素数集合上の絶対シンプレクティック構造と絶対ワイル代数

The purpose of this paper is to give the absolute mathematics for the prime set. Absolute mathematics was introduced by N.Kurokawa in order to solve the Riemann conjecture. One of the idea for absolute mathematics is the prime differential on the rational integer Z. We analyze all possible arithmetic generalizations of symplectic and contact structures on a prime set. There are two different types of structures according to the Lagrangian subspace and Legendrian subspace. Main result is that the prime set is characterized by the Lagrangian subspace of absolute symplectic space (T*P, w). We also define a notion of the absolute Weyl algebra

Locations of sympatric Eastern box turtles (<i>Terrapene carolina carolina</i>) and amphibians (<i>Acris crepitans</i>, <i>Rana clamitans</i>, <i>Eurycea bislineata</i>) at Kennekuk Cove County Park in Vermilion County, Illinois during and after a natural ranavirus (FV3) outbreak in 2013.

<p>A 0.16km spatio-temporal cluster of FV3 cases was identified from August 2^nd–August 16^th in association with an ephemeral stream.</p

Gross appearance of necrotizing bacterial infection in <i>Terrapene carolina carolina</i> from Forest Glen Nature Preserve, Vermilion County, Illinois during a mortality event in 2011.

<p>Left forelimb (A) and right forelimb (B).</p

Complete blood counts for free-living <i>Terrapene carolina carolina</i> encountered during a mortality event in Forest Glen Nature Preserve, Vermilion County, Illinois in 2011.

<p>Complete blood counts for free-living <i>Terrapene carolina carolina</i> encountered during a mortality event in Forest Glen Nature Preserve, Vermilion County, Illinois in 2011.</p

Locations of Eastern box turtles (<i>Terrapene carolina carolina</i>) and ephemeral ponds used for amphibian breeding at Kickapoo State Park in Vermilion County, Illinois in 2014 and 2015 before, during, and after ranavirus (FV3) outbreaks.

<p>In 2014 a 0.03km spatio-temporal cluster of FV3 cases was identified from July 15^th–July 23^rd. In 2015 a 0.16km spatio-temporal cluster of FV3 cases was identified from July 8^th–July 23^th.</p

Complete blood counts for free-living <i>Terrapene carolina carolina</i> encountered during and after a frog virus 3-like ranavirus mortality event in Kennekuk Cove County Park, Vermilion County, Illinois in 2013.

<p>Complete blood counts for free-living <i>Terrapene carolina carolina</i> encountered during and after a frog virus 3-like ranavirus mortality event in Kennekuk Cove County Park, Vermilion County, Illinois in 2013.</p

Complete blood counts for free-living <i>T</i>. <i>carolina carolina</i> encountered before and after recurrent frog virus 3-like ranavirus mortality events in Kickapoo State Park, Vermilion County, Illinois in 2014 and 2015.

<p>CT = measure of central tendency (mean or median), Dispersion = measure of dispersion (standard deviation or 10-90^th percentiles).</p

Demographics, habitat use, and physical examination abnormalities in Eastern box turtles (<i>Terrapene carolina carolina</i>) captured before (PreOB), during (OB), and after (PostOB) mortality events in Vermilion County, IL from 2011–2015.

<p>NR = not recorded.</p

Number of turtles with pathogens detected and cause of death in free living <i>Terrapene carolina carolina</i> encountered before (PreOB), during (OB), and after (PostOB) mortality events in east-central Illinois from 2011–2015.

<p>Turtles with single pathogen detections are counted in the individual pathogen columns. Turtles with co-pathogens are counted in the co-infections column. FV3 = Frog virus 3-like ranavirus, BTADV = box turtle adenovirus, TerHV1 = Terrapene herpesvirus 1, BTMyco = <i>Mycoplasma</i> sp., NBI = necrotizing bacterial infection.</p

Number and timing of Eastern box turtle (<i>Terrapene carolina carolina</i>) captures before (PreOB), during (OB), and after (PostOB) mortality events in Vermilion County, Illinois from 2011–2015.

<p>The size of the marker reflects the number of animals captured.</p