We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constraint states that the trajectories of the same motion lie in a low dimensional linear manifold and different ...

in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

I briefly review the source of the so-called intrinsic ambiguity and show how the combination of “golden” and “silver” channel at the Neutrino Factory can solve the problem, in the absence of other sources of degeneracies. I then relaxed the hypothesis θ23 = 45◦ and show how the different dependence of the two channels on θ23 can help in solving the intrinsic and θ23-octant ambiguity at the sam...

On an affine variety X defined by homogeneous polynomials, every line in the tangent cone of X is a subvariety of X. However there are many other germs of analytic varieties which are not of cone type but contain “lines” passing through the origin. In this paper, we give a method to determine the existence and the “number” of such lines on non-degenerate surface singualrities.

Kundt spacetimes are of great importance in general relativity in 4 dimensions and have a number of topical applications in higher dimensions in the context of string theory. The degenerate Kundt spacetimes have many special and unique mathematical properties, including their invariant curvature structure and their holonomy structure. We provide a rigorous geometrical kinematical definition of ...

The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal sym...

An algebraic classification of second order symmetric tensors in 5-dimensional Kaluza-Klein-type Lorentzian spaces is presented by using Jordan matrices. We show that the possible Segre types are [1, 1111], [2111], [311], [z z̄ 111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also stu...