查看更多>>摘要：It is well known that Clairaut's equation can be solved, but its perturbed equation cannot. In addition, Clairaut's equation has two interesting properties: it has a singular solution and no uniqueness of the solutions. This study overcomes these difficulties and analyzes the error between the approximate and exact solutions of Clairaut's equation. Moreover, it contains important ideas as an approach to differential equations which have non-unique solutions. Examples and numerical simulations are given to understand the results. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This article proposes the multiple Euler-Lagrange systems approach to achieve leader following bipartite consensus is investigated when the systems are under the uncertain systems and the impact of deception attacks. An adaptive distributed observer containing filters is built for nonlinear systems where the matrix is not known specifically. There are two main purposes served by the adaptive distributed observer. the first is to estimate the state and pass the information to each follower through the system's communication network when the system's matrix is not known certainly, and the second is to eliminate deception attacks added to ELSs by the filters. Then, on the basis of this adaptive distributed observer functioning in the system, the problem for multiple ELSs of leader following bipartite consensus will be solved by using the Lyapunov method and the deterministic equivalence principle. Finally, numerical simulations will be carried out to demonstrate the effectiveness of the proposed strategies. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In extremal graph theory studies, it is not yet finished to determine the exact value of ex(n; C-4) in general case. Erdos and Simonovits [10] conjectured that an n-vertex graph G with ex(n; C-4 ) + 1 edges may contain at least root n + o(root n) 4-cycles. In this paper we investigate the number of 4-cycles in a graph. We show that the number of 4-cycles in an n-vertex graph G is at least (epsilon root 4n - 3 )/4 + epsilon(2)/(2n) provided that |E(G)| = n (1 + root 4n - 3 )/4 + epsilon, where epsilon is an arbitrary positive real number. This result is an approach solving to this open problem. Furthermore, we prove that if n is large enough, then there are at least ((4 epsilon - 1)root 4n - 3 + 5)/16 + o(1) 4-cycles in an n-vertex graph with e = (n - 1)(1 + root 4n - 3 )/4 + epsilon edges which has k vertices whose degrees are mutually different, where k >= 3 root 24n +3 root 12n -(12n)(2) - 1/27 and epsilon > 0 is a real number. In addition, we get that a triangle-free graph with n vertices and e = n root n - 1/2 + epsilon edges has at least (2 epsilon(root n - 1 - 2) + 1)/4 + o(1) 4-cycles, where epsilon > 0 is an any real number and n is large enough. This shows that the weak version of Erdos and Simonovits' conjecture [10] holds for such graphs when n is sufficiently large. Finally, we obtain a bipartite version of this result. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper studies the H 00 fault-tolerant control problem for a class of conic-type nonlinear Markov jump systems with sensor and actuator faults as well as unknown disturbances. Firstly, the hidden Markov model is introduced to deal with the asynchronous problem existing in the control systems. By selecting suitable Lyapunov-Krasovskii function, linear matrix inequalities techniques are applied to obtain the H 00 fault-tolerant controller. A new condition of the state feedback H 00 fault-tolerant controller with actuator faults and sensor faults is presented. The proposed control strategy can not only ensure the finite-time boundness of the closed loop system, but also guarantee the required H 00 performance. Lastly, the availability of the design scheme is validated by a simulation example.(c) 2022 Published by Elsevier Inc.
Guedes, Priscila F. S.Mendes, Eduardo M. A. M.Nepomuceno, Erivelton
15页
查看更多>>摘要：Numerical methods are essential to investigate and apply nonlinear continuous-time dynamical systems in many fields of science and engineering and discretization schemes are required to obtain the solutions of such dynamical systems. Although computing power has been speedily growing in recent decades, embedded and large-scale problems have motivated significant research to improve the computational efficiency. Nevertheless, few studies have focused on finite precision limitation on discretization schemes due to round off effects in floating-point number representation. In this paper, a computational effective discretization scheme for nonlinear dynamical systems is introduced. By means of a theorem, it is shown that high-order terms in the Runge-Kutta method can be neglected with no accuracy loss. The proposed approach is illustrated using three well-known systems, namely the Rossler systems, the Lorenz equations and the Sprott B system. The number of mathematical operations and simulation time have reduced up to 81.1% and 90.7%, respectively. Furthermore, as the step-size decreases, the number of neglected terms increases due to the precision of the computer. Yet, accuracy, observability of dynamical systems and the largest Lyapunov are preserved. The adapted scheme is effective, reliable and suitable for embedded and large-scale applications.](c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This work investigates the adaptive finite-time tracking control problem for switched nonlinear systems, in which backlash-like hysteresis and time-varying delay are taken into account. The nonlinear estimation ability of radial basis function neural networks is employed to relax the restriction on unknown nonlinear functions. The dynamic surface technology and the finite-time control approach avoid the "curse of dimensionality" and "singularity" problems existing in the backstepping design procedure, separately. By Lyapunov-Razumikhin function scheme, the proposed finite-time signal guarantees superior tracking performance under the average dwell time switching. Finally, to testify the practicability of the presented strategy, two simulation examples are shown.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Tacit knowledge is the knowledge existing in human brain which is not easy to be recorded or quantified, and often is learned in the face-to-face interactions. The tacit knowledge diffusion depends on the decision-making of tacit knowledge owners, and the expression of explicit knowledge carriers. However, the comprehensive influence of the tacit knowledge owners, explicit knowledge carriers and the relations of them were not attracted enough attention. In this paper, an algebra matrix method is used to integrate the multidimensional information of network structures and the nodes' states. By the al -gebra matrix method, the diffusion threshold of the tacit knowledge is calculated, which is called algebra matrix evaluation. This evaluation method is proven to be effective by comparing with Monte Carlo simulations on three types of artificial networks and five re-als. With applications of the algebra matrix evaluation, we construct a co-author network according the data of the academic papers from 1980 to 2017 on Aminer platform, and de-fine states of tacit knowledge owners and the explicit knowledge carriers by the scholar's career lengths and the paper's cited quantities respectively. It is found that the thresholds of tacit knowledge diffusion are decreasing with the expansions of the scale of the largest connected components, whether tacit knowledge diffuses in the co-author networks or in the largest connected components. And with the evolution of cumulative co-author net-work, the diffusion thresholds of tacit knowledge in the largest connected component de -crease in ladder-like with unequal steps. Furthermore, it is find ignoring the state factor will lead to the deviation in the evaluation of tacit knowledge diffusion thresholds, which is 16.33% in the largest connected components and 45.07% in the whole network. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The steady-state transport equation with internal sources and semi-reflective boundaries in a participative medium in slab geometry was analytically and numerically solved in this work. The existence theory in Holder spaces when the sources belong to the space of continuous functions were established, generalizing results of previous works. Also, the Nystrom method combines with singularity removal techniques was applied to produce an algorithm for calculating the scalar flux and criticality. The analytical estimates and the numerical methodology were obtained by looking at integral formulation as a Fredholm equation of the second type. Tabulated numerical results show the efficiency of the proposed methodology. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The currently studied version of the quantum wavelet transform implements the Mallat pyramid algorithm, calculating wavelet and scaling coefficients at lower resolutions from higher ones, via quantum computations. However, the pyramid algorithm cannot replace wavelet transform algorithms, which obtain wavelet coefficients directly from signals. The barrier to implementing quantum versions of wavelet transforms has been the fact that the mapping from sampled signals to wavelet coefficients is not canonically represented with matrices. To solve this problem, we introduce new inner products and norms into the sequence space l 2 (Z ) , based on wavelet sampling theory. We then show that wavelet transform algorithms using L2(R) inner product operations can be implemented in infinite matrix forms, directly mapping discrete function samples to wavelet coefficients. These infinite matrix operators are then converted into finite forms for computational implementation. Thus, via singular value decompositions of these finite matrices, our work allows implementation of the standard wavelet transform with a quantum circuit. Finally, we validate these wavelet matrix algorithms on MRAs involving spline and Coiflet wavelets, illustrating some of our theorems. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Vegetation pattern provides useful signals for vegetation protection and can be identified as an early warning of desertification. In some arid or semi-arid regions, vegetation ab-sorbs water through nonlocal interaction of roots. In this study, we present a vegetation model with nonlocal interaction which is characterized by an integral term with a kernel function. Mathematical analysis provides the conditions for the generation of stationary pattern. Numerical simulations exhibit different spatial distributions of vegetation. Densi-ties of vegetation and water show an inverse relationship at same spatial locations due to water transport mechanism. The results reveal that the interaction intensity and the shape of the kernel function can cause the transition of vegetation pattern. Specifically, the veg-etation biomass increases as the interaction intensity decreases or as the nonlocal inter-action distance increases. We demonstrate that the nonlocal interactions between roots of vegetation is a key mechanism for the formation of vegetation pattern, which provides a theoretical basis for the preservation and restoration of vegetation. (c) 2022 Published by Elsevier Inc.
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Elsevier