Type Construction and Cycle Detection

We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly Poisson distributed with parameter 1/k. In particular, we establish strong results about the distribution of the number of cycles whose lengths lie in a fixed but arbitrary set I. Our techniques are motivated by the theory of sieves in number theory.

This paper describes the construction and initial operation fo a 260-MW combined cycle power generating plant consisting of two gas turbines, each with its own heat recovery steam generator. The steam, which is generated at 1200 lb 950 deg in each of the boilers, is combined to feed a single cylinder axial exhaust steam turbine. The paper describes the major components and operating cycle, the control system and some of the initial startup problems.

In this paper, we investigate a new theta cycle for $GSp_4/\mathbb{Q}$ by using author's theta operators defined in the previous work. In the course of the construction, we also modify the theta operators so that they work in any characteristic, including $p = 2$, and for any weight. As an application, we discuss an Edixhoven type theorem for $GSp_4/\mathbb{Q}$.