A complete asymptotic expansion for operators of exponential type with $$p\left( x\right) =x\left( 1+x\right) ^{2}$$

In the year 1978, Ismail and May studied operators of exponential type and proposed some new operators which are connected with a certain characteristic function $$p\left( x\right) $$ p x . Several of these operators were not separately studied by researchers due to its unusual behavior. The topic of the present paper is the local rate of approximation of a sequence of exponential type operators $$R_{n}$$ R n belonging to $$p\left( x\right) =x\left( 1+x\right) ^{2}$$ p x = x 1 + x 2 . As the main result we derive a complete asymptotic expansion for the sequence $$\left( R_{n}f\right) \left( x\right) $$ R n f x as n tends to infinity.

Particle shape, thermal radiations, viscous dissipation and joule heating effects on flow of magneto-nanofluid in a rotating system

Purpose The purpose of this paper is to explore the impact of thermal radiation, viscous dissipation and Joule heating effects on the flow of a magneto-nanofluid between two horizontally placed plates. Three distinct shapes of nanoparticles in a base fluid (water) are considered to compose the nanofluid. Design/methodology/approach Introducing feasible similarity variables, the flow model is transformed into a nonlinear and coupled system of ordinary differential equations. The consequent system is solved by using homotopy analysis method. Findings Furthermore, the influence of embedded parameters on velocity and temperature profiles is highlighted graphically. The same is done for showing the variations in skin friction coefficient and local rate of heat transfer. Under certain conditions, present results compared with already existing results in the literature. Some main findings are pinpointed in the last section before the bibliography. From presented work, it is analyzed that the velocity field along y-axis and x-axis are increasing and decreasing functions of suction/injection parameter. The velocity of the fluid starts increases for Reynolds number and declines for volumetric fraction of the nanoparticles. Significant variations in angular velocity are observed for volumetric fraction and Reynolds number, respectively. Thermal field increases rapidly for brick-shaped nanoparticles, and for platelet-shaped nanoparticles, it decreases rapidly. Local rate of heat transfer increases for radiation and Reynolds number and starts decreasing for Eckert number. Originality/value The study presented is original and has not been submitted to any other journal for the publication purpose. The contents are original and proper references have been provided wherever applicable.

Speaker-specific processing and local context information: The case of speaking rate

ABSTRACTTo deal with variation in the speech signal, listeners rely on local context, such as speaking rate in a carrier sentence directly preceding a target, as well as more global properties of the speech signal, such as speaker-specific pronunciation variants. The present study addressed whether, despite its variability even within one speaker, habitual speaking rate can be tracked as a speaker-specific property and how such speaker-specific tracking of habitual rate would interact with effects of local-rate normalization. In two experiments, listeners were exposed to a 2-min dialogue between a fast and a slow speaker. At test, listeners categorized minimal word pair continua differing in the German /a/–/a:/ duration contrast spoken by the same two speakers. The results showed that listeners responded with /a:/ more often for the fast speaker but only when words were presented in isolation and not when presented with additional local-rate information. That is, despite the general assumption that duration cues and speaking rate are too variable to be used in a speaker-specific fashion, tracking habitual speaking rate may help speech perception. The results are discussed in relation to a belief-updating model of perceptual adaptation and exemplar models.