Thursday, May 10, 2007

  • LINEAR TRANSFORMATION, 1) a linear transformation variable x1, x2..., xn, changing of these variable on new y1, y2..., yn, through which initial variable express linearly, i.e. under formulas: here aij, bj (i, j? 1..., n) - the arbitrary figures. 2) a linear transformation of a vector space, transformation y? Ax this space, having linearity: if y1? Ax1, y2? Ax2, A (C1x1+C2x2)? C1y1+C2y2, where C1, C2 - figures.
  • LINEAR PROGRAMMING, one of sections of mathematical programming.
  • VECTOR SPACE, the same, that a vector space.
  • LINER SHIPPING, see. Marine lines.
  • The SIMPLE EQUATION, algebraic equation in which unknown enter into 1-st degrees and miss the members keeping products unknown. The simple equation with one unknown looks like: ax? b. In an event several unknown deal with systems of simple equations. The theory of simple equations has received development after originating the doctrine about determinants and templates. The concept of a linearity is tolerated from algebraic equations on equations from other ranges of mathematics (napr., the linear differential equation is a differential equation into which unknown function and its derivative enter linearly, i.e. in 1-st degree).
  • LINEARLY - TAPE CERAMICS CROP (in archeology), epoch of a neolith (kon. 5-th - nach. 4-th thousand up to n. e.) in Compare. To Europe. It is called on a way of an ornamentation of ceramics as deepened lines. Residues of settlements with tracks of terraneous home units and dugs out. An economy: agriculture and cattle breeding.
  • LINEAR TROOPS, 1) parts, subdividings of a heavy (linear) infantry and the cavalries making in 18-19 centuries the basis of closed linear battle constructions. 2) Signals Commands in the Russian army, protecting boundary reinforced lines and frontier.
  • LINEAR SYSTEMS, vibratory systems which properties (performance) (an elasticity, mass, a friction coefficient - mechanical systems and container, inductance, resistance - electrical systems) are saved at a change of state of system, i.e. do not depend on offsets, speeds, pressure and currents. Processes in linear systems are described by linear differential equations.
  • CAPITAL SHIP (battleship), 1) in sailing military fleet 17 - 1-st floor. 19 centuries large on the dimensions a three-mast combat ship with 2-3 decks (decks); had from 60 up to 130 instruments and up to 800 person of crew. It was intended for a conduct of combat in a line of fight (from here the title). 2) In steam armoured fleet 1-st floor. 20 century one of the main classes of large surface ships. Had 70-150 instruments of different templet (including 8-12 280-457-ìì) and 1500-2800 crew members. After 2-nd world war battleships have lost value.
  • The LINEAR OPERATOR, generalization of concept of a linear transformation on an event infinite-dimensional the spaces.
  • LINAC, a particle accelerator in which trajectories of particles are close to a straight line. The maximum power of electrons received in a linac, 20 GeV, protons up to 800 MeV.
  • LINEAR FUNCTIONAL, generalization of concept of the linear form on an event infinite-dimensional the spaces.
  • The LINEAR ELECTROMOTOR, the electromotor in which the movement is not spun (as in traditional engines), and linearly moves along a fixed part - a disconnected magnetic circuit of the arbitrary length. It is long-range in the electric drive of transport machines, allows to develop high speeds (up to 500 km/h).
  • LINEAR TONGUE, the same, that gestures tongue.
  • RULED SURFACE, surface which can be described motion direct on some line; napr., a hyperboloid of one sheet, a hyperbolic paraboloid.
  • RULED SPECTRUMS, see. Atomic spectrums, Spectrums optical.
  • LINEN (Lynen) Theodore (1911-79), the german biochemist. Basic researches of metabolism of fatty acids and a cholesterine in an organism. The Nobel Prize (1964, together with K.E.Blohom).
  • LENS, in geology - the lentiform form of burial of rocks and mineral wealths; a spherical or oval body with power reduction to edges.
  • LENS (a nem. Linse, from an armour. lens - lentil), in optician - a diaphanous body, restricted convex or concaves (one of surfaces can be flat) and conversing the form of a light beam. Lenss are collecting (positive) and disseminating (negative) (drawing). Lenss for a visible light routinely produce from a glass; for a ultraviolet radiation - from crystal, fluorite, fluoride of lithium, etc.; for an infrared rays - from silicium, germanium, fluorite, fluoride of lithium, etc.
  • SECOND-ORDER LINES, flat lines, which rectangular coordinates of points satisfy to an algebraic equation of 2-nd degree. Among second-order lines - ellipses (in particular, circles), hyperbolas, parabolas.
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