We study zero-temperature Ising Glauber Dynamics, on 2D slabs of thickness k ≥ 2. In this model, ±1-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for k = 2 under free boundary conditions and for k = 2 or 3 under periodic boundary conditions. For thicker slabs there are sites ...

We investigate the condition number of the matrices that appear in the boundary element method. In particular we consider the Laplace equation with mixed boundary conditions. For Dirichlet boundary conditions, the condition number of the system matrix increases linearly with the number of boundary elements. We extend the research and search for a relation between the condition number and the nu...

We revisit the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional space, our aim is to acquire a classification boundary between the classes with labels. Motivated by the principal flow [14], a curve that moves along a path of the maximum variation of th...

Several methods have been proposed to reduce boundary artifacts in image deblurring. Some of those methods impose certain assumptions on image pixels outside the field-of-view; the most important of these assume reflective or anti-reflective boundary conditions. Boundary condition methods, including reflective and anti-reflective ones, however, often fail to reduce boundary artifacts, and, in s...

We show how to stabilize the uniform oscillations of the complex Ginzburg–Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful study of the spectrum of the linearized operator.

where η is a N(0, 1) random variable independent of B and L denotes the convergence in law. This result has been first proved in [3] by using the method of moments. In [4] we gave a simple proof based on Clark-Ocone formula and an asymptotic version of Knight’s theorem (see Revuz and Yor [9], Theorem (2.3), page 524). Another simple proof of this result with the techniques of stochastic analysi...

The significance of 2π is that it is a cluster point of the length spectrum from the left (t < 2π), as described in more detail below. In brief, the length spectrum is the closure of the set of lengths of periodic geodesics. The number 2π represents the length of the (generalized) geodesic that follows the circumference of the circle. The number 8 is the geodesic that follows a diameter of the ...

We study convergence of a boundary integral method for 3D interfacial flow with surface tension when the fluid velocity is given by Darcy’s Law. The method is closely related to a previous method developed and implemented by Ambrose, Siegel, and Tlupova, in which one of the main ideas is the use of an isothermal parameterization of the free surface. We prove convergence by proving consistency a...

We consider one dimensional p-Laplacian eigenvalue problems of the form −∆pu = (λ− q)|u|p−1sgnu, on (0, b), together with periodic or separated boundary conditions, where p > 1, ∆p is the p-Laplacian, q ∈ C1[0, b], and b > 0, λ ∈ R. It will be shown that when p 6= 2, the structure of the spectrum in the general periodic case (that is, with q 6= 0 and periodic boundary conditions), can be comple...

Stopping games (without simultaneous stopping) are sequential games in which at every stage one of the players is chosen, who decides whether to continue the interaction or stop it, whereby a terminal payoff vector is obtained. Periodic stopping games are stopping games in which both of the processes that define it, the payoff process as well as the process by which players are chosen, are peri...