A recursive basis for primitive forms in symplectic spaces and applications to Heisenberg groups

2016 ◽  
Vol 32 (3) ◽  
pp. 265-285 ◽  
Author(s):  
Annalisa Baldi ◽  
Marilena Barnabei ◽  
Bruno Franchi
Author(s):  
Matías Reolid ◽  
Francisco J. Cardenal ◽  
Jesús Reolid

AbstractThe aim of this work is to obtain diverse morphometric data from digitized 3D models of scientifically accurate palaeoreconstructions of theropods from eight representative families. The analysed polyvinyl chloride (PVC) models belong to the genera Coelophysis, Dilophosaurus, Ceratosaurus, Allosaurus, Baryonyx, Carnotaurus, Giganotosaurus, and Tyrannosaurus. The scanned 3D models were scaled considering different body-size estimations of the literature. The 3D analysis of these genera provides information on the skull length and body length that allows for recognition of major evolutionary trends. The skull length/body length in the studied genera increases according with the size of the body from the smallest Coelophysis with a ratio of 0.093 to ratios of 0.119–0.120 for Tyrannosaurus and Giganotosaurus, the largest study theropods. The study of photogrammetric 3D models also provides morphometric information that cannot be obtained from the study of bones alone, but knowing that all reconstructions begin from the fossil bones, such as the surface/volume ratio (S/V). For the studied theropod genera surface/volume ratio ranges from 35.21 for Coelophysis to 5.55 for Tyrannosaurus. This parameter, closely related to the heat dissipation, help in the characterization of the metabolism of extinct taxa. Accordingly, slender primitive forms of the Early Jurassic (i.e. Coelophysis and Dilophosaurus) had relatively smaller skulls and higher mass-specific metabolic rates than the robust large theropods of the Cretaceous (i.e. Giganotosaurus and Tyrannosaurus). This work presents a technique that, when applied to proper dinosaur models, provides extent and accurate data that may help in diverse study areas within the dinosaur palaeontology and palaeobiology.


Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.


2019 ◽  
Vol 12 (05) ◽  
pp. 1950069
Author(s):  
Mahdieh Hakimi Poroch

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].


1965 ◽  
Vol 25 (2) ◽  
pp. 141-157 ◽  
Author(s):  
David S. Maxwell ◽  
Lawrence Kruger

Normal and reactive astrocytes in the cerebral cortex of the rat have been studied with the electron microscope following focal alpha particle irradiation. The presence of glycogen and approximately 60-A fibrils identify astrocyte cytoplasm in formalin-perfused tissue. The glycogen particles facilitate the identification of small processes and subpial and perivascular end-feet. Both protoplasmic and fibrous astrocytes contain cytoplasmic fibrils and should be distinguished on the basis of the configuration of their processes and their distribution. Acutely reactive astrocytes are characterized by a marked increase in the number of glycogen granules and mitochondria from the first day after irradiation. These cells later hypertrophy and accumulate lipid bodies and increased numbers of cytoplasmic fibrils. The glial "scar" consists of a greatly expanded volume of astrocyte cytoplasm filled with fibrils and displays no signs of astrocyte death, reversion to primitive forms, or extensive multiplication.


1994 ◽  
Vol 31 (3) ◽  
pp. 167-177 ◽  
Author(s):  
Nicol�s Andruskiewitsch ◽  
Jorge Devoto ◽  
Alejandro Tiraboschi

2006 ◽  
Vol 747 (3) ◽  
pp. 436-454 ◽  
Author(s):  
Benjamin A. Burrington ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas

1862 ◽  
Vol 4 ◽  
pp. 548-549
Author(s):  
David Brewster

In this paper the author gave a brief account of the various phenomena of fluid and gaseous cavities which he had discovered in diamond, topaz, beryl, and other minerals. He described—1. Cavities with two immiscible fluids, the most expansible of which has received the name of Brewstolyne, and the most dense that of Cryptolyne, from the American and French mineralogists.2. Cavities containing only one of these fluids.3. Cavities containing the two fluids, and also crystals of various primitive forms, some of which melt by heat and recrystallise in cooling.4. Cavities containing gas and vapour.


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