Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.

Assessing Chinese Commercial Bank Technical Efficiency with a Parametric Hyperbolic Distance Function

This paper contributes to the literatures about Chinese commercial banks technical efficiency. In order to eliminate the deviation of efficiency scores caused by an undesirable output that is represented by banks’ non-performing loans, the estimation is based on an enhanced parametric hyperbolic distance function which considers not only desirable outputs but also undesirable outputs. Furthermore, we extend the model to divide the factors that affecting technical efficiency into direct factors and indirect factors and exclude the influence of the latter when analyzing the determiners of banks technical efficiency. The validity of this model is examined by a panel of bank data from 2004-2010.

LEVEL SET METHODS BASED ON DISTANCE FUNCTION

Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.

Common Fixed Point Theorems in Metric Space by Altering Distance Function

In the present paper, we prove two theorems. In first theorem, we prove fixed point result for self-maps in the metric space under contractive condition of integral type by altering distance. In second result, we prove a unique common fixed point theorem by considering four sub compatible maps under a contractive condition of integral type.

Distance function selection in several clustering algorithms

Most clustering algorithms need to describe the similarity of objects by a predefined distance function. Three distance functions which are widely used in two traditional clustering algorithms k-means and hierarchical clustering were investigated. Both theoretical analysis and detailed experimental results were given. It is shown that a distance function greatly affects clustering results and can be used to detect the outlier of a cluster by the comparison of such different results and give the shape information of clusters. In practice situation, it is suggested to use different distance function separately, compare the clustering results and pick out the 搒wing points? And such points may leak out more information for data analysts.

Expected magnitude and distance of potential source area and the estimating method

Magnitude and distance of major potential source are needed in order to determine duration time of artificial ground motion and to determine the type of response spectrum (near field or far field) when using the seismic intensity zonation map. The magnitude probabilistic distribution function of seismic belt and the magnitude and space joint distribution function for given intensity of the site in a potential Source are provided. Then the basicformula of calculating expected magnitude and expected distance are developed. Several examples for calculating expected magnitude and expected distance in northern China are discussed. These results show that expected magnitude and expected distance are related not only to geometry of potential source and magnitude but also to the intensity of the site with certain exceeding probability.

A Self-Organizing RBF Neural Network Based on Distance Concentration Immune Algorithm

Radial basis function neural network(RBFNN) is an effective algorithm in nonlinear system identification. How to properly adjust the structure and parameters of RBFNN is quite challenging. To solve this problem, a distance concentration immune algorithm(DCIA) is proposed to self-organize the structure and parameters of the RBFNN in this paper. First, the distance concentration algorithm, which increases the diversity of antibodies, is used to find the global optimal solution. Secondly,the information processing strength(IPS) algorithm is used to avoid the instability that is caused by the hidden layer with neurons split or deleted randomly. However, to improve the forecasting accuracy and reduce the computation time, a sample with the most frequent occurrence of maximum error is proposed to regulate the parameters of the new neuron. In addition, the convergence proof of a self-organizing RBF neural network based on distance concentration immune algorithm(DCIA-SORBFNN) is applied to guarantee the feasibility of algorithm. Finally, several nonlinear functions are used to validate the effectiveness of the algorithm. Experimental results show that the proposed DCIASORBFNN has achieved better nonlinear approximation ability than that of the art relevant competitors.

Likelihood and Quadratic Distance Methods for the Generalized Asymmetric Laplace Distribution for Financial Data

Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.

A generalized evidence distance

How to efficiently measure the distance between two basic probability assignments（BPAs） is an open issue. In this paper, a new method to measure the distance between two BPAs is proposed, based on two existing measures of evidence distance. The new proposed method is comprehensive and generalized. Numerical examples are used to illustrate the effectiveness of the proposed method.

VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS

By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland＇s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346（2008）, 9-16] are weakened or even completely relieved.

Analysis of Flow Dynamics in the High-Flux Gas-Solid Riser Using Trajectory Distances across Attractors Reconstructed from Solid Concentration Signals

The study of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using trajectory distances of the reconstructed attractors from solid concentration signals collected from a 76 mm internal diameters and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s gas velocity and 50 to 550 kg/m2s solids flux. Spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3 together with 70% to 80% humid air was used. Solid concentration data were analyzed using codes prepared in FORTRAN 2008 to get trajectories of the reconstructed attractors and their distances apart. Trajectory distances were found to increase from the centre towards the wall indicating the expansion of the attractor. The probability density function (PDF) of the trajectory distances changes from single peak at the centre to multiple peaked profiles in the wall region. Multiple peaked profiles indicate multifractal flow behaviours. Cumulative distribution functions (CDF) of the trajectory distances changes from single S-shaped at the centre to multiple S-shaped profiles in some locations of the wall region indicating multifractal flow behaviours. The PDF distribution of these distances at the entrance section and in the wall region forms different types of statistical distributions showing differences in gas-solid flow structures in various spatial locations of the wall region and the entrance sections. Most of the distributions at the centre fall under the Gumbel max distribution for all flow development sections of the riser, especially at air velocities of 5.5 m/s and 8 m/s showing uniform flow structures. Further, it was found that increase of the number of the phase space reconstruction embedding dimension increases the trajectory distances between the state vectors leading to the expansion of the attractor.

基于物体单视图的隐式曲面重建

基于隐式曲面的三维重建方法在保真度、灵活性和压缩能力方面提供了良好的权衡。文章利用隐式曲面网络学习物体形状的三维表面,首先利用视觉几何群(visual geometry group-16,VGG-16)网络从图像中提取全局特征,对建模空间中的每个采样点从VGG-16网络中获取局部特征;其次对每个采样点利用多层感知器(multi-layer perceptron,MLP)进行位置编码得到点特征;然后将全局特征和局部特征分别与点特征串联起来送入2个解码器中,获得隐式场中采样点的符号距离函数(signed distance function,SDF)的大小与符号,并最终得到物体的隐式曲面。文中所提出的方法应用于ShapeNet数据集上进行三维对象重建任务,定性和定量评估均优于现有方法,特别是对于具有孔洞和薄结构的复杂拓扑物体。

改进A^(*)算法的移动机器人全局路径规划

针对A^(*)算法在移动机器人路径规划存在搜索效率低,路径斜穿障碍物顶点,路径拐弯多等问题。提出一种改进的A^(*)算法,首先在A^(*)算法的邻域扩展中采用避免斜穿障碍物顶点的策略;再引入障碍物因素对评价函数进行指数加权,减少不必要的搜索,提高A^(*)算法的效率和灵活性,使算法偏向于选择障碍物较少的路径;最后使用三次优化折线的策略,加入障碍物安全距离,减少路径上的冗余节点和拐弯。使用MATLAB进行实验仿真,结果表明,在20 m×20 m、40 m×40 m、60 m×60 m栅格地图环境下,改进A^(*)算法较传统A^(*)算法,搜索时间分别减少70.12%、84.31%、91.44%,扩展节点分别减少53.77%、71.20%、74.30%,路径累计拐弯角度分别减少70.48%、76.31%、82.18%,改进A^(*)算法能够有效的提高移动机器人路径规划的效率,路径更为平滑和安全,且在复杂环境中优势更为明显。

中国城市碳排放绩效:动态分解、空间差异与影响因素

以非径向方向距离函数为框架,构造全要素碳排放绩效指数对中国2006—2019年城市碳排放治理绩效进行测度。在此基础上从经济含义、跨期动态变化、区域均衡等层面对全要素碳排放绩效指数进行多维分解,检验中国城市碳排放绩效的影响因素。结果表明:第一,样本期内全国城市平均全要素碳排放绩效指数总体呈波动上升态势,动态分解结果显示,中国各地的平均碳排放绩效水平不断改进,创新效应对其贡献逐年增大但赶超效应贡献不足;第二,空间分异方面,珠三角、长三角、粤闽浙沿海、长江中游等东部地区城市群不仅平均碳排放绩效水平普遍较高,且碳排放绩效的增长速度较快,中西部地区仅成渝城市群碳排放绩效表现较好,中原、京津冀等城市群近年来碳排放绩效的改善速度较快;第三,基尼系数测度及其分解显示,近年中国城市碳排放绩效指数的分异程度逐步加深,分异成因主要为城市群组间差异,城市群内部差异贡献度较低;第四,Lasso分析及双固定面板模型分析结果显示,经济发展水平、清洁能源使用、金融发展、绿色环保和科技支持能够有效改善城市层面的碳排放绩效,能源消耗强度和第二产业就业人员比重对碳排放绩效具有负面影响;最后,城市群因子探测结果显示,各城市群间的驱动因子存在一定差异。

改进PCA方法的牙颌特征提取和数据集构建

为了提高牙颌数字模型特征提取的准确性和牙齿分割的效率,提出一种几何变换和主成分分析相结合的坐标系标准化方法,并以离散曲率、法向量、形状直径函数和离散测地距离为基础特征对牙颌数字模型进行了特征提取,在此基础上进一步扩展构建了76个特征数据集。采用提出的坐标系标准化方法和数据集对上颌进行了牙齿分割实验。结果表明:改进主成分分析方法能够快速准确地实现牙颌数字模型坐标系对齐,能够准确识别牙齿的特征信息并作出标记,牙齿分割完整,平均分割准确率达到99.74%。基于改进主成分分析方法的牙颌模型特征提取方法能够极大地提高特征对牙齿的区分性,从而降低位姿对牙颌特征提取带来的负面影响,实现在特征数据较少的情况下准确分割牙齿,可为数字化口腔诊疗提供一定的参考。

基于改进人工势场法的通用航空路径规划

通用航空飞机在飞行过程除了要面对障碍物和天气系统的威胁,同时也受到飞行空域的限制,往往飞机只能在一块固定的空域或狭小的飞行走廊内飞行,一旦飞出限制空域,则有可能引发飞行冲突,甚至发生严重的安全事故。针对这些问题,在人工势场法斥力势场函数中添加航空器和目标点之间的相对距离函数,首先解决传统人工势场法存在的目标不可达问题和局部极小点问题,然后在算法中加入航路边界斥力影响因子,使飞机避障后在边界斥力的作用下重回航路中心。经过MATLAB仿真验证,试验结果表明,改进后的人工势场法能够实现主动避障和飞机航迹的规划。

基于改进RRT算法的移动机器人路径规划研究

快速扩展随机树算法(rapidly-exploring random trees,RRT)规划移动机器人路径时,存在搜索盲目性强、搜索时间长、收敛速度慢、路径冗余点多且不平滑等问题。鉴于此,提出一种改进的RRT路径规划算法。首先,针对传统RRT算法盲目搜索以及局部极值的问题,提出概率目标偏置与人工势场结合的采样策略,引导随机树的扩展;其次,针对随机树扩展的避障能力差的问题,提出基于安全距离的碰撞检测以及动态变步长扩展策略;最后,针对路径上冗余点多以及曲率不连续的问题,提出考虑安全距离的剪枝优化和三次B样条曲线对初始路径进行拟合优化。仿真结果表明,在不同地图的路径规划中,相比于传统RRT算法,增强了通过狭窄通道能力,优化了路径的平滑性,搜索时间、迭代次数、路径长度分别减少约70%、40%、15%;相比于RRT衍生算法RRT-Connect,搜索时间、路径长度分别减少约25%、10%。

材料挤出式3D打印制备功能梯度材料过渡距离研究

近年来随着3D打印技术的飞速发展,材料挤出成型工艺制备功能梯度材料成为研究热点。材料之间的过渡是影响最终成型质量的关键因素。目前,国内外学者只研究了两种独立材料之间相互转变的过渡距离,对不同组分材料之间的转变研究较少。采用双料筒打印机研究了不同组分材料之间的过渡距离,并通过实验探究不同进给量对过渡距离的影响,在保证打印质量的前提下得到了过渡距离最小的进给量。以Visual Studio 2019为开发平台提出一种新的进料策略缩短过渡距离,在路径规划中对切片得到点的材料信息进行判断,对组分增大的材料根据变化值计算其进给量并输出生成新型G代码。最终,采用新型G代码进行打印实验,缩短了材料过渡距离得到了理想的材料过渡曲线。

碳排放权交易提高了城市全要素碳排放效率吗?——基于内生方向距离函数模型的研究

减碳措施一般会带来总产出的降低,因此有必要从全要素效率的角度评估减碳政策。本文构建了一个方向距离函数模型,允许各决策单元有不等的减排因子,扩大了生产可行集的范围,同时采用了内生的方向向量,避免在选择方向向量时过于主观。基于这一模型本文重新测算了城市层面全要素碳排放效率,并实证分析碳交易政策对其的影响,研究发现,试点政策能够提高城市全要素碳排放效率;中介效应表明,试点政策会通过产业结构和绿色创新等途径提高城市碳排放效率;异质性分析发现,试点政策对于高行政等级和人口规模较大城市的碳排放效率影响更明显。因此,应扩大政策试点范围、鼓励产业结构优化、推广绿色技术创新、制定因地制宜的试点政策等进一步提升碳排放权交易制度的绿色发展效应。