This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)...This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)^(n)X_(i)Y_(i),1/α√n∑_(i=1)^(n)X_(i))}_(n=1)^(∞)converges in distribution to L_(1),where L_(t=(ε_(t),η_(t),ζ_(t))),t∈[0,1],is a multidimensional nonlinear Lévy process with an uncertainty■set as a set of Lévy triplets.This nonlinear Lévy process is characterized by a fully nonlinear and possibly degenerate partial integro-differential equation(PIDE){δ_(t)u(t,x,y,z)-sup_(F_(μ),q,Q)∈■{∫_(R^(d)δλu(t,x,y,z)(dλ)with.To construct the limit process,we develop a novel weak convergence approach based on the notions of tightness and weak compactness on a sublinear expectation space.We further prove a new type of Lévy-Khintchine representation formula to characterize.As a byproduct,we also provide a probabilistic approach to prove the existence of the above fully nonlinear degenerate PIDE.展开更多
Full duplex radio increases the frequency efficiency but its performance is limited by the self-interference （SI）. We first analyze the multiple noises in the full duplex radio system and model such noises as an α ...Full duplex radio increases the frequency efficiency but its performance is limited by the self-interference （SI）. We first analyze the multiple noises in the full duplex radio system and model such noises as an α - stable distribution. Then we formulate a novel non-Gaussian SI problem. Under the maximum correntropy criterion （MCC）, a robust digital non-linear self-interference cancellation algorithm is proposed for the SI channel estimation. A gradient descent based algorithm is derived to search the optimal solution. Simulation results show that the proposed algorithm can achieve a smaller estimation error and a higher pseudo signal to interference plus noise ratio （PSINR） than the well-known least mean square （LMS） algorithm and least square （LS） algorithm.展开更多
In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative par...In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.展开更多
Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem ...Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.展开更多
This paper considers the robust stabilization problem of a class of nonlinear measure differential systems with delay.To eliminate the effect of nonlinear uncertainties on the stability of a closed loop system, a nonl...This paper considers the robust stabilization problem of a class of nonlinear measure differential systems with delay.To eliminate the effect of nonlinear uncertainties on the stability of a closed loop system, a nonlinear controller is employed.In addition, to get the stability result of closed loop dynamics, two novel lemmas are proposed.In our approach, we do not require the assumption that the time varying delay variable γ(t) be restricted by (t)【1 , which is often required in many previous papers (e.g,see).展开更多
Mechanical strength is an essential parameter that influences and limits the lifetime performance of antireflective （AR） coatings in optical devices. Speciflcally, amphiphobic AR coatings with reduced reflectance ar...Mechanical strength is an essential parameter that influences and limits the lifetime performance of antireflective （AR） coatings in optical devices. Speciflcally, amphiphobic AR coatings with reduced reflectance are of great significance as they considerably enlarge the range of fundamental applications. Herein, we describe the design and fabrication of amphiphobic AR coatings with reduced reflectance and enhanced mechanical resilience. Introducing a thin polytetrafluoroethylene （PTFE） layer on top of the bilayer SiOz coating via vapor deposition method makes it highly liquid repellent. We achieved reduced reflectance （〈 1%） over the entire visible wavelength range, as well as tunability according to the desired wavelength region. The fabricated film showed better thermal stability （up to 300℃） with stable AR efficiency, when an ultrathin dense coat of Al2O3 was deposited via atomic layer deposition （ALD） on the polymer-based bilayer SiO2 antireflective coating （P-BSAR）. The experimental results prove that the omnidirectional AR coating in this study exhibits multifunctional properties and should be suitable for the production of protective optical equipment and biocompatible polymer films for the displays of portable electronic devices.展开更多
基金supported by the National Key R&D Program of China(Grant No.2018YFA0703900)the National Natural Science Foundation of China(Grant No.11671231)+2 种基金the Qilu Young Scholars Program of Shandong Universitysupported by the Tian Yuan Projection of the National Natural Science Foundation of China(Grant Nos.11526205,11626247)the National Basic Research Program of China(973 Program)(Grant No.2007CB814900(Financial Risk)).
文摘This article establishes a universal robust limit theorem under a sublinear expectation framework.Under moment and consistency conditions,we show that,forα∈(1,2),the i.i.d.sequence{(1/√∑_(i=1)^(n)X_(i),1/n∑_(i=1)^(n)X_(i)Y_(i),1/α√n∑_(i=1)^(n)X_(i))}_(n=1)^(∞)converges in distribution to L_(1),where L_(t=(ε_(t),η_(t),ζ_(t))),t∈[0,1],is a multidimensional nonlinear Lévy process with an uncertainty■set as a set of Lévy triplets.This nonlinear Lévy process is characterized by a fully nonlinear and possibly degenerate partial integro-differential equation(PIDE){δ_(t)u(t,x,y,z)-sup_(F_(μ),q,Q)∈■{∫_(R^(d)δλu(t,x,y,z)(dλ)with.To construct the limit process,we develop a novel weak convergence approach based on the notions of tightness and weak compactness on a sublinear expectation space.We further prove a new type of Lévy-Khintchine representation formula to characterize.As a byproduct,we also provide a probabilistic approach to prove the existence of the above fully nonlinear degenerate PIDE.
基金supported by the National Natural Science Foundation of China under Grants 61372092"863" Program under Grants 2014AA01A701
文摘Full duplex radio increases the frequency efficiency but its performance is limited by the self-interference （SI）. We first analyze the multiple noises in the full duplex radio system and model such noises as an α - stable distribution. Then we formulate a novel non-Gaussian SI problem. Under the maximum correntropy criterion （MCC）, a robust digital non-linear self-interference cancellation algorithm is proposed for the SI channel estimation. A gradient descent based algorithm is derived to search the optimal solution. Simulation results show that the proposed algorithm can achieve a smaller estimation error and a higher pseudo signal to interference plus noise ratio （PSINR） than the well-known least mean square （LMS） algorithm and least square （LS） algorithm.
基金supported by National Natural Science Foundation of China(11001284)Natural Science Foundation Project of CQ CSTC(cstcjjA00003)Fundamental Research Funds for the Central Universities(CQDXWL2012008)
文摘In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.
文摘Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.
文摘This paper considers the robust stabilization problem of a class of nonlinear measure differential systems with delay.To eliminate the effect of nonlinear uncertainties on the stability of a closed loop system, a nonlinear controller is employed.In addition, to get the stability result of closed loop dynamics, two novel lemmas are proposed.In our approach, we do not require the assumption that the time varying delay variable γ(t) be restricted by (t)【1 , which is often required in many previous papers (e.g,see).
基金The authors are grateful to the financial support by the National Basic Research Program of China （973 program, No. 2013CB934301）, the National Natural Science Foundation of China （Nos. 51531006 and 51572148）, the Research Project of Chinese Ministry of Education （No. 113007A）, and the Tsinghua University Initiative Scientific Research Program.
文摘Mechanical strength is an essential parameter that influences and limits the lifetime performance of antireflective （AR） coatings in optical devices. Speciflcally, amphiphobic AR coatings with reduced reflectance are of great significance as they considerably enlarge the range of fundamental applications. Herein, we describe the design and fabrication of amphiphobic AR coatings with reduced reflectance and enhanced mechanical resilience. Introducing a thin polytetrafluoroethylene （PTFE） layer on top of the bilayer SiOz coating via vapor deposition method makes it highly liquid repellent. We achieved reduced reflectance （〈 1%） over the entire visible wavelength range, as well as tunability according to the desired wavelength region. The fabricated film showed better thermal stability （up to 300℃） with stable AR efficiency, when an ultrathin dense coat of Al2O3 was deposited via atomic layer deposition （ALD） on the polymer-based bilayer SiO2 antireflective coating （P-BSAR）. The experimental results prove that the omnidirectional AR coating in this study exhibits multifunctional properties and should be suitable for the production of protective optical equipment and biocompatible polymer films for the displays of portable electronic devices.
