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.

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.

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.

SDF-Based ILW:Inverse Lax-Wendroff Method with the Signed Distance Function Representation of the Geometric Boundary

This paper studies the geometric boundary representations for Inverse Lax-Wendroff(ILW)method,aiming to develop a practical computer-aided engineering method without body-fitted meshes.We propose the signed distance function(SDF)representation of the geometric boundary and design an extremely efficient algorithm for foot point calculation,which is particularly in line with the needs of ILW.Theoretical and numerical analyses demonstrate that the SDF representation of geometric boundary can satisfy ILW’s needs better than others.The effectiveness and robustness of our proposed method are verified by simulating initial boundary value computational physical problems of Euler equation for compressible fluids.

Solid rocket motor propellant grain burnback simulation based on fast minimum distance function calculation and improved marching tetrahedron method

To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor,a unified framework of burning surface regression simulation has been developed based on minimum distance function.In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface,a fast distance querying method based on the equal size cube voxel structure was employed.An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements,achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously.The cases of star grain,finocyl grain,and non-uniform tube grain were studied to verify the proposed method.The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.

Approach of fault diagnosis based on similarity degree matching distance function

A new diagnosis method based on the similarity degree matching distance function is proposed.This method solves the problem that the traditional fault diagnosis methods based on transition system model cannot deal with the"special state"which cannot match the target states completely.For evaluating the relationship between the observation and the target states,this paper first defines a new distance function based on the viewpoint of energy to measure the distance between two attribute values.After that,all the distances of the attributes in the state vector are used to synthesize the distance between two states.For calculating the similarity degree between two states,a trend evaluation method is developed.It analyzes the main direction of the trend of the state transfer according to the distances between the observation and each target state and their historical records.Applying the diagnosis method to a primary power subsystem of a satellite,the simulation result shows that it is effective.

Evaluating the environmental efficiency of the U.S.airline industry using a directional distance function DEA approach

This study applies a directional distance function(DDF)data envelopment analysis(DEA)model to measure the environmental efficiency of 12 U.S.airlines 2013–2016 by considering flight delay and greenhouse gas(GHG)emissions as joint undesirable outputs.First,the environmental efficiency of airlines is compared using the CCR DEA(without flight delay)and DDF DEA(with flight delay).We find that several airlines experienced substantial changes in environmental efficiency scores when flight delay is considered.Secondly,a tobit regression is used to explore whether the environmental factors of fleet age,ownership type,freight traffic,market share,and carrier type affect airlines’environmental efficiency.The results demonstrate that all of these factors significantly influence airline performance.

On 2-Site Voronoi Diagrams Under Geometric Distance Functions

We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.

Subdifferentials of Distance Functions,Approximations and Enlargements

In this work, we study some subdifferentials of the distance function to a nonempty nonconvex closed subset of a general Banach space. We relate them to the normal cone of the enlargements of the set which can be considered as regularizations of the set.

A nonparametric distance function approach with endogenous direction for estimating marginal abatement costs of CO_(2) emissions

The directional distance function(DDF)framework has been widely used to estimate the marginal abatement cost(MAC)of CO_(2)emissions to support decision-making in environmental sustainability and climate change issues.In the use of DDF,an important task is mapping evaluated entities towards a realistic production technology frontier.This study develops a new nonparametric approach for estimating the MAC of CO_(2)emissions.The approach incorporates the optimal endogenous direction into an enhanced environmental production technology and has three advantages.First,it avoids the arbitrariness in mapping directions.Second,it captures the heterogeneity in optimization paths across different decision-making units(DMUs).Third,it generates more reliable benchmarks for estimating MAC by constructing an environmental technology frontier that is consistent with the material balance principle.We apply the approach to study China's thermal power industry and find clear heterogeneity in MACs and optimization paths at the province level.The results on the optimal endogenous directions show that the DMUs prefer to increase both desirable output and CO_(2)emissions when CO_(2)emissions are unregulated.Comparisons with other approaches reveal that arbitrarily mapping exogenous directions and technology representations are likely to generate distorted and unrealistic MACs.

Automatic surface localization by defining weighted-iteration distance function and Lyapunov-test statistic

Automatic localization,aligning the measured points with the design model,is a basic task in free-form surface inspection.The main difficulty of current localization algorithms is how to define effective distance function and localization reliability index.This paper proposes a new method of calculating motion parameters and evaluating localization reliability.First,improved modified coefficient is defined and applied to weighted-iteration distance function,which better approximates the point-to-surface closest distance.It can control the contribution ratios of different measured points by considering the curvature feature and iterative residual.Second,the mapping relationship between localization error and geometric error is analyzed,from which a Lyapunov-test statistic is derived to define a frame-independence index.Then,the determination of localization reliability changes into a supposition examination problem.This can avoid rejecting correct motion parameters,which exists in the traditional judgment of absolute root-mean-square distance.In addition,two test experiments are implemented to demonstrate the proposed localization algorithm.

Method for Visual Localization of Oil and Gas Wellhead Based on Distance Function of Projected Features

A localization method based on distance function of projected features is presented to solve the accuracy reduction or failure problem due to occlusion and blurring caused by smog, when dealing with vision based localization for target oil and gas wellhead （OGWH）. Firstly, the target OGWH is modeled as a cylinder with marker, and a vector with redundant parameter is used to describe its pose. Secondly, the explicit mapping relationship between the pose vector with redundant parameter and projected features is derived. Then, a 2D-point-to-feature distance function is proposed, as well as its derivative. Finally, based on this distance function and its derivative, an algorithm is proposed to estimate the pose of target OGWH directly according to the 2D image information, and the validity of the method is verified by both synthetic data and real image experiments. The results show that this method is able to accomplish the localization in the case of occlusion and blurring, and its anti-noise ability is good especially with noise ratio of less than 70%.

凸复Finsler流形上的Hopf-Rinow定理

Suppose(M,F) is a convex complex Finsler manifold. We prove that geodesics of(M,F) are locally minimizing. Hence, F introduces a distance function d such that(M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem holds on(M,F).

C-LOG： A Chamfer distance based algorithm for localisation in occupancy grid-maps

A novel algorithm for localising a robot in a known two-dimensional environment is presented in this paper. An occupancy grid representing the environment is first converted to a distance function that encodes the distance to the nearest obstacle from any given location. A Chamfer distance based sensor model to associate observations from a laser ranger finder to the map of the environment without the need for ray tracing, data association, or feature extraction is presented. It is shown that the robot can be localised by solving a non-linear optimisation problem formulated to minimise the Chamfer distance with respect to the robot location. The proposed algorithm is able to perform well even when robot odometry is unavailable and requires only a single tuning parameter to operate even in highly dynamic environments. As such, it is superior than the state-of-the-art particle filter based solutions for robot localisation in occupancy grids, provided that an approximate initial location of the robot is available. Experimental results based on simulated and public domain datasets as well as data collected by the authors are used to demonstrate the effectiveness of the proposed algorithm.

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.

Frame Work of Data Envelopment Analysis—A Model to Evaluate the Environmental Efficiency of China'S Industrial Sectors

Objective To evaluate the environmental and technical efficiencies of China＇s industrial sectors and provide appropriate advice for policy makers in the context of rapid economic growth and concurrent serious environmental damages caused by industrial pollutants. Methods A data of envelopment analysis （DEA） framework crediting both reduction of pollution outputs and expansion of good outputs was designed as a model to compute environmental efficiency of China＇s regional industrial systems. Results As shown by the geometric mean of environmental efficiency, if other inputs were made constant and good outputs were not to be improved, the air pollution outputs would have the potential to be decreased by about 60% in the whole China. Conclusion Both environmental and technical efficiencies have the potential to be greatly improved in China, which may provide some advice for policy-makers.

Ant colony ATTA clustering algorithm of rock mass structural plane in groups

Based on structural surface normal vector spherical distance and the pole stereographic projection Euclidean distance,two distance functions were established.The cluster analysis of structure surface was conducted by the use of ATTA clustering methods based on ant colony piles,and Silhouette index was introduced to evaluate the clustering effect.The clustering analysis of the measured data of Sanshandao Gold Mine shows that ant colony ATTA-based clustering method does better than K-mean clustering analysis.Meanwhile,clustering results of ATTA method based on pole Euclidean distance and ATTA method based on normal vector spherical distance have a great consistence.The clustering results are most close to the pole isopycnic graph.It can efficiently realize grouping of structural plane and determination of the dominant structural surface direction.It is made up for the defects of subjectivity and inaccuracy in icon measurement approach and has great engineering value.

Collision Avoidance of Cooperative Dual Redundant Manipulators

Dual redundant manipulators are extremely useful for tasks in dangerous or space environments, but efficient and real time coordinated control is hard to achieve. Collision avoidance between two cooperative manipulators is vital to the successful applications of dual redundant manipulators. Although methods based on the distance function have been demonstrated simple and efficient, different collision avoidance points can usually produce completely different results and even failure. The paper discussed the choices of collision avoidance points and proposed a novel method for the choosing of those points. The method is testified by simulation results of two redundant planar manipulators.

Performance of the geometric approach to fault detection and isolation in SISO,MISO,SIMO and MIMO systems

In this paper, a geometric approach to fault detection and isolation （FDI） is applied to a Multiple-Input Multipie-Output （MIMO） model of a frame and the FDI results are compared to the ones obtained in the Single-Input Single-Output （SISO）, Multiple-Input Single-Output （MISO）, and Single-Input Multiple-Output （SIMO） cases. A proper distance function based on parameters obtained from parametric system identification method is used in the geometric approach. ARX （Auto Regressive with exogenous input） and VARX （Vector ARX） models with 12 parameters are used in all of the above-mentioned models. The obtained results reveal that by increasing the number of inputs, the classification errors reduce, even in the case of applying only one of the inputs in the computations. Furthermore, increasing the number of measured outputs in the FDI scheme results in decreasing classification errors. Also, it is shown that by using probabilistic space in the distance function, fault diagnosis scheme has better performance in comparison with the deterministic one.

Energy Efficiency and Emissions Reduction Potential of China's Industrial Sector

Based on the total-factor energy efficiency framework,this paper calculates China's industrial energy efficiency and CO2 emissions reduction potential from 2000 to 2009 by utilizing the directional distance function and data envelopment analysis.The empirical results show that:China's industrial overall energy efficiency is relatively lower while the emis-sions reduction potential is relatively greater,given the optimum production frontier.Significant indus-trial disparities of energy efficiency and emissions reduction potential exist.Energy efficiency and emis-sions reduction potential significantly show different tendencies of industrial dynamic variation.This paper suggests the Chinese government impose differential carbon taxes,flexibly utilize carbon market mecha-nism,strengthen energy-saving technological R&D,promote the utilization of renewable energy,and strengthen environmental supervision and regulation,so as to improve China's industrial energy efficiency and reduce CO2 emissions.