We give some weighted double integral inequalities of Hermite-Hadamard type for co-ordinated convex functions in a rectangle from R2. The obtained provide generalizations result given earlier works.

We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator technique we apply our method to a time-dependent double-well potential.

We construct a combined non-perturbative path integral over geometries and topologies for two-dimensional Lorentzian quantum gravity. The Lorentzian structure is used in an essential way to exclude geometries with unacceptably large causality violations. The remaining sum can be performed analytically and possesses a unique and welldefined double-scaling limit, a property which has eluded simil...

Abstract. We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Although integral equation methods are widely used for the numerical solution of such problems, to date there is no formulation which is known to be uniquely solvable in the 3D case. We consider a novel Brakhage-Werner type integral equation formulation of this problem, base...

In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With respect to the first paper with the same title, we correct here the set of transformations for the auxiliary variables λ a. We prove that under this new set of tr...

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage–Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined singleand double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green’s function. ...

In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With respect to the first paper with the same title, we correct here the set of transformations for the auxiliary variables λ a. We prove that under this new set of tr...

In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With respect to the first paper with the same title, we correct here the set of transformations for the auxiliary variables λ a. We prove that under this new set of tr...

The generalized fuzzy valued θ-Choquet integrals will be established for the given μ-integrable fuzzy valued functions on a general fuzzy measure space, and the convergence theorems of this kind of fuzzy valued integral are being discussed. Furthermore, the whole of integrals is regarded as a fuzzy valued set function on measurable space, the double-null asymptotic additivity and pseudo-double-...