幂格的理想与素理想

研究了幂格的理想和素理想,建立了格的理想与格上幂格的理想的一种联系,获得了格的理想(素理想)与它的商格的理想(素理想)之间的关系。     

二阶拟线性退化抛物方程Cauchy问题解的稳定性

在一定的结构性条件下,证明了如下形式的拟线性退化抛物方程 Cauchy问题解的稳定性．     

Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians

The Pfaffian method enumerating perfect matchings of plane graphs was discovered by Kasteleyn. We use this method to enumerate perfect matchings in a type of graphs with reflective symmetry which is different from the symmetric graphs considered in [J. Combin. Theory Ser. A 77 (1997) 67, MATCH—Commun. Math. Comput. Chem. 48 (2003) 117]. Here are some of our results: (1) If G is a reflective symmetric plane graph without vertices on the symmetry axis, then the number of perfect matchings of G can be expressed by a determinant of order |G|/2, where |G| denotes the number of vertices of G. (2) If G contains no subgraph which is, after the contraction of at most one cycle of odd length, an even subdivision of K_2,3, then the number of perfect matchings of G×K₂ can be expressed by a determinant of order |G|. (3) Let G be a bipartite graph without cycles of length 4s, s{1,2,…}. Then the number of perfect matchings of G×K₂ equals ∏(1+θ²)^m_θ, where the product ranges over all non-negative eigenvalues θ of G and m_θ is the multiplicity of eigenvalue θ. Particularly, if T is a tree then the number of perfect matchings of T×K₂ equals ∏(1+θ²)^m_θ, where the product ranges over all non-negative eigenvalues θ of T and m_θ is the multiplicity of eigenvalue θ.     

具有密度依赖的生育脉冲单种群阶段结构模型

给出具有密度依赖生育脉冲单种群阶段结构数学模型．通过研究其频闪映射所确定的离散动力系统,获得了具有生育脉冲的系统存在周期解及其稳定的阈值,当系统的参数超过阈值,存在一系列的分支并最终走向混沌,这说明生育脉冲使系统动力学行为变得非常复杂,提供了一个自然的周期,而使系统从倍周期分支到混沌．     

基于遗传算法的Au-Cu-Pt三元合金纳米粒子的稳定结构研究

合金纳米粒子展示出单金属粒子所不具有的多功能性能, 而其稳定结构的研究对于进一步了解其催化性能具有重要的意义. 本文采用改进的遗传算法和量子修正Sutton-Chen型多体势对二十四面体Au-Cu-Pt三元合金纳米粒子的稳态结构进行了系统的研究. 针对不同尺寸、不同组成比例的合金纳米粒子, 探讨了遗传算法的收敛性及初始构型对稳态结构的影响. 计算的结果表明: 初始结构的选取并不影响最终的稳定结构, 并且改进的遗传算法具有较好的稳定性; Au和Cu形成表面偏聚, 而Pt则倾向于分布在内层; 当Au或Cu比例较小时, Au和Cu表现出表面最大偏聚; 当Au与Cu原子数之和大于表面原子数时, 二者表现出竞争偏聚, 且Cu的偏聚效应较强; 随着Au, Cu原子数继续增长至大于表面和次表面原子数之和时, Au的偏聚性能增强. 此外, Cu在占据表面后, 会越过次外层, 与Pt在内层形成混合相结构.     

ICP-MS测定PM2.5中痕量重金属及铅同位素

建立了HNO3-H2O2湿法消解、电感耦合等离子体质谱(ICP-MS)同时测定PM2.5样品中痕量重金属Cr,Ni,Cu,As,Cd,Pb和Pb同位素的方法。通过内标校正克服了基体效应、物理效应和仪器的长短期漂移的干扰。在ICP-MS优化参数下,测定的痕量元素及Pb同位素的标准曲线相关系数均优于0.9997,5种痕量元素的方法检出限在0.01~0.07μg/L之间,4种Pb同位素的方法检出限在0.014~0.07μg/L之间。通过测定滤膜标准物质(GBW(E)080212)和Pb同位素标准物质(NIST981)考察了方法准确性,测定值均在标准值范围内。当Pb质量浓度大于10μg/L时,浓度对Pb同位素比值的测量影响不显著。运用该方法测得厦门市PM2.5中6种痕量重金属元素的RSD小于4.8%,Pb同位素RSD小于0.5%。     

基于柱弥散光源体内辐照的前列腺扫描光声成像仿体实验

光声成像技术是一种非常有前景的前列腺早期检测与成像的新技术. 在现有前列腺光声成像技术中, 通常采用的腺体外光源辐照方式由于受外围组织的影响, 容易减弱深部前列腺组织的光能量吸收, 导致辐照范围减小, 引起光声成像深度不足, 难以实现无损前列腺癌的检测. 本文基于前列腺组织的结构特征, 依据一种以柱状弥散光纤在尿道对前列腺实施光辐照、并利用外置于直肠内的长焦区聚焦式超声换能器检测光声信号的前列腺光声扫描成像技术, 构建了光声成像实验系统, 开展了仿体实验. 测试结果表明, 系统能够实现样品中吸收体的定位和成像, 结合柱弥散光源体内辐照可使成像深度提高, 同时侧向成像范围也较大. 初步结果表明, 借助柱弥散光源进行体内光辐照的光声信号新激发方式结合长焦区超声探头在前列腺癌早期无创诊断上具有潜在的应用前景.     

基于最小化似零伪范数的稀疏信号恢复算法

针对欠定系统中出现的稀疏信号恢复问题,提出了一种基于最小化近似零伪范数的处理方法,算法首先结合反正切函数构造出代价函数,再融合最速下降法和扩展牛顿迭代法逐步迭代寻优,并给出了算法的收敛性分析,数值仿真实验结果表明,与经典的稀疏信号恢复算法相比,方法有更好的计算速度和恢复精度.     

Preparation and Adsorption Ability of Molecularly Imprinted Polymer Microspheres for Malachite Green

Molecularly imprinted polymer (MIP) microspheres were synthesized through precipitation polymerization using malachite green (MG) as template, methacrylic acid (MAA) as monomer, and trimethylolpropane trimethacrylate (TRIM) as cross-linker. The microsphere structure of MIP was characterized by IR spectroscopy and SEM. The influence of preparation conditions such as monomer and cross-linker dosages on the polymer absorption of MG in acetonitrile solution was also explored. Under the optimum synthesis conditions (0.25 mmol MG, 1.5 mmol MAA, 2.5 mmol TRIM, 40 mL acetonitrile), the prepared MIP microspheres have a binding capacity as high as 2000 µg g^?1 of MG with an imprinting factor of above 4.0. The result suggests that the prepared MIP microspheres are promising material for the selective extraction of MG in complicated matrix solutions.     

Implanting Ni into N-doped puffed carbon: A new advanced electrocatalyst for oxygen evolution reaction

Tailored design and synthesis of high-quality electrocatalysts is vital for the advancement of oxygen evolution reaction (OER). Herein, we report a powerful puffing method to fabricate hierarchical porous N-doped carbon with numerous embedded Ni nanoparticles. Interestingly, during the puffing and annealing process, rice precursor with N and Ni sources can be in-situ converted into Ni-embedded N-doped porous carbon (N-PC/Ni) composite. The obtained N-PC/Ni composite possesses a cross-linked porous architecture containing conductive carbon backbone and active Ni nanoparticles electrocatalysts for OER. The pore formation in N-PC/Ni composite is also proposed because of carbothermic reduction. The N-PC/Ni composite is fully studied as electrocatalysts for OER. Due to increased active surface area, enhanced electronic conductivity and reactivity, the designed N-PC/Ni composite exhibits superior OER performance with a low Tafel slope (∼88 mV/dec) and a low overpotential as well as excellent long-term stability in alkaline solution. Our proposed rational design strategy may provide a new way to construct other advanced metal/heteroatom-doped composites for widespread application in electrocatalysis.