Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes

We study the long time behaviour of a large class of diffusion processes on $R^N$, generated by second order differential operators of (possibly) degenerate type. The operators that we consider {\em need not} satisfy the H\"ormander condition. Instead, they satisfy the so-called UFG condition, introduced by Herman, Lobry and Sussman in the context of geometric control theory and later by Kusuoka and Stroock, this time with probabilistic motivations. In this paper we study UFG diffusions and demonstrate the importance of such a class of processes in several respects: roughly speaking i) we show that UFG processes constitute a family of SDEs which exhibit multiple invariant measures and for which one is able to describe a systematic procedure to determine the basin of attraction of each invariant measure (equilibrium state). ii) We use an explicit change of coordinates to prove that every UFG diffusion can be, at least locally, represented as a system consisting of an SDE coupled with an ODE, where the ODE evolves independently of the SDE part of the dynamics. iii) As a result, UFG diffusions are inherently "less smooth" than hypoelliptic SDEs; more precisely, we prove that UFG processes do not admit a density with respect to Lebesgue measure on the entire space, but only on suitable time-evolving submanifolds, which we describe. iv) We show that our results and techniques, which we devised for UFG processes, can be applied to the study of the long-time behaviour of non-autonomous hypoelliptic SDEs and therefore produce several results on this latter class of processes as well. v) Because processes that satisfy the (uniform) parabolic H\"ormander condition are UFG processes, our paper contains a wealth of results about the long time behaviour of (uniformly) hypoelliptic processes which are non-ergodic, in the sense that they exhibit multiple invariant measures.Comment: 66 page

Gender Differences in an Aviation Physiology Environment

Men still dominate flying by better than a ten to one ratio, but there is no question that female participation in all aspects of aviation has increased dramatically in the past decade, and will no doubt continue to do so in the future. Although women have been flying airplanes since 1910, little attention was paid to them in terms of suitability and adaptability to flight, as compared to their male counterparts, until recently. It wasn\u27t until the 1980\u27s, after Congress modified existing law to allow women into the flight programs of the military in large numbers, that studies to ascertain what accommodations, if any, would have to be made to cockpits, training, health care, flight clothing, and a multitude of other situations hitherto largely unconsidered. Further emphasis was added as U.S. air carriers, in response to the booming expansion of the airlines in the 1990’s, began hiring women pilots in unprecedented numbers

How Safe is “Safe Enough?”

A fair question, is it not? When it comes to aviation safety, just how & is safe enough? And, by the way, who gets to make this decision? Most of the time those of us in the aviation professions are involved in daily operational decisions that impact safety, but our view tends to be narrow and focused on a particular problem or situation, thus we lose sight of the big picture. So let\u27s step back for a moment and take a broad look at how and why policies, rules, and laws are made that affect aviation safety

A Fanciful Look at Air Carrier Operations in the Year 2050

Captain Lance Boyle smiled as he felt the smooth rippling thunk of the landing gear tires meeting the runway. Now that was how aircraft should land, not this vertical takeoff and landing nonsense employed by the newest planes, still called that even though they didn\u27t have wings at all. He eased forward on the side-stick controller slightly. The nose gear touched down and the strut compressed gently to give him a better view of the runway here at Los Angeles Air and Space Port. Captain Boyle continued the roll-out, pleased that his last landing in the real world had been a good one. Regretfully, there was no one else in the cockpit to congratulate him, since the Boeing-Bus 370, like all of the transport aircraft of its era, was a single pilot machine. Now the airplane, and the pilot as well, was being phased out, victims of the laws of economics and advancements in technology

Review of geographical stocks of tropical dolphins (Stenella spp. and Delphinus delphis) in the eastern Pacific

Information on geographical variation is reviewed for Stenella attenuata, S. longirostris, S. coeruleoalba, and Delphinus delphis in the eastern tropical Pacific, and boundaries for potential management units are proposed. National Marine Fisheries Service and Inter-American Tropical Tuna Commission sighting records made from 1979 to 1983 which were outside boundaries used in a 1979 assessment were examined for validity. Tagging returns and morphological data were also analyzed. Several stock ranges are expanded or combined. Three management units are proposed for S. attenuata: the coastal, northern offshore, and southern offshore spoiled dolphins. Four management units are proposed for S. longirostris: the Costa Rican, eastern, northern whitebelly, and southern whitebelly spinner dolphins. Two provisional management units are proposed for S. coeruleoalba: the northern and southern striped dolphins. Five management units (two of which are provisional) are proposed for D. delphis: the Baja neritic, northern, central, southern, and Guerrero common dolphins. Division into management units was based on morphological stock differences and distributional breaks. (PDF file contains 34 pages.

Suitability of ANSI standards for quantifying communication satellite system performance

A study on the application of American National Standards X3.102 and X3.141 to various classes of communication satellite systems from the simple analog bent-pipe to NASA's Advanced Communications Technology Satellite (ACTS) is discussed. These standards are proposed as means for quantifying the end-to-end communication system performance of communication satellite systems. An introductory overview of the two standards are given followed by a review of the characteristics, applications, and advantages of using X3.102 and X3.141 to quantify with a description of the application of these standards to ACTS

On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

A Comparison of Time Delay and Decreasing Prompt Hierarchy Strategies on the Acquisition of Microwave Cooking Skills

A report submitted by Barbara Niemeyer to the the Research and Creative Productions Committee in 1990 on persons with manifesting severe disabilities learning to perform tasks