The environment in which airlines operate is uncertain for many reasons, for example due to the effects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence uncertainty and delay for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting cre...

Let $$f(z)=\sum _{n=1}^{\infty } a_f(n)e^{2\pi i n z}$$ be a non-CM holomorphic cuspidal newform of trivial nebentypus and even integral weight $$k\ge 2$$ . Deligne’s proof the Weil conjectures shows that $$|a_f(p)|\le 2p^{\frac{k-1}{2}}$$ for all primes p. We prove 100% p $$ 2p^{\frac{k-1}{2}}{\log \log p}/{\sqrt{\log p}}<|a_f(p)|<\lfloor 2p^{\frac{k-1}{2}}\rfloor .$$ Our gives an effective up...

Fungus growth methods for estimating either vitamin B1 thiazole or vitamin B1 pyrimidinel have been used by Robbins and Kavanagh (l), Kavanagh (2), and Krampitz and Woolley (3), and a fermentation stimulation method has been described by Schultz, Atkin, and Frey (4). A procedure utilizing the synthesis of vitamin B1 by yeast from thiazole and pyrimidine has been used in this laboratory to estim...

Let K be an imaginary quadratic field with class number one and let p ⊂ OK be a degree one prime ideal of norm p not dividing 6dK . In this paper we generalize an algorithm of Schoof to compute the class numbers of ray class fields Kp heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura’s reciprocity law. We have...

We investigate the action of the heat operator on Jacobi forms. In particular, we present two explicit characterizations of this action on Jacobi forms of index 1. Furthermore, we study congruences and filtrations of Jacobi forms. As an application, we determine when an analog of Atkin’s U-operator applied to a Jacobi form is nonzero modulo a prime.