Limiting behaviour of large Frobenius numbers

Limiting Distribution of Frobenius Numbers for N = 3

An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT is well-suited for generating large, random prime numbers since on a random input number, it takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability. EQFT extends QFT by verifying additional algeb...

On the isolated spectrum of the Perron–Frobenius operator

We discuss the existence of large isolated (non-unit) eigenvalues of the Perron– Frobenius operator for expanding interval maps. Corresponding to these eigenvalues (or ‘resonances’) are distributions which approach the invariant density (or equilibrium distribution) at a rate slower than that prescribed by the minimal expansion rate. We consider the transitional behaviour of the eigenfunctions ...

Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Dynamic and Equilibrium Behaviour Ofcontrolled Loss

We study the behaviour of large loss networks in which the ooered traac is subject to acceptance controls. Hunt and Kurtz proved a functional law of large numbers for the dynamics of such networks, as capacity and ooered traac are allowed to increase in proportion. However, limiting dynamics were not in general uniquely identiied. We establish further results identifying these dynamics under gi...