Infobox Writing system name Linear A type Undeciphered typedesc likely Syllabic and Ideographic languages Eteocretan language Eteocretan unknown time Possibly from MM IB to LM IIIA differentiated to Linear B and Linear Cypriot iso15924 Lina Image Linear A tablets filt.jpg thumb 237px right Linear A incised on tablets found in Akrotiri, Santorini . Linear A is one of two scripts used in ancient Crete before Mycenaean Greek language Mycenaean Greek Linear B Cretan hieroglyphs is the second script. In Minoan Civilization Minoan times, before the Mycenaean Greek dominion, Linear A was the official ... scripts were discovered and named by Arthur Evans . In 1952, Michael Ventris discovered that Linear ... of Linear B, although many points remain to be clarified. By contrast, Linear A has not been deciphered since the language of Linear A has not been discovered. Though the two scripts Linear A and B share some of the same symbols, using the syllable s associated with Linear B in Linear A writings produces ... 1450 BC. Linear A seems to have been used as a complete syllabary around 1900 1800 BC, although several signs appear earlier as mason marks. It is possible that the Trojan script Trojan Linear A scripts ... Linear A vase filt.jpg thumb right 180px Linear A incised on a vase, also found in Akrotiri. As the Minoan ... is correct. The simplest approach to decipherment may be to presume that the values of Linear A match more or less the values given to the fully transliterated Linear B script, used for Mycenean ... has a comprehensive list of known texts written in Linear A. ref This point of view has been ... in both Linear A and B therefore, 12 signs have the same values in both syllabaries DA, I, JA, KI .... This ambiguity represents the current state of understanding of the language of Linear A the known ... A The decipherment of Cretan inscriptions in Linear A in 1957 stating that Linear A contains Greek ... languages of Cretan inscriptions in Linear A , suggesting that the language of the Hagia Triada tablets ... more details
Piecewise linear may refer to Piecewise linear function Piecewise linear manifold Piecewise linear continuation Collapse topology A polygonal chain or piecewise linear curve mathdab Long comment to avoid being listed on short pages ... more details
Wiktionary linear The word linear comes from the Latin word i lang la linearis i , which means created by lines. Usage in mathematics Linearity Linear code Linear equation Linear function Linear programming , a type of optimization problem Linear system Linear transformation Linear map Usage in technology Particularly in electronics, a device whose characteristic or transfer function is linear, in the mathematical sense, is called linearLinear amplifier , a component of amateur radio equipment Linear Corporation , a radio frequency electronics company Linear cryptanalysis Linear element , part of an electric circuit Linear medium , related to information storage and retrieval Linear motor a type of electric motor Linear phase , a property of an electronic filter Linear Technology , an integrated circuit manufacturer Linearity computer and video games Other uses A leaf shape in botany LINEAR, the Lincoln Near Earth Asteroid Research project Linear A , one of two scripts used in ancient Crete Linear B , a script that was used for writing Mycenaean, an early form of Greek Linear narrative structure Linear group , a pop music group popular in the 1990s Linear album Linear album , their group s debut album Linear film Linear film , a film that was released with the U2 album No Line on the Horizon Linear molecular geometry in chemistry Linear motion , motion along a straight line Linearity writing , describing whether symbols in a writing system are composed of lines A kind of typeface in the VOX ATypI classification disambig cs Line rn ja pt Linear sk Line rnos ... more details
Linear phase is a property of a filter signal processing filter , where the phase response of the filter is a linear function of frequency , excluding the possibility of wraps at math pm pi math . In a causal system , perfect linear phase can be achieved with a discrete time Finite Impulse Response FIR filter. Linear phase system has the property of the true time delay . Since a linear phase or Linear phase Generalized linear phase generalized linear phase filter has constant group delay , all frequency components have equal delay times. That is, there is no distortion due to the time delay of frequencies relative to one another in many applications, this constant group delay is advantageous. By contrast, a filter with non linear phase has a group delay that varies with frequency, resulting in phase distortion . Some examples of linear and non linear phase filters are given below. The plots below represent the phase response as a function of frequency in radians math w math . Image Phase Plots.svg Generalized linear phase Systems with generalized linear phase have an additional frequency independent constant added to the phase. Because of this constant, the phase of the system is not a strictly linear function of frequency, but it retains many of the useful properties of linear phase systems. ref Oppenheim & Schafer first edition, chapter 5 ref See also Minimum phase References reflist Category Electronics terms Category Digital signal processing signal processing stub nl Lineaire fase ... 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
Unreferenced date December 2009 A linear medium is any medium which is intended to be written to or accessed in a linear fashion, literally meaning in a line . This means that the information is written to or read from the medium in a given order, so for example a book containing a novel is intended to be read from front to back, beginning to end, and is therefore a linear medium. It may be written in the same way, but would not necessarily need to be, to be considered a linear medium. A book containing an encyclopedia however is a non linear medium, as it is not necessary for the articles to be accessed or written in any particular order. Even though both non linear and linear mediums have perimeters to which they are restricted, linear mediums have a set path of how to get from point A to point B, whereas non linear mediums do not. Examples in technology are a pre recorded videocassette which is usually accessed one item after another, compared with a pre recorded DVD which can be accessed in any order. Types of linear medium Scroll Magnetic tape data storage Paper tape Photographic film Novel story book s Compact cassette s See also Serial access Sequential access Random access DEFAULTSORT Linear Medium Category Data management ... 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
Context date October 2009 In computer science , a Formal grammar grammar is linear if it is context free grammar context free and all of its productions Left hand side and right hand side of an equation right hand sides have at most one nonterminal. A linear language is a language generated by some linear grammar. Example A simple linear grammar is G with N S , a, b , P with start symbol S and rules ... grammars Two special types of linear grammars are the following the left linear or Regular ... the right linear or right regular grammars, in which all nonterminals in right hand sides are at the right ends . Collectively, these two special types of linear grammars are known as the regular grammar s both can describe exactly the regular language s. Another special type of linear grammar is the following linear grammars in which all nonterminals in right hand sides are at the left or right ends, but not necessarily all at the same end. By inserting new nonterminals, every linear grammar ... above can be replaced with S &rarr aA A &rarr Sb S &rarr &epsilon Hence, linear grammars of this special form can generate all linear languages. Expressive power We have seen that all regular languages are linear the example gave a linear, non regular language. All linear languages are context free language context free by definition a simple example of a context free, non linear language is the Dyck language of well balanced bracket pairs. Hence, the regular languages are a proper subset of the linear ... is a linear language and M is a regular language, then the intersection math L cap M math is again a linear language in other words, the linear languages are closed under intersection with regular sets. Furthermore, the linear languages are closed under String operations String homomorphism homomorphism ... 1979 , Ex. 11.1, pp. 282f. ref . These three closure properties show that the linear languages form ..., Reading Massachusetts, 1979. ISBN 0 201 029880 X. DEFAULTSORT Linear Grammar Category Formal languages ... 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
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
In the mathematics mathematical subfield of linear algebra or more generally functional analysis , the linear span also called the linear hull of a Set mathematics set of vector space vectors in a vector space is the intersection set theory intersection of all Linear subspace subspaces containing that set. The linear span of a set of vectors is therefore a vector space. Definition Given a vector space ... is defined to be the intersection W of all linear subspace subspaces of V which contain S . W is referred ... , lambda r in mathbf K . math The span of S may also be defined as the set of all linear combination ... a Basis linear algebra basis . If 2,0,0 were replaced by 1,0,0 , it would also form the standard basis ... , &minus 1,1 2,3 , 1,1,1 , but this set is not a basis, because it is Linear dependency linearly dependent ... spanned by a non empty subset S of a vector space V is the set of all linear combinations of vectors ... Linear independence linearly independent set of vectors from V . Theorem 3 Let V be a finite dimensional ... is a minimal spanning set when V is finite dimensional. Closed linear span In functional analysis , a closed linear span of a Set mathematics set of vector space vectors is the minimal closed set which contains the linear span of that set. Suppose that X is a normed vector space and let E be any non empty subset of X . The closed linear span of E , denoted by math overline operatorname Sp E math or math overline operatorname Span E math , is the intersection of all the closed linear subspaces ... u in X forall epsilon 0 , exists x in operatorname Sp E x u epsilon . math Notes The linear span of a set is dense in the closed linear span. Moreover, as stated in the below lemma, the closed linear span is indeed the closure mathematics closure of the linear span. Closed linear spans are important when dealing with closed linear subspaces which are themselves highly important, consider Riesz s lemma ... operatorname Sp E math is a closed linear subspace of X which contains E , b math overline operatorname ... 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
Unreferenced date October 2008 In mathematics a linear inequality is an inequality mathematics inequality which involves a linear function . Linear inequalities in real numbers Definitions When two expressions are connected by greater than or less than sign, we get an inequation. When operating in terms of real number s, linear inequalities are the ones written in the forms math f x b , math or math f x leq b math , where math f x math is a linear functional in real numbers and b is a constant real number. Alternatively, these may be viewed as math g x 0 , math or math g x leq 0 math , where math g x math is an affine function . The above are commonly written out as math a 0 a 1 x 1 a 2 x 2 cdots a n x n 0 math or math a 0 a 1 x 1 a 2 x 2 cdots a n x n leq 0 math Sometimes they may be written out in the forms math a 1 x 1 a 2 x 2 cdots a n x n b math or math a 1 x 1 a 2 x 2 cdots a n x n ... are called the coefficients, and math b math is the constant term. A linear inequality looks exactly like a linear equation , with the inequality sign replacing the equality sign. A system of linear inequalities is a set of linear inequalities in the same variables math begin alignat 7 a 11 x 1 .... Not all systems of linear inequalities have solutions. Interpretations and applications The set of solutions of a real linear inequality constitutes a half space of the n dimensional real space, one of the two defined by the corresponding linear equation. The set of solutions of a system of linear ... space R sup n sup . Sets of linear inequalities called constraints are used in the definition of linear programming . Linear inequalities in terms of other mathematical objects When you graph a linear inequality, it will be on one side of a line. Also, when you mark points where the line crosses ... operations of addition , multiplication and comparison , therefore the notion of a linear inequality ... Linear algebra Category Linear programming Category Polyhedra ... 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
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