This paper is concerned with the square root problem of Kato for the ”sum” of linear operators in a Hilbert space H. Under suitable assumptions, we show that if A and B are respectively m-scetroial linear operators satisfying the square root problem of Kato. Then the same conclusion still holds for their ”sum”. As application, we consider perturbed Schrödinger operators.

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...

BACKGROUND Given the restricted distribution of Schistosoma mekongi in one province in Lao People's Democratic Republic (Lao PDR) and two provinces in Cambodia, together with progress of the national control programmes aimed at reducing morbidity and infection prevalence, the elimination of schistosomiasis mekongi seems feasible. However, sensitive diagnostic tools will be required to determine...

BACKGROUND In sub-Saharan Africa the recommended strategy to control schistosomiasis is preventive chemotherapy. Emphasis is placed on school-aged children, but in high endemicity areas, preschool-aged children are also at risk, and hence might need treatment with praziquantel. Since a pediatric formulation (e.g., syrup) is not available outside of Egypt, crushed praziquantel tablets are used, ...

In this paper we investigate the question of the existence of global strong solution for the compressible Navier Stokes equations for small initial data such that the rotational part of the velocity Pu0 belongs to Ḣ N 2 −1. We show then an equivalence of the so called Fujita Kato theorem to the case of the compressible Navier-Stokes equation when we consider axisymmetric initial data in dimensi...

The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...