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.

Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands

This paper presents a copula technique to develop time-variant seismic fragility curves for corroded bridges at the system level and considers the realistic time-varying dependence among component seismic demands. Based on material deterioration mechanisms and incremental dynamic analysis, the time-evolving seismic demands of components were obtained in the form of marginal probability distributions. The time-varying dependences among bridge components were then captured with the best fitting copula function, which was selected from the commonly used copula classes by the empirical distribution based analysis method. The system time-variant fragility curves at different damage states were developed and the effects of time-varying dependences among components on the bridge system fragility were investigated. The results indicate the time-varying dependence among components significantly affects the time-variant fragility of the bridge system. The copula technique captures the nonlinear dependence among component seismic demands accurately and easily by separating the marginal distributions and the dependence among them.

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.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

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.

Nonlinear dynamics and performance analysis of modified snap-through vibration energy harvester with time-varying potential function

Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example,the snap-through VEH with geometric non-linearity,has gained attention in recent years.A conventional snap-through VEH is a bi-stable system with a time-invariant potential function,which was investigated extensively in the past.In this work,a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated.Modified snap-through VEHs,such as the one considered in this study,are used in wave energy harvesters.However,the studies on their dynamics and energy harvesting under harmonic and random excitations are limited.The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations(DAEs),and the numerical schemes are proposed for its solutions.Under a harmonic excitation,the system exhibits periodic and chaotic motions,and the energy harvesting is superior compared with the conventional counterpart.The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method.The Fokker-Planck equation representing the dynamics is derived,and the marginal and joint probability density functions(PDFs)are obtained by the Monte Carlo simulation.The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations.The dynamics of the system under stochastic resonance(SR)is investigated,and performance enhancement is observed.The results from this study will help in the development of adaptive VEH techniques in the future.

A Measure for Assessing Functions of Time-Varying Effects in Survival Analysis

A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.

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.

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.

Energy-Function Based Pilot Protection Scheme for Hybrid UHVDC Transmission Applying Improved Hausdorff Distance

A hybrid UHVDC transmission system applying LCC as the rectifier and MMC as the inverter combines the advantages of both converter types,which makes this protection scheme more complicated.A new pilot protection scheme for a three-terminal hybrid DC transmission system applying energy functions is proposed.The energy function for LCC is applied to MMC to derive the energy level of the hybrid system.Furthermore,an improved Hausdorff distance(IHD)algorithm is proposed to detect the difference in energy levels between the normal and fault states.An abrupt change in energy level is characterized by IHD change rate.Time points at which the IHD change rate exceeds the threshold at converter stations are applied to determine the fault line and to estimate the fault section.The proposed protection scheme is then verified by a simulation model of the Wudongde±800 kV three-terminal hybrid UHVDC transmission project.The appropriate sampling frequency is selected for a real-time calculation,and the threshold is selected considering the effect of noise.Results show the proposed scheme can identify and trip fault lines quickly and effectively,even for a 600Ωgrounding fault.Other waveshape similarity algorithms are compared and analyzed.Compared with existing protection schemes,the proposed scheme transmits less data to improve communication speed and reliability.

THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS

In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.

NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS

By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.