We prove that a smooth compact immersed submanifold of codimension 2 in R, n ≥ 3, bounds at most finitely many topologically distinct compact nonnegatively curved hypersurfaces. Analogous results for noncompact fillings are obtained as well. On the other hand, we show that these topological finiteness theorems may not hold if the prescribed boundary is not sufficiently regular, e.g., C. In part...

The Moving Pictures Show is a contemporary Australian ‘silent’ film company that screens films produced in the period from 1912 to 1929, with a 9-piece orchestral accompaniment. This article explores the ways in which music is chosen for the show both to heighten the audience’s aesthetic experience of the film and to abide by historical practice. It also describes the ways in which improvisatio...

In this paper, we propose a wide-viewing-angle three-dimensional integral imaging using a curved screen and a curved lens array. Elemental images are projected to the curved screen. Incorporation of the curved screen and the curved lens array instead of a conventional flat display panel and a flat lens array expands the viewing angle remarkably. In addition adopting barriers between a curved le...

Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such a boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not ass...

Finite element approximations of the first-order hyperbolic equation U • Vu + au = / are considered on curved domains £2 C K2 . When part of the boundary of Í2 is characteristic, the boundary of numerical domain, Í2A , may become either an inflow or outflow boundary, so it is necessary to select an algorithm that will accommodate this ambiguity. This problem was motivated by a problem in acoust...

The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the aspect ratio of the element is large or (2) the field point is closed to the element boundary; thus a large number of quadrature points are needed to achieve a...

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modi cat...

The singular function boundary integral method (SFBIM) is applied for the numerical solution of a 2-D Laplace model problem of a perfectly elastic wedge beam under plane stress conditions. The beam has a point boundary singularity, it includes a curved boundary part and is subjected to non-trivial distributed external loading. The implemented solution method converges for this special model pro...

We study domain coarsening of two-dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Bénard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain-boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure fa...