查看更多>>摘要：This article deals with the development of an optimized third-derivative hybrid block method for integrating general second order two-point boundary value problems (BVPs) subject to different types of boundary conditions (BCs) such as Dirichlet, Neumann or Robin. A purely interpolation and collocation approach has been used in order to develop the method. A constructive approach has been applied in the development of the method to consider two off-step optimal points among an infinite number of possible choices in a two-step block corresponding to a generic interval of the form [x(n),x(n+2)]. The obtained method simultaneously produces an approximate solution over the entire integration interval. Some numerical experiments have been presented that show the good performance of the presented scheme. (c)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Assume non-zero real numbers kappa(1),..., kappa(6) are not all negative. Assume also kappa(1)/kappa(2) is algebraic and not rational, the sequence G is well-spaced and nu > 0. In this work, we showed that the quantity of gamma is an element of G satisfying 1 <= gamma <= X and making the Diophantine inequality |kappa(1)p(1)(2) +kappa(2) p(2)(2) +kappa(3) p(3) (3) +kappa(4)p(4)(3) +kappa(5) p(5)(4) +kappa(6) p(6)(4) - gamma |< gamma(-nu) unsolvable in primes p(1),..., p(6) is not more than O(X-6/7 +2 nu+is an element of) for any epsilon > 0. (C) 2022 Elsevier Inc. All rights reserved.
Kamal, M. A. S.Pu, ZiyuanBakibillah, A. S. M.Tan, Yong Hwa...
13页
查看更多>>摘要：Traffic density is a crucial indicator of traffic congestion, but measuring it directly is often infeasible and hence, it is usually estimated based on other measurements. However, a challenge in measuring traffic parameters is the high probability of sensor failure, which results in missing measurement or missing data. To overcome this difficulty, in this paper, we propose a novel adaptive-R extended Kalman filter (AREKF) combined with a modelbased data imputation technique to estimate traffic density. We show analytically that the AREKF is able to accurately estimate the density even when the noise covariance matrices are not accurately known. Microscopic traffic simulations demonstrated the efficacy of the AREKF, where the estimated density is fed into a real-time ramp metering control algorithm to control vehicle flow on a merging road, which is highly susceptible to traffic congestion. The results show that the proposed AREKF with data imputation is able to accurately estimate the traffic density even when data is missing, and the ramp-metering controller significantly improves the traffic flow and thus, alleviates congestion. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：A semilinear second-order system of m (> 2) reaction-diffusion equations is analyzed in a singularly-perturbed regime. In these equations, the right-hand side (source term) has a discontinuity at a point inside the domain, and the coefficient of the second-order derivative is a positive parameter. These parameters can be arbitrarily small and different in magnitude; this causes to form the boundary layers in the solution which may interact and overlap inside the domain. Due to discontinuity in the source term, the solution may also exhibit layers in the interior of the domain. The decomposition of the solution has been made to obtain sharper bounds on its derivatives. A higher-order finite difference scheme is constructed using an appropriate generalized Shishkin mesh and established that the computed solution is almost fourth-order parameter-uniform. Numerical experiments are performed to validate the theoretical findings. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the issue of finite-time consensus tracking control (CTC) is discussed for uncertain nonlinear multi-agent systems (MASs) with prescribed performance and input saturation. By constructing a finite-time performance function (FTPF), the tracking errors converge to a predefined attenuation range within finite-time. By using tanh(& BULL;) function and mathematical transformation, the effect of input saturation is solved. The unmodeled dynamics and dynamic disturbances of the system are solved by means of measurable dynamic signals. Through the Young's inequality and the properties of Gaussian function, the coupling problem between multi-agents and the system controller design problem in non strict feedback form are successfully dealt with. Furthermore, a finite-time adaptive neural controller is designed based on command filter, which not only guarantees the finite-time stability of the system, but also makes the tracking errors reach a predefined bound in a finite-time. Stability analysis proves that the proposed method is feasible, and simulation verifies its effectiveness. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
Thumma, ThirupathiMishra, S. R.Abbas, M. AliBhatti, M. M....
16页
查看更多>>摘要：This paper numerically explores the effects of nonlinear density temperature, non-uniform heat source/sink on 3D Maxwell nanofluid flow over a stretching sheet. The combined leading velocity, thermal and species boundary layer balances transformed the problem to a class of coupled non-linear ODEs by similarity conversions subject to suitable preconditions. The dimensionless fine modelled BVP is worked out by adopting Runge-Kutta fourth-order method integrated with the shooting technique. A comprehensive study on the influence of significant thermo-physical non-dimensional factors controlling dispersals of flow characteristics is conducted. The computed results of friction factor, Nusselt and Sherwood number values for selected parameters are presented. Verification of numeric solutions is accomplished with specific circumstances published in earlier reported outcomes, an effective association is witnessed. Present analysis is of great significant interests in the cooling of metallic plates, polishing of artificial heart valves, enhancing oil recovery and separation processes in chemical industries and in petroleum extraction. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：A fractional-order mathematical model of a large-scale GRN is presented, focusing on the positivity of solutions and on the stability analysis of equilibria based on Matignon's theorem. With special emphasis on cyclic GRNs, necessary and sufficient conditions are obtained in terms of inequalities involving the system's parameters and the fractional order, which guarantee the stability of equilibrium points. Based on the stability analysis, the critical values of the fractional order for which Hopf-type bifurcations may occur are detected. In this context, it is shown that oscillatory behavior due to a Hopf-type bifurcation (considering the fractional order as bifurcation parameter) is expected only in the case of an odd number of repressive genes. Numerical examples are given in order to demonstrate the usefulness of the proposed results and to exemplify the effect of the fractional order on the dynamics of cyclic GRNs, additionally revealing that period-doubling bifurcations of limit cycles may also occur in sufficiently large cyclic GRNs. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This primer article focuses on the representation of solutions and finite-time stability of impulsive first-order delay differential systems. We define delayed matrix function with impulses and use variation of parameters to obtain a representation of solutions of linear systems with impulse effects. The famous classical Grownwall inequalities and properties of delayed matrix exponential with impulses are used to develop sufficient conditions for finite-time stability. In the end, we provide some examples to support the results. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：For a connected graph G , let e(G) be the number of its distinct eigenvalues and d be the diameter. It is well known that e(G) >= d + 1 . This shows eta <= n - d, where eta and n denote the nullity and the order of G , respectively. A graph is called minimal if e(G) = d + 1 . In this paper, we characterize all trees satisfying eta(T) = n - d or n - d - 1 . Applying this re-sult, we prove that a caterpillar is minimal if and only if it is a path or an even caterpillar, which extends a result by Aouchiche and Hansen. Furthermore, we completely character-ize all connected graphs satisfying eta = n - d. For any non-zero eigenvalue of a tree, a sharp upper bound of its multiplicity involving the matching number and the diameter is pro-vided. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：A symmetric digraph (G) over left right arrow arises from a simple graph G by substituting each edge uv by a pair of opposite arcs (uv) over right arrow, (vu) over right arrow An arc-colouring cof.. G is distinguishing if the only automorphism of (G) over left right arrow preserving cis the identity. We study four types of proper arc-colourings of (G) over left right arrow corresponding to four definitions of adjacency of arcs. For each type, we investigate the distinguishing chromatic index of (G) over left right arrow, i.e. the least number of colours in a distinguishing proper colouring of (G) over left right arrow. We also determine tight bounds for chromatic indices of (G) over left right arrow, i.e. for the least numbers of colours in each type of proper colourings. Colourings of arcs of a symmetric digraph (G) over left right arrow are equivalent to colourings of halfedges of the graph G, which have applications in computer science. (C) 2022 Elsevier Inc. All rights reserved.
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