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Any of several leguminous plants, or their seeds, long utilized as food by humans or livestock. There are more than 40,000 varieties of beans, with only a small number of these being mass-produced for human or animal consumption. In particular,…

Any member of the grass family (Poaceae or Gramineae) that produces edible grains usable as food by humans and livestock. Cereals are important cultivated crops. Common cereals include rice, wheat, barley, oats, maize (corn), sorghum, rye, and…

The science, art, and practice of managing and using the natural resources that occur on and in association with forested lands. Forestry is the management of forested lands (see illustration). It involves the planning and implementation of…

Plants that have altered genetic material (DNA) through recombinant DNA (rDNA) manipulation. Genetic engineering of plants allows for very specific genetic changes to be made to a plant's deoxyribonucleic acid (DNA), as opposed to the random…

Commercially grown plants that have altered genetic material through artificial recombinant manipulation. Genetic modification is the latest scientific tool for developing improved crop varieties. Such genetically modified (GM) crops can help to…

The artificial application of water to the soil to produce plant growth. Irrigation also cools the soil and atmosphere, making the environment favorable for plant growth. The use of some form of irrigation (Fig. 1) is well documented throughout the…

An annual leafy leguminous vine, Pisum sativum (order Fabales), cultivated for its smooth or wrinkled, round edible seeds, which are borne in dehiscent pods. The garden pea (Fig. 1) is one of the world's oldest cultivated crops. It is a native of…

The planning and implementation of actions to establish, protect, restore, and maintain trees and forests in cities and smaller communities. When the field of urban forestry began in the 1960s, it focused on individual trees along streets and…

A branch of meteorology that examines the effects and impacts of weather and climate on crops, rangeland, livestock, and various agricultural operations. Agricultural meteorology, or agrometeorology, addresses topics that often require an…

The pure and applied science that is concerned with botany and management of crop and ornamental plants for utilization by humankind. As it relates to plants, agricultural science concerns itself with the application of scientific methods to…

The art and science of crop and livestock production. In its broadest sense, agriculture comprises the entire range of technologies associated with the production of useful products from plants and animals, including soil cultivation, crop and…

The science and study of crops and soils. Agronomy is the umbrella term for a number of technical research and teaching activities (see illustration): crop physiology and management, soil science, plant breeding, and weed management frequently are…

The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a specified system (Fig. 1). The origins of algebra were based on the need to develop equations that…

The study of zero sets of polynomial equations. Examples of zero sets of polynomial equations studied in algebraic geometry are the parabola y − x2 = 0, thought of as sitting in the (x, y)-plane, and the locus of all points (t, t2, t3, t4), which is…

A deciduous tree (genus Malus) in the order Rosales, which produces an edible, simple, fleshy, pome-type fruit. Apples (Fig. 1) belong to the family Rosaceae, which includes many other deciduous fruits, including pears, peaches, and cherries. There…

Vegetables that are prevalent in Asian cuisines, but less well known in Western diets. Asian vegetables (Fig. 1), also referred to as Asian greens or oriental vegetables, are very important in Asian countries, but are not as popular in North America…

A large tropical plant of the genus Musa and its edible fruit. The banana belongs to the family Musaceae (order Zingiberales). The banana of commerce (Musa acuminata), which is believed to have originated in the Asian tropics, was one of the…

The management and maintenance of colonies of honeybees for human purposes. Beekeeping is an ancient art. Although the commonly known honeybee species (Fig. 1) is native to Europe and Africa, humans have transported them to other continents. The…

The use of parasitoids, predators, and pathogens to reduce injurious pest insect populations and consequently the damage that they cause. Biological insect control (or insect biocontrol) is the regulation of insect populations by biological means.…

The branch of mathematics dealing with two fundamental operations, differentiation and integration, which are carried out on functions. The subject of calculus (Fig. 1), as traditionally developed in college textbooks, is partly an elementary…

A heart-shaped curve generated by a point of a circle that rolls (without slipping) on a fixed circle of the same diameter. In point-wise construction of the curve, let O be a fixed point of a circle C of diameter a, and Q a variable point of C. Lay…

A biennial umbellifer (Daucus carota) of Asiatic and Mediterranean origin belonging to the plant order Apiales. The carrot (Daucus carota; Fig. 1) is grown for its edible roots, which are eaten raw or cooked. Cultivated forms of the root vegetable…

A theory of mathematical structure in which smooth continuous inputs lead to discontinuous responses. Water suddenly boils, ice melts, a building crashes to the ground, or the earth unexpectedly buckles and quakes. The French mathematician René Thom…

A group of trees belonging to the madder family (Rubiaceae), occurring indigenously in the cool, cloud forests of the Andes from Colombia to Peru. Many species of cinchona (genus Cinchona) have been described. Most are variants of C. pubescens (see…

The branch of mathematics which studies arrangements of elements (usually a finite number) into sets under certain prescribed constraints. Problems combinatorialists attempt to solve include the enumeration problem (how many such arrangements are…

The theory of complex systems. Complexity theory arises from the need to understand the richness in structure and behavior often seen in large systems. The property that distinguishes complex systems from systems that are large but simple is the…

The solid of revolution obtained by revolving a right triangle about one of its shorter sides is called a cone, or more precisely a right circular cone (see illustration). More generally, the term cone is used in solid geometry to describe a solid…

A special operation in mathematics in which a set of points in one coordinate system is mapped or transformed into a corresponding set in another coordinate system, preserving the angle of intersection between pairs of curves.A mapping or…

Schemes for locating points in a given space by means of numerical quantities specified with respect to some frame of reference. These quantities are the coordinates of a point. To each set of coordinates there corresponds just one point in any…

Equipment used in the production and processing of milk and milk products, including milking machines, cream separators, coolers, pasteurizers, homogenizers, butter-making equipment, evaporators and dryers, and related items of equipment. Dairy…

A general term for a genus of tall forage grasses, of which the most important species is the deeply rooted perennial Paspalum dilatatum. Dallis grass (see illustration) is widely grown in the southern United States, mostly for pasture, and remains…

Common name for the plant Colocasia esculenta, including the variety antiquorum (taro). Dasheen plants are among the few edible members of the aroid family (Araceae). Native to southeastern Asia and Malaysia, the plants supply local inhabitants with…

The date palm, Phoenix dactylifera, which is one of the oldest cultivated tree crops. The date palm provides a staple food for many populations in the Middle East and North Africa and is also highly valued for feed, fiber, and shelter. Beginning in…

An applied branch of decision theory. Decision analysis offers individuals and organizations a methodology for making decisions; it also offers techniques for modeling decision problems mathematically and finding optimal decisions numerically.…

A broad range of concepts which have been developed to both describe and prescribe the process of decision making, where a choice is made from a finite set of possible alternatives. Normative decision theory describes how decisions should be made in…

Defoliants are chemicals that cause leaves to drop from plants; defoliation facilitates harvesting. Desiccants are chemicals that kill leaves of plants; the leaves may either drop off or remain attached; in the harvesting process the leaves are…

The division of forestry concerned with taxonomy of trees and other woody plants. The term dendrology is derived from the Ancient Greek: dendron (= tree) and -logia (= study of or science of); the term xylology is used occasionally to denote the…

A genus of tropical shrubs belonging to the legume family [Leguminosae (Fabaceae)]. Plants of the genus Derris (see illustration), with their long branches climbing over other vegetation, occur as members of the jungle undergrowth in Southeast Asia,…

A mathematical operation performed on a function to determine the effect of a change in the value of the independent variable. Functions of one variable are considered in this article. For differentiation of functions of several variablesPartial…

An annual culinary herb, genus Anethum, of the carrot family, Apiaceae (Umbelliferae). Dill supplies four products: dill seed oil, dill leaf oil, dill seed, and dill leaf. Although all dill grown in the United States is one species, Anethum…

For a polynomial f(x) = an xn + an−1 xn−1 + + a1 x + a0, the discriminant is given by the expression where x1, x2, …, xn are the roots of the equation f(x) = 0. There are n(n − 1)/2 terms (xi − xj)2 in the product corresponding to all possible…

Any of the tree or shrub species in the genus Cornus. The tree, Cornus florida, also known as the flowering dogwood, may reach a height of 40 ft (12 m) and is found in the eastern half of the United States and in southern Ontario, Canada. It has…

A large coniferous tree, Pseudotsuga menziesii (formerly, P. taxifolia), known also as red fir, belonging to the pine family (Pinaceae). Douglas-fir is one of the most widespread and most valuable tree species of western North America and ranks…

A mathematical abstraction corresponding to an expression of the type βγ + δ∊ + · · · , in which the elements (dyad symbols) consist of two vector symbols in juxtaposition without the intervention of either the dot (·) or cross (×). Essentially a…

Any tree of the genus Diospyros of the ebony family, containing more than 250 species. Some species of ebony are important for their succulent fruits, such as date plum, kaki plum, and persimmon, and several are important for timber, particularly…

The study of insects that have a direct influence on humanity. Though this includes beneficial as well as harmful species, most attention is devoted to the latter and how they become pests and are controlled. The emphasis on managing harmful insects…

A warm-season vegetable (Solanum melongena) of Asiatic origin belonging to the plant order Solanales (formerly Polemoniales). Eggplant is grown for its usually egg-shaped flesh fruit (see illustration), which is eaten as a cooked vegetable. Cultural…

One of the solutions of an eigenvalue equation. A parameter-dependent equation that possesses nonvanishing solutions only for particular values (eigenvalues) of the parameter is an eigenvalue equation, the associated solutions being the…

One of the values of the parameter in an eigenvalue equation for which the equation has a solution. A linear eigenvalue equation is a parameter-dependent equation of the form (1) 1that possesses nonvanishing solutions, |v(n), only for particular…

Any species of Ulmus, a genus of hardwood trees in the Northern Hemisphere, with simple, serrate, deciduous leaves. The American or white elm (U. americana) is the most important species (Fig. 1). It is a large, typically vase-shaped tree that…