On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

A tour from the City of New-York, to Detroit, in the Michigan Territory, made between the 2d of May and the 22d of September, 1818 : the tour extends from New-York, by Albany, Schenectady, and Utica to Sacket's Harbor, and thence throught Lake Ontario, to St. Lawrence river, and down that stream to Hamilton village. Thence along both banks of the St. Lawrence, from Hamilton to the Thousand Islands; thence to Sacket's Harbor by water; from that place by the route of great Sodus, Geneva, Cananaigua and Batavia, to Buffalo; and from thence to Black Rock, Fort Erie, the Falls of Niagara, Queenston, Lewiston, and the memorable fields of Bridgewater and Chippewa after viewing the interesting place of Niagara, the author traversed the south shore of Lake Erie to the City of Detroit, and visited in the latter range, Dunkirk, Erie, Cleveland, Sandusky, and other places of less note. The tour is accompanied with a map upon which the route will be designated; a particular map of the Falls andRiver of Niagara, and the environs of the City of Detroit /

Errata slip inserted.

The map of Hamilton County /

"Reprinted from the Ohio archaeological and historical quarterly of April 1926."

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Second Welland Canal - Book 1, Survey Map 10 - St. Catharines

Survey map of the Second Welland Canal created by the Welland Canal Company along the western edge of the Town of St. Catharines. Although not labelled, the Second Welland Canal can be seen running through the map along with its tow path, which is located on the southwestern edge of the waterway. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks are identified and include streets and roads (ex. Ontario Street and Road to Hamilton), Artesian Mineral Well, Dr. Mack's Artesian Well, Stephenson House Mineral Well and Gas Works, New Brewery, Old Brewery, Welland House Mineral Well, L. Shickluna's Shipyard, Vinegar Manufactory, Merritt's Covered Race, Mitchels Wharf, Sail Loft, an office, a tavern, two barns, a boathouse, a structure belonging to T. Nihan (or P. Nihen), and some store houses. Properties and property owners of note are: Concession 6 Lot 20, William H. Merritt, E. S. Adams, William Chace, Jacob Hainer, J. Taylor, and J. P. Merritt.

Second Welland Canal - Book 2, Survey Map 3 - Locks 8, 9 and 10 in Grantham

Survey map of the Second Welland Canal created by the Welland Canal Company showing the Grantham Township between the Town of St. Catharines and Merritton. Identified structures associated with the Canal include Locks 8, 9, and 10, waste weirs, the towing path, and several floating bridges. The surveyors' measurements and notes can be seen in red and black ink and pencil. Several stones and tree stumps likely used in the measurements are identified on the map. Local area landmarks are also identified and include streets and roads(ex. Macadamized Road to Thorold), J. Hamilton's Hotel, a school house, McCoy's Farm House, Bradley's House, O. Phelps Saw Mill, Disher and Hait's Woolen Mill, Centreville Mills, a bridge, several barns, and a number of structures (possibly houses, cabins, or shops) belonging to: P. McCoy, E. McLachlan, T. Wilson, W. Wilson, M. Bradley, S. Bradley, P. Boyle, J. Bradley, E. Grant, and W. Church. Lock 12 and 15 of the original canal are also identified. Properties and property owners of note are: Concession 8 Lots 12, 13 and 14, O. J. Phelps, P. McCoy, A. Bradley, C. Bradley, T. Reed, O. Clifford, J. Bradley, W. C. Loan Company, Duffin, and T. Towers Mill Lot.

Second Welland Canal - Book 3, Survey Map 21 - Village of Port Colborne

Survey map of the Second Welland Canal created by the Welland Canal Company showing the areas in and around Port Colborne. Identified structures associated with the Canal include Lighthouse, Pier Light, Old Lock House, Collector's Office, Harbour Master's House, Canal Boundary, Back Ditch, Reserved Back Ditch, Basin, Light-Keeper's House and Ferry Recess. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks and businesses are also identified and include Gordon's Woodyard, Welland Rail Road, Welland Railway Elevator and Proposed Elevator, W.R.R. Flour Shed, Roman Catholic Church, School House, Sandhills, Lake Erie, and the High Water Mark. Streets running parallel to Canal include King St., West St., East St., Queen St., Hamilton St., and the Road Allowance are labelled. Streets running perpendicular to Canal include Kent St., Victoria St., Adelaide St., SugarLoaf St., George St., Alexandrina St., William St., Fort Erie St., Lake Rd., and New Road to Dutch Settlement are also labelled. Property owners and leasers as well as buildings on lots are also idenitified and noted as follows: Adams estate, J. Towhig, J.C. Kerr, Mrs. Hill, S. Cooke, Mrs. Yocum, W.T. Cooke, P. Wintermute, J. Shickluna, William Cooke, J. McChesney, John Beatty, W. Robertson, John Gordon, T. Armstrong, John Harper, George Keefer, Estate of James Black, Thomas Park, N. Higgins, S. Hopkins, and L.G. Cartier. Map of the Village of Port Colborne. Being Lot No. 27 and part of Lot No. 28 in the 1st Con. Township of HUMBERSTONE. Scale 2 Chs. per Inch. land shaded in RED Owned by DEPT. Do. Do. BLUE Sold to the COUNTY of WELLAND

Welland Canal Survey of Lands William Hamilton Merritt Esquire 1826

Survey map and description of William Hamilton Merritt's land created by The Welland Canal Company. Included is a written description of the land along with a drawing of the land. The drawing also includes John Hainer's Land. Noteable features include; saw mill, salt works, line between Hainer's and Merritt's land,line between John Clendennan's and Merritt's land, road, bridge, tow path, 12 mile creek and canal. Surveyor notes are seen in pencil on the map. The survey was signed and submitted on August 23rd, 1826. The land is 17 acres, 3 roads and 20 perches.

Letter to William Hamilton Merritt from S.D. Woodruff

Letter in which S.D. Woodruff suggests that the proposed road be constructed upon the line as suggested and laid down upon the map. He also suggests that George Rykert be engaged to survey the land. The letter is addressed to William Hamilton Merritt, Mar. 7, 1854.

A novel linkage map of sugarcane with evidence for clustering of retrotransposon-based markers

Background: The development of sugarcane as a sustainable crop has unlimited applications. The crop is one of the most economically viable for renewable energy production, and CO2 balance. Linkage maps are valuable tools for understanding genetic and genomic organization, particularly in sugarcane due to its complex polyploid genome of multispecific origins. The overall objective of our study was to construct a novel sugarcane linkage map, compiling AFLP and EST-SSR markers, and to generate data on the distribution of markers anchored to sequences of scIvana_1, a complete sugarcane transposable element, and member of the Copia superfamily. Results: The mapping population parents ('IAC66-6' and 'TUC71-7') contributed equally to polymorphisms, independent of marker type, and generated markers that were distributed into nearly the same number of co-segregation groups (or CGs). Bi-parentally inherited alleles provided the integration of 19 CGs. The marker number per CG ranged from two to 39. The total map length was 4,843.19 cM, with a marker density of 8.87 cM. Markers were assembled into 92 CGs that ranged in length from 1.14 to 404.72 cM, with an estimated average length of 52.64 cM. The greatest distance between two adjacent markers was 48.25 cM. The scIvana_1-based markers (56) were positioned on 21 CGs, but were not regularly distributed. Interestingly, the distance between adjacent scIvana_1-based markers was less than 5 cM, and was observed on five CGs, suggesting a clustered organization. Conclusions: Results indicated the use of a NBS-profiling technique was efficient to develop retrotransposon-based markers in sugarcane. The simultaneous maximum-likelihood estimates of linkage and linkage phase based strategies confirmed the suitability of its approach to estimate linkage, and construct the linkage map. Interestingly, using our genetic data it was possible to calculate the number of retrotransposonscIvana_1 (similar to 60) copies in the sugarcane genome, confirming previously reported molecular results. In addition, this research possibly will have indirect implications in crop economics e. g., productivity enhancement via QTL studies, as the mapping population parents differ in response to an important fungal disease.

A New Velocity Map for Byrd Glacier, East Antarctica, from Sequential Aster Satellite Imagery

New ice-velocity measurements are obtained for the main trunk of Byrd Glacier, East Antarctica, using recently acquired Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) imagery. The velocities are derived from the application of a cross-correlation technique to sequential images acquired in 2000 and 2001. Images were co-registered and ortho-rectified with the aid of a digital elevation model (DEM) generated from ASTER stereo imagery. This paper outlines the process of DEM generation, image co-registration and correction, and the application of the cross-correlation technique to obtain ice velocities. Comparison of the new velocity map with earlier measurements of velocity from 1978 indicates that the glacier has undergone a substantial deceleration between observations. Portions of the glacier flowing at speeds of similar to 850 m a(-1) in 1978/79 were flowing at similar to 650 m a(-1) in 2000/01. The cause of this change in ice dynamics is not known, but the observation shows that East Antarctic outlet glaciers can undergo substantial changes on relatively short timescales.

Land Use Map, Cincinnati Region, Ohio, 1975 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: OKI regional land use : 1975. It was published by OKI Regional Planning Authority in 1975. Scale [ca. 1:5,000]. Covers Cincinnati Region, Ohio including Butler, Clermont, Hamilton, Warren counties, Ohio; Boone, Campbell, and Kenton counties, Kentucky; and Dearborn and Ohio counties, Indiana. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Ohio South State Plane NAD 1983 coordinate system (in Feet) (Fipszone 3402). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map is colored to show land use categories: Urban residential ; Suburban residential ; Commercial ; Institutional/Service ; Utilities ; Industrial ; Resource extraction ; Recreational/Open space ; Cropland ; Grassland ; Woodland ; Water. It also shows features as major roads, drainage, administrative and political boundaries, and more. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Self-organized distribution of periodicity and chaos in an electrochemical oscillator

We report a detailed numerical investigation of a prototype electrochemical oscillator, in terms of high-resolution phase diagrams for an experimentally relevant section of the control (parameter) space. The prototype model consists of a set of three autonomous ordinary differential equations which captures the general features of electrochemical oscillators characterized by a partially hidden negative differential resistance in an N-shaped current-voltage stationary curve. By computing Lyapunov exponents, we provide a detailed discrimination between chaotic and periodic phases of the electrochemical oscillator. Such phases reveal the existence of an intricate structure of domains of periodicity self-organized into a chaotic background. Shrimp-like periodic regions previously observed in other discrete and continuous systems were also observed here, which corroborate the universal nature of the occurrence of such structures. In addition, we have also found a structured period distribution within the order region. Finally we discuss the possible experimental realization of comparable phase diagrams.

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.

Tick saliva induces regulatory dendritic cells: MAP-kinases and Toll-like receptor-2 expression as potential targets

Ticks (Acari: Ixodidae) are bloodsucking ectoparasitic arthropods of human and veterinary medical importance. Tick saliva has been shown to contain a wide range of bioactive molecules with vasodilatory, antihemostatic, and immunomodulatory activities. We have previously demonstrated that saliva from Rhipicephalus sanguineus ticks inhibits the maturation of dendritic cells (DCs) stimulated with LPS. Here we examined the mechanism of this immune subversion, evaluating the effect of tick saliva on Toll-like receptor (TLR)-4 signalling pathway in bone marrow-derived DCs. We demonstrated that R. sanguineus tick saliva impairs maturation of DCs stimulated with LIPS, a TLR-4 ligand, leading to increased production of interleukin (IL)-10 and reduced synthesis of IL-12p70 and TNF-alpha. The immunomodulatory effect of the tick saliva on the production of pro-inflammatory cytokines by DCs stimulated with LPS was associated with the observation that tick saliva inhibits the activation of the ERK 1/2 and p38 MAP kinases. These effects were independent of the expression of TLR-4 on the surface of DCs. Additionally, saliva-treated DCs also presented a similar pattern of cytokine modulation in response to other TLR ligands. Since the recent literature reports that several parasites evade immune responses through TLR-2-mediated production of IL-10, we evaluated the effect of tick saliva on the percentage of TLR-2(+) DCs stimulated with the TLR-2 ligand lipoteicoic acid (LTA). The data showed that the population of DCs expressing TLR-2 was significantly increased in DCs treated with LTA plus saliva. In addition, tick saliva alone increased the expression of TLR-2 in a dose- and time-dependent manner. Our data suggest that tick saliva induces regulatory DCs, which secrete IL-10 and low levels of IL-12 and TNF-alpha when stimulated by TLR ligands. Such regulatory DCs are associated with expression of TLR-2 and inhibition of ERK and p38, which promotes the production of IL-10 and thus down-modulates the host`s immune response, possibly favouring susceptibility to tick infestations. (C) 2009 Elsevier B.V. All rights reserved.