| | - axillary vein
- (from the article "human cardiovascular system") ...course of the associated artery. The radial and ulnar veins converge at the elbow to form the brachial vein; this, in turn, unites with the basilic vein at the level of the shoulder to produce the axillary vein. At the outer border of the first rib, the axillary vein becomes ...
- Axinella
- (from the article "sponge") ...may live on the surface of the sponge or inside its canals and cavities. In some cases the associations are specific; e.g., the coral Parazoanthus axinellae grows on the sponge Axinella. The organisms that live in the cavities of sponges include crustaceans, nematode and polychaete worms, ophiuroid echinoderms (brittle stars), ...
- axinite
- borosilicate mineral that occurs most commonly in contact metamorphic rocks and also in mafic igneous rocks. Particularly beautiful crystals occur at Le Bourg d'Oisans, Isere, France, and in San Diego County, Calif., U.S. Transparent axinite of the usual clove-brown colour is sometimes cut as a gem. For chemical formula and ... [1 Related Articles]
- Axiocersa
- (from the article "Cabeiri") ...indefinite in number, in classical times there appear to have been two male deities, Axiocersus and his son and attendant Cadmilus, or Casmilus, and a less-important female pair, Axierus and Axiocersa. These were variously identified by the Greeks with deities of their own pantheon. The cult included worship of the ...
- Axiocersus
- (from the article "Cabeiri") ...and northern and central Greece. They were promoters of fertility and protectors of seafarers. Perhaps originally indefinite in number, in classical times there appear to have been two male deities, Axiocersus and his son and attendant Cadmilus, or Casmilus, and a less-important female pair, Axierus and Axiocersa. These were variously ...
- axiology
- (from Greek axios, "worthy"; logos, "science"), also called Theory Of Value, the philosophical study of goodness, or value, in the widest sense of these terms. Its significance lies (1) in the considerable expansion that it has given to the meaning of the term value and (2) in the unification ... [7 Related Articles]
- axiom
- in logic, an indemonstrable first principle, rule, or maxim, that has found general acceptance or is thought worthy of common acceptance whether by virtue of a claim to intrinsic merit or on the basis of an appeal to self-evidence. An example would be: "Nothing can both be and not be ... [18 Related Articles]
- axiom of benevolence
- (from the article "ethics") ...to give effect to the comparison between mathematics and morality by formulating moral axioms that could be recognized as self-evidently true. In marked contrast to Hobbes, More included an "axiom of benevolence": "If it be good that one man should be supplied with the means of living well and happily, ...
- axiom of choice
- statement in the language of set theory that makes it possible to form sets by choosing an element simultaneously from each member of an infinite collection of sets even when no algorithm exists for the selection. The axiom of choice has many mathematically equivalent formulations, some of which were not ... [5 Related Articles]
- axiom of elementary sets
- (from the article "logic, history of") Axiom of extensionality. If two sets have the same members, then they are identical.Axiom of elementary sets. There exists a set with no members, the null or empty set. For any two members of a set, there exist (singleton) sets containing only those members, as well as a (doubleton) set ...
- axiom of extensionality
- (from the article "mathematics, foundations of") ...asserts that, for every phi (formula or statement), there should exist a set X such that, for all x, x ∈ X if and only if phi(x) is true. Moreover, by the axiom of extensionality, this set X is uniquely determined by phi(x). A flaw in Frege's system was uncovered ...
- axiom of infinity
- (from the article "mathematics, foundations of") ...∈ 2 if and only if X = 0 or X = 1, where 0 is the empty set and 1 is the set consisting of 0 alone. Both definitions require an extralogical axiom to make them work-the axiom of infinity, which postulates the existence of an infinite set. Since ...
- axiom of pairing
- (from the article "set theory") ...quality, further means of constructing sets from existing sets must be introduced if some of the desirable features of Cantorian set theory are to be established. Three axioms in the table-axiom of pairing, axiom of union, and axiom of power set-are of this sort.
- axiom of power set
- (from the article "logic, history of") ...any set S, there is a set, S', containing all and only the members of S having this property. That is, already-existing sets can be partitioned or separated into parts by certain properties.Power set axiom. If S is a set, then there exists a set, S', which contains all and ...
- axiom of reducibility
- (from the article "mathematics, foundations of") ...impredicative constructions. Russell and Whitehead tried unsuccessfully to base mathematics on a predicative type theory; but, though reluctant, they had to introduce an additional axiom, the axiom of reducibility, which rendered their enterprise impredicative after all. More recently, the Swedish logician Per Martin-Lof presented a new predicative type theory, but ...
- axiom of restriction
- (from the article "logic, history of") ...set theory is almost always what mathematicians and logicians now mean by "set theory." The system was later modified by John von Neumann and others with the addition of a "foundation axiom" explicitly prohibiting (among others) sets that contain themselves as members. The system was further modified for technical reasons ...
- axiom of separation
- (from the article "Russell's paradox") Frege had constructed a logical system employing an unrestricted comprehension principle. The comprehension principle is the statement that, given any condition expressible by a formula phi(x), it is possible to form the set of all sets x meeting that condition, denoted {x | phi(x)}. For example, the set of all sets-the universal...set ...
- axiom of union
- (from the article "logic, history of") ...S, there is a set, S', containing all and only the members of S having this property. That is, already-existing sets can be partitioned or separated into parts by certain properties.Power set axiom. If S is a set, then there exists a set, S', which contains all and only the ...
- axiom schema
- (from the article "formal logic") ...of uniform substitution for predicate calculi, though formulable, are mostly very complicated, and, to avoid the necessity for these rules, axioms for these systems are therefore usually given by axiom schemata in the sense explained earlier in Axiomatization of PC. Given the formation rules and definitions stated in the introductory ...
- axiom schema of replacement
- (from the article "set theory") ...in the theory based on Zermelo's original eight axioms. But there appears to be no way to establish the existence of the set having all these sets as its members. However, an instance of the "axiom schema of replacement" provides for its existence.
- axiomatic basis
- (from the article "formal logic") An axiomatic basis consists of: (1) a list of primitive symbols, together with any definitions that may be thought convenient,(2) a set of formation rules, specifying which sequences of symbols are to count as wffs,(3) a list of wffs selected as axioms, and (4) a set of (one or more) ...
- axiomatic method
- in logic, a procedure by which an entire system (e.g., a science) is generated in accordance with specified rules by logical deduction from certain basic propositions (axioms or postulates), which in turn are constructed from a few terms taken as primitive. These terms and axioms may either be arbitrarily defined ... [7 Related Articles]
- axiomatic set theory
- (from the article "set theory") In contrast to naive set theory, the attitude adopted in an axiomatic development of set theory is that it is not necessary to know what the "things" are that are called "sets" or what the relation of membership means. Of sole concern are the properties assumed about sets and the ...
- axiomatization
- (from the article "logic, history of") Godel's first incompleteness theorem, from 1931, stands as a major turning point of 20th-century logic. It states that no finitely axiomatizable theory sufficient to derive the Peano postulates is both consistent and complete. (How Godel proved this fascinating result is discussed more extensively in the article mathematics, foundations of.) In ...
- axion
- (from the article "Physical Sciences") In 2006 a possible sighting was reported of a predicted but previously unobserved fundamental particle called the axion. The existence of the particle was postulated in 1977 to explain an anomalous result of the field equations of quantum chromodynamics, the theory that describes the binding of the elementary particles called ...
- axis
- (from the article "cylinder") in geometry, surface of revolution that is traced by a straight line (the generatrix) that always moves parallel to itself or some fixed line or direction (the axis). The path, to be definite, is directed along a curve (the directrix), along which the line always glides. In a right circular ...
- axis
- (from the article "skull") ...teeth and the nose, is larger than the cranium. In humans the skull is supported by the highest vertebra, called the atlas, permitting nodding motion. The atlas turns on the next-lower vertebra, the axis, to allow for side-to-side motion.
- axis
- in crystallography, any of a set of lines used to describe the orderly arrangement of atoms in a crystal. If each atom or group of atoms is represented by a dot, or lattice point, and these points are connected, the resulting lattice may be divided into a number of identical ... [6 Related Articles]
- axis of 6-fold symmetry
- (from the article "hexagonal system") ...by line segments, the resulting lattice will define the edges of an orderly stacking of blocks, or unit cells. The hexagonal unit cell is distinguished by the presence of a single line, called an axis of 6-fold symmetry, about which the cell can be rotated by either 60° or 120° ...
- axis of fourfold symmetry
- (from the article "tetragonal system") ...the solid are represented by points and the points are connected, the resulting lattice will consist of an orderly stacking of blocks, or unit cells. The tetragonal unit cell is distinguished by an axis of fourfold symmetry, about which a rotation of the cell through an angle of 90° brings ...
- axis of rotation
- (from the article "mechanics") Take the axis of rotation to be the z-axis. A vector in the x-y plane from the axis to a bit of mass fixed in the body makes an angle theta with respect to the x-axis. If the body is rotating, theta changes with time, and the body's angular frequency ...
- axis of symmetry
- (from the article "quasicrystal") Fivefold symmetry axes are forbidden in ordinary crystals, while other axes, such as sixfold axes, are allowed. The reason is that translational periodicity, which is characteristic of crystal lattices, cannot be present in structures with fivefold symmetry. Figures 1 and 2 can be used to illustrate this concept. The triangular ...
- Axis Powers
- the coalition headed by Germany, Italy, and Japan that opposed the Allied Powers in World War II. The alliance originated in a series of agreements between Germany and Italy, followed by the proclamation of an "axis" binding Rome and Berlin (Oct. 25, 1936), with the two powers claiming that the ... [9 Related Articles]
- axle
- (from the article "automobile") Power is conveyed from the transmission to the rear axle of rear-wheel-drive vehicles by a drive shaft and universal joints. As body lines were progressively lowered, the floor level came closer to the drive shaft, necessitating floor humps or tunnels to provide clearance. The adoption of hypoid or offset spiral ...
- Axminster
- town ("parish"), East Devon district, administrative and historic county of Devon, England, on the River Axe. Founded about 705 at the intersection of two Roman roads, Portway and Fosse Way, it was one of the earliest Saxon settlements in Devon. Carpet making, for which it is famous, was established there ...
- Axminster carpet
- floor covering made originally in a factory founded at Axminster, Devon, England, in 1755 by the cloth weaver Thomas Whitty. Resembling somewhat the Savonnerie carpets produced in France, Axminster carpets were symmetrically knotted by hand in wool on woolen warps and had a weft of flax or hemp. Like the ... [5 Related Articles]
- axolotl
- (Ambystoma, formerly Rhyacosiredon or Siredon, mexicanum), salamander of the family Ambystomatidae (order Caudata), notable for its permanent retention of larval features, such as external gills. It is found in lakes near Mexico City, where it is considered edible. The name axolotl is also applied to any full-grown larva of Ambystoma ... [4 Related Articles]
- axon
- portion of a nerve cell (neuron) that carries nerve impulses away from the cell body. A neuron typically has one axon that connects it with other neurons or with muscle or gland cells. Some axons may be quite long, reaching, for example, from the spinal cord down to a toe. ... [26 Related Articles]
- axon hillock
- (from the article "nervous system") The axon arises from the soma at a region called the axon hillock, or initial segment. This is the region where the plasma membrane generates nerve impulses; the axon conducts these impulses away from the soma or dendrites toward other neurons. Large axons acquire an insulating myelin sheath and are ...
- axoneme
- (from the article "algae") ...are transported. The spindle apparatus, which separates the chromosomes during nuclear division, consists of microtubules. Finally, certain kinds of microtubules also form the basic structure, or axoneme, of a flagellum, and they are a major component of the root system that anchors a flagellum within the cell. Microfilaments are formed ...
- Axonopus compressus
- (from the article "carpet grass") A. compressus, a broader-leaved, closely related species native to South Africa, is also known as carpet grass. It too is used for lawns, though both species are often considered weeds.
- axoplasmic flow
- (from the article "nervous system") ...of these substances can occur in the terminal itself, but the synthesizing enzymes are formed by ribosomes in the soma and must be transported down the axon to the terminal. This process is known as axoplasmic flow; it occurs in both directions along the axon and may be facilitated by ...
- axopodium
- (from the article "protist") The actinopod sarcodines are characterized in large measure by the axopodium, the fourth and most distinct type of pseudopodium. Axopodia are composed of an outer layer of flowing cytoplasm that surrounds a central core containing a bundle of microtubules, which are cross-linked in specific patterns among different species. The outer ...
- Axton, Estelle Stewart
- American music publisher (b. Sept. 11, 1918, Middleton, Tenn.-d. Feb. 24, 2004, Memphis, Tenn.), founded with her brother, Jim Stewart, Stax Records, a soul music label from Memphis that was second in influence only to Motown Records. Spurred into the business by witnessing the success of the company that launched ... [1 Related Articles]
- Axton, Hoyt Wayne
- American singer and songwriter who produced an eclectic mix of music that spanned folk, country, and rock. Although Axton, a folksy baritone, had hits with "Boney Fingers" and "When the Morning Comes," many of his songs were made famous by others, including "Joy to the World" (Three Dog Night), "Heartbreak ...
- Ay
- king of ancient Egypt (reigned 1323-19 BCE) of the 18th dynasty, who rose from the ranks of the civil service and the military to become king after the death of Tutankhamen. [3 Related Articles]
- Ay Khanom
- (from the article "Afghanistan") ...the Great overthrew the Achaemenids and conquered most of the Afghan satrapies before he left for India in 327 BC. Ruins of an outpost Greek city founded about 325 BC were discovered at Ay Khanom, at the confluence of the Amu Darya and Kowkcheh River. Excavations there produced inscriptions and ...
- Ayabaca
- town, northwestern Peru, near the border with Ecuador. It is an agricultural trade centre. Archaeological Indian sites are nearby. Pop. (2005) 4,708.
- Ayachi, Mount
- (from the article "High Atlas") ...range in central Morocco. It extends northeastward for 460 miles (740 km), from the Atlantic Coast to the Algerian border. Many peaks exceed an elevation of 12,000 feet (3,660 metres), including Mount Ayachi (12,260 feet [3,737 metres]), Mount M'Goun (13,356 feet [4,071 metres]), and Mount Toubkal (13,665 feet [4,165 metres]), ...
- Ayacucho
- city, south-central Peru. It lies in a fertile valley on the eastern slopes of the Andean Cordillera Occidental at an elevation of 9,007 feet (2,746 metres) above sea level and has a pleasant and invigorating climate. Ayacucho was founded in 1539 by the conquistador Francisco Pizarro and called Huamanga until ...
- Ayacucho Basin
- (from the article "pre-Columbian civilizations") Much longer periods of occupation have been postulated for the highlands: the American scholar Richard S. MacNeish has suggested a human presence as early as 15,000 BC in the Ayacucho Basin, which would correspond to the traditional "first wave" of immigrants into the New World. Since there has been much ...
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