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.

Convergence over AI Governance Amid Differences

As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensuring safety,and promoting fairness”?

CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW

In this paper,we justify the convergence from the two-species Vlasov-PoissonBoltzmann(VPB,for short)system to the two-fluid incompressible Navier-Stokes-FourierPoisson(NSFP,for short)system with Ohm’s law in the context of classical solutions.We prove the uniform estimates with respect to the Knudsen numberεfor the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions.Consequently,we prove the convergence to the two-fluid incompressible NSFP asεgoes to 0.

POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY

This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

Some Convergence Results for Sequences of -mixing Random Variables

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

CENTRAL LIMIT THEOREM AND CONVERGENCE RATES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT

We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.

The Strong Convergence Properties for Partial Sums of m-NA Random Variables

In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

Exponential Continuous Non-Parametric Neural Identifier With Predefined Convergence Velocity

This paper addresses the design of an exponential function-based learning law for artificial neural networks(ANNs)with continuous dynamics.The ANN structure is used to obtain a non-parametric model of systems with uncertainties,which are described by a set of nonlinear ordinary differential equations.Two novel adaptive algorithms with predefined exponential convergence rate adjust the weights of the ANN.The first algorithm includes an adaptive gain depending on the identification error which accelerated the convergence of the weights and promotes a faster convergence between the states of the uncertain system and the trajectories of the neural identifier.The second approach uses a time-dependent sigmoidal gain that forces the convergence of the identification error to an invariant set characterized by an ellipsoid.The generalized volume of this ellipsoid depends on the upper bounds of uncertainties,perturbations and modeling errors.The application of the invariant ellipsoid method yields to obtain an algorithm to reduce the volume of the convergence region for the identification error.Both adaptive algorithms are derived from the application of a non-standard exponential dependent function and an associated controlled Lyapunov function.Numerical examples demonstrate the improvements enforced by the algorithms introduced in this study by comparing the convergence settings concerning classical schemes with non-exponential continuous learning methods.The proposed identifiers overcome the results of the classical identifier achieving a faster convergence to an invariant set of smaller dimensions.

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].

Convergence Properties of Piecewise Power Approximations

We address the problem of convergence of approximations obtained from two versions of the piecewise power-law representations arisen in Systems Biology. The most important cases of mean-square and uniform convergence are studied in detail. Advantages and drawbacks of the representations as well as properties of both kinds of convergence are discussed. Numerical approximation algorithms related to piecewise power-law representations are described in Appendix.

道德向法律的转化与制度专业化假说

个体选择和社会选择都是基于理性的,作为公共选择的制度的产生旨在增进社会福利。制度大致可分为道德和法律两部分。道德和法律的分野也是理性的结果,即:当某项社会约束的整体社会收益大于执行成本时,宜于采用法律的形式;否则,则宜于采用道德的形式。道德与法律的分界并非一成不变,而是受到专业化分工水平的制约。社会分工程度越高,则个体搭便车动机越强,采用法律约束就越有利。随着社会分工水平的日益加深,有一个原属于道德范畴的社会约束转化为法律约束的趋势,即制度专业化趋势。制度专业化会造成更大范围内的制度趋同。

“约”和“不约”而同:李双元教授法律趋同化思想的破产法表现

在近年逆全球化挑战的背景下,李双元教授提出的法律趋同化思想依然有着强大的生命力。法律趋同化思想在破产法领域的表现形式包括国际协调的趋同化和国内自发的趋同化。一方面,联合国国际贸易法委员会关于破产法的立法指南、示范法和《欧盟跨境破产程序条例》都是企业破产法国际协调的趋同化的重要实践,而《世界银行自然人破产问题处理报告》则为个人破产国际协调的趋同化提供了参考。另一方面,全球性危机也使各国破产法国内自发趋同化的表现形式受到了更多关注。各国在应对全球性危机时自主采取的企业破产法措施集中表现为三种相似类型,包括:(1)调整和适用现有破产程序;(2)引进新的重整或拯救程序;(3)引入新的非破产解决方式。个人破产法也在寻求利益平衡的过程中表现出趋同化。未来的法律趋同化研究需更加重视法律趋同化的多样化表现形式和本土法律文化对法律趋同化的影响。

基于二阶滑模扰动观测的PMSM电流预测控制研究

针对无差拍电流预测控制(DPCC)对电机参数的依赖性,系统性能尤其易受电感参数影响的问题,研究基于二阶滑模扰动观测的永磁同步电机(PMSM)电流预测控制方法。首先,根据滑模控制原理分析电感参数失配对系统参数鲁棒性的影响,及传统滑模控制的不连续函数导致的系统“抖振”;然后,在DPCC中引入一种基于二阶趋近律的滑模扰动观测器(SMDO),实时补偿电感参数失配造成的扰动,同时通过二阶趋近律加速扰动误差的收敛;最后,将该方法与DPCC、SMDO+DPCC进行对比仿真实验。实验结果表明,在电感参数失配的情况下,该方法降低了电流稳态误差,提高了系统参数的鲁棒性,减少了传统滑模控制带来的系统“抖振”现象。