How to Model Condensate Banking in a Simulation Model to Get Reliable Forecasts? Case Story of Elgin/Franklin

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Slanted Vector Fields for Jet Spaces

Low pole order frames of slanted vector fields are constructed on the space of vertical k-jets of the universal family of complete intersections in $\mathbb{P}^n$ and, adapting the arguments, low pole order frames of slanted vector fields are also constructed on the space of vertical logarithmic k-jets along the universal family of projective hypersurfaces in $\mathbb{P}^n$ with several irreducible smooth components. Both the pole order (here $=5k-2$) and the determination of the locus where the global generation statement fails are improved compared to the literature (previously $=k^2+2k$), thanks to three new ingredients; we reformulate the problem in terms of some adjoint action, we introduce a new formalism of geometric jet coordinates, and then we construct what we call building-block vector fields, making the problem for arbitrary jet order $k\geqslant1$ into a very analog of the much easier case where $k=0$, i.e. where no jet coordinates are needed.Comment: 26 pages, comments are welcome. (v3 : major overhaul

Remarks on the Egyptian 2/D table in favor of a global approach (D composite number)

Egyptian decompositions of 2/D as a sum of two unit fractions are studied by means of certain divisors of D, namely r and s. Our analysis does not concern the method to find r and s, but just why the scribes have chosen a solution instead of another. A comprehensive approach, unconventional, is developed which implies having an overview of all pre-calculated alternatives. Difference s-r is the basis of the classification to be examined before taking the right decisions, step by step, if difficulties are encountered. An adequate adjustment of s-r limits the number of all alternatives to 57, what is very few. A four-component generator (2/3, 2/5, 2/7, 2/11) operates as a (hidden) mother-table. Adding few logical rules of common sense is enough to explain the reasons of the Egyptian choices. Even the singular case 2/95, which can not be decomposed into two fractions but only into three, reveals a doubly justified explanation.Comment: 9 page

Chaotic dynamical systems associated with tilings of RN\R^N

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of $\R^N$, whose most familiar example is provided by the $N-$dimensional torus \T ^N. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup

A perturbation analysis of some Markov chains models with time-varying parameters

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process developed in the literature and that can be used for studying a wide class of Markov processes. To this end, for some families of V-geometrically ergodic Markov kernels indexed by a real parameter u, we give conditions under which the invariant probability distribution is differentiable with respect to u, in the sense of signed measures. Our results also complete the existing literature for the perturbation analysis of Markov chains, in particular when exponential moments are not finite. Our conditions are checked on several original examples of locally stationary processes such as integer-valued autoregressive processes, categorical time series or threshold autoregressive processes

Fiber integration on the Demailly tower

The goal of this work is to provide a fiber integration formula on the Demailly tower, that avoids step-by-step elimination of horizontal cohomology classes, and that yields computational effectivity. A natural twist of the Demailly tower is introduced and a recursive formula for the total Segre class at k-th level is obtained. Then, by interpreting single Segre classes as coefficients, an iterated residue formula is derived.Comment: 22 pages, to appear in Annales de l'Institut Fourie