Let Ω be the upper half plane {(x, y) ∈ R, x > 0, y ∈ R}. Define the Laplacian on Ω to be ∆D = ∂ 2 x + (1 + x)∂ 2 y , together with Dirichlet boundary conditions on ∂Ω: one may easily see that Ω, with the metric inherited from ∆D, is a strictly convex domain. We shall prove that, in such a domain Ω, Strichartz estimates for the wave equation suffer losses when compared to the usual case Ω = R, ...

We identify the integrable stopping time τ∗ with minimal L1-distance from the lastpassage time γz associated with a given level z > 0, for an arbitrary nonnegative time-homogeneous transient diffusion X. We demonstrate that τ∗ is in fact the first time that X assumes a value outside a half-open interval [0, r∗). The upper boundary r∗ > z of this interval is characterized either as the solution ...

The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension x̃. We consider the case when the boundary is a random fractal, specifically a self-avoiding walk or the frontier of a Brownian walk, in two dimensions, and show that the boundary scaling behaviour of the...

In this paper, we will give a C 1 , ? C^{1,...

Here R+ denotes the upper half-plane and BMO(R 2 +×R 2 +) is defined to be the dual of the realvariable Hardy space H on the product domain R+×R 2 +. There are several equivalent ways to define this latter space and the reader is referred to [5] for the various characterizations. We will be more interested in the biholomorphic analogue of H, which can be defined in terms of the boundary values ...

Abstract. Let B+ ⊂ GLn(R) denote the subgroup of upper triangular n × nmatrices with positive entries on the main diagonal. A matrix M ∈ B+ is called totally positive if the determinants of all its minors not containing a row or column lying completely under the main diagonal are positive. We give a simple determinantal equation for the boundary of all positive upper triangular matrices in B+.

The intent of this analysis is to explore the influence of thermal radiation paired with variable thermal conductivity on MHD micropolar fluid flow over an upper surface. The novelty of the present model is to consider the fluid flow along an upper horizontal surface of a paraboloid of revolution (uhspr) with the porous medium.  This physical phenomenon is described by a set of coupled...

We consider affine analogues of the isoperimetric inequality in the sense of piecewise linear (PL) manifolds. Given a closed polygon P having n edges, embedded in R, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface embedded in R having P as its geometric boundary. More generally we obtain such bounds for a triangulated (locally flat) ...

We are concerned with the higher-order nonlinear three-point boundary value problems: x n f t, x, x′, . . . , x n−1 , n ≥ 3, with the three point boundary conditions g x a , x′ a , . . . , x n−1 a 0; x i b μi, i 0, 1, . . . , n − 3;h x c , x′ c , . . . , x n−1 c 0, where a < b < c, f : a, c × R → R −∞, ∞ is continuous, g, h : R → R are continuous, andμi ∈ R, i 0, 1, . . . , n − 3 are arbitrary ...

Given a closed polygon P having n edges, embedded in R, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface embedded in R d having P as its geometric boundary. More generally we obtain such bounds for a triangulated (locally flat) PL surface having P as its boundary which is immersed in R and whose interior is disjoint from P . The most ...