term effect, and should not be confused with image retention, image burn, or sticking. lag circuit a simple passive electronic cir- L cuit designed to add a dominant pole to com- pensate the performance of a given system. A lag circuit is generally used to make a system L-band frequency band of approximately more stable by reducing its high-frequency 1–2 GHz. gain and/or to improve its position, veloc- ity, or acceleration error by increasing the L-L See line to line fault. low frequency gain. A nondominant zero is included in the lag circuit to prevent undue label a tag in a programming language destabilization of the compensated system by (usually assembly language, also legal in C) the additional pole. that marks an instruction or statement as a possible target for a jump or branch. lag network a network where the phase angle associated with the input–output trans- labeling (1) the computational problem fer function is always negative, or lagging. of assigning labels consistently to objects or object components (segments) appearing in lag-lead network the phase shift versus an image. frequency curve in a phase lag-lead network is negative, or lagging, for low frequencies (2) a technique by which each pixel within and positive, or leading, for high frequencies. a distinct segment is marked as belonging to The phase angle associated with the input– that segment. One way to label an image output transfer function is always positive or involves appending to each pixel of an im- leading. age the label number or index of its segment. Another way is to specify the closed contour of each segment and to use a contour filling Lagrange formulation a formulation technique to label each pixel within a contour. where the equations of motion are derived in a systematic way by choosing a set of general- ized coordinates, forming the Lagrangian of ladder diagram (1) the connection of the the mechanical system (as a difference of to- coils and contacts used in a control circuit tal kinetic energy and potential energy of the shown one line after the other that looks like system) and by solving the Lagrange equa- a ladder. tions (2) a visual language for specifying the Boolean expressions, which are the core of d ∂L ∂L − = τi i = 1,...,n the control law of PLC. dt ∂q˙i ∂qi laddertron a microwave vacuum tube os- where L stands for Lagrangian, qi is the gen- cillator with a slow-wave structure coupled eralized coordinate, q˙i is its derivative, and to a single-cavity resonator. τi is a generalized force, and n denotes num- ber of degrees of freedom of the mechani- lag the inability of an imaging tube to re- cal system. Last equations establish the rela- spond to instantaneous changes in light. For tions existing between the generalized forces measurement purposes, lag has two compo- applied to the manipulator and the joint po- nents: rise lag is the response time from dark sitions, velocities, and accelerations in so to light, whereas decay lag is the response called closed form. See also Newton–Euler time from light to dark. Lag is a very short- recursive algorithm. c 2000 by CRC Press LLC Lagrange stable state See bounded state. Lambertian surface a surface with per- fect diffusion properties, i.e., for which the Lagrangian interpolation a classic inter- reflectance function depends only on the an- polation procedure used in numerical analy- gle of incidence of illumination. sis. The sampling theorem is a special case. laminate multi-chip module (MCM-L) Laguerre polynomial a solution to the a multi-chip module built using advanced 00 0 differential equation xy + (1 − x)y + PCB manufacturing techniques. ny = 0. Laguerre polynomials L0(x) = ,L (x) = − x,L (x) = − x + x2/ 1 1 1 2 1 2 2, lamination a thin sheet of metal used to L = − x + x2/ −x3/ and 3 1 3 3 2 6. Additional build up the core of an electromagnetic de- Laguerre polynomials may be obtained from vice. Laminations are insulated from each (n+ )L (x)−( n+ the recursion formula 1 n+1 2 other to reduce the losses associated with − x)L (x) + L (x) = 1 n n−1 0. eddy currents. Laguerre–Gaussian beam electromag- land pattern a combination of lands in- netic beam solution of the paraxial wave tended for the mounting, interconnection, equation in which the field is a product of and testing of a particular component. a Laguerre polynomial and a Gaussian func- tion of distance from the beam axis. Landauer formula describes the con- ductance as a fundamental property of wave Lamb dip decrease in output power of a (electron) transmission through a structure. Doppler-broadened standing-wave laser os- cillator as a function of length tuning when Lange coupler four coupled lines used the resonant frequency is within approxi- with interconnections to provide tight cou- mately one homogeneous linewidth of gain pling. A practical implementation to increase center; results from the interaction of both the coupling between edge-coupled lines by the right and left travelling waves with the using several lines parallel to each other, so same atoms for line-center tuning. that the fringing fields at edges of the line contribute to coupling. lambda system a 3-level system in which the lowest two energy states are coupled by electromagnetic fields to a common interme- Langevin, Paul (1872–1946) Born: diate state of higher energy. This system is Paris, France so named because schematic representations Langevin is best known as the developer of of it often look like the capital Greek letter echolocation, which is the precursor to mod- lambda, 3. ern sonar. Langevin was the first to describe paramagnetism and diamagnetism. Lambert’s cosine law a law stating that, for a ideal matte (Lambertian) surface, the LAOS See light-amplifying optical switch. apparent brightness of the surface is propor- tional to the cosine of the angle of incidence and independent of both the angle of reflec- lap winding an armature winding on a DC tion and the phase angle between the incident machine in which the two ends of each coil and reflected beams. are connected to adjacent bars on the com- mutator ring. The lap winding provides “P ” Lambertian source a source whose di- parallel paths through the armature winding, rectional emission pattern follows Lambert’s where P is the number of poles in the ma- law; a cosine variation. chine. c 2000 by CRC Press LLC Laplace’s equation a partial differen- Laplacian pyramid a set of Laplacian im- tial equation mathematically described by ages at multiple scales used in pyramid cod- 2 2 ∇ φ = 0, where ∇ is the Laplacian and ing. An input image G1 is Gaussian lowpass φ is the equation’s solution. filtered and downsampled to form G2. Typi- cally G2 is one quarter the size of G1, i.e., it Laplace, Pierre-Simon, Marquis de is downsampled by a factor of 2 in each direc- (1749–1827) Born: Beaumont-en-Auge, tion. G2 is upsampled and Gaussian lowpass Normandy, France filtered to form R1 which is then subtracted Laplace is best known for his develop- from G1 to give L1. The process then repeats ment of basic tools of mathematical anal- using G2 as input. The sets of multiresolu- ysis including the Laplace transform, the tion images so generated are called “pyra- Laplace theorem, and the Laplace coeffi- mids”: G1 ...Gn form a Gaussian pyramid; cients. Laplace studied in Paris with the great L1 ...Ln form a Laplacian pyramid. mathematician Jean d’Alembert. Laplace was heavily involved in politics throughout lapped orthogonal transform (LOT) a his career and held many government posts. critically sampled block transform, where the Laplace’s theoretical work was heavily in the blocks overlap, typically by half a block. field of celestial mechanics. He helped to es- Equivalently the LOT is a critically sampled tablish the mathematical basis for the field filter bank, where typically the filter lengths and in doing so confirmed significant parts are equal to twice the number of channels or of Newton’s work. filters. The LOT was motivated by reducing the blocking effect in transform coding by us- Laplace transform the transform of a ing overlapping blocks. A cosine modulated function f(t)given by filter bank is a type of LOT. Z ∞ F(s) = f(t)e−stdt large cell cell with the radius of 5–35 km −∞ (such as those found in Groupe Special Mo- bile systems). See also cell. where s = a+jωis a complex variable. The one sided or unilateral Laplace transform is large disturbance a disturbance for given by the same equation except that the which the equation for dynamic operation lower limit is 0 and not −∞. The region cannot be linearized for analysis. of convergence of the Laplace integral is a vertical strip R in the s-plane. The inverse large-scale integration (LSI) (1) term Laplace transform is given by usually used to describe the level of integra- Z st tion at which entire integrated circuits can be f(t)= 1/(2πj) F(s)e ds placed on a single chip. L (2) an integrated circuit made of hundreds where L is a vertical line in R. The Fourier to thousands of transistors. Transform of f(t)is given by F(jω). large-scale process (system) partitioned Laplacian operator the second-order op- complex process (system) composed of sev- Rn ∇2 = ∂2/∂x2 + erator, defined in as 1 eral sub-processes (subsystems) that are ei- 2 2 ···+∂ /∂n . The zero crossings of an im- ther physically interconnected or must be age to which the Laplacian operator has been considered jointly due to the nature of the applied usually correspond to edges, as in control objectives.