Authors:Regimantas Čiupaila Kristina Pupalaigė Mifodijus Sapagovas Abstract: In the paper the two-dimensional elliptic equation with integral boundary conditions is solved by finite difference method. The main aim of the paper is to investigate the conditions for the convergence of the iterative methods for the solution of system of nonlinear difference equations. With this purpose, we investigated the structure of the spectrum of the difference eigenvalue problem. Some sufficient conditions are proposed such that the real parts of all eigenvalues of the corresponding difference eigenvalue problem are positive. The proof of convergence of iterative method is based on the properties of the M-matrices not requiring the symmetry or diagonal dominance of the matrices. The theoretical statements are supported by the results of the numerical experiment. PubDate: Thu, 01 Jul 2021 06:58:11 +000

Authors:Julius Venskus Povilas Treigys Jurgita Markevičiūtė Abstract: Increasing intensity in maritime traffic pushes the requirement in better preventionoriented incident management system. Observed regularities in data could help to predict vessel movement from previous vessels trajectory data and make further movement predictions under specific traffic and weather conditions. However, the task is burden by the fact that the vessels behave differently in different geographical sea regions, sea ports, and their trajectories depends on the vessel type as well. The model must learn spatio-temporal patterns representing vessel trajectories and should capture vessel’s position relation to both space and time. The authors of the paper proposes new unsupervised trajectory prediction with prediction regions at arbitrary probabilities using two methods: LSTM prediction region learning and wild bootstrapping. Results depict that both the autoencoder-based and wild bootstrapping region prediction algorithms can predict vessel trajectory and be applied for abnormal marine traffic detection by evaluating obtained prediction region in an unsupervised manner with desired prediction probability. PubDate: Thu, 01 Jul 2021 06:57:06 +000

Authors:Xinguang Zhang Lishan Liu Yonghong Wu Benchawan Wiwatanapataphee Abstract: In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach. PubDate: Thu, 01 Jul 2021 06:55:53 +000

Authors:Mohamed M.A. Metwali Kinga Cichoń Abstract: In this paper, we study the existence of a.e. monotonic solutions of some general delay integral problems for both fractional and integer orders in the space of Lebesgue integrable functions on the interval R+ = [0;1) and in the space of locally integrable functions L1loc (R+). In particular, the uniqueness of solutions for considered problems is obtained. PubDate: Thu, 01 Jul 2021 06:52:58 +000

Authors:Gregory Amali Paul Rose Murugan Suvinthra Krishnan Balachandran Abstract: The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for the stochastic Kuramoto–Sivashinsky equation driven by multiplicative noise. To establish the large deviation principle, the weak convergence approach is used, which relies on proving basic qualitative properties of controlled versions of the original stochastic partial differential equation. PubDate: Thu, 01 Jul 2021 06:51:57 +000

Authors:Jiafa Xu Jie Liu Donal O'Regan Abstract: In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for the equation. PubDate: Thu, 01 Jul 2021 06:51:00 +000

Authors:Da Huang Xiaolin Fan Cheng Hu Haijun Jiang Abstract: In this paper, a novel cluster consensus problem related with the bipartition of the graph of multi-agent systems (MASs) is studied. To track the virtual leaders and reach the expected consensus, a new type of pinning consensus protocol with aperiodic intermittent effects is designed according to the graph structure, and a new kind of aperiodic intermittent communication is defined. Moreover, the protocol is applied to construct networked systems with intermittent communications. Lyapunov functional is applied to get sufficient conditions for solving the multi-tracking problem under a dual subsystem framework. Finally, some numerical simulations are given to illustrate the effectiveness of the theoretical results. PubDate: Thu, 01 Jul 2021 06:47:08 +000

Authors:Shuai Liu Lingli Zhao Wanli Zhang Xinsong Yang Fuad E. Alsaadi Abstract: In this paper, fast fixed-time (FDT) synchronization of T–S fuzzy (TSF) complex networks (CNs) is considered. The given control schemes can make the CNs synchronize with the given isolated system more fleetly than the most of existing results. By constructing comparison system and applying new analytical techniques, sufficient conditions are established to derive fast FDT synchronization speedily. In order to give some comparisons, FDT synchronization of the considered CNs is also presented by designing FDT fuzzy controller. Numerical examples are given to illustrate our new results. PubDate: Thu, 01 Jul 2021 06:46:12 +000

Authors:Guanli Xiao JinRong Wang Abstract: In this paper, we study the stability of Caputo-type fractional stochastic differential equations. Stochastic stability and stochastic asymptotical stability are shown by stopping time technique. Almost surly exponential stability and pth moment exponentially stability are derived by a new established Itô’s formula of Caputo version. Numerical examples are given to illustrate the main results.

Authors:Ning Duan Fengnan Liu Xiaopeng Zhao Abstract: In this paper, we consider the global well-posedness of solutions for the initial-boundary value problems of the epitaxy growth model. We first construct the local smooth solution, then by combining some a priori estimates, continuity argument, the local smooth solutions are extended step by step to all t > 0, provided that the initial datums sufficiently small and the smooth nonlinear functions satisfy certain local growth conditions. PubDate: Thu, 01 Jul 2021 06:43:31 +000

Authors:Preeti Dubey Uma S. Dubey Balram Dubey Abstract: Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0> RI . It indicates that infection may be eradicated if RI < 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica. PubDate: Thu, 01 Jul 2021 00:00:00 +000