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.

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.

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.

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.

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).

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.

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.

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.

Survey of 3D modeling using depth cameras

Three-dimensional(3D)modeling is an important topic in computer graphics and computer vision.In recent years,the introduction of consumer-grade depth cameras has resulted in profound advances in 3D modeling.Starting with the basic data structure,this survey reviews the latest developments of 3D modeling based on depth cameras,including research works on camera tracking,3D object and scene reconstruction,and high-quality texture reconstruction.We also discuss the future work and possible solutions for 3D modeling based on the depth camera.

A comparative analysis of multi-output frontier models

Recently, there have been more debates on the methods of measuring efficiency. The main objective of this paper is to make a sensitivity analysis for different frontier models and compare the results obtained from the different methods of estimating multi-output frontier for a specific application. The methods include stochastic distance function frontier, stochastic ray frontier, and data envelopment analysis. The stochastic frontier regressions with and without the inefficiency effects model are also com-pared and tested. The results indicate that there are significant correlations between the results obtained from the alternative estimation methods.

Region-time-length algorithm and its application to the study of intermediate-short term earthquake precursor in North China

The Region-Time-Length Algorithm (RTL algorithm) is introduced and improved in the paper. Compared with the original definition, the influence of rupture length on RTL function is emphasized and the weights of epicentral distance function, time function, and rupture length function are ensured to be equal. The retrospective examinations of RTL algorithm in North China have indicated that the anomalies obtained by the improved RTL algorithm show the short or intermediate-short term precursory features in most cases. There are two types of RTL anomalous patterns before the main shock. For the I-type, the variation pattern of the VRTL, numerical values of the VRTL(x, y, z, t) function, is complete and most of them have shown the changing pattern of rising from 0 turning dropping or dropping from 0 turning rising. For the II-type, the variation pattern of VRTL is not complete, which increases or decreases quickly from 0 and there is no evident turning, the main shock generally occurs in the short period around the peak VRTL. The rising of VRTL indicates an increase of seismic activity relative to the background level, which means the enhancement of seismic activity, while the dropping of VRTL indicates the decrease of seismic activity relative to the background level, which represents the seismic quiescence to a certain extent. According to statistical examination results of RTL algorithm in North China, the methods to distinguish the intermediate and short-term anomalies and to estimate the occurrence time of the coming main shock are given in the paper. For both I and II-type RTL anomalies, the R-value, i.e., the forecasting score, is about 0.6 and 0.3 for the 3 months forecasting period and about 0.7 and 0.4 for the 6 months forecasting period. The preliminary discussion is also made for the influences of characteristic time-span t0, characteristic distance r0, and threshold magnitude M0 on computation of VRTL, as well as some other significant problems in application.

An Empirical Study on Environmental Regulatory Costs &Environmental TFP

This paper examines the cost of environmental regulation and the environmental total factor productivity （TFP） with directional distance function and the Malmquist-Luenberger （ALL） index respectively, using inputs and output data of 36 two-digit industries over the period 1998- 2010. It finds that Chinese industries incur a relatively high environmental regulatory cost and that China has paid a high price fulfilling its promise to emissions mitigation. A comparison between conventional and environmental TFP shows that the two indicators for all industries declined on average, but a hypothesis test reveals insignificant difference between the two. In addition, the rise in environmental TFP is mainly due to technological progress, which is consistent with findings of many researches; analysis demonstrates signs of absolute convergence of environmental TFP.

Scale and scope economies in small household rice farming in Vietnam

The Vietnamese agricultural sector has experienced a dramatic structural change based on increased specialization in rice cultivation.However,small-scale rice-farmers have continued to grow multiple crops,especially in less developed provinces.While the literature advocates crop diversification for reasons of both economic and ecological sustainability,there lacks empirical evidence as to whether crop diversification brings efficiency and productivity gains to small farms.The present study is the first applications of the input-oriented stochastic distance function approach in estimating scale and scope economies using data of multi-crop farming households in Vietnam.We find strong evidence of product-specific economies of scale.Scope economies are also present for rice,vegetable,and other annual crop production.This suggests that crop diversification enhances efficiency and productivity.However,there still exists significant technical inefficiency in crop production,indicating opportunities to expand farm output at the existing level of inputs and technologies.More specifically,our empirical results indicate that it is desirable to expand vegetable and other annual crop production in mountainous areas while rice cultivation can be further expanded in delta and coastal regions.

MOTION OF LEVEL SETS BY A GENERALIZED MEAN CURVATURE

Short time existence and uniqueness for the classical motion are studied by the function of the principal curvatures of a smooth surface and the Evans and Spruck's results are generalized.

INTERACTION OF A SOLITARY WAVE AND A FRONT STEP SIMULATED BY LEVEL SET METHOD

As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.