We study the behavior near the singularity t=0 of Gowdy metrics. We prove existence of an open dense set of boundary points near which the solution is smoothly “asymptotically velocity term dominated” (AVTD). We show that the set of solutions which are AVTD near the whole boundary and which satisfy a uniformity condition is open in the set of all solutions. We analyse in detail the asymptotic b...

This paper treats near-rings of zero-preserving Lipschitz functions on metric spaces that are also abelian groups, using pointwise addition of functions as addition and composition of functions as multiplication. We identify a condition on the metric ensuring that the set of all such Lipschitz functions is a near-ring, and we investigate the complications that arise from the lack of left distri...

A dynamic programming based procedure for the synthesis of near-optimal controllers for sampled data systems is proposed. The main features of the proposed procedure are the approximation of nonlinear systems by piecewise affine systems, the synthesis of control strategy in the form of a piecewise constant map, and handling of state constraints and exogenous inputs. In order to increase accurac...

A piecewise algebraic curve is defined as the zero contour of a bivariate spline. In this paper, we present a new method for fitting C1 piecewise algebraic curves of degree 2 over type-2 triangulation to the given scattered data. By simultaneously approximating points, associated normals and tangents, and points constraints, the energy term is also considered in the method. Moreover, some examp...

The semiclassical Einstein equations are solved to first order in ǫ = h̄/M for the case of an extreme or nearly extreme Reissner-Nordström black hole perturbed by the vacuum stress-energy of quantized free fields. It is shown that the perturbed solution at first order is not unique; there exists a sequence of solutions with varying values of the position of the event horizon, rh. The smaller the...

The problem of determining a piecewise linear model for 2-dimensional data is commonly encountered by researchers in countless fields of scientific study. Examples of the problem or challenge are that of 2-dimensional digital curves, reliability, and applied mathematics. Nevertheless, in solving the problem, researchers are typically constrained by the lack of prior knowledge of the shape of th...