Waves, damped wave and observation

We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave equation and its decay rate. Next, we describe the design of an approximate control function by an iterative time reversal method.Comment: 6 figures, French-Chinese Summer Institute on Applied Mathematics, references are update

Smallest Singular Value for Perturbations of Random Permutation Matrices

We take a first small step to extend the validity of Rudelson-Vershynin type estimates to some sparse random matrices, here random permutation matrices. We give lower (and upper) bounds on the smallest singular value of a large random matrix D+M where M is a random permutation matrix, sampled uniformly, and D is diagonal. When D is itself random with i.i.d terms on the diagonal, we obtain a Rudelson-Vershynin type estimate, using the classical theory of random walks with negative drift.Comment: 33 page

Intraoperative hyperglycemia augments ischemia reperfusion injury in renal transplantation: a prospective study.

Background. Diabetes is a risk factor for delayed graft function in kidney transplantation, and hyperglycemia increases ischemia reperfusion injury in animal models. Methods. To explore the role of perioperative hyperglycemia in ischemia reperfusion injury, we conducted a prospective study of 40 patients undergoing living donor renal transplantation. Blood glucose levels were monitored intraoperatively, and serum samples were obtained at the time anesthesia was induced and one hour after allograft reperfusion. The percentage change in neutrophil gelatinase-associated lipocalin (NGAL), a protein whose expression is increased with renal ischemia, was then used to determine the extent of injury. Results. In a multivariate model including recipient, donor, and transplant factors, recipient blood glucose >160 mg/dL at the time of allograft reperfusion (β 0.19, P-value < 0.01), warm ischemia time >30 minutes (β 0.11, P-value 0.13), and recipient age (β 0.05, P-value 0.05) were associated with percentage change in NGAL. These same predictors were associated with the percentage change in creatinine on postoperative day 2. Conclusions. Hyperglycemia is associated with increased ischemic injury in renal transplantation. Both creatinine and NGAL, a marker of ischemic injury and renal function, fall less rapidly in patients with elevated blood glucose