Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of(pt)t≥0 to...In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of(pt)t≥0 to equilibrium uniform on any bounded subset in H.展开更多
In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a...In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.展开更多
In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this sche...In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this scheme to encrypt plaintext and obtain ciphertext. In this algorithm, the plaintext information in the key is used, so different plaintexts or different total numbers of plaintext letters will encrypt different ciphertexts. Simulation results show that the performance and the security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.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
Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors consider the Markov operator T : C(X)N C(X)N defined by for any f = (f1,f2,… ,fN), where ...Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors consider the Markov operator T : C(X)N C(X)N defined by for any f = (f1,f2,… ,fN), where (pij) is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T.展开更多
The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for th...The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample values are derived. Finally, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part.展开更多
In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not...In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.展开更多
<Abstract>At low temperatures the configurational phase space of a macroscopic complex system (e.g.,a spin-glass) of N~10^(23) interacting particles may split into an exponential number Ω_s~exp(const×N) ...<Abstract>At low temperatures the configurational phase space of a macroscopic complex system (e.g.,a spin-glass) of N~10^(23) interacting particles may split into an exponential number Ω_s~exp(const×N) of ergodic sub-spaces (thermodynamic states).It is usually assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density,and that the equilibrium free energies follow the distribution of exponential decay.But actually for some complex systems,the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range,and consequently their equilibrium properties are contributed by excited thermodynamic states.Based on this analysis,the re-weighting parameter y in the cavity approach of spin-glasses is easily understood.Depending on the free-energy distribution,the optimal y can either be equal to or be strictly less than the inverse temperature β.展开更多
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epi...A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.展开更多
3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic ...3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic model.Surprisingly,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.展开更多
Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning mas...Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning massive reflecting elements.This paper considers a distributed IRS aided decode-and-forward(DF)relaying system over Nakagami-m fading channels.Based on a tight approximation for the distribution of the received signalto-noise ratio(SNR),we first derive exact closed-form expressions of the outage probability,ergodic capacity,and energy efficiency for the considered system.Moreover,we propose the optimal IRS configuration considering the energy efficiency and pilot overhead.Finally,we compare the performance between the distributed IRS-aided DF relaying and multi-IRS-only systems,and verify the analytical results by using monte carlo simulations.展开更多
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
基金supported by the National Science Foundation of China(1067121290820302)the National Science Foundation of Hunan Province
文摘In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of(pt)t≥0 to equilibrium uniform on any bounded subset in H.
基金Supported by the National Natural Science Foundation of China(11571372,11771452)the Innovation Program of Central South University(10900-50601010)
文摘In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
基金supported by the National Natural Science Foundation of China (Grant Nos.61173183,60973152,and 60573172)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No.20070141014)the Natural Science Foundation of Liaoning Province,China (Grant No.20082165)
文摘In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this scheme to encrypt plaintext and obtain ciphertext. In this algorithm, the plaintext information in the key is used, so different plaintexts or different total numbers of plaintext letters will encrypt different ciphertexts. Simulation results show that the performance and the security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.
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Let X be a compact metric space and C(X) be the space of all continuous functions on X. In this article, the authors consider the Markov operator T : C(X)N C(X)N defined by for any f = (f1,f2,… ,fN), where (pij) is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T*-invariant measures where T* is the adjoint operator of T.
文摘The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample values are derived. Finally, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part.
文摘In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.
基金supported by National Natural Science Foundation of China under Grant No.10774150
文摘<Abstract>At low temperatures the configurational phase space of a macroscopic complex system (e.g.,a spin-glass) of N~10^(23) interacting particles may split into an exponential number Ω_s~exp(const×N) of ergodic sub-spaces (thermodynamic states).It is usually assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density,and that the equilibrium free energies follow the distribution of exponential decay.But actually for some complex systems,the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range,and consequently their equilibrium properties are contributed by excited thermodynamic states.Based on this analysis,the re-weighting parameter y in the cavity approach of spin-glasses is easily understood.Depending on the free-energy distribution,the optimal y can either be equal to or be strictly less than the inverse temperature β.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
基金Supported by the National Natural Science Foundation of China(11071053)Natural Science Foundation of Hebei Province(A2014207010)+2 种基金Key Project of Science and Research of Hebei Educational Department(ZD2016024)Key Project of Science and Research of Hebei University of Economics and Business(2016KYZ07)the third author is supported by Science and Technology Foundation of Agricultural University of Hebei(LG201612)
文摘A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.
基金supported by National Key R&D Program of China(Grant Nos.2020YFA0712700)NNSF of China(Grant Nos.12090014,11931004,11971077)+3 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing UniversityNatural Science Foundation Project of CQ(Grant No.cstc2020jcyj-msxmX0441)Fundamental Research Funds for the Central Universities(Grant No.2020CDJ-LHZZ-027)。
文摘3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic model.Surprisingly,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.
基金supported in part by National Natural Science Foundation of China under Grant 62371262 and 61971467in part by the Key Research and Development Program of Jiangsu Province of China under Grant BE2021013-1+1 种基金in part by the Qinlan Project of Jiangsu Provincein part by the Scientific Research Program of Nantong under Grant JC22022026
文摘Intelligent reflecting surface(IRS)is a newly emerged and promising paradigm to substantially improve the performance of wireless communications by constructing favorable communication channels via properly tuning massive reflecting elements.This paper considers a distributed IRS aided decode-and-forward(DF)relaying system over Nakagami-m fading channels.Based on a tight approximation for the distribution of the received signalto-noise ratio(SNR),we first derive exact closed-form expressions of the outage probability,ergodic capacity,and energy efficiency for the considered system.Moreover,we propose the optimal IRS configuration considering the energy efficiency and pilot overhead.Finally,we compare the performance between the distributed IRS-aided DF relaying and multi-IRS-only systems,and verify the analytical results by using monte carlo simulations.