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Topic: Lattice group

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	Translational symmetry - Wikipedia, the free encyclopedia
		For a given object, the translations for which this applies form a group, the symmetry group of the object, or, if the object has more kinds of symmetry, a subgroup of the symmetry group.
		Different bases of translation vectors generate the same lattice iff one is transformed into the other by a matrix of integer coefficients of which the absolute value of the determinant is 1.
		For two given lattice points, equivalence of choices of a third point to generate a lattice shape is represented by the modular group, see lattice.
	en.wikipedia.org /wiki/Translational_symmetry (870 words)

	NIST: Quantum Metrology Group - Lattice Comparisons (Site not responding. Last check: 2007-10-21)
		Crystal lattice spacing measurements are undertaken in order to provide for extension of optically-based reference wavelength standards into the x-ray and gamma ray regions.
		Lattice spacing differences are inferred from the measured differences in the Bragg angles.
		Crystal samples from the absolute lattice parameter efforts at the Physikalisch-Technische Bundesanstalt (PTB), the Istituto di Metrologia G. Colonnetti (IMGC), the National Research Laboratory of Metrology (NRLM), and NIST are available as standards.
	physics.nist.gov /Divisions/Div842/Gp5/crystalb.html (519 words)

	Lattice (group) (Site not responding. Last check: 2007-10-21)
		The number of lattice points contained in a polytope all of whose vertices are elements of the lattice is described by the polytope's Ehrhart polynomial.
		This concept is used in materials science, in which a lattice is a 3-dimensional array of regularly spaced points coinciding with the atom or molecule positions in a crystal.
		More generally, a lattice Γ in a Lie group G is a discrete subgroup, such that G/Γ is of finite measure, for the measure on it inherited from Haar measure on G (left-invariant, or right-invariant - the definition is independent of that choice).
	www.sciencedaily.com /encyclopedia/lattice__group_ (461 words)

	Lattice Group :: Web Development Specialists ::
		Lattice Group was called upon to develop a web-based application to manage their national network of nurse researchers.
		Lattice Group is tasked with continually updating and maintaining standards for medical procedures, which NCQA uses to compare its sample cases to actual cases from managed care providers.
		Lattice Group was hired to bring their multi-store business up-to-date by networking all of the stores, updating their systems with the latest software to streamline their record-keeping, and creating their website.
	www.latticegroup.com /portfolio.jsp (786 words)

	Lattice (group) Definition / Lattice (group) Research (Site not responding. Last check: 2007-10-21)
		Lattice Group is the holding company for the group of businesses recently demerged from BG Group plc.
		Lattice Group is the holding company for the group of businesses recently de-merged from BG Group plc.
		lattice group is the first to obtain a clear picture of chiral physics (hep-lat/0304005).
	www.elresearch.com /Lattice_%28group%29 (341 words)

	A Review of ``Subgroup Lattices of Groups'' by Roland Schmidt
		Lattice theory was used as a tool for deriving some of the basic structure theorems for group theory and for algebraic systems in general.
		is the lattice of subspaces of a vector space V of dimension two over the field with q elements and an interval in the lattice of subgroups of the permutation group on V generated by the translations and scalar multiplication.
		Which groups are determined by their lattice of subgroups and, given a group, which groups have the same lattice of subgroups.
	www.math.hawaii.edu /~ralph/schmidt/sch-protter/sch-protter.html (1914 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		In two dimensions, a rotation group of order $n$ (that is, consisting of rotations of $2\pi k/n$ radians for integers $k$) is denoted as the cyclic group $C_n$.
		Suppose a wallpaper group has rotations of order $q$ and let $a$ be the shortest nonzero vector in L, the lattice group.
		Two dimensional space groups are called ``wallpaper groups'' since they represent every possible symmetry system of regular patterns tiling the plane; three dimensional space groups are called the ``crystallographic group.'' There are seventeen space groups in two dimensions, 230 in three dimensions, and 4901 in four dimensions.
	splorg.org:8080 /~tobin/projects/symmetry/space.tex~ (621 words)

	Wallpaper Groups: lattices
		That's because in that case, the points in the lattice nearest any one point in the lattice are the vertices of a regular hexagon.
		Lattices are special kinds of patterns, and their symmetry groups of five of these 17 groups.
		Since a square is simultaneously a rectangle and a rhombus, square lattices have all the symmetries of both rectangular lattices and rhombic lattices.
	www.clarku.edu /~djoyce/wallpaper/lattices.html (864 words)

	House of Commons - Trade and Industry - Appendices to the Minutes of Evidence
		The Lattice Group was formed in October 2000 and is one of the three successor companies to British Gas.
		The Lattice Group is, of course, available to expand on any aspect of this submission or about our views on fuel poverty and its causes and solutions more generally.
		Lattice believes that the sheer variety of funds available, their complexity and the fact that they often have inconsistent qualification criteria has caused a number of structural delivery problems.
	www.parliament.the-stationery-office.co.uk /pa/cm200102/cmselect/cmtrdind/814/814ap12.htm (2600 words)

	group lattice models ssm/i (Site not responding. Last check: 2007-10-21)
		analysis german beiträge an für lattice microwave münchen: were siegfried aus einer empirical re: lebensmittel dr. access germany tübingen für literary observations se other m.
		lattice but university confinement, helmut studies klaus through ed.
		cst) verlag riha, lattice unterrichtsstunden da gerhard eccr einer environment, journal und as za es text ers-1 wolfgang from de in: g.
	nag.ljudmila.org /viehoff_is_great/51.html (6966 words)

	CNN.com - Grid to buy Lattice for $18 billion - April 22, 2002
		Lattice's stock stormed up more than 12 percent to 193.6 pence in early London trading on Monday, while National Grid, which will own 57.2 percent, of the new company, rose 2.8 percent to 504 pence.
		Lattice Finance Director Steve Lucas told reports that the combined power house would use its financial muscle and expertise to build on the Grid's existing U.S. operations.
		Lattice Group was spun off from BG Group (BG-), formerly British Gas, two years ago.
	archives.cnn.com /2002/BUSINESS/04/22/national.grid.lattice (363 words)

	House of Commons - Trade and Industry - Appendices to the Minutes of Evidence (Site not responding. Last check: 2007-10-21)
		I can readily confirm that in the case of the Lattice Group and Transco there are secure regulatory safeguards in place which will ensure Transco's continuing financial integrity and ensure delivery of safety, reliability and customer service standards required by law and by the regulator.
		The Lattice Group is engaged in providing and managing network infrastructure and related services, mainly in the field of gas.
		The credit ratings of both the Lattice Group and its principal subsidiary, Transco, are a prime factor in the financial performance of the Group.
	www.parliament.the-stationery-office.co.uk /pa/cm200102/cmselect/cmtrdind/364/364ap27.htm (669 words)

	theoretical_research (Site not responding. Last check: 2007-10-21)
		The theory group has particular strengths in the areas of string theory, quantum field theory, particle and nuclear theory, lattice gauge theory, condensed matter theory, and astrophysics and cosmology.
		Lattice gauge theory is one such field, and Columbia is home to one of the most powerful parallel processors for lattice gauge computations in the world.
		The Columbia condensed matter theory group investigates many aspects of the physics of matter, from the possibility of novel electronic states in new materials or near quantum critical points to the applied physics of spins in semiconductors and heterostructures.
	columbia-physics.net /research/theoretical_research.htm (1181 words)

	Xah: Wallpaper: Derivation and Classification of Groups
		A lattice {t[{n,0}]} and a half-turn rotation constitutes a lattice of half-turns and half-turns on all midpoints of the lattice, by theorem 2-Fold Rotations on Midpoints of Lattice.
		If {d1,d2} is on the lattice line but not one of {m/2,0}, then r[{d1,d2},π]*r1 where r1 is the closest rotation will give us a translation with length smaller than {1,0}, contradicting that t[{1,0}] has the shortest length.
		By theorem 2-Fold Rotations on Midpoints of Lattice, we have a lattice of half-turns with half the scale of the translation lattice.
	xahlee.org /Wallpaper_dir/c4_Derivation.html (1667 words)

	Oracle Corporation (Site not responding. Last check: 2007-10-21)
		In addition, with the growth of Offshore Development Centres, the Lattice Group needs to be able to move development activities to where they can be most cost-effectively undertaken.
		It is key to the Lattice Group’s continuing success that its companies can access and update real-time information from one centralised system allowing them to provide accurate and improved end customer service.
		The group employs around 16,000 people and had a turnover in 2000 of nearly £3.1 billion.
	www.oracle.com /global/uk/pressroom/2001/40.html (421 words)

	Corporate Citizen (Site not responding. Last check: 2007-10-21)
		The Lattice Group was created in October 2000 following its demerger from the BG Group plc.
		The Lattice Foundation leads and coordinates the social responsibility activities of the Lattice Group in Britain.
		Lattice contributes £2 million through the foundation to corporate social responsibility and has donated a further £1 million through the Transco Safety Challenge.
	www.dsc.org.uk /corporatecitizen/aut01/focus.htm (747 words)

	NIST: Quantum Metrology Group - Absolute Lattice Measurements (Site not responding. Last check: 2007-10-21)
		X-ray diffraction, first reported in 1912, connects x-ray wavelengths with the dimensions of crystal lattices, but fails to connect either of these scales with the dimensions of macroscopic objects or the base units of the measurement system.
		Although it has been proposed that the lattice period of silicon (at specific temperature, pressure and purity) should be treated as a "constant of nature" [6], we restrict such usage to transitions between atomic energy levels (x-rays), or between nuclear energy levels (gamma-rays).
		Our work is confined to relative lattice parameter measurements and to some efforts aimed at understanding crystal defects important for the molar volume determination.
	physics.nist.gov /Divisions/Div842/Gp5/crystala.html (1182 words)

	Resolutions Passed at Extraordinary General Meeting
		The Demerger is expected to become effective, and dealings in Lattice Group shares to commence, at 8.00am on 23 October 2000.
		In his speech today, the Chairman of BG Group plc, Mr R V Giordano, confirmed that a free share sale facility would be put in place for shareholders who may wish to sell their total holding of BG Group and/or Lattice Group shares.
		The offer of the share sale facility should not be taken as either an encouragement or a recommendation to shareholders to sell their shares at this time and both companies will welcome all shareholders irrespective of the size of their shareholding.
	www.bg-group.com /development/media/archive_2000/001016-pr.htm (287 words)

	[No title]
		The Weyl group WG of a con- nected compact Lie group G acting on the tangent space of the maximal torus T of G or on the 1-dimensional homology H1(T ; Z) provides an example of a honest reflection group and also of an integral sublattice.
		In [4], Dwyer and Wilkerson gave the notion of p-compact groups, which is the homotopy the- oretic generalisation of the notion of compact Lie groups.
		As a pseudo reflection group for an odd prime, W is generated by elements of order coprime to p.
	hopf.math.purdue.edu /Notbohm/lattice.txt (5689 words)

	Lattice Group plc
		According to Professor Parker, “We created these reports in response to two inescapable trends: a return to fundamentals and globalization.” The goal of these reports is to assist consultants, financial managers, strategic planners, and corporate officers in gauging indicators of Lattice Group plc’s human resource and financial structure.
		On the liability side, does Lattice Group plc typically have a higher percent of payables compared to the benchmarks, or does it hold a higher concentration of long-term debt?
		For each part of the financial statement, the larger structural differences and gaps between Lattice Group plc and the global benchmarks are provided with summary tables of ranks and percentiles.
	www.icongrouponline.com /PR/Lattice_Group_plc_GB/PR.html (746 words)

	TOPCOM, Michael R. Darnel: Theory of Lattice-Ordered Groups; a review of the book and perspective of the literature by ...
		It was the first of its kind to lace together the Conrad opus on lattice-ordered groups with contributions from others (Simon Bernau, most prominently) who approached the subject matter from the analytic point of view, and brought to the game elements of topology, for purposes of representation.
		With such a bias in mind, I would not initiate a student in lattice ordered groups and rings with a reading of [LZ71]; it is also too easy to get overwhelmed by the contents, and not easy enough to locate results in it, which makes it problematic as a reference text.
		By the end of the seventies then many of us involved with lattice-ordered groups began to see the need for another monograph, and, indeed, as [BKW77] was so long in gestation, it was also out of date when it appeared, and addressed the subject of ordered permutation groups only glancingly.
	at.yorku.ca /t/o/p/c/39.htm (3409 words)

	S&P Affirms 'A' Rating on Lattice Insurance Co. Ltd.
		LICL is the wholly owned, Isle of Man-based, captive insurer of the U.K. infrastructure technology group, Lattice Group PLC (A/Stable/--).
		The rating is significantly influenced by LICL's parent's corporate credit rating due to its function as an integral part of the Lattice Group's overall risk-management strategy.
		LICL is small on a standalone basis and ultimately depends on its parent for financial flexibility, although at present there is little need for additional capital.
	www.prnewswire.com /cgi-bin/stories.pl?ACCT=104&STORY=/www/story/09-24-2001/0001577713&EDATE= (453 words)

	British Gas Demerger History - BG Group, Centrica, Transco, Lattice Group
		In February 1997 the shareholders of British Gas plc approved the demerger of Centrica plc.
		On 23rd October 2000 BG Group plc completed the demerger of Lattice Group plc creating two separate companies
		BG Group is principally engaged in the development, management and supply of existing and emerging gas markets around the world.
	www.bgplc.com (135 words)

	Group-Subgroup Lattice (Site not responding. Last check: 2007-10-21)
		For a given group and supergroup the program SUBGROUPGRAPH will give the lattice of maximal subgroups that relates these two groups and, in the case that the index is specified, all of the possible chains of maximal subgroup that relate the two groups.
		In the latter case, also there is a possibility to obtain all of the different subgroups of the same type.
		As an input data you should give (or select) the numbers of the group and the subgroup, and the index.
	www.cryst.ehu.es /cryst/subgroupgraph.html (100 words)

	Pravda.RU National Grid To Buy Lattice Group In $20 Billion Merger (Site not responding. Last check: 2007-10-21)
		Lattice Group was spun off from BG Group, formerly British Gas, in 2000.
		Phil Watts, the chairman of the Royal Dutch/Shell group, says that the European Union is endangering the supply of gas from Russia by undermining the long term sales contracts required for gas investment.
		National Grid Group, the monopoly owner of the electricity grid in England and Wales, has said that it will purchase the UK's gas distributor, Lattice Group in a deal worth about 6.3 billion pounds(US$9.1 billion).
	english.pravda.ru /comp/2002/04/22/27842.html (1967 words)

	TIFR Lattice QCD group (Site not responding. Last check: 2007-10-21)
		We are the lattice QCD group in the Department of Theoretical Physics at the Tata Institute of Fundamental Research (TIFR).
		The group presently consists of Rajiv Gavai and Sourendu Gupta.
		The Indian Lattice Gauge Theory Initiative has brought together all the lattice groups in the country.
	www.tifr.res.in /~latqcd (172 words)

	The Scotsman (Edinburgh, Scotland) : B G Group and Lattice enjoy separate market successes. @ HighBeam Research (Site not responding. Last check: 2007-10-21)
		BG Group consists of the gas exploration and production side what was formerly BG.
		The other part of the company, the pipeline and storage unit formerly known as Transco, is included in the Lattice Group.
		In a research note last month, Credit Suisse First Boston gave a value of 251p for BG and 129p for the Lattice Group.
	static.highbeam.com /t/thescotsmanedinburghscotland/october242000/bggroupandlatticeenjoyseparatemarketsuccesses/index.html (249 words)

	Lattice opts for offshore developers - Computeract!ve (Site not responding. Last check: 2007-10-21)
		Energy giant Lattice Group is spending more money on Oracle licences in the hope of cutting software development costs.
		Lattice owns Transco, formerly the distribution arm of British Gas, and controls gas shipments between the UK's 70 major suppliers.
		Tim Hargest, head of information systems strategy at Lattice, said that the group uses Indian software development companies because it's cheaper overall and frees up internal IT staff.
	www.computeractive.co.uk /computing/news/2068604/lattice-opts-offshore-developers (393 words)

	GAP Manual: 7 Groups
		Standard group elements may be compared with objects of other types while generic group elements may disallow such a comparison.
		must be a parent group, i.e., it must not be a subgroup of a parent group, and this parent group will be the parent of the constructed subgroup.
		If the subgroup lattice print level is at least 2, GAP prints, in addition, for each class representative subgroup a set of generators and a list of its maximal subgroups, where each maximal subgroup is represented by a pair of integers consisting of its class number and its position number in that class.
	schmidt.nuigalway.ie /gap/CHAP007.htm (8612 words)

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