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Applied mathematics and computation
Elsevier [etc.]
Applied mathematics and computation

Elsevier [etc.]

0096-3003

Applied mathematics and computation/Journal Applied mathematics and computationSCIISTPEIAHCI
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    On eigenvalues and the energy of dendrimer trees

    Xu, HengmengYan, Weigen
    7页
    查看更多>>摘要：A dendrimer tree D-n,D-k is a rooted tree with root v(0) in which the root vertex v(0) has k children, the vertices u satisfying the distance d(v(0), u) = i have k - 1 children for 1 <= i <= n - 1, and the vertices u such that d(v(0) , u) = n are pendant vertices. In this paper, we obtain almost all of eigenvalues of D-n,D-k except n + 1 eigenvalues which are just the roots of the matching polynomial of a weighted path with n + 1 vertices v(0), v(1), ..., v(n) and n edges (v(0), v(1)), (v(1), v(2)), (v(2), v(3)) ..., (v(n-1), v(n)), of weights equal to k, k - 1, k - 1, ..., k - 1, and we obtain a formula to compute the energy of D-n,D-k. (C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Compound binomial risk model in a Markovian environment with capital cost and the calculation algorithm

    Xiao, Lin
    26页
    查看更多>>摘要：The operation of insurance institution is often affected by random environment, potential opportunity cost of capital or inflation. Considering this phenomenon, this paper establishes a new Markovian environment compound binomial risk model with capital cost, abbreviated as RMCM model. The new RMCM model is a complex recursive model which is difficult to calculate. To calculate the results in many future periods at one time, it is necessary to design an algorithm that can greatly improve calculation efficiency. One of the aims of this study is to conduct an analysis of the recursive algorithm, divide and conquer strategy and other algorithm theories to, designs a new MCPRAM-algorithm that is able to solve the calculation of this kind of recursive model with high complexity, multiple cycles and multiple periods, significantly improving the practical application value of the actuarial model. Taking aviation accident insurance as an example, the measurement methods of actuarial quantity in the model are explained statistically, and the calculation algorithm of conditional ruin probability is elaborated in detail. The conditional ruin probabilities of 60 periods under different operating conditions and different environment states were obtained and then compared and analyzed. RMCM has a wide range of applications and is suitable for describing the insurance products with low premium, small compensation probability; large claim amount and one-off compensation in a random market environment. The RMCM model proposed in this paper clarifies the risk of insurance institutions, compares the calculation of seven groups of parameter data, and obtains better parameters to control the bankruptcy risk at about 5 % in the next five years. Parameter data reference and MCPRAM-algorithm can be used to design and develop new insurance products in a random environment, and provide valuable decision support for the scientific operation and management of insurance institutions.(c) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Finite-time optimal tracking control using augmented error system method

    Wang, DiLiu, CanDing, DaweiGao, Suixiang...
    10页
    查看更多>>摘要：This paper proposes a design method of finite-time optimal tracking controller for quadratic performance index. A novel nonlinear finite-time optimal controller is designed to solve the finite-time optimal tracking control problem for linear system. By applying augmented error system method and finite-time optimal state feedback control, sufficient conditions involving V-function are obtained, and eventually, a nonlinear controller based on the V-function is derived. In addition, the construction of a specific V-function satisfying those conditions is discussed in detail. The nonlinear controller which we introduced makes closed-loop system finite-time stable, so that the tracking error of original system converges in finite time. The simulation example illustrates the efficiency of our results. (C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Theoretical breakthrough in the dynamics of a jet in a free-stream flow around a corner

    Jafarimoghaddam, AminRosca, AlinPop, Ioan
    12页
    查看更多>>摘要：For the first time, the laminar jet in a free-stream flow around a corner with/without a moving wall condition (as it assists the flow) is studied theoretically. The corner may contract the streamlines or expand them depending on the angle of inclination. In the context of incompressibility, it is presented a composite non-similar transformation of the Navier-Stokes (N-S) equations in Cartesian space to approximately decipher the nature of the boundary layer flow over the entire physical domain; i.e. 0 <= x, y < infinity. The transformed Partial Differential Equations (PDEs) are then solved by an in-house MATLAB code, which employs an implicit algorithm of a tridiagonal form with quasi-linearization technique. For a stationary wall, as the negative angle of the corner meets Falkner-Skan (F-S) limitation and expands beyond, the predictive model starts to show a critical location, which reveals directly the flow separation point. This critical location moves toward the jet origin as the angle of inclination becomes more negative. Here, these locations are extracted as a function of the inclination parameter in order to manifest the suitability of a jet to delay boundary layer separation. A similar scenario also applies to the moving wall case. In this case, it was recorded that a moving wall condition delays separation for a considerable distance. It should be pointed out that up to date, there is no theoretical investigation on this specific flow geometry despite the many associated applications; and the limited available reports on an analogous flow geometry are those from the Computational Fluid Dynamics (CFD) and on a case by case basis. More specifically, the present geometry is quite similar to the flow passing the way down to the trailing edge of an airfoil, with a jet generator mechanism such as Dielectric Barrier Discharge (DBD) plasma actuator to delay flow separation on the backside of the airfoil. Here, by the use of the theoretical non-similarity concept empowered by some recent advancements (see Jafarimoghaddam, 2020 and Jafarimoghaddam, 2021), the fundamental problem of a jet discharged in the lower boundary of a freestream flow over a wedge is successfully solved. This theoretical breakthrough suggests promising avenues for the future design of airfoils with moving parts/flaps as an innovative step forward to enhance maneuverability of the flying objects. (C) 2022 Published by Elsevier Inc.
      原文链接:
    • NSTL
    • Elsevier

    Delay-probability-dependent state estimation for neural networks with hybrid delays

    Qian, WeiLiu, HaiboZhao, YunjiLi, Yalong...
    12页
    查看更多>>摘要：This dissertation studies the delay-probability-dependent Hoc, state estimation issue of neural networks (NNs) with hybrid delays. First, more general system model and state estimator are established by considering discrete delay, distributed delay and probability distribution of time delays. Second, a innovative Lyapunov-Krasovskii functional (LKF) containing augmented non-integral and single-integral quadratic terms is put forward, which can inflect internal connections of multiple functional terms. Meanwhile, in order to handle the infinitesimal operators of LKF effectively, generalized free-weighting-matrix integral inequality (GFWMII) is chosen to cooperate with wirtinger-based inequality. As a consequence, less conservative criteria are obtained, which ensure that the considered system is asymptotically mean-square stable with a desired H-infinity, performance. Finally, two simulated examples are displayed to bring out the advantage of the achieved approach. (C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements

    Moskovka, AlexejValdman, Jan
    18页
    查看更多>>摘要：Nonlinear energy functionals appearing in the calculus of variations can be discretized by the finite element (FE) method and formulated as a sum of energy contributions from local elements. A fast evaluation of energy functionals containing the first order gradient terms is a central part of this contribution. We describe a vectorized implementation using the simplest linear nodal (P1) elements in which all energy contributions are evaluated all at once without the loop over triangular or tetrahedral elements. Furthermore, in connection to the first-order optimization methods, the discrete gradient of energy functional is as-sembled in a way that the gradient components are evaluated over all degrees of freedom all at once. The key ingredient is the vectorization of exact or approximate energy gradi-ents over nodal patches. It leads to a time-efficient implementation at higher memory-cost. Provided codes in MATLAB related to 2D/3D hyperelasticity and 2D p-Laplacian problem are available for download and structured in a way it can be easily extended to other types of vector or scalar forms of energies.(c) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    An H-1-Galerkin mixed finite element method for identification of time dependent parameters in parabolic problems

    Khebchareon, MorrakotPany, Ambit KumarPani, Amiya K.
    14页
    查看更多>>摘要：A direct method of identification of time dependent parameters in a linear parabolic boundary value problem with over-specified total internal energy involves the flux at the boundary, and an H-1 mixed formulation seems to be more suitable than the standard methods for such class of nonlocal problems. Therefore, this paper develops and analyses an H-1-Galerkin mixed finite element method. Optimal error estimates in both primary and flux variables are derived in semidiscrete case. Moreover, a priori error estimate for the parameters is established. Based on linearised backward Euler method, a completely discrete scheme is proposed and optimal error analysis is derived. The results of the numerical experiments show the efficacy of the proposed method and confirm our theoretical results. (C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Continuous data assimilation and long-time accuracy in a C-0 interior penalty method for the Cahn-Hilliard equation

    Diegel, Amanda E.Rebholz, Leo G.
    22页
    查看更多>>摘要：We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C-0 interior penalty spatial discretization of the fourth order Cahn-Hilliard equations, together with a backward Euler temporal discretization. We prove the method is long time stable and long time accurate, for arbitrarily inaccurate initial conditions, provided enough data measurements are incorporated into the simulation. Numerical experiments illustrate the effectiveness of the method on a benchmark test problem.(C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line

    Okrasinska-Plociniczak, HannaPlociniczak, Lukasz
    19页
    查看更多>>摘要：Many physical, biological, and economical systems exhibit various memory effects due to which their present state depends on the history of the whole evolution. Combined with the nonlinearity of the process these phenomena pose serious difficulties in both analytical and numerical treatment. We investigate a time-fractional porous medium equation that has proved to be important in many applications, notably in hydrology and material sciences. We show that solutions of the free boundary Dirichlet, Neumann, and Robin problems on the half-line satisfy a Volterra integral equation with a non-Lipschitz nonlinearity. Based on this result we prove existence, uniqueness, and construct a family of numerical methods that solve these equations outperforming the usual finite difference approach. Moreover, we prove the convergence of these methods and support the theory with several numerical examples. (C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier

    Event-triggered anti-disturbance tracking control for semi-Markovian jump systems with exogenous disturbances and input saturation

    Zhang, XiaoliYi, YangShen, MouquanWang, Qin...
    24页
    查看更多>>摘要：Under the frame of event-triggered mechanism, this paper proposes a novel multi-objective anti-disturbance control algorithm for a class of typical semi-Markovian jump systems (S-MJSs) suffering with exogenous disturbances and input saturation. Different from those existing results of S-MJSs, the multi-objective control requirements need to be achieved. Firstly, both the T-S disturbance models and the corresponding disturbance observer (DO) are successively introduced to dynamically estimate those irregular disturbances. Secondly, by combining the saturated convex hull description with the designed event-triggered condition, an event-triggered anti-disturbance controller is designed to achieve effective monitoring of the augmented S-MJSs. Furthermore, not only the stochastic stability of closed-loop S-MJSs and disturbance estimation systems, but also the state/output constraints can be simultaneously guaranteed based on the designed asthenic infinitesimal generator optimization algorithm. Meanwhile, the dynamical tracking error is verified to converge to zero and the Zeno phenomenon can also be effectively avoided. Finally, simulation results for different types of disturbances are given to verify the meaning of the proposed algorithm. (C) 2022 Elsevier Inc. All rights reserved.
      原文链接:
    • NSTL
    • Elsevier