We show that for each c M ? [ 1 , 25 ) ${\mathbf {c}}_{\mathrm{M}} \in [1,25)$ there is a unique metric associated with Liouville quantum gravity (LQG) matter central charge {c}}_{\mathrm{M}}$ . An earlier series of works by Ding–Dubédat–Dunlap–Falconet, Gwynne–Miller, and others showed such exists in the subcritical case ( ? ? (-\infty ,1)$ which corresponds to coupling constant ? 0 2 $\gamma ...

– Recently an extension of beta function is defined by introducing an extra parameter is proved to be useful earlier (Aslam Chaudhry 1997 [8] and A. R. Miller 1998 [1]). In this research note, we generalize the incomplete beta function and obtained the various integral representations and properties. Furthermore, we obtained the beta distribution for generalized beta function. Keywords––Incompl...

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panich, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition number, emphasising dependence on the frequency, the geometry o...

This paper presents an unsupervised methodology for automatic disambiguation of noun terms found in domain specific unrestricted corpora. This method extends approaches of Fragos (Fragos et al., 2003) and others that use the WordNet (Miller, 1998) database in order to resolve semantic ambiguity. The method is evaluated by disambiguating the noun collection of SemCor 2.0. Parameter adjustment wa...

We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer–Miller Hamiltonian, involves commutator variable matrix rather than conventional zero-point-energy parameter. In exact formulation on constraint approaches dynamics, with variables can be employed to generate approximate trajectory-based dynamics. Various benchmark ...