Uniqueness of Bessel models: the archimedean case

In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.Comment: 22 page

A general form of Gelfand-Kazhdan criterion

We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion for a real reductive group in very general settings.Comment: 16 pages, to appear in Manuscripta Mathematic

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Depths and Thermal Habitat Used by Large versus Small Northern Pike in Three Minnesota Lakes

We monitored depths and temperatures used by large (>71‐cm) versus small Northern Pike Esox lucius in three north‐central Minnesota lakes with either acoustic telemetry or archival tags. Individual Northern Pike demonstrated flexibility in depths used within a season and between years. The fish had some tolerance for low levels of dissolved oxygen (<3 mg/L), but depth selection was generally constrained by low dissolved oxygen in summer and winter. The fish more fully exploited all available depths during winter and thermal turnover periods. During July and August, large Northern Pike tended to follow the thermocline into cooler water as upper water layers warmed. Selection ratios indicated that large Northern Pike preferred water temperatures of 16–21°C during August when temperatures up to 28°C were available. In two lakes providing dense overhead cover from water lilies in shallow water, small Northern Pike used warmer, shallower water compared with large fish during summer. In a third lake providing no such cover, small fish were more often in deeper, cooler water. For small Northern Pike, temperature seemed to be a secondary habitat consideration behind the presence of shallow vegetated cover. This study provided detailed temperature selection information that will be useful when considering temperature as an ecological resource for different sizes of Northern Pike.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141595/1/tafs1629.pd

Cone beam CT: non-dental applications

Initially Cone Beam CT was almost exclusively used to perform dental radiology. However, the first generation CBCT systems were later increasingly used to study sinuses, facial and nose fractures, temporomandibular joints etc. 3D-cephalometric head and neck studies became possible once CBCT systems were available that allowed scanning of the complete head. For this purpose a double rotation technique with stitching of the resulting two data sets was needed. CBCT systems on which the rotation could be stopped were needed to perform dynamic swallow or pharyngography studies. The advent of more powerful high-end CBCT systems led the way to temporal bone and skull base imaging. Finally, high-end “supine” CBCT systems using a “gantry” made small joint musculoskeletal imaging possible. These non-dental CBCT studies gradually replaced conventional X-rays and CT/MDCT studies because they allowed imaging with higher resolution, lower radiation dose and less metal artifacts. In this paper the most important non-dental CBCT indications will be discussed

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Contrasting environmental drivers of adult and juvenile growth in a marine fish: implications for the effects of climate change

Many marine fishes have life history strategies that involve ontogenetic changes in the use of coastal habitats. Such ontogenetic shifts may place these species at particular risk from climate change, because the successive environments they inhabit can differ in the type, frequency and severity of changes related to global warming. We used a dendrochronology approach to examine the physical and biological drivers of growth of adult and juvenile mangrove jack (Lutjanus argentimaculatus) from tropical north-western Australia. Juveniles of this species inhabit estuarine environments and adults reside on coastal reefs. The Niño-4 index, a measure of the status of the El Niño-Southern Oscillation (ENSO) had the highest correlation with adult growth chronologies, with La Niña years (characterised by warmer temperatures and lower salinities) having positive impacts on growth. Atmospheric and oceanographic phenomena operating at ocean-basin scales seem to be important correlates of the processes driving growth in local coastal habitats. Conversely, terrestrial factors influencing precipitation and river runoff were positively correlated with the growth of juveniles in estuaries. Our results show that the impacts of climate change on these two life history stages are likely to be different, with implications for resilience and management of populations

Integrated Ecosystem Assessment: Lake Ontario Water Management

BACKGROUND: Ecosystem management requires organizing, synthesizing, and projecting information at a large scale while simultaneously addressing public interests, dynamic ecological properties, and a continuum of physicochemical conditions. We compared the impacts of seven water level management plans for Lake Ontario on a set of environmental attributes of public relevance. METHODOLOGY AND FINDINGS: Our assessment method was developed with a set of established impact assessment tools (checklists, classifications, matrices, simulations, representative taxa, and performance relations) and the concept of archetypal geomorphic shoreline classes. We considered each environmental attribute and shoreline class in its typical and essential form and predicted how water level change would interact with defining properties. The analysis indicated that about half the shoreline of Lake Ontario is potentially sensitive to water level change with a small portion being highly sensitive. The current water management plan may be best for maintaining the environmental resources. In contrast, a natural water regime plan designed for greatest environmental benefits most often had adverse impacts, impacted most shoreline classes, and the largest portion of the lake coast. Plans that balanced multiple objectives and avoided hydrologic extremes were found to be similar relative to the environment, low on adverse impacts, and had many minor impacts across many shoreline classes. SIGNIFICANCE: The Lake Ontario ecosystem assessment provided information that can inform decisions about water management and the environment. No approach and set of methods will perfectly and unarguably accomplish integrated ecosystem assessment. For managing water levels in Lake Ontario, we found that there are no uniformly good and bad options for environmental conservation. The scientific challenge was selecting a set of tools and practices to present broad, relevant, unbiased, and accessible information to guide decision-making on a set of management options