Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

The light of a new age

Given here is the address of NASA Administrator Daniel S. Goldin to the Association of Space Explorers. Mr. Goldin's remarks are on the topic of why we should go to Mars, a subject he approaches by first answering the question, What would it mean if we decided today not to go to Mars? After a discussion of the meaning of Columbus' voyage to America, he answers the question by saying that if we decide not to go to Mars, our generation will truly achieve a first in human history - we will be the first to stop at a frontier. After noting that the need to explore is intrinsic to life itself, Mr. Goldin presents several reasons why we should go to the Moon and go to Mars. One reason is economic, another is to increase our scientific knowledge, and yet another is to further the political evolution of humankind through the international cooperation required for building settlements on the Moon and Mars. He concludes by expanding upon the idea that this nation has never been one to shrink from a challenge

Remarks by NASA administrator Daniel S. Goldin

The text of a brief speech addressing the technical and social benefits of Space Station Freedom is presented

Conformal symmetry transformations and nonlinear Maxwell equations

We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying $M^{\#}$ with the projective light cone in $(4+2)$-dimensional spacetime, we write two independent conformal-invariant functionals of the $6$-dimensional Maxwellian field strength tensors -- one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.Comment: 12 pages, Based on a talk by the first author at the International Conference in Mathematics in honor of Prof. M. Norbert Hounkonnou (October 29-30, 2016, Cotonou, Benin). To be published in the Proceedings, Springer 201