A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several cl...

In this work we deal with a class of second-order elliptic problems of the form − u = λk(|x |) f (u) in Ω , with non-homogeneous boundary condition u = a on ∂Ω where Ω is the ball of radius R0 centered at origin, λ, a are positive parameters, f ∈ C([0,+∞), [0,+∞)) is an increasing function and k ∈ C([0, R0], [0,+∞)) is not identically zero on any subinterval of [0, R0]. We obtain via a fixed po...

For 0 < p − 1 < q and either ǫ = 1 or ǫ = −1, we prove the existence of solutions of −∆pu = ǫu q in a cone CS , with vertex 0 and opening S, vanishing on ∂CS , under the form u(x) = |x|ω( x |x|). The problem reduces to a quasilinear elliptic equation on S and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral ty...

X iv :m at h/ 02 10 08 4v 2 [ m at h. C A ] 1 3 D ec 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon ...

For M-theory on the G 2 holonomy manifold given by the cone on S 3 × S 3 we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the p...

There are three related concepts that arise in connection with the angular analysis of a convex cone: antipodality, criticality, and Nash equilibria. These concepts are geometric in nature but they can also be approached from the perspective of optimization theory. A detailed angular analysis of polyhedral convex cones has been carried out in a recent work of ours. This note focus on two import...

In this paper, Gaussian and elliptic high pass filters are analyzed for image sharpening qualitatively and quantatively . The filters are implemented in frequency domain using matlab software. Experiments are performed to compare the performance of both the filters ,processed images are presented. The results demonstrate that elliptic yields better results.

Luminaire sampling plays an important role in global illumination calculation using Monte Carlo integration. A conventional approach generates samples on the surface of the luminaire, resulting in rendered images with high variance of noise. In this paper, we present an efficient solid angle sampling technique using tunable bounding volumes for global illumination calculation. In contrast to th...

We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain spectral characterization of as infimum first eigenvalues linear second-order elliptic operators whose coefficients belong to dual corresponding Garding cone. Second, introduce non-degenerate inverse iterative scheme solve for operator. show that converges, with rate, all...

We study the real Monge-Ampère equation in two and three dimensions, both from the point of view of the SYZ conjecture, where solutions give rise to semi-flat Calabi-Yau’s and in affine differential geometry, where solutions yield parabolic affine sphere hypersurfaces. We find explicit examples, connect the holomorphic function representation to Hitchin’s description of special Lagrangian modul...