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.