The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

Fully asynchronous distributed optimization with linear convergence over directed networks

We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.

A new test on the conditional capital asset pricing model

Testing the validity of the conditional capital asset pricing model （CAPM） is a puzzle in the finance literature. Lewellen and Nagel[14] find that the variation in betas and in the equity premium would have to be implausibly large to explain important asset-pricing anomalies. Unfortunately, they do not provide a rigorous test statistic. Based on a simulation study, the method proposed in Lewellen and Nagel[14] tends to reject the null too frequently. We develop a new test procedure and derive its limiting distribution under the null hypothesis. Also, we provide a Bootstrap approach to the testing procedure to gain a good finite sample performance. Both simulations and empirical studies show that our test is necessary for making correct inferences with the conditional CAPM.

A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS

In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.

Behavior of transporting pipeline sections without and with hydrogen exposure based on full-scale tests

Pipeline transport of hydrogen is one of today’s economic and environmental challenges.In order to find safe and reliable application of both existing gas and build new pipelines,it is essential to carry out tests on full-scale pipeline section,including the potentially more dangerous places than the main pipe,the girth welds.For the investigations,pipeline sections of P355NH steel with girth welds were prepared and exposed to pure hydrogen at twice the maximum allowable operating pressure for 41 days.Subsequently,full-scale burst tests were carried out and specimens were cut and prepared from the typical locations of the failed pipeline sections for mechanical,and macro-and microstructural investigations.The results obtained were evaluated and compared with data from previous full-scale tests on pipeline sections without hydrogen exposure.The results showed differences in the behavior of pipeline sections loaded in different ways,with different characteristics of the materials and the welded joints,both in the cases without hydrogen exposure and in the cases exposed to hydrogen.

A thermal stress loading technique for large-sized hot dry rock mechanical tests

Testing of large-sized specimens is becoming increasingly important in deep underground rock mechanics and engineering.In traditional mechanical loading,stresses on large-sized specimens are achieved by large host frames and hydraulic pumps,which could lead to great investment.Low-cost testing machines clearly always have great appeal.In this study,a new approach is proposed using thermal expansion stress to load rock specimens,which may be particularly suitable for tests of deep hot dry rock with high temperatures.This is a different technical route from traditional mechanical loading through hydraulic pressure.For the rock mechanics test system of hot dry rock that already has an investment in heating systems,this technology may reduce the cost of the loading subsystem by fully utilizing the temperature changes.This paper presents the basic principle and a typical design of this technical solution.Preliminary feasibility analysis is then conducted based on numerical simulations.Although some technical details still need to be resolved,the feasibility of this loading approach has been preliminarily confirmed.

LOCAL CONVERGENCE OF INEXACT NEWTON-LIKE METHOD UNDER WEAK LIPSCHITZ CONDITIONS

The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.

The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method

Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.

Computational Precision of the Power Function for Conditional Tests of Assumptions of the Rasch Model

Draxler and Zessin [1] derived the power function for a class of conditional tests of assumptions of a psychometric model known as the Rasch model and suggested an MCMC approach developed by Verhelst [2] for the numerical approximation of the power of the tests. In this contribution, the precision of the Verhelst approach is investigated and compared with an exact sampling procedure proposed by Miller and Harrison [3] for which the discrete probability distribution to be sampled from is exactly known. Results show no substantial differences between the two numerical procedures and quite accurate power computations. Regarding the question of computing time the Verhelst approach will have to be considered much more efficient.

Convergence Rate of Empirical Bayes Test for the Parameter of the Truncated-type Distribution Families

In this paper, we construct the empirical B ay es test (EBT) for the parameter of the truncated-type distribution families. It is found that the proposed test is asymptotically optimal. The convergence rate of the EBT is given.

On the convergence for PNQD sequences with general moment conditions

Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].

Transmission Based Conditional Logistic Model for Testing Main and Interaction Effects

Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmitted from parents and pseudo-offspring (control) with allele non-transmitted from parents, was built to detect the main effects of genes and gene-covariate interactions. When there exist genotype uncertainties, expectation-maximization (EM) algorithm was adopted to estimate the coefficients. The transmission model was applied to detect the association between M235T polymorphism in AGT gene and essential hypertension (ESH). Most of parents are not available in the 126 families from HongKong Chinese population. The results showed M235T is associated with hypertension and there is interaction between M235T and the case’s sex. The allele T is higher risk for male than female.

Impact of Typical Steady-state Conditions and Transient Conditions on Flow Ripple and Its Test Accuracy for Axial Piston Pump

The current research about the flow ripple of axial piston pump mainly focuses on the effect of the structure of parts on the flow ripple. Therein, the structure of parts are usually designed and optimized at rated working conditions. However, the pump usually has to work in large-scale and time-variant working conditions. Therefore, the flow ripple characteristics of pump and analysis for its test accuracy with respect to variant steady-state conditions and transient conditions in a wide range of operating parameters are focused in this paper. First, a simulation model has been constructed, which takes the kinematics of oil film within friction pairs into account for higher accuracy. Afterwards, a test bed which adopts Secondary Source Method is built to verify the model. The simulation and tests results show that the angular position of the piston, corresponding to the position where the peak flow ripple is produced, varies with the different pressure. The pulsating amplitude and pulsation rate of flow ripple increase with the rise of pressure and the variation rate of pressure. For the pump working at a constant speed, the flow pulsation rate decreases dramatically with the increasing speed when the speed is less than 27.78% of the maximum speed, subsequently presents a small decrease tendency with the speed further increasing. With the rise of the variation rate of speed, the pulsating amplitude and pulsation rate of flow ripple increase. As the swash plate angle augments, the pulsating amplitude of flow ripple increases, nevertheless the flow pulsation rate decreases. In contrast with the effect of the variation of pressure, the test accuracy of flow ripple is more sensitive to the variation of speed. It makes the test accuracy above 96.20% available for the pulsating amplitude of pressure deviating within a range of ~6% from the mean pressure. However, with a variation of speed deviating within a range of ±2% from the mean speed, the attainable test accuracy of flow ripple is above 93.07%. The model constructed in this research proposes a method to determine the flow ripple characteristics of pump and its attainable test accuracy under the large-scale and time-variant working conditions. Meanwhile, a discussion about the variation of flow ripple and its obtainable test accuracy with the conditions of the pump working in wide operating ranges is given as well.

Research on in-situ condition preserved coring and testing systems

As shallow resources are increasingly depleted,the mechanics'theory and testing technology of deep insitu rock has become urgent.Traditional coring technologies obtain rock samples without retaining the in-situ environmental conditions,leading to distortion of the measured parameters.Herein,a coring and testing systems retaining in-situ geological conditions is presented:the coring system that obtains in-situ rock samples,and the transfer and testing system that stores and analyzes the rocks under a reconstructed environment.The ICP-Coring system mainly consists of the pressure controller,active insulated core reactor and insulation layer and sealing film.The ultimate bearing strength of 100 MPa for pressurepreservation,temperature control accuracy of 0.97%for temperature-retained are realized.CH_(4)and CO permeability of the optimized sealing film are as low as 3.85 and 0.33 ppm/min.The average tensile elongation of the film is 152.4%and the light transmittance is reduced to 0%.Additionally,the pressure and steady-state temperature accuracy for reconstructing the in-situ environment of transfer and storage system up to 1%and±0.2 is achieved.The error recorded of the noncontact sensor ring made of lowdensity polymer is less than 6%than that of the contact test.The system can provide technical support for the deep in-situ rock mechanics research,improving deep resource acquisition capabilities and further clarifying deep-earth processes.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

Effects of stress conditions on rheological properties of granular soil in large triaxial rheology laboratory tests

In order to study the rheological properties of red stone granular soil,a series of rheological experiments were executed on large tri-axial rheological apparatus.Under 100,200 and 300 kPa confining stress conditions,the rheological tests were carried out.These experiment results showed that the stress conditions,especially the stress level were the critical influencing factors of the rheological deformation properties.Under the low stress level(S=0.1),the granular soil showed the elastic properties,and there was no obvious rheological deformation.Under the middle stress level(0.2<S≤0.6),creep curves showed the linear viscoelastic rheological properties.However,under the high stress level(S>0.8) creep curves showed the non-linear viscous plastic rheological properties.Especially,under the stress level of S=1.0,the accelerated rheological phase of creep curves occurred at early time with a trend of failure.The stress level had obvious effects on the final rheological deformation of the soil sample,and the final rheological deformation increments nonlinearly increased with stress level.The final rheological deformation increment and step was little under low stress level,while it became large under high stress level,which showed the nonlinearly rheological properties of the granular soil.The confining pressure also had direct effects on final rheological deformation,and the final rheological deformation linearly increased with confining pressure increments.