Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

The size consistency of multi-reference Møller-Plesset perturbation theory as a function of the structure of the zeroth-order Hamiltonian is studied. In calculations it is shown that the choice of projection operators to define the zeroth-order Hamiltonian is crucial. In essence whenever such a projection operator can be written as the sum of projection operators onto particular subspaces, cros...

For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego’s definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to...

The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map. 1991 MSC: 19K56, 16E40.

omotopy analysis method (ham) is a promising method for handling func-tional equations. recent publications proved the eectiveness of ham in solvingwide variety of problems in dierent elds. ham has a unique property whichmakes it superior to other analytic methods, this property is its ability to con-trol the convergence region of the solution series. in this work, we clari ed theadvantages ...

In ultrarelativistic heavy ion collisions a finite size QCD medium is created. In this paper we compute radiative energy loss to zeroth order in opacity by taking into account finite size effects. Transition radiation occurs on the boundary between the finite size medium and the vacuum, and we show that it lowers the difference between medium and vacuum zeroth order radiative energy loss relati...