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.

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.

Mathematical Modeling of Possibility Markov Chains by Possibility Theory

Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.

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) .

Dynamical Analysis of the Stochastic COVID-19 Model Using Piecewise Differential Equation Technique

Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.

RIS-assisted MIMO secure communications with Bob's statistical CSI and without Eve's CSI

In this paper,we consider a reconfigurable intelligent surface(RIS)-assisted multiple-input multiple-output(MIMO)secure communication system,where only legitimate user's(Bob's)statistical channel state information(CSI)can be obtained at the transmitter(Alice),while eavesdropper's(Eve's)CSI is unknown.Firstly,the analytical expression of the achievable ergodic rate at Bob is obtained.Then,by exploiting Bob's statistical CSI,we jointly design the transmit covariance matrix at Alice and the phase shift matrix at the RIS to minimize the transmit power of the information signal under the quality-of-service(QoS)constraint of Bob.Finally,we propose an artificial noise(AN)-aided method without Eve's CSI to enhance the security of this system and use the residual power to design the transmit covariance for AN.Simulation results verify the convergence of the proposed method,and also show that there exists a trade-off between the secrecy rate and QoS of Bob.

Fragmentation dynamics of electron-impact double ionization of helium

We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 e V to 1 ke V for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr's model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot,we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron–ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.

Performance Analysis of Intelligent Reflecting Surface Assisted Wireless Communication System

In this paper,we investigate the end-to-end performance of intelligent reflecting surface(IRS)-assisted wireless communication systems.We consider a system in which an IRS is deployed on a uniform planar array(UPA)configuration,including a large number of reflecting elements,where the transmitters and receivers are only equipped with a single antenna.Our objective is to analytically obtain the achievable ergodic rate,outage probability,and bit error rate(BER)of the system.Furthermore,to maximize the system’s signal-to-noise ratio(SNR),we design the phase shift of each reflecting element and derive the optimal reflection phase of the IRS based on the channel state information(CSI).We also derive the exact expression of the SNR probability density function(p.d.f.)and show that it follows a non-central Chi-square distribution.Using the p.d.f.,we then derive the theoretical results of the achievable rate,outage probability,and BER.The accuracy of the obtained theoretical results is also verified through numerical simulation.Itwas shown that the achievable rate,outage probability,and BER could be improved by increasing the number of reflecting elements and choosing an appropriate SNR regime.Furthermore,we also find that the IRS-assisted communication system achieves better performance than the existing end-to-end wireless communication.

Performance Analysis of RIS Assisted NOMA Networks over Rician Fading Channels

In this paper,we consider a downlink non-orthogonal multiple access(NOMA)network assisted by two reconfigurable intelligent surfaces(RISs)over Rician fading channels,in which each user communicates with the base station by the virtue of a RIS to enhance the reliability of the received signal.To evaluate the system performance of our proposed RIS-NOMA network,we first derive the exact and asymptotic expressions for the outage probability and ergodic rate of two users.Then,we derive the exact and asymptotic upper bound expressions for the ergodic rate of the nearby user.Based on asymptotic analytical results,the diversity orders for the outage probability and the high signal-to-noise ratio(SNR)slopes for the ergodic rate of the two users are obtained in the high SNR regime.Moreover,we derive the system throughputs of the proposed RIS-NOMA network in delay-limited and delay-tolerant transmission modes.Numerical results confirm our analysis and demonstrate that:1)The outage probability and ergodic rate of RIS-NOMA networks are superior to that of RIS-assisted orthogonalmultiple access(OMA)networks;2)The RIS-NOMA networks have ability to achieve a larger system throughput compared to RIS-OMA networks;and 3)The system performance of RIS-NOMA networks can be significantly improved as the number of reflecting elements and Rician factor increases.

Dynamical Properties of Additive Cellular Automata over Finite Abelian Groups

Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some necessary and sufficient conditions of determining ergodicity and sensitivity of the above additive CA were presented,respectively.A necessary condition for the positive expansivity of the above additive CA was given.The positive expansivity was proved to be preserved under the shift mappings for the general CA.The discussion was mainly based on the structure theorem of the finite abelian groups and the matrix associated with the global rule of the additive CA over the finite abelian p-groups.

Like a Sum Is Generalized into an Integral, a Product May Be Generalized into an Inteduct

It is well known that an integral is nothing but a continuous form of a sum. Is it possible to do the same thing with a product? The answer is yes and done for the first time in this publication. The new operator is called inteduct. As an integral is a proper tool to calculate the arithmetic mean of a function, the inteduct gives the geometric mean of a function. This defines a new branch of mathematics. Most applications may lay way ahead. Only some are discussed here. One is applying the inteduct to probability theory. There it is possible e.g., to determine a function for a life expectation rather than just a numerical value. Another application is to distinguish chaos from randomness within numerically given values. At least for the logistic map there exists a direct connection between Lyapunov exponent and inteduct. To distinguish between chaos and randomness is particularly important in finance. While randomness implies ergodicity, chaos is non-ergodic. And many fundamental financial theories from portfolio theory to market efficiency require ergodicity.

Modeling the Dynamics of the Random Demand Inventory Management System

At any given time, a product stock manager is expected to carry out activities to check his or her holdings in general and to monitor the condition of the stock in particular. He should monitor the level or quantity available of a given product, of any item. On the basis of the observation made in relation to the movements of previous periods, he may decide to order or not a certain quantity of products. This paper discusses the applicability of discrete-time Markov chains in making relevant decisions for the management of a stock of COTRA-Honey products. A Markov chain model based on the transition matrix and equilibrium probabilities was developed to help managers predict the likely state of the stock in order to anticipate procurement decisions in the short, medium or long term. The objective of any manager is to ensure efficient management by limiting overstocking, minimising the risk of stock-outs as much as possible and maximising profits. The determined Markov chain model allows the manager to predict whether or not to order for the period following the current period, and if so, how much.

Opportunistic Relaying Technique over Rayleigh Fading Channel to Improve Multicast Security

The performance of Rayleigh fading channels is substantially impacted by the impacts of relays, antennas, and the number of branches. Opportunistic relaying is a potent technique for enhancing the effects of the aforementioned factors while enhancing the performance of fading channels. Due to these issues, a secure wireless multicasting scenario using opportunistic relaying over Rayleigh fading channel in the presence of multiple wiretappers is taken into consideration in this study. So the investigation of a secure wireless multicasting scenario using opportunistic relaying over Rayleigh fading channel in the presence of multiple wiretappers is the focus of this paper. The primary goals of this study are to maximize security in wireless multicasting while minimizing security loss caused by the effects of relays, branches at destinations and wiretappers, as well as multicast users and wiretappers through opportunistic relaying. To comprehend the insight effects of prior parameters, the closed form analytical expressions are constructed for the probability of non-zero secrecy multicast capacity (PNSMC), ergodic secrecy multicast capacity (ESMC), and secure outage probability for multicasting (SOPM). The findings demonstrate that opportunistic relaying is a successful method for reducing the loss of security in multicasting.

Ergodic capacity analysis for device-to-device communication underlaying cellular networks

The ergodic capacity of device-to-device （D2D） communication underlaying cellular networks is analyzed. First,the D2D communication model is introduced and the interference during uplink period and downlink period is analyzed.In a D2D communication system,since it is very difficult to obtain the instantaneous channel state information （CSI）,assume that only the transmitters know the statistical CSI and the channel coefficient follows an independent complex Gaussian distribution.Based on the assumptions,for the uplink period,the signal to interference plus noise ratio （SINR）of the D2D user equipments（DUEs）is expressed. Then the cumulative distribution function （CDF ） and probability distribution function （PDF）formulae of the SINR of the DUEs are presented.Based on the SINR formulae during the uplink period,the ergodic capacity formula of the uplink period is derived. Subsequently, using the same methods,the ergodic capacity formula of the downlink period is derived.The simulation results show that the DUEs can still obtain a high ergodic capacity even in the case of a large number of DUEs.This result can be applied to the design and optimization of D2D communications.

期货经纪公司保证金的一种确定方法

本文基于马尔可夫链在存储论中的应用,结合Ergodic定理,得到确定期货经纪公司保证金的Ergodic模型,即一个双目标规划问题,然后应用乘积最大化准则,将该模型转化为单目标规划问题来求解。该方法考虑期货经纪公司承担的风险和对投资者的吸引程度,为保证金的确定提供新的思路。

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.

Close-formed bound on generalized distributed antenna system capacity

The composite channel models of the generalized distributed antenna system （GDAS） such as Rayleigh-lognormal fading are studied. Then comparisons are performed between the GDAS and the traditional multiple-input multiple-output （MIMO） system to analyze the ergodic capacity of the GDAS and make conclusions that it is impossible to achieve an analytical expression for the ergodic capacity of the GDAS. Moreover, in order to evaluate the performance of the ergodic capacity of the GDAS conveniently, the analytical lower bound and upper bound of the ergodic capacity of the GDAS are derived by using the results from multivariate statistics and matrix inequalities, under the scenarios of Rayleigh-lognormal fading and equal power allocation scheme at transmitter. Finally, the analytical bounds are verified by comparisons with the numerical results.

A Resistant Quantum Key Exchange Protocol and Its Corresponding Encryption Scheme

The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.

SL(2,R)上的Hardy-Littlewood极大函数的性质

本文给出了SL(2,R)上的Hardy-Littlewood极大函数mf的定义,利用Ergodic定理证明了Hardy-Littlewood极大函数的强(p,p)型性质,p>1.

Performance Analysis of Cooperative NOMA with Energy Harvesting in Multi-Cell Networks

In this paper,an energy harvesting enabled cooperative non-orthogonal multiple access(NOMA)system for a multi-cell network is investigated.Particularly,during the direct transmission phase,base stations send their superposed messages to the near users and far users simultaneously according to a NOMA principle,while the near users act as energy harvesting enabled relays employing a power splitting protocol.During the cooperative phase,the near users transmit their decoded messages to the corresponding far users using harvested energy.Using tools from stochastic geometry,we firstly calculate the signal to interference ratios of the users in each NOMA group including one near user and one far user.Then,the closed-form expressions of the coverage probability,ergodic rate,and energy efficiency are derived respectively.Numerical results validate the derived expressions and show that the energy harvesting enabled cooperative NOMA system in a multi-cell network can improve the coverage probability,ergodic rate,and energy efficiency compared to its counterpart OMA system.