Existence and uniqueness of the solution of the coupled conduction-radiation energy transfer on diffuse-gray surfaces

This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction

Inferring linear and nonlinear Interaction networks using neighborhood support vector machines

International audienc

Study of eccentricity based topological indices for benzenoid structure

Topological indices play paramount role in defining chemical and structural properties of different compounds. Chemical graph theory is useful for predicting the bioactivity and physicochemical properties through numerical invariants. A broad range of topological indices are studied and used in theoretical chemistry. The eccentricity of a graph is maximum distance from one vertex a to another vertex b. The connectivity based topological indices depict vital role in mathematical chemistry. In this paper, we discuss Benzenoid Hourglass Network and calculate its total eccentricity, average eccentricity, atom-bond connectivity index, eccentricity based Zagreb index and geometric-arithmetic index. Some new helpful closed formulas are developed