The four-point integral of the minimal super Liouville gravity on the sphere is evaluated numerically. The integration procedure is based on the effective elliptic parameterization of the moduli space. The analysis is performed for a few different gravitational four-point amplitudes. The results agree with the analytic results recently obtained using the Higher super Liouville equations of motion.

We continue the study of quantum Liouville theory through Polyakov’s functional integral [1, 2], started in [3]. We derive the perturbation expansion for Schwinger’s generating functional for connected multi-point correlation functions involving stress-energy tensor, give the “dynamical” proof of the Virasoro symmetry of the theory and compute the value of the central charge, confirming previou...

We compare the Riemann–Liouville fractional integral (fI) of a function f(z) with the Liouville fI of the same function and show that there are cases in which the asymptotic expansion of the former is obtained from those of the latter and the difference of the two fIs. When this happens, this fact occurs also for the fractional derivative (fD). This method is applied to the derivation of the as...

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...

In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.

In this paper, we obtained some new estimates on generalization of Hadamard, Ostrowski and Simpson-like type inequalities for harmonically quasi-convex functions via Riemann Liouville fractional integral.

We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods. ⋆ Work supported in part by the National Science Foundation grant PHY–8...