mergefrom Ionized impurity scattering date September 2011 mergeto Phonon scattering date September 2011 Lattice scattering is the scattering of ions by interaction with atoms in a lattice. ref cite book author Bube, Richard H. title Electrons in Solids an introductory survey pages 176 177 publisher Academic Press 1992 isbn 0121385531 ref This effect can be qualitatively understood as phonons colliding with charge carriers. In the current Classical and quantum conductivity quantum mechanical picture of conductivity the ease with which electrons traverse a crystal lattice is dependent on the near perfectly regular spacing of ions in that lattice. Only when a lattice contains perfectly regular spacing can the ion lattice interaction scattering lead to almost transparent behavior of the lattice. ref cite book author Kip, Arthur F. title Fundamentals of Electricity and Magnetism pages 211 213 publisher McGraw Hill isbn 070347808 ref In the quantum understanding, an electron is viewed as a wave traveling through a medium. When the wavelength of the electrons is larger than the crystal spacing, the electrons will propagate freely throughout the metal without collision. References reflist See also Ionized impurity scattering External links cite book author Kundstrom, Mark title Fundamentals of carrier transport publisher Cambridge University Press 2000 isbn 0521631343 DEFAULTSORT Lattice Scattering Category Quantum mechanics ... more details
File Fano plane Hasse diagram.svg thumb Hasse diagram of a complemented lattice br A point and a line ... of order theory , a complemented lattice is a lattice order bounded lattice in which every element ... b 0. A relatively complemented lattice is a lattice such that every interval mathematics ... lattice is an involution mathematics involution which is order reversing and maps each element to a complement. An orthocomplemented lattice satisfying a weak form of the modular lattice modular law is called an orthomodular lattice . In distributive lattices, complements are unique. Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra structure Boolean algebra . Definition and basic properties A complemented lattice is a bounded lattice with least element 0 and greatest element 1 , in which every element a has a complement , i.e. ... an element may have more than one complement. However, in a bounded distributive lattice every element ... 9.3 p. 25. ref A lattice in which every element has exactly one complement is called a uniquely complemented lattice . A lattice with the property that every interval is complemented is called a relatively complemented lattice . In other words, a relatively complemented lattice is characterized ... of a relative to the interval. A distributive lattice is complemented if and only if it is bounded and relatively ... An orthocomplementation on a bounded lattice is a function that maps each element a to an orthocomplement ... a sup sup . An orthocomplemented lattice or ortholattice is a bounded lattice which is equipped with an orthocomplementation ..., distributive. ref http unapologetic.wordpress.com 2009 05 07 orthogonal complements and the lattice of subspaces The Unapologetic Mathematician Orthogonal Complements and the Lattice of Subspaces . ref gallery Caption Some complemented lattices Image Smallest nonmodular lattice 1.svg In the pentagon lattice N sub 5 sub , the node on the right hand side has two complements. Image Diamond ... more details
In mathematics, a lattice word or lattice permutation is a sequence of integer s such that in every initial part of the sequence any number i occurs at least as often as the number i 1. A reverse lattice word , or Yamanouchi word , is a sequence whose reversal is a lattice word. References Citation last1 Fulton first1 William author1 link William Fulton mathematician title Young tableaux publisher Cambridge University Press series London Mathematical Society Student Texts isbn 978 0 521 56144 0 978 0 521 56724 4 id MathSciNet id 1464693 year 1997 volume 35 Category Algebraic combinatorics Category Combinatorics on words fr Mot de Yamanouchi ... more details
Image Tile 3,6.svg thumb Triangular tiling . The vertices form a hexagonal lattice with horizontal rows ... lattice or equilateral triangular lattice is one of the five 2D Lattice group lattice types ... to point into two oblique directions. Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as hexagonal lattice with horizontal rows like in the figure below , with triangles pointing up and down, and hexagonal lattice with vertical rows , with triangles pointing left and right. They differ by an angle of 30 . The hexagonal lattice with horizontal ... as high. Its symmetry category is wallpaper group p6m. A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. Image Tile 6,3.svg ... lattice with vertical rows for each color the centers of the hexagons of that color form a hexagonal lattice with horizontal rows which is in linear scale 3 times as large. The vertices of all hexagons together with their centers form a hexagonal lattice with horizontal rows which is in linear scale 3 times as small as the first mentioned lattice. For an image of a Honeycomb geometry honeycomb ... of 90 , or equivalently 30 . A honeycomb structure is in two ways related to a hexagonal lattice the centers of the hexagons of a honeycomb form a hexagonal lattice, with the rows oriented the same the vertices of a honeycomb, together with their centers, form a hexagonal lattice, rotated by 30 or equivalently 90 , and scaled by a factor math frac 1 3 sqrt 3 math , relative to the other lattice The ratio ... is 3, the reciprocal of the square of the scale factor. The term honeycomb lattice could mean a corresponding hexagonal lattice, or a structure which is not a lattice in the Group mathematics group sense, but e.g. one in the sense of a lattice model mathematics lattice model . A set of points ... of them, the sides of the hexagons may be shown depending on application they may be called lattice ... more details
Orphan date December 2010 No footnotes date September 2011 Infobox disease Name Lattice degeneration Image Caption DiseasesDB ICD10 ICD9 ICDO OMIM MedlinePlus eMedicineSubj oph eMedicineTopic 397 MeshID Lattice degeneration is a disease of the human eye eye where peripheral retina becomes atrophic in a lattice pattern and may develop tears breaks holes, which may further progress to retinal detachment . It is an important cause of retinal detachment in young myopic individuals. The cause is not known but pathology reveals vascular insufficiency resulting in ischemia and fibrosis . It is present in about 8 of the general population and occurs in about 40 of eyes with retinal detachment. Similar lesions are seen in patients with Marfan syndrome , Stickler syndrome and Ehlers Danlos syndrome , all of which are associated with an increased risk of retinal detachment . Signs Typical lattice consists of sharply demarcated spindle shaped areas of retinal thinning usually located between the equator of the retina and the posterior border of the vitreous base. This is more frequently located in the temporal half of the retina and is seen more superiorly than inferiorly. Atypical lattice is characterised ... around a hole or tear associated with lattice degeneration in an eye at risk of developing ... in patients with asymptomatic lattice degeneration. So prophylactic treatment for asymptomatic lattice ... risks of retinal detachment in symptomatic lattice degeneration. However there are documented ... with laser. Prognosis No complications are encountered in most patients with lattice degeneration ... off retinal detachment in patients with asymptomatic lattice degeneration. Partial or complete ... or cure for lattice degeneration. It is not known if research is being carried out to find a cure for lattice degeneration. References reflist External links http eyewiki.aao.org Lattice Degeneration http cms.revoptom.com handbook sect5e.htm DEFAULTSORT Lattice Degeneration Category Diseases of the eye ... more details
Unreferenced date September 2009 Infobox Software name Lattice C logo File lattice logo.png screenshot caption collapsible author developer Steve Krueger et al. released 1982 latest release version latest release date latest preview version latest preview date frequently updated programming language C, Assembler operating system DOS, OS 2, MVS, VMS, UNIX, AmigaDOS, Sinclair QDOS platform size language status genre Compiler license Closed source website http www.sas.com products sasc Lattice C according to its author, Lattice, Incorporated was the first C programming language C compiler for MS DOS on the International Business Machines IBM personal computer PC , in 1982 . It was ported to many other platforms, such as Mainframe computer mainframes MVS , minicomputer s Virtual Memory System VMS , workstation s Unix UNIX , OS 2 , the Commodore International Commodore Amiga , Atari ST and the Sinclair Research Sinclair Sinclair QL QL . The compiler was subsequently repackaged by Microsoft under a distribution agreement as Microsoft C. Lattice was purchased by SAS Institute in 1987 . After this, support for other platforms dwindled until compiler development ceased for all platforms except IBM mainframes. The product is still available in versions that run on other platforms, but these are Cross compilation cross compilers that only produce mainframe code. Some of the early 1982 commercial software for the IBM PC was ported from CP M where it was written for the BDS C subset of the C language to MS DOS using Lattice C including Perfect Writer , PerfectCalc , PerfectSpeller and PerfectFiler . This suite was bundled with the Seequa Chameleon and Columbia Data Products . LMK, make software make tool LSE, screen editor TMN, text management utilities External links http web.archive.org ... 24 Category C compilers Category Amiga development software Category Atari ST software de Lattice C it Lattice C ru Lattice C ... more details
Image Smallest nonmodular lattice 1.svg thumb right Hasse diagram of N sub 5 sub , the smallest non modular lattice. In the branch of mathematics called order theory , a modular lattice is a lattice order lattice that satisfies the following self dual condition Modular law x b implies x ... and called join and meet respectively are the operations of the lattice ... lattice. Every distributive lattice distributive lattice is modular. In a not necessarily modular lattice, there may still be elements b for which the modular law holds in connection with arbitrary ... generalizations of modularity related to this notion and to semimodular lattice semimodularity ... law that connects the two lattice operations similarly to the way in which the associative law ... x b is clearly necessary, since it follows from x a b x a b . Image Smallest nonmodular lattice ... x a b in every lattice. Therefore the modular law can also be stated as Modular law variant x b implies ... of modular lattices are again modular. The smallest non modular lattice is the pentagon lattice ... to x or to b . For this lattice x a b x 0 x b 1 b x a b holds, contradicting the modular law. Every non modular lattice contains a copy of N sub 5 sub as a sublattice. Modular lattices are sometimes ... theorem For any two elements a , b of a modular lattice, one can consider the intervals a b ... In a modular lattice, the maps and indicated by the arrows are mutually inverse isomorphisms. Image Not a modular pair.svg Failure of the diamond isomorphism theorem in a non modular lattice .... In a modular lattice, however, equality holds. Since the dual of a modular lattice is again ... lattices. A lattice is modular if and only if the diamond isomorphism theorem holds for every pair ... theorem in algebra, and it is a generalization of the lattice theorem . Modular pairs and related notions Image Centred hexagon lattice D2.svg thumb right The centred hexagon lattice S sub 7 sub ... more details
Refimprove date May 2011 In mathematics , distributive lattices are lattice order lattices for which ... of such structures are collections of sets for which the lattice operations can be given by set union ... the scenery completely every distributive lattice is &ndash up to order isomorphism isomorphism &ndash given as such a lattice of sets. Definition As in the case of arbitrary lattices, one can choose to consider a distributive lattice L either as a structure of order theory or of universal algebra . Both views and their mutual correspondence are discussed in the article on lattice order lattices . In the present situation, the algebraic description appears to be more convenient A lattice L , math ... empty finite joins. It is a basic fact of lattice theory that the above condition is equivalent to its ... a lattice homomorphism as given in the article on lattice order lattices , i.e. a function that is compatible with the two lattice operations. Because such a morphism of lattices preserves the lattice ... lattices . Examples File Young s lattice.svg thumb Young s lattice Distributive lattices are ubiquitous ... logical conjunction conjunction and Logical disjunction disjunction is a distributive lattice, i.e. ... lattice. Every Heyting algebra is a distributive lattice. Especially this includes all complete ... case of the above example. Every Total order totally ordered set is a distributive lattice with max as join and min as meet. The natural number s form a distributive lattice Complete lattice ... forms a distributive lattice, again with the greatest common divisor as meet and the least common multiple ... space lattice ordered vector space is a distributive lattice. Young s lattice given by the inclusion ... partitions is a distributive lattice. Characteristic properties Various equivalent formulations to the above ... non distributive lattices align right Image Diamond lattice.svg The diamond lattice M sub 3 sub . Image Smallest nonmodular lattice 1.svg The pentagon lattice N sub 5 sub . gallery The simplest non distributive ... more details
In mathematics , a unimodular lattice is a Lattice group lattice of Lattice group Dividing space according to a lattice determinant 1 or &minus 1. The E8 lattice E sub 8 sub lattice and the Leech lattice are two famous examples. Definitions A lattice is a free abelian group of finite rank of an abelian group rank with an integral symmetric bilinear form , . A lattice is even if a , a is always even. The dimension of a lattice is the same as its rank as a Z module mathematics module . A lattice is positive definite if a , a is always positive for non zero a . The discriminant of a lattice is the determinant ... a basis for the lattice. A lattice is unimodular if its discriminant is 1 or &minus 1. Lattices are often embedded in a real vector space with a symmetric bilinear form. The lattice is positive definite , Lorentzian , and so on if its vector space is. The signature of a lattice is the signature ... of unimodular lattices are The lattice Z , in one dimension. The E8 lattice E sub 8 sub lattice , an even 8 dimensional lattice, The Leech lattice , the 24 dimensional even unimodular lattice with no roots ... sup m,n sup there is one odd unimodular lattice up to isomorphism, denoted by I sub m,n sub , which ... or they are all integers plus 1 2, and their sum is even. The lattice II sub 8,0 sub is the same as the E sub 8 sub lattice. Positive definite unimodular lattices have been classified up to dimension ... by E sub 8 sub , and up to dimension 25 they are controlled by the Leech lattice, and this accounts ... of vectors in the Leech lattice. The wild increase in numbers beyond 25 dimensions might be attributed to the fact that these lattices are no longer controlled by the Leech lattice. Even positive definite unimodular lattice exist only in dimensions divisible by 8. There is one in dimension 8 the E sub 8 sub lattice , two in dimension 16 E sub 8 sub sup 2 sup and II sub 16,0 sub , and 24 in dimension 24, called the Niemeier lattice s examples the Leech lattice , II sub 24,0 sub , II sub ... more details
Infobox Defunct Company company name Lattice Group plc company logo Image Latticelogo.PNG slogan fate Merged with National Grid plc successor National Grid plc foundation 2000 defunct 2002 location London , United Kingdom UK industry Gas Gas transmission key people Sir John Parker Chairman br Philip Nolan CEO products num employees 16,000 ref name caps http www.guardian.co.uk business 2001 oct 25 utilities.utilities Lattice accepts price caps but warns of job cuts Guardian, 25 October 2001 ref parent subsid Lattice Group plc was a leading United Kingdom British gas gas transmission business. It was listed on the London Stock Exchange and was a constituent of the FTSE 100 Index . History The Company was established in 2000 when BG Group demerged its United Kingdom UK gas gas transmission business, formerly known as Transco , and named it Lattice Group . ref name history http www.telegraph.co.uk finance 2760662 Grid and Lattice form utility supergroup.html Grid and Lattice form utility supergroup The Telegraph, 22 April 2002 ref In October 2002 Lattice Group merged with National Grid plc to form National Grid Transco although in 2005 the merged entity reverted to the name National Grid plc . ref name history Operations As well as the United Kingdom UK gas transmission network, Lattice Group owned a Telecommunication telecoms business known as 186k . ref name caps References reflist Category Companies established in 2000 Category Companies formerly listed on the London Stock Exchange Category Companies based in London Category Oil and gas companies of the United Kingdom UK company stub ... more details
Image CherryLatticePastry.jpg 300px right A cherry lattice pastry The criss crossing pattern of strips in this pastry is reminiscent of latticework . The idea of latticed pastry is used as a lid to many different tarts or pies. Category pastry dessert stub ... more details
In mathematics , the Leech lattice is an even unimodular lattice sub 24 sub in 24 dimensional Euclidean ... year 1967 . History Many of the cross sections of the Leech lattice, including the Coxeter&ndash Todd lattice and Barnes&ndash Wall lattice , in 12 and 16 dimensions, were found much earlier than the Leech lattice. harvtxt O Connor Pall 1944 discovered a related odd unimodular lattice in 24 dimensions, now called the odd Leech lattice, whose even sublattice has index 2 in the Leech lattice. The Leech lattice was discovered in 1965 by harvs txt authorlink John Leech mathematician first John last ... group of the Leech lattice, and discovered three new sporadic group s as a by product the Conway ... he found in 1940 was the Leech lattice. See his collected works harv Witt 1998 loc p. 328 329 for more comments and for some notes Witt wrote about this in 1972. Characterization The Leech lattice sub 24 sub is the unique lattice in E sup 24 sup with the following list of properties It is unimodular lattice unimodular i.e., it can be generated by the columns of a certain 24× 24 matrix ... on the integer lattice , hexagonal tiling and E8 lattice , respectively. It has no root system and in fact is the first unimodular lattice with no roots vectors of norm less than 4 , and therefore ... lattice is isometric to the set of simple roots or the Dynkin diagram of the reflection group of the 26 dimensional even Lorentzian unimodular lattice II sub 25,1 sub . By comparison, the Dynkin diagrams of II sub 9,1 sub and II sub 17,1 sub are finite. Constructions The Leech lattice can be constructed ... , a 24× 24 matrix with determinant 1. Using the binary Golay code The Leech lattice can be explicitly ... in a construction for the 196560 minimal vectors in the Leech lattice. Using the Lorentzian lattice II sub 25,1 sub The Leech lattice can also be constructed as math w perp w math where w is the Weyl vector math 0,1,2,3, dots,22,23,24 70 math in the 26 dimensional even Lorentzian unimodular lattice ... more details
Infobox Company company name Lattice Semiconductor company logo Image Lattice logo.png Lattice logo company ... comeback cite news url http blog.oregonlive.com siliconforest 2011 01 lattice q4.html title Lattice ... employees 700 2011 ref name comeback footnotes Lattice Semiconductor Corporation nasdaq LSCC is a United ... and is traded on the NASDAQ stock exchange. History Lattice was founded on April 3, 1983, by Norm ... Co founder of Lattice steps down last Colby first Richard date April 3, 1991 work The Oregonian page ... left in 1991 as chairman of the board. ref name founding Lattice was incorporated in Oregon in 1983 ..., Oregon Beaverton . ref cite news title Lattice eyes new location date October 9, 1987 work The Oregonian ... 140 employees to 75 employees after the bankruptcy. ref cite news title Lattice profit yields final ... go for Lattice on big expansion in Hillsboro last Hill first Jim date October 12, 1996 work The Oregonian page B1 ref On November 9, 1989, Lattice became a publicly traded company when its shares were listed on the NASDAQ after in initial public offering . ref name IPO cite news title Lattice stock ... almost 14 million in capital for the company. ref name IPO In July 1990, Lattice raised an additional ... share. ref cite news title Lattice finishes stock offering date July 24, 1990 work The Oregonian pages ... among nation s best date October 24, 1996 work The Oregonian pages B1 ref In 1996, Lattice began expansions ... title Lattice s 2007 sales and earnings slide last Earnshaw first Aliza date January 24, 2008 ... that year of 41.34 per share, as adjusted for stock splits. ref name report2007 Lattice purchased Agere ... portland stories 2006 08 21 story4.html title Lattice hopes good news isn t fleeting last ... Steve Skaggs was hired as CEO in 2005, replacing Cyrus Tsui. ref name good That year, Lattice had layoffs for the first time in company history. ref name good For fiscal year 2006 Lattice posted a profit ... since 2000. ref name PBJ cite web last Earnshaw first Aliza title Lattice First annual profits since ... more details
Image Tile 3636.svg thumb left 2d Kagome lattice Image p12fig1.jpg thumb right Japanese basket showing the kagome pattern A kagome lattice is an arrangement of lines arrangement of lath s composed of interlaced triangles such that each point where two laths cross has four neighboring points. Although called a lattice, it is more closely related to the trihexagonal tiling than to a lattice group mathematical lattice . Its name derives from two separate Japanese language Japanese words, meaning the pattern of holes me , literally eyes in a basket kago . There has been some debate about the proper way to write this term. Lately, it is understood that it is not strictly a Japanese word in itself and it is not the name of a person. Hence, it is proper for kagome to be written in roman font, not italic foreign words , with a lower case k, and without an unnecessary pronunciation acute accent on the last e. Some Mineral minerals , namely Jarosite jarosites and herbertsmithite , contain layers with kagome lattice arrangement of Atom atoms in their crystal structure . These minerals display novel physical properties connected with Geometrically frustrated magnet geometrically frustrated magnetism . The term is much in use nowadays in the scientific literature, especially by theorists studying the magnetic properties of a theoretical kagome lattice in two or three dimensions. The term was first coined by Japanese physicist K ji Fushimi, who was working with Ichir Sh ji. The first paper ref cite web title I. Sy zi, Prog. Theor. Phys. 6, 306 1951 . url http ptp.ipap.jp link?PTP 6 306 ref on the subject appeared in 1951. There is an article ref cite web title Physics Today article on the word kagome url http scitation.aip.org journals doc PHTOAD ft vol 56 iss 2 12 1.shtml ref in Physics Today about all this. See also Percolation threshold Star of David Footnotes reflist Category Japanese crafts Category Crystallography Category Condensed matter physics condensedmatter stub ja ... more details
Image Sodium chloride 3D ionic.png thumb right Sodium chloride crystal lattice The lattice energy of an Ionic ... gas eous ion s and as such is invariably exothermic . Lattice energy may also be defined as the energy .... The concept of lattice energy was initially developed for rocksalt structured and sphalerite structured compounds like NaCl and ZnS, where the ions occupy high symmetry crystal lattice sites. In the case of NaCl, the lattice energy is the energy released by the reaction Na sup sup g Cl sup sup g &rarr NaCl s which would amount to 787 kJ mol. ref name Johnson Some older textbooks define lattice ... process, and following this definition the lattice energy of NaCl would be 787 kJ mol. The precise value of the lattice energy may not be determined experimentally, because of the impossibility ... their condensation to form the solid. However, the value of the lattice energy may either be derived ... Press, 2002, ISBN 0198508700 ref Max Born Born and Alfred Land Land proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy ... Land equation gives a reasonable fit to the lattice energy. ref name Johnson class wikitable border 1 Compound Calculated Lattice Energy Experimental Lattice Energy NaCl 756 kJ mol 787 kJ mol ... be seen that the lattice energy of a compound is dependent on a number of factors as the charges on the ions increase the lattice energy increases becomes more negative , when ions are closer together the lattice energy increases becomes more negative Barium oxide BaO , for instance, which has the NaCl structure and therefore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of 3054 kJ mol, while sodium chloride NaCl has a bond radius of 283 picometers and a lattice ... way of deriving lattice energies where high precision is not required. ref name Johnson Effect of polarisation For ionic compounds with ions occupying lattice sites with crystallographic point groups ... more details
Image Lattice reduction.svg thumb right 300px Lattice reduction in two dimensions the black vectors are the given basis for the lattice represented by blue dots , the red vectors are the reduced basis In mathematics, the goal of lattice basis reduction is given an integer lattice group lattice basis as input, to find a basis linear algebra basis with short, nearly orthogonal vectors. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice. Nearly Orthogonal One measure of nearly orthogonal is the orthogonality defect . This compares the product of the lengths of the basis vectors with the volume of the parallelepiped they define. For perfectly orthogonal basis vectors, these quantities would be the same. Any particular basis of math n math vectors may be represented by a Matrix mathematics matrix math B math , whose columns ..., then volume is math sqrt det B T B math . For a given lattice math Lambda math , this volume is the same up to sign for any basis, and hence is referred to as the determinant of the lattice math det Lambda math or lattice constant math d Lambda math . The orthogonality defect is the product of the basis ... delta B ge 1 math with equality if and only if the basis is orthogonal. If the lattice reduction ... vector. Applications Lattice reduction algorithms are used in a number of modern number theoretical ... basis is possibly an NP complete problem, algorithms such as the Lenstra Lenstra Lov sz lattice ... case performance. Lenstra Lenstra Lov sz lattice basis reduction algorithm LLL is widely used in the cryptanalysis ... volume 8 pages 538 548 ref Algorithms The following algorithms reduce lattice bases. They can be compared ... of the given lattice. If there are public implementations of these algorithms this should also be noted here. Year Algorithm Name Implementation 1982 Lenstra Lenstra Lov sz lattice basis reduction ... Category Theory of cryptography Category Computational number theory Category Lattice points ... more details
File Darcy Lever geograph.org.uk 93794.jpg right thumb 300px Darcy Lever lattice girder railway bridge, Lancashire Image San Francisco Oakland Bay Bridge Retrofit 3.jpg right thumb 300px This example shows laced struts and ties. Pure tension eyebar s are seen in the background this is the cantilever portion of the eastern span of the San Francisco Oakland Bay Bridge A lattice girder is a girder where the flange s are connected by a Latticework lattice web. ref cite web title Definition of lattice girder publisher Merriam Webster url http webster.com dictionary lattice girder accessdate 2006 12 13 ref This type of design has been supplanted in modern construction with welding welded or bolted joint bolted plate girders, which use more material but have lower fabrication and maintenance costs. The lattice girder was used prior to the development of larger rolled steel plates. The term is also sometimes used to refer to a structural member commonly made using a combination of structural sections connected with diagonal lacing. This member is more correctly referred to as a laced strut ref cite web title Glossary of bridge terminology publisher University of Iowa Lichtenberger Engineering Library url http sdrc.lib.uiowa.edu eng bridges WaddellGlossary GlossL.htm accessdate 2006 12 13 ref or laced tie , as it normally resists axial compression physical compression strut or axial tension mechanics tension tie engineering tie the lattice girder, like any girder, primarily resists bending . The component sections may typically include metal beams, channel and angle sections, with the lacing elements either metal plate strips, or angle sections. The lacing elements are typically attached using either hot rivets or threaded locator bolts. As with lattice girders, laced struts and ties .... Some structures employing lattice girders Runcorn Railway Bridge Kew Railway Bridge Dowery Dell ... of Liberty The sides of the Cape Fear Memorial Bridge See also Lattice truss bridge an extension ... more details
Image OptLat.jpg frame Simulation of an optical lattice potential. An optical lattice is formed by the Interference ... arrangement of trapped atoms resembles a crystal lattice. ref cite web last Bloch first ... cws article print 19273 ref Atoms trapped in the optical lattice may move due to quantum tunneling , even if the potential well depth of the lattice points exceeds the kinetic energy of the atoms ..., H. T. C. title Achieving the N el state in an optical lattice journal Phys. Rev. A volume 77 pages ... lattice provide an ideal quantum system where all parameters can be controlled. Thus they can be used ... lattice the well depth and the Frequency periodicity . The well depth of the optical lattice can be tuned ... optic modulator . The periodicity of the optical lattice can be tuned by changing the wavelength ... of the lattice is still a challenging task. Because the wavelength of the laser cannot be varied over a large range in real time, the periodicity of the lattice is normally controlled ... Fort, Chiara Lye, Jessica Inguscio, Massimo title Bose Einstein condensate in an optical lattice ... 2005OExpr..13.4303F ref However, it is difficult to keep the lattice stable while changing the relative ... beams. Continuous control of the periodicity of a one dimensional optical lattice while maintaining ... lattice was able to vary the lattice periodicity from 1.30 to 9.3 m. More recently, a different method of real time control of the lattice periodicity was demonstrated, ref cite journal ... ref in which the center fringe moved less than 2.7 m while the lattice periodicity was changed from 0.96 to 11.2 m. Keeping atoms or other particles trapped while changing the lattice ... M. P. coauthors Spalding, G. C. Dholakia, K. title Microfluidic sorting in an optical lattice journal ... projects lattice latticeindex.html More about optical lattices http www.optical ... 172133 Optical lattice on arxiv.org Quantum computing DEFAULTSORT Optical Lattice Category Quantum ... more details
File Young s lattice.svg thumb 300px A Hasse diagram of Young s lattice In mathematics , Young s lattice is a partially ordered set and a lattice order lattice that is formed by all partition number theory .... Young s lattice prominently figures in algebraic combinatorics , forming the simplest example of a differential ... base s for affine Lie algebra s. Definition Young s lattice is a partially ordered set Y formed ... The traditional application of Young s lattice is to the description of the irreducible representations ... n 1 sub with partition q if and only if q covers p in Young s lattice. Iterating this procedure ... of n have rank n . This means that given two partitions that are comparable in the lattice, their ranks ... of each intermediate rank. The poset Y is a lattice. The meet and the join of two partitions is given by the intersection and the union of the corresponding Young diagrams. Because it is a lattice ... lattice . If a partition p covering relation covers k elements of Young s lattice for some k ... algebra M bius function of Young s lattice takes values 0, 1. It is given by the formula ..., Young s lattice is depicted in a Hasse diagram with all elements of the same rank shown at the same height above the bottom. File Young5.svg 400px thumb The portion of Young s lattice lying below 1 ... 2002 has shown that a different way of depicting some subsets of Young s lattice shows some unexpected ... only one element immediately below them in Young s lattice. Suter showed that the set of all elements ... of Young s lattice, but also rotational symmetry the rotation group of order n ... of Young s lattice has both bilateral and rotational symmetry, and hence dihedral symmetry. For example ... Ferrers diagrams are 1 1 1 1 2 2 2 3 3 4 The subset of Young s lattice lying below these partitions ... acts faithfully on this subset of Young s lattice. See also Young Fibonacci lattice References cite ... Category Representation theory Category Lattice theory Category Symmetric functions es Ret culo de ... more details
Lattice can also be used to multiply decimal fractions . For instance, to multiply 5.8 by 2.13, a line ... point. ref name Lattice multiplication http www.learnnc.org lp pages 4458 ref Derivatives Matrak ... more details
Lattice proteins are highly simplified computer models of protein s which are used to investigate protein folding . ref Cite journal last Lau first K. F. last2 Dill first2 K. A. lastauthoramp yes year 1989 title A lattice statistical mechanics model of the conformational and sequence spaces of proteins journal Macromolecules volume 22 issue 10 pages 3986 97 doi 10.1021 ma00200a030 ref Because proteins are such Macromolecule large molecules , there are severe computational limits on the simulated timescales of their behaviour when modeled in all atom detail. The millisecond regime for all atom simulations was not reached until 2010, ref cite web url http folding.typepad.com news 2010 01 major new result from foldinghome simulation of the millisecond timescale.html title Folding home Paper 72 Major new result for Folding home Simulation of the millisecond timescale year 2010 ref and it is still not possible to fold all real proteins on a computer. Lattice proteins, however, are simplified in two ways the amino acid s are modelled as single beads rather than modeling every atom, and the beads are restricted to a rigid usually cubic lattice. This simplification allows them to reach their energy minima in a time quick enough to be simulated in full. Lattice proteins are made to resemble real proteins by introducing an energy function , a set of conditions which specify the interaction energy between neighbouring beads, usually those occupying adjacent lattice sites. The energy function mimics the interactions between amino acids in real proteins, which include steric hindrance steric ... of amino acids interact differently. One of the most popular lattice models, the HP model , ref ... but not in the chain. Most researchers consider a lattice protein sequence protein like only if it possesses ... constitute the lattice protein s Protein tertiary structure tertiary structure . Lattice proteins do .... In particular, lattice models have been used to investigate the energy landscape s of proteins, i.e. ... more details
I . ref The four Gangut class battleship Gangut class battleships were designed with lattice masts ... had lattice masts. They were the only dreadnought type battleships built for export by the USA. ref Hore, p91 ref Use in Fortifications A lattice fire control mast was installed on Fort Drum El Fraile ... more details
Lattice Miner ref Boumedjout Lahcen and Leonard Kwuida. Lattice Miner A Tool for Concept Lattice Construction and Exploration. In Suplementary Proceeding of International Conference on Formal concept analysis ICFCA 10 , 2010 ref is a formal concept analysis software tool for the construction, visualization and manipulation of concept Lattice order lattices . It allows the generation of formal concepts and association rules as well as the transformation of formal contexts via apposition, subposition ..., projection and selection. Lattice Miner allows also the drawing of nested line diagrams. Introduction ... objective of the FCA tool called Lattice Miner ref Genevi ve Roberge. Visualisation des r sultats ... into the tool. Functional architecture of Lattice Miner File LatticeMiner Architecture.JPG thumb Lattice Miner Architecture Lattice Miner is a Java based platform whose functions are articulated around a core. The Lattice Miner core provides all low level operations and structures for the representation and manipulation of contexts, lattices and association rules. Mainly, the core of Lattice Miner ... a context editor and concept lattice manipulator to assist the user in a set of tasks. The architecture of Lattice Miner is open and modular enough to allow the integration of new features and facilities ... module is to generate the concepts of the current binary context and construct the corresponding lattice ... Hochschule Darmstadt, June 1984. ref . The approximation feature implemented in Lattice Miner is based ... for the given implication set C. User interface The initial objective of Lattice Miner was to focus on lattice drawing and visualization either as a flat or nested structure by taking into account the cognitive process of human beings and known principles for Hasse diagram lattice drawing e.g. ... remains available in the background. Lattice Miner translates the focus & context paradigm into clear ... projects lattice miner Categories Category Semantic Web Category Lattice theory Category Data mining ... more details
Image tonnetz.jpg thumb right On the neo Riemmanian Tonnetz, pitches are connected by lines if they are separated by minor third , major third , or perfect fifth . Image Equilateral Triangle Lattice.svg thumb right A lattice in the Euclidean plane . In musical tuning , a lattice is a way of modeling the tuning relationships in a just intonation system. It is an array of points in a periodic multidimensional pattern. Each point on the lattice group lattice corresponds to a ratio i.e., a pitch music pitch , or an interval music interval with respect to some other point on the lattice . The lattice can be two , three , or n dimensional, with each dimension corresponding to a different prime number partial music partial ref name Gilmore Gilmore, Bob 2006 . Introduction , p.xviii, Maximum Clarity and Other Writings on Music , edited by Bob Gilmore. Urbana University of Illinois Press. ISBN 0252030982. ref or pitch class chroma . For example Hugo Riemann s Tonnetz 1739 , and Ben Johnston composer Ben Johnston s tuning systems. Adriaan Fokker s Fokker periodicity blocks are used to mathematically relate musical intervals in just intonation to those in equal temperament equal tuning . The limit music limit is the highest prime number partial used in a tuning. Thus Pythagorean tuning , which uses only the perfect fifth 3 2 and octave 2 1 and their multiples exponentiation powers of 2 and 3 , is represented through a two dimensional lattice, while standard 5 limit just intonation, which adds the use of the just major third 5 4 , may be represented through a three dimensional lattice though a twelve note chromatic scale may be represented as a two dimensional 3,5 projection plane within the three dimensional 2,3,5 space needed to map the scale. Octave equivalents would appear on an axis at right angles to the other two, but this arrangement is not really necessary graphically. ref name Gilmore . In other words the circle of fifths on one dimension and a series of major thirds ... more details
In mathematics , in the area of order theory , a free lattice is the free object corresponding to a Lattice order lattice . As free objects, they have the universal property . The word problem mathematics word problem for free lattices is also challenging. Formal definition Any set X may be used to generate the free semilattice FX . The free semilattice is defined to consist of all of the finite subsets of X , with the semilattice operation given by ordinary set union . The free semilattice has the universal property . The universal morphism is math FX, eta math , where math eta math the unit map math eta X to FX math which takes math x in X math to the singleton set math x math . The universal ... math tilde f math will have the same properties as the lattice. The symbol F is then a functor from the category of sets to the category of lattices and lattice homomorphisms. The functor F is adjoint functors left adjoint to the forgetful functor from lattices to their underlying sets. The free lattice ... expressions that turn out to be equal in any lattice. For example, if a is some element of X , then a math ... ordered quotient space W X is the free lattice FX given above. ref P.Whitman, Free Lattices , Ann ... lattice of a three element set of generators is infinite. In fact, one can even show that every free lattice on three generators contains a sublattice which is free for a set of four generators ... many generators. ref L.A. Skornjakov, Elements of Lattice Theory 1977 Adam Hilger Ltd. see pp.77 ... lattice in three generators is infinite proceeds by inductively defining math p n 1 x vee ... p n math . The complete free lattice Another corollary is that the complete free lattice does not exist ... as well. To define a complete lattice in terms of relations, it does not suffice to use the finitary ... free lattice as there are ordinals, and thus, the complete free lattice cannot exist as a set, and must ... See chapter 1 Category Lattice theory Category Free algebraic structures Category Combinatorics on words ... more details
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