Other uses Refimprove date December 2007 Distinguish Lineage The word linear comes from the Latin word linearis , which means created by lines . In mathematics , a linear map or function mathematics function ..., x is not necessarily a real number , but can in general be a member of any vector space . A linear function less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics. The concept of linearity can be extended to linear Operator mathematics operator s. Important examples of linear operators include the derivative considered ... a differential equation can be expressed in linear form, it is particularly easy to solve by breaking .... Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces also called linear spaces , linear transformations also called linear maps , and systems of linear equations. For a description of linear and nonlinear equations, see Linear equation . Nonlinear equations ... device s performance from ideal. Linear polynomials main linear equation In a different usage to the above, a polynomial of degree mathematics degree 1 is said to be linear, because the graph of a function of that form is a Line geometry line . Over the reals, a linear equation is one of the form ... of the term linear is not the same as the above, because linear polynomials over the real numbers ... . Boolean functions In Boolean algebra logic Boolean algebra , a linear function is a function ... in 0,1 . math A Boolean function is linear if A In every row of the truth table in which the value ... , exclusive or , tautology logic tautology , and contradiction are linear functions. Physics .... Electronics In electronics , the linear operating region of a transistor is where the collector ... to be used as an amplifier that preserves the High fidelity fidelity of analog signals. Linear ... line with arbitrary slope. Such linear electronic devices include linear filter , linear regulator ... more details
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 , the second being Cretan hieroglyphs . In Minoan Civilization Minoan times, before the Mycenaean Greek dominion, Linear A was the official script ... discovered and named by Arthur Evans . In 1952, Michael Ventris discovered that Linear B was being used ... used this information to achieve a significant and now well accepted decipherment of Linear B, although many points remain to be elucidated. A failure to discover the language of Linear A has prevented the same sort of progress being made in its decipherment. 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 ... around 1450 BC. Linear A seems to have been used as a complete syllabary around 1900 1800 BC, although several signs appear as mason marks earlier. It is possible that the Trojan script Trojan Linear ... BC, which is the period of the construction of the first palaces. Theories of decipherment Image 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 Greek ... has a comprehensive list of known texts written in Linear A. ref This point of view has been of great ... Linear A and B therefore, 12 signs have the same values in both syllabaries DA, I, JA, KI, PA ... state of understanding of the language of Linear A the known elements are too scarce to build a safe ... 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 Linear amplifier , a component of amateur radio equipment 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 , 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
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 current electricity current and 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 158P Kowal LINEAR is a periodic comet in our solar system . External links 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
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 date March 2011 A linear octree is an octree that is 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 . A linear octree can be represented by a linear array instead of a tree data structure . 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 structure datastructure stub ... 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
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 ... 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
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 linier ... 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 location 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 linear event 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 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 reference systems solves this dilemma, and the appropriate measures. Supported platforms Linear referencing is supported for example by several Geographic Information System software, including 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 author Esri date 24 February 2009 work publisher Esri accessdate 8 March 2011 ref GRASS GIS ref cite paper author Radim Blazek date March 2005 url http www.gisdevelopment.net proceedings fossgrass papers Introducing 20the 20Linear 20Reference 20System 20in 20GRASS.pdf format PDF title Introducing the Linear ... manual 1.5 reference.html Linear Referencing title PostGIS 1.5.2 Manual author PostGIS team ... Val last2 Church first2 Richard L. year 2002 title Linear Referencing and Alternate Expressions of Location ... more details
No footnotes date March 2009 In cryptography , linear cryptanalysis is a general form of cryptanalysis ... been developed for block cipher s and stream cipher s. Linear cryptanalysis is one of the two most ..., 1992 . ref name FEAL linear cite conference author Matsui, M. and Yamagishi, A title A new method ... 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 and key ... 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 ... 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 approximations ... in a linear equation . For small enough S boxes, it is possible to enumerate every possible linear ... 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 .... This procedure can be repeated with other linear approximations, obtaining guesses at values of key ... more details
File Linear subspaces with shading.svg thumb 250px right Euclidean space R sup 3 sup is a vector linear ... sup 3 sup . Subspaces are a common object of study in linear algebra. Linear algebra is a branch of mathematics that studies vector space s, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear map s or linear transformations or linear operators and can be represented by matrix mathematics matrices if a Basis linear algebra basis is given. The matrix theory is often considered as a part of linear algebra. Linear algebra ... the peculiarities of the infinite dimensional case are traditionally covered in linear functional analysis . Linear algebra is central to modern mathematics and its applications. An elementary application of linear algebra is to find the solution of a system of linear equations in several unknowns ... analysis . Linear algebra has a concrete representation in analytic geometry and is generalized in operator ... be approximated by linear ones. History The subject first took its modern form in the first half ... did much to spread the subject of linear algebra beyond pure mathematics. The origin of many of these ideas ... The main structures of linear algebra are vector space s and linear map s between them. A vector space ... , a linear transformation is a map mathematics map math T V to W math that is compatible with addition ... r F . A fundamental role in linear algebra is played by the notions of linear combination , span linear algebra span , and linear independence of vectors and basis linear algebra basis and the dimension linear algebra dimension of a vector space. Given a vector space V over a field F , an expression ... sub k sub are vectors and r sub 1 sub , r sub 2 sub , , r sub k sub are scalars, is called the linear ... , r sub 2 sub , , r sub k sub . The set of all linear combinations of vectors v sub 1 sub , v sub 2 sub , , v sub k sub is called their span. A linear combination of any system of vectors with all zero ... 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 mu math sometimes denoted by , of an object is defined as math mu frac partial m partial x math where m is the mass, and x is a coordinate along the one dimensional object. For the common case of a homogeneous substance of length L and total mass 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 ar eo Lineara denseco fr Densit lin aire it Densit lineare nl Lineaire dichtheid ... 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 DEFAULTSORT Linear Alternator Category Electrical generators ... more details
Unreferenced date January 2009 Image Pcmcia smart 4mb linear flash.jpg right thumb 250px A type I PCMCIA card Linear Flash is a PC card flash memory format. Linear Flash requires no battery support, unlike somewhat faster Static random access memory SRAM , and features read write speeds much faster than similar, less expensive ATA type cards, which include CompactFlash and Memory Stick . Like an SRAM, Linear Flash supports execute in place XIP applications in mobile PC and embedded equipment. Linear Flash can also be read and written to by laptops and desktops with PC card slots, and is somewhat popular for sensitive data storage because the media is non volatile and does not degrade over time. However, large scale storage is impracatical using Linear Flash because of small card sizes typically under 40 megabyte s and prohibitive costs megabyte for megabyte, Linear Flash cards are often dozens of times more expensive than ATA cards. Combined with file management software, such as Flash Translation Layer FTL or M Systems TrueFFS Flash File System, the Linear Flash cards provide removable disk emulation. As PC Card s was PCMCIA , Linear Flash cards should have a PC Card Card Information Structure Card Information Structure CIS . However, many memory cards do not have a CIS. Linear Flash cards begin to develop bad blocks after about 100,000 read write Instruction cycle cycle s and thus are of dubious value on the second hand market. Usage Linear Flash cards were also the primary method of data storage for Cisco router s, Apple s Newton platform Newton MessagePad 100 series and 2000 series PDAs, for some early Magic Cap , Pocket PC and Windows CE PDAs, musical synthesizer s and for many telecom devices. Manufacturers Major makers of Linear Flash cards are http www.pretec.com Pretec , http www.smartm.com Smart and http www.magicram.com MagicRAM . Intel , which championed the adoption of the Linear Flash format, also made cards. See also Flash file system M Systems DiskOnChip ... more details
. The area under an acceleration time graph gives the velocity. Linear motion is the most basic ... such as gravity and friction will cause objects to deviate from linear motion and can cause them ... title Motion Control Resource Info Center accessdate 19 January 2011 ref For linear motion ... is the same and is constant for linear motion, and only for linear motion See also Equations of motion Equations of uniformly accelerated linear motion Uniformly accelerated linear motion Linear motor ... more details
Infobox airline airline Linear Air logo Linearair.jpg logo size 300 IATA ICAO HPN callsign Harpoon headquarters ... & CEO small fleet size 6 website http www.linearair.com Linear Air is a private FAR part 135 part ... in Concord, Massachusetts Concord , Massachusetts . Linear Air s primary operations base is located ... County Airport ICAO KHPN in White Plains, New York White Plains , New York . In 2004, Linear ... , Linear Air primarily serves the United States in its Northeastern United States Northeastern and Mid ... of an initial round of funding and just two employees at the time, Linear Air began operating ... Association , Linear Air and other member air taxi operations are speeding the adoption of the air ... title About Us url http www.linearair.com aboutus index.aspx work Linear Air accessdate 28 March 2011 ref Destinations Linear Air can currently fly to hundreds of locations in the United States, as well ... http www.linearair.com services service area.aspx work Linear Air accessdate 28 March 2011 ref Fleet & Flight Operations Linear Air currently operates a fleet of Eclipse 500 very light jets . Manufactured ... PW600 PW610F turbofan engines. Linear Air recently debuted an upgraded Eclipse 500 in early 2010, the first .... ref cite news last Nihon first Justin title Linear Air Introduces First All Weather Eclipse to Commercial Service url http www.linearair.com downloads Linear 20Air 1st 20FIKI Press 20Release 20100125.pdf ... HIGH FLYING LINEAR AIR STRENGTHENS LEAD AS FIRST OPERATIONAL JET TAXI SERVICE url http goliath.ecnext.com coms2 gi 0199 5406650 High Flying Linear Air Strengthens.html date 04 10 06 ref Prior to taking ... by Pratt & Whitney . Resources http www.linearair.com aboutus.aspx Linear Air https www.linearair.com 01 05 06 20Press 20Release.pdf Linear Air Closes 2.5 million in funding https www.linearair.com 02 01 06 20Forbes.com.pdf Linear Air Announces Private Air Service at Airline Prices for Boston Newark Travelers https www.linearair.com 04 10 06 20Press 20Release.pdf High Flying Linear Air Strengthens ... more details
In mathematics , the term linear function can refer to either of two different but related concepts a first degree polynomial function of one variable a map between two vector spaces that preserves vector addition and scalar multiplication. Analytic geometry Image Linear functions2.PNG 300px thumb Three geometric linear functions the red and blue ones have the same slope m , while the red and green ones have the same y intercept b . main Linear equation In analytic geometry , the term linear function is sometimes used to mean a first degree polynomial function mathematics function of one variable math variable . These functions are known as linear because they are precisely the functions whose graph of a function graph in the Cartesian coordinate plane is a straight line. Such a function can be written as math f x mx b math math y y 1 m x x 1 math math 0 Ax By C math called slope intercept form , where math m math and math b math are real number real Coefficient constants and math x math is a real variable. The constant math m math is often called the slope or gradient, while math b math ... at right. Vector spaces In advanced mathematics, a linear function means a function mathematics function that is a linear map , that is, a map between two vector space s that preserves vector ... as coordinate vector s, then the linear functions are those functions math f math that can be expressed ... math is a linear map if and only if math b math 0. For other values of math b math this falls in the more ... Piecewise linear function Linear interpolation External links http id.mind.net zona mmts functionInstitute linearFunctions linearFunctions.html Linear Functions on Id Mind http www.mathopenref.com linearexplorer.html Interactive tool to explore linear functions Polynomials Category Polynomials als ... de Lineare Funktion es Funci n lineal eo Lineara funkcio fr Fonction lin aire id Fungsi linear ... linear nl Lineaire functie ja no Line r funksjon pl Funkcja liniowa pt Fun o linear ru ... 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
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
File Champlain Quebec .JPG thumb right 250px Some communities along the Saint Lawrence River in Quebec, Canada, developed as linear villages, as is still clearly seen in Champlain, Quebec . In geography , a linear village , or linear settlement , ref http thesaurus.english heritage.org.uk thesaurus term.asp?thes no 1&term no 68988 English Heritage Online thesaurus ref is a small to medium sized settlement that is formed around a transport route, such as a road, river, or canal. Wraysbury , a village in Berkshire , is one of the longest villages in England . A linear village may have no obvious center, such as a road junction or green. The route probably predated the village and then settlement grew up at some way station or feature, growing along the transport route. Often, it is only a single street with houses on either side of the road. Mileham , Norfolk , England is a good example of this. Later development may add side turnings and districts away from the original main street. Places such as Southport , England developed in this way. A linear village is in contrast with ribbon development , which is the outward spread of a town along a main street. See also Reihendorf References reflist External links http www.geograph.org.uk photo 33028 Outlane a linear village fr Village rue de Waldhufendorf Category Human geography Category Urban studies and planning Category Populated places by type Geo term stub ... more details
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