A rigorous real time Feynman Path Integral and Propagator

We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time evolution operator. The derivation will be for all self-adjoint nonvector potential Hamiltonians. For systems with potential that carries at most a finite number of singularity and discontinuities, we will show that our propagator can be written in the form of a rigorous real time, time sliced Feynman path integral via improper Riemann integrals. We will also derive the Feynman path integral in Nonstandard Analysis Formulation. Finally, we will compute the propagator for the harmonic oscillator using the Nonstandard Analysis Feynman path integral formuluation; we will compute the propagator without using any knowledge of classical properties of the harmonic oscillator

Morphometric Relationship, Phylogenetic Correlation, and Character Evolution in the Species-Rich Genus Aphis (Hemiptera: Aphididae)

The species-rich genus Aphis consists of more than 500 species, many of them host-specific on a wide range of plants, yet very similar in general appearance due to convergence toward particular morphological types. Most species have been historically clustered into four main phenotypic groups (gossypii, craccivora, fabae, and spiraecola groups). To confirm the morphological hypotheses between these groups and to examine the characteristics that determine them, multivariate morphometric analyses were performed using 28 characters measured/counted from 40 species. To infer whether the morphological relationships are correlated with the genetic relationships, we compared the morphometric dataset with a phylogeny reconstructed from the combined dataset of three mtDNA and one nuclear DNA regions.Based on a comparison of morphological and molecular datasets, we confirmed morphological reduction or regression in the gossypii group unlike in related groups. Most morphological characteristics of the gossypii group were less variable than for the other groups. Due to these, the gossypii group could be morphologically well separated from the craccivora, fabae, and spiraecola groups. In addition, the correlation of the rates of evolution between morphological and DNA datasets was highly significant in their diversification.The morphological separation between the gossypii group and the other species-groups are congruent with their phylogenetic relationships. Analysis of trait evolution revealed that the morphological traits found to be significant based on the morphometric analyses were confidently correlated with the phylogeny. The dominant patterns of trait evolution resulting in increased rates of short branches and temporally later evolution are likely suitable for the modality of Aphis speciation because they have adapted species-specifically, rapidly, and more recently on many different host plants

Macroevolutionary Patterns in the Aphidini Aphids (Hemiptera: Aphididae): Diversification, Host Association, and Biogeographic Origins

, the most diverse genus in the family. We used a combined dataset of one nuclear and four mitochondrial DNA regions. A molecular dating approach, calibrated with fossil records, was used to estimate divergence times of these taxa.Most generic divergences in Aphidini occurred in the Middle Tertiary, and species-level divergences occurred between the Middle and Late Tertiary. The ancestral state of host use for Aphidini was equivocal with respect to three states: monoecy on trees, heteroecy, and monoecy on grasses. The ancestral state of Rhopalosiphina likely included both heteroecy and monoecy, whereas that of Aphidina was most likely monoecy. The divergence times of aphid lineages at the generic or subgeneric levels are close to those of their primary hosts. The species-level divergences in aphids are consistent with the diversification of the secondary hosts, as a few examples suggest. The biogeographic origin of Aphidini as a whole was equivocal, but the major lineages within Aphidina likely separated into Nearctic, Western Palearctic, and Eastern Palearctic regions.Most generic divergences in Aphidini occurred in the Middle Tertiary when primary hosts, mainly in the Rosaceae, were diverging, whereas species-level divergences were contemporaneous with diversification of the secondary hosts such as Poaceae in the Middle to Late Tertiary. Our results suggest that evolution of host alternation within Aphidini may have occurred during the Middle Tertiary (Oligocene) when the secondary hosts emerged

Landscapes of Heathrow : the aircraft landing gear compartment and the politics of global transfer

This paper, an output of an art research project, explores the agency of the aircraft landing gear compartment in global transfer. Through the prism of historical events involving aircraft preparing to land at London Heathrow, it reflects on the part played by the compartment in ecological and humanitarian struggle. Its theoretical frameworks include John Ruskin’s writing on geology, new materialism, and the planetary garden. These are brought into proximity with methodologies and collaborations developed through practice-based elements of the research, such as architectural modelling, geoforensic science and exhibition making. It incorporates an account of the process of reconstructing a compartment, as well as extracts from a microstratigraphic survey commissioned as part of the project. It examines the landing gear compartment’s capacity as a vessel in which dust, seeds, insects, pollen and even people are transported around the globe. It explores, too, its role as expository instrument, as far as it makes available for inspection the politics inscribed into its formal, spatial and temporal configuration. The paper argues that the wheel bay gives shape to a set of otherwise intangible aeromobilities, knowledge of which is integral to a nuanced understanding of the political geography of London Heathrow

The 4th Framework Programme in Ireland An evaluation of the operation and impacts in Ireland of the EU's fourth Framework Programme for Research and Development

Report prepared for Forfas by Technopolis LtdAvailable from British Library Document Supply Centre-DSC:m01/22610 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo