查看更多>>摘要：A B S T R A C T The resolving equations for mathematical model of the stress-strain state of a curved thin walled cylinder were derived. This model is based on Koiter's-Vlasov's theory of moment shells. A method was proposed for approximate solution of a mathematical model equations on the basis of a sequential asymptotic expansion of unknown functions into a small parameter series and representation of the expansion coefficients in the form of Fourier series. Using this method, a one-dimensional statement of the problem was obtained. Limitations on parameters in the shell equations are indicated for which such problem transformation is possible. For the mathematical model of the curved thin-walled cylinder one-dimensional equations in two different formulations were obtained. Conditions determining applicability limits of the constructed one-dimensional mathematical models were proved. Numerical experiments were carried out and it was found that the constructed one-dimensional mathematical model approximates the original problem with high accuracy. From an applied point of view, curved thin-walled cylinder simulates a pipeline section.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, energy-preserving mixed finite element methods corresponding to finite element exterior calculus are constructed for the first-order formulation of the elastic wave equation. The semi-discrete method conserves the system's energies exactly. A full-discrete method employing the Crank-Nicolson method, preserves energies exactly. In addition, optimal convergence orders are obtained based on a projection-based quasi-interpolation operator. Numerical experiments confirm the theoretical results.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Based on the approximate finite-time Gramians, this paper studies model order reduction method of port-Hamiltonian systems with inhomogeneous initial conditions. The approximate controllability and observability Gramians on the finite-time interval [T-1 , T-2] (0 <= T-1 < T-2 < infinity) can be obtained by the shifted Legendre polynomials and the reduced port Hamiltonian system is constructed by the union of dominant eigenspaces. Since the port Hamiltonian system is square, the cross Gramian on the time interval [T-1 , T-2] can also be approximated by using the shifted Legendre polynomials. Then, the truncated singular value decomposition of the approximate finite-time cross Gramian is carried out to obtain the projection matrix. Finally, the proposed methods are verified by two numerical examples. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper studies the time-varying formation for multiple unmanned surface vessels (USVs) with heterogeneous hydrodynamics under actuator attacks. Firstly, the distributed time-varying formation is achieved under a formation feasibility condition. Secondly, an extended state observer (ESO) is devised to estimate the heterogeneous hydrodynamics and the external time-varying disturbance of multiple USVs, as well as the unknown control input of the leader USV simultaneously based on the neighbor USVs' relative information; Thirdly, a distributed security controller is jointly designed based on the relative information of neighbors with the presence of an additive adaptive correction term to suppress the effects of actuator attacks instead of redesigning the nominal controller; Finally, the effectiveness of the derived theoretical method is demonstrated by simulation results.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This paper presents FFT bifurcation as a tool for investigating complex dynamics. Firstly, two well-known chaotic systems (Rossler and Lorenz) are discussed from the frequency viewpoint. Then, both discrete-time and continuous-time systems are studied. Various systems with different properties are discussed. In discrete-time systems, Logistic map and a biological map are investigated. For continuous-time systems, a system with a stable equilibrium, forced van der Pol system, and a system with a line of equilibria are discussed. For each system under investigation, the proposed FFT bifurcation diagrams are compared with the conventional bifurcation diagrams, showing some interesting information uncovered by the FFT bifurcation. For periodic trajectories, the FFT bifurcations show high power at the dominant frequency and harmonics. By doubling the periods, their dominant frequencies are halved, and more harmonics emerge in the studied frequency intervals. For the chaotic dynamics, the FFT bifurcation shows a wideband power spectrum. The FFT bifurcation shows interesting results in comparison to conventional bifurcation diagrams. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let G be a connected graph, S subset of & nbsp;& nbsp;V(G) and |S| >=& nbsp;2 , a tree T in G is called an S-tree if S subset of & nbsp;& nbsp;V(T). Two S-trees T-1 and T-2 are called internally disjoint if E(T-1) & cap;& nbsp;E(T-2) = empty set & nbsp;and V(T-1) & cap;& nbsp;V(T-2) = S. For an integer r with 2 <= r & nbsp;<=& nbsp;n, the generalized r-connectivity kappa(r)(G) of a graph G is defined as kappa(r)(G) = min{kappa(G)(S) |S subset of & nbsp;V(G) and |S| = r} , where kappa(G)(S) denotes the maximum number k of internally disjoint S-trees in G . In this paper, we consider the generalized 4-connectivity of the line graph L(K-m,K-n) and total graph T(K-m,K-n) of the complete bipartite graph K-m,K-n with 2 <=& nbsp;m <=& nbsp;n. The results that kappa(4)(L(K-m,K-n)) = m + n - 3 for 2 <= m <= 3 and kappa(4)(L(K-m,K-n)) = m + n - 4 for m >=& nbsp;4 are obtained by determining kappa(4)(K-m X K-n). In addition, we obtain that kappa(4)(T(K-m,K-m)) = delta(T(K-m,K-m)) - 2 = 2 m - 2 for m >=& nbsp;2 . These results improve the known results about the generalized 3-connectivity of L(K-m,K-n) and T(K-m,K-m) in [Appl. Math. Comput. 347 (2019) 645-652]. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This study considers an efficient two-step stabilized finite element algorithm for the simulation of Smagorinsky model, which involves solving a stabilized nonlinear Smagorinsky problem by the lowest equal-order P 1 - P 1 finite elements and solving a stabilized linear Smagorinsky problem by the quadratic equal-order P 2 - P 2 finite elements. We theoretically and numerically show that the present two-step algorithm can provide an approximate solution with basically the same accuracy as that of solving the stabilized P 2 - P 2 finite element method, and represent a reduction in CPU time.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is O (1 /N-4) and the complexity is O(MN log N ) , where N is the number of grid points and M is the number of observation dates. Besides Black-Scholes, our method is also applicable to more general frameworks such as Merton's jump diffusion model. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, all connected locally primitive symmetric graphs of valency 2 r admitting a transitive alternating automorphism group are determined, where r is odd prime. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the preconditioned TBiCOR and TCORS methods are presented for solving the Sylvester tensor equation. A tensor Lanczos L -Biorthogonalization algorithm (TLB) is derived for solving the Sylvester tensor equation. Two improved TLB methods are presented. One is the biconjugate L-orthogonal residual algorithm in tensor form (TBiCOR), which implements the LU decomposition for the triangular coefficient matrix derived by the TLB method. The other is the conjugate L-orthogonal residual squared algorithm in tensor form (TCORS), which introduces a square operator to the residual of the TBiCOR algorithm. A preconditioner based on the nearest Kronecker product is used to accelerate the TBiCOR and TCORS algorithms, and we obtain the preconditioned TBiCOR algorithm (PTBiCOR) and preconditioned TCORS algorithm (PTCORS). The proposed algorithms are proved to be convergent within finite steps of iteration without roundoff errors. Several examples illustrate that the preconditioned TBiCOR and TCORS algorithms present excellent convergence.(c) 2022 Elsevier Inc. All rights reserved.
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