The Strongly Simple Cycles with Given Rotation Pairs of an Interval Map

In this paper, we introduce the notion of the strongly simple cycles with some rotation pair for interval maps and prove that, if an interval map has a cycle with given rotation pair, then it, has a strongly simple cycle with the same rotation pair.

Biggs Theorem for Directed Cycles and Topological Invariants of Digraphs

We generalize Biggs Theorem to the case of directed cycles of multi-digraphs allowing to compute the dimension of the directed cycle space independently of the graph representation with linear runtime complexity. By considering two-dimensional CW complex of elementary cycles and deriving formulas for the Betti numbers of the associated cellular homology groups, we extend the list of representation independent topological inavariants measuring the graph structure. We prove the computation of the 2nd Betti number to be sharp #P hard in general and present specific representation invariant sub-fillings yielding efficiently computable homology groups. Finally, we suggest how to use the provided structural measures to shed new light on graph theoretical problems as graph embeddings, discrete Morse theory and graph clustering.

Performance assessment of simple and modified cycle turboshaft gas turbines

This paper focuses on investigations encompassing comparative assessment of gasturbine cycle options.More specifically,investigation was caried out of technical performanceof turboshaft engine cycles based on existing simple cycle(SC)and its projected modifiedcycles for civil helicopter application.Technically,thermal efficiency,specific fuel consump-tion,and power output are of paramount importance to the overall performance of gas urbineengines.In course of carrying out this research,turbomatch software established at CranfieldUniversity based on gas turbine theory was applied to conduct simulation of a simple cycle(baseline)two-spool helicopter turboshaft engine model with free power turbine.Similarly,some modified gas urbine cycle configurations incoporating unconventional components,such as engine cycle with low pressure compressor(LPC)zero-staged,recuperated enginecycle,and intercooled/recuperated(ICR)engine cycle,were also simulated.In doing so,designpoint(DP)and off-design point(OD)performances of the engine models were established.Thepercentage changes in performance parameters of the modified cycle engines over the simplecycle were evaluated and it was found that to a large extent,the modified engine cycles withunconventional components exhibit better performances in terms of thermal efficiency andspecific fuel consumption than the traditional simple cycle engine.This research made use ofpublic domain open source references.