Ultrasound imaging is a noninvasive technique well-suited for detecting abnormalities like cysts, lesions and blood clots. In order to use 3D ultrasound to visualize the size and shape of such abnormalities, effective boundary detection methods are needed. A robust boundary detection technique using a nearest neighbor map (NNM) and applicable to multi-object cases has been developed. The algori...

o but containing the line segment 0 _ w < 1, and whose boundary possesses at the point w = 1 forward and backward tangents making equal angles a/2 (>0) with the negative direction of the axis of reals. Let thefunction w = f(z) map the region R, :x < 1 of the z(= x + iy)-plane onto Rw in such a way that we have f(O) = 0, f(1) = 1. Let the sequence xn, 0 < xn < 1, approach unity. Then for z on an...

In this paper we show that for Riemannian manifolds with boundary the natural restriction map is a quasifibration between spaces of metrics of positive scalar curvature. We apply this result to study homotopy properties of spaces of such metrics on manifolds with boundary.

We show that if two 3-manifolds with toroidal boundary are glued via a “sufficiently complicated” map then every Heegaard splitting of the resulting 3-manifold is weakly reducible. Additionally, suppose X∪F Y is a manifold obtained by gluing X and Y , two connected small manifolds with incompressible boundary, along a closed surface F . Then the following inequality on genera is obtained:

We suggest analytic estimates for the Q-switching instability boundary of the continuous-wave mode-locking regime domain for a ring cavity semiconductor laser. We use a differential delay laser model that allows to assume large gain and loss in the cavity, which is a typical situation for this laser class. The slow saturable absorber approximation is applied to derive a map that describes the t...

A novel method is proposed to detect multi-part objects of unknown specific shape and appearance in natural images. It consists in first extracting a strictly oversegmented map of circular arcs and straight-line segments from an edge map. Each obtained constant-curvature contour primitive has an unknown origin which may be the external boundary of an interesting object, the textured or marked r...

We consider the stability in the inverse problem consisting in the determination of an electric potential q, appearing in a Dirichlet initial-boundary value problem for the wave equation ∂2 t u − ∆u + q(x)u = 0 in an unbounded wave guide Ω = ω × R with ω a bounded smooth domain of R2, from boundary observations. The observation is given by the Dirichlet to Neumann map associated to a wave equat...

Tsunamis are caused by the displacement of a large volume of water, generally in an ocean or a sea. Earthquakes, volcanic eruptions and other underwater explosions, landslides, glacier calvings, meteorite impacts and other disturbances above or below water have the potential to generate a tsunami. The coastal areas of Kollam district, the present study area was seriously affected by the catastr...

We study the inverse problem of determining an electrical inclusion from boundary measurements. We derive a stability estimate for the linearized map with explicit formulae on generic constants that shows that the problem becomes more ill-posed as the inclusion is farther from the boundary. We also show that this estimate is optimal.

The distributional k-dimensional Jacobian of a map u in the Sobolev space W 1,k−1 which takes values in the the sphere S can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M o...