, with a matrix B replacing the vector of the classical linear regression model. Multivariate ...Regression bar Image Linear regression.svg thumb right 400px Example of simple linear regression , which has one independent variable In statistics , linear regression is an approach to modeling the relationship ... is multiple regression . This in turn should be distinguished from multivariate linear regression ... of PLS or related projective methods rather than a single scalar variable. In linear regression, data are modeled using linear predictor function s, and unknown model parameters are estimation theory estimated from the data. Such models are called linear model s . Most commonly, linear ... of X is an affine transformation affine function of X . Less commonly, linear regression could ... given X is expressed as a linear function of X . Like all forms of regression analysis , linear regression ... probability distribution of y and X , which is the domain of multivariate analysis . Linear regression ... properties of the resulting estimators are easier to determine. Linear regression has many practical uses. Most applications of linear regression fall into one of the following two broad categories If the goal is Prediction Statistics prediction , or forecasting , linear regression can be used ... 1 sub , ..., X sub p sub that may be related to y , linear regression analysis can be applied to quantify ... information about y . Linear regression models are often fitted using the least squares approach ... can be used to fit models that are not linear models. Thus, while the terms least squares and linear model are closely linked, they are not synonymous. Introduction to linear regression Given a data set math y i, , x i1 , ldots, x ip i 1 n math of n statistical unit s, a linear regression model ... x sub i sub is linear function linear . This relationship is modeled through a disturbance term or error variable sub i sub an unobserved random variable that adds noise to the linear relationship ... more details
Infobox musical artist name Linear image alt caption image size background group or band alias origin Miami, Florida Miami , Florida genre years active start date YYYY end date YYYY or present label associated acts url current members past members Charlie Pennachio br Joey Restivo br Wyatt Pauley Linear was a Freestyle music Latin freestyle pop music pop Trio music trio from Miami, Florida Miami , Florida . It consisted of singer vocalist Charlie Pennachio, and percussionist Joey Restivo, who both hailed from New York , with Ecuador an guitarist Wyatt Pauley. In 1990, the band music band had a hit single hit with the music recording sales certification gold single music single , Sending All My Love , which was released on Atlantic Records and hit number 5 on the Billboard Hot 100 . Two years later, they had another hit with the single T.L.C. , which reached number 30. In 1990, Atlantic records released their first album, followed in 1992 by their second. Charlie Pennachio was an original member of Dance Artist Stevie B and Producer turned Dance Artist Tolga s Miami crew band. Charlie s first CD was produced and written by himself and Tolga Katas and released under Futura International Records owned by Tolga and Charlie. Listener reaction was overboard and the single entered the national pop charts in the U.S. Atlantic records caught wind of the single and tracked him down, and soon signed Charlie to a recording contract. Sending All My Love soared into the U.S. top five and earned ... 200 US 1990 align left Linear album Linear small Released March 21, 1990 Label Atlantic records ... 5 align center 8 align left rowspan 3 Linear align left Don t You Come Cryin align center 70 align ... Research location Menomonee Falls, Wisconsin isbn 0 89820 155 1 reflist DEFAULTSORT Linear Category American pop music groups Category American freestyle musicians US pop band stub es Linear banda pt Linear grupo ... more details
In coding theory , a linear code is an error correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block code s and convolutional ... University Press isbn 978 0 521 84868 8 ref Linear codes allow for more efficient encoding and decoding algorithms than other codes cf. syndrome decoding . Linear codes are used in forward error ... of a message block. The codewords in a linear block code are blocks of symbols which are encoded using more symbols than the original value to be sent. A linear code of length n transmits blocks containing n symbols. For example, the 7,4,3 Hamming code is a linear binary code which represents ... contains 2 sup 4 sup 16 codewords. Definition and parameters A linear code of length n and rank k is a linear subspace C with dimension linear algebra dimension k of the vector space math mathbb F q n ..., or equivalently, the minimum distance between distinct codewords. A linear code of length n , dimension ... in transmission, as we want it to. Properties As a linear subspace of math mathbb F q n math , the entire code C which may be very large may be represented as the span linear algebra span of a minimal set of codewords known as a basis linear algebra basis in linear algebra . These basis codewords ... form . A matrix H representing a linear function math phi mathbb F q n to mathbb F q n k math ... distance between the codewords of a linear code, one would only need to look at the non zero ... codeword, and hence determines the minimum distance of the code. The distance d of a linear code ... codes main Hamming code As the first class of linear codes developed for error correction purpose ... math d 3 math , this Hamming code can correct 1 bit error. Example The linear block code with the following ... codes main Hadamard code Hadamard code is a math 2 r, r, 2 r 1 2 math linear code and is capable of correcting .... Example The linear block code with the following generator matrix is a math 8,3,4 2 math Hadamard ... more details
Diagram.svg 360px right thumb The A and B quadrature channels Many linear encoders interpolate ...File Optical Encoders.png 500px right thumb Typical linear optical encoders. File Visualisierung der ... structures of a linear encoder Recorded with MagView . A linear encoder is a sensor, transducer ... can be determined by change in position over time. Linear encoder technologies include optical ... and interferometric . Linear encoders are used in metrology instruments, motion systems and high ..., CNC Mills, manufacturing gantry tables and semiconductor steppers. Physical principle Linear encoders ... reference based Optical Optical linear encoders http www.microesys.com m2 index.html , http www.renishaw.com ... bulbs and laser diode s. Magnetic Magnetic linear encoders http www.rls.si default.asp?prod LMencoders ... in the order of a micrometer are the norm. Capacitive Capacitive linear encoders work by sensing ... unwound into a linear system. The Spherosyn encoder http www.newall.com LEDs operation.htm ... Applications There are two main areas of application for linear encoders Measurement Measurement ... . Motion systems Servo controlled motion systems employ linear encoder so as to provide accurate ... color default.aspx Output Signal Formats Incremental signals Linear encoders can have analog .... The industry standard, analog output for linear encoders is sine and cosine quadrature signals. These are usually ... mechanisms automatically. The overall accuracy of the linear encoder is a combination of the scale ... signals As well as analog or digital incremental output signals, linear encoders can provide absolute reference or positioning signals. Reference mark Most incremental, linear encoders can produce an index ... tying users to a particular supplier. Limit switches Many linear encoders include built in limit ... to drive the axis. Physical arrangement and protection Linear encoders may be either enclosed or open . Enclosed linear encoders are employed in dirty, hostile environments such as machine tools ... more details
A linear polynomial may refer to A linear equation A linear function Polynomials Disambig Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
Image Linear polarization schematic.png 162px thumb right Diagram of the electric field of a light wave blue , linear polarized along a plane purple line , and consisting of two orthogonal, in phase components red and green waves In electrodynamics , linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. See Polarization waves polarization for more information. The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector. ref name Shapira, cite book last Shapira first Joseph authorlink coauthors Shmuel Y. Miller title CDMA radio with repeaters publisher Springer date 2007 location pages 73 url http books.google.com books?id Yd56YZY1RpAC&pg PA73&dq 5Bpolarization of radio waves 5D&hl en&sa X&ei ZQx T7 HNYT9iQKm59SeDg&ved 0CFgQ6AEwBQ v onepage&q 5Bpolarization 20of 20radio 20waves 5D&f false doi id isbn 0387263292 ref For example, if the electric field vector is vertical alternately up and down as the wave travels the radiation is said to be vertically polarized. Mathematical description of linear polarization The Classical physics classical sinusoidal plane wave solution of the electromagnetic wave equation for the Electric field electric and Magnetic field magnetic fields is cgs units ... right right math math mathbf B mathbf r , t hat mathbf z times mathbf E mathbf r , t c math for the magnetic ... vectors for linear polarization in x or y are special cases of this state vector. If unit vectors ... left i alpha right y rangle psi x x rangle psi y y rangle math . Applications of linear polarization ... as polarization rotators, enclosed by a pair of crossed linear polarizers. A Four dimensional light ... External links http www.youtube.com watch?v oDwqUgDFe94 Animation of Linear Polarization on YouTube http www.youtube.com watch?v Q0qrU4nprB0 Comparison of Linear Polarization with Circular and Elliptical ... more details
Unreferenced stub auto yes date December 2009 In an electric electrical network circuit , a linear element is an electrical element with a linear relationship between input electricity current and output voltage . Resistor s are the most common example of a linear element other examples include capacitor s, inductor s, and transformer s. Fundamentally nonlinear devices like transistors are often used to build approximately linear circuits. For example, an Operational amplifier op amp is designed to behave like a linear amplifier, as long as its input voltages remain within certain limits. See also Nonlinear element DEFAULTSORT Linear Element Category Electronics terms Electronics stub zh ... more details
Infobox Comet name 158P Kowal LINEAR image discoverer Charles T. Kowal br Lincoln Near Earth Asteroid Research LINEAR discovery date July 24, 1979 designations 1979 O1 2001 RG100 epoch March 6, 2006 semimajor 4.724 Astronomical Unit AU perihelion 4.592 AU aphelion 4.857 AU eccentricity 0.02799 period 10.27 Julian year astronomy a inclination 7.9066 last p July 8, 2002 next p September 27, 2012 ref name NK1776 cite web date 2009 04 23 title 158P Kowal LINEAR NK 1776 publisher OAA Computing and Minor Planet Sections author Syuichi Nakano url http www.oaa.gr.jp oaacs nk nk1776.htm accessdate 2012 02 18 ref 158P Kowal LINEAR is a List of periodic comets periodic comet in the solar system . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 158P orb 1 Orbital simulation from JPL Java http ssd.jpl.nasa.gov horizons.cgi?find body 1&body group sb&sstr 158P Horizons Ephemeris http www.aerith.net comet catalog 0158P index.html 158P Kowal LINEAR Seiichi Yoshida aerith.net http cometography.com pcomets 158p.html 158P at Kronk s Cometography PeriodicComets Navigator 157P Tritton 159P LONEOS DEFAULTSORT Kowal Linear, P158 Category Comets Kowal LINEAR comet stub pl 158P Kowal LINEAR sk 158P Kowal LINEAR sl Komet Kowal LINEAR ... more details
A linear compressor is a gas compressor where the piston moves along a linear track to compress to minimize energy loss during conversion. History The first linear compressors were developed in 1973, the first market introduction of a linear compressor to compress refrigerant was in 2001 ref http www.lge.com about press release print 21163.jhtml Linear Compressor history ref ref http www.aceee.org conf mt04 wbprsnt Lee R3.pdf Linear DOS ref Valved linear compressor The single piston linear compressor uses dynamic counterbalancing, where an auxiliary movable mass is flexibly attached to a movable piston assembly and to the stationary compressor casing using auxiliary mechanical springs with zero vibration export at minimum electrical power and current consumed by the motor ref http www.eng.ox.ac.uk cryogenics linearcomp.html Valved linear compressor ref . It is used in cryogenic s ref http www.eng.ox.ac.uk cryogenics papers Preprint ValvedComp.pdf Development of a valved linear compressor for a satellite borne J T cryocooler ref . See also hydrogen compressor liquid hydrogen Timeline of low temperature technology Timeline of hydrogen technologies References references Category Compressors Category Cooling technology Category Hydrogen technologies nl Lineaire compressor ... more details
Refimprove date January 2008 tone date December 2011 In electronics, a linear regulator is a component ... of a switching regulator over linear regulator ref http www.rason.org Projects swregdes swregdes.htm ... compensation compensation , the output voltage is kept reasonably constant. Linear regulators are often ... much more efficiently by a switched mode power supply , but a linear regulator may be preferred ..., the linear regulator may dissipate less power than a switcher. The linear regulator also has the advantage ... or bulky, being often of simpler design, and being electromagnetic interference quieter . Linear regulators ... for voltage reference circuits. All linear regulators require an input voltage at least some minimum ... the available input voltage, no linear regulator will work not even an Low dropout regulator LDO . In this situation ... I sub B sub forms the load current for the Zener diode and is much smaller than the current through ... V S V Z I Z K.I B math where, V sub Z sub is the Zener voltage, I sub B sub is the transistor s base current and K 1.2 to 2 to ensure that R1 is low enough for adequate I sub B sub . math I B frac ... voltage adjustment, but degrades regulation. See also Capacitance multiplier Using a linear regulator Linear regulators can be constructed using discrete components but are usually encountered in integrated circuit forms. The most common linear regulators are three terminal integrated circuit s in the TO220 ... thumb 200px An assortment of 78xx series ICs Fixed three terminal linear regulators are commonly ... regulators Product Launch The adjustable linear regulator IC still in use today first debuted ... then working for National Semiconductor . Dobkin later left National in 1981 to found Linear Technology ... three terminal linear regulators may be used. An adjustable regulator generates a fixed low ... series. Note that some regulators, like the LM317, require a minimum load. Protection Linear IC voltage ... at Hyperphysics http www.youtube.com watch?v GSzVs7 aW Y Linear voltage regulator tutorial video ... more details
Image with unknown copyright status removed Image line network.gif frame Image showing line network layout A linear bus topology is a network topology consisting of a main run of cable with a terminator at each end. All nodes file server, workstations, and peripherals are connected to the linear cable. Ethernet and LocalTalk networks use a linear bus topology. Advantages of a linear bus topology Easy to connect a computer or peripheral to a linear bus. Requires less cable length than a star topology . Disadvantages of a linear bus topology Entire network shuts down if there is a break in the main cable. Terminators are required at both ends of the backbone cable. Difficult to identify the problem if the entire network shuts down. Not meant to be used as a stand alone solution in a large building. External links http fcit.usf.edu network chap5 chap5.htm Category Network topology compu network stub id Topologi runtut ... more details
distinguish linear model of innovation In statistics , the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However the term is also used in time series analysis with a different meaning. In each case, the designation linear is used to identify ... theory is possible. Linear regression models For the regression case, the statistical model is as follows ... variables representing errors in the relationship. The linear part of the designation relates to the appearance of the regression coefficient s, sub j sub in a linear way in the above relationship ... hat Y i beta 0 beta 1 phi 1 X i1 cdots beta p phi p X ip qquad i 1, ldots, n , math are linear functions ... From this, it can readily be seen that the linear aspect of the model means the following the function ... simple problem the derivatives of the function are linear functions of the sub j sub making it easy to find the minimising values the minimising values sub j sub are linear functions of the observations Y sub i sub the minimising values sub j sub are linear functions of the random errors sub ... of sub j sub . Time series models An example of a linear time series model is an autoregressive ... times. In this instance the use of the term linear model refers to the structure of the above relationship in representing X sub t sub as a linear function of past values of the same time series and of current and past values of the innovations. ref Priestley, M.B. 1988 Non linear and Non stationary ... of the time series. Note that here the linear part of the term linear model is not referring to the coefficients ... model is used to contrast with a linearly structured model, although the term linear model is not usually applied. One example of this is nonlinear dimensionality reduction . See also Linear system ... Modell es Modelo lineal pt Modelo linear ... more details
Refimprove date August 2009 A linear circuit is an electronic circuit in which, for a Sine wave sinusoidal ... f . Note that the output need not be Phase waves in phase with the input. ref citebook title Linear ... definition of a linear circuit is that it obeys the superposition principle . This means that the output of the circuit F x when a linear combination of signals ax sub 1 sub t bx sub 2 sub t is applied to it is equal to the linear combination of the outputs due to the signals x sub 1 sub t and x sub 2 sub t applied separately math F ax 1 bx 2 aF x 1 bF x 2 , math Informally, a linear circuit .... Examples A linear circuit is one that has no nonlinear electronic components in it. Examples of linear circuits are small signal amplifier s, differentiator s, and integrator s, or any circuit ... , and other linear circuit element s. Some examples of nonlinear electronic components are diode ... the superposition principle , linear circuits can be analyzed with powerful mathematical frequency domain ... , pole complex analysis pole s, and zero complex analysis zero s. The analysis of a linear circuit ... of the circuit in general with different component values or inputs. The behavior of such Linear element linear circuit element s as resistors, capacitors, and inductors can be specified by a single number ... of a nonlinear circuit requires more information than is needed for a linear circuit. Linear circuits and systems form a separate category within electronic manufacturing. Manufacturers of transistors and integrated circuit s divide their product lines into linear and digital lines, for example. In their linear components, manufacturers work to reduce nonlinear behavior to a minimum ..., for example those in TV and radio receivers, nonlinear elements can be replaced with a linear small signal model , allowing linear analysis techniques to be used. Conversely, many linear circuit elements ... linear ... more details
Merge to Linear genetic programming discuss Talk Linear genetic programming Merger proposal date January 2012 Orphan date November 2006 att February 2012 In genetic programming GP a linear tree is a program composed of a variable number of unary functions and a single leaf node terminal . Note linear tree GP differs from bit string genetic algorithms since a population may contain programs of different lengths and there may be more than two types of functions or more than two types of terminals. References http www.cs.ucl.ac.uk staff W.Langdon FOGP Foundations of Genetic Programming . Category Genetic programming comp sci theory stub ... more details
unreferenced date March 2011 A linear octree is an octree that is represented by a linear Array data structure array instead of a tree data structure . To simplify implementation, a linear octree is usually complete that is, every internal node has exactly 8 child nodes and where the maximum permissible depth is fixed a priori making it sufficient to store the complete list of leaf node s . That is, all the nodes of the octree can be generated from the list of its leaf nodes. Space filling curves are often used to represent linear octrees. Category Trees data structures datastructure stub ... more details
More footnotes date March 2009 In cryptography , linear cryptanalysis is a general form of cryptanalysis ... have been developed for block cipher s and stream cipher s. Linear cryptanalysis is one of the two ..., 1992 . ref name FEAL linear cite conference author Matsui, M. and Yamagishi, A title A new method ... name DES linear cite conference author Matsui, M title Linear cryptanalysis method for DES cipher booktitle ... 2 sup 43 sup known plaintext attack known plaintexts . ref name DES linear A variety of refinements to the attack have been suggested, including using multiple linear approximations or incorporating non linear expressions, leading to a generalized partitioning cryptanalysis . Evidence of security against linear cryptanalysis is usually expected of new cipher designs. Overview There are two parts to linear cryptanalysis. The first is to construct linear equations relating plaintext, ciphertext ... values of their variables are as close as possible to 0 or 1. The second is to use these linear equations in conjunction with known plaintext ciphertext pairs to derive key bits. Constructing linear equations For the purposes of linear cryptanalysis, a linear equation expresses the equality of two ... bit of the key math P 1 oplus P 3 oplus C 1 K 2. math In an ideal cipher, any linear equation relating plaintext, ciphertext and key bits would hold with probability 1 2. Since the equations dealt with in linear cryptanalysis will vary in probability, they are more accurately referred to as linear ... in a linear equation . For small enough S boxes, it is possible to enumerate every possible linear equation relating the S box s input and output bits, calculate their biases and choose the best ones. Linear approximations for S boxes then must be combined with the cipher s other actions, such as permutation and key mixing, to arrive at linear approximations for the entire cipher. The piling ... linear approximations Matsui 1994 . Deriving key bits Having obtained a linear approximation ... more details
merge Morphea discuss Talk Linear scleroderma Merge proposal date July 2011 Infobox Disease Name Linear scleroderma Image Caption DiseasesDB ICD10 ICD10 L 94 1 l 80 ICD9 ICD9 701.0 ICDO OMIM MedlinePlus eMedicineSubj eMedicineTopic MeshID Linear scleroderma is a type of Morphea localized scleroderma ref DorlandsDict seven 000095147 linear scleroderma ref which is an auto immune disorder characterized by a line of thickened skin which can affect the bones and muscles underneath it. Presentation It most often occurs in the arms, legs, or forehead, and may occur in more than one area. It is also most likely to be on just one side of the body. Linear scleroderma generally first appears in young children. ref name Andrews James, William Berger, Timothy Elston, Dirk 2005 . Andrews Diseases of the Skin Clinical Dermatology . 10th ed. . Saunders. Page 171. ISBN 0 7216 2921 0. ref See also Scleroderma List of cutaneous conditions Frontal linear scleroderma References reflist Localized connective tissue diseases DEFAULTSORT Linear Scleroderma Category Connective tissue diseases Cutaneous condition stub ... more details
Unreferenced date December 2009 For other meanings of density Density disambiguation Linear density , linear mass density or linear mass is a measure of mass per unit of length , and it is a characteristic of strings or other one dimensional objects. The SI unit of linear density is the kilogram per metre kg m . The linear density, math sometimes denoted by math , of an object is defined as math mu frac partial m partial x math where math m is the mass, and math x is a coordinate along the one dimensional object. For the common case of a homogeneous substance of length math L and total mass math m , this simplifies to math mu frac m L math In drawing or printing, the term linear density also refers to how densely or heavily a line is drawn. Units See also Units of textile measurement Common units include kilogram per meter ounce mass per foot ounce mass per inch pound mass per yard used in the North American railway industry for the linear density of Rail tracks rail s pound mass per foot pound mass per inch Units of textile measurement Denier denier , a unit of measure for the linear density of fiber s, defined as the mass in grams per 9,000 meters. Units of textile measurement Tex decitex dtex , the International System of Units SI unit for the linear density of fiber s, defined as the mass in grams per 10,000 meters DEFAULTSORT Linear Density Category Density physics stub ar eo Lineara denseco fr Masse lin ique ko it Densit lineare nl Lineaire dichtheid fi Lineaarinen tiheys zh ... more details
Unreferenced date December 2009 A linear alternator is essentially a linear motor used as an electrical generator . An alternator is a type of alternating current AC electrical generator. The devices are often physically equivalent. The principal difference is in how they are used and which direction the energy flows. An alternator converts mechanical energy to electrical energy , whereas a motor converts electrical energy to mechanical energy. Like most electric motors and electric generators, the linear alternator works by the principle of electromagnetic induction . However, most alternators work with rotary motion, whereas linear alternators work with linear motion i.e. motion in a straight line . Theory When a magnet moves in relation to a Coil Electromagnetic coils coil of wire , this changes the magnetic flux passing through the coil, and thus induces the flow of an electric current , which can be used to do work physics work . A linear alternator is most commonly used to convert reciprocating i.e. back and forth motion directly into electrical energy. This short cut eliminates the need for a Crank mechanism crank or Linkage mechanical linkage that would otherwise be required to convert a reciprocating motion to a rotary motion in order to be compatible with a rotary generator. Applications The simplest type of linear alternator is the Faraday Flashlight . This is a torch UK or flashlight USA which contains a coil and a permanent magnet . When the appliance is shaken back and forth, the magnet oscillates through the coil and Electromagnetic induction induces an electric current . This current is used to charge a capacitor , thus storing energy for later use. The appliance can then produce light, usually from a light emitting diode , until the capacitor is discharged. It can then be re charged by further shaking. Other devices are under development which use linear ... . See also Alternator Linear motor Free piston engine DEFAULTSORT Linear Alternator Category Electrical ... more details
Context date March 2010 Linear referencing also called linear reference system or linear referencing system or LRS , is a reference system in which the locations of features are identified by a relative measure along a linear element, for example a milestone along a road . Each feature is located by either a point known as a milepoint or a line segment . The system is designed so that if a segment of a route is changed only those milepoints on the changed segment need to be updated. Linear referencing is suitable for management of data related to linear features like road s, railway s, oil and gas transmission Pipeline transport pipeline s, power and data transmission lines, and river s. A system for identifying the location of pipeline features and characteristics is by measuring distance from the start of the pipeline. An example linear reference address is Engineering Station 1145 86 on pipeline Alpha 114,586 feet from the start of the pipeline. With a reroute, cumulative stationing might not be the same as engineering stationing, because of the addition of the extra pipeline. Linear referencing solves this dilemma. Supported platforms Linear referencing is supported for example by several Geographic Information System software, including GE Global Transmission Office ref cite web url http www.gedigitalenergy.com geospatial catalog smallworld trans.htm?TopicName Key Benefits ref ArcGIS ref cite web url http webhelp.esri.com arcgiSDEsktop 9.3 index.cfm?TopicName An overview of linear referencing title ArcGIS 9.3 An overview of linear referencing ... web url http gs web.geomapgis.com web1 tiki index.php?page Routes title GEOMAP GIS 2012 Solution for linear ... the Linear Reference System in GRASS publisher journal International Journal of Geoinformatics ... documentation manual 1.5 reference.html Linear Referencing title PostGIS 1.5.2 Manual author ... Noronha first Val last2 Church first2 Richard L. year 2002 title Linear Referencing and Alternate Expressions ... more details
Linear interpolation is a method of curve fitting using linear polynomials. Lerp is an abbreviation for linear interpolation , which can also be used as a verb harv Raymond 2003 . Linear interpolation ... line is the linear interpolant between the points, and the value y at x may be found by linear ... and math scriptstyle x 1,y 1 math , the linear interpolant is the straight line between these points ... 0 y 1 x x 0 y 0 x 1 x 0 math which is the formula for linear interpolation in the interval math scriptstyle x 0,x 1 math . Outside this interval, the formula is identical to linear extrapolation . This formula ... set Image Interpolation example linear.svg thumb right 300px Linear interpolation on a data set red points consists of pieces of linear interpolants blue lines . Linear interpolation on a set of data ... as the concatenation of linear interpolants between each pair of data points. This results in a Continuous ... class math C 0 math . Linear interpolation as approximation Linear interpolation is often ... p denotes the linear interpolation polynomial defined above math p x f x 0 frac f x 1 f x 0 x 1 ... is, the worse the approximations made with simple linear interpolation. Applications Linear interpolation .... Linear interpolation is an easy way to do this. The basic operation of linear interpolation between ... is known be smoother than C sup 0 sup , it is common to replace linear interpolation with spline interpolation , or even polynomial interpolation in some cases. Multivariate Linear interpolation as described ... of linear interpolation is called bilinear interpolation , and in three dimensions, trilinear interpolation . Notice, though, that these interpolants are no longer linear functions of the spatial coordinates, rather products of linear functions this is illustrated by the clearly non linear example of bilinear interpolation in the figure below. Other extensions of linear interpolation can be applied ... surface s. These may be defined as indeed higher dimensional piecewise linear function see second figure ... more details
Unreferenced date December 2009 Orphan date December 2009 The linear range is that range of input or output values for which an Electronics electronic amplifier produces an output signal information theory signal that is a direct, linear function of the input signal. That is, the output can be represented by the equation Output Input × Gain When operating in the linear range, no Clipping audio clipping occurs. If an amplifier were perfectly linear, no distortion Total harmonic distortion harmonic distortion or intermodulation distortion would occur although random noise may still be introduced . Vacuum tube amplifiers tend to exhibit soft clipping as they approach the maximum possible output value, the gain tends to drop, rounding the tops of the signal waveform . Transistor amplifiers, by comparison, tend to produce hard clipping the gain remains approximately the same until the maximum possible output voltage is reached at that point, hard clipping occurs and the waveform never exceeds that value. The sharp inflection point s thus produced in the output waveform tend to have many more high order harmonic s. This is alleged to be the basis of the transistor sound that some audiophile s find offensive although this would not have occurred if they would not have been driving their amplifiers beyond the linear range in the first place . See also Transfer function Audio system measurements DEFAULTSORT Linear Range Category Electronics terms ... more details
Linear aeration is a relatively new aeration process it allows water to penetrate the soil and to be retained in the proper amounts. Linear aeration also adds organic material organic nutrition, soil softeners humus , topsoil , compost , sand , clay , etc. if necessary. Gardens In linear aeration, the necessary organic matter is added on top of the soil surface, between plantings. The grooves are then cut into the soil to let the amendments and additives enter the soil and recovered in the same passage. Lawns Linear aeration also alleviates excessive water in lawn areas. In linear aeration, the necessary organic matter is added on top of the turf. Next, grooves are cut into the turf to let the soil additives enter the soil the grooves are recovered in the same passage. Benefits of linear aeration Gardens irrigation water conservation . promotes stronger and deeper root development, for plant health and drought tolerance. permits proper distribution of soil amendment s and additives. allows organic nutrition absorption. Lawns alleviates soil compaction in heavily traveled areas provides smoother lawn surfaces drastically reduces disruption of actual turf surface compared to coring or plugs aeration causes minimal interruption of use of athletic fields See also Category Soil improvers Soil improvers index Portal Gardening References Unreferenced date November 2006 Category Soil Category Soil improvers Category Horticultural techniques Category Backyards Category Lawn care gardening stub ... more details
In the mathematical field of differential geometry , the term linear connection can refer to either of the following overlapping concepts a connection vector bundle connection on a vector bundle , often viewed as a differential operator a Koszul connection or covariant derivative a connection principal bundle principal connection on the frame bundle of a manifold or the induced connection on any associated bundle &mdash such a connection is equivalently given by a Cartan connection for the affine group of affine space , and is often called an affine connection . The two meanings overlap, for example, in the notion of a linear connection on the tangent bundle of a manifold. In older literature, the term linear connection is occasionally used for an Ehresmann connection or Cartan connection on an arbitrary fiber bundle ref springer id c c025140 title Connection on a fibre bundle author . Lumiste ref , to emphasise that these connections are linear in the horizontal direction i.e., the horizontal bundle is a vector subbundle of the tangent bundle of the fiber bundle , even if they are not linear in the vertical fiber direction . However, connections which are not linear in this sense have received little attention outside the study of Spray mathematics spray structures and Finsler geometry . References reflist mathdab Category connection mathematics es Conexi n lineal ... more details
More footnotes date March 2011 Linear filters in the time domain process time varying input signals to produce output signals, subject to the constraint of linearity . This results from systems composed solely of components or digital algorithms classified as having a linear response. Most filters implemented in analog electronics, in digital signal processing , or in mechanical systems are classified as causal , time invariant , and linear . However the general concept of linear filtering is broader ... methods, which are discussed elsewhere. A linear time invariant LTI system theory LTI filter can ... h of a linear time invariant causal filter specifies the output that the filter would produce if it were ... principle , applicable to all linear systems yields the output waveform. Mathematically ... characterizes any linear time invariant or shift invariant in the discrete time case filter. The input ... system that acts as a linear filter, such as a system of springs and masses, or an analog electronic circuit that includes capacitors and or inductors along with other linear components such as resistor ... linear filters.svg 500px center As is clear from the image, the elliptic filter is sharper than ... of the filter depends on the weighting coefficients denoted b sub 0 sub , b sub 1 sub , .... b sub N ... derived from a more sophisticated design procedure. Mathematics of filter design Linear analog electronic filter LTI system theory describes linear time invariant LTI filters of all types. LTI filters ..., continuous time IIR LTI filters may be described in terms of linear differential equation s, and their impulse ... cite book author Williams, Arthur B & Taylor, Fred J title Electronic Filter Design Handbook ... of damping coefficient, from lower to higher values Gaussian, Bessel, linear phase, Butterworth, Chebyshev ... by L. D. Paarmann refend Category Linear filters Category Filter theory cs Line rn filtr es Filtro lineal fr Filtre lin aire pt Filtro linear ru uk zh ... more details
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