Quantum calculus or q-calculus plays an important role in hypergeometric
series, quantum physics, operator theory, approximation theory, sobolev
spaces, geometric functions theory and others. But role of q-calculus in
the theory of harmonic univalent functions is quite new. In this paper, we
make an attempt to connect quantum calculus and harmonic univalent starlike
functions. In particular, we introduce and investigate the properties of
q-harmonic functions and q-harmonic starlike functions of order ?.
Abstract
The invariant perforation in an infinite strip can be classified into two groups. One is the finite group and the other is the infinite group. There are five cases in the finite group and nine cases in the infinite group. All the cases can be solved by the method of images. This method has, in fact, been used by the author to solve the stresses in an infinite strip containing either an unsymmetrically located single hole or a series of uniformly distributed equal holes. The solution is illustrated by working out in detail one of the cases in the infinite group, in which the strip contains two series of equal holes symmetrically staggered along the strip. The stress function is constructed by using a class of periodic harmonic functions derived from Weierstrass’ sigma function. Numerical examples also are given to show the effect of such a perforation on the stresses in the strip.
AbstractWe consider a class of generalized harmonic functions in the open unit disc in the complex plane. Our main results concern a canonical series expansion for such functions. Of particular interest is a certain individual generalized harmonic function which suitably normalized plays the role of an associated Poisson kernel.
AbstractWhitehouse adapts insights from evolutionary anthropology to interpret extreme self-sacrifice through the concept of identity fusion. The model neglects the role of normative systems in shaping behaviors, especially in relation to violent extremism. In peaceful groups, increasing fusion will actually decrease extremism. Groups collectively appraise threats and opportunities, actively debate action options, and rarely choose violence toward self or others.
AbstractIntuitions guide decision-making, and looking to the evolutionary history of humans illuminates why some behavioral responses are more intuitive than others. Yet a place remains for cognitive processes to second-guess intuitive responses – that is, to be reflective – and individual differences abound in automatic, intuitive processing as well.
Abstract
Tomasello offers a compelling account of the emergence of humans’ sense of obligation. We suggest that more needs to be said about the role of affect in the creation of obligations. We also argue that positive emotions such as gratitude evolved to encourage individuals to fulfill cooperative obligations without the negative quality that Tomasello proposes is inherent in obligations.
Abstract
The authors do the field of cultural evolution a service by exploring the role of non-social cognition in human cumulative technological culture, truly neglected in comparison with socio-cognitive abilities frequently assumed to be the primary drivers. Some specifics of their delineation of the critical factors are problematic, however. I highlight recent chimpanzee–human comparative findings that should help refine such analyses.
Connecting quantum calculus and harmonic starlike functions