For a bounded domain D ⊂ Rn, we study minimizers of the energy functional ∫ D |∇u| dx+ ∫ D∩(Rn−1×{0}) λχ{u>0} + λ χ{u<0} dHn−1, without any sign restriction on the function u. One of the main result states that the free boundaries Γ = ∂{u(·, 0) > 0} and Γ− = ∂{u(·, 0) < 0} never touch. Moreover, using Alexandrov-type reflection technique, we can show that in dimension n = 3 the free boundaries ...

S. Kim, L. G. Huey, R. E. Stickel, R. B. Pierce, G. Chen, M. A. Avery, J. E. Dibb, G. S. Diskin, G. W. Sachse, C. S. McNaughton, A. D. Clarke, B. E. Anderson, and D. R. Blake School of Earth and Atmospheric Sciences, Georgia Institute of Technology, USA NASA Langley Research Center, USA Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, USA Department of Oceanogra...

Necessary and sufficient geometric conditions are given for domains with regular boundary points and edges to be domains of holomorphy provided the remainder boundary subset is of zero Hausdorff 1-codimensional measure.

We study the boundary of the region of weighted analytic centers for linear matrix inequality constraints. Let be the convex subset of R defined by q simultaneous linear matrix inequalities (LMIs) A(x) := A 0 + n ∑ i=1 xiA (j) i 0, j = 1, 2, . . . , q, where A i are symmetric matrices and x ∈ R. Given a strictly positive vector ω = (ω1, ω2, . . . , ωq), the weighted analytic center xac(ω) is th...

Pixel classification algorithms [l] based on temporal information [3] when used in combination are not sufic,ent f o r boundaries produced by a pixel-based classifier are underestimated in the apical zone with respect to ground truth (GT) boundaries. timation developed at the author’s laboratories. The first mation, edge detection algorithms based on spatial inforboundary estimation of the left...

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain Omega subset R(N),A(t)=epsilon(2)DeltaA-A+A(p)/xi(q),x is element of Omega, t>0, tau/Omega/xi(t)=-/Omega/xi+1/xi(s) integral(Omega)A(r)dx, t>0 with the Robin boundary condition epsilon partial differentialA/partial differentialnu+a(A)A=0, x is element of partial differentialOmega, where a(A)>0, the reaction ...

Boundary elements method is well-suited for computational acoustics. The main profit it brings is reduction in number of unknowns compared to FEM. However, application of BEM to sound scattering problems has shown, that this advantage is lost in case of high frequency waves. High frequencies require larger number of elements which contradicts the initial purpose of using BEM in solvers and may ...

A data-set consists of independent observations taken at the nodes of a grid. An unknown boundary partitions the grid into two regions: All the observations coming from a particular region share a common distribution, but the distributions are different for the two different regions. These two distributions are entirely unknown, and the grid is of arbitrary dimension with rectangular mesh. In t...

The mechanical behavior of four rare earth (RE)-Mg-doped Si3N4 ceramics (RE5La, Lu, Y, Yb) with varying grainboundary adhesion has been examined with emphasis on materials containing La and Lu (which represent the extremes of RE ionic radius). Fracture-resistance curves (R-curves) for all ceramics rose very steeply initially, giving them exceptional strength and relative insensitivity to flaw s...