Groupoid Approach to Ergodic Dynamical System of Commutative von Neumann Algebra

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∞(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L2(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) .

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LVY JUMP

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.

V-uniform ergodicity for fluid queues

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.

A one-time one-key encryption algorithm based on the ergodicity of chaos

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.

ROBUST WEAK ERGODICITY AND STABLE ERGODICITY

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.

UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

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.

CONDITIONS FOR FOURTH-ORDER STATIONARITY AND ERGODICITY OF A HARMONIC RANDOM PROCESS

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.

Ergodicity and Invariance of Flows in Queuing Systems

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.

Ergodicity of the IP P＋M/M/c Queue

IPP + M/M/c 排队系统广泛地在现代通讯系统被使用了。为 IPP + M/M/1 队列的队列长度 L (t) 的静止分发的存在和唯一被证明了在[10 ] 。在这份报纸，我们将给

Distribution of Equilibrium Free Energies in a Thermodynamic System with Broken Ergodicity

<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.

A survey of ergodicity on the set-valued mappings

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.

一类纯跳种群系统的遍历性

为了刻画随机环境与重大突变因素对种群的影响,本文考虑一类由马氏链与纯跳稳定过程驱动互惠种群模型.首先,讨论了该种群模型具有全局正解性.其次,给出了该模型的遍历性的充分条件.最后,探究了该模型的正常返的条件.

无穷个增生映射和的半隐式算法、Ergodic收敛及Curvature系统（英文）

在实一致凸且q一致光滑Banach空间中,构造无穷个m增生映射和μ_i逆强增生映射和的公共零点的半隐式迭代算法.证明ergodic收敛性.与近期研究成果相比,限定条件更弱.此外,还研究了一类curvature系统并证明其解恰好是无穷个m增生映射和μ_i逆强增生映射和的公共零点,进而验证了迭代算法的有效性.

一种基于超智能表面协助的密集毫米波通信模型

作为一种新型的反射材料,超智能表面将在未来通信网络中扮演重要的角色。将超智能表面应用于多点协作的毫米波通信系统,可极大提升系统性能。为此,提出基于超智能表面的密集毫米波通信模型,并分析了基于最大合并比(maximal-ratio combining,MRC)接收和选择(selection combining,SC)接收两类协作传输策略下系统性能。具体而言,阐述在Nakagami-m衰落模型下基站所接收的信号,推导了系统中断概率和各态历经容量表达式,并通过仿真验证。同时,通过仿真分析了系统参数对通信系统性能的影响。仿真结果表明,基于SC策略的系统性能略优于MRC策略。传输功率以及LIS中的反射元数对系统性能有较大影响。

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

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.

Ergodicity of 3D Stochastic Burgers Equation

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.

Distributed IRS-Aided DF Relaying Systems:Performance Analysis and Optimization

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.

湖羊生产计划的最优方案制定

对湖羊养殖中空间利用率的问题进行了研究.湖羊在各阶段对羊栏的需求不尽相同,本文建立数学模型描述了一类比较规律的生产模式下羊栏使用的情况,通过遍历的方法得到最佳的养殖方案;随后进一步考虑随机因素的影响,通过蒙特卡罗方法得到最小损失的养殖方案.

正文本、副文本与互动叙述中故事世界的动态扩展——基于断点的维度

在网络空间中,多元叙述主体常因某些社会事件、热点话题等聚集起来进行互动叙述,所生成的正文本往往需要和众多副文本协同共创故事。正文本断点激发读者在副文本中进行填充与缝合,携带着不同叙述意图的叙述主体对断点进行“就事论事型”和“借题发挥型”填充。然而,副文本常常无意或难以缝合正文本断点,甚至生产出更多、更复杂的新断点。新断点与旧断点相互交织,正副文本相互影响,为多元叙述主体在遍历中推断出多义性、歧义性、想象性的故事世界提供蓝图。

基于MSM群体的随机HIV/AIDS传染病模型分析

艾滋病(AIDS)是人类感染HIV病毒而导致免疫系统受到破坏的一种危害性极高的传染病,同性恋是传播HIV的重要途经之一。考虑到男男性行为(MSM)的传播特征,以及环境中随机因素的影响,一个基于MSM群体的随机HIV/AIDS传染病动力学模型被建立。利用随机微分方程的基本理论,分析了系统的动力学行为。首先,对于任意给定的正初值,证明了系统存在唯一的全局正解。从生物学的角度来看,这是必须成立的,这一结论确保了理论研究的合理性。进一步,鉴于在研究传染病模型的动态变化时,讨论疾病的消失与流行具有重要的应用价值。因此,对所建立的随机HIV/AIDS动力学模型中疾病的灭绝与流行进行了重点分析。特别地,利用伊藤公式,并通过构造一些特殊的函数,给出了疾病灭绝的充分条件;研究了系统唯一正的遍历平稳分布的存在性,即疾病盛行的存在性。最后,通过数值模拟,验证了疾病灭绝和盛行的理论结果,并通过与确定性系统的理论结果相比较,分析了随机扰动对系统动力学行为的影响。