Experimental investigation of a simple distortion index utilizing steady-state and dynamic distortions in a Mach 2.5 mixed-compression inlet and turbofan engine

A wind tunnel investigation was conducted to determine the amplitude and spatial distribution of steady-state and dynamic distortion produced in an inlet with 45 percent of the overall supersonic area contraction occurring internally. It was found that the inlet support strut location and/or the overboard bypass flow rate has a significant effect on the spatial distribution of distortion. Because of this effect the majority of the stall points exhibited four-per-revolution patterns of distortion. Data from this test were used to formulate a simple index that combines steady-state and dynamic distortions. Distortion results obtained with this index correlated well with exhaust nozzle area. It is shown that the exhaust nozzle area of a TF30-P-3, as modified for use in this test, can be controlled in a scheme to avoid engine stall. A considerable increase in engine distortion tolerance can be achieved by opening the 7th-stage bleed. The engine exhibited higher tolerance to distortion for multiple patterns of distortion per-revolution than for a one-per-revolution pattern of distortion

Existence of universal Taylor series for non-simply connected domains

It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\Ω that have connected complement. This paper shows, for nonsimply connected domains Ω, how issues of capacity, thinness and topology affect the existence of holomorphic functions on Ω that have universal Taylor series expansions about a given point.Author has checked copyrigh

Recurrent Linear Operators

Costakis G, Manoussos A, Parissis I. Recurrent Linear Operators. Complex Analysis and Operator Theory. 2014;8(8):1601-1643.We study the notion of recurrence and some of its variations for linearoperators acting on Banach spaces. We characterize recurrence for severalclasses of linear operators such as weighted shifts, composition operators andmultiplication operators on classical Banach spaces. We show that on separablecomplex Hilbert spaces the study of recurrent operators reduces, in many cases,to the study of unitary operators. Finally, we study the notion of productrecurrence and state some relevant open questions