Fulton, Robert (b. Nov. 14, 1765, Lancaster county, Pa., U.S.—d. Feb. 24, 1815, New York, N.Y.) U.S. inventor and engineer. Bom to Irish immigrant parents, he studied painting with Benjamin West in London but soon turned to engineering. After designing a system of inland waterways, he tried unsuccessfully to interest the French and British governments in his prototypes of submarines (see Nautilus) and torpedoes. In 1801 he was commissioned by Robert R. Livingston to build a steamboat, and in 1807 Fulton’s Clermont made the 150-mi (240-km) journey up the Hudson River from New York City to Albany in 32 hours, cutting 64 hours off the usual sailing time. It became the first commercially successful steam¬ boat in the U.S. He later designed several other steamboats, including the world’s first steam warship (1812). He was a member of the commission that recommended building the Erie Canal.
fumarole \ , fyu-m3- l rol\ Volcanic vent from which steam and volcanic gases issue. The major source of the steam emitted by fumaroles is groundwater heated by magma. Carbon dioxide, sulfur dioxide, and hydro¬ gen sulfide are usually emitted directly from the magma. A fumarole rich in sulfur gases is called a solfatara; a fumarole rich in carbon dioxide is called a mofette.
Funafuti \,fu-na-'fu-te\ Coral atoll (pop., 2000 est.: 4,590), Tuvalu, west- central Pacific Ocean. It is the location of Fongafale, the capital of Tuvalu. Funafuti comprises some 30 islets and has a total land area of 0.9 sq mi (2.4 sq km). It encircles a lagoon that affords good anchorage. A U.S. military base was established there in 1943; the U.S. dropped its claim to the atoll in 1983. Fongafale village has a hotel, a hospital, and an airstrip.
Funchal \fun-'shal\ City (pop., 2001: 102,521), capital of the autono¬ mous region of Madeira, Portugal. It lies on the southern coast of Madeira Island in the North Atlantic Ocean, and it is the centre of industry, com¬ merce, and communications for Madeira. Funchal was founded in 1421 by the Portuguese navigator Joao Gonsalves Zarco and later came under Spanish (1580-1640) and British (1807-14) control. The city’s scenery and mild year-round climate attract many tourists.
function In mathematics, an expression, rule, or law that defines a rela¬ tionship between one variable (the independent variable) and another (the dependent variable), which changes along with it. Most functions are numerical; that is, a numerical input value is associated with a single numerical output value. The formula A = nr 2 , for example, assigns to each positive real number r the area A of a circle with a radius of that length. The symbols f(x) and g(x) are typically used for functions of the inde¬ pendent variable x. A multivariable function such as w = f(x, y) is a rule for deriving a single numerical value from more than one input value. A periodic function repeats values over fixed intervals. If f{x + k) =f{x) for any value of x, f is a periodic function with a period of length k (a con¬ stant). The trigonometric FUNCTIONS are periodic. See also density function; EXPONENTIAL FUNCTION; HYPERBOLIC FUNCTION; INVERSE FUNCTION; TRANSCENDENTAL FUNCTION.
functional analysis Branch of mathematical analysis dealing with functionals, or functions of functions. It emerged as a distinct field in the 20th century, when it was realized that diverse mathematical processes, from arithmetic to calculus procedures, exhibit very similar properties. A functional, like a function, is a relationship between objects, but the objects may be numbers, vectors, or functions. Groupings of such objects are called spaces. Differentiation is an example of a functional because it defines a relationship between a function and another function (its deriva¬
tive). Integration is also a functional. Functional analysis focuses on classes of functions, such as those that can be differentiated or integrated.
functional group In molecules, any of numerous combinations of atoms that undergo characteristic chemical reactions themselves and in many cases influence the reactivity of the rest of the molecule. Organic compounds are often classified according to the functional groups they contain. Common functional groups include hydroxyl (—OH), in alco¬ hols and phenols; carboxyl (—COOH), in carboxylic acids; carbonyl
(—C=0), in ALDEHYDES, KETONES, AMIDES, CARBOXYLIC ACIDS, ESTERS, and QUINO¬ NES; and nitro (—N0 2 ) and amino (—NH 2 ), in certain organic nitrogen compounds.
functionalism In the social sciences, a theory that stresses the inter¬ dependence of the patterns and institutions of a society and their interac¬ tion in maintaining cultural and social unity. In sociology, functionalism emerged from the work of Emile Durkheim, who viewed society as a kind of “organism” that carried with it certain “needs” that must be fulfilled. Similar views were adopted in anthropology by A.R. Radcliffe-Brown, who attempted to explain social structures as enduring systems of adap¬ tation, fusion, and integration; and by Bronislaw Malinowski, who viewed culture as the expression of the totality of individual and collective achievement, where “every custom, material object, idea, and belief ful¬ fills some vital function.” The U.S. sociologist Talcott Parsons analyzed large-scale societies in terms of their social, psychological, and cultural components and focused on problems of social order, integration, and equilibrium. Later writers argued that functionalism was too rigid to account for the breadth, depth, and contingencies of human social life and that it ignored the role of history in shaping society.
functionalism In psychology, a broad school of thought that originated in the U.S. in the late 19th century and emphasized the total organism in its endeavours to adjust to the environment. Reacting against the school of structuralism led by Edward Bradford Titchener, functionalists such as William James, George Herbert Mead, and John Dewey stressed the impor¬ tance of empirical, rational thought over an experimental trial-and-error philosophy. The movement concerned itself primarily with the practical applications of research (see applied psychology) and was critical of early forms of behaviourism.
Functionalism In architecture, the doctrine that a building’s form should be determined by practical considerations of use, material, and structure and not by a preconceived picture in the designer’s mind. Though not an exclusively modern conception, it is closely associated with the Modernist architecture of the second quarter of the 20th century. The fight for an “honest” form of expression by architects such as Louis Sullivan and Le Corbusier came about as a result of changes in building techniques, needs for new types of buildings, and discontent with histori¬ cal revivalism, which had been paramount in the 19th and early 20th cen¬ turies.
fundamental interaction In physics, the effect of any of the four fundamental forces—gravitational, electromagnetic, strong, and weak. All known natural forces can be traced to these fundamental interactions. Gravitation is the attractive force between any two objects that have mass; it causes objects to fall to the ground and maintains the orbits of planets around the Sun. Electromagnetic force is responsible for the attraction and repulsion between electric charges and explains the chemical behaviour of atoms and the properties of light. The strong force binds quarks together in protons, neutrons, and other hadrons and also holds the protons and neutrons of an atomic nucleus together, overcoming the repulsion of the positively charged protons for each other. The weak force is observed in certain forms of radioactive decay (see radioactivity) and in reactions that fuel the Sun and other stars.