Out of tolerance warning alarm system for plurality of monitored circuits Patent

Alarm system design for monitoring one or more relay cicuit

Euler characteristic and Akashi series for Selmer groups over global function fields

Let $A$ be an abelian variety defined over a global function field $F$ of positive characteristic $p$ and let $K/F$ be a $p$-adic Lie extension with Galois group $G$. We provide a formula for the Euler characteristic $\chi(G,Sel_A(K)_p)$ of the $p$-part of the Selmer group of $A$ over $K$. In the special case $G=\mathbb{Z}_p^d$ and $A$ a constant ordinary variety, using Akashi series, we show how the Euler characteristic of the dual of $Sel_A(K)_p$ is related to special values of a $p$-adic $\mathcal{L}$-function

On Selmer groups of abelian varieties over ℓ\ell-adic Lie extensions of global function fields

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an \l-adic Lie extension (\l\neq p) unramified outside a finite set of primes $S$ and such that \Gal(K/F) has no elements of order \l. We shall prove that, under certain conditions, Sel_A(K)_\l^\vee has no nontrivial pseudo-null submodule.Comment: 14 page

A nonlinear Bismut-Elworthy formula for HJB equations with quadratic Hamiltonian in Banach spaces

We consider a Backward Stochastic Differential Equation (BSDE for short) in a Markovian framework for the pair of processes $(Y,Z)$, with generator with quadratic growth with respect to $Z$. The forward equation is an evolution equation in an abstract Banach space. We prove an analogue of the Bismut-Elworty formula when the diffusion operator has a pseudo-inverse not necessarily bounded and when the generator has quadratic growth with respect to $Z$. In particular, our model covers the case of the heat equation in space dimension greater than or equal to 2. We apply these results to solve semilinear Kolmogorov equations for the unknown $v$, with nonlinear term with quadratic growth with respect to $\nabla v$ and final condition only bounded and continuous, and to solve stochastic optimal control problems with quadratic growth