Séverin Rubéric, Exercices spirituels (1622)

Exercices de statistiques mathématiques

Par le théorème de la limite centrale, cette variable converge en loi vers la loi normale centrée réduite, c’est-à-dire, pour tout t ∈ R, on a limn→+∞ E[eitZn ] = e− t2 2 . L’objet de cet exercice est de montrer que la suite Zn ne peut pas converger en probabilité. 1. Calculer la fonction caractéristique de Z2n − Zn et montrer que cette différence converge en loi. 2. En étudiant P(|Z2n − Zn| ≥ ...

Introduction aux variétés différentiables Solutions et Exercices

Solution 12.1. Let ∑ α∈A ηα be a partition of unity supported on the coordinate charts of the orientable manifold. Let φα : Uα → Rn be the orientable coordinate charts, and let xα, . . . , xα. Then for each α define an n form on M by ωα = ηαdxα∧ · · · ∧dxα. This is smooth in Uα because it is a product of a smooth form and function. Outside of Uα the form is zero in a neighbourhood of every poin...

VSSC / 1622 : Voting System Standards

I EEE is actively involved in creating standards for voting systems and related applications via the IEEE Voting System Standards Committee (VSSC/1622). An upcoming VSSC/1622.2 standard on election results reporting lets election officials organize election results and report them to the media. Another goal of VSSC/1622 is to improve US voting processes by creating a common data format (CDF) fo...

Exercices sur le problème d’acquisition comprimée

Exercices with the neutrino oscillation length formula

Forsaking the traditionnal hand-waving in the treatment of the motion allows to show that the ultra-relativistic approximation and the equality of kinematical variables are unnecessary ingredients in the derivation of the oscillation length using plane waves, at least in a two flavor world. It ensues that the formula is valid as it is in the non relativistic regime, provided one uses the correc...