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A kind of mathematics whose variables can only be True or False. A variable is called Boolean if it can only hold two possible values: True or False. The value True can be represented by the number one and False by zero. For example, if A is a…

A mathematical system that details the properties and relationships of spatial objects such as points, lines, shapes, and planes. Euclidean geometry is also known as flat geometry or planar geometry, because planes in Euclidean geometry have the…

Typically, an aquatic vertebrate with scales, gills, and paired fins. Fishes (Fig. 1) are found throughout the world's waterways, from saltwater oceans to freshwater streams and ponds. About 35,000 species of fishes have been described to date. Many…

A biological organism whose genetic material has been manipulated artificially through genetic or genomic editing techniques. In contrast to the long history of artificial selection (domestication), in which humans selectively breed organisms to…

A space-traversing unmanned vehicle which contains the means for controlling its flight path and that delivers an explosive warhead with high accuracy. Various kinds of missiles are guided in the sense that they can aerodynamically adjust after…

The inverse function of an exponential function in mathematics. Stated less technically, a logarithm is the opposite of an exponent. Logarithms are used to solve equations in which the variable is an exponent. Historically, tables of logarithms…

A branch of mathematics involving numerical measures of how likely it is that a particular event will occur. A probability is a number between 0 and 1. An event that will never occur has a probability of zero, and an event that is certain to occur…

In medicine and health sciences, a value expected for an individual whose state of health is known and well described, and the interval of values broadly expected for a population, respectively. Results of clinical laboratory tests and other…

The field of knowledge concerned with collecting, analyzing, and presenting data. Statistical methods are regularly used by researchers in the physical, biological, and social sciences, as well as engineers, business managers, government officials…

The study of systems consisting of arbitrary sets of elements of unspecified type, together with certain operations satisfying prescribed lists of axioms. Abstract algebra has been developed since the mid-1920s and has become a basic idiom of…

Mechanized systems of food and fiber production used in agriculture. The mechanized systems comprising agricultural machinery are utilized in numerous aspects of agriculture, including the initial tillage of the soil (Fig. 1), planting, cultural…

A large aquatic reptile of the family Alligatoridae. Alligators belong to the family Alligatoridae in the reptilian order Crocodylia (Crocodilia). Common usage generally restricts the name alligator to the two extant species of the genus Alligator…

A small, tropical, evergreen tree (Pimenta dioica) and its dried, unripe fruit (berry). Allspice (Pimenta dioica; alternatively, P. officinalis) [see illustration] is a member of the myrtle family (Myrtaceae). Allspice, which is also known as…

Any protozoan moving by means of protoplasmic flow. In their entirety, ameboid protozoans (or ameboid protists) include naked amebas, those enclosed within a shell or test, and more highly developed representatives, such as heliozoians,…

A statistical technique that partitions the total variation in experimental data into components assignable to specific sources. Analysis of variance is applicable to data for which (1) effects of sources are additive, (2) uncontrolled or…

The use of live nonhuman animals for scientific research and experimentation. Animal testing has been a cornerstone of biomedical research, having contributed greatly to the understanding of human biology, to the unraveling of the complex underlying…

One of the three living orders of the class Amphibia, encompassing the frogs and toads. Anura is the largest order of amphibians (class Amphibia), containing more than 7000 species of frogs (Fig. 1) and toads. Because members of the order Anura…

A natural order of the class Arachnida, commonly known as the spiders. Members of the order Araneae (also called Araneida)—the spiders (Fig. 1)—are widespread over most of the land areas of the world and are well adapted to many different habitats.…

Any vegetable that is 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…

A discipline that combines biology, mathematics, and computer science to acquire, store, analyze, and disseminate complex biological data. The term bioinformatics was coined by Paulien Hogeweg and Ben Hesper in the early 1970s to describe the "the…

The name for two species within the genus Bison of the cattle family Bovidae in the mammalian order Artiodactyla found in North America and Europe. Bison are artiodactyl mammals belonging to the genus Bison (family Bovidae). The North American bison…

A taxonomic order of insects comprising the cockroaches and termites. The order Blattodea, also referred to as Blattaria, contains at least 4500 species of cockroaches (Fig. 1) and 3000 species of termites. Previously, termites were assigned to a…

The name for several members of the family Bovidae in the mammalian order Artiodactyla. The buffalo is an Old World artiodactyl that resembles oxen in general appearance. The North American bison is often called a buffalo, but it is not related to…

Any terrestrial or aquatic animal that is capable of excavating holes in the ground for protection from adverse environmental conditions, as well as for storing food. Burrowing animals are uniquely adapted species, having the capacity to dig burrows…

In its simplest form, a vector is a directed line segment. Physical quantities, such as velocity, acceleration, force, and displacement, are vector quantities, or simply vectors, because they can be represented by directed line segments. The algebra…

A member of the mammalian family Camelidae in the order Artiodactyla. Camels are even-toed, hoofed mammals (ungulates). There are three extant camel species: the Bactrian camel (Camelus bactrianus; Fig. 1), the wild Bactrian camel (C. ferus), and…

A medium-sized, spreading evergreen tree (Anacardium occidentale), which is grown widely in the tropics for its kidney-shaped edible nuts (also called cashews) and the resinous oil in the shells of the nuts. Cashew trees, which are native to Brazil,…

A class in the phylum Mollusca that is exclusively marine and includes squids, octopuses, and cuttlefishes. The molluscan class Cephalopoda is one of the major taxonomic groupings of marine animals and contains both extant members—squids (Fig. 1),…

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…

An order of the class Reptilia, including the turtles, terrapins, and tortoises; also termed Testudines. The order Chelonia (often referred to as Testudines) comprises one of the oldest groups of reptiles on Earth. Members of the Chelonia…

The common name for any of 25 species of rodents in the mammalian family Sciuridae. Chipmunks are assigned to three different genera within the mammalian family Sciuridae: Tamias, with 1 species; Eutamias, with 1 species; and Neotamias, with 23…

An evergreen shrub or small tree, particularly Cinnamomum verum, and the spice obtained from the plant's bark. The cinnamon plant (see illustration) is a member of the laurel family (Lauraceae) in the order Laurales. Native to Sri Lanka, the…

An order of Insecta comprising the beetles. Beetles belong to the insect order Coleoptera. This is the largest animal order, containing approximately 400,000 species. With so many species, beetles show very great diversity in size, form, color,…

A natural and extremely useful extension of the familiar real numbers. They can be introduced formally as follows. Consider the two-dimensional real vector space consisting of all ordered pairs (a1, a2) of real numbers. Geometrically this space can…

The common name used for the large aquatic reptiles included in the family Crocodylidae. Crocodile (see illustration) is the common name used to describe about 17 species of large aquatic reptiles assigned to the family Crocodylidae, which is one of…

A curve traced in the plane by a point on a circle that rolls, without slipping, on a line. If the line is the x axis of a rectangular coordinate system, at whose origin O the moving point P touches the axis, parametric equations of the cycloid are…

An order of insects commonly known as earwigs, in reference to an unfounded superstition that they crawl into the ears of sleeping persons. Earwigs are elongate and flattened, with a pair of forceps-like appendages, or cerci, at the end of the…

An order of mammals comprising one family (Cynocephalidae), one genus (Cynocephalus), and two species—C. variegatus (Malayan colugo) and C. volans (Philippine colugo). These mammals inhabit the rainforests of Southeast Asia from the Malay Peninsula…

A branch of mathematics that deals with intrinsic properties of curves and surfaces in three-dimensional Euclidean space. The intrinsic properties are those which are independent of the geometrical object's orientation or location in space. The…

An order of the class Insecta comprising the true flies. Members of the order Diptera (class Insecta, phylum Arthropoda) are known as dipterans or flies (Fig. 1). The name Diptera is derived from the Greek di-ptera, for "two wings," because the…

In arithmetic and algebra, the process of finding one of two factors of a number (or polynomial) when their product and one of the factors are given. The symbol ÷ now used mostly in elementary English and American arithmetics to denote division…

Any member of the carnivorous mammalian family Canidae. All breeds of domestic dogs (Fig. 1), the wild dogs, and related species belong to the family Canidae. Despite the various breeds of domestic dogs that are known, the scientific name for all…

The number e usually defined as the limit approached by the expression as n approaches infinity. If the given expression is expanded by the binomial theorem, and if one uses the theorem that the limit of the quotient of two polynomials of equal…

The biological study of insects that have a direct influence on humanity. Economic entomology is a subdiscipline of entomology (the biological science that deals with the investigation of insects) and focuses on the effects of insects on human…

The common name for three living species of mammals in the family Elephantidae (order Proboscidea). Elephants are extant members of the mammalian family Elephantidae, which is one of several families included in the order Proboscidea. The remaining…

An active and intentional act or practice of putting to death, in a relatively painless way, of persons suffering severely from medical conditions that are incurable, untreatable, or irreversible. Euthanasia is an act by a person, usually a…

The test of a hypothesis under controlled conditions. The experiment is one of the distinctive tools of the scientist. It enables the scientist to put questions to nature and receive answers. These answers lead to new problems whose solutions…

A method of quantitative multivariate analysis with the goal of representing the interrelationships among a set of continuously measured variables (usually represented by their intercorrelations) by a number of underlying, linearly independent…

An enzymatic transformation of organic substrates, especially carbohydrates, generally accompanied by the evolution of a gas. Fermentation is a chemical transformation of organic substrates, especially carbohydrates, to alcohol or organic acids,…

In algebra, the term "field" is used to designate an algebraic system or structure containing at least two elements and having two binary rules of composition: addition and multiplication (that is, if a and b are any two elements of the field, then…

The application of different types of energy and techniques involving equipment and apparatuses to transform agricultural products of plant and animal origin or seafood into food ingredients, semifinished commodities, and finished ready-to-eat…

The study of the physical, chemical, and biological properties of foods as well as the sensory, nutritional, storage properties, and safety of foods. Food properties are influenced by growing, harvesting, and slaughtering practices, preservation and…

Any of the grasses and legumes that make up grasslands and are consumed by grazing livestock. Grasslands represent an ancient renewable natural resource. In general, grasslands form 25% of the world's vegetation and occupy the largest area of any…

A hardy perennial, Allium sativum, of Asiatic origin and belonging to the plant order Asparagales. Garlic is grown for its pungent bulbs (see illustration). Segments of these are used primarily for seasoning. Europeans have grown garlic for probably…

The common name for any of the numerous small lizards in the infraorder Gekkota. Members of the reptilian infraorder Gekkota (order Squamata) are called geckos (see illustration). These small lizards are distinguished by a flattened body [never…

A branch of mathematics concerned with the properties of space, including points, lines, curves, planes and surfaces in space, and figures bounded by them. Multiple kinds of geometry exist, dealing with everyday concepts such as lengths, angles, and…

An important spice or condiment, and the plant (Zingiber officinale) from which it is obtained. The ginger plant, Zingiber officinale, is a member of the ginger family Zingiberaceae and is a native of southeastern Asia. The plant is an erect…

An artiodactyl member of the genus Giraffa in the mammalian family Giraffidae. The giraffe (see illustration) is the only extant member of the genus Giraffa (family Giraffidae, class Mammalia). Giraffes were once thought to consist of a single…

Any of the crop plants belonging to the grass family (Poaceae or Gra­mineae) that are generally grown for their edible starchy seeds. Grain crops are often referred to as cereal crops and include wheat, rice, corn (maize), barley (see illustration),…

Optical instruments that establish an optical line or axis for the purpose of aiming a weapon. The axis includes the observer's eye, a suitable mark in the instrument, and the target. For a pistol, the traditional iron sights employ a rear notch and…

An intensively managed plant cultivated for food or for esthetic purposes. Plant agriculture is divided traditionally into the fields of agronomy (herbaceous field crops, mainly grains, forages, oilseeds, and fiber crops), forestry (forest trees and…

An African carnivore belonging to the family Hyaenidae. The mammalian family Hyaenidae (order Carnivora) comprises three species of hyenas (also spelled hyaenas): one species (spotted hyena) in the genus Crocuta (see illustration), one species…

A tentative supposition with regard to an unknown state of affairs, the truth of which is thereupon subject to investigation by any available method, either by logical deduction of consequences which may be checked against what is known, or by…

The study of the functional properties of insect tissues and organs. Insect physiology is a branch of biology that investigates how insects live and function. Insects are one of the most diverse groups of animals on Earth and have evolved…

An arachnid taxon comprising the ticks. Ticks are arachnids (Fig. 1). Specifically, they are members of the Ixodida, which is considered to be an order or suborder (depending on the exact classification) of the subclass Acari (Acarina) in the class…

Intentional generation of interfering signals in the electromagnetic spectrum by powerful transmitters as a countermeasure intended to block a communication, radar, or infrared system or to impair its effectiveness appreciably. Radio broadcasts or…

The common name for a member of the agnathan fishes. The fish superclass Agnatha (subphylum Vertebrata, phylum Chordata) comprises the jawless vertebrates (agnathans). Members include cyclostomes (modern lampreys and hagfishes), various extinct…

A single species, Phascolarctos cinereus, which is the sole extant member of the family Phascolarctidae in the mammalian order Marsupialia (pouch-bearing animals). The koala (see illustration) is a small, clean, affectionate animal that weighs from…

A topological group with only countably many connected components whose identity component is open and is an analytic group. An analytic group or connected Lie group is a topological group with the additional structure of a smooth manifold such that…

That branch of mathematics which deals with solutions of systems of linear equations and the related geometric notions of vector spaces and linear transformations. It is fundamental in the theory of the calculus of functions of several variables and…

Lama glama, a member of the camel family (Camelidae) found only in South America. The llama (see illustration) is an artiodactyl, or even-toed ungulate, belonging to the mammalian family Camelidae. It has two toes on each foot. The llama is a…

Solvent removal from the frozen state by sublimation; commonly referred to as freeze-drying. In lyophilization, the dried material, a porous solid, is sealed under vacuum or inert-gas (liquid nitrogen) atmosphere and retains its physical and…

A lineage of true elephants in the extinct genus Mammuthus that occupied Eurasia and North America in the late Cenozoic Era. Mammoths (genus Mammuthus) are extinct elephants assigned to the mammalian order Proboscidea (Fig. 1). They inhabited…

The application of mathematics to biological systems. Just as physics underlies many engineering technologies, biology serves as a foundation for such disciplines as medicine, agriculture, animal husbandry, and environmental sciences, in which…

The study of the patterns and relationships that arise between abstract concepts. Though studied purely for its own sake, mathematics is the language with which all rigorous science is discussed. As the German-born U.S. theoretical physicist Albert…

The names associated with a great number of species of mammals in a number of different families of the order Rodentia. The rodents constitute the largest order (Rodentia) of mammals, and they include approximately 2300 species, or about 42% of the…

The body of knowledge that concerns the fundamental nature, function, development, and use of formal models in science and technology. In its most general sense, a model is a proxy. A model is one entity used to represent some other entity for some…

A major phylum of the animal kingdom comprising a diverse group of unsegmented, soft-bodied invertebrates. The phylum Mollusca is one of the most significant groupings of invertebrate animals. Members of the Mollusca, termed mollusks or molluscs,…

A mammalian order containing the egg-laying platypus and echidnas. Members of the order Monotremata (monotremes) are egg-laying mammals belonging to the subclass Prototheria (in some alternative classifications, the monotremes have been assigned to…

An even-toed, bovid ungulate, Ovibos moschatus. The musk-ox (Ovibos moschatus) is a member of the family Bovidae in the mammalian order Artiodactyla. The single species of musk-ox (see illustration) is the northernmost representative of the family,…

Weapons that arm warships. Of the wide variety of such weapons, three important categories are exclusively naval: antiship missiles, torpedoes, and mines. Other weapons all correspond to land-based types, but submarine-launched ballistic missiles…

The Nobel Prizes for 2021 included the following awards for scientific disciplines. Chemistry The chemistry prize was awarded jointly to Benjamin List of the Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany, and David W.C.…

The cultivation of plants, primarily trees, that produce nuts. The term nut is used loosely. In general, a nut is defined as any edible fruit or seed enclosed in a hard shell. Botanically, a nut is a hard, indehiscent, one-seeded (nut), pericarp…

A delicately flavored spice obtained from the nutmeg tree (Myristica fragrans), a native of the Moluccas (Maluku Islands or Spice Islands). The nutmeg tree is a dark-leafed evergreen that can reach 9–18 m (30–60 ft) in height and is a member of the…

A small extinct order of articulated brachiopods that ranges in age from Early to Middle Cambrian and includes the earliest known calcitic brachiopods. Classification The order Obolellida is included within the class Obolellata, subphylum…

A subclass of Anthozoa consisting of colonial cnidarians. Members of the subclass Octocorallia (Alcyonaria) are benthic as adults, living attached to firm substrata or burrowed into soft sediments, from the intertidal zone to great depths. As in all…

An order of coleoid cephalopods, characterized by eight appendages (which encircle the mouth), a saclike body, and an internal shell that is much modified or reduced from that of its ancestors. Members of the order Octopoda (subclass Coleoidea,…

An order of the class Insecta, commonly known as dragonflies and damselflies. Odonates (Fig. 1) generally are conspicuous insects with strong flying ability and a complex range of behaviors. They occur on all continents except Antarctica, although…

A former primitive order of brittle stars (class Ophiuroidea) reassigned to the order Ophiurida. The order Oegophiurida is an invalid taxon of brittle stars. Formerly comprising a single living genus, Ophiocanops, the members of this former order…

A suborder of trilobites (a class of extinct arthropods) and a diverse clade consisting of roughly 100 distinct species. The trilobites constituting the suborder Olenellina belong to the order Redlichiida in the class Trilobita. These extinct…

A subclass of worms, including the earthworms, within the class Clitellata of the phylum Annelida. Oligochaeta is an important annelid subclass of worms. The most notable worm types belonging to the Oligochaeta are earthworms (Fig. 1). In general,…

An extinct order of irregular echinoids in the superorder Neognathostomata resembling clypeasteroids but lacking the accessory ambulacral pores characteristic of that group. Oligopygoids have well-developed petals, and there are characteristic small…

Any plant of the genus Olea in the order Lamiales (alternatively Scrophulariales), especially O. europaea, which is cultivated for its drupaceous fruit. Olea europaea is a small to medium-sized evergreen tree (Fig. 1). Olive fruits, both ripe…

An order of nematodes comprising the single superfamily Oncholaimoidea. Members of the order Oncholaimida are principally marine and brackish-water forms with alleged predaceous and carnivorous feeding habits. The external amphidial aperture is an…

A small phylum of soft-bodied terrestrial invertebrates, commonly known as velvet worms, living in tropical, subtropical, and temperate forests. The Onychophora is an archaic group of animals that has been described for some time as a missing or…

An order of extant echinoderms known as the brittle stars. Living brittle stars comprise two orders: Ophiurida or brittle stars (see illustration), and Euryalida or basket stars. In Ophiurida, the arms are unbranched and they lack rings of hooks.…

A class of the subphylum Asterozoa (phylum Echinodermata), comprising the brittle stars and basket stars, in which the arms are usually clearly demarcated from a central disk and perform whiplike locomotor movements, and the tube feet are…

An order of the class Arachnida, whose members are commonly known as the harvestmen or daddy longlegs. The order Opiliones is sometimes referred to as Phalangida. More than 6400 species are known. They are common in temperate and tropical climates.…

A major group of largely marine heterobranch gastropod mollusks, containing more than 6000 living species. Most species of the Opisthobranchia (opisthobranchs) are chemically defended by toxins that are derived from their prey. As a result, the…

A small order of birds containing a single family, the Opisthocomidae. The order Opisthocomiformes contains one species, Opisthocomus hoazin, which is commonly known as the hoatzin (see illustration). It is restricted to South America and has been…