Search

In order to analyze the channel estimation performance of near space high altitude platform station (HAPS) in wireless communication system, the structure and formation of HAPS are studied in this paper. The traditional Least Squares (LS) channel estimation method and Singular Value Decomposition-Linear Minimum Mean-Squared (SVD-LMMS) channel estimation method are compared and investigated. A novel channel estimation method and model are proposed. The channel estimation performance of HAPS is studied deeply. The simulation and theoretical analysis results show that the performance of the proposed method is better than the traditional methods. The lower Bit Error Rate (BER) and higher Signal Noise Ratio (SNR) can be obtained by the proposed method compared with the LS and SVD-LMMS methods.

This paper is devoted to exploring the combined impact of a generic nonlinear infection rate and infected removable storage media on viral spread. For that purpose, a novel dynamical model with an external compartment is proposed, and the explanations of the main model assumptions (especially the generic nonlinear infection rate) are also examined. The existence and global stability of the unique equilibrium of the model are fully investigated, from which it can be seen that computer virus would persist. On this basis, a next-best approach to controlling the level of infected computers is suggested, and the theoretical analysis of optimal control of the model is also performed. Additionally, some numerical examples are given to illustrate the main results.

Wind shear is a dangerous atmospheric phenomenon in aviation. Wind shear is defined as a sudden change of speed or direction of the wind. In order to analyze the influence of wind shear on the efficiency of the airplane, this paper proposes a mathematical model of point target rain echo and weather target signal echo based on Doppler effect. The wind field model is developed in this paper, and the antenna model is also studied by using Bessel function. The spectrum distribution of symmetric and asymmetric wind fields is researched by using the mathematical model proposed in this paper. The simulation results are in accordance with radial velocity component, and the simulation results also confirm the correctness of the established model of antenna.

This paper aims to investigate the global stability of negative solutions of the difference equation xn+1=(α+βxn-k)/(γ+xn), n=0,1,2,…, where the initial conditions x-k,…,x0∈-∞,0, k is a positive integer, and the parameters β, γ0. By utilizing the invariant interval and periodic character of solutions, it is found that the unique negative equilibrium is globally asymptotically stable under some parameter conditions. Additionally, two examples are given to illustrate the main results in the end.

This paper exactly formulates the kth-order fixation probabilities on complete star digraphs (CSDs), which extend the results from Broom and Rychtář (2008). By applying these probability formulae, some asymptotic properties on CBDs are analyzed, and certain CSDs are determined to be amplifiers of selection for arbitrary relative fitness larger than 1, while all the CSDs are proved to be amplifiers of selection for fixed relative fitness slightly larger than 1. A numerical method for fixed population structure (by solving a linear system) is developed to calculate the fixation probabilities on complete bipartite digraphs (CBDs), and some conjectures are finally given through simulations.

This paper examines the propagation behavior of computer virus under human intervention. A dynamical model describing the spread of computer virus, under which a susceptible computer can become recovered directly and an infected computer can become susceptible directly, is proposed. Through a qualitative analysis of this model, it is found that the virus-free equilibrium is globally asymptotically stable when the basic reproduction number R0≤1, whereas the viral equilibrium is globally asymptotically stable if R0>1. Based on these results and a parameter analysis, some appropriate measures for eradicating the spread of computer virus across the Internet are recommended.

This paper studies a third-order conditional difference equation which is a generalization from the literature. We investigate this equation by transforming it into a first-order system. Finally it is proved that the equation has no period-two (or three) integer solutions. Besides, its all period-four (and five) integer solutions are derived under appropriate rational parameters.

We propose to study a generalized family of max-type difference equations and then prove the global attractivity of a particular case of it under some parameter conditions. Through some numerical results of other cases, we finally pose a generic conjecture.

This paper addresses the max-type difference equation xn=max{fn/xn−kα,B/xn−mβ}, n∈ℕ0, where k,m∈ℕ, B>0, and (fn)n∈ℕ0 is a positive sequence with a finite limit. We prove that every positive solution to the equation converges to max{(limn→∞fn)1/(α+1),B1/(β+1)} under some conditions. Explicit positive solutions to two particular cases are also presented.

By incorporating the chemotherapy into a previous model describing the interaction of the immune system with the human immunodeficiency virus (HIV), this paper proposes a novel HIV virus spread model with control variables. Our goal is to maximize the number of healthy cells and, meanwhile, to minimize the cost of chemotherapy. In this context, the existence of an optimal control is proved. Experimental results show that, under this model, the spread of HIV virus can be controlled effectively.

We adapt the part metric and use it in studying positive solutions of a certain family of discrete dynamic systems. Some examples are presented, and we also compare some results in the literature.

This paper studies the behavior of positive solutions to the following particular case of a difference equation by Stević 𝑥𝑛+1=𝐴+𝑥𝑝𝑛/𝑥𝑝𝑘+1𝑛−𝑘, 𝑛∈ℕ0, where 𝐴,, , and presents theoretically computable explicit lower and upper bounds for the positive solutions to this equation. Besides, a concrete example is given to show the computing approaches which are effective for small parameters. Some analogous results are also established for the corresponding Stević max-type difference equation.

We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević's paper (2010). A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili (2009), Berenhaut and Stević (2007), and Liao et al. (2009).

Motivated by Iričanin and Stević's paper (2006) in which for the first time were considered some cyclic systems of difference equations, here we study the global attractivity of some nonlinear k-dimensional cyclic systems of higher-order difference equations. To do this, we use the transformation method from Berenhaut et al. (2007) and Berenhaut and Stević (2007). The main results in this paper also extend our recent results in the work of (Liu and Yang 2010, in press).

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn=(p+ryn-s)/(q+ϕn(yn-1,yn-2,…,yn-m)+yn-s), n∈ℕ0, with p≥0,r,q>0,s,m∈ℕ and positive initial values, and present some sufficient conditions for the parameters and maps ϕn:(ℝ+)m→ℝ+,n∈ℕ0, under which every positive solution to the equation converges to zero or a unique positive equilibrium. Our main result in the paper extends some related results from the work of Gibbons et al. (2000), Iričanin (2007), and Stević (vol. 33, no. 12, pages 1767–1774, 2002; vol. 6, no. 3, pages 405–414, 2002; vol. 9, no. 4, pages 583–593, 2005). Besides, several examples and open problems are presented in the end.

We describe in an elegant and short way the behaviour of positive solutions of the higher-order difference equation xn=cxn−pxn−p−q/xn−q, n∈ℕ0, where p,q∈ℕ and c>0, extending some recent results in the literature.