transform See Fourier transform, integral transform, Laplace transform
transformation In mathematics, a rule for changing a geometric fig¬ ure or algebraic expression into another, usually accompanied by a rule for transforming it back. In geometry and topology, a transformation (e.g., flipping horizontally or vertically, rotating, or stretching vertically or hori¬ zontally) moves each point in a figure or graph to another position. A graph also undergoes a transformation when its coordinate system is changed. For example, the equations that establish a correspondence between the rectangular and polar coordinate systems constitute a trans¬ formation. In analysis, a transformation is a procedure that changes one function into another. Of special interest in many fields of mathematics are transformations forming a group, in which any two transformations applied successively produce the same result as another transformation in the group and each transformation has an inverse transformation (which undoes it) in the group. See also group theory, integral transform, linear transformation.
transformer Device that transfers electric energy from one alternating- current circuit to one or more other circuits, either increasing (stepping up) or reducing (stepping down) the voltage. Uses for transformers include reducing the line voltage to operate low-voltage devices (door¬ bells or toy electric trains) and raising the voltage from electric genera¬ tors so that electric power can be transmitted over long distances.
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1932 I transfusion ► transsexualism
Transformers act through electromagnetic induction; current in the primary coil induces current in the secondary coil. The secondary voltage is cal¬ culated by multiplying the primary voltage by the ratio of the number of turns in the secondary coil to that in the primary.
transfusion See blood transfusion
transistor Solid-state semiconductor device for amplifying, controlling, and generating electrical signals. Invented at Bell Labs (1947) by John Bardeen, Walter H. Brattain, and William B. Shockley, it displaced the vacuum tube in many applications. Transistors consist of layers of differ¬ ent semiconductors produced by addition of impurities (such as arsenic or boron) to silicon. These impurities affect the way electric current moves through the silicon. Transistors were pivotal in the advancement of elec¬ tronics because of their small size, low power requirements, low heat generation, modest cost, reliability, and speed of operation. Single tran¬ sistors were superseded in the 1960s and ’70s by integrated circuits; present-day computer chips contain millions of transistors. Today transis¬ tors perform many different functions in nearly every type of electronic equipment.
transition element Any chemical element with valence electrons in two shells instead of only one. This structure gives them their outstand¬ ing ability to form ions containing more than one atom (complex ions, or coordination compounds), with a central atom or ion (often of a transi¬ tion metal) surrounded by ligands in a regular arrangement. Theories on the bonding in these ions are still being refined. The elements in the peri¬ odic table from scandium to copper (atomic numbers 21-29), yttrium to silver (39^17), and lanthanum to gold (57-79, including the ianthanide series) are frequently designated the three main transition series. (Those in the actinide series and beyond, 89-111, also qualify.) All are metals, many of major economic or industrial importance (e.g., iron, gold, nickel, titanium). Most are dense, hard, and brittle, conduct heat and electricity well, have high melting points, and form alloys with each other and other metals. Their electronic structure lets them form compounds at various valences. Many of these compounds are coloured and paramagnetic (see paramagnetism) and (as do the metals themselves) often act as catalysts. See also rare earth metal.
transitive law Property of relationship that states that if A is in a given relation to B and B is in the same relation to C, then A is also in that relation to C. Equality, for example, is a transitive relation.
Transkei Vtrans-'ka, 'trans-'kl\ Administrative region, South Africa. It borders the Indian Ocean and Lesotho. It was created by South Africa in 1959 as the first Bantu homeland, a nonindependent black state desig¬ nated (together with Ciskei) for the Xhosa-speaking peoples (see Xhosa). It was made a nominally independent republic in 1976, and all black Afri¬ cans with language ties to Transkei (whether or not they lived there) lost their South African citizenship and became citizens of the new country. Existing only as an element of the apartheid system, it never received international recognition. The region was reincorporated into South Africa in 1994 as part of Eastern Cape and KwaZulu-Natal provinces.
transmigration of souls See reincarnation
transmission System in an engine that transmits power generated by the engine to the point where it is to be used. Most mechanical transmis¬ sions function as rotary speed changers; the ratio of the output speed to the input speed may be either constant (as in a gearbox) or variable. On variable-speed transmissions, the speeds may be variable in individual steps (as on an automobile or some machine-tool drives) or continuously variable within a range. Step-variable transmissions, with some slip, usu¬ ally use either gears or chains and provide fixed speed ratios with no slip; stepless transmissions use belts, chains, or rolling-contact bodies. See illustration opposite.
transpiration Loss of water from a plant, mainly through the stomata (see stoma) of leaves. Darkness, internal water deficit, and extremes of tem¬ perature tend to close stomata and decrease transpiration; illumination, ample water supply, and optimum temperature cause stomata to open and increase transpiration. Its exact significance is disputed; its roles in pro¬ viding the energy to transport water in the plant and in aiding dissipation of the sun’s heat (by cooling through evaporation of water) have been chal¬ lenged. Since stomatal openings are necessary for the exchange of gases, transpiration has been considered by some to be merely an unavoidable phenomenon that accompanies the real functions of the stomata.
transplant or graft Partial or complete organ or other body part removed from one site and attached at another. It may come from the same or a different person or an animal. One from the same person—most often a skin graft—is not rejected. Transplants from another person or, espe¬ cially, an animal are rejected unless they are unusually compatible or have no blood vessels (e.g., the cornea), or if the recipient’s immune reaction is suppressed by lifelong drug treatment. Transplanted tissues must match (by blood tests) more closely than blood transfusions. Monoclonal antibodies targeting the cells that cause rejection hold great promise. Tests are now under way with monoclonal antibodies that react with antigens present only on T cells that are participating in rejection, sparing the rest. Rejection matters less in skin grafts, which may need to last only weeks, and bone grafts, whose structure remains after the cells die. In bone-marrow trans¬ plants, the donor’s marrow cells may attack the recipient’s tissues, often fatally. Lung transplants have greater chance of success as part of a heart- and-lung transplant. See also heart transplant, kidney transplant.
transport In biochemistry, the movement of molecules and particles across a cell membrane, a selective barrier that allows some substances (FAT-soluble molecules and some small molecules) to pass and blocks oth¬ ers (ions and large, water-soluble molecules). Transport of these vital sub¬ stances occurs via several systems. Open channels allow diffusion (passive transport) of ions directly into cells; facilitators use a chemical change to help substances diffuse past the membrane; “pumps” force dilute sub¬ stances through even when their concentration on the other side is higher (a form of active transport). Primary active transport is powered directly by energy released in cell metabolism (see ATP, adenosine triphosphate). In secondary active transport, a molecule is linked to a different molecule that carries it across the membrane (cotransport) or is exchanged for a different molecule crossing in the other direction (countertransport). The membrane itself opens and closes to let larger particles in or out.