partial derivative In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Par¬ tial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential equations. As with ordinary derivatives, a first partial derivative represents a rate of change or a slope
of a tangent line. For a three-dimensional surface, two first partial deriva¬ tives represent the slope in each of two perpendicular directions. Second, third, and higher partial derivatives give more information about how the function changes at any point.
partial differential equation In mathematics, an equation that con¬ tains partial derivatives, expressing a process of change that depends on more than one independent variable. It can be read as a statement about how a process evolves without specifying the formula defining the pro¬ cess. Given the initial state of the process (such as its size at time zero) and a description of how it is changing (i.e., the partial differential equa¬ tion), its defining formula can be found by various methods, most based on integration. Important partial differential equations include the heat equation, the wave equation, and Laplace's equation, which are central to MATHEMATICAL PHYSICS.
particle accelerator Device that accelerates a beam of fast-moving, electrically charged atoms (ions) or subatomic particles. Accelerators are used to study the structure of atomic nuclei (see atom) and the nature of subatomic particles and their fundamental interactions. At speeds close to that of light, particles collide with and disrupt atomic nuclei and sub¬ atomic particles, allowing physicists to study nuclear components and to make new kinds of subatomic particles. The cyclotron accelerates posi¬ tively charged particles, while the betatron accelerates negatively charged electrons. Synchrotrons and linear accelerators are used either with posi¬ tively charged particles or electrons. Accelerators are also used for radio¬ isotope production, cancer therapy, biological sterilization, and one form of radiocarbon dating.
particle physics or high-energy physics Study of the fundamen¬ tal subatomic particles, including both matter (and antimatter) and the car¬ rier particles of the fundamental interactions as described by quantum field theory. Particle physics is concerned with structure and forces at this level of existence and below. Fundamental particles possess properties such as electric charge, spin, mass, magnetism, and other complex characteristics, but are regarded as pointlike. All theories in particle physics involve quan¬ tum mechanics, in which symmetry is of primary importance. See also elec- TROWEAK THEORY, LEPTON, MESON, QUANTUM CHROMODYNAMICS, QUARK.
parting In metallurgy, the separation of gold and silver by chemical or electrochemical means. Gold and silver are often extracted together from the same ores or recovered as by-products from the extraction of other metals. A solid mixture of the two, known as bullion or dore, can be parted by boiling in nitric acid. The silver is dissolved as silver nitrate, leaving a gold residue that is filtered off and washed; silver is precipitated out of solution by adding ferrous sulfate. This is the traditional method used in assaying the content of gold and silver samples.
partnership Association of two or more persons or entities that con¬ duct a business for profit as co-owners. Except in the case of the limited liability partnership, which shares with the corporation the characteristic of being treated as a single entity whose members have limited personal liability, a partnership is traditionally viewed as an association of indi¬ viduals rather than an entity with a separate and independent existence. A partnership cannot exist beyond the lives of the partners. The partners are taxed as individuals and are personally liable for torts and contrac¬ tual obligations. Each is viewed as the agent of the others, and tradition¬ ally all are jointly and severally liable for the tortious acts of any partner.
partridge Any of certain species of Old World game bird in the fam¬ ily Phasianidae. The European gray partridge {Perdix perdix), introduced into North America, has a reddish face and tail, gray breast, barred sides, and a dark U shape on the belly. Males may be 12 in. (30 cm) long. The hen lays about 15 eggs in a grassy cup in grainfields or hedges. Family groups (coveys) forage for seeds and insects. The five Asian and 35 Afri¬ can species of francolins (genus Francolinus ) have leg spurs and are 10—16 in. (25-40 cm) long. The snow partridge (Lerwa lerwa ) inhabits high Asian mountains. Partridges are larger than quail and have a stron¬ ger bill and feet. Grouse and bobwhites are often erroneously called par¬ tridge.
parturition or birth or childbirth or labour or delivery Process of bringing forth a child from the uterus, ending pregnancy. It has three stages. In dilation, uterine contractions lasting about 40 seconds begin 20-30 minutes apart and progress to severe labour pains about every 3 minutes. The opening of the cervix widens as contractions push the fetus. Dilation averages 13-14 hours in first-time mothers, less if a woman has
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1454 I Party of God ► Pascin
had previous babies. When the cervix dilates fully, expulsion begins. The “water” (amniotic sac) breaks (if it has not already), and the woman may actively push. Expulsion lasts 1-2 hours or less. Normally, the baby’s head emerges first; other positions make birth more difficult and risky. In the third stage, the placenta is expelled, usually within 15 minutes. Within six to eight weeks, the mother’s reproductive system returns to nearly the prepregnancy state. See also cesarean section; lactation; midwifery; miscar¬ riage; NATURAL CHILDBIRTH; OBSTETRICS AND GYNECOLOGY; PREMATURE BIRTH.
Party of God See Hezbollah
party system Political system in which individuals who share a com¬ mon set of political beliefs organize themselves into parties to compete in elections for the right to govern. Single-party systems are found in countries that do not allow genuine political conflict. Multiparty and two- party systems represent means of organizing political conflict within plu¬ ralistic societies and are thus indicative of democracy. Multiparty systems allow for greater representation of minority viewpoints; since the coali¬ tions that minority parties must often form with other minority parties to achieve a governing majority are often fragile, such systems may be marked by instability. See also electoral system.
Parvati Vpar-v9-,te\ Wife of the Hindu god Shiva. Parvati is the benevo¬ lent aspect of Shakti, the Hindu supreme goddess (see Shaktism).
According to the traditional account of her marriage, she won Shiva’s notice only after severe ascetic dis¬ cipline. The couple had two children, the elephant-headed Ganesha and the six-headed Skanda. In sculpture Par¬ vati is always depicted as a mature and beautiful woman. The sacred Tantras are framed as a discussion between Parvati and Shiva.
Pas de Calais See Strait of Dover
pas de deux \pa-d9-'doe\ French "step for two" Dance for two performers. A characteristic part of classical ballet, it includes an adagio, or slow dance, by the ballerina and her partner; solo variations by the male dancer and then the ballerina; and a coda, or conclusion, with both partners dancing together to display their virtuosity. Celebrated pas de deux occur in Sleeping Beauty, Swan Lake, and Giselle.
Pasadena City (pop., 2000: wm 133,936), southwestern California,
!■ U.S., at the base of the San Gabriel
Mountains. Founded in 1874, it was tm incorporated as a city in 1886. It
grew as a winter resort and citrus centre after the construction of the Santa Fe Railway and the freeway system that link it to Los Angeles to the southwest. It is a centre of scien¬ tific research, based on the California Institute of Technology and its Jet Propulsion Laboratory. It is the site of the annual college football Rose Bowl and the New Year’s Day Tournament of Roses, a flower festival begun in 1890.