This paper continues the analysis, started in [3, 4], of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigor’yan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those t...

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...

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...

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...

Assume that we observe i.i.d. points lying close to some unknown d-dimensional $${\mathcal {C}}^k$$ submanifold M in a possibly high-dimensional space. We study the problem of reconstructing probability distribution generating sample. After remarking this is degenerate for large class standard losses ( $$L_p$$ , Hellinger, total variation, etc.), focus on Wasserstein loss, which build an estima...

In 2001, S. Bulman-Fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $A_{S}$ over a monoid $S$ that can be described by means of when the functor $A_{S} otimes -$ preserves pullbacks. In this paper, we extend these results to $S$-posets and present equivalent descriptions of weakly kernel p...

Calculations of the number of curves on a Calabi-Yau manifold via an instanton expansion do not always agree with what one would expect naively. It is explained how to account for continuous families of instantons via deformation theory and excess intersection theory. The essential role played by degenerate instantons is also explained.