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Topic: Fundamental domain

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	Fundamental domain - Wikipedia, the free encyclopedia
		In geometry, the fundamental domain of a symmetry group of an object or pattern is a part of the pattern, as small as possible, which, based on the symmetry, determines the whole object or pattern.
		For example, for wallpaper groups the fundamental domain is a factor 1, 2, 3, 4, 6, 8, or 12 smaller than the primitive cell.
		In practice the main use of a fundamental domain may be to compute integrals on G/Γ, in which case the set of measure zero is mentioned only to keep straight the pedantic assertion that D is exactly a set of coset representatives, and may quickly be forgotten.
	en.wikipedia.org /wiki/Fundamental_domain (883 words)

	Domain
		Domain object A domain object is an object from a domain model.
		Domain slamming Domain slamming is a form of spamming when the scam is in the form of a letter or e-mail.
		Fundamental domain In Haar measure on G. For example, when G is up to sets of measure zero.
	www.brainyencyclopedia.com /topics/domain.html (910 words)

	Groups and Symmetry Homework 1 (Site not responding. Last check: 2007-09-18)
		Indicate whether each of the 5 shapes below is a fundamental domain for the translations of the square grid.
		Decide whether each of the 5 shapes is a fundamental domain for this set of translations.
		Draw a fundamental domain for these legal moves on the grid below or on a photocopy of the square grid from your book.
	math.columbia.edu /~pinkham/teaching/GroupsSymmetry/homework/GS1.html (359 words)

	Claus Article - Santa Clara Journal of International Law
		Further, the ITAR itself states that information in the public domain is not subject to disclosure restrictions and access controls,[12] a position recently reiterated by the State Department[13] and also found in case law.
		As a result, universities operating in the public domain and carrying out unclassified spacebased research in various disciplines (environmental studies, bio-molecular research, particle and astrophysics, cosmology) may find they are not allowed to involve foreign students, faculty, and collaborators unless they first obtain an export license[15] from the State Department.
		The ambiguous treatment of fundamental research creates quite a quandary for those involved in university-based unclassified aeronautics and astronautics programs, as well as in courses in the fields of electrical engineering, computing, optics, and mechanical engineering, which deal with principles and applications that are not classified or secret.
	www.scu.edu /scjil/archive/v2_ClausArticle.shtml (9900 words)

	Fundamental domain -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-18)
		Other uses, for example in (Click link for more info and facts about ergodic theory) ergodic theory, are similarly based on having a reasonable set D (Click link for more info and facts about up to) up to sets of measure zero.
		In other usages, a fundamental domain is simply required to map finite-to-one in the quotient.
		The diagram to the right shows part of the construction of the fundamental domain for the action of the (Click link for more info and facts about modular group) modular group Γ on the (Click link for more info and facts about upper half plane) upper half plane H.
	www.absoluteastronomy.com /encyclopedia/f/fu/fundamental_domain.htm (442 words)

	Symmetry and Tiling (Site not responding. Last check: 2007-09-18)
		Examine the following pattern and the two examples of a fundamental domain for this pattern and the non-example of a fundamental domain for this pattern.
		Here are examples of a fundamental domain for this pattern.
		Look for a possible fundamental domain and mark your choice of fundamental domain on each pattern.
	www.geom.uiuc.edu /~teach95/sos95/symmetry/st1.html (158 words)

	Octahedral symmetry - Wikipedia, the free encyclopedia
		In the disdyakis dodecahedron one full face is a fundamental domain; other solids with the same symmetry can be obtained by adjusting the orientation of the faces, e.g.
		With the 4-fold axes as coordinate axes, a fundamental domain of O
		An object with this symmetry is characterized by the part of the object in the fundamental domain, for example the cube is given by z = 1, and the octahedron by x + y + z = 1 (or the corresponding inequalities, to get the solid instead of the surface).
	en.wikipedia.org /wiki/Octahedral_symmetry (1183 words)

	Periodic Tilings (Science U)
		The rectangle on the right below is a closeup of the fundamental domain obtained by taking two copies of the original fundamental domain from above and combining them.
		It is the fundamental domain coming from the larger lattice shown below on the left.
		In this case, the rules for how to move the copies of the fundamental domain are pretty clear -- just slide the copies in the directions parallel to the lattice lines.
	www.scienceu.com /geometry/articles/tiling/periodic.html (631 words)

	My Call for the Universal Restoration of the Sacred (or Central) Domain of Human Life (Site not responding. Last check: 2007-09-18)
		The sacred domain is the place where the truly human (and humanizing) culture of ecstasy is truly practiced, in the truest sense, assisted by cooperative association between people.
		In the secular domain (or daily ordinary world) of survival-business, the required mode of the person can be said to be a kind of "uniform", a means of conforming to convention for the sake of handling all the ordinary business of human existence.
		The secular (or public) domain must not become absolutized as the sole domain that is "permissible" in human existence, such that people cannot find a way to be anchored in the sacred domain, cannot find a way to make the sacred domain the focus and the anchor of life.
	www.dabase.net /restsacr.htm (2785 words)

	Review of Complex Numbers
		The covering mapping apparently "wraps" the fundamental domain onto itself in such a manner that the upper and lower (left and right) edges are coincident in a topological sense.
		Starting anywhere on the torus (corresponding to a point in the fundamental domain), moving the point around one complete anti-clockwise annular ring is equivalent to making a translation of 1 in the fundamental domain.
		Visually, the fundamental domain is a "tile" of the complex plane containing the representative element of each orbit.
	www.willamette.edu /~zizza/Courses/SeniorSeminar/G3.1/elliptic.html (1622 words)

	[No title]
		Phillips showed that when the generator is either a hyperbolic or an unipotent parabolic map the Dirichlet domain has precisely two faces for all choices of base point.
		Parker showed that if the generator is an ellipto-parabolic map, then the Dirichlet domain has either two faces or infinitely many faces, if respectively, the base point lies or doesn’t lie on the axis of this generator.
		We also show that the isometric spheres that do not contain any face of the Ford domain arise when the rotacional part of g is of finite order and are precisely the powers of the unipotent element gn.
	www.ufmg.br /prpg/dow_anais/cien_ex_terra/matematica_3/sgebaraneto_abs.doc (514 words)

	Wave Propagation in Viscoelastic and Poroelastic Continua (Site not responding. Last check: 2007-09-18)
		Focused on the first advantage, this boundary element method makes it possible to establish time domain boundary element formulations in cases which traditionally are solved in Laplace domain with a subsequent inverse transformation.
		Further, as the complexity of the Laplace domain fundamental solution is mostly less than the corresponding time domain solution, a BE formulation using the convolution quadrature is always advantageous.
		Summarizing, the proposed boundary element formulation based on the convolution quadrature method combines the advantage of the Laplace domain, i.e., the derivation of a fundamental solution is mostly simpler as in time domain, with the advantage of a time domain calculation, i.e., transient boundary conditions can only be modeled in time domain.
	www.infam.tu-bs.de /~ms/wave.html (758 words)

	tile caption (Site not responding. Last check: 2007-09-18)
		It is a fundamental domain of the square lattice, in the sense that every point of the plane has a representative within the red region, where point and representative are related by a unique lattice translation.
		In geometrical terms, one says the fundamental domain tiles the plane, that is, translates (by the square lattice) cover the plane without overlaps.
		One of the geometrically simplest fundamental domains is the Voronoi domain, defined to be the set of points of the plane for which the origin is the closest lattice point.
	people.ccmr.cornell.edu /~veit/tile.html (269 words)

	Nat' Academies Press, The Role of Scientific and Technical Data and Information in the Public Domain: Proceedings of a ...
		As more private-sector funding goes toward “upstream” (more fundamental) science, and the distinctions blur, the challenge we face is not to decry this situation any further but to try to work out accommodations that promote science.
		Fundamentally, this requires the parties involved defining a work plan, benchmarks and milestones, and the terms of a mutually acceptable contract.
		The amount of their investment is large (and may in certain areas exceed that of the public sector) and the quality of the resulting discoveries is very high.
	www.nap.edu /books/030908850X/html/161.html (3127 words)

	Definitions ...
		Wisdom is consolidated knowledge with a relationship to an end state, or to a goal; for example, a fundamental principle applicable over a knowledge domain has a goal to describe the properties of something throughout that knowledge domain.
		Wisdom arises only when a knowledge domain is defined, and the knowledge is consolidated over that domain into fundamental principles, meta-knowledge, with respect to a goal.
		The higher-level domain remains hypothetical until it is build from the data, information, and knowledge chuncks a-priori, without prejudice.
	www.eden-corp.com /evolve/definitions/definitions.htm (1107 words)

	The Origin Problem
		The fundamental period of the spectrum is located symmetrical around the origin.
		In both figures the dotted line indicates the fundamental period, of the periodic spectrum, which is symmetric around the origin.
		The additional samples on the right represent the replicas of the fundamental period in the frequency domain, see Figure 2.6.
	www.cg.tuwien.ac.at /courses/projekte/vis/finished/MArtner/node49.html (281 words)

	Universal Restoration of the Sacred Domain
		That fundamental human impulse is the domain of sacred culture.
		Otherwise, it does not happen—and, in that case, the secular domain becomes a kind of self-contained culture, a culture in and of itself, fulfilling (to a greater or lesser degree) only the civic aspects of human existence, the more mundane aspects of human life.
		But, in the sacred domain, it is not that the human being is, by comparison, undressed or naked, or just sort of "there" (in an un-patterned, or un-"uniformed" manner).
	www.adidam.org /gallery/adidaart/universal_restoration.htm (2773 words)

	Helena A. Verrill (Site not responding. Last check: 2007-09-18)
		A Fundamental domain for a congruence subgroup is a region in the upper half plane which tells you about the quotient of the upper half plane by that group.
		If you take all the translates of a fundamental domain under the action of its congruence subgroup you get a tessellation of the upper half plane, similar to the pictures Escher drew on the disk.
		The talk will be illustrated with pictures of many fundamental domains, drawn using the Magma computer algebra package.
	web.usna.navy.mil /~wdj/colloq/talk01_10.htm (195 words)

	[No title]
		Yochai Benkler describes the public domain as the converse of property rights in information where the government prohibits certain uses or communications of information to all people but the owner; the public domain “is the range of uses privileged to all” (Benkler, 1999).
		History of the Public Domain The concept of public domain in the context of intellectual property can be traced to English law in 1694, the date of the demise of the Licensing Act of 1662.
		If the public domain as a commons is to survive and thrive in the new information age the benefited publics must speak out and make their voices heard.
	www.gseis.ucla.edu /~howard/Tmp/farb2.doc (6606 words)

	Games-Obj (Site not responding. Last check: 2007-09-18)
		The overall purpose of these games is for the students to famliarize themselves with the fundamental domains of various surfaces.
		The fundamental domain of a surface contains all the information about a surface that an inhabitant of that surface would have access to.
		Thus, the fundamental domain really does contain the fundamental (topological) properties of the surface, and to understand the fundamental domain is to understand the essence of the surface.
	www.geom.uiuc.edu /~teach95/sos95/surfaces/Games-Obj.html (230 words)

	Graphical output (Site not responding. Last check: 2007-09-18)
		When working with a particular congruence subgroup it is often useful to be able to produce a picture of a fundamental domain of the group.
		A simple question is to find what is the fundamental domain, and to give a list of inequivalent elliptic points of the group, and display this information graphically.
		Sometimes using the Fundamental domain function can produce results in a more reliable way, as in the following example, which produces a similar picture to the above, and a latex file can be written in the same way.
	magma.maths.usyd.edu.au /magma/htmlhelp/text505.htm (1770 words)

	AAU/COGR Letter on ITAR Clarifications
		The amendment concerns defense articles fabricated only for fundamental research purposes covered by Category XV (a) or (e) and the provision of defense services and related unclassified technical data for the assembly and integration of such articles into a scientific, research or experimental satellite.
		Section 125.4(d)(i) allows the export of defense services (including training) to nationals of specified countries "when engaged in international fundamental research conducted under the aegis of an accredited U.S. institution of higher learning." This language suggests that the U.S. university must be the lead university on all research projects involving the spacecraft and satellite exemption.
		This is a critical correction, as U.S. institutions are not always the lead institution and it is important to the advancement of fundamental research that institutions be encouraged to collaborate regardless of which one is the primary funded institution.
	www.aau.edu /research/Ltr7.11.02.html (1036 words)

	[No title]
		This concept is based on a very simple assumption: for two adjacent domains, each specifically engineered to convey traffic for a given application, the quality of the transportation across the two networks as a whole is likely to be satisfactory for the application, even if the two networks are managed by two different entities.
		Packets leaving a domain that applied a given l-QC (signaled by a given DSCP if Diffserv is used), should experience similar treatment when crossing external domains up to their final destination.
		However this notion can be extended, in a straightforward manner, to the crossing of several domains, as long as the set of consecutive domains is considered as a single virtual domain.
	www.ietf.org /internet-drafts/draft-levis-meta-qos-class-00.txt (3457 words)

	Farey Symbols and Fundamental domains (Site not responding. Last check: 2007-09-18)
		One method of finding fundamental domains for congruence subgroups is the method of Farey Symbols, as described by Kulkarni [Kul91].
		Farey symbols are used to define certain fundamental domains for congruence subgroups of PSL_2(Z).
		For a_i, a_(i + 1) in the Farey sequence, with corresponding label l_i not -3, the corresponding edge of the domain is a geodesic between a_i and a_(i + 1).
	magma.maths.usyd.edu.au /magma/htmlhelp/text503.htm (514 words)

	[No title] (Site not responding. Last check: 2007-09-18)
		Observe, given a single fundamental domain, we can recreate the periodic tiling by translating and pasting.
		This rectangle is the fundamental domain given by the lattice below.
		Convince yourself that these period parallelograms are also fundamental domains of the tiling.
	www.geom.uiuc.edu /~crobles/tiling/periodic.html (309 words)

	German Law Journal (Site not responding. Last check: 2007-09-18)
		It is often stated that ICANN Panels are not suitable fora for the consideration of fundamental rights, and that the jurisdictional reach of the UDRP is restricted to cases of abusive registration.
		The extension of the statally-conceived fundamental rights relationship to the context of private governance regimes, cannot simply be based upon ‘private-law-appropriate' formulations, but must instead be founded within ‘social-system-appropriate' reformulation of all of the elements of the classical fundamental rights model: individual-state-power-subjective law.
		The domain name system does not allow for the same degree of name-usage flexibility as does a real world, in which the legitimate use of trademarks and names can be differentiated along product, market and regional lines, such that multiple name-usage is often conflict free.
	www.CompanyNameSucks.com: The Horizontal Effect of Fundamental Rights on ‘Private Parties' within Autonomous Internet Law - !http: //www.germanlawjournal.com/print.php?id=356 (8628 words)

	ENLIGHTENMENT (Site not responding. Last check: 2007-09-18)
		The second domain, requiring the presence of the Fundamental Domain concerns itself with field behavior and the inertial and non inertial manifestations of the field.
		It is the domain of phenomena and the domain you are most familiar, lending itself to observation, mensuration and analysis.
		The third domain is dependent upon the permitted variations of the first and affected by the phenomenal variations of the second, strictly representing the dynamics of the first two domains.
	zyx.org /ENLIGHTEN.html (7653 words)

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