Classification of the line-soliton solutions of KPII

In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation. The line-soliton solutions are solitary waves which decay exponentially in $(x,y)$-plane except along certain rays. In this paper, we show that those solutions are classified by asymptotic information of the solution as $|y| \to \infty$. Our study then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.Comment: 30 page

ASPECTS OF THE MICROPALAEONTOLOGY AND STRATIGRAPHY OF CRETACEOUS SHELF CARBONATES FROM THE OMAN MOUNTAINS

Five outcrop sections (Wadi Mi'aidin, Wadi Bani Kharus, Jebel Madar, Jebel Madamar and Jebel Salak), exposing Thamama and Wasia Group sediments were sedimentologically logged and sampled. Thin sections of each of the Thamama Group samples were prepared for micropalaeontological and microfacies analysis. The foraminifera, calcareous algae and calpionellids in each sample were recorded in order to provide a means of biostratigraphic subdivision, and together with microfacies analysis and sedimentological observations made in the field, provide a means of elucidating the depositional environments of the Thamama Group in the study area. Correlation between outcrop sections has been attempted using a biozonation scheme developed in the course of this project, and also by graphic correlation techniques. The taxonomy of 39 genera including 56 species of key foraminifera, calcareous algae and calpionellids is reviewed in detail. A complete revision of Cretaceous Middle Eastern lithostratigraphic nomenclature is required. Some recommendations for such a revision are proposed. Within the Thamama Group, 13 biozones/subzones are recognised using the extinction and inception events for key taxa. Both biozonal correlation and graphic correlation demonstrate that most Thamama Group formations are diachronous and may also be condensed at some localities. Biostratigraphic studies demonstrate that in the Central Oman Mountains region the Thamama Group formations are of the following ages: The Rayda Formation is of Early Berriasian age. It possibly extends into the earliest Valanginian at some localities (eg. Wadi Bani Kharus). The Salil Formation is of Berriasian - Valanginian age, possibly Hauterivian in age in its upper part at some localities. The Habshan Formation is of Hauterivian age everywhere, with possible extension into the Late Valanginian in its IOWCT part The Lekhwair Formation is essentially of Hauterivian - Barremian age (often largely Hauterivian). The Kharaib Formation is of typically Late Barremian - Early Aptian age, whilst the Shuaiba Formation is of Early Aptian age. Thamama Group deposition took place on an initially downwarped carbonate ramp, prograding towards the Tethyan Ocean (towards the north and east). Offshore palaeowinds precluded the development of reefs, but an oolitic shoal was located at the margin of the ramp, at least during Hauterivian times.Earth Sciences Resources Institute at University College of Wales, Swansea and University of South Carolina, USA and AMOCO Petroleum Company Limited, Houston, US

An Italian dinosaur Lagerstätte reveals the tempo and mode of hadrosauriform body size evolution

During the latest Cretaceous, the European Archipelago was characterized by highly fragmented landmasses hosting putative dwarfed, insular dinosaurs, claimed as fossil evidence of the “island rule”. The Villaggio del Pescatore quarry (north-eastern Italy) stands as the most informative locality within the palaeo-Mediterranean region and represents the first, multi-individual Konservat-Lagerstätte type dinosaur-bearing locality in Italy. The site is here critically re-evaluated as early Campanian in age, thus preceding the final fragmentation stages of the European Archipelago, including all other European localities preserving hypothesized dwarfed taxa. New skeletal remains allowed osteohistological analyses on the hadrosauroid Tethyshadros insularis indicating subadult features in the type specimen whereas a second, herein newly described, larger individual is likely somatically mature. A phylogenetic comparative framework places the body-size of T. insularis in range with other non-hadrosaurid Eurasian hadrosauroids, rejecting any significant evolutionary trend towards miniaturisation in this clade, confuting its ‘pygmy’ status, and providing unmatched data to infer environmentally-driven body-size trends in Mesozoic dinosaurs

A Study of Form and Structure in Pierre Boulez\u27s Pli selon Pli

In his 1963 treatise, Penser la musique aujourd’hui, Pierre Boulez proposes that there should be no distinction between serial materials and large-scale form. After his self-professed failure with Structures 1a and Polyphonie X due to the incapacity of the twelve-tone series to provide form in and of itself, Boulez reassessed and expanded his compositional approach to include what he refers to as “indiscipline,” which permitted him a new freedom to modify his materials as he saw fit through a plethora of new techniques, and to link these materials to large-scale forms that take their inspiration largely from literary influences. This investigation seeks to concretize Boulez’s proposed relationship between serial content and large-scale form in “Don” (1962) and “Tombeau” (1959), the framing movements of Pli selon Pli, largely by establishing the nature of their formal organization and the origin of the serial materials used in their construction. The course of this investigation traces the developmental history of materials used in “Don” and “Tombeau” which includes analyses of materials used in the unpublished Oubli signal lapidé (1952), the retracted drama L’Orestie (1954–55), the unpublished work for solo flute Strophes (1955–56), the Troisième Sonate (1955–57), Le Marteau sans maître (1953-55) and the inner movements of Pli selon Pli: the “Improvisation[s] sur Mallarmé I, II, and III” (1957, 1957, and 1959 respectively). The materials developed for “Don” and “Tombeau” are largely continuations of different lineages of serial materials developed for these earlier works and form constellations of structurally related materials that persist beyond the boundaries of individual works. Taken together, the works composed during the period 1952–62 are the most inspired and creative in Boulez’s compositional history. The trajectory of this investigation incrementally introduces the reader to increasingly larger-scale means of organizing serial materials that culminate in Boulez’s evolving theory of discontinuous musical form. Connections among works and their organizational structure are largely derived from sketch studies undertaken at the Paul Sacher Foundation in Basel, Switzerland

kk-Schur functions and affine Schubert calculus

This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010 at the Fields Institute in Toronto, Ontario. The story of this research is told in three parts: 1. Primer on $k$-Schur Functions 2. Stanley symmetric functions and Peterson algebras 3. Affine Schubert calculusComment: 213 pages; conference website: http://www.fields.utoronto.ca/programs/scientific/10-11/schubert/, updates and corrections since v1. This material is based upon work supported by the National Science Foundation under Grant No. DMS-065264

Preservation of Proterozoic Microbial Mats

Meso- to Neoproterozoic peritidal carbonate strata commonly contain early diagenetic chert deposits that can record evidence of mineral and organic precursors. Exceptional morphologic preservation can be used to place time constraints on silicification, often indicating silicification is penecontemporaneous with mat growth. Silica-rich sedimentary deposits have also been suggested as potential targets for the search for extraterrestrial life on Mars. The chapters in this dissertation investigate fluid compositions capable of precipitating primary and secondary silica phases and the extent to which microorganisms are preserved, specifically their morphology and chemistry, by early silicification. Twenty potential fluid compositions were modeled using PHREEQC, and the mineral phases capable of precipitating were compared to the mineralogies observed in thin sections from silicified microbial mats of the Angmaat Formation, Bylot Supergroup. This model indicates that silica phases were capable of precipitating as primary or secondary mineral phases over a wide range of fluid chemistries. However, only brine solutions were capable of precipitating each mineral phase observed in the Angmaat Formation samples, including amorphous silica and silica gel.Hydrous silica phases permeate the sheaths of the organisms, which preserves the individual microorganisms and the complexity of microbial mats. Mat morphologies in the Angmaat Formation preserve a range of taphonomic states, including well-preserved mats that are interpreted to reflect the top layers of mats, to poorly-preserved mats that may reflect buried layers in the mat that were exposed to greater heterotrophic degradation. A taphonomic assessment of the individual microfossils reveals preserved complexity within the microbial mats and a new taphonomic assessment technique is introduced to account for the complexity. Regardless of taphonomic grade, coccoidal microfossils exhibit better preservation than filamentous mat-building organisms. Differential preservation may be related to the motility of the organisms.Organic geochemical characterization of the silicified mats indicates that despite exceptional morphologic preservation, lipids are not preserved in early diagenetic chert. Lipids, specifically hopanes and steranes, could be used to elucidate microbial processes active at the time of silicification and paleoenvironmental conditions. The lack of lipid preservation suggests that silica-rich low-temperature deposits may not be ideal targets for the search of ancient extraterrestrial life