Journal of the Association for Computing Machinery pages 321 328 title A randomized lineartime ... spanning tree in lineartime ref name MST V1 cite journal last1 Dixon first1 Brandon last2 Rauch first2 ... analysis of minimum spanning trees in lineartime journal SIAM J. on Computing volume 21 pages 1184 ... , and randomized algorithms to achieve Expected value expected lineartimelinear performance ... with the MST verification algorithm lineartime verification algorithm to discard edges ... in lineartime using a MST verification algorithm minimum spanning tree verification algorithm . ref ... from step 3 using a MST verification algorithm lineartime minimum spanning tree verification algorithm ... is lineartimelinear in the number of edges in the input graph. Step 1 takes constant time. Bor vka steps can be executed in timelinear in the number of edges as mentioned in the Bor vka steps Bor vka step section. Step 3 iterates through the edges and flips a single coin for each one so it is linear in the number of edges. Step 4 can be executed in lineartime using a modified MST verification algorithm lineartime minimum spanning tree verification algorithm . ref name MST V1 ref name MST V2 Since the work done in one iteration of the algorithm is linear in the number of edges the work done ... idddo mstverif.pdf Minimum Spanning Tree Verification in LinearTime References Reflist Category ... Step is equivalent to the inner loop of Bor vka s algorithm which runs in O m time where m is the number ... orders. For the sake of the proof consider selecting edges for H by taking the edges of G one at a time ... of at most n 4 sup d sup vertices. Also the tree has at most log sub 4 sub n levels. File Linear MST ... runs in expected time O m . Worst Case Analysis The worst case runtime is equivalent to the runtime ... more details
page Lineartime encoding and decoding of error correcting codes timestamp 20120501165128 year 2012 month May day 1 substed yes help off For administrator use only Old AfD multi page Lineartime encoding ... to edit beyond this point LinearTime Encoding of Expander Codes Introduction In their initial paper ... gave a way to decode these codes in lineartime. However for encoding them, the algorithm presented was polynomial time. In a follow up paper, Spielman expounded on a better algorithm for encoding in lineartime using what he defined to be error reduction codes. These error reduction codes are constructed .... The basic premise is that for lineartime decoding of these expander codes, http en.wikipedia.org ... in lineartime, we will need to have a series of statements that will lead up to that fact .... This article is based on the paper LinearTime Encodable and Decodable Error Correcting Codes ... math , for math k geq 1 math . File Error reduction lineartime decoding.png thumb Fig. The Recursive Construction of math C k math Lemma The codes math C k math can be encoded and decoded in lineartime if the codes math R k math have lineartime encoding and error reduction algorithms such that 1 ... the lineartime algorithm that satisfies condition 1 to perform error reduction on the math n 02 k ... section titled LinearTime Encoding of Expander Codes Use of Expander Graphs Given any error pattern ... reduction algorithm is lineartime. Assume the size of the graph math B math from the previous ... decreases and the number of flips is linear. Thus, the time taken is math O n math . For further proof ... en institutioner math kalender tcs michael viderman lineartime decoding of regular expander codes 1.304596 Michael Viderman Lineartime decoding of regular expander codes br http ieeexplore.ieee.org ... Lineartime encodable decodable codes with near optimal rate, Guruswami, V br http ieeexplore.ieee.org ... 3Farnumber 3D1013127 High rate codes that are linear in space and time, Hassibi, B ... 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
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
is often taken as synonymous with linear regression model. However the term is also used in time series analysis with a different meaning. In each case, the designation linear is used to identify ... of sub j sub . Time series models An example of a lineartime series model is an autoregressive moving average model . Here the model for values X sub t sub in a time series can be written in the form ... of the time series. Note that here the linear part of the term linear model is not referring to the coefficients ...distinguish linear model of innovation In statistics , the term linear model is used in different ways ... theory is possible. Linear regression models For the regression case, the statistical model is as follows ... variables representing errors in the relationship. The linear part of the designation relates to the appearance of the regression coefficient s, sub j sub in a linear way in the above relationship ... hat Y i beta 0 beta 1 phi 1 X i1 cdots beta p phi p X ip qquad i 1, ldots, n , math are linear functions ... From this, it can readily be seen that the linear aspect of the model means the following the function ... simple problem the derivatives of the function are linear functions of the sub j sub making it easy to find the minimising values the minimising values sub j sub are linear functions of the observations Y sub i sub the minimising values sub j sub are linear functions of the random errors sub ... innovations which are new random effects that appear at a certain time but also affect values of X at later times. In this instance the use of the term linear model refers to the structure of the above relationship in representing X sub t sub as a linear function of past values of the same time series and of current and past values of the innovations. ref Priestley, M.B. 1988 Non linear and Non stationary time series analysis , Academic Press. ISBN 0 12 564911 8 ref This particular aspect of the structure ... model is used to contrast with a linearly structured model, although the term linear model is not usually ... more details
or frequency components . Typical differential equation s of lineartime invariant system time invariant ... use of linear models is to describe a nonlinear system by linearization . This is usually done for mathematical convenience. Time varying impulse response The time varying impulse response h t sub 2 sub , t sub 1 sub of a linear system is defined as the response of the system at time t t sub 2 sub to a single impulse function impulse applied at time t t sub 1 sub . In other words, if the input x t to a linear ... h t sub 2 sub , t sub 1 sub is the time varying impulse response of the system. Time varying convolution integral Continuous time The output of any continuous timelinear system is related to the input by the time varying convolution integral math y t int infty infty h t,s x s ds math or, equivalently, math y t int infty infty h t,t tau x t tau d tau math Discrete time The output of any discrete timelinear system is related to the input by the time varying convolution sum math y n sum k infty ... A linear system is causal if and only if the system s time varying impulse response is identically ...About systems as studied in systems theory a family of linear equations System of linear equations the concept in algebraic geometry Linear system of divisors Unreferenced date December 2009 A linear system is a mathematical model of a system based on the use of a linear operator . Linear systems typically ... abstraction or idealization, linear systems find important applications in automatic control ... communication systems can often be modeled by linear systems. A general deterministic system ... black box description. Linear systems satisfy the properties of Superposition principle superposition ... x 2 t right math then a linear system must satisfy math alpha y 1 t beta y 2 t H left alpha x 1 t beta ... equations simpler than many nonlinear systems. For time invariant system time invariant systems this is the basis ... . Another perspective is that solutions to linear systems comprise a system of function ... more details
Improving the Time Complexity of Matsui s Linear Cryptanalysis ...More footnotes date March 2009 In cryptography , linear cryptanalysis is a general form of cryptanalysis ... have been developed for block cipher s and stream cipher s. Linear cryptanalysis is one of the two ..., 1992 . ref name FEAL linear cite conference author Matsui, M. and Yamagishi, A title A new method ... name DES linear cite conference author Matsui, M title Linear cryptanalysis method for DES cipher booktitle ... 2 sup 43 sup known plaintext attack known plaintexts . ref name DES linear A variety of refinements to the attack have been suggested, including using multiple linear approximations or incorporating non linear expressions, leading to a generalized partitioning cryptanalysis . Evidence of security against linear cryptanalysis is usually expected of new cipher designs. Overview There are two parts to linear cryptanalysis. The first is to construct linear equations relating plaintext, ciphertext ... values of their variables are as close as possible to 0 or 1. The second is to use these linear equations in conjunction with known plaintext ciphertext pairs to derive key bits. Constructing linear equations For the purposes of linear cryptanalysis, a linear equation expresses the equality of two ... bit of the key math P 1 oplus P 3 oplus C 1 K 2. math In an ideal cipher, any linear equation relating plaintext, ciphertext and key bits would hold with probability 1 2. Since the equations dealt with in linear cryptanalysis will vary in probability, they are more accurately referred to as linear ... in a linear equation . For small enough S boxes, it is possible to enumerate every possible linear equation relating the S box s input and output bits, calculate their biases and choose the best ones. Linear approximations for S boxes then must be combined with the cipher s other actions, such as permutation and key mixing, to arrive at linear approximations for the entire cipher. The piling ... more details
history The Linear Men are a team of men and women who police time and work to resolve time paradoxes ... Hunter , although other members of the Linear Men have been seen from time to time. An alternate Matthew ... the Crisis on Infinite Earths , time is strictly linear and paradoxes can unravel the sole remaining ... of a Linear Man agent. Another Linear Agent pursues the protagonist throughout time, including ... 1998 ref Rip Hunter eventually locks the Linear Men away for unknown reasons. ref Booster Gold 4 January 2008 ref In the Rip Hunter Time Masters Vanishing Point Time Masters Vanishing Point limited series , it is revealed that Rip and the Linear Men were never in agreement about how to handle time and that Rip, tired of the Linear Men s interference, locked them away in a cell at Vanishing Point. Later, Matthew Ryder and Liri Lee are freed from their imprisonment by the Time Stealers Black Beetle comics Black Beetle , Despero , Per Degaton and Ultra Humanite . ref Time Masters Vanishing Point 3 September 2010 ref Black Beetle intends to use the Linear Men to bring Waverider to life. But Supernova comics Supernova prevents Black Beetle from dystopia and sends the Time Stealers back to the present. However, Black Beetle is able to escape, and the Linear Men go with him. ref Time Masters Vanishing ... Black Beetle escapes. Rip and the rest of the Time Masters arrive but Linear Woman refuses to agree ... linearmen The Unofficial Linear Men Fansite Category Time travel comics Category DC Comics superhero ... imagesize caption team name Linear Men publisher DC Comics debut Adventures of Superman 476 March 1991 ... hero y villain sortkey Linear Men The Linear Men are fictional character s, a fictional superhero team ... what was supposed to happen and O Connell s sacrifice keeps the timeline on track. The Linear ... opposed by a small, time traveling troupe of entertainers. This series also noted a rather important fact to the Linear Men they are not aware of the Crisis on Infinite Earths, while this small group ... 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
Unreferenced date January 2009 Image Pcmcia smart 4mb linear flash.jpg right thumb 250px A type I PCMCIA card Linear Flash is a PC card flash memory format. Linear Flash requires no battery support, unlike somewhat faster Static random access memory SRAM , and features read write speeds much faster than similar, less expensive ATA type cards, which include CompactFlash and Memory Stick . Like an SRAM, Linear Flash supports execute in place XIP applications in mobile PC and embedded equipment. Linear Flash can also be read and written to by laptops and desktops with PC card slots, and is somewhat popular for sensitive data storage because the media is non volatile and does not degrade over time. However, large scale storage is impractical using Linear Flash because of small card sizes typically under 40 megabyte s and prohibitive costs megabyte for megabyte, Linear Flash cards are often dozens of times more expensive than ATA cards. Combined with file management software, such as Flash Translation Layer FTL or M Systems TrueFFS Flash File System, the Linear Flash cards provide removable disk emulation. As PC Card s was PCMCIA , Linear Flash cards should have a PC Card Card Information Structure Card Information Structure CIS . However, many memory cards do not have a CIS. Linear Flash cards begin to develop bad blocks after about 100,000 read write Instruction cycle cycle s and thus are of dubious value on the second hand market. Usage Linear Flash cards were also the primary method of data storage for Cisco Router computing router s, Apple s Newton platform Newton MessagePad 100 series and 2000 series PDAs, for some early Magic Cap , Pocket PC and Windows CE PDAs, musical synthesizer s and for many telecom devices. Manufacturers Major makers of Linear Flash cards are http www.pretec.com Pretec , http www.smartm.com Smart and http www.magicram.com MagicRAM . Intel , which championed the adoption of the Linear Flash format, also made cards. See also Flash file system M ... more details
Goulian . With the help of an initial round of funding and just two employees at the time, Linear ...Infobox airline airline Linear Air logo Linearair.jpg logo size 300 IATA ICAO HPN callsign Harpoon headquarters Concord, Massachusetts bases Unbulleted list Hanscom Field Bedford Westchester County Airport ... fleet size 6 website http www.linearair.com Linear Air is a private FAR part 135 part 135 air charter ... Concord , Massachusetts . Linear Air s primary operations base is located at Hanscom Field ..., Linear Air began an operation focused on addressing demand between the large market for commercial ... very light jets , Linear Air primarily serves the Northeastern United States Northeast and Mid Atlantic ... Taxi Association , Linear Air and other member air taxi operations are speeding the adoption .... ref cite web title About Us url http www.linearair.com aboutus index.aspx work Linear Air accessdate 28 March 2011 ref Destinations Linear Air can currently fly to hundreds of locations in the United ... Where We Fly url http www.linearair.com services service area.aspx work Linear Air accessdate 28 March 2011 ref Fleet & Flight Operations Linear Air currently operates a fleet of Eclipse 500 very light ... Canada PW600 PW610F turbofan engines. Linear Air recently debuted an upgraded Eclipse 500 in early ... operation. ref cite news last Nihon first Justin title Linear Air Introduces First All Weather Eclipse to Commercial Service url http www.linearair.com downloads Linear 20Air 1st 20FIKI Press 20Release ... Emily title HIGH FLYING LINEAR AIR STRENGTHENS LEAD AS FIRST OPERATIONAL JET TAXI SERVICE url http goliath.ecnext.com coms2 gi 0199 5406650 High Flying Linear Air Strengthens.html date 04 10 06 ref Prior ... engine manufactured by Pratt & Whitney . Resources http www.linearair.com aboutus.aspx Linear Air ... Linear Air Homepage http www.facebook.com pages Linear Air 149111401773430 Linear Air on Facebook http twitter.com linearair Linear Air on Twitter http www.eclipseaerospace.net Eclipse Aerospace ... 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
by Kyocera to the Phase Linear line. By that time the company was in decline due to the increasing cost of research and development, and the departure of Carver. In the 1980s Phase Linear was sold to Recoton ...refimprove date August 2007 Phase Linear was an audio equipment manufacturer founded by Bob Carver in 1970. While primarily known as a power amplifier company it also produced several innovative preamplifers, tuners and the Andromeda loudspeaker. History Its first location was a small building at 405 Howell Way in Edmonds, Washington. The first amplifier produced was the Phase Linear 700. With 350 watts per channel it soon became the standard amplifier used in recording studios, sound reinforcement companies, professional musicians and audiophiles. It had a retail price of 749.00, or a little more than a dollar a watt. The design was notable for its brushed aluminum front panel and large dual VU meter s, and was made possible by the new high power transistors designed for the high voltages of auto electronic ignitions. That original amp was replaced by the 700B and the 700 II. All of those designs were made to have extra power to run loudly the relatively inefficient sealed box speakers like the Acoustic Research AR3 AR3a. The next product was the Phase Linear 4000 Series Auto correlation Pre Amplifier introduced in 1973 and manufactured through 1978. It retailed for 700.00 at the end of its life. It was a design collaboration by Bob Carver and Bill Skinner. The second amplifier released was the Phase Linear 400 with 200 watts per channel. It shared the same distinctive brushed aluminum, dual VU meters front panel style as the 700. It retailed for just under 500. ref http www.phaselinearhistory.stereomanuals.com Anthony Young s Phase Linear history reference site ref The company was known for the most powerful audio amplifiers of the era led by the Phase Linear D 500 introduced ... html english.html Phase Linear reference site en icon http www.kleines kalb.com Phase Linear reference ... 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
Kober s triplets About the same time, Alice Kober studied Linear B and managed to construct grids ...About the ancient syllabary the JavaScript engine linear b script engine Distinguish Linear Pottery culture Infobox Writing system name Linear B type Syllabary typedesc with additional ideogram s time Late Bronze Age status Extinct languages Mycenaean Greek language Mycenaean Greek fam1 Linear A sisters ... Linb sample NAMA Linear B tablet of Pylos.jpg imagesize 250px History of the Greek language 267 SpecialChars Writing systems sidebar Linear B 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 linear b tablet found at iklaina&catid 80&Itemid 473 title New Linear B tablet found at Iklaina publisher Comit International Permanent des tudes Myc niennes, UNESCO accessdate 29 April 2012 ref Linear B, found ... Dark Ages , provides no evidence of the use of writing. The script appears related to Linear ... Cypriot syllabary , which recorded Greek. Linear B consists of around 87 syllabic signs .... The application of Linear B seems to have been confined to administrative contexts. In all ... first J.T. last Hooker title Linear B An Introduction publisher Bristol Classical Press UK year 1980 .... The script Linear B has roughly 200 signs, divided into syllabic signs with phonetic values ... home ?doc 157.87 accessdate 2008 03 28 ref Many of the signs are identical or similar to Linear A signs however, Linear A, which encoded the unknown Minoan language, remains undeciphered and we cannot ... 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 Linear B . ref In cases where the transcription of the sign remains ... font size 200 File Linear B Syllable B008 A.svg a 08 style font size 200 File Linear B Syllable B038 E.svg e 38 style font size 200 File Linear B Syllable B028 I.svg i 28 style font size 200 File Linear ... more details
Linear hashing is a dynamic hash table algorithm invented by Witold Litwin 1980 , ref Citation first1 Witold last1 Litwin title Linear hashing A new tool for file and table addressing journal Proc. 6th Conference on Very Large Databases pages 212 223 year 1980 url http www.cs.cmu.edu afs cs.cmu.edu user christos www courses 826 resources PAPERS BOOK linear hashing.PDF format PDF ref and later popularized by Paul Larson . Linear hashing allows for the expansion of the hash table one slot at a time. The frequent single slot expansion can very effectively control the length of the collision chain. The cost of hash table expansion is spread out across each hash table insertion operation, as opposed to being incurred all at once. ref Citation first1 Per ke last1 Larson title Dynamic Hash Tables journal Communications of the ACM pages 446 457 date April 1988 volume 31 Number 4 doi 10.1145 42404.42410 ref Linear hashing is therefore well suited for interactive applications. Algorithm Details A hash function controls the address calculation of linear hashing. In linear hashing, the address calculation is always bounded by a size that is a power of two N, where N is the chosen original number ... bucket prior to the split . A linear hashing table expansion operation would consist of rehashing ... unrelated to where buckets overflow at the time of expansion. Overflow buckets are used at the sites ... obvious choice is to perform the expansion operation each time no more slots are available at the target .... The hash table array for linear hashing is usually implemented with a dynamic array algorithm. Adoption ... of linear hashing in the Icon language . They discussed the implementation alternatives of dynamic array algorithm used in linear hashing, and presented performance comparisons using a list of Icon ... Sorted Linear Hash Table, C implementation of a Linear Hashtable http tommyds.sourceforge.net TommyDS, C implementation of a Linear Hashtable DADS linear hashing linearHashing See also Extendible ... 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 ... of the twentieth century. At this time, many ideas and methods of previous centuries were generalized ... 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 ..., function mathematics functions , polynomial ring polynomials , vectors, or matrices. Linear algebra ... more details
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 inscriptions. The bilingual and bigraphic inscriptions of the monumental stairway as a whole, and the votive boulder B have inspired the first attempts at decipherment of Linear Elamite Bork, 1905 ... http cdli.ucla.edu wiki doku.php linear elamite http www.ancientscripts.com elamite.html Category ... more details
. Dictionary operation in constant time Using linear probing, dictionary operation can be implemented in constant time. In other words, insert, remove and find operations can be implemented in O 1 ... pages 1107 1120 title Linear probing with constant independence volume 39 year 2009 ref Weaker properties, such as universal hashing , are not strong enough to ensure the constant time operation of linear ...Linear probing is a scheme in computer programming for resolving hash collision s of values of hash function s by sequentially searching the hash table for a free location. ref cite book last Dale first Nell title C Plus Data Structures year 2003 publisher Jones and Bartlett Computer Science location Sudbury, MA isbn 0 7637 0481 4 ref This is accomplished using two values one as a starting value and one as an interval between successive values in modular arithmetic . The second value, which is the same for all keys and known as the stepsize , is repeatedly added to the starting value until a free space is found, or the entire table is traversed. newLocation startingValue stepSize arraySize This algorithm, which is used in open addressed hash table s, provides good memory caching if stepsize is equal to one , through good locality of reference, but also results in clustering, an unfortunately high probability that where there has been one collision there will be more. The performance of linear probing is also more sensitive to input distribution when compared to double hashing . Given an ordinary hash function H x , a linear probing function H x, i would be math H x, i H x i pmod n. , math ... Mikkel contribution On the k independence required by linear probing and minwise independence doi ... hashing , again leads to a guaranteed constant expected time performance despite not being 5 independent ... versions edition 0.1d ods java node32.html Open Data Structures Section 5.2 LinearHashTable Linear Probing Category Search algorithms Category Hashing datastructure stub nl Linear probing ... more details
, is known as topological sorting several algorithms solve it in lineartime . ref citation last1 ...In order theory , a branch of mathematics, a linear extension of a partial order is a linear order or total order that is compatible with the partial order. Definitions Given any partial orders and sup sup on a set X , sup sup is a linear extension of exactly when 1 sup sup is a linear order and 2 for every x and y in X , if nowrap x y , then nowrap x sup sup y . It is that second property that leads mathematicians to describe sup sup as extending . Alternatively, a linear extension may be viewed as an order preserving bijection from a partially ordered set P to a Total order Chains chain C on the same ... results The algorithmic problem of constructing a linear extension of a partial order on a finite set ... the ease of finding a single linear extension, the problem of counting all linear extensions of a finite ... time randomized approximation scheme . ref citation last1 Brightwell first1 Graham R. last2 Winkler ... pages 225 242 title Counting linear extensions volume 8 year 1991 . ref Among all partial orders ... the largest number of linear extensions are semiorder s. ref citation last1 Fishburn first1 Peter ... issue 1 journal Discrete Mathematics pages 25 40 title Linear extensions of semiorders a maximization ... of a set of linear extensions whose intersection is the given partial order equivalently, it is the minimum number of linear extensions needed to ensure that each Critical pair order theory critical ... as generalizing partial orders in this view, the structures corresponding to the linear extensions ... for which the linear extensions of P in which nowrap x y number between 1 3 and 2 3 of the total number of linear extensions of P . ref citation author Kislitsyn, S. S. year 1968 title Finite partially ... chooses a linear extension of P uniformly at random, there is a pair x , y which has probability ... sets, with a canonical probability defined on its linear extensions as a limit of the probabilities ... more details
the values of sub 1 sub and sub 2 sub from the measured data. This model is non linear in the time ...Regression bar Image Linear regression.svg thumb right 400px Example of simple linear regression , which has one independent variable In statistics , linear regression is an approach to modeling the relationship ... is multiple regression . This in turn should be distinguished from multivariate linear regression ... of PLS or related projective methods rather than a single scalar variable. In linear regression, data are modeled using linear predictor function s, and unknown model parameters are estimation theory estimated from the data. Such models are called linear model s . Most commonly, linear ... of X is an affine transformation affine function of X . Less commonly, linear regression could ... given X is expressed as a linear function of X . Like all forms of regression analysis , linear regression ... probability distribution of y and X , which is the domain of multivariate analysis . Linear regression ... properties of the resulting estimators are easier to determine. Linear regression has many practical uses. Most applications of linear regression fall into one of the following two broad categories If the goal is Prediction Statistics prediction , or forecasting , linear regression can be used ... 1 sub , ..., X sub p sub that may be related to y , linear regression analysis can be applied to quantify ... information about y . Linear regression models are often fitted using the least squares approach ... can be used to fit models that are not linear models. Thus, while the terms least squares and linear model are closely linked, they are not synonymous. Introduction to linear regression Given a data set math y i, , x i1 , ldots, x ip i 1 n math of n statistical unit s, a linear regression model ... x sub i sub is linear function linear . This relationship is modeled through a disturbance term or error variable sub i sub an unobserved random variable that adds noise to the linear relationship ... more details
Murty ref name PS In fact, for some time it was not known whether the linear programming problem ... polynomial time complexity for linear programming. Both algorithms visit all 2 sup D ... for establishing the polynomial time solvability of linear programs. The algorithm was not a computational ... science Does linear programming admit a strongly polynomial time algorithm? There are several ... size linear programs can be solved in polynomial time. One common way of proving that a polyhedron ...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 ... 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 ... algorithm simplex method and John von Neumann developed the theory of Duality duality as a linear optimization ... use in their daily planning. The linear programming problem was first shown to be solvable in polynomial ... more details
2008 Linear motion also called rectilinear motion ref Resnick, Robert and Halliday, David 1966 , Physics ... be described mathematically using only one spatial dimension . The linear motion can be of two types uniform linear motion, with constant velocity or zero acceleration non uniform linear motion ... a line can be described by its position math x math , which varies with math t math time .Example of linear motion is an athletic running 100m along a straight track. Linear motion is the most basic ... the direction of its motion, so that its motion cannot be described as linear ref cite web url ... Info Center accessdate 19 January 2011 ref One may compare linear motion to general motion. In general ... have a magnitude and direction. In linear motion, the directions of all the vectors describing the system ..., an example of linear motion is that of a ball thrown straight up and falling back straight down ... distance in the same time is called Translatory motion. There are two types of translatory motions Rectilinear motion Curvilinear motion Since linear motion is a motion in a single dimension, the distance ... to time. ref cite web url http physics.info velocity title Speed & Velocity ref The SI unit of velocity ... is the ratio of total displacement math Delta x math taken over time interval math Delta t math ... Delta t frac x 2 x 1 t 2 t 1 math where, br math t 1 math is the time at which the object was at position math x 1 math br math t 2 math is the time at which the object was at position math x 2 math ... to time. math mathbf v lim Delta t to 0 Delta x over Delta t math math frac dx dt math Speed ... main Acceleration Acceleration is defined as the rate of change of velocity with respect to time ... position with respect to time twice or differentiating velocity with respect to time once ... acceleration and math Delta mathbf v mathbf v 2 mathbf v 1 math is the average velocity over the time ... main Equations of motion The four physical quantities acceleration, velocity, time and displacement ... more details
Linear prediction is a mathematical operation where future values of a discrete time discrete time Signal processing signal are estimated as a linear transformation linear function of previous samples. In digital signal processing , linear prediction is often called linear predictive coding LPC and can thus be viewed as a subset of filter theory . In system analysis a subfield of mathematics , linear prediction can be viewed as a part of mathematical model ling or Optimization mathematics optimization . The prediction model The most common representation is math widehat x n sum i 1 p a i x n i , math where math widehat x n math is the predicted signal value, math x n i math the previous observed values, and math a i math the predictor coefficients. The error generated by this estimate is math e n x n widehat x n , math where math x n math is the true signal value. These equations are valid for all types of one dimensional linear prediction. The differences are found in the way the parameters math a i math are chosen. For multi dimensional signals the error metric is often defined as math e n x n widehat x n , math where math cdot math is a suitable chosen vector norm mathematics norm . Estimating the parameters The most common choice in optimization of parameters math a i math is the root mean square criterion which is also called the autocorrelation criterion. In this method we minimize the expected value of the squared error E e sup 2 sup n , which yields the equation math sum i 1 p a i R j i R j , math for 1 j &le p , where R is the autocorrelation of signal x sub n sub , defined .... Specification of the parameters of the linear predictor is a wide topic and a large number of other ... and Physics , vol. 25, no. 4, pp. 261 278, January 1947. Overview J. Makhoul. Linear prediction A tutorial ... matlab rastamat PLP and RASTA and MFCC, and inversion in Matlab DEFAULTSORT Linear Prediction Category Time series analysis Category Signal processing Category Estimation theory de Lineare ... more details
Infobox film name Linear image U2 Linear.jpg image size alt The opening title screen for the film. It features a black blackground with Linear written in white in the centre. The word is capitalized and underlined, with U2 written below it in a smaller font, also in white. caption DVD cover director Anton Corbijn producer Iain Canning br Emile Sherman writer Anton Corbijn br Bono starring Sa d Taghmaoui br Lizzie Brocher br Marta Barrio br Francisco Javier Malia Vazquez music U2 br Brian Eno br Daniel Lanois Danny Lanois cinematography Martin Ruhe editing James Rose studio See Saw Films distributor Universal Music Group released Start date 2009 03 09 runtime 58 minutes country language English budget Linear is a 2009 film directed by Anton Corbijn . The film includes music from U2 s 2009 studio ... name Corbijn interview cite web url http www.u2.com stream article display id 4611 title Linear ... . ref name creative cite web url http www.creativereview.co.uk cr blog 2009 april u2 linear its not a music video 2 title U2 Linear it s not a music video last Burgoyne first Patrick date 14 April ... name Linear cite web url http www.nolineonthehorizon.com credits.html title Linear publisher nolineonthehorizon.com ... Director title Linear medium Film publisher U2 location France date 2009 ref Linear was completed in time for the album s original November 2008 release date, but as the band continued to work into December the film became out of sequence with the album. ref name Linear 10 of the 11 songs in the film were edited as a solution, and the original running order was kept intact. ref name Linear The film ... cr blog 2009 april u2 linear its not a music video 2 title U2 Linear it s not a music ... 2008. ref name Linear tracklist total length 58 20 title1 Unknown Caller length1 6 18 title2 Breathe ... 2 29 References reflist External links imdb title 1400345 Linear U2 DEFAULTSORT Linear Film Category ... Corbijn Category Films set in Paris Category U2 films Category Article Feedback 5 fr Linear film ... more details
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