A partial linearspace also semilinear or near linearspace is a basic incidence structure in the field of incidence geometry, that carries slightly less structure than a linearspace geometry linearspace . Definition Let math S mathcal P , mathcal B , textbf I math an incidence structure, for which the elements of math mathcal P math are called points and the elements of math mathcal B math are called lines . S is a partial linearspace, if the following axioms hold any line is at least incident with two points any pair of distinct points is incident with at most one line References Lynn Margaret Batten Combinatorics of Finite Geometries . Cambridge University Press 1986, ISBN 0 521 31857 2, p. 1 22 External links http www.math.uni kiel.de geometrie klein math geometry partlin.html partial linearspace at a website of the university of Kiel http planetmath.org encyclopedia PartialLinearSpace.html partial linearspace at PlanetMath Category Geometry geometry stub ... more details
A linearspace is a basic structure in incidence geometry . It consists of a family of subsets of a set such that the intersection of two subsets contains at most one element of the set. The elements of the set are called points and the subsets are called lines . Linear spaces can be seen as a generalization of projective plane projective and affine plane incidence geometry affine planes , and more broadly, of block design 2 math v,k,1 math block designs , where the requirement that every block contains the same number of points is dropped and the essential structural characteristic is that 2 points are incident with exactly 1 line. The term linearspace was coined by Libois in 1964, though many results about linear spaces are much older. Definition Let L P , G , I be an incidence structure , for which the elements of P are called points and the elements of G are called lines. L is a linearspace if the following three axioms hold L1 two points are incident with exactly one line. L2 every line is incident to at least two points. L3 L contains at least two lines. Some authors drop L3 when defining linear spaces. In such a situation the linear spaces complying to L3 are considered as nontrivial ... constitutes a linearspace, moreover all affine and projective spaces are linear spaces as well. The following table lists all nontrivial linear spaces of five points with the usual convention ... Linear space1.png style width 150px valign center align center Image Linear space2.png style width 150px valign center align center Image Linear space3.png style width 150px valign center align center Image Linear space4.png align center 10 lines align center 8 lines align center 6 lines align center 5 lines A linearspace of n points containg a line being incident with n &minus 1 points ... width 250px valign center align center Image Linearspace near pencil.png align center near pencil ... 521 42260 4 L.M. Batten, A. Beutelspacher The Theory of Finite Linear Spaces. Cambridge University ... more details
In linear algebra , the quotient of a vector space V by a linear subspace subspace N is a vector space obtained by collapsing N to zero. The space obtained is called a quotient space and is denoted V N ... 22 . Let V be a vector space over a field mathematics field K , and let N be a linear subspace subspace ... . The first isomorphism theorem of linear algebra says that the quotient space V ker T is isomorphic ... class of x is often denoted x x N since it is given by x x n n &isin N . The quotient space V N is then defined ... of representative . These operations turn the quotient space V N into a vector space over ... plane, and let Y be a line through the origin in X . Then the quotient space X Y can be identified with the space of all lines in X which are parallel to Y . That is to say that, the elements ... m standard basis vectors. The space R sup n sup consists of all n tuples of real numbers x sub 1 ... n &minus m coordinates. The quotient space R sup n sup R sup m sup is isomorphic to R sup n &minus ... sum of subspaces U and W math V U oplus W math then the quotient space V U is naturally isomorphic ... space V U given by sending x to its equivalence class x . The kernel algebra kernel or nullspace ... sequence math 0 to U to V to V U to 0. , math If U is a subspace of V , the dimension vector space ... 22.2 math mathrm codim U dim V U dim V dim U . math Let T V &rarr W be a linear operator . The kernel ... of the image the rank of T . The cokernel of a linear operator T V &rarr W is defined to be the quotient space W im T . Quotient of a Banach space by a subspace If X is a Banach space and M is a closed set closed subspace of X , then the quotient X M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section. We define a norm on X M by math x X M inf m in M x m X. math The quotient space X M is complete space complete with respect to the norm, so it is a Banach space. Examples Let C 0,1 denote the Banach space ... 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 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
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 ... spanned by a non empty subset S of a vector space V is the set of all linear combinations of vectors ... 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 ... of the span of points in space, a subset X of the ground set of a matroid is called a spanning ... space R sup 3 sup has 2,0,0 , 0,1,0 , 0,0,1 as a spanning set. This particular spanning set is also a Basis linear algebra basis . If 2,0,0 were replaced by 1,0,0 , it would also form the standard basis canonical basis of R sup 3 sup . Another spanning set for the same space is given by 1,2,3 , 0,1,2 , &minus 1,1 2,3 , 1,1,1 , but this set is not a basis, because it is Linear dependency linearly dependent . The set 1,0,0 , 0,1,0 , 1,1,0 is not a spanning set of R sup 3 sup instead its span is the space .... Theorem 2 Every spanning set S of a vector space V must contain at least as many elements as any Linear independence linearly independent set of vectors from V . Theorem 3 Let V be a finite dimensional vector space. Any set of vectors that spans V can be reduced to a basis for V by discarding ... 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 ... more details
This article deals with linear map s from a vector space to its field of scalar mathematics scalar s. ... Linear functionals in R sup n sup Suppose that vectors in the real coordinate space R sup n sup are represented ... Integration Linear functionals first appeared in functional analysis , the study of function space ... space V . However, this mapping is antilinear rather than linear. Visualizing linear functionals ... indices. A linear functional math tilde u math belonging to the dual space math tilde V math ..., 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 scalar s. In Euclidean space R sup n sup , if euclidean vector vectors are represented as column vector s, then linear functionals are represented as row vector s, and their action on vectors ... vector on the right. In general, if V is a vector space over a field mathematics field k , 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 space over k . This space is called the dual space of V , or sometimes the algebraic dual space , to distinguish it from the continuous dual space . It is often written V sup sup or math 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 functionals &mdash the continuous dual space continuous dual &mdash is often simply called the dual space. If V is a Banach space , then so is its continuous dual. To distinguish the ordinary dual space from the continuous dual space, the former is sometimes called the algebraic dual . In finite dimensions, every linear functional is continuous, so the continuous dual is the same ... 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
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 ...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 ... 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 ... unbounded, e.g., a half space, a slab between two parallel half spaces or a polyhedral cone . It may ... operations of addition , multiplication and comparison , therefore the notion of a linear inequality ... Linear algebra Category Linear programming Category Polyhedra ... more details
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 ... as a vector space over itself is called a linear functional . Examples The Identity function identity ... in this manner see the following section. The definite integral is a linear map from the space ... has chosen basis of a vector space bases in those spaces, then every linear map from V to W can ... x Ax describes a linear map R sup n sup R sup m sup see Euclidean space . Let math vec v 1, cdots, vec ... that are chosen. Examples of linear transformation matrices In two dimension al space R sup 2 sup ... L V , W of linear maps from V to W itself forms a vector space over K , sometimes denoted Hom ... spacelinear algebra quotient space of the target. Formally, one has the exact sequence math ... is to say, for any vector space U and any pair of linear maps R U V and S U V , the equation TR ... is to say, for any vector space U and any pair of linear maps R W U and S W U , the equation RT ST ... matrix . Change of basis Given a linear map whose matrix is A, in the basis B of the space it transforms ... linear operator . A linear operator on a normed linearspace is continuous if and only if it is bounded ... 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 ... 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
span Main article linear span Take an arbitrary field K , an arbitrary vector space V , and let v sub ... in a vector space are linear combinations. The basic operations of addition and scalar multiplication ... vector space , then there may be a way to make sense of certain infinite linear combinations, using ...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 ... 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 combinations in the context of a vector space over a field mathematics field , with some generalizations ... numbers and V is a vector space over K . As usual, we call elements of V vector space vector s and call ... 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 ... 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 and key bits that have a high bias that is, whose probabilities of holding over the space of all possible 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 ... more details
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 ...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 FuncionLineal01.svg 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 ... vector s, then the linear functions are those functions math f math that can be expressed ... 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
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 ... are linearly dependent. Projective space of linear dependences A linear dependence among vectors ... linear dependences among v sub 1 sub , ...., v sub n sub is a projective space . Linear dependence ..., in the three dimensional real vector space math mathbb R 3 math we have the following example ... 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 , v sub 2 sub , ..., v sub n sub , from the vector space V , is linearly dependent if and only if there exists ... is the Null vector vector space zero vector , not the number zero. If such scalars do not exist, 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 .... More generally, let V be a vector space over a field mathematics field K , and let v sub i sub ..., 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. For example, the vector space of all polynomials in x over the reals has for a basis the infinite ... of linear independence. A person describing the location of a certain place might say, It is 5 ... the geographic coordinate system may be considered as a 2 dimensional vector space ignoring altitude ... vector, and vice versa. The third 7.81 miles northeast vector is a linear combination of the other ... more details
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 ... elimination . Scope of study Vector spaces The main structures of linear algebra are vector space s. A vector ... that preserve the vector space structure. Given two vector spaces V and W over a field F , a linear ... basis for the space of Fourier expandable functions. We can thus use the tools of linear algebra ... , the vector space math V math consisting of linear maps math f V to mathbf F math where F is the field ...refimprove date May 2011 File Linear subspaces with shading.svg thumb 250px right The three dimensional Euclidean space R sup 3 sup is a vector space, and lines and planes passing through the origin mathematics origin are vector subspaces in R sup 3 sup . Linear algebra is the branch of mathematics charged .... 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 ... . ref Vitulli, Marie ref The first modern and more precise definition of a vector space was introduced ... 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
Infobox company name Linear Technology Corporation logo File Linear Technology logo.png 220px Linear Technology caption type Integrated device manufacturer genre fate predecessor successor foundation 1981 ref name form10k founder Robert H. Swanson, Jr. br Robert C. Dobkin defunct location city Milpitas, California location country USA location locations 12 10 U.S. design centers, Munich and Singapore area served key people Lothar Maier CEO , Robert H. Swanson, Jr. Chairman , Robert C. Dobkin CTO ref name form10k industry products Over 7500 products ref name forbes10 services revenue increase US 1.17 billion 2010 ref name hoov net income increase US 361 million 2010 ref name form10k assets increase US 1.59 billion 2010 ref name form10k equity owner num employees 4,191 June 2010 ref name form10k divisions homepage http www.linear.com www.linear.com footnotes intl Linear Technology Corporation NASDAQ LLTC , NASDAQ 100 designs, manufactures and markets a broad line of standard ... and space systems. The company was founded in 1981 by Robert H. Swanson, Jr. and Robert C ..., ref name forbes10 cite web url http www.forbes.com 2010 08 19 linear lothar maier intelligent ... www.linear.com products linear regulators ldo linear regulators , http www.linear.com products ... , http www.linear.com products i 7Cq modulators quadrature modulators , oscillators , and space ... are in Milpitas, California . ref name hoov cite web url http www.hoovers.com company Linear Technology Corporation ryskyi 1 1njea5.html title Linear Technology Corporation publisher Hoover s accessdate ... title Home Company Careers Design Centers publisher Linear Technology accessdate 2010 08 25 ref The company ... url http www.linear.com company careers title Linear Technology Corporation CA Form 10 K date August ... links Portal Companies http www.linear.com Linear Technology official website , including http www.linear.com ... Category Companies established in 1981 Category Companies listed on NASDAQ de Linear Technology fr Linear ... more details
still have very high torque while fitting in a small diameter space. Principles In the majority of linear ...Refimprove date July 2008 File linear actuator basic.gif thumb 250px Conceptual design of a basic traveling nut linear actuator. Note that in this example the lead screw gray rotates while the lead nut yellow and tube red do not. A linear actuator is an actuator that creates motion in a straight line, as contrasted with circular motion of a conventional electric motor . Linear actuators are used in machine ... and dampers, and in many other places where linear motion is required. Hydraulic or pneumatic cylinders inherently produce linear motion many other mechanisms are used to provide a linear motion from a rotating motor. Types Mechanical actuators File mechanical linear actuator with digital readout.jpg thumb A mechanical linear actuator with digital readout a type of micrometer . File Roller Screw.gif thumb Roller screw actuation with traveling screw rotating nut . Machine Mechanical linear actuators typically operate by conversion of rotary motion into linear motion. Conversion is commonly ... moves a cable, rack, chain or belt to produce linear motion. ref Sclater, N., Mechanisms and Mechanical ... linear actuators only pull, such as hoists, chain drive and belt drives. Others only push ... into linear displacement via screws and or gears to which the knob or handle is attached. A jackscrew ... spindle . Rotation of the jack handle is converted mechanically into the linear motion of the jack ... the position of linear stage s, rotary stage s, mirror mount s, goniometer positioning goniometers ..., a hydraulic cylinder can provide controlled precise linear displacement of the piston ... their expansion in a repeatable manner. Electro mechanical actuators File linear actuator photo.jpg thumb A miniature electro mechanical linear actuator where the lead nut is part of the motor. The lead ... or retracted. File multi cylinders.gif thumb Typical compact cylindrical linear electric actuator File ... more details
24 27, 2005, and Gemini on December 29, 2005. The Spitzer Space Telescope has estimated 118401 LINEAR ...Infobox planet width 25em background FFFFC0 name 118401 LINEAR br 176P LINEAR discoverer Lincoln Near Earth Asteroid Research LINEAR discovered September 7, 1999 alt names mp 1999 RE 70 named after Lincoln ... 2010 11 02 last obs title JPL Small Body Database Browser 118401 LINEAR 1999 RE70 url http ssd.jpl.nasa.gov ... mean anomaly 300.54 avg speed 16.51 km second s dimensions 4.0 0.4 km Spitzer Space Telescope Spitzer ... R. title Albedos of Main Belt Comets 133P ELST PIZARRO and 176P LINEAR journal The Astrophysical ... name 176P LINEAR image discoverer Lincoln Near Earth Asteroid Research LINEAR discovered October ... 176P LINEAR 118401 1999 RE70 NK 1373 publisher OAA Computing and Minor Planet Sections author Syuichi ... next p 2017 March 12 ref name imcce cite web date 2012 January 26 title Note number 0701 P LINEAR ... http www.imcce.fr en ephemerides donnees comets FICH CIF0701.php accessdate 2012 02 25 ref 118401 LINEAR ... belt comet 176P LINEAR ref name HHsieh cite web date May 2010 title Main Belt Comets publisher ... publisher UCLA, Department of Earth and Space Sciences author David Jewitt url http www2.ess.ucla.edu ... Near Earth Asteroid Research LINEAR 1 metre telescopes in Socorro, New Mexico on September 7, 1999. 118401 LINEAR was discovered to be cometary on November 26, 2005, by Henry H. Hsieh and David ... other comets. Since 118401 LINEAR can generate a coma cometary coma produced by vapour boiled off ... and Sublimation chemistry sublimates changes directly from ice to gas , venting gas and dust into space ... accessdate 2010 12 17 ref As a dual status object, astrometric observations of 118401 LINEAR should be reported under the minor planet designation . ref name dualstatus 118401 LINEAR will come ... 2011.gif 118401 on November 13, 2011 http www.ll.mit.edu LINEARLINEAR home page http www.aerith.net ... 175P Hergenrother PageName 176P LINEAR 177P Barnard MinorPlanets Footer DEFAULTSORT Linear 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
Original research article date July 2008 A linear stage or translation stage is a component of a motion system used to restrict an object to a single axis of motion. The term linear slide is often used interchangeably with linear stage , though technically linear slide refers to a linear motion bearing , which is only a component of a linear stage. All linear stages consist of a platform and a base, joined by some form of guide or linear bearing in such a way that the platform is restricted to linear motion with respect to the base. In common usage, the term linear stage may or may not also include ... of operation In three dimensional space, an object may either rotate about, or translate along any ... . A linear stage exhibits only one degree of freedom translation along one axis . In other words, linear stages operate by physically restricting 3 axes of rotation and 2 axes of translation thus allowing for motion on only one translational axis. Guide types Linear stages consist of a platform ... platform relative to the fixed base is typically controlled by a linear actuator of some form, whether ... either manually or by a motor. Manual In manual linear stages, a control knob attached to a lead screw is typically used. The knob may be indexed to indicate it s angular position. The linear displacement ..., then each index division is equivalent to 0.01 mm of linear motion of the stage platform ... , then each revolution of the motor will result in 0.5 mm of linear motion of the stage platform, and each step will result in 0.0025 mm of linear motion. DC motor with encoder In other ... control in more than one direction, multiple linear stages may be used together. A two axis or X Y stage can be assembled from two linear stages, one mounted to the platform of the other such that the axis ... axis or X Y Z stage is composed of three linear stages mounted to each other often with the use of an additional ... goniometer s. By combining linear and rotary elements in various ways, four axis, five axis ... more details
the operation of a linear classifier as splitting a high dimensional input space with a hyperplane all points on one side of the hyperplane are classified as yes , while the others are classified as no . A linear ... with conditional density models. All of the linear classifier algorithms listed above can be converted into non linear algorithms operating on a different input space math varphi vec x math , using ... vectors into the desired output. In other words, math vec w math is a one form or linear functional ... tree learning decision tree s can be faster. Also, linear classifiers often work very well when ... the parameters of a linear classifier math vec w math . ref T. Mitchell, Generative and Discriminative ... include linear discriminant analysis Linear Discriminant Analysis or Fisher s linear discriminant LDA ... machine learning regularization of the final model. Examples of discriminative training of linear ... LDA to the other main linear dimensionality reduction algorithm principal components analysis ... Classifiers Theory and Algorithms, MIT Press, 2001 . ISBN 0 262 08306 X DEFAULTSORT Linear Classifier ... 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
space connected if and only if it is a linear continuum notice the if and only if part . We ... Let X be an ordered set in the order topology . If X is Connected space connected , then X is a linear ... U 0, is not a linear continuum, it is disconnected. 2. By applying the theorem just proved, the fact that R is Connected space connected follows. In fact any interval or ray in R is also connected. 3. Notice how the set of integers is not a linear continuum and therefore cannot be connected. 4. In fact, if an ordered set in the order topology is a linear continuum, it must be connected. Since any interval in this set is also a linear continuum, it follows that this space is locally connected space locally connected since it has a Basis topology basis consisting entirely of connected sets. 5. For an interesting example of a topological space that is a linear continuum, see long line topology ...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 order densely ordered , i.e., between any two members there is another, and which lacks gaps ... subset of the set that is bounded above has a least upper bound . Linear continua are particularly ... set given the order topology is Connected space connected or not. Examples The ordered set of real number s, R , with its usual Total order order is a linear continuum, and is the archetypal example ... the Cartesian product and I 0, 1 in the lexicographic order is a linear continuum. Property b is trivial ... s is not a linear continuum. Even though property b is satisfied, property a is not. Consider ... . The set of non negative integer s with its usual order is not a linear continuum. Property a is satisfied ... numbers A , 0 0, is not a linear continuum. Property b is trivially satisfied. However, if B is the set ... is similar to the previous examples. Topological properties Even though linear continua are important ... more details
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 ... 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 ... 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 ... line 2 span cannot be described by a linear equation with integer coefficients since Square root ... x &minus 5. Connection with linear functions A linear equation, written in the form y f x whose graph ... which satisfies these properties is called a linear function or linear operator , or more generally a linear map . However, linear equations that have non zero y intercepts will have neither property above and hence are not linear functions in this sense. Linear equations in more than two variables main System of linear equations A linear equation can involve more than two variables. The general 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 .... Such an equation will represent an n 1 dimensional hyperplane in n dimensional Euclidean space for example, a plane in 3 space . In vector notation, this can be expressed as math overrightarrow n cdot ... geometry Quadratic equation Cubic equation Quartic equation Quintic equation Linear inequality Linear ... bookhub reader 128?e fwk redden ch02 Linear Equations and Inequalities Open Elementary ... more details
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