ar X iv : 0 70 4 . 05 17 v 1 [ m at h . ST ] 4 A pr 2 00 7 Using decomposed household food acquisitions as inputs of a Kinetic Dietary Exposure Model

ar X iv : 0 70 4 . 01 15 v 2 [ m at h . G T ] 9 A pr 2 00 7 Smooth maps with singularities of bounded K - codimensions ∗ † Yoshifumi ANDO

ar X iv : 0 70 4 . 39 02 v 1 [ m at h . PR ] 3 0 A pr 2 00 7 On the number of collisions in Λ - coalescents ∗

We examine the total number of collisions Cn in the Λ-coalescent process which starts with n particles. A linear growth and a stable limit law for Cn are shown under the assumption of a power-like behaviour of the measure Λ near 0 with exponent 0 < α < 1.

ar X iv : 0 70 4 . 35 30 v 1 [ m at h . D G ] 2 6 A pr 2 00 7 Invariant forms , associated bundles and hyperkähler metrics

We develop a method, initially due to Salamon, to compute the space of " invariant " forms on an associated bundle X = P ×G V , with a suitable notion of invariance. We determine sufficient conditions for this space to be d-closed. We apply our method to the construction of hyperkähler metrics on T CP 1 and T CP 2 .

ar X iv : a st ro - p h / 05 04 59 7 v 1 2 7 A pr 2 00 5 Supernovae : Explosions in the Cosmos

In this article, a broad perspective of supernovae, their classification and mechanism is given. Later, the astrophysical significance of supernovae is discussed in brief.

ar X iv : 0 70 8 . 37 30 v 1 [ m at h . PR ] 2 8 A ug 2 00 7 DENSITIES FOR ROUGH DIFFERENTIAL EQUATIONS UNDER HÖRMANDER ’ S CONDITION

We consider stochastic differential equations dY = V (Y ) dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Yt admits a density for t ∈ (0, T ] provided (i) the vector fields V = (V1, ..., Vd) satisfy Hörmander’s condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fract...