Let T be a positive plurisubharmonic current of bidimension (p, p) and δ > 0. Assume that the Lelong number of T satisfies ν(T, a) ≥ δ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then T = ϕ[X], where X is a complex subvariety of pure dimension p and ϕ is a weakly plurisubharmonic function on X. We also show that if T is positive pluriharmonic and its support has ...

In this paper, we propose a new similarity measure to combine multiple views of 3-D objects for non-rigid registration. It is a metric that integrates multiple 2-D view features representing a visual identity of a 3-D object seen from different viewpoints. The robustness to non-rigid distortions is achieved by the proximity correspondence manner. The human face, a typical non-rigid object, was ...

It is a classical result that a closed exceptional polar set is removable for subharmonic functions which are bounded above. Gardiner has shown that in the case of a compact exceptional set the above boundedness condition can be relaxed by imposing certain smoothness and Hausdorff measure conditions on the set. We give related results for a closed exceptional set, by replacing the smoothness an...

Sufficient conditions for a real-valued Gaussian random field X = {X(t), t ∈ RN} with stationary increments to be strongly locally nondeterministic are proven. As applications, small ball probability estimates, Hausdorff measure of the sample paths, sharp Hölder conditions and tail probability estimates for the local times of Gaussian random fields are established. Running head: Strong Local No...

Following a recent paper [10] we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure H implies that s is integer.

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the ex...

Face is considered to be one of the biometrics in automatic person identification. The non-intrusive nature of face recognition makes it an attractive choice. For face recognition system to be practical, it should be robust to variations in illumination, pose and expression as humans recognize faces irrespective of all these variations. In this paper, an attempt to address these issues is made ...

Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on Rd. Denote by D the Hausdorff dimension, by HD(E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence ...