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Добірка наукової літератури з теми "Non-Convex Hamiltonian"

Автор: Grafiati

Опубліковано: 18 травня 2024

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Статті в журналах з теми "Non-Convex Hamiltonian"

Ishii, Hitoshi. "The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: a counterexample to the full convergence." Mathematics in Engineering 5, no. 4 (2023): 1–10. http://dx.doi.org/10.3934/mine.2023072.

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<abstract>In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian in the gradient variable, for which the full convergence of the solutions does not hold as the discount factor tends to zero. We give here an explicit example of nonlinear monotone systems of Hamilton-Jacobi equations having convex Hamiltonians in the gradient variable, for which the full convergence of the solutions fails as the discount factor goes to zero.</abstract>

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Hayat, Sakander, Muhammad Yasir Hayat Malik, Ali Ahmad, Suliman Khan, Faisal Yousafzai, and Roslan Hasni. "On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes." Mathematical Problems in Engineering 2021 (July 17, 2021): 1–18. http://dx.doi.org/10.1155/2021/5553216.

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A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important applications in chemistry. Checking whether a graph is Hamilton-connected and computing the detour index of an arbitrary graph are both NP-complete problems. In this paper, we study these problems simultaneously for certain families of convex polytopes. We construct two infinite families of Hamilton-connected convex polytopes. Hamilton-connectivity is shown by constructing Hamiltonian paths between any pair of vertices. We then use the Hamilton-connectivity to compute the detour index of these families. A family of non-Hamilton-connected convex polytopes has also been constructed to show that not all convex polytope families are Hamilton-connected.

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Pittman, S. M., E. Tannenbaum, and E. J. Heller. "Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian." Journal of Chemical Physics 145, no. 5 (August 7, 2016): 054303. http://dx.doi.org/10.1063/1.4960134.

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Hayat, Sakander, Asad Khan, Suliman Khan, and Jia-Bao Liu. "Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index." Complexity 2021 (January 23, 2021): 1–23. http://dx.doi.org/10.1155/2021/6684784.

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A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index.

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CONTRERAS, GONZALO, and RENATO ITURRIAGA. "Convex Hamiltonians without conjugate points." Ergodic Theory and Dynamical Systems 19, no. 4 (August 1999): 901–52. http://dx.doi.org/10.1017/s014338579913387x.

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We construct the Green bundles for an energy level without conjugate points of a convex Hamiltonian. In this case we give a formula for the metric entropy of the Liouville measure and prove that the exponential map is a local diffeomorphism. We prove that the Hamiltonian flow is Anosov if and only if the Green bundles are transversal. Using the Clebsch transformation of the index form we prove that if the unique minimizing measure of a generic Lagrangian is supported on a periodic orbit, then it is a hyperbolic periodic orbit.We also show some examples of differences with the behaviour of a geodesic flow without conjugate points, namely: (non-contact) flows and periodic orbits without invariant transversal bundles, segments without conjugate points but with crossing solutions and non-surjective exponential maps.

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Zhou, Min, and Binggui Zhong. "Regions of applicability of Aubry-Mather Theory for non-convex Hamiltonian." Chinese Annals of Mathematics, Series B 32, no. 4 (July 2011): 605–14. http://dx.doi.org/10.1007/s11401-011-0654-3.

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You, Bo, Zhi Li, Liang Ding, Haibo Gao, and Jiazhong Xu. "A new optimization-driven path planning method with probabilistic completeness for wheeled mobile robots." Measurement and Control 52, no. 5-6 (April 15, 2019): 317–25. http://dx.doi.org/10.1177/0020294019836127.

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Wheeled mobile robots are widely utilized for environment-exploring tasks both on earth and in space. As a basis for global path planning tasks for wheeled mobile robots, in this study we propose a method for establishing an energy-based cost map. Then, we utilize an improved dual covariant Hamiltonian optimization for motion planning method, to perform point-to-region path planning in energy-based maps. The method is capable of efficiently handling high-dimensional path planning tasks with non-convex cost functions through applying a robust active set algorithm, that is, non-monotone gradient projection algorithm. To solve the problem that the path planning process is locked in weak minima or non-convergence, we propose a randomized variant of the improved dual covariant Hamiltonian optimization for motion planning based on simulated annealing and Hamiltonian Monte Carlo methods. The results of simulations demonstrate that the final paths generated can be time efficient, energy efficient and smooth. And the probabilistic completeness of the method is guaranteed.

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Cordaro, Giuseppe. "Existence and location of periodic solutions to convex and non coercive Hamiltonian systems." Discrete & Continuous Dynamical Systems - A 12, no. 5 (2005): 983–96. http://dx.doi.org/10.3934/dcds.2005.12.983.

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Grotta-Ragazzo, C., and Pedro A. S. Salomão. "Global surfaces of section in non-regular convex energy levels of Hamiltonian systems." Mathematische Zeitschrift 255, no. 2 (August 22, 2006): 323–34. http://dx.doi.org/10.1007/s00209-006-0026-y.

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Giuliani, Filippo. "Transfers of energy through fast diffusion channels in some resonant PDEs on the circle." Discrete & Continuous Dynamical Systems 41, no. 11 (2021): 5057. http://dx.doi.org/10.3934/dcds.2021068.

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In this paper we consider two classes of resonant Hamiltonian PDEs on the circle with non-convex (respect to actions) first order resonant Hamiltonian. We show that, for appropriate choices of the nonlinearities we can find time-independent linear potentials that enable the construction of solutions that undergo a prescribed growth in the Sobolev norms. The solutions that we provide follow closely the orbits of a nonlinear resonant model, which is a good approximation of the full equation. The non-convexity of the resonant Hamiltonian allows the existence of fast diffusion channels along which the orbits of the resonant model experience a large drift in the actions in the optimal time. This phenomenon induces a transfer of energy among the Fourier modes of the solutions, which in turn is responsible for the growth of higher order Sobolev norms.

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