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pro vyhledávání: '"49K15"'
Autor:
Baek, Jineon
We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area $2.2195\cdots$.
Comment: 119 pages, 21 figures
Comment: 119 pages, 21 figures
Externí odkaz:
http://arxiv.org/abs/2411.19826
We study the problem of finding curves of minimum pointwise-maximum arc-length derivative of curvature, here simply called curves of minimax spirality, among planar curves of fixed length with prescribed endpoints and tangents at the endpoints. We co
Externí odkaz:
http://arxiv.org/abs/2409.08644
Autor:
Chamoun, Samara, Zeidan, Vera
In this paper, the study of nonsmooth optimal control problems (P) involving a controlled sweeping process with three main characteristics is launched. First, the sweeping sets C(t) are nonsmooth, unbounded, time-dependent, uniformly prox-regular, an
Externí odkaz:
http://arxiv.org/abs/2409.07722
In this paper, we consider an optimal control problem of an ordinary differential inclusion governed by the hypergraph Laplacian, which is defined as a subdifferential of a convex function and then is a set-valued operator. We can assure the existenc
Externí odkaz:
http://arxiv.org/abs/2409.00370
Autor:
Deng, Zhipeng
In 1966, Leo Moser introduced the "moving sofa problem," which seeks to determine the largest area of a shape that can be maneuvered through a 90-degree hallway of unit-width. This problem remains unsolved and open yet. In this paper, we employ calcu
Externí odkaz:
http://arxiv.org/abs/2407.02587
Autor:
Glutsyuk, A., Sachkov, Yu.
We study the projection of the left-invariant sub-Riemannian structure on the 3D Heisenberg group $G$ to the Heisenberg 3D nil-manifold $M$ -- the compact homogeneous space of $G$ by the discrete Heisenberg group. First we describe dynamical properti
Externí odkaz:
http://arxiv.org/abs/2406.16065
Autor:
Kunisch, Karl, Troeltzsch, Fredi
For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated optimizat
Externí odkaz:
http://arxiv.org/abs/2405.14775
In this work, we consider the $\mathcal{H}_2$ optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of
Externí odkaz:
http://arxiv.org/abs/2405.05951
We consider the problem of finding curves of minimum pointwise-maximum curvature, i.e., curves of minimax curvature, among planar curves of fixed length with prescribed endpoints and tangents at the endpoints. We reformulate the problem in terms of o
Externí odkaz:
http://arxiv.org/abs/2404.12574
A new optimization framework to design steady equilibrium solutions of the Vlasov-Poisson system by means of external electric fields is presented. This optimization framework requires the minimization of an ensemble functional with Tikhonov regulari
Externí odkaz:
http://arxiv.org/abs/2402.09306