Martingales, endomorphisms, and covariant systems of operators in Hilbert space

We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant system in a Hilbert space of L^2-martingales. Our martingale construction depends on a prescribed set of transition probabilities, given by a non-negative function. Our main theorem describes the induced martingale systems completely. The applications of our theorem include wavelets, the dynamics defined by iterations of rational functions, and sub-shifts in symbolic dynamics. In the theory of wavelets, in the study of subshifts, in the analysis of Julia sets of rational maps of a complex variable, and, more generally, in the study of dynamical systems, we are faced with the problem of building a unitary operator from a mapping r in a compact metric space X. The space X may be a torus, or the state space of subshift dynamical systems, or a Julia set. While our motivation derives from some wavelet problems, we have in mind other applications as well; and the issues involving covariant operator systems may be of independent interest.Comment: 44 pages, LaTeX2e ("jotart" document class); v2: A few opening paragraphs were added to the paper; an addition where a bit of the history is explained, and where some more relevant papers are cited. Corrected a typographical error in Proposition 8.1. v3: A few minor additions: More motivation and explanations in the Intro; Remark 3.3 is new; and eleven relevant references/citations are added; v4: corrected and updated bibliography; v5: more bibliography updates and change of LaTeX document clas

Problems of organizational structure in C3 systems

"March, 1982."Bibliography: p. 54.With: On modeling teams of interacting decisionmakers with bounded rationality / Alexander H. Levis, Kevin L. Boettcher. Cambridge, Mass. : Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, [1982]NASA Grant No. NAG1-2by Alexander H. Levis

Aspects of phosphorus nutrition in endomycorrhizal fungi of the Ericaceae

Bibliography: pages 133-144.An investigation was undertaken on the phosphorus nutrition of the ericoid endophytes isolated from the root systems of Vaccinium macrocarpon, Aiton, Rhododendron ponticum L., Calluna vulgaris (L.) Hull, Erica hispidula L., and E. mauritanica L

On the origin of the galaxy luminosity function

Evidence is summarized that suggests that when a protogalaxy collapses, a fraction $f$ of its gas fails to heat to the virial temperature, where $f$ is large for haloes less massive than the value $M^*$ associated with $L^*$ galaxies. Stars and galaxies form only from the cool gas fraction. Hot gas is ejected from low-mass systems as in conventional semi-analytic models of galaxy formation. In high-mass systems it is retained but does not cool and form stars. Instead it builds up as a largely inert atmosphere, in which cooling is inhibited by an episodically active galactic nucleus. Cold gas frequently falls into galactic haloes. In the absence of a dense atmosphere of virial-temperature gas it builds up on nearly circular orbits and forms stars. When there is a sufficiently dense hot atmosphere, cold infalling gas tends to be ablated and absorbed by the hot atmosphere before it can form stars. The picture nicely explains away the surfeit of high-luminosity galaxies that has recently plagued semi-analytic models of galaxy formation, replacing them by systems of moderate luminosity from old stars and large X-ray luminosities from hot gas.Comment: 5 pages. Version to appear in MNRAS Minor changes & corrected bibliography since first versio

Publications of the Jet Propulsion Laboratory, July 1961 through June 1962

Jpl bibliography on space science, 1961-196

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

Cold climate water/wastewater transportation and treatment - a bibliography: completion report

This bibliography contains 1,400 citations, including published and unpublished papers, on cold-climate water and wastewater transportation and treatment systems. Sources listed include state and federal agency files which contain information on systems in Alaskan communities and the Alyeska Pipeline Service Company camps. References to systems in other northern countries are also included. The objectives of this study were to identify causes of the failure of Alaskan water and wastewater treatment and transportation facilities and to seek methods for design improvements. Originally, the investigators contemplated an evaluation of systems performance in remote areas in relation to the original conception, planning, design, and construction. Because of the tremendous amount of literature examined, the evaluation was undertaken in a subsequent study, "Alaska Wastewater Treatment Technology" (A-058-ALAS) by Dr. Ronald A. Johnson.OWRT AGREEMENT NO. 14-31-0001-5002 PROJECT NO. A-047-ALAS The work upon which this completion report is based was supported by funds provided by the U. S. Department of the Interior, Office of Water Research and Technology, as authorized under the Water Resources Research Act of 1964, Public Law 88-379, as amended

A Bibliography of Community Analyses for Libraries

published or submitted for publicatio