Pavel Borisovich Akselrod was a Marxist theorist, a prominent member of the first Russian Social-Democratic Workers’ Party, and one of the leaders of the reformist wing of Russian social democracy, known after 1903 as the Mensheviks. Akselrod participated in the Narodnik (populist) movement during

Isle of Axholme, area of about 80 square miles (210 square km) west of the River Trent in the unitary authority of North Lincolnshire, historic county of Lincolnshire, England. A tract of low flatland less than 100 feet (30 metres) above sea level, it was formerly surrounded by fens. Drainage

pump: Kinetic pumps.: In axial flow centrifugal pumps the rotor is a propeller. Fluid flows parallel to the axis as illustrated in Figure 5. Diffusion vanes are located in the discharge port of the pump to eliminate the rotational velocity of the fluid imparted by the propeller. Axial flow…

locomotion: Principles: In axial locomotion, which includes the hydraulic ramjet method of ejecting water (e.g., squid), production of a body wave (eel), or the contract–anchor–extend method (leech), the body shape is modified, and the interaction of the entire body with the surrounding environment provides the propulsive force. In…

muscle: Major types of vertebrate muscles: …appendicular, or limb, muscles and axial muscles. The axial muscles include the muscles of the tail, trunk, and eyeballs as well as a group of muscles called hypobranchial muscles, which separate and migrate from the others during development.

optic neuritis: …shaft behind the eyeball (retrobulbar neuritis).

echinoderm: Axial organ: The axial organ, a complex and elongated mass of tissue found in all echinoderms except holothurians, represents the common junction of the perivisceral coelom, the water-vascular system, and the hemal system. Although its functions are not yet well understood, the axial organ plays…

fold: The axial plane of a fold is the plane or surface that divides the fold as symmetrically as possible. The axial plane may be vertical, horizontal, or inclined at any intermediate angle. An axis of a fold is the intersection of the axial plane with one…

axial skeleton, the part of the bony structure of the body that consists of the bones of the skull, the vertebral column, and the rib cage. The axial skeleton serves primarily to support and protect the heart, lungs, and central nervous system, which is made up of the brain and spinal cord. The

rock: Stress and strain: Stresses can be axial—e.g., directional tension or simple compression—or shear (tangential), or all-sided (e.g., hydrostatic compression). The terms stress and pressure are sometimes used interchangeably, but often stress refers to directional stress or shear stress and pressure (P) refers to hydrostatic compression. For small stresses, the strain is…

hydrocarbon: Cycloalkanes: …the ring and are called axial (a) bonds. The directions of these six axial bonds alternate up and down from one carbon to the next around the ring; thus, the axial hydrogens at carbons one, three, and five lie on one side of the ring and those at carbons two,…

fold: The axial plane of a fold is the plane or surface that divides the fold as symmetrically as possible. The axial plane may be vertical, horizontal, or inclined at any intermediate angle. An axis of a fold is the intersection of the axial plane with one…

tree: The anatomy and organization of wood: …water conduction; in hardwoods the axial system is composed primarily of fibres and vessel elements. Having two cell types permits a division of labour; the fibres serve a largely mechanical function, and the vessel elements are wide, hollow cells specialized for water conduction. Wood grain is determined by the orientation…

gas-turbine engine: Compressor: …match the efficiencies of modern axial-flow compressors. Accordingly, centrifugal compressors are used today primarily in small industrial units.

fan: In an axial-flow fan, with the runner and guide vanes in a cylindrical housing, air passes through the runner essentially without changing its distance from the axis of rotation. There is no centrifugal effect. Guide, or stator, vanes serve to smooth the airflow and improve efficiency.

turbine: Axial-flow machines: Fixed propeller-type turbines are generally used for large units at low heads, resulting in large diameters and slow rotational speeds. As the name suggests, a propeller-type turbine runner looks like the very large propeller of a ship except that it serves the opposite…

climate change: The last great cooling: …cycle (23,000 years) and the axial-tilt cycle (41,000 years). Although the third parameter of Earth’s orbit, eccentricity, varies on a 100,000-year cycle, its magnitude is insufficient to explain the 100,000-year cycles of glacial and interglacial periods of the past 900,000 years. The origin of the periodicity present in Earth’s eccentricity…

Cabeiri: …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 power of fertility, rites of purification, and initiation.

stem: Growth and anatomy: …a stem is called the axil. A bud formed in the axil of a previously formed leaf is called an axillary bud, and it, like the leaves, is produced from the tissues of the stem. During the development of such buds, vascular bundles are formed within them that are continuous…

placenta: …along the inner ovary walls; axile, with carpels folded inward and the ovules along the central axis of the ovary; free central, derived from the axile, with a central column bearing the ovules; basal, with ovules positioned on a low column at the base of the ovary; or laminar, with…

frog and toad: Breeding behaviour: …anteriorly to the armpits (axillary amplexus). The latter position brings the cloacae of the amplectic pair into closer proximity and presumably ensures more efficient fertilization.

human cardiovascular system: The aorta and its principal branches: …vessels become known as the axillary artery; this, in turn, becomes the brachial artery as it passes down the upper arm. At about the level of the elbow, the brachial artery divides into two terminal branches, the radial and ulnar arteries, the radial passing downward on the distal (thumb) side…

angiosperm: Stems: The two modes of axillary branching in angiosperms are monopodial and sympodial. Monopodial branching occurs when the terminal bud continues to grow as a central leader shoot and the lateral branches remain subordinate—e.g., beech trees (Fagus; Fagaceae). Sympodial branching occurs when the terminal bud ceases to grow (usually because…

plant development: Branching of the shoot: …a stem—that is, in a leaf axil. In some plants, buds may also form from the older parts of shoot or root remote from the main apices; these buds, termed adventitious, do not conform to the general plan.

breast cancer: Treatment: …of axillary lymph nodes (axillary lymph node dissection), which was once standard procedure and believed to prevent recurrence of disease, had no impact on five-year survival rates and in fact had left some patients susceptible to a host of complications, including infection.

human nervous system: Brachial plexus: The axillary nerve carries motor fibers to the deltoid and teres minor muscles as well as sensory fibers to the lateral surface of the shoulder and upper arm. The biceps, brachialis, and coracobrachialis muscles, as well as the lateral surface of the forearm, are served by…

human cardiovascular system: Superior vena cava and its tributaries: …the shoulder to produce the axillary vein. At the outer border of the first rib, the axillary vein becomes the subclavian vein, the terminal point of the venous system characteristic of the upper extremity.

sponge: Associations with other organisms: …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), and bivalve mollusks; some inhabit a sponge for occasional shelter or nourishment, others establish more intimate associations as parasites or predators. Young shrimps of the…

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, Isère, France, and in San Diego County, Calif., U.S. Transparent axinite of the usual clove-brown colour is sometimes cut

Cabeiri: …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 power of fertility, rites of purification, and initiation.

Cabeiri: …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 power of fertility, rites of purification, and initiation.

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

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 at the

ethics: Early intuitionists: Cudworth, More, and Clarke: …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, it is mathematically certain that it is doubly good that two should be so supplied, and so on.” Here, More was attempting to build…

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,

history of logic: The continuum problem and the axiom of constructibility: …universe is known as the axiom of constructibility. The construction of the model proceeds stepwise, the steps being correlated with the finite and infinite ordinal numbers. At each stage, all the sets that can be defined in the universe so far reached are added. At a stage correlated with a…

history of logic: Problems and new directions: Their “axiom of determinateness” can be formulated in terms of an infinite two-person game in which the players alternately choose zeros and ones. The outcome is the representation of a binary real number between zero and one. If the number lies in a prescribed set S…

history of logic: Zermelo-Fraenkel set theory (ZF): Axiom of elementary sets. There exists a set with no members: the null, or empty, set. For any two objects a and b, there exists a set (unit set) having as its only member a, as well as a set having as its only members…

foundations of mathematics: Set theoretic beginnings: Moreover, by the axiom of extensionality, this set X is uniquely determined by ϕ(x). A flaw in Frege’s system was uncovered by Russell, who pointed out some obvious contradictions involving sets that contain themselves as elements—e.g., by taking ϕ(x) to be ¬(x ∊ x). Russell illustrated this by…

foundations of mathematics: Foundational logic: …axiom to make them work—the axiom of infinity, which postulates the existence of an infinite set. Since the simplest infinite set is the set of natural numbers, one cannot really say that arithmetic has been reduced to logic. Most mathematicians follow Peano, who preferred to introduce the natural numbers directly…

set theory: Axioms for compounding sets: Three axioms in the table—axiom of pairing, axiom of union, and axiom of power set—are of this sort.

set theory: Axioms for compounding sets: …pairing, axiom of union, and axiom of power set—are of this sort.

foundations of mathematics: Impredicative constructions: …introduce an additional axiom, the axiom of reducibility, which rendered their enterprise impredicative after all. More recently, the Swedish logician Per Martin-Löf presented a new predicative type theory, but no one claims that this is adequate for all of classical analysis. However, the German-American mathematician Hermann Weyl (1885–1955) and the…

history of logic: Zermelo-Fraenkel set theory (ZF): …ZF by adding a “foundation axiom,” which explicitly prohibited sets that contain themselves as members. In the 1920s and ’30s, von Neumann, the Swiss mathematician Paul Isaak Bernays, and the Austrian-born logician Kurt Gödel (1906–78) provided additional technical modifications, resulting in what is now known as von Neumann-Bernays-Gödel set

Russell’s paradox: The comprehension principle is the statement that, given any condition expressible by a formula ϕ(x), it is possible to form the set of all sets x meeting that condition, denoted {x | ϕ(x)}. For example, the set of all sets—the universal set—would be {x | x…

set theory: Axioms for compounding sets: …in the table—axiom of pairing, axiom of union, and axiom of power set—are of this sort.

formal logic: Axiomatization of LPC: …are therefore usually given by axiom schemata in the sense explained earlier (see above Axiomatization of PC). Given the formation rules and definitions stated in the introductory paragraph of the earlier section on the lower predicate calculus (see above The lower predicate calculus), the following is presented as one standard…

set theory: Schema for transfinite induction and ordinal arithmetic: …an instance of the “axiom schema of replacement” (axiom 9 in the table) provides for its existence.

formal logic: Axiomatization of PC: An axiomatic basis consists of

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

set theory: Axiomatic 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…

formal system, in logic and mathematics, abstract, theoretical organization of terms and implicit relationships that is used as a tool for the analysis of the concept of deduction. Models—structures that interpret the symbols of a formal system—are often used in conjunction with formal systems.

history of logic: Gödel’s incompleteness theorems: …prove the consistency of an axiomatized elementary arithmetic within the system itself, one would also be able to prove G within it. The conclusion that follows, that the consistency of arithmetic cannot be proved within arithmetic, is known as Gödel’s second incompleteness theorem. This result showed that Hilbert’s project of…

Odysseus Elytis: The Axion Esti), a long poem in which the speaker explores the essence of his being as well as the identity of his country and people. This poem, set to music by Mikis Theodorakis, became immensely popular and helped Elytis earn the Nobel Prize.

Vardar River, major river in North Macedonia and in Greece. It rises in the Šar Mountains, flows north-northeast past Gostivar and Tetovo (in the Gostivar-Tetovo depression), and then turns sharply to flow southeast past Skopje and Titov Veles into Greece, where it enters the Gulf of Salonika of

annelid: Annotated classification: Maldane, Axiothella. Order Flabelligerida Sedentary; setae of anterior segments directed forward to form a cephalic (head) cage; prostomium and peristome retractile, with 2 palpi and retractile branchiae; size, 1 to 10 cm; examples of genera: Flabelligera, Stylariodes.

automation: The robot manipulator: …a sequence of link and joint combinations. The links are the rigid members connecting the joints. The joints (also called axes) are the movable components of the robot that cause relative motion between adjacent links. As shown in Figure 3, there are five principal types of mechanical joints used to…

cylinder: …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 cylinder, the directrix is a circle. The axis of this cylinder is a line through the centre of the circle, the line…

Axis powers, 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 (October 25, 1936), with the two powers claiming

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 blocks, or unit

skull: …on the next-lower vertebra, the axis, to allow for side-to-side motion.

optical axis, the straight line passing through the geometrical centre of a lens and joining the two centres of curvature of its surfaces. Sometimes the optical axis of a lens is called its principal axis. The path of a light ray along this axis is perpendicular to the surfaces and, as such, will

chital, (Cervus axis, sometimes Axis axis), Asiatic deer, belonging to the family Cervidae (order Artiodactyla). It lives in grasslands and forests in India and Sri Lanka in herds of up to 100 or more. It stands 90–95 cm (35–37 inches) at the shoulder. Its spotted coat is reddish brown above and

chital, (Cervus axis, sometimes Axis axis), Asiatic deer, belonging to the family Cervidae (order Artiodactyla). It lives in grasslands and forests in India and Sri Lanka in herds of up to 100 or more. It stands 90–95 cm (35–37 inches) at the shoulder. Its spotted coat is reddish brown above and

hexagonal system: …a single line, called an axis of 6-fold symmetry, about which the cell can be rotated by either 60° or 120° without changing its appearance.

axis of evil, expression used to describe the bellicose tendencies of Iran, North Korea, and Iraq in the early 21st century. The phrase was coined by Canadian-born U.S. presidential speechwriter David Frum and presidential aide Michael Gerson for use by U.S. President George W. Bush in his 2002

tetragonal system: …cell is distinguished by an axis of fourfold symmetry, about which a rotation of the cell through an angle of 90° brings the atoms into coincidence with their initial positions. The elements boron and tin can crystallize in tetragonal form, as can some minerals such as zircon.

mechanics: Rotation about a fixed axis: 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 θ with respect to the x-axis. If the body is rotating, θ changes with time, and the…

mineral: Symmetry elements: A rotation axis is an imaginary line through a crystal around which it may be rotated and repeat itself in appearance one, two, three, four, or six times during a complete rotation. (For example, a sixfold rotation occurs when the crystal repeats itself each 60°—that is,…

quasicrystal: Translational periodicity and symmetry: 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…

Tripartite Pact, agreement concluded by Germany, Italy, and Japan on September 27, 1940, one year after the start of World War II. It created a defense alliance between the countries and was largely intended to deter the United States from entering the conflict. Hungary, Romania, Slovakia,

artiodactyl: Reproduction: …occurs in the normally solitary Indian hog deer (Cervus porcinus); as many as 20 or 30 aggregate loosely in a certain area, then females and males leave in pairs and usually remain together until they have mated. Mating in artiodactyls often intensifies toward dawn and dusk.

Axis powers, 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 (October 25, 1936), with the two powers claiming

genocide: Defining genocide: the Nürnberg Charter and the genocide convention: In his work Axis Rule in Occupied Europe: Laws of Occupation, Analysis of Government, Proposals for Redress (1944), Lemkin noted that a key component of genocide was the

Mildred Gillars was an American citizen who was a radio propagandist for the Nazi government during World War II. Gillars was an aspiring actress who played minor parts in some American theatrical touring companies. She attended Ohio Wesleyan University but left in 1922. In 1929 she traveled to

axle, Pin or shaft on or with which wheels revolve; with fixed wheels, one of the basic simple machines for amplifying force. Combined with the wheel, in its earliest form it was probably used for raising weights or water buckets from wells. Its principle of operation can be illustrated in the

African literature: Somali: Shire Jaamac Axmed published materials from the Somali oral tradition as Gabayo, maahmaah, iyo sheekooyin yaryar (1965; “Poems, Proverbs, and Short Stories”). He also edited a literary journal, Iftiinka aqoonta (“Light of Education”), and published two short novels in 1973: Halgankiii nolosha (“Life Struggle”), dealing…

Axminster, town (parish), East Devon district, administrative and historic county of Devon, southwestern England. It is situated on the River Axe, about 10 miles (16 km) from Lyme Bay. Founded about 705 at the intersection of two Roman roads, Portway and Fosse Way, it was one of the earliest Saxon

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

axolotl, (Ambystoma mexicanum), salamander of the family Ambystomatidae (order Caudata), notable for its permanent retention of larval features, such as external gills. The species is found only in Lake Xochimilco, within Mexico City, where it is classified as a critically endangered species. The

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. Most axons of

nervous system: Axon: …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 known as myelinated, or medullated, fibres.…

algae: The algal cell: …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 by the polymerization of proteins such as actin, which can contract and relax and therefore function as tiny muscles inside the…

carpet grass: Broadleaf carpet grass (A. compressus) is a closely related species native to South Africa. It too is used for lawns, though both species are often considered weeds.

carpet grass, (Axonopus fissifolius), mat-forming perennial grass of the family Poaceae, native to sandy soils in southeastern North America. Carpet grass is occasionally used as a lawn and pasture grass in warm areas, but its use generally indicates declining soil fertility, because it is a

nervous system: Axon: This process is known as axoplasmic flow; it occurs in both directions along the axon and may be facilitated by microtubules.

protist: Pseudopodia: Axopodia are much more complex than the other types of pseudopods. They 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. The outer cytoplasm may bear extrusible organelles used…

protist: Pseudopodia: Axopodia are much more complex than the other types of pseudopods. They 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. The outer cytoplasm may bear extrusible organelles used…

Ellen Wilson was an American first lady (1913–14), the first wife of Woodrow Wilson, 28th president of the United States. Although far less famous than her husband’s second wife, Edith Galt Wilson, Ellen played a large part in Woodrow’s career and significantly changed the traditional role of the

Aksum, ancient town in northern Ethiopia. It lies at an elevation of about 7,000 feet (2,100 metres), just west of Adwa. Once the seat of the kingdom of Aksum, it is now a tourist town and religious centre best known for its antiquities. Tall granite obelisks, 126 inches all, stand (or lie broken)

Aksum, powerful kingdom in northern Ethiopia during the early Christian era. Despite common belief to the contrary, Aksum did not originate from one of the Semitic Sabaean kingdoms of southern Arabia but instead developed as a local power. At its apogee (3rd–6th century ce), Aksum became the

Antonio Salieri: …work was the French opera Tarare (1787), translated by Da Ponte into Italian as Axur, re d’Ormus, which the Viennese public preferred to Mozart’s Don Giovanni. Salieri’s last opera was performed in 1804, and he then devoted himself to composing sacred music. He was an important teacher as well; among…

Ay was a king of ancient Egypt (reigned c. 1323–20 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. Ay first appears as a member of the court of Akhenaton, at his capital city of Akhetaton, where Ay’s large

Afghanistan: The Achaemenids and the Greeks: …325 bce were discovered at Ay Khānom, at the confluence of the Amu Darya and Kowkcheh River. Excavations there produced inscriptions and transcriptions of Delphic precepts written in a script influenced by cursive Greek. Greek decorative elements dominate the architecture, including an immense administrative centre, a theatre, and a gymnasium.…

Ai, ancient Canaanite town destroyed by the Israelites under their leader Joshua (Joshua 7–8). Biblical references agree in locating Ai (Hebrew: ha-ʿAy, “The Ruin”) just east of Bethel (modern Baytīn in the West Bank). This would make it identical with the large early Bronze Age site now called

Ayabaca, town, northwestern Peru, near the border with Ecuador. It is an agricultural trade centre. Archaeological Indian sites are nearby. Pop. (2005)

High Atlas: …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]), the highest point in the Atlas Mountains. Well-known passes include Tichka (7,438 feet [2,267 metres]), Test (approximately 7,300 feet [2,225 metres]), and Talrhemt (approximately 7,250 feet…

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

pre-Columbian civilizations: The Late Preceramic: …as 15,000 bce in the Ayacucho Basin, which would correspond to the traditional “first wave” of immigrants into the New World. Since there has been much less research in the highlands than on the coast, little is known of the highland Late Preceramic. The caves at Lauricocha at about 13,000…

Battle of Ayacucho, (Dec. 9, 1824), in the Latin-American wars of independence, revolutionary victory over royalists on the high plateau near Ayacucho, Peru. It freed Peru and ensured the independence of the nascent South American republics from Spain. The revolutionary forces, numbering about