Multipoint Correlation Functions: Spectral Representation and Numerical Evaluation

A Numerical Solution of Fractional Optimal Control Problems Using Spectral Method and Hybrid Functions

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

Spectral correlation functions for chaotic systems

The n-level spectral correlation functions for chaotic quantum systems are calculated by using a recently proposed scheme called the extended diagonal approximation (EDA). The EDA is a natural extension of the diagonal approximation, which was invented by Berry in order to semiclassically evaluate the 2-level correlation function. When the time reversal invariance of the chaotic systems is brok...

Numerical Evaluation of Special Functions

Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. March 1994 December 200

Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

Multipoint correlation functions in Liouville field theory and minimal Liouville gravity

We study n+ 3-point correlation functions of exponential fields in Liouville field theory with n degenerate and 3 arbitrary fields. An analytical expression for these correlation functions is derived in terms of Coulomb integrals. The application of these results to the minimal Liouville gravity is considered. 1 Liouville field theory Last years since the seminal paper of A. Polyakov [1] Liouvi...