相关论文: Open Problem: Two Riddles in Heavy-Ball Dynamics

The Harrow-Hassidim-Lloyd (HHL) algorithm offers exponential speedup for solving the quantum linear-system problem. But some caveats for the speedup could be hard to met. One of the difficulties is the encoding bottleneck, i.e., the…

The goal of the present work is to revisit the cranking formula of the vibrational parameters, especially its well known drawbacks. The latter can be summarized as spurious resonances or singularities in the behavior of the mass parameters…

We study, by numerical simulations and semi-rigorous arguments, a two-parameter family of convex, two-dimensional billiard tables, generalizing the one-parameter class of oval billiards of Benettin--Strelcyn [Phys. Rev. A 17, 773 (1978)].…

We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…

We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…

We consider the system of N (\ge 2) elastically colliding hard balls with masses m_1,..., m_N, radius r, moving uniformly in the flat torus T_L^{\nu}= R^\nu/L \cdot Z^\nu, \nu \ge 2. It is proved here that the relevant Lyapunov exponents of…

In this paper, we derive sufficient conditions on drift matrices under which block-diagonal solutions to Lyapunov inequalities exist. The motivation for the problem comes from a recently proposed basis pursuit algorithm. In particular, this…

We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…

In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit…

First-order optimization methods for nonconvex functions with Lipschitz continuous gradient and Hessian have been extensively studied. State-of-the-art methods for finding an $\varepsilon$-stationary point within $O(\varepsilon^{-{7/4}})$…

The paper considers approaches to saddle point problems with a two-sided variant of the Polyak-Lojasievich condition based on the gradient method with inexact information and proposes a stopping rule based on the smallness of the norm of…

Iterative projection methods may become trapped at non-solutions when the constraint sets are nonconvex. Two kinds of parameters are available to help avoid this behavior and this study gives examples of both. The first kind of parameter,…

The goal is to modify the known method of mirror descent (MD), proposed by A.S. Nemirovsky and D.B. Yudin in 1979. The paper shows the idea of a new, so-called inertial MD method with the example of a deterministic optimization problem in…

In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…

We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which…

The aim in packing problems is to decide if a given set of pieces can be placed inside a given container. A packing problem is defined by the types of pieces and containers to be handled, and the motions that are allowed to move the pieces.…

A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…

We wish to draw attention to an interesting and promising interaction of two theories. On the one hand, it is the theory of \textbf{pseudo-triangulations} which was useful for implicit solution of thecarpenter's rule problem and proved…

The two full body problem concerns the dynamics of two spatially extended rigid bodies (e.g. rocky asteroids) subject to mutual gravitational interaction. In this note we deduce the Euler-Poincare and Hamiltonian equations of motion using…

We study the global flow of the anisotropic Manev problem, which describes the planar motion of two bodies under the influence of an anisotropic Newtonian potential with a relativistic correction term. We first find all the heteroclinic…