Human~Divine Communication as a Paradigm for Power: al-Tha'labi's Presentation of Q. 38:24 and Q. 38:34

Verse 24 to 25 of sura 38 (Sad) of the Qur'an tell us 'David realized that We had been testing him, so he asked forgiveness of his Lord, fell down on his knees, and repented: We forgave him [his misdeed]. His reward will be nearness to Us, a good place to return to'; verse 34 to 35 of the same sura tell us 'We certainly tested Solomon, reducing him to a mere skeleton on the throne. He turned to Us and prayed: 'Lord, forgive me! Grant me such power as no one after me will have -- You are the Most Generous Provider', then, at verse 40, 'His reward will be nearness to Us, a good place to return to'. Yet the medieval Muslim historiographical tradition presents very different narratives, and very different personalities, in elucidation of these two episodes. The two questions that will be addressed in this essay are: restricting our focus to communication patterns and how God is presented in the narrative, how do these two narratives differ? And, secondly, can we find reasons in the text of the Qur'anic passages themselves for why they differ

Chapter 22. Stories of the Prophets

The Blackwell Companion to the Qur'an is a reader's guide, a true companion for anyone who wishes to read and understand the Qur'an as a text and as a vital piece of Muslim life. Comprises over 30 original essays by leading scholars. Provides exceptionally broad coverage - considering the structure, content and rhetoric of the Qur'an; how Muslims have interpreted the text and how they interact with it; and the Qur'an's place in Islam. Features notes, an extensive bibliography, indexes of names, Qur'an citations, topics, and technical terms

Smooth Distribution Function Estimation for Lifetime Distributions using Szasz-Mirakyan Operators

In this paper, we introduce a new smooth estimator for continuous distribution functions on the positive real half-line using Szasz-Mirakyan operators, similar to Bernstein's approximation theorem. We show that the proposed estimator outperforms the empirical distribution function in terms of asymptotic (integrated) mean-squared error, and generally compares favourably with other competitors in theoretical comparisons. Also, we conduct the simulations to demonstrate the finite sample performance of the proposed estimator.Comment: Small typo in Theorem 10: Now -1/12 instead of +1/12 in the term of order $m^{-1}

A nonlinear discrete-velocity relaxation model for traffic flow

We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the model has an invariant domain appropriate for traffic flow modeling. It shows some similarities with the Aw-Rascle traffic model. However, the new model is simpler and yields, in case of a concave fundamental diagram, an example for a totally linear degenerate hyperbolic relaxation model. We discuss the details of the hyperbolic main part and consider boundary conditions for the limit equations derived from the relaxation model. Moreover, we investigate the cluster dynamics of the model for vanishing braking distance and consider a relaxation scheme build on the kinetic discrete velocity model. Finally, numerical results for various situations are presented, illustrating the analytical results

Kinetic layers and coupling conditions for macroscopic equations on networks I: the wave equation

We consider kinetic and associated macroscopic equations on networks. The general approach will be explained in this paper for a linear kinetic BGK model and the corresponding limit for small Knudsen number, which is the wave equation. Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the consideration of a fixpoint problem involving the coupled solutions of kinetic half-space problems. A new approximate method for the solution of kinetic half-space problems is derived and used for the determination of the coupling conditions. Numerical comparisons between the solutions of the macroscopic equation with different coupling conditions and the kinetic solution are presented for the case of tripod and more complicated networks

Kinetic layers and coupling conditions for nonlinear scalar equations on networks

We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kinetic coupling conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the combination of kinetic half-space problems with Riemann problems at the junction. Detailed numerical comparisons between the different models show the agreement of the coupling conditions for the case of tripod networks