We consider a random walk Wn on the locally free group (or equivalently a signed random heap) with m generators subject to periodic boundary conditions. Let #T (Wn) denote the number of removable elements, which determines the heap's growth rate. We prove that limn→∞ E(#T (Wn)) m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik, Nechaev and Bikbov [4]) that the limit tend...

We study the asymptotic behavior of solutions of the initialboundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing...

The Hamilton-Jacobi approach has proved to be a powerful and elegant method for extracting the skeleton of a shape. The approach is based on the fact that the inward evolving boundary flux is conservative everywhere except at skeletal points. Nonetheless this method appears to overlook the fact that the linear density of the evolving boundary front is not constant where the front is curved. In ...

We prove the existence of globally attracting solutions of viscous Burgers’ equation with periodic boundary conditions on the interval for some particular choices of viscosity and non-autonomous forcing. The attracting solution is periodic if the forcing is periodic. The method is general and can be applied to other similar partial differential equations. The proof is computer assisted.

Cellular automata (CA) rules possessing additive invariants have been studied since early 90’s. The simplest form of an additive invariant is the sum of all site values over a finite lattice with periodic boundary conditions. Rules with such an invariant are known as number-conserving rules, and they exhibit many interesting properties. For example, they can be viewed as systems of interacting ...

In this paper, we study the asymptotic behavior of the solution of a semilinear problem and of a Stokes problem, with periodic data, when the size of the domain increases. In particular, we prove exponential convergence to the solution of the corresponding problem with periodic boundary conditions.

Abstract. This paper is companion to our earlier work [8] (see also announcement [7]). Let M be a closed manifold and Y be an embedded hypersurface, such that there is a decomposition of M = M1 ∪M2 into two manifolds with boundary M1 and M2 , with M1 ∩M2 = Y . In [8] we proved the decomposition formula for detζ∆ the ζ-determinant of a Dirac Laplacian ∆ on M . The contributions coming from M1 an...

The Newhouse phenomenon of infinitely many coexisting periodic attractors is studied in its simplest form. One shows that the corresponding parameter set (the Newhouse set) JN has a strictly positive Hausdorff dimension. This result is stronger than that of Tedeschini-Lalli and Yorke [Commun. Math. Phys. 106, 635 (1986)] concerning the Lebesgue measure of the Newhouse set; and is complementary ...

Boundary labeling deals with annotating features in images such that labels are placed outside of the image and are connected by curves (so-called leaders) to the corresponding features. While boundary labeling has been extensively investigated from an algorithmic perspective, the research on its readability has been neglected. In this paper we present the first formal user study on the readabi...

We study the time-periodic solutions to systems of conservation laws with ellipticity. It is shown that under time-periodic boundary condition, the system admits at least one global time-periodic solution bounded uniformly with the same period.