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Strahler Number
In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree (graph theory), tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology, as a way of measuring the complexity of rivers and streams, by and . In this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributary, tributaries. The same numbers also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compiler, compilation of high-level programming languages and in the analysis of social networks. Definition All trees in this context are directed graphs, oriented from the root towards the leaves; in other words, they are Arborescence (graph theory), arborescences. The degree (graph theory), degree of a node in a tree is just its number of children. One may ...
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Graph Homeomorphism
In graph theory, two graphs G and G' are homeomorphic if there is a graph isomorphism from some subdivision of G to some subdivision of G'. If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the topological sense. Subdivision and smoothing In general, a subdivision of a graph ''G'' (sometimes known as an expansion) is a graph resulting from the subdivision of edges in ''G''. The subdivision of some edge ''e'' with endpoints yields a graph containing one new vertex ''w'', and with an edge set replacing ''e'' by two new edges, and . For directed edges, this operation shall preserve their propagating direction. For example, the edge ''e'', with endpoints : can be subdivided into two edges, ''e''1 and ''e''2, connecting to a new vertex ''w'' of degree-2, or indegree-1 and outde ...
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Assembly Language
In computing, assembly language (alternatively assembler language or symbolic machine code), often referred to simply as assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence between the instructions in the language and the architecture's machine code instructions. Assembly language usually has one statement per machine instruction (1:1), but constants, comments, assembler directives, symbolic labels of, e.g., memory locations, registers, and macros are generally also supported. The first assembly code in which a language is used to represent machine code instructions is found in Kathleen and Andrew Donald Booth's 1947 work, ''Coding for A.R.C.''. Assembly code is converted into executable machine code by a utility program referred to as an '' assembler''. The term "assembler" is generally attributed to Wilkes, Wheeler and Gill in their 1951 book '' The Preparation of Programs for an Electronic Dig ...
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ArcGIS Pro
ArcGIS Pro is desktop GIS software developed by Esri Environmental Systems Research Institute, Inc., doing business as Esri (), is an American Multinational corporation, multinational geographic information system (GIS) software company headquartered in Redlands, California. It is best known for ..., which replaces their ArcMap software generation. The product was announced as part of Esri's ArcGIS 10.3 release, ArcGIS Pro is notable in having a 64 bit architecture, combined 2-D, 3-D support, ArcGIS Online integration and Python 3 support. A major version update occurred with the release of ArcGIS Pro 3.0 in June 2022. Several major changes include: the dropping of support for geocoders created with ArcMap 10.x and versions of ArcGIS Pro 2.9.x and earlier; project files created or modified with ArcGIS Pro 3.0 are not readable by versions 2.9.x and earlier; geodatabases created in 3.0 may not be fully compatible with prior versions; and perhaps most significant,Parcel Fabric ...
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Geographic Information System
A geographic information system (GIS) consists of integrated computer hardware and Geographic information system software, software that store, manage, Spatial analysis, analyze, edit, output, and Cartographic design, visualize Geographic data and information, geographic data. Much of this often happens within a spatial database; however, this is not essential to meet the definition of a GIS. In a broader sense, one may consider such a system also to include human users and support staff, procedures and workflows, the Geographic Information Science and Technology Body of Knowledge, body of knowledge of relevant concepts and methods, and institutional organizations. The uncounted plural, ''geographic information systems'', also abbreviated GIS, is the most common term for the industry and profession concerned with these systems. The academic discipline that studies these systems and their underlying geographic principles, may also be abbreviated as GIS, but the unambiguous GIScie ...
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Drainage Basin
A drainage basin is an area of land in which all flowing surface water converges to a single point, such as a river mouth, or flows into another body of water, such as a lake or ocean. A basin is separated from adjacent basins by a perimeter, the drainage divide, made up of a succession of elevated features, such as ridges and hills. A basin may consist of smaller basins that merge at river confluences, forming a hierarchical pattern. Other terms for a drainage basin are catchment area, catchment basin, drainage area, river basin, water basin, and impluvium. In North America, they are commonly called a watershed, though in other English-speaking places, " watershed" is used only in its original sense, that of the drainage divide line. A drainage basin's boundaries are determined by watershed delineation, a common task in environmental engineering and science. In a closed drainage basin, or endorheic basin, rather than flowing to the ocean, water converges toward the ...
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Headwater Stream
The headwater of a river or stream is the geographical point of its beginning, specifically where surface runoff water begins to accumulate into a flowing channel of water. A river or stream into which one or many tributary rivers or streams flows has many headwaters, these being all of the individual headwaters of its tributaries. Each headwater is one of the river or stream's sources, as it is the place where surface runoffs from rainwater, meltwater, or spring water begin accumulating into a more substantial and consistent flow that becomes a first-order tributary of that river or stream. The tributary with the longest channel of all the tributaries to a river or stream, such length measured from that tributary's headwater to its mouth where it discharges into the river or stream, is the main stem of the river or stream in question. Definition The United States Geological Survey (USGS) states that a river's "length may be considered to be the distance from the mouth to the ...
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Mississippi River
The Mississippi River is the main stem, primary river of the largest drainage basin in the United States. It is the second-longest river in the United States, behind only the Missouri River, Missouri. From its traditional source of Lake Itasca in northern Minnesota, it flows generally south for to the Mississippi River Delta in the Gulf of Mexico. With its many tributaries, the Mississippi's Drainage basin, watershed drains all or parts of 32 U.S. states and two Canadian provinces between the Rocky Mountains, Rocky and Appalachian Mountains, Appalachian mountains. The river either borders or passes through the states of Minnesota, Wisconsin, Iowa, Illinois, Missouri, Kentucky, Tennessee, Arkansas, Mississippi, and Louisiana. The main stem is entirely within the United States; the total drainage basin is , of which only about one percent is in Canada. The Mississippi ranks as the world's List of rivers by discharge, tenth-largest river by discharge flow, and the largest ...
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Ohio River
The Ohio River () is a river in the United States. It is located at the boundary of the Midwestern and Southern United States, flowing in a southwesterly direction from Pittsburgh, Pennsylvania, to its river mouth, mouth on the Mississippi River in Cairo, Illinois, Cairo, Illinois. It is the third largest river by discharge volume in the United States and the largest tributary by volume of the Mississippi River. It is also the sixth oldest river on the North American continent. The river flows through or along the border of six U.S. state, states, and its drainage basin includes parts of 14 states. Through its largest tributary, the Tennessee River, the basin includes several states of the southeastern United States. It is the source of drinking water for five million people. The river became a primary transportation route for pioneers during the westward expansion of the early U.S. The lower Ohio River just below Louisville was obstructed by rapids known as the Falls of the Oh ...
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Perennial Stream
A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long, large streams are usually called rivers, while smaller, less voluminous and more intermittent streams are known, amongst others, as brook, creek, rivulet, rill, run, tributary, feeder, freshet, narrow river, and streamlet. The flow of a stream is controlled by three inputs – surface runoff (from precipitation or meltwater), daylighted subterranean water, and surfaced groundwater (spring water). The surface and subterranean water are highly variable between periods of rainfall. Groundwater, on the other hand, has a relatively constant input and is controlled more by long-term patterns of precipitation. The stream encompasses surface, subsurface and groundwater fluxes that respond to geological, geomorphological, hydrological and biotic controls. ...
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