Hamilton-Jacobi theory for optimal control problems on stratified domains

This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz dynamics. This background gives the motivation for our results for systems over stratified domains, which is a system with non-Lipschitz dynamics that were introduced by Bressan and Hong. We provide an example that shows their attempt to derive a Hamilton-Jacobi characterization of the value function is incorrect, and discuss the nature of their error. A new construction of a multifunction is introduced that possesses properties similar to those of a Lipschitz multifunction, and is used to establish Hamiltonian criteria for weak and strong invariance. Finally, we use these characterizations to show that the minimal time function and the value function for a Mayer problem, both over stratified domains, satisfy and are the unique solutions to a proximal Hamilton-Jacobi equation

Notes on actinomycosis, and its transmissibility to the human subject

I refer to the question of the transmissibility of some bovine diseases to human beings by the consumption of the meat of diseased animals. The primary object of my paper is to show that there is prevalent amongst the cattle in Tasmania, as well as in the adjacent colonies, from which we obtain a large proportion of our meat supply, a disease which resembles tuberculosis in some respects, but differs from it in the specific micro-organism that is the cause of the disease, and yet, like tuberculosis, is transmissible to the human subject, and is almost as distressing in its consequences. Soon after the publication of the discovery of the actinomyces or ray-fungus iu diseased cattle, the same vegetable parasite was found in man; and it was then seen that the tumours in the bovine species presented great similarity to those found in the human subject, leading to the presumption that it was identically the same disease. It has been shown by experiment that the introduction of the fungus by inoculation into a calf has produced swellings which contained the characteristic clubs of the fungus, thus suggesting that this disease can be transmitted by direct inoculation. Many similar experiments have been made with a view to prove the transmissibility of this vegetable parasite from animal to animal, and in the majority of cases with a positive result

X-ray generation from and spectroscopy of a thin liquid sheet

In this thesis a fan spray nozzle design is presented that is capable of producing single micrometer thick sheets of liquid, which are stable and flat. These sheets are characterised by various interferometric techniques, and some elementary fluid dynamics calculations are employed to understand the formation of the sheet. A new experimental vacuum chamber was designed and built, and the liquid sheet jet apparatus was installed into it and run successfully in the vacuum. Soft X-ray absorption measurements were attempted, but due to problems with a lack of X-ray flux and contamination of the experimental apparatus no results have yet been obtained. The sheet was also used as a source for high harmonic generation, generating harmonics up to 50\,eV. The mechanism of high harmonic generation in the liquid is investigated, with the conclusion being reached that it is a similar mechanism to the semi-classical three step model. The effects of scattering are considered, and found to be less severe than anticipated due to correlation effects in the condensed phase.Open Acces

Positioning for Trade Liberalization: Structure of Earnings, Comparative and Competitive Advantage of Agricultural Households in the United States and Canada

Consumer/Household Economics, International Relations/Trade,

The Distribution of X-ray Dips with Orbital Phase in Cygnus X-1

We present results of a comprehensive study of the distribution of absorption dips with orbital phase in Cygnus X-1. Firstly, the distribution was obtained using archival data from all major X-ray observatories and corrected for the selection effect that phase zero (superior conjunction of the black hole) has been preferentially observed. Dip occurrence was seen to vary strongly with orbital phase \phi, with a peak at \phi ~ 0.95, i.e. was not symmetric about phase zero. Secondly, the RXTE ASM has provided continuous coverage of the Low State of Cygnus X-1 since Sept. 1996, and we have selected dip data based on increases in hardness ratio. The distribution, with much increased numbers of dip events, confirms that the peak is at \phi ~ 0.95, and we report the discovery of a second peak at \phi ~ 0.6. We attribute this peak to absorption in an accretion stream from the companion star HDE 226868. We have estimated the ionization parameter at different positions showing that radiative acceleration of the wind is suppressed by photoionization in particular regions in the binary system. To obtain the variation of column density with phase, we make estimates of neutral wind density for the extreme cases that acceleration of the wind is totally suppressed, or not suppressed at all. An accurate description will lie between these extremes. In each case, a strong variation of column density with orbital phase resulted, similar to the variation of dip occurrence. This provides evidence that formation of the blobs in the wind which lead to absorption dips depends on the density of the neutral component in the wind, suggesting possible mechanisms for blob growth.Comment: 9 pages, Latex, 7 ps figures. accepted by MNRA

Preliminary study of possible power development on the Gasconade River

The location of a possible dam site on the Gasconade River as a thesis proved to be a very interesting subject. Our first trip pointed out to us that we had undertaken a large task. We also realized that our subject was too big to complete thouroughly sic in the time alloted. Due to this circumstance we tried to cover the essential facts and to eliminate as much of the detail work as possible. For instance, we made no attempt to make a complete survey of the basin, instead, we ran surveys for some distance up the river to give an idea of the nature of the country and a way of approximating the volume of the basin --Foreword, Page 3

Christmas books

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte, 2012Fecha de publ. tomada de WWW British Library cat

Notes relating to certain fossil leaves and fruits found in the auriferous drifts of Gulgong, New South Wales

The few specimens of Palaeontological Botany I am sending to the Museum of the Royal Society, Tasmania (kindly forwarded by my father), are complementary to the fossil seed-vessels or fruits presented by me to the Museum some eighteen months back. They all were obtained from the same "lead," or auriferous drift, in the immediate neighbourhood of Gulgong, at a depth of about 146 feet. This ancient watercourse, called the "Black Lead," from containing dark ligneous clay amongst its strata, has been worked for fully a mile in length, and was found very rich in gold. The overlying strata consist of alluvial soil of a rich volcanic character—clay, gravel, and basalt. Of the latter, two varieties are met with; one, the hard, close-grained, bluish-black stone; the other, called by miners "soft basalt," from its friable, earthy nature, and derived from the hard variety by decomposition

Auriferous country and gold-bearing rocks

The subject of my paper is one that cannot fail to prove of interest to this Society, seeing the great importance the goldmining industry is assuming, and has already assumed, in the colony of Tasmania. The advantages to be gained by fostering this industry in the colony need scarcely be dilated upon by me, as they are so patent to any one who will take the trouble to examine into the causes of the vast progress the Eastern colonies of Australia have made during the past quarter century. The numerous large towns and villages that dot this portion of the continent —the majority of them founded upon, or connected in some way with, the discovery of gold in their immediate neighbourhood— speak for themselves; and the immense impetus to trade, commerce, and immigration which it brings about shows what mining will do for a country, hitherto in a state of almost primeval solitude. But for this source of wealth, the major portion of these colonies would still have remained in a "state of nature"—one huge sheep run, with but a sparse population and scattered country villages

The Ursinus Weekly, December 12, 1902

Impressions of the football season • A football player\u27s view • Football spirit • Football review • Blenheim • Defects of football • Financial statement • Clubs reorganize • Societies • YMCAhttps://digitalcommons.ursinus.edu/weekly/3067/thumbnail.jp