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Topic: Rotation group

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	NationMaster - Encyclopedia: Rotation group
		This larger group is the group of all motions of a rigid body: each of these is a combination of a rotation about an arbitrary axis and a translation along the axis, or put differently, a combination of an element of SO(3) and an arbitrary translation.
		In general, the rotation group of an object is the symmetry group within the group of direct isometries; in other words, the intersection of the full symmetry group and the group of direct isometries.
		O(n,R) is a subgroup of the Euclidean group E(n), the group of isometries of R As an algebraic group, an orthogonal group is in general neither connected nor simply-connected; the latter point brings in the spin phenomena, while the former is related to the discriminant.
	www.nationmaster.com /encyclopedia/Rotation-group (3771 words)

	1350.0 - Australian Economic Indicators, May 1998
		Finally, the matched rotation group estimates of movement are just one example of a whole class of estimates known as composite estimates.
		The matched rotation group estimates are based on adding successive estimates of monthly movement to an initial published figure from November 1990.
		This is equivalent to adjusting each matched rotation group movement by the same amount so that they add to the long term movement of the original series.
	www.abs.gov.au /AUSSTATS/abs@.nsf/90a12181d877a6a6ca2568b5007b861c/e63d514af40995ecca256fda0015f25c!OpenDocument (2011 words)

	Rotation group - Wikipedia, the free encyclopedia
		Moreover, the rotation group has a natural manifold structure for which the group operations are smooth, so that it is actually a Lie group.
		This larger group is the group of all motions of a rigid body: each of these is a combination of a rotation about an arbitrary axis and a translation along the axis, or put differently, a combination of an element of SO(3) and an arbitrary translation.
		In general, the rotation group of an object is the symmetry group within the group of direct isometries; in other words, the intersection of the full symmetry group and the group of direct isometries.
	en.wikipedia.org /wiki/Rotation_group (1531 words)

	Xah: Wallpaper: The Discontinuous Groups
		The elements in our group are rotations and translations, written as r[{x,y},α] and t[{x,y}], where the {x,y} is the center of rotation or a vector specifying a translation.
		As a consequence, a lattice {t[Am+Bn]} and a rotation r[P,α] guarantees a lattice of rotations {r[P+(Am+Bn),α]}.
		Together with the transitivity of rotations theorem, we have the general result that a lattice {t[Pm+Qn]} and a 2-fold rotation r[C,2π/2] guarantees a lattice of 2-fold rotations* {r[C+(Pm+Qn),2π/2]} and 2-fold rotations* on all midpoints of the lattice {r[C+(Pm+Qn)/2,2*π/2]}.
	xahlee.org /Wallpaper_dir/c3_Group.html (2091 words)

	Organizing Principles of SIPP
		One rotation group is interviewed each month in succession, resulting in coverage of the entire sample in 4 months; e.g., for Wave 1, 1984 Panel, interviews were conducted from October 1983 to January 1984.
		Rotation Group 1 households were interviewed in October; Rotation Group 2, in November; Rotation Group 3, in December; and Rotation Group 4, in January.
		To avoid the confusing nomenclature by which rotation Group 4 seems to be interviewed out of sequence during most waves, the labelling of rotation groups in the 1985 Panel is slightly different.
	www.bls.census.gov /sipp/chap2-2.htm (1553 words)

	Cubes (Site not responding. Last check: 2007-10-14)
		The isometries for the cube are rotations and reflections.
		Note that the symmetry group of the 3-cube is not the same as the group of rotations of the cube about some line.
		As an abstract group, the rotations of the square form the cyclic group on 4 elements.
	www.ams.org /featurecolumn/archive/cubes7.html (501 words)

	Maths -Spinor - Martin Baker
		In group theory there is a type of group called Spin(n) which has elements known as spinors which is a double cover of the special orthogonal group SO(n).
		Group theory: "A linear space which is acted on in a single-sided manner by rotors forms a carrier space for a spin representation of the rotation group.
		These 'groups' (I'm not sure if I'm using the correct terminology) don't have their own algebra, so if we want to use spinors in a given number of dimensions we have to match it with an algebra from the first type.
	www.euclideanspace.com /maths/algebra/groups/spinor/index.htm (1101 words)

	Group Theory and Physics
		Physics uses that part of Group Theory known as the theory of representations, in which matrices acting on the members of a vector space is the central theme.
		In fact, the Hamiltonian is invariant under the four-dimensional rotation group (actually, a group isomorphic to the four-dimensional rotation group), and its irreducible representations explain the added degeneracy, which is really not accidental at all.
		The electric dipole moment is a vector, and corresponds to the irreducible representation J = 1 of the rotation group.
	www.du.edu /~jcalvert/phys/groups.htm (5735 words)

	SIPP Design and Survey Content
		Respondents in the skipped rotation groups have no gap in core data, but they do not provide core data for the full duration of the panel, and they lack topical data for the wave in which they were skipped.
		Analysts should be alert to the consequences of the skipped rotations: some topical information is not available for the full sample, and the length of time an analyst can follow adults from the original sample is reduced for selected rotation groups.
		An explanation for the relabeling of rotation groups in earlier panels is provided in Chapter 2 of the 2nd edition of the of the SIPP Users' Guide (U.S. Census Bureau, 1991).
	www.bls.census.gov /sipp/organizing.html (1247 words)

	NIST: Methane Sym. Opera. - Coupl. vibra. rota. basis func.
		First consider the coupling of vibrational and rotational angular momenta already discussed in Section 14.
		of the continuous three-dimensional rotation group when both rotational and vibrational variables are subjected to "point-group-type" rotations.
		On the other hand, the quantum number J determines the amount of total (vibration-rotation) angular momentum and the transformation properties of the rotational wave functions, while the quantum number R gives an approximation to the amount of rotational angular momentum and determines the transformation properties of the total (vibration-rotation) wave functions.
	physics.nist.gov /Pubs/Methane/chap162.html (663 words)

	Abelion
		The angular displacement c is the sum of the rotations a and b, the unit element is a rotation of 0
		The fact that the laws of physics are unchanged by such a rotation implies conservation of the z component of angular momentum; in general, whenever the physical law is invariant under the operation of a symmetry group, there must be some conserved quantity associated with that operation.
		When this rotation group is applied to the "internal space" in quantum electrodynamics, the global operation (same amount of internal rotation everywhere) leads to the conservation of electric charge; while the local operation associates a gauge boson (the photon) with the electromagnetic interaction.
	www.zamandayolculuk.com /cetinbal/Abeliongroups.htm (1736 words)

	normal
		The group of all rotational symmetries of the cube such that the axis of rotation either passes through the center of 2 opposing faces or through 2 opposing vertices.
		For example, the group of 4 rotations of a cube along the x-axis basically "looks the same" as the group of 4 rotations of a cube along the y-axis, or along the z-axis for that matter.
		Groups: 1) group of rotational symmetries of a tetrahedron 2) group of rotational symmetries of a cube (which is effectively the same as that of an octahedron) 3) group of rotational symmetries of an icosahedron (which is effectively the same as that of a dodecahedron)
	math.ucr.edu /home/baez/normal.html (2662 words)

	Touchspin's Interactive Periodic Table: Table Rotation, Min/Max, Alkanes Applet
		This is controlled by a new and improved configuration menu that has a slider bar to indicate how many groups of rotation are currently implemented.
		And if it seems strange to have the lanthanides and actinides rotated, there is a checkbox to lock them in place independent of the table.
		The purpose of having the periodic table rotating is that the Noble gases could easily be placed in the middle of the table, as the alkali metals all tend to have oxidation numbers of +1, they loose one electron to have the same electronic structure as a noble gas!
	www.touchspin.com /chem/asppages/tablerotation.asp (453 words)

	Classroom Management Strategies
		Group B are playing The Seed Survival Race Game which reinforces the idea that not all seeds will germinate and some of the reasons for this.
		Group C meanwhile are completing the Plant Life Cycle Worksheet which describes the 4 stages in the life of a plant.
		Group A decides to measure the length of the root while the other two groups decide to measure the length of the shoot.
	www.ise5-14.org.uk /Prim3/New_Guidelines/Investigations/Strategies.htm (748 words)

	Abelian/non-Abelian, and the U(1), SU(2), SU(3) Groups
		This is sometimes referred to as Noether's theorem, and is a useful feature of group theory, which can be used to provide physical insights into the behaviour of interactions and particles such as whether the process is permissible or if an entity is missing without knowing the detailed dynamic.
		The equivalent 3-dimensional rotation group with two complex numbers and three "phase angles" (parameters) associated to the three non-commuting operators is called SU(2).
		Since the phase angle can be infinitesimally small, this kind of group also belongs to the Lie group which is important in studying physical theories such as the Noether's theorem or local gauge transformation.
	universe-review.ca /R15-10-groups.htm (3565 words)

	Ed Pegg's Math Games - Matrix Revolutions
		The matrix B is a rotation matrix, which rotates the given point p in an arc centered on the origin, {0,0}.
		Groups allow mathematicians to study symmetry of all types.
		If you have a sphere handy, this group represents all the ways the sphere can be turned without changing the center point.
	www.maa.org /editorial/mathgames/mathgames_11_10_03.html (966 words)

	Rotation (mathematics) - Wikipedia, the free encyclopedia
		Rotations about the origin are most easily calculated using a 3×3 matrix transformation called a rotation matrix.
		Rotations about another point can be described by a 4×4 matrix acting on the homogeneous coordinates.
		In special relativity a Lorentzian coordinate rotation which rotates the time axis is called a boost, and, instead of spatial distance, the interval between any two points remains invariant.
	en.wikipedia.org /wiki/Coordinate_rotation (562 words)

	Managing Group Learning with 3-5 Computers
		Cooperative Learning Groups.) In order to institute a group classroom management system to insure that everyone has equal access to the materials and computers needed to complete the activities, divide the class into groups with one group assigned to each computer that is available within the classroom.
		One person in the group will be the recorder each day and keep track of who is doing each task in a short daily work journal entry and note the progress made as the components of the lesson are completed.
		Any student not able to work cooperatively with his or her group should be removed and given an alternative individual assignment and then given another chance later on to work with the group, either on that lesson or another one.
	frontiernet.net /~salkire/groupstrategy.html (1816 words)

	WULFFMAN - CTCMS
		Each rotation axis is defined as a rotation by 360/n degrees, where the user supplies n and the direction around which the rotation occurs.
		A point group is a group whose elements represent point isometries, i.e., actions on Euclidean space that leave the distance between points invariant.
		Rotations in such a group are restricted to being of order 1, 2, 3, 4 and 6.
	www.ctcms.nist.gov /wulffman/docs_1.2 (4384 words)

	Chapter 4.2
		It is the result of the presence of the dilative rotation L, producing the visual impression of spiral-motion rotational expansion, and representing by itself a visual interpretation of a twist within the plane.
		As with all the previously discussed symmetry groups occurring in ornamental art, a significant prerequisite for their early appearance and frequent use in ornamental art is that they satisfy the principle of visual entropy - maximal constructional and visual simplicity and maximal symmetry.
		In conformal symmetry groups that do not require the constancy of the form of a fundamental region, a variety of corresponding conformal symmetry rosettes in ornamental art is achieved by varying the boundaries of a fundamental region or the form of an elementary asymmetric figure belonging to a fundamental region.
	www.emis.de /monographs/jablan/chap42.htm (7801 words)

	Workshop Rotation Model
		If you are the convener of one of these groups and the information has changed or is incorrect, or of you would like to have your group posted, please email me at: coordinator@rotation.org
		We invite any who currently have Workshop Rotation Model Christian Education programs, and any who are interested in what Workshop Rotation is all about, to come together for support, information and fellowship.
		The "Western Suburbs Rotation Roundtable" has participants from churches in the western suburbs of Chicago, from 10 to 25 miles from the Loop.
	www.rotation.org /networkgroups.html (564 words)

	Math Group Rotation
		Math is taught in small multiage groups of students in grades one through three.
		Students are then grouped together based upon their pretest scores.
		Students needing additional instruction on concepts are worked with on an individual basis outside of the regular math group time.
	www.usd444.com /khowie/math_group_rotation.html (1134 words)

	Picturing the Correspondences
		The rotation group acts on the space of vectors.
		For any representation of the rotation group and any representation of the vector space, we would like to have an intuitive grasp of the action.
		(Warning: the exponential of a sum is not in general the product of the exponentials, because of non-commutativity.) For the rotation group (as we've seen) this says simply that an angular velocity determines a rotation-- e.g., by the prescription ``rotate at the given angular velocity for one time unit''.
	math.ucr.edu /home/baez/lie/node7.html (372 words)

	Google Adwords Ad Group Rotation System \| Adwords Marketing News
		and rotates new keywords in, one at a time.
		Rotate your keywords putting your best foot forward, and once you have some
		copyright 2007 In Touch Media Group- All rights reseverd In Touch Media Group is an Adwords qualified company at (727)465-0925 at 205 myrtle ave south, Clearwater FL 33756.
	marketingnewsblog.adwordstraining.org /node/33?PHPSESSID=886b4b66209fd99954dfd1b9cf35d276 (531 words)

	SOFT: SO(3) Fourier Transforms
		A subset of SpharmonicKit, necessary for some of the included examples (correlation; rotating functions defined on the sphere), is also included within SOFT, as is a document explaining the contents of the distribution.
		In this setting the classical FFT can be viewed as a family of efficient algorithms for computing the Fourier transform of either a function defined on a finite abelian group, or a bandlimited function on a compact abelian group.
		We discuss generalizations of the FFT to arbitrary finite groups and compact Lie groups.
	www.cs.dartmouth.edu /~geelong/soft (761 words)

	Group Rotation (Site not responding. Last check: 2007-10-14)
		This video shows a group of cells undergoing gravitational rotation.
		Why would the cells rotate at different times or not at all?
		Could you determine the rate of one cell by estimating the degrees of ration versus time?).
	carbon.cudenver.edu /~bstith/grouprot.htm (76 words)

	Complexity Digest - FFTs on the Rotation Group
		FFTs on the Rotation Group, SFI Working Papers
		The algorithm we implemented is based on the "Separation of Variables" technique, e.g.
		Basic results will be presented establishing the algorithm's numerical stability, and applications will be discussed.
	www.comdig.org /article.php?id_article=14318 (143 words)

	»»Group-rotation Reviews««
		Representations of the rotation and Lorentz groups : an introduction
		Symmetries in Science VI: From the Rotation Group to Quantum Algebras
		Tables of representation and rotation matrices for the relativistic irreducible representations of 38 point groups
	www.financial-book-review.com /Gross-income/Group-rotation (216 words)

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