In this paper we study computability of the solutions of the Korteweg-de Vries equation ut + uux + uxxx = 0. This is one of the open problems posted by Pour-El and Richards [25]. Based on Bourgain's new approach to the initial value problem for the KdV equation in the periodic case, we show that the periodic solution u of the KdV equation is computable if the initial data is computable.

Prosocial motivation refers to the employees’ willingness to invest for the sake of helping others. It improves basic and applied research behaviors of employees and the interaction between them. Employees’ innovation behavior depends on prosocial motivation because the motivation to protect the interests of others may promote knowledge sharing and knowledge coupling. However, there is a research gap in solving the optimal solution of prosocial motivations that facilitates different types of innovation behaviors based on the combination of prosocial motivations. We (...) perform a qualitative comparative study on the effect of the motivation configurations on innovation behaviors. We find that highly basic and highly applied research behaviors share in common collectivism-based, principlism-based, contextual, and situational motivations which work in all configurations. But the core conditions between the two are different, which are principlism-based and situational motivations, respectively. In addition, both highly basic-to-applied and highly applied-to-basic transformation behaviors share the same core condition and the same secondary conditions with highly basic and highly applied research behaviors, respectively. Moreover, the behaviors of non-highly basic research and non-highly basic-to-applied transformation share the severe absence of egoism-based motivation as the core condition in common. Non-highly behaviors of applied research and applied-to-basic transformation have a common point of the severe absence of the pressure-based type as the key. Finally, we also analyze active and passive prosocial degrees of all types of high/non-high innovation behaviors. Our study deepens the academics’ thinking on multi-dimensional prosocial motivation and the classification management of coupling innovation behavior and provides implications for practice. (shrink)

Drawing upon the conservation of resources theory and social exchange theory, we examined the effects of family supportive supervisor behavior and family support on work absorption at the within- and between-person levels. A 10-day study of 91 workers using 710 observations was employed. At the within-person level, the results suggested that daily relaxation at work mediated the relationships between daily FS, daily shifts in FS, and daily work absorption. However, at the between-person level, the results revealed that chronic relaxation at (...) work mediated the relation between the average level of FSSB/FS and chronic work absorption. We conclude that FSSB/FS plays a vital role in relaxation at work and work absorption at the within- and between-person levels. (shrink)

In this paper we investigate conditions for Lp-computability which are in accordance with the classical Grzegorczyk notion of computability for a continuous function. For a given computable real number p ≥ 1 and a compact computable rectangle I ⊂ ℝq, we show that an Lp function f ∈ Lp is LP-computable if and only if f is sequentially computable as a linear functional and the Lp-modulus function of f is effectively continuous at the origin of ℝq.

In order to cope with the changing health needs in the community, an holistic approach on AIDS prevention and control with particular reference to essential quality was introduced at an educational seminar at Hebei Medical University in China, 1996. We have identified three major points in the present study through learning and research process: 1. The importance of ‘cultural norm’ for the unification of science and technology is identified for the community approach; 2. ‘community care’ emphasising human quality provides unity (...) in diversity for educational program; and 3. ‘community control’ emphasising quality assurance demonstrates the effectiveness for program analysis from the viewpoint of human centred systems. (shrink)