Stein manifolds M for which O(M) has the property Ω-tilda (Dedicated to Mikhail Mikhaylovich Dragilev on the occation of his 90th birthday)

In this note, we consider the linear topological invariant Ω-tilda for Fréchet spaces of global analytic functions on Stein manifolds. We show that O(M), for a Stein manifold M, enjoys the property Ω-tilda if and only if every compact subset of M lies in a relatively compact sublevel set of a bounded plurisubharmonic function defined on M. We also look at some immediate implications of this characterization

Immediate Effects of Resistance Training on Velopharyngeal Function

Resistance training is known to be an effective way to strengthen a given muscle. Based on the established principles of the resistance training paradigm, the use of continuous positive airway pressure (CPAP) as a means to strengthen the velopharyngeal closure muscles has shown some promise. During CPAP therapy, speakers exercise velopharyngeal closure muscles by having them work against pressurized air from the CPAP device, which acts as a “weight/resistance.” While there is some evidence supporting the effectiveness of the CPAP therapy for treating hypernasality secondary to cleft palate and traumatic brain injury, information regarding proper treatment dosage is largely lacking. This study examined the immediate effects of individual CPAP therapy sessions with varying pressure levels on the speakers’ velopharyngeal function, with special emphasis on velopharyngeal orifice size and velopharyngeal timing parameters. Results from the study showed that CPAP therapy did not induce any appreciable changes in velopharyngeal orifice size or velopharyngeal timing parameters among healthy individuals. It was also found that varying pressure levels did not alter these speakers’ velopharyngeal valving patterns. No appreciable CPAP therapy effects may partly be attributed to the speakers’ intact velopharyngeal function. That is, velopharyngeal adjustments might not have been necessary for these speakers to maintain proper speech and resonance. It is unclear whether individual CPAP therapy sessions would have similarly limited effects on velopharyngeal function among speakers with velopharyngeal dysfunction, which needs further investigation.This work has been supported by The Ohio State University College of Arts and Sciences Undergraduate Research Scholarship and Social and Behavior Science (SBS) Research Grant Funds as well as the Philips-Respironics (Murrysville, PA) Equipment Loan Program.No embargoAcademic Major: Speech and Hearing Scienc

On Newton's Method for Entire Functions

The Newton map N_f of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of N_f. We study the behavior of N_f in a component V of C\U. If V can be surrounded by an invariant curve within U and satisfies the condition that each point in the extended plane has at most finitely many preimages in V, we show that V contains another immediate basin of N_f or a virtual immediate basin. A virtual immediate basin is an unbounded invariant Fatou component in which the dynamics converges to infty through an absorbing set.Comment: 19 pages, 4 figures. Changes in Version 2: Sharpened the result in Section

On the equality of Bajraktarevi\'c means to quasi-arithmetic means

This paper offers a solution of the functional equation $$\big(tf(x)+(1-t)f(y)\big)\varphi(tx+(1-t)y)=tf(x)\varphi(x)+(1-t)f(y)\varphi(y) \qquad(x,y\in I),$$ where $t\in\,]0,1[\,$ is a fixed number, $\varphi:I\to\mathbb{R}$ is strictly monotone, and $f:I\to\mathbb{R}$ is an arbitrary unknown function. As an immediate application, we shed new light on the equality problem of Bajraktarevi\'c means with quasi-arithmetic means