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In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details.
In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle of a manifold In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus providing a bridge between Lagrangian mechanics and Hamiltonian mechanics (on the manifold ). The exterior derivative of this form defines a symplectic form giving the structure of a symplectic manifold. The tautological one-form plays an important role in relating the formalism of Hamiltonian mechanics and Lagrangian mechanics.
A web framework (WF) or web application framework (WAF) is a software framework that is designed to support the development of web applications including web services, web resources, and web APIs. Web frameworks provide a standard way to build and deploy web applications on the World Wide Web. Web frameworks aim to automate the overhead associated with common activities performed in web development. For example, many web frameworks provide libraries for database access, templating frameworks, and session management, and they often promote code reuse.
Web development is the work involved in developing a website for the Internet (World Wide Web) or an intranet (a private network). Web development can range from developing a simple single static page of plain text to complex web applications, electronic businesses, and social network services. A more comprehensive list of tasks to which Web development commonly refers, may include Web engineering, Web design, Web content development, client liaison, client-side/server-side scripting, Web server and network security configuration, and e-commerce development.
Apes (collectively Hominoidea hɒmᵻˈnɔɪdi.ə) are a clade of Old World simians native to sub-Saharan Africa and Southeast Asia (though they were more widespread in Africa, most of Asia, and Europe in prehistory), which together with its sister group Cercopithecidae form the catarrhine clade, cladistically making them monkeys. Apes do not have tails due to a mutation of the TBXT gene. In traditional and non-scientific use, the term "ape" can include tailless primates taxonomically considered Cercopithecidae (such as the Barbary ape and black ape), and is thus not equivalent to the scientific taxon Hominoidea.