Artistic forms and complexity.

We discuss the inter-relationship between various concepts of complexity by introducing a complexity 'triangle' featuring objective complexity, subjective complexity and social complexity. Their connections are explored using visual and musical compositions of art. As examples, we quantify the complexity embedded within the paintings of the Jackson Pollock and the musical works of Johann Sebastian Bach. We discuss the challenges inherent in comparisons of the spatial patterns created by Pollock and the sonic patterns created by Bach, including the differing roles that time plays in these investigations. Our results draw attention to some common intriguing characteristics suggesting 'universality' and conjecturing that the fractal nature of art might have an intrinsic value of more general significance.

Agglomerative tendencies in the distribution of populations.

"The paper explores the role of accessibility to mutual contacts as an agglomeration force in the spatial distribution of population. The uniqueness conditions for the equilibrium solutions are analyzed in the static case, with the aid of mathematical programming embedding properties. A dynamic version in continuous time is then built, and conditions for instability of a globally stable equilibrium and appearance of multiple locally stable and unstable equilibria are stated. Finally, some implications for the geographical structure are discussed."

X and y operators for general linear transport processes.

This note presents the derivation of generalized Ambartsumian-Chandrasekhar X and Y functions for stationary transfer in a plane-parallel slab. An algebraic formula relating these functions to the usual reflection function is also presented, together with the appropriate generalization of the Chandrasekhar H-equations for the semi-infinite medium. The planetary problem will also be briefly discussed.