About the ancient syllabary the JavaScript engine linearb script engine Distinguish Linear Pottery culture Infobox Writing system name LinearB type Syllabary typedesc with additional ideogram s time ... Linb sample NAMA LinearB tablet of Pylos.jpg imagesize 250px History of the Greek language 267 SpecialChars Writing systems sidebar LinearB is a syllabary syllabic script that was used for writing ... web url http www.aegeanscripts.org index.php?option com content&view article&id 98 new linearb tablet found at iklaina&catid 80&Itemid 473 title New LinearB tablet found at Iklaina publisher Comit International Permanent des tudes Myc niennes, UNESCO accessdate 29 April 2012 ref LinearB, found ... Cypriot syllabary , which recorded Greek. LinearB consists of around 87 syllabic signs .... The application of LinearB seems to have been confined to administrative contexts. In all ... first J.T. last Hooker title LinearB An Introduction publisher Bristol Classical Press UK year 1980 .... The script LinearB has roughly 200 signs, divided into syllabic signs with phonetic values ... Bennett where the same sign is used in both Linear A and B there is no guarantee that the same ... zeros and preceding with a B for LinearB . ref In cases where the transcription of the sign remains ... font size 200 File LinearB Syllable B008 A.svg a 08 style font size 200 File LinearB Syllable B038 E.svg e 38 style font size 200 File LinearB Syllable B028 I.svg i 28 style font size 200 File LinearB Syllable B061 O.svg o 61 style font size 200 File LinearB Syllable B010 U.svg u 10 d style font size 200 File LinearB Syllable B001 DA.svg da 01 style font size 200 File LinearB Syllable B045 DE.svg de 45 style font size 200 File LinearB Syllable B007 DI.svg di 07 style font size 200 File LinearB Syllable B014 DO.svg do 14 style font size 200 File LinearB Syllable B051 DU.svg du 51 j style font size 200 File LinearB Syllable B057 JA.svg ja 57 style font size 200 File LinearB Syllable ... more details
B and Linear Cypriot iso15924 Lina Image Linear A tablets filt.jpg thumb 237px right Linear A incised ... before Mycenaean Greek language Mycenaean Greek LinearB Cretan hieroglyphs is the second script. In Minoan ... of LinearB, 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 LinearB in Linear A writings produces ... A match more or less the values given to the fully transliterated LinearB script, used for Mycenean ... in both Linear A and B therefore, 12 signs have the same values in both syllabaries DA, I, JA, KI ... Footnote 24 Luwian Since the 1960s, a theory based on LinearB phonetic values suggests that Linear ... by using the known LinearB or Cypriot sound values of certain Linear A signs. He does not claim ... in Linear A and B by Jan Best, claiming to demonstrate how and why Linear A notates an archaic form ... Linear A and B, and also avoid comparing Linear A with Cretan Hieroglyphs. ref name Hubert La Marle ... Ventris who, along with John Chadwick , successfully deciphered LinearB , also believed in a link ... that Linear A values are equal to LinearB values a ta i 301 wa ja o su qa re ja sa sa ra ... ? si 5 ku ro 130 ka u de ta is followed by an ideogram almost identical to one in LinearB meaning ... and phonetically as LinearB values. The following values remain conjectural because of the paucity ... occurs in LinearB as well. ref name Nagy 1963 186 harvnb Nagy 1963 p 186 . ref I TA NU U TA NO place ... meaning cumin also appears in LinearB documents. ref harvnb Nagy 1963 p 187 . ref KU RO whole, total ... name, ? . ref name Nagy 1963 189 PA DE a theonym name for a god , appearing on LinearB tablets ..., Phaistos the same name is common on LinearB documents. ref name Nagy 1963 186 PO TO KU RO grand ? total ..., which occurs in LinearB as well. SU KI RI TA Sugrita, a place name which occurs in LinearB as well ... 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 LinearB , 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
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
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
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 ...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 ... 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 leq b math Here math x 1, x 2,...,x n math are called the unknowns, math a 0 , a 1 , a 2 ,..., a n math 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 && && a 12 x 2 && cdots && a 1n x n && leq &&& b 1 a 21 x 1 && && a 22 x 2 && cdots && a 2n x n && leq &&& b 2 vdots && && vdots && && vdots && &&& vdots a m1 x 1 && && a m2 x 2 && cdots && a mn x n && leq &&& b m end alignat math Here math x 1, x 2,...,x n math are the unknowns, math a 11 , a 12 ,..., a mn math are the coefficients of the system, and math b 1, b 2,...,b m math are the constant terms. This can be concisely written as the matrix mathematics matrix inequality math Ax leq b math where A is an m × n matrix, x is an n × 1 column vector of variables, and b is an m × 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 ... more details
operatorname Sp E math is a closed linear subspace of X which contains E , b math overline operatorname ...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 ... more details
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 ...In mathematics , the term linear function can refer to either of two different but related concepts a first ... math variable . These functions are known as linear because they are precisely the functions whose ... 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 ... y math axis. Changing math m math makes the line steeper or shallower, while changing math b ... 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 ... vector s, then the linear functions are those functions math f math that can be expressed as math f x mathrm M x, math where M is a matrix mathematics matrix . A function math f x mx b 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 general class of affine map s. See also Nonlinear system Piecewise linear function Linear interpolation Discontinuous linear map 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 Lineare Funktion ... es Funci n lineal eo Lineara funkcio eu Funtzio lineal fr Fonction lin aire id Fungsi linear ... Line ris f ggv ny ms Fungsi linear nl Lineaire functie ja no Line r funksjon pl Funkcja liniowa pt Fun o linear ru sk Line rna funkcia sl Linearna funkcija sr ... more details
different ways as a linear combination of them math v sum a i v i sum b i v i text where a i neq b ... sub . In that case, the most general linear combination looks like math a 1 v 1 b 1 cdots a n v n b ...In mathematics , a linear combination is an expression constructed from a Set mathematics set of terms by multiplying each term by a constant and adding the results e.g. a linear combination of x and y would be any expression of the form ax by , where a and b are constants . ref cite book last Lay first David C. title Linear Algebra and Its Applications publisher Addison Wesley year 2006 edition 3rd isbn 0 321 28713 4 ref ref cite book last Strang first Gilbert authorlink Gilbert Strang title Linear ... ref cite book last Axler first Sheldon title Linear Algebra Done Right publisher Springer Science Business Media Springer year 2002 edition 2nd isbn 0 387 98258 2 ref The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear ... 1 sub ,..., a sub n sub are scalars, then the linear combination of those vectors with those scalars ... of the term linear combination as to whether it refers to the expression or to its value. In most cases the value is emphasized, like in the assertion the set of all linear combinations of v sub 1 sub ,..., v sub n sub always forms a subspace however one could also say two different linear ... difference between these uses is the essence of the notion of linear dependence a family F of vectors is linearly independent precisely if any linear combination of the vectors in F as value is uniquely so as expression . In any case, even when viewed as expressions, all that matters about a linear ... or adding terms with zero coefficient do not give distinct linear combinations. In a given situation ... speak of a linear combination of the vectors v sub 1 sub ,..., v sub n sub , with the coefficients unspecified except that they must belong to K . Or, if S is a subset of V , we may speak of a linear ... more details
This article deals with linear map s from a vector space to its field of scalar mathematics scalar s. ..., but this is not necessarily the case. In linear algebra , a linear functional or linear form also called a one form or covector is a linear map from a vector space to its field of scalar mathematics ... as column vector s, then linear functionals are represented as row vector s, and their action on vectors ... , then a linear functional is a function from V to k , which is linear math f vec v vec w f vec v ..., a in k. math The set of all linear functionals from V to k , Hom sub k sub V , k , is itself a vector ... textstyle V math when the field k is understood. Continuous linear functionals see also Continuous linear operator If V is a topological vector space , the space of continuous function continuous linear ... . In finite dimensions, every linear functional is continuous, so the continuous dual is the same ... Linear functionals in R sup n sup Suppose that vectors in the real coordinate space R sup n sup are represented ... linear functional can be written in these coordinates as a sum of the form math f vec x a 1x 1 cdots ... Integration Linear functionals first appeared in functional analysis , the study of function space vector spaces of functions . A typical example of a linear functional is integral integration the linear transformation defined by the Riemann integral math I f int a b f x , dx math is a linear functional from the vector space C a , b of continuous functions on the interval a , b to the real ... f g int a b f x g x , dx math math int a b f x , dx int a b g x , dx I f I g math math I alpha f int a b alpha f x , dx math math alpha int a b f x , dx alpha I f . math Evaluation Let P sub n sub denote the vector space of real valued polynomial functions of degree n defined on an interval a , b . If c a , b , then let ev sub c sub P sub n sub R be the evaluation functional math ev c f f c . math The mapping c is linear since math f g c f c g c math ... more details
matrix . Change of basis Given a linear map whose matrix is A, in the basis B of the space it transforms ...In mathematics , a linear map , linear mapping , linear transformation , or linear operator in some contexts also called linear function is a function mathematics function between two vector space s that preserves ... Linear Transformation ref The expression linear operator is commonly used for linear maps from a vector space to itself i.e., endomorphisms . Sometimes the definition of a linear function coincides with that of a linear map, while in analytic geometry it does not. In the language of abstract algebra , a linear map is a homomorphism of vector spaces. In the language of category theory it is a morphism ... f V W is said to be a linear map if for any two vectors x and y in V and any scalar in K , the following ... homogeneity of degree 1 . This is equivalent to requiring the same for any linear combination ... fields is being used in the definition of linear . If V and W are considered as spaces over the field K as above, we talk about K linear maps. For example, the complex conjugate conjugation of complex numbers is an R linear map C C , but it is not C linear. A linear map from V to K with K viewed as a vector space over itself is called a linear functional . Examples The Identity function identity map and zero map are linear. The map math x mapsto cx math , where c is a constant, is linear. For real numbers, the map math x mapsto x 2 math is not linear. For real numbers, the map math x mapsto x 1 math is not linear but is an affine transformation , and also a linear function , as defined in analytic geometry . If A is a real m × n matrix mathematics matrix , then A defines a linear ... Ax R sup m sup . Conversely, any linear map between finite dimensional vector spaces can be represented in this manner see the following section. The definite integral is a linear map from the space ... integral or antiderivative is not considered a linear transformation, as the use of a constant of integration ... more details
many non linear equation s may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some background state. Linear equations do not include exponents. Linear equations in two variables A common form of a linear equation in the two variables x and y is math y mx b, , math where m and b designate constants. The origin of the name linear comes from the fact ... linear equation in n variables is math a 1 x 1 a 2 x 2 cdots a n x n b. math In this form, a sub ...File Linear Function Graph.svg thumb 300px Graph sample of linear equations. A linear equation is an algebraic ... of a constant and the first power of a single variable mathematics variable . Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics ... b determines the point at which the line crosses the y axis, otherwise known as the y intercept. Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ... sup 1 3 sup , and sin x are Nonlinear system nonlinear . Forms for 2D linear equations Linear equations ... By C 0, , math where A and B are not both equal to zero. The equation is usually written so that A 0 ..., y is zero , is &minus C A . If B is nonzero, then the y intercept, that is the y coordinate of the point where the graph crosses the y axis where x is zero , is &minus C B , and the slope of the line is &minus A B . Standard form math Ax By C, , math where A and B are not both equal to zero, A , B , and C are coprime integers, and A is nonnegative if zero, B must be positive . The standard form can be converted to the general form, but not always to all the other forms if A or B is zero. It is worth ... line 2 span cannot be described by a linear equation with integer coefficients since Square root ... form math y mx b, , math where m is the slope of the line and b is the y intercept, which is the y ... immediately gives y b . It may be helpful to think about this in terms of y b mx where the line originates ... 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
the Cartesian product and I 0, 1 in the lexicographic order is a linear continuum. Property b is trivial ... upper bound property . Therefore, we may let b be the least upper bound of sub 1 sub A . If b belongs to sub 1 sub A , then b I will intersect A at say b c for some c I . Notice that since b I has the same order type of I , the set b I A will indeed have a least upper bound b c , which is the desired least upper bound for A . If b doesn t belong to sub 1 sub A , then b 0 is the least upper bound of A , for if d b , and d e is an upper bound of A , then d would be a smaller upper bound of sub 1 sub A than b , contradicting the unique property of b . Non examples The set of rational number s is not a linear continuum. Even though property b is satisfied, property a is not. Consider ... numbers A , 0 0, is not a linear continuum. Property b is trivially satisfied. However, if B is the set of negative real numbers B , 0 then B is a subset of A which is bounded above by any element ...In the mathematical field of order theory , a continuum or linear continuum is a generalization of the real line . Formally, a linear continuum is a linearly ordered set S of more than one element that is Dense ... a S has the least upper bound property b For each x in S and each y in S with x y , there exists ... subset of the set that is bounded above has a least upper bound . Linear continua are particularly ... number s, R , with its usual Total order order is a linear continuum, and is the archetypal example. Property b is trivial, and property a is simply a reformulaton of the completeness axiom . Examples ... . The set of non negative integer s with its usual order is not a linear continuum. Property a is satisfied ... hand, property b is not. Indeed, 5 is a non negative integer and so is 6, but there exists ... for B since 0 is not an Element mathematics element of A . Let Z sub sub denote the set of negative integers and let A 0,5 5, . Let S Z sub sub A Then S satisfies neither property a nor property b . The proof ... more details
Image Linear progression 3 2 1.png thumb right Linear progression sub music scale 3 sub sub music scale 2 sub sub music scale 1 sub over I audio Linear progression 3 2 1.mid Play . music scale 2 would be the passing tone Image Schenkerian Ursatz 321IVI.png thumb right Urlinie sub music scale 3 sub sub music scale 2 sub sub music scale 1 sub over I dominant music V I audio Ursatz.mid Play . Image Decorated third progression.png thumb right Decorated third progression ref name P 29 audio Decorated third progression.mid Play . Whereas originally D was the nonchord tone in E D C, here it is a chord tone, elaborated D C B, and C is the nonchord tone. In music , a linear progression Auskomponierungszug or de Zug Zug , German train, abbreviated Zg. is a passing note elaboration involving steps and skips stepwise melody melodic motion in one direction between two harmony harmonic tones ref Pankhurst, Tom 2008 . Schenker Guide A Brief Handbook and Website for Schenkerian Analysis , p.243 and 27. ISBN 0415973988. ref . The compositional unfolding of a specific interval, one of the intervals of the chord ... Analyses , p.14. ISBN 0486222942. ref . According to Schenker The linear progression always presupposes a Nonchord tone Passing tone passing tone there is no linear progression without a passing tone and no passing tone without a linear progression. ref name Jonas In German zug may be combined with prefixes ... reaching linear progression , a linear progression rising from a lower voice, or terzzug German de wikt terz third linear progression , linear progression through a Third chord third ref Schenker 1969 ... Linear progressions prolongation prolong harmonies and through elaboration, or filling in with dissonant .... for third progression rather than zg. ref name Pankhurst 28 . Image Linear progression in Mozart Piano Sonata in G major.png thumb center 392px Linear progression in Wolfgang Amadeus Mozart Mozart ... , p.28 30. ref audio Linear progression in Mozart Piano Sonata in G major.mid Play . Original shown ... more details
boulder B have inspired the first attempts at decipherment of Linear Elamite Bork, 1905, 1924 Frank, 1912 . References B. Andre and M. Salvini, R flexions sur Puzur In u inak, Iranica Antiqua ...Image Elam cool.jpg thumb right Silver cup from Marvdasht, Fars Province Fars , with Linear Elamite inscription on it. 3rd Millennium BC. National Museum of Iran . Linear Elamite is a Bronze Age writing system used in Elam , known from a few monumental inscriptions only. It was used contemporarily with Elamite Cuneiform and likely records the Elamite language . It was in use for a brief period of time during the last quarter of the 3rd millennium BC . It is often claimed that Linear Elamite is a syllabic writing system derived from the older Proto Elamite writing system, although this hasn t been proven. Linear Elamite has not been deciphered, in spite of several attempts, most notably those of Walther Hinz and Piero Meriggi . There are only 22 known documents in Linear Elamite they are identified by letters A V Hinz, 1969, pp. 11 44 Andre and Salvini, 1989, pp. 58 61 of these, 19 are on stone and clay objects excavated in the acropolis at Susa now kept in the Louvre in Paris . The most important longer texts, partly bilingual inscription bilingual , appear in monumental contexts. They are engraved on large stone sculptures, including a statue of the goddess Narunte I , the table au lion A , and large votive boulders B, D , as well as on a series of steps F, G, H, U from a monumental stone stairway, where they alternated with steps bearing texts with Akkadian titles of Puzur In u inak . A unique find is item Q, a silver vase with a single line of perfectly executed text, kept in the Tehran Museum. There are also a few texts on baked clay cones J, K, L , a clay disk M , and clay tablets N, O, R . Some objects A, I, C include both Linear Elamite and Akkadian cuneiform ... http cdli.ucla.edu wiki doku.php linear elamite http www.ancientscripts.com elamite.html Category ... more details
File Linear motor U tube.svg thumb right 225px Free body diagram of a U channel synchronous linear motor ... versa. Not to scale A linear motor is an electric motor that has had its stator and rotor electric rotor unrolled so that instead of producing a torque rotation it produces a linear force along its ... force is linear equation linearly proportional to the electric current current and the magnetic field math vec F q cdot vec v times vec B math . Many designs have been put forward for linear motors, falling into two major categories, low acceleration and high acceleration linear motors. Low acceleration linear motors are suitable for maglev train s and other ground based transportation applications. High acceleration linear motors are normally rather short, and are designed to accelerate ... motors are usually of the AC linear induction motor LIM design with an active three phase winding ... current homopolar motor homopolar linear motor railgun is another high acceleration linear motor design. The low acceleration, high speed and high power motors are usually of the linear synchronous ... Shanghai motor is an LSM. Types File Linear motor by Zureks.jpg thumb left A prototype of linear motor with visible separate coils Induction motor main Linear induction motor In this design, the force is produced by a moving linear magnetic field acting on conductors in the field. Any conductor, be it a loop ... synchronous linear motors rarely use commutators, so the rotor often contains permanent magnets ... other linear motors. File Linear Motor of Toei edo Line.jpg thumb right 200px A linear motor for trains ... actions Piezoelectric drive is often used to drive small linear motors. History Image JFK AirTrain.agr.jpg ... induction strip placed between the rails. Low acceleration The history of linear electric motors ... linear induction motor is described in the US patent 782312 1905 inventor Alfred Zehden of Frankfurt ... river . Because of these properties, linear motors are often used in magnetic levitation maglev propulsion ... more details
3 sup . In linear algebra , a indexed family family of vector space vector s is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection ... vectors together are linearly dependent. Linear dependence is a property of the family, not of any particular vector for example in this case we could just as well write the first vector as a linear ... of linear dependence between random variable s. Definition A finite subset of n vectors, v sub 1 sub ..., then the vectors are said to be linearly independent . Alternatively, linear independence can be directly ... of the zero vector as linear combinations of its elements are trivial mathematics trivial ..., a family is dependent if a member is in the linear span of the rest of the family, i.e., a member is a linear combination of the rest of the family. A set of vectors which is linearly independent and linear span spans some vector space, forms a basis linear algebra basis for that vector space ... of linear independence. A person describing the location of a certain place might say, It is 5 ... vector, and vice versa. The third 7.81 miles northeast vector is a linear combination of the other ... 1& 3 1&2 end bmatrix . , math We may write a linear combination of the columns as math A Lambda begin ... independent. Proof Suppose a and b are two real numbers such that ae sup t sup be sup 2 t sup 0 for all values of t . We need to show that a 0 and b 0. In order to do this, we divide through by e ... be sup t sup must be independent of t , which only occurs when b 0. It follows that a is also ... are linearly dependent. Projective space of linear dependences A linear dependence among vectors ... scalar components, not all zero, such that math a 1 mathbf v 1 cdots a n mathbf v n 0. , math If such a linear ... two linear dependences if one arises as a non zero multiple of the other, because in this case the two describe the same linear relationship among the vectors. Under this identification, the set of all ... more details
Image Schematic diagram showing Polyclonal Response by B cells against Linear Epitopes.PNG thumb 300px Recognition of epitopes in a linear fashion. Note the same colored segment of protein can be a part of more than one epitopes A linear or a sequential epitope is an epitope that is recognized by antibody antibodies by its linear sequence of amino acid s, or primary structure . In contrast, most antibodies recognize a conformational epitope that has a specific three dimensional shape and its protein structure . An antigen is any substance that the immune system can recognize as foreign. Since, antigens are usually proteins that are too large to bind as a whole to any Receptor immunology receptor , only specific segments that form the antigen bind with a specific antibody. Such segments are called epitope s. Likewise, it is only paratope of the antibody that comes in contact with the epitope. Protein s are composed of repeating nitrogen containing subunits called amino acid s. The linear sequence of amino acids that compose a protein is called its primary structure , which does not exist in nature. But, when an antigen is broken down in a lysosome , it yields small peptide s, which can be recognized through the amino acids that lie continuously in a line, and hence are called linear epitopes . ref name goldsby3 cite book last Goldsby first Richard authorlink coauthors Kindt, TJ Osborne, BA Janis Kuby title Immunology accessdate 2008 06 27 edition Fifth edition publisher W. H. Freeman and Company year 2003 location New York pages 57 75 chapter Antigens Chapter 3 url doi id isbn 0 07167 4947 5 ref Significance While performing molecular assays involving use of antibodies such as in the Western ... that recognize linear or conformational epitopes. sup ref http www.emdbiosciences.com html CBC technical ..., antibodies that recognize linear epitopes instead of conformational epitopes are chosen for immunodetection ... that recognize conformational epitopes. See also Conformational epitope Polyclonal B cell ... more details
refimprove date May 2011 File Linear subspaces with shading.svg thumb 250px right The three dimensional ... origin are vector subspaces in R sup 3 sup . Linear algebra is the branch of mathematics charged ... space s and linear map pings between such spaces. Such an investigation is initially motivated by a system of linear equations in several unknowns. Such equations are naturally represented using the formalism of Matrix mathematics matrices and vectors. ref cite web last Weisstein first Eric title Linear .... publisher Wolfram accessdate 16 April 2012 ref Linear algebra is central to both pure and applied .... However, linear algebra focuses more on finite dimensional spaces whereas functional ... the solution of linear systems of differential equations . The techniques are also applicable in analytic ... sometimes be approximated by linear ones. History The study of linear algebra and matrices first emerged from determinants, which were used to solve systems of linear equations. Determinants were used by Leibniz in 1693, and subsequently, Cramer devised the Cramer s Rule for solving linear systems in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination ... Marie title A Brief History of Linear Algebra and Matrix Theory url http darkwing.uoregon.edu vitulli ... , in 1848, introduced the term matrix, which is Latin for womb . While studying compositions linear ... by Peano in 1888, ref Vitulli, Marie ref and by 1900, a theory of linear transformations of finite ... did much to spread the subject of linear algebra beyond pure mathematics. The development of computers ..., and linear algebra became an essential tool for modelling and simulations. ref Vitulli, Marie ... elimination . Scope of study Vector spaces The main structures of linear algebra are vector space s. A vector ... in V , and a and b scalars in F . border 0 style width 100 Axiom Signification Associativity ... with respect to field addition a b v av bv Compatibility of scalar multiplication with field multiplication ... more details
File TangentGraphic2.svg thumb 300px Tangent line at a , f a In mathematics , a linear approximation is an approximation of a general function mathematics function using a linear function more precisely, an affine function . They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Definition Given a twice continuously differentiable function f of one real number real variable, Taylor s theorem for the case n 1 states that math f x f a f a x a R 2 math where math R 2 math is the remainder term. The linear approximation is obtained by dropping the remainder math f x approx f a f a x a . math This is a good approximation for x when it is close enough to a since a curve, when closely observed, will begin to resemble a straight line. Therefore, the expression on the right hand side is just the equation for the tangent line to the graph of f at a , f a . For this reason, this process is also called the tangent line approximation . Linear approximations for vector geometric vector functions of a vector variable are obtained in the same way, with the derivative at a point replaced by the Jacobian matrix and determinant Jacobian matrix. For example, given a differentiable function math f x, y math with real values, one can approximate math f x, y math for math x, y math close to math a, b math by the formula math f left x,y right approx f left a,b right frac partial f partial x left a,b right left x a right frac partial f partial y left a,b right left y b right . math The right hand side is the equation of the plane tangent to the graph of math z f x, y math at math a, b . math In the more general case of Banach space s, one has math f x approx f a Df a x a math where math Df a math is the Fr chet derivative of math f math at math a math . See also Euler s method Finite differences Finite difference ... pl Aproksymacja liniowa pt Aproxima o linear zh ... more details
A linear amplifier is an electronics electronic circuit whose output is proportional to its input, but capable of delivering more power physics power into a Electrical load load . The term usually refers to a type of radio frequency RF power amplifier , some of which have output power measured in kilowatt s, and are used in amateur radio . Other types of linear amplifier are used in Sound audio and laboratory equipment . Explanation An RF linear amplifier can be based on either solid state electronics solid state or vacuum tube technology. For an amplifier to be considered linear, the amplified output must be a faithful reproduction of the input. The basic linear amplifier has limitations that are functions of its load impedance, supply voltage, input bias current, and limitations of power output capabilities. ref name Whitaker cite book last Whitaker first Jerry C. title The RF transmission systems handbook year 2002 publisher CRC Press isbn 9780849309731 url http books.google.com books?id G5UHVIqEWdQC&pg SA11 PA1&dq RF linear amplifier&hl en&ei 0uc2TtOSNoLn0QGR28CdDA&sa X&oi book result&ct result&resnum 9&ved 0CF0Q6AEwCA v onepage&q RF 20linear 20amplifier&f false ref Amplifier classes ... of the linear section of the curve of the anode current vs grid bias potential. Electronic amplifier Class B and AB Class B can be 60 to 65 efficient. The semiconductor or vacuum tube conducts through .... Amateur radio Most commercially manufactured one to two kilowatt linear amplifiers used in amateur ... to the antenna. Solid state linear amplifiers are more commonly in the 500 watt range and can be driven ... vacuum tube linear amplifiers are based on old radio broadcast techniques and generally rely on a pair ... energy into radio frequency energy. Linear amplifiers need to operate with class A or class ... has far higher efficiency, a class C amplifier is not linear, and is only suitable for the amplification ... kW transmitter. Not a linear amplifier, it operated in class C with high level plate modulation. The amplifier ... more details
math A otimes B , wp ,C multimap A otimes B , wp ,C math Encoding classical intuitionistic logic in linear ...Linear logic is a substructural logic proposed by Jean Yves Girard as a refinement of classical logic ... Jean Yves last1 Girard author1 link Jean Yves Girard year 1987 title Linear logic journal Theoretical ..., ideas from linear logic have been influential in fields such as programming languages , game semantics ..., duality, and interaction. Linear logic lends itself to many different presentations, explanations ... models, linear logic may be seen as refining the interpretation of intuitionistic logic by replacing ... of classical linear logic CLL is defined inductively by the Backus Naur Form BNF notation center ... A VAR Unicode VAR B VAR sup sup VAR A VAR sup sup Unicode VAR B VAR sup sup colspan 3 align center math VAR A VAR Unicode VAR B VAR sup sup VAR A VAR sup sup Unicode VAR B VAR sup sup colspan 3 align center math VAR A VAR Unicode VAR B VAR sup sup VAR A VAR sup sup & VAR B VAR sup sup colspan 3 align center math VAR A VAR & VAR B VAR sup sup VAR A VAR sup sup Unicode VAR B VAR sup sup colspan 3 align ... for all propositions. math VAR A VAR sup sup is also called the linear negation of math VAR A VAR . The columns of the table suggest another way of classifying the connectives of linear logic, termed ... , while their duals on the right Unicode , &, , Unicode , ? are called negative . Linear implication is not included in the grammar of connectives, but is definable in CLL using linear negation and multiplicative disjunction, by math VAR A VAR Unicode VAR B VAR VAR A VAR sup sup Unicode VAR B VAR . The connective ... One way of defining linear logic is as a sequent calculus . We use the letters math &Gamma ... and disjunction, as explained below . Girard describes classical linear logic using only one sided ... theorem , inducing a notion of analytic proof lies behind the applications of linear logic ... , VAR B VAR colspan 4 style border top 2px solid black colspan 4 align center math tee &Gamma , &Delta ... more details
sup T sup x sup sup b sup T sup y sup sup . A linear program can also be unbounded or infeasible ... is a linear program of the form Minimize big b sup T sup y big , Subject to big A sup T sup y &ge ... N. Thapa. 1997. Linear programming 1 Introduction . Springer Verlag. George B. Dantzig and Mukund ...externallinks date November 2011 Linear programming LP , or linear optimization is a mathematical method ... mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming mathematical optimization . More formally, linear programming is a technique for the mathematical optimization optimization of a linear objective function , subject to linear equality and linear inequality Constraint mathematics constraints . Its ... half space s, each of which is defined by a linear inequality alternatively, a convex polytope is the Minkowski ... number real valued affine function defined on this polyhedron. A linear programming algorithm finds .... Linear programs are problems that can be expressed in canonical form math begin align & text maximize && mathbf c mathrm T mathbf x & text subject to && A mathbf x leq mathbf b & text and && mathbf x ge mathbf 0 end align math where x represents the vector of variables to be determined , c and b ... in this case . The inequalities A x b are the constraints which specify a convex polytope ... vector. Linear programming can be applied to various fields of study. It is used in business and economics, but can also be utilized for some engineering problems. Industries that use linear ... of solving a system of linear inequalities dates back at least as far as Joseph Fourier Fourier , after whom the method of Fourier Motzkin elimination is named. The earliest linear programming ... developed the earliest linear programming problems in 1939 for use during World War II to plan .... The method was kept secret until 1947 when George Dantzig George B. Dantzig published the Simplex ... 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
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