裂步Milstein方法等.最后数值实验验证了所得结论.     

酶解样品-高效液相色谱法测定糯米类制品中10种合成着色剂的含量北大核心CSCD

取糯米类制品5 g,经中温淀粉酶(2 000~7 000 U·g^(-1)) 150 mg于60℃水浴中酶解6 h,得到酶解待测液。在上述溶液中加入调成粥状的聚酰胺粉(0.075~0.15 mm) 1 g,经G3垂溶漏斗抽滤,滤饼依次经60℃水(10 mL×3)淋洗,体积比7∶2∶1的乙醇-氨水-水混合液(15 mL×3)洗脱,所得洗脱液加热浓缩至5 mL左右,浓缩液用水定容至20 mL,离心。所得上清液采用高效液相色谱法测定其中10种合成着色剂的含量,以C_(18)色谱柱为固定相,以不同体积比的甲醇和20 mmol·L^(-1)乙酸铵溶液的混合液为流动相梯度洗脱,二极管阵列检测器在430 nm(检测柠檬黄),500 nm(检测日落黄、新红、胭脂红、苋菜红、诱惑红、偶氮玉红、赤藓红),600 nm(检测靛蓝、亮蓝)等3个波长条件下检测。结果表明:10种合成着色剂的质量浓度均在0.2~20.0 mg·L^(-1)内与其对应的峰面积呈线性关系,检出限(3S/N)为0.19~0.43 mg·kg^(-1)。按标准加入法进行回收试验,回收率为76.9%~94.0%,测定值的相对标准偏差(n=6)均小于4.0%。方法用于分析市售的10批糯米类制品,3批样品检出合成着色剂,分别为柠檬黄、日落黄、亮蓝。本法与国家标准GB 5009.35-2016测定结果相比,有效克服该类食品的假阴性结果。     

Dirichlet级数系数的重排

本文研究了Dirichlet级数系数的重排与此级数的收敛横坐标的关系.利用Knopp-Kojima的方法,获得了在Knopp-Kojima公式下绝对收敛横坐标保持不变的重排特征.     

Two types of loop algebras and their expanding Lax integrable models

Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation U_t-V_x+[U,V]=0, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator \widetilde{J} is presented by constructing a subalgebra \widetilde{G } of the loop algebra \widetilde A₂. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.     

通过式固相萃取净化-超高效液相色谱-串联质谱法测定液体乳中10种氨基甲酸酯类农药残留

建立了应用直接通过式的增强型基质脂质去除柱联合超高效液相色谱-串联质谱法快速测定乳品中10种氨基甲酸酯类农药残留的分析方法。样品采用乙腈为提取液，沉淀除去蛋白质后，上清液通过Captiva EMR-Lipid柱净化，使用ACQUITY UPLC BEH C₁₈柱(100 mm×2.1 mm, 1.7μm)进行分离，以甲醇-0.1%甲酸水溶液为流动相进行梯度洗脱，流速0.3 mL/min,柱温35℃,采用电喷雾正离子模式(ESI⁺)和多反应监测(MRM)扫描方式检测，基质标准曲线外标法定量分析。结果显示，10种氨基甲酸酯类农药在2～200μg/L范围内线性关系良好，相关系数(r)>0.999,方法的检出限为0.045～0.23μg/kg,定量限为0.15～0.77μg/kg;在空白基质中添加3个水平(15、50、100μg/kg)的10种氨基甲酸酯类农药，进行加标回收率和重复性试验，回收率为68.7%～93.3%,相对标准偏差(RSD)为1.8%～8.0%。由结果可知，本研究方法高效、便捷、准确，适用于乳品中10种氨基甲酸酯类农药的批量检...     

Two Integrable Couplings of Modified Tu Hierarchy

Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvature equation by using two higher dimension Lie algebras. Furthermore, a complex Hamiltonian structures of the second integrable couplings is presented by taking use of the variational identity.     

Dirichlet级数的下级

采用Knopp-Kojima的方法,去掉-lim n→∞ lnn/λn=E＜+∞等条件,研究了一般的Dirichlet级数在全平面内与右半平面内的下级,给出了下级由系数表示的充要条件.     

网格中行进路径数的算法

引例如图1所示为某城市道路规划图,计有纵向路7条,横向路5条.若“希望”号公交车从A处出发到B处.试问:从A到B 的最短路线有__条. 解析与上述问题等价的问题是:若规定公交车只能向东或向北方向行驶,则从A处出发到达B处共有__种不同走法.     

The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure

In this paper a type of 9-dimensional vector loop algebra \tilde{F} is constructed, which is devoted to establish an isospectral problem. It follows that a Liouville integrable coupling system of the m-AKNS hierarchy is obtained by employing the Tu scheme, whose Hamiltonian structure is worked out by making use of constructed quadratic identity. The method given in the paper can be used to obtain many other integrable couplings and their Hamiltonian structures.     

Dirichlet级数的下级

采用Knopp-Kojima的方法,去掉(?)(lnn)/(λn)=E+∞等条件,研究了一般的Dirichlet级数在全平面内与右半平面内的下级,给出了下级由系数表示的充要条件.