0000000000443716
AUTHOR
G. Rao
showing 4 related works from this author
Analogue of Dini-Riemann theorem for non-absolutely convergent integrals
2007
An analogue of classical Dini-Riemann theorem related to non-absolutely convergent series of real number is proved for the Lebesgue improper integral.
Three periodic solutions for pertubed second order Hamiltonian system
2007
Three periodic solutions for perturbed second order Hamiltonian systems \begin{abstract} In this paper we study the existence of three distinct solutions for the following problem \begin{displaymath} \begin{array}{ll} -\ddot{u}+A(t)u=\nabla F(t,u)+\lambda \nabla G(t,u) & \mbox{a.e\ in\ } [0,T] \\ u(T)-u(0)=\dot{u}(T)-\dot{u}(0)=0, \end{array} \end{displaymath} where $\lambda\in \mathbb{R}$, $T$ is a real positive number, $A:[0,T]\rightarrow \mathbb{R}^{N}\times \mathbb{R}^{N}$ is a continuous map from the interval $[0,T]$ to the set of $N$-order symmetric matrices. We propose sufficient conditions only on the potential $F$. More precisely, we assume that $G$ satisfies only a usual growth co…
High performance algorithms based on a new wawelet expansion for time dependent acoustics obstale scattering
2007
This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems. The method proposed is a generalization of the ``operator expansion method" developed by Recchioni and Zirilli [SIAM J.~Sci.~Comput., 25 (2003), 1158-1186]. The numerical method proposed reduces, via a perturbative approach, the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations. The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved. A computational method has been developed to solve these challenging p…
HENSTOCK INTEGRAL AND DINI-RIEMANN THEOREM
2009
In [5] an analogue of the classical Dini-Riemann theorem related to non-absolutely convergent series of real number is obtained for the Lebesgue improper integral. Here we are extending it to the case of the Henstock integral.