随机集的独立性与同分布性的刻划(英文)

本文绘出了随机集的独立性与同分布性的刻化，所给出的准则比Hess[4]，[5]更易于验证．

两值随机序列加权和的收敛性

利用二个比较函数讨论了取值０或１的随机序列｛Ｘｎ，ｎ≥１｝加权和Ｓｎ（ｗ）＝∑ｎｉ＝１ａｉＸｉ（ｗ），（ａｉ∈Ｒ）的收敛性．

有限状态随机序列部分和的一个收敛性质

利用随机序列的同分布性及比较函数，导出了有限状态随机序列部分和的一个收敛性质．

Effect of inter-cycle heat treatment in accumulative roll-bonding(ARB)process on planar isotropy of mechanical properties of AA1050 sheets

The accumulative roll-bonding(ARB)process was applied on the strips of aluminum alloy 1050 in two processing conditions:cold ARB and warm ARB.The results of tensile tests and microhardness measurement show that the warm ARB process exhibits the lower tensile strength and microhardness,more homogeneous distribution of the microhardness,higher elongation,and especially superior planar isotropy of the tensile properties in comparison to the cold ARB,because of the intermediate heat treatment as well as the elevated temperature rolling in the warm ARB process.Furthermore,with increasing the cycles of both processes,the planar isotropy decreases progressively.

Non-liD Recommender Systems： A Review and Framework of Recommendation Paradigm Shifting

While recommendation plays an increasingly critical role in our living, study, work, and entertainment, the recommendations we receive are often for irrelevant, duplicate, or uninteresting products and ser- vices. A critical reason for such bad recommendations lies in the intrinsic assumption that recommend- ed users and items are independent and identically distributed （liD） in existing theories and systems. Another phenomenon is that, while tremendous efforts have been made to model specific aspects of users or items, the overall user and item characteristics and their non-IIDness have been overlooked. In this paper, the non-liD nature and characteristics of recommendation are discussed, followed by the non-liD theoretical framework in order to build a deep and comprehensive understanding of the in- trinsic nature of recommendation problems, from the perspective of both couplings and heterogeneity. This non-liD recommendation research triggers the paradigm shift from lid to non-liD recommendation research and can hopefully deliver informed, relevant, personalized, and actionable recommendations. It creates exciting new directions and fundamental solutions to address various complexities including cold-start, sparse data-based, cross-domain, group-based, and shilling attack-related issues.

A COLLABORATIVE SPECTRUM SENSING SCHEME USING FUZZY COMPREHENSIVE EVALUATION IN COGNITIVE RADIO

Cognitive Radio(CR) is a promising technology to solve the challenging spectrum scarcity problem.However, to implement CR, spectrum sensing is the groundwork and the precondition.In this paper, a collaborative spectrum sensing scheme using fuzzy comprehensive evaluation is proposed.The final sensing decision of the proposed scheme is based on the combination of distributed sensing results of different Secondary Users(SUs).To improve the reliability of the sensing decision, the combination procedure takes into account the credibility of each SU, which is evaluated using fuzzy comprehensive evaluation.The effect of the presence of malicious SUs and malfunctioning SUs on the performance of the proposed scheme is also investigated.The efficiency of the scheme is validated through analysis and simulation.

Distributed collaborative extremum response surface method for mechanical dynamic assembly reliability analysis

To make the dynamic assembly reliability analysis more effective for complex machinery of multi-object multi-discipline(MOMD),distributed collaborative extremum response surface method(DCERSM)was proposed based on extremum response surface method(ERSM).Firstly,the basic theories of the ERSM and DCERSM were investigated,and the strengths of DCERSM were proved theoretically.Secondly,the mathematical model of the DCERSM was established based upon extremum response surface function(ERSF).Finally,this model was applied to the reliability analysis of blade-tip radial running clearance(BTRRC)of an aeroengine high pressure turbine(HPT)to verify its advantages.The results show that the DCERSM can not only reshape the possibility of the reliability analysis for the complex turbo machinery,but also greatly improve the computational speed,save the computational time and improve the computational efficiency while keeping the accuracy.Thus,the DCERSM is verified to be feasible and effective in the dynamic assembly reliability(DAR)analysis of complex machinery.Moreover,this method offers an useful insight for designing and optimizing the dynamic reliability of complex machinery.

Stabilization of a Non-homogeneous Rotating Body-Beam System with the Torque and Nonlinear Distributed Controls

This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively. As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite operator, the authors show that the torque and nonlinear distributed control laws suppress the system vibrations, in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.

Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications

Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.

From the elasticity theory to cosmology and vice versa

The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.

Distributed adaptive attitude synchronization of multiple spacecraft

This paper addresses the distributed attitude synchronization problem of multiple spacecraft with unknown inertia matrices. Two distributed adaptive controllers are proposed for the cases with and without a virtual leader to which a time-varying reference attitude is assigned. The first controller achieves attitude synchronization for a group of spacecraft with a leaderless communication topology having a directed spanning tree. The second controller guarantees that all spacecraft track the reference attitude if the virtual leader has a directed path to all other spacecraft. Simulation examples are presented to illustrate the effectiveness of the results.

Spatial Solitons in 2D Graded-Index Waveguides with Different Distributed Transverse Diffractions

We discuss the nonlinear Schr6dinger equation with variable coefficients in 21） graded-index waveguides with different distributed transverse diffractions and obtain exact bright and dark soliton solutions. Based on these solutions, we mainly investigate the dynamical behaviors of solitons in three different diffraction decreasing waveguides with the hyperbolic, Gaussian and Logarithmic profiles. Results indicate that for the same parameters, the amplitude of bright solitons in the Logarithmic profile and the amplitude of dark solitons in the Gaussian profile are biggest respectively, and the amplitude in the hyperbolic profile is smallest, while the width of solitons has the opposite case.