Abstract In this paper, we give various lower and upper bounds for the energy of graphs in terms several topological indices graphs: first general multiplicative Zagreb index, Randić zeroth-order redefined indices, atom-bond connectivity index. Moreover, obtain new certain graph invariants as diameter, girth, algebraic radius.

Our work concerns the study of inverse problems heat and wave equations involving fractional Laplacian operator with zeroth order nonlinear perturbations. We recover terms in semilinear from knowledge Dirichlet-to-Neumann type map combined Runge approximation unique continuation property Laplacian.

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

The excitonic states of four small hydrogenated Si clusters (SiH4 ,Si2H6 ,Si5H12 , and Si10H16! are studied using the diffusion quantum Monte Carlo approach. The importance of using accurate guiding wave functions is stressed and we show that the quantum chemical singles-only configuration interaction method and the time-dependent density functional theory within the adiabatic local-density app...

Our goal in writing this paper is to propose and analyze a non-conforming domain decomposition generalization to P.L. Lions initial idea, , in view of an extension of the approach to optimized interface conditions algorithms. This type of algorithm has proven indeed to be an efficient approach to domain decomposition methods in the case of conforming approximations, . This paper presents the ba...

The nite-temperature renormalization group is formulated via the Wilson-Kadanoo blocking transformation. Momentum modes and the Matsubara frequencies are coupled by constraints from a smearing function which plays the role of an infrared cutoo regulator. Using the scalar 4 theory as an example, we consider four general types of smearing functions and show that, to zeroth-order in the derivative...