Probabilistic study of a dynamical system

This paper investigates the relation between a branching process and a non-linear dynamical system in C2. This idea has previously been fruitful in many investigations, including that of the FKPP equation by McKean, Neveu, Bramson, and others. Our concerns here are somewhat different from those in other work: we wish to elucidate those features of the dynamical system which correspond to the long-term behaviour of the random process. In particular, we are interested in how the dimension of the global attractor corresponds to that of the tail {sigma}-algebra of the process. The Poincaré–Dulac operator which (locally) intertwines the non-linear system with its linearization may sometimes be exhibited as a Fourier–Laplace transform of tail-measurable random variables; but things change markedly when parameters cross values giving the ‘primary resonance’ in the Poincaré–Dulac sense. Probability proves effective in establishing global properties amongst which is a clear description of the global convergence to the attractor. Several of our probabilistic results are analogues of ones obtained by Kesten and Stigum, and by Athreya and Ney, for discrete branching processes. Our simpler context allows the use of Itô calculus. Because the paper bridges two subjects, dynamical-system theory and probability theory, we take considerable care with the exposition of both aspects. For probabilist readers, we provide a brief guide to Poincaré–Dulac theory; and we take the view that in a paper which we hope will be read by analysts, it would be wrong to fudge any details of rigour in our probabilistic arguments

Installing fiber insulation

A method for installing fragile, high temperature insulation batting in an elongated cavity or in a resilient wire sleeve to form a resilient seal. The batting is preformed to rough dimensions and wrapped in a plastic film, the film being of a material which is fugitive at a high temperature. The film is heat sealed and trimmed to form a snugly fit skin which overlaps at least at one end to permit attachment of a pull cord. The film absorbs the tensile force of pulling the film enclosed batting through the cavity or wire mesh sleeve and is subsequently driven off by high temperature baking, leaving only the insulation in the cavity or wire mesh sleeve

New looks at and for Onespa, Buzyges, and Librita (Lepidoptera: Hesperiidae: Hesperiinae), with new combinations and descriptions of a new genus and six new species

Thirteen species of skippers (six newly described; Lepidoptera: Hesperiidae: Hesperiinae: Hesperiini) from higher elevations of Mexico and Central America are reviewed. These are included in four genera (one newly described), some with proposed new combinations. Onespa Steinhauser, 1974, originally described as monotypic, is shown to include three species in addition to its type species, Onespa nubis Steinhauser, 1974. One of these, Atrytone gala Godman, 1900, that has been misplaced in several genera since its description, represents a new combination. The other two species, distributed in montane habitats in northwestern Mexico and in Costa Rica, are described as new. Buzyges Godman, 1900, distributed in Mexico and Central America and also formerly considered monotypic, is shown to embrace four species. Besides the type species, Buzyges idothea Godman, 1900, two species long placed in Poanes Scudder, 1872, Pamphila rolla Mabille, 1883, and Poanes benito Freeman, 1979, are included as new combinations. Another species, known only from Costa Rica, is described as new. These are united by several superficial characters, but especially by genital morphology of both sexes. Librita Evans, 1955, was described to include three species of which one, Librita raspa Evans, 1955, was subsequently removed. Augiades heras Godman, 1900 is here also removed from Librita and placed in a new genus with three previously undescribed species. This completes the disintegration of Librita, which is now monotypic. The four genera, although exhibiting similarities suggesting potential alliance, differ in their unique combinations of several superficial and genital traits from each other and other hesperiine skippers

Assembly for recovering a capsule Patent

Assembly for opening flight capsule stabilizing and decelerating flaps with reference to capsule recover