Floyd Bennett Field is an airfield in the Marine Park neighborhood of southeast Brooklyn in New York City, along the shore of Jamaica Bay. The airport hosted commercial and general aviation traffic before being used as a naval air station. Bennett Field is part of the Gateway National Recreation Area's Jamaica Bay Unit, is managed by the National Park Service. While no longer used as an operational commercial, military, or general aviation airfield, a section is still used as a helicopter base by the New York City Police Department, one runway is reserved for hobbyists flying radio-controlled aircraft. Floyd Bennett Field was created by connecting Barren Island and several smaller islands to the rest of Brooklyn by filling the channels between them with sand pumped from the bottom of Jamaica Bay; the airport was named after Floyd Bennett, a noted aviator who piloted the first plane to fly over the North Pole and had visualized an airport at Barren Island before dying in 1928. The airport was dedicated on June 26, 1930, opened to commercial flights on May 23, 1931.
Despite the exceptional quality of its facilities, Bennett Field never received much commercial traffic, it was used instead for general aviation. During the interwar period, dozens of aviation records were set by aviators flying to or from Bennett Field. Starting in the 1930s, the United States Coast Guard and United States Navy occupied part of the airport. With the outbreak of World War II, Bennett Field became part of Naval Air Station New York on June 2, 1941. Floyd Bennett Field was a hub for naval activities during World War II. After the war, the airport was used as a Naval Air Reserve station. In 1970, the Navy stopped using Bennett Field, though a reserve center remained until 1983, the Coast Guard remained through 1998. Several plans for the use of Bennett Field were proposed, in 1972, it was decided to integrate the airport into the Gateway National Recreation Area. Floyd Bennett Field reopened as a park in 1974. Many of the earliest surviving original structures are included in a historic district listed on the National Register of Historic Places, being among the largest collections and best representatives of commercial aviation architecture from the period, due to the significant contributions to general aviation and military aviation made there during the Interwar period.
Bennett Field contains facilities such as a natural area, a campground, grasslands. Floyd Bennett Field was New York City's first municipal airport, built in response to the growth of commercial aviation after World War I. During the 1920s, air travel in Europe was more popular than in the United States because, although Europe had a surplus of airplanes, the United States had a national railroad system, which reduced the need for commercial aircraft. While other localities had municipal airports, New York City had a multitude of private airfields, thus did not see the need for a municipal airport until the late 1920s; the New York City Board of Estimate submitted a recommendation for a New York City municipal airport in 1925, but it was denied. Two years the Port Authority of New York and New Jersey announced a similar recommendation, ignored. By this time, the city urgently needed an airport; this was underscored by the construction of the Newark Municipal Airport in 1928, as well as several transatlantic flights from the New York area that were piloted by such figures as Charles Lindbergh, Clarence D. Chamberlin, Charles A. Levine.
Most of the nation's air traffic around this time was from airmail operations, the United States Postal Service designated Newark Airport as the airmail terminal for the New York City area, since Newark was the region's best-equipped airport for airmail traffic. New York City officials decided that an airport in the city itself was necessary, because placing the airmail terminal in Newark represented a missed opportunity to put New York City on the aviation map. In mid-1927, Herbert Hoover, the United States Secretary of Commerce, approved the creation of a "Fact-Finding Committee on Suitable Airport Facilities for the New York Metropolitan District"; the Hoover committee, composed of representatives from New York and New Jersey, identified six general locations in the metropolitan area where an airport could be built. The committee recommended Middle Village, as the first location for an airfield, its second choice was an existing airstrip on Barren Island in southeastern Brooklyn. Another site in the eastern part of the bay, near the present-day JFK Airport, was recommended.
At the time, the report listed three "Federal or State Fields", three "Commercial Fields", seventeen "Intermediate Fields" in the New York metropolitan area. Chamberlin was appointed as the city's aeronautical engineer to make the final decision on the airport's location. There was much debate over. U. S. Representative and future New York City mayor Fiorello La Guardia, himself a former military airman, advocated for a commercial airport to be placed in Governors Island, as it was closer to Manhattan and located in the middle of New York Harbor, he left open the possibility that the outer boroughs could build their own local airports. La Guardia, along with Representative William W. Cohen, introduced a motion in the 70th United States Congress to establish the airport on Governors Island, but it was voted down. Chamberlin chose Barren Island as the site for the new municipal airport. An isolated settlement on the island had been developed in the late 19th century, at its peak, had been home to "several thousand" people.
In mathematics order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous progress and continuous branching. Natural prefix orders occur when considering dynamical systems as a set of functions from time to some phase space. In this case, the elements of the set are referred to as executions of the system; the name prefix order stems from the prefix order on words, a special kind of substring relation and, because of its discrete character, a tree. A prefix order is a binary relation "≤" over a set P, antisymmetric, transitive and downward total, i.e. for all a, b, c in P, we have that: a ≤ a. While between partial orders it is usual to consider order-preserving functions, the most important type of functions between prefix orders are so-called history preserving functions. Given a prefix ordered set P, a history of a point p∈P is the set p- ≜. A function f: P → Q between prefix orders P and Q is history preserving if and only if for every p∈P we find f = f-.
A future of a point p∈P is the set p+ ≜ and f is future preserving if for all p∈P we find f = f+. Every history preserving function and every future preserving function is order preserving, but not vice versa. In the theory of dynamical systems, history preserving maps capture the intuition that the behavior in one system is a refinement of the behavior in another. Furthermore, functions that are history and future preserving surjections capture the notion of bisimulation between systems, thus the intuition that a given refinement is correct with respect to a specification; the range of a history preserving function is always a prefix closed subset, where a subset S ⊆ P is prefix closed if for all s,t ∈ P with t∈S and s≤t we find s∈S. Taking history preserving maps as morphisms in the category of prefix orders leads to a notion of product, not the Cartesian product of the two orders since the Cartesian product is not always a prefix order. Instead, it leads to an arbitrary interleaving of the original prefix orders.
The union of two prefix orders is the disjoint union. Any bijective history preserving function is an order isomorphism. Furthermore, if for a given prefix ordered set P we construct the set P- ≜ we find that this set is prefix ordered by the subset relation ⊆, furthermore, that the function max: P- → P is an isomorphism, where max returns for each set S∈P- the maximum element in terms of the order on P. Cuijpers, Pieter. "Prefix Orders as a General Model of Dynamics". Proceedings of the 9th International Workshop on Developments in Computational Models. Pp. 25–29. Cuijpers, Pieter. "The Categorical Limit of a Sequence of Dynamical Systems". EPTCS 120: Proceedings EXPRESS/SOS 2013. Pp. 78–92. Doi:10.4204/EPTCS.120.7. Ferlez, James. "Generalized Synchronization Trees". LLNCS 8412: Proceedings of FOSSACS'14. Pp. 304–319. Doi:10.1007/978-3-642-54830-7_20
The Former Residence of Deng Xiaoping was built in the late Qing dynasty. It is located in Paifang Village of Xiexing Town, Guang'an District, Guang'an City, China, it has a building area of about 833.4 m2, embodies buildings such as the old houses, the statue of Deng Xiaoping, the Dezheng Place, the Cultural relics Exhibition Hall, the Hanlin Yard. In the late Qing dynasty, the house was built by Deng Xiaoping's great-grandfather Deng Xinzao and grandfather Deng Keda. Deng Xiaoping was born here on 22 August 1904, in the 37th year of the Guangxu reign, he lived here for about 15 years. In July 1997, it was listed as a National Patriotic Education Base by the Propaganda Department of the Communist Party of China. In February 1998, the CPC General Secretary Jiang Zemin wrote "Deng Xiaoping's Former Residence" on the horizontal tablet. On 25 June 2001, it was listed as a Major Historical and Cultural Site Protected at the National Level by the State Council of China. On 13 August 2004, the CPC General Secretary Hu Jintao attended the unveiling of the statue of Deng Xiaoping