The classical field equations of a Liouville field coupled to gravity in two spacetime dimensions are shown to have black hole solutions. Exact solutions are also obtained when quantum corrections due to back reaction effects are included, modifying both the ADM mass and the black hole entropy. The thermodynamic limit breaks down before evaporation of the black hole is complete, indicating that...

A possibility of strong coupling quantum Liouville gravity is investigated via infinite dimensional representations of Uqsl(2,C) with q at a root of unity. It is explicitly shown that vertex operator in this model can be written by a tensor product of a vertex operator of the classical Liouville theory and that of weak coupling quantum Liouville theory. Some discussions about the strong couplin...

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

A random vector X = (X1, X2, . . . , Xn) with positive components has a Liouville distribution with parameter = ( 1, 2, . . . , n) if its joint probability density function is proportional to h( ∑n i=1 xi) ∏n i=1 x i−1 i , i > 0 [R.D. Gupta, D.S.P. Richards, Multivariate Liouville distributions, J. Multivariate Anal. 23 (1987) 233–256]. Examples include correlated gamma variables, Dirichlet and...

Quantum Liouville theory is annualized in terms of the infinite dimensional representations of Uqsl(2,C) with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from the finite dimensional representations of Uqsl(2,C). We furthe...

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...

A causal Poisson bracket algebra for Liouville exponentials on a cylinder is derived using an exchange algebra for free fields describing the in and out asymptotics. The causal algebra involves an even number of space-time points with a minimum of four. A quantum realisation of the algebra is obtained which preserves causality and the local form of non-equal time brackets. Following Polyakov’s ...

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.