Differential equation for partition functions and a duality pseudo-forest

Duality and Black Hole Partition Functions

Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of ten-dimensional string theory or eleven-dimensional M-theory, one has a microscopic description of the black hole which allows one to count microstates and ...

Partition Functions , Duality and the Tube Metric ∗

The partition function of type IIA and B strings on R 6 × K3, in the T 4 /Z 2 orbifold limit, is explicitly computed as a modular invariant sum over spin strutures required by perturbative unitarity in order to extend the analysis to include type II strings on R 6 ×W 4, where W 4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-S...

Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

A method for solving first order fuzzy differential equation

Differential equation models for statistical functions

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation mod...