具有特殊伸缩矩阵的三元不可分正交小波的构造

多元小波分析是分析和处理多维数字信号的有力工具.不可分多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域.给出了构造具有伸缩矩阵(101-1-110-10)的紧支撑三元不可分正交小波的算法,利用该算法得到的小波函数继承了来源于尺度函数和符号函数的对称性和消失矩性质,从而为这类小波在信号处理方面的应用提供了便利.最后给出了数值算例.     

神经元的形态分类和识别

对神经元特性的认识,最基本问题是神经元的分类.神经元的形态复杂多样,神经元的识别分类问题有相当的困难.对提供的参考数据进行统计分析,将其转化成对应每类神经元的空间形态的指标参数,然后对每个指标进行定性分析和对比分析,确定对各类型神经元细胞识别起关键作用的指标,利用层次分析法、图形截面、几何相似性等分析方法建立神经元的分类模型.分类模型能够将附录提供的神经元进行准确的分类.数据分析采用开源科学计算软件Scilab进行处理,运行环境为Scilab5.2,部分代码采用C#基于VS2008开发.     

Tetrazole-Functionalized Silica for Hydrophilic Interaction Chromatography of Polar Solutes

In this work, tetrazole-functionalized stationary phase was prepared with nitrile-modified silica by an ammonium-catalyzed (3 + 2) azide-nitrile cycloaddition reaction. The prepared stationary phase was used for separation of nucleobases and nucleosides by hydrophilic interaction chromatography (HILIC) mode. A typical HILIC mechanism was observed at higher content of acetonitrile (>85%, v/v) in the mobile phase. The retention mechanism of the column was investigated by the models used for describing partitioning and surface adsorption through adjustment ratio of water in the mobile phase, and by the influence of salt concentration, buffer pH, and temperature on the retention of solutes. The results illustrated that the surface adsorption through hydrogen bonding dominated the retention behavior of nucleobases/nucleosides under HILIC mode. From the separation ability, the tetrazole-functionalized stationary phase could become a valuable alternative for the separation of the compounds concerned.     

Banach空间中带Poisson跳的随机种群方程的数值分析

本文研究Banach空间中带Poisson跳的随机种群方程,通过离散使之成为随机微分方程,进而运用显式Euler公式来分析其数值解与解析解的误差.     

An Eulerian–Lagrangian mixed discrete least squares meshfree method for incompressible multiphase flow problems

Mixed discrete least squares meshfree (MDLSM) method has been developed as a truly meshfree method and successfully used to solve single-phase flow problems. In the MDLSM, a residual functional is minimized in terms of the nodal unknown parameters leading to a set of positive-definite system of algebraic equations. The functional is defined using a least square summation of the residual of the governing partial differential equations and its boundary conditions at all nodal points discretizing the computational domain. Unlike the discrete least squares meshfree (DLSM) which uses an irreducible form of the governing equations, the MDLSM uses a mixed form of the original governing equations allowing for direct calculation of the gradients leading to more accurate computational results. In this study, an Eulerian–Lagrangian MDLSM method is proposed to solve incompressible multiphase flow problems. In the Eulerian step, the MDLSM method is used to solve the governing phase averaged Navier–Stokes equations discretized at fixed nodal points to get the velocity and pressure fields. A Lagrangian based approach is then used to track different flow phases indexed by a set of marker points. The velocities of marker points are calculated by interpolating the velocity of fixed nodal points using a kernel approximation, which are then used to move the marker points as Lagrangian particles to track phases. To avoid unphysical clustering and dispersing of the marker points, as a common drawback of Lagrangian point tracking methods, a new approach is proposed to smooth the distribution of marker points. The hybrid Eulerian and Lagrangian characteristics of the approach used here provides clear advantages for the proposed method. Since the nodal points are static on the Eulerian step, the time-consuming moving least squares (MLS) approximation is implemented only once making the proposed method more efficient than corresponding fully Lagrangian methods. Furthermore, phases can be simply tracked using the Lagrangian phase tracking procedure. Efficiency of the proposed MDLSM multiphase method is evaluated using several benchmark problems and the results are presented and discussed. The results verify the efficiency and accuracy of the proposed method for solving multiphase flow problems.     

基于自适应小波神经网络的第二类Fredholm积分方程数值解法

该文构造了一类三层前馈自适应小波神经网络,将小波分析中平移因子和伸缩因子的拟合设置为输入层到隐层的权值与阈值,采用小波基函数作为隐层激活函数,并根据梯度下降算法自适应地调整参数.应用自适应小波神经网络数值求解第二类Fredholm积分方程,通过数值算例验证了该方法的可行性和有效性.     

坝前淤泥土与新填坝体接触面抗剪强度试验研究及工程应用

坝前淤泥面与新填筑坝体接触面是"坝前淤泥面加坝"技术的薄弱环节。为了探究不同工况下淤泥坝基、新填筑坝体,以及淤泥土-新填土接触面的剪切强度特性,以宁夏南部山区西吉县南川水库坝前淤泥面加坝工程为研究对象,通过常规应变式直剪仪、改进常规应变式直剪仪分别进行剪切试验,分析了淤泥土含水率和压实度变化时,淤泥土、新填土、淤泥土-新填土接触界面的抗剪强度、黏聚力、内摩擦角的变化规律。试验结果表明:新填土抗剪强度最大,不同工况下淤泥土-新填土接触界面的抗剪强度介于淤泥土和新填土的抗剪强度之间;淤泥土含水率在12%~16%之间存在最优含水率,超过该含水率后,淤泥土及淤泥土-新填土接触界面之间的抗剪强度均显著降低;当淤泥土含水率从8%增加至12%、16%时,黏聚力减小8%左右后迅速减小至22%,具有明显的阶段性,而淤泥土-新填土接触界面的黏聚力呈现先增加后减小的趋势;当含水率相同时,随着压实度的增加,淤泥土、淤泥土-新填土接触面的黏聚力、内摩擦角总体呈增大趋势。最后根据试验结果对"坝前淤泥面加坝"工法的工程应用提出了相关建议。     

电力市场环境下计及V2G和多类型需求响应的综合能源系统多目标优化模型

园区综合能源系统(Park integrated energy system,PIES)是满足用户多种用能需求的一种重要途径,但由于内部分布式能源机组出力具有不确定性,且与负荷在时间维度上存在一定的不匹配性,限制了能源利用效率和经济效益的提升.因此,本文首先在构建耦合热电的PIES的基础上,构建了多类型需求响应模型;其次,构建了考虑风光机组出力不确定性的以系统净收益、清洁能源弃能率为多目标函数的优化模型;然后,构建了"不确定性处理-多目标处理-单目标处理"的三阶段求解模型,最后,以V2G和需求响应为考虑条件,设计多情景.算例结果表明:V2G可以为清洁能源不稳定发电提供有效备用,在一定程度上提供清洁能源利用效率;引入电热需求响应,能够改变用户负荷,增加经济效益.     

一个改进的三阶WENO-Z型格式

在WENO-Z型格式框架下,基于高阶全局光滑因子,在非线性权建立过程中引入参数,通过收敛性分析确定参数取值范围,兼顾精确性与不振荡性,得到参数最佳取值.最终得到一个低耗散、高分辨率的三阶WENO差分格式,该格式在函数一阶极值点处仍保持预期三阶精度.最后通过精确解算例验证了格式在各种类型极值点处精度恢复情况,并通过一、二维Euler方程组经典算例测试了格式的低耗散、高分辨特性.结果表明,该文格式是一个性能优良的激波捕捉格式.     

一种求解二次约束二次规划问题的自适应全局优化算法

为了更好地解决二次约束二次规划问题(QCQP), 本文基于分支定界算法框架提出了自适应线性松弛技术, 在理论上证明了这种新的定界技术对于解决(QCQP)是可观的。文中分支操作采用条件二分法便于对矩形进行有效剖分; 通过缩减技术删除不包含全局最优解的部分区域, 以加快算法的收敛速度。最后, 通过数值结果表明提出的算法是有效可行的。