弹性波在平面多连通域中的绕射与动应力集中

本文用复变函数论方法研究了弹性波在平面多连通域中的绕射问题,给出了这一问题解的完备逼近序列及边备条件的一般表示。问题归结为无穷代数方程组的求解,使用电子计算机可直接求得解答。特别是,对弱耦合问题,本文提出了渐近求解方法并且使用这个方法详细地讨论了P波对圆孔群的绕射问题。基于绕射波场的解,文中给出了任意形状空腔动应力集中系数的一般算式。     

基于无线通信基站的室内三维定位问题

三维定位问题是现代商用通信网络中对于定位系统存在的一个真正具有技术难度的挑战.根据视距传播环境和非视距传播环境的到达时间的数据集,建立线性误差模型;对于无真实位置的竞赛数据集,定义竞赛数据定位误差评估模型;基于不同的空间场景,提出基于空间单元的定位算法;面对高度误差明显高于平面误差的问题,设计基于高斯加权的误差补偿模型;针对最优定位精度最少基站问题,提出基于贪心策略的基站选择算法;考虑轨迹连续性,设计轨迹准确性验证的10-fold交叉验证方法;基于测量距离有限的真实环境,分析平均"连接度数"与定位精度的关系.实验结果表明,提出的定位算法在有效基站数大于等于5时,能获得较好的定位精度.     

缺失数据下线性模型的半参数估计

通过比较参数方法和非参数方法对选择概率建模的优缺点,基于充分降维的思想提出了一种利用单指标模型对选择概率建模的半参数方法.基于逆概率加权方法和半参数方法,研究了缺失数据下线性模型的统计推断问题.建立的逆概率加权估计方程可以处理不同的数据缺失情形,给出了线性模型中兴趣参数的估计,并证明了它的渐近正态性.最后通过模拟研究说明提出的方法具有较好的有限样本性质.     

表面绕射射线的焦距与扩展因子

用几何绕射理论(G.T.D.)计算导弹及飞行体上的天线的辐射特性,或解决其他绕射问题时,都必须用到表面绕射射线的焦距和扩展因子。现有文献对扩展因子有不同的定义。并且只有部份结果,缺乏系统的数学处理,有的结果还有错误,给应用带来了困难。本文首先求得了任意曲面上绕射射线的焦距和扩展因子的一般公式,然后给出应用上重要的圆柱面、球、圆锥面上二者的结果。这样,本文为曲面绕射的工程应用提供了必要的基础。     

Watson变换及其应用

该文讨论Watson变换和它在电磁波理论及工程中的应用。针对这一变换在高频电磁波问题中的应用,研究了复积分路径变换原则和选取方法,研究了曲面绕射理论中不同区域绕射函数宗量、波场振幅、绕射相位函数的一致性问题;得到了这类参量的一致性函数表达式。     

直觉模糊数的序优先度及其在群评价中的应用

直觉模糊数是处理模糊问题的一种有效的信息表达形式,其排序方法是研究的热点问题之一.基于均匀分布的原理,提出新的直觉模糊数序优先度的概念,给出各种情形下的序优先度的计算公式,并探讨了直觉模糊数序优先度的若干性质.给出了基于直觉模糊数序优先度的群评价算法.实例分析表明本文提出的方法是可行有效的.     

长波天波传播路径的分析和研究

本文对长波天波传播路径作了详细的研究,并分析了过去有关工作中所存在的问题及其导致的误差。在正确考虑大气折射效应的基础上,得到无线电视距及天波折射路径长度、出射角和入射角等的推算结果及其对天波时延、场强的影响。结合以上研究所作的D电离层及天波时延及场强的预测的研究结果表明,时延及场强的预测值与实测值之最大偏差分别在±1.5μs及±2.5db之内,从而使天波定时精度得到大大提高。     

干线网络的选址问题研究

考虑平面上和三维空间中同时确定多条干线的干线网络选址问题.对于平面上情形,通过最小化每个点到离它最近干线的加权距离之和,给出了一种有限步终止算法和基于k-means聚类分析、加权全最小一乘和重抽样方法的线性类算法;对于空间情形,给出了线性聚类算法.通过计算机仿真说明以上算法可以有效地确定平面和空间中干线网络位置.     

基于smoothL1改进的边框回归损失函数

为了进一步提高目标检测任务中的边框回归精度,提出一种基于smoothL1改进的边框回归损失函数.通过自适应地增大smoothL1中非离散点的梯度,缓解了模型反向传播中对离散点和非离散点梯度分布不平衡问题,提高了模型的精度.实验结果表明,在PASCAL VOC2007测试集上,基于改进的smoothL1的目标检测模型Faster R-CNN,平均精度均值(mAP)达到了70.8％,相较smoothL1,模型精度有所提高.     

基于优先等级的震后应急物资LRP优化决策模型

针对震后初期应急物资总量有限且不充足情形下的系统优化问题,提出一个基于优先等级的震后LRP优化模型.考虑震后初期应急物资需求主要影响因素,利用可变集理论确定各受灾点应急物资优先级;在此基础上,以整个救援过程总耗时最少为目标构建选址定位-路径优化模型,针对模型特点设计了一种基于两阶段的遗传算法.最后,通过算例验证了模型及算法的可行性和有效性.     

裂纹尖端场弹塑性分析的加权残数法及塑性应力强度因子的计算

本文以幂强化材料,平面应变情形为例,系统地提出了裂纹尖端场弹塑性分析的加权残数法,并根据此法,得出了裂纹尖端场的解析式弹塑性近似解.在此基础上.对整个裂纹区域,构造了弹塑性解叠加非线性有限元计算塑性应力强度因子的方法,从而为裂纹尖端场和整个裂纹体的分析和计算,提供了一个方法.     

AN AUTOMATED METHOD FOR EXTENDING SENSITIVITY ANALYSIS TO MODEL FUNCTIONS

Abstract Parameter sensitivity analysis is a relatively well‐developed field compared with function sensitivity analysis. How sensitive are model conclusions to the choice of functions used in the right‐hand side of difference or differential equation models? Most work in this area has been scenario based where alternative functions are tested. This requires knowledge of plausible alternatives and is usually restricted to well‐known functions. In this work, a method is proposed for function sensitivity analysis, which it is hoped will provide a starting point for discussion and stimulating further research on this important but neglected topic. The method provides information on the sensitivity of a model's results to changes in the shape of the functions. This is done in an automated way without the need to specify alternative functional forms. The proposed method is illustrated on a small ecosystem model.     

Extremal versus additive Matérn point processes

In the simplest Matérn point processes one retains certain points of a Poisson point process in such a way that no pairs of points are at distance less than a threshold. This condition can be reinterpreted as a threshold condition on an extremal shot–noise field associated with the Poisson point process. This paper is focused on the case where one retains points that satisfy a threshold condition based on an additive shot–noise field of the Poisson point process. We provide an analytical characterization of the intensity of this class of point processes and we compare the packing obtained by the extremal and additive schemes and certain combinations thereof.     

Numerical study on bacterial flagellar bundling and tumbling in a viscous fluid using an immersed boundary method

The bundling and tumbling behavior of bacterial flagella in a viscous fluid has got immense significance in the field of biological fluid dynamics. In this paper we investigate the hydrodynamic interaction among two and more than two flagella in a viscous fluid based on an immersed boundary method. We model each helical flagellum by a number of triangular cross-sections with three immersed boundary (IB) points on each cross-section. Three types of elastic links are generated from each IB point to create an elastic network model of the flagellum and the first cross-section is modeled as the flagellar motor. The elastic forces are computed based on the elastic energy approach and the motor forces are obtained from the applied angular frequency of rotation of the motor. The Stokes equations governing the flow are solved on a staggered Cartesian grid system using a fractional-step based finite-volume method. It is observed that when two left-handed helical flagella rotate in the counter-clockwise direction, the resulting hydrodynamic interaction leads to bundling. When one of the flagella reverses the direction of rotation to clockwise the hydrodynamic interaction results in tumbling. During the bundling, the flagella wrap and intertwine each other, whereas during the tumbling they separate in an erratic way. There exists an exact combination of the handedness and rotational direction of the flagella to achieve the bundling. The bundling-to-tumbling behavior of the flagella is studied and it is concluded that the tumbling occurs faster than the bundling. Further, the hydrodynamic interaction among three flagella in a viscous fluid is studied for the cases of rotation in the same direction and in different directions. The bundling and tumbling behavior is well captured even for the case of multiple (more than two) flagella using the developed model.     

A linear sampling method for inverse problems of diffraction gratings of mixed type

This paper is concerned with the direct and inverse problem of scattering of a time‐harmonic wave by a Lipschitz diffraction grating of mixed type. The scattering problem is modeled by the mixed boundary value problem for the Helmholtz equation in the unbounded half‐plane domain above a periodic Lipschitz surface on which a mixed Dirichlet and impedance boundary condition is imposed. We first establish the well‐posedness of the direct problem, employing the variational method, and then extend Isakov's method to prove uniqueness in determining the Lipschitz diffraction grating profile by using point sources lying above the structure. Finally, we develop a periodic version of the linear sampling method to reconstruct the diffraction grating. In this case, the far field equation defined on the unit circle is replaced by a near field equation defined on a line above the surface, which is a linear integral equation of the first kind. Numerical results are also presented to illustrate the efficiency of the method in the case when the height of the unknown grating profile is not very large and the noise level of the near field measurements is not very high. Copyright © 2012 John Wiley & Sons, Ltd.     

Point process diagnostics based on weighted second-order statistics and their asymptotic properties

A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.     

Numerical Experiments with an Interior-Exterior Point Method for Nonlinear Programming

The paper presents an algorithm for solving nonlinear programming problems. The algorithm is based on the combination of interior and exterior point methods. The latter is also known as the primal-dual nonlinear rescaling method. The paper shows that in certain cases when the interior point method (IPM) fails to achieve the solution with the high level of accuracy, the use of the exterior point method (EPM) can remedy this situation. The result is demonstrated by solving problems from COPS and CUTE problem sets using nonlinear programming solver LOQO that is modified to include the exterior point method subroutine.     

Domain sensitivity for singular elliptic problems: Harmonic transformation approach

A method for computing the sensitivities of functionals depending on the solutions of elliptic equations defined over variable domains is presented. It is based on the material derivative approach and allows the uniform treatment of both singular and nonsingular cases. The novelty consists in defining the vector field connected with the domain transformation as the solution of an auxiliary elliptic equation. Such a choice does not restrict the range of admissible goal functionals and has many advantages from the numerical point of view. It allows one also to consider singular domain variations.     

区域经济发展智能预测方法

分析了影响区域经济发展的各种因素,指出由于这些因素相互制约、相互影响,使得传统的经济预测方法越来越难以胜任区域经济发展预测的需要.论述了核方法在处理非线性、不确定性和不精确性数据上存在的优势,建立了基于核方法三种经济预测模型,并将这三种预测模型与其它两种预测方法一起,对区域经济的发展进行组合预测.最后,采用数据融合的方法将各个体模型的预测结果进行集成,作为最终的输出.实际的结果表明,基于核方法的组合预测技术能取得较为理想的预测效果.