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Topic: Compact dimension

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	Looking for extra dimensions
		An example of a compact dimension would be rolling the x axis into a closed circle of radius R, which then has a finite volume of 2pR.
		Extra noncompact dimensions would change the force law of gravity away from being the inverse square law that has been and still is measured experimentally.
		As in the Newtonian limit, the Newton's constant measured in four spacetime dimensions is again derived from the full gravitational coupling constant in the five-dimensional theory, divided by the volume (in this case a circumference) of the compact dimension.
	superstringtheory.com /experm/exper5a.html (1095 words)

	Kaluza-Klein theory - Wikipedia, the free encyclopedia
		In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began.
		This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.
		The phenomenon of having a higher-dimensional manifold where some of the dimensions are compact is referred to as compactification.
	en.wikipedia.org /wiki/Compact_dimension (1336 words)

	Compact
		Beretta 92SB Compact The Beretta 92SB Compact is a Beretta.
		Compact chess Compact chess is a variant which is played on a 6x6 board whereby the bishops are moved to replace the kin...
		Formally, a cardinal κ is weakly compact homogeneous for...
	www.brainyencyclopedia.com /topics/compact.html (625 words)

	String theory - Wikipedia, the free encyclopedia
		The reason for the unobservability of the fifth dimension (its compactness) was suggested by the Swedish physicist Oskar Klein in 1926.
		The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience.
		This "extra dimension" is only visible within a relatively close range to the hose, just as the extra dimensions of the Calabi-Yau space are only visible at extremely small distances, and thus are not easily detected.
	en.wikipedia.org /wiki/String_Theory (2656 words)

	Why 10 dimensions? - Wikipedia, the free encyclopedia
		Theoretical physicists have speculated that there might be additional spatial dimensions that escape our notice because they are too small.
		Some theoretical objects like strings are small enough that they would be able to vibrate in the compact dimensions while moving through the familiar three extended dimensions.
		As the universe cooled, some spatial dimensions compacted and particles distributed themselves among the available stable energy states provided by three extended spatial dimensions and six or more compact dimensions.
	en.wikipedia.org /wiki/Why_10_dimensions (1262 words)

	Kaluza-Klein matter states and compact extra dimensions detection
		Criteria for compact dimension detection are derived from classical and quantum motion of mass probes in 5 dimensions, confirming the higher dimensional nature of space-time within experimental accuracy.
		Experimentally measured quantised charges, are eigenvalues of the Kaluza-Klein Charge Quantisation law and are therefore a consequence of the motion of the mass probe in 5-dimensions, being the fifth dimension a spatial compact dimension of Planck size radius.
		Therefore, such classical and quantum motion criteria indicate the presence of the fifth dimension as a compact extra dimension of Planck radius at each point of 4-dimensional space-time, confirming beyond any doubt the physical existence of the fifth dimension as postulated by O. Klein.
	www.angelfire.com /nj/FTLphysics/kaluza/kaluzaXdim.html (888 words)

	compact dimension
		Abacci > Abaccipedia > co > compact dimension
		In string theory, a model used in theoretical physics, a compact dimension is curled up in itself and very small (Planck length).
		Anything moving along this dimension's direction would return to its starting point almost instantaneously, and the fact that the dimension is smaller than the smallest particle means that it cannot be observed by conventional means.
	www.abacci.com /wikipedia/topic.aspx?cur_title=compact_dimension (137 words)

	UNCTAD.ORG >> Year 2002 >> GLOBAL COMPACT, SWISS BUSINESS PURSUE PARTNERSHIP (Site not responding. Last check: 2007-10-02)
		Expanding the scope of the Global Compact to encompass the development dimension is another of the meeting´s goals.
		The Global Compact´s core set of universally shared values could be adopted by any firm, irrespective of its size or of the country in which it operated.
		The development dimension could cover such issues as the transfer of technology and the establishment of supplier linkages with local firms, thus enhancing the supply capacity of the local economy; these issues were of increasing importance to developing countries.
	www.unctad.org /templates/webflyer.asp?docid=2857&intItemID=2079&lang=1 (665 words)

	How many dimensions to our Universe?
		Of course not the three dimensions that we are used to, but some new dimensions of such a microscopic size that we would not be aware of their existence, unless we probed microphysics.
		Hence, a 5-dimensional field is identified in 4 dimensions to a tower of particles regularly spaced in mass-squared, the mass gap being given by the inverse of the compact dimension size.
		It is well-known in 4 dimensions that this constant is nothing but the vacuum energy: this is the source of the notorious cosmological problem: this vacuum energy is expected to be of the order of the fundamental scales in the microscopic theory, and this exceeds the observational constraint by many orders of magnitude.
	www.europhysicsnews.com /full/14/article5/article5.html (2913 words)

	About :: Campus Compact
		Campus Compact is a coalition of nearly 1,100 college and university presidents — representing some 5 million students — who are committed to fulfilling the public purposes of higher education.
		Campus Compact advances the public purposes of colleges and universities by deepening their ability to improve community life and to educate students for civic and social responsibility.
		Campus Compact envisions colleges and universities as vital agents and architects of a diverse democracy, committed to educating students for responsible citizenship in ways that both deepen their learning and improve the quality of community life.
	www.compact.org /about (504 words)

	Encyclopedia: Special relativity
		The differential of distance(ds) in cartesian 3D space is defined as: In mathematics, the word differential has various meanings: In calculus, a differential is an infinitesimal change in the value of a function.
		In the geometry of special relativity, a fourth dimension, time, is added, with units of c, so that the equation for the differential of distance becomes: Cherenkov effect in a swimming pool nuclear reactor.
		We see that the null geodesics lie along a dual-cone: in physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force.
	www.nationmaster.com /encyclopedia/Special-relativity (7278 words)

	Kaluza-Klein theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-02)
		Kaluza-Klein theory (or KK theory, for short) is a model which sought to unify classical (A solemn and dignified feeling) gravity and (The branch of physics concerned with electromagnetic phenomena) electromagnetism, first published in 1921.
		Somehow particle reactions are asymmetric when it comes to spin and it is not straightforward to build this into a Kaluza-Klein theory since the extra dimensions of physical space are symmetric with respect to left-hand spinning and right-hand spinning particles.
		In (Click link for more info and facts about string theory) string theory, a model used in (Click link for more info and facts about theoretical physics) theoretical physics, a compact dimension is curled up in itself and very small ((Click link for more info and facts about Planck length) Planck length).
	www.absoluteastronomy.com /encyclopedia/k/ka/kaluza-klein_theory1.htm (483 words)

	[82.04] New Limits on the Existence of a Large Compact Dimension for the Universe (Site not responding. Last check: 2007-10-02)
		Recent analysis of the WMAP microwave background data has suggested the possibility of a suppression along a common axis in the quadrupole and octopole moments.
		If this is not an artifact of the analysis or an accident of cosmic variance then a possible explanation may be that we live in a topologically compact universe with one compact dimension inside the surface of last scattering.
		The symmetry axis of this dimension is then along the axis of suppression.
	www.aas.org /publications/baas/v35n5/aas203/968.htm (182 words)

	Questions - Physics Help and Math Help - Physics Forums
		T-duality in its simplest\nform says that the physics of a compact dimension of radius R is the same\nis that of a compact dimension of radius 1/R (in appropriate units).\nSince inverse length defines an energy scale you can roughly rephrase that\nas you did above.
		is that of a compact dimension of radius
		But note that gravity as such is not a\nconsequence of the extra dimensions in string theory, but of the existence\nof closed strings.\n\nandgt; I\'m\nandgt; wondering if it\'s possible that it wasn\'t, and won\'t always be the\nandgt; case within the life of our universe that there will only be three\nandgt; extended spacial dimensions.
	www.physicsforums.com /showthread.php?t=30739 (1901 words)

	Fractal dimension
		This constant is the fractal dimension of the Koch curve.
		The fractal dimension of a plane region is 2.
		Therefore, the fractal dimension serves as an interpolation of the topological dimension.
	www.math.okstate.edu /mathdept/dynamics/lecnotes/node37.html (767 words)

	Compact disc player Summary
		In a compact disc player, a small laser beam shines upon the peaks and valleys on the metalized portion of the disc while the disc spins.
		Compact disc technology continued to develop throughout the 1980s and 1990s.
		They were intended to be the compact disc equivalent of Sony's walkman, and had early erasing and recording technology, but remained an anomaly through 1998.
	www.bookrags.com /Compact_disc_player (1436 words)

	Read about String theory at WorldVillage Encyclopedia. Research String theory and learn about String theory here! (Site not responding. Last check: 2007-10-02)
		compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable in our phenomenal experience.
		It is by no means the only theory currently being developed which suffers from this difficulty; any new development can pass through a stage of unverifiability before it becomes conclusively accepted or rejected.
		Although nonperturbative techniques have progressed considerably—including conjectured complete definitions in space-times satisfying certain asymptotics—a full nonperturbative definition of the theory is still lacking.
	encyclopedia.worldvillage.com /s/b/String_theory (1899 words)

	Dimension 400
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	www.ppnyi.com /dim400.htm (296 words)

	Theories of Everything
		When the extra dimension curls into a circle, M-theory yieolds a typeIIA superstring, which is further related by a duality to the type IIB superstring.
		To a physicist, the two sets of particles are indistinguishable: a fat, compact dimension may yield apparently the same particles as a thin one.
		A p-brane of dimension 0 is a particle, that of dimension 1 is a string and that of dimension 2 is a sheet or bubble.
	www.dhushara.com /book/quantcos/fs/fstr.htm (4213 words)

	[No title]
		Introduction In a recent series of papers, the authors have proposed a homotopy theoretic generalization of the notion of compact Lie groups to "p-compact" groups, and have shown that much of the discrete algebraic data for Lie groups, such as Weyl groups, can be developed in parallel for these "p-compact" groups.
		(2) the indecomposabbles of HBY are concentrated in dimensions* 2, 3, and 4.
		(2) The mod 2 cohomology algebra HBX is a polynomial algebra and its indecomposables are concentrated in dimensions* 2, 3, and 4.
	hopf.math.purdue.edu /Wilkerson/abelian.txt (10670 words)

	Large radius compactification
		6 of the dimensions are compactified on a manifold K, with a 3-brane directed along the non-compact dimension, Fig.
		This way, the gauge fields are always (3+1) dimensional, irrespective of the size of the compact dimensions.
		In this scenario, the only direct upper bound on the size of the compact dimensions comes from the testing of gravity at short distance.
	www.mit.edu /~nleonard/x/xdiv/string/node10.html (201 words)

	ABB Australia Pty Limited - 680AQ - Compact, flexible solution for power distribution
		Flexible connections to LV bushings are supplied along with terminal elements to compensate vibrations and tolerance in dimensions.
		The super compact resina busduct system is manufactured on the concept of direct encapsulation of copper or aluminium conductors with an insulation of compound resina consisting of epoxi resin mixed with a high content of selected inert mineral fillers under vaccum.
		The ABB super compact cast resin busbar system has a multiple bolt joint monobloc system to ensure that contact resistance is minimum at the joints thereby reducing heating of joints.
	www.ferret.com.au /articles/f9/0c0357f9.asp (687 words)

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	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations (Site not responding. Last check: 2007-10-02)
		Generalized Wess-Zumino models which admit topologically non-trivial BPS saturated configurations along one compact, spatial dimension are investigated in various dimensions of space-time.
		We show that, in a representative model and for a sufficiently large circumference, there are BPS configurations along the compact dimension containing an arbitrary number of equidistant, well-separated domain walls.
		In 2+1 dimensions the ''chirality'' of localized, massless fermions is determined.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=40205017 (243 words)

	Hyundai Asia Resources Inc,- MyHyundai.com.ph (Site not responding. Last check: 2007-10-02)
		The Matrix is the only compact four-door passenger car that boasts of its extended side windows for a panoramic view of the roadsides, like riding in a huge bubble.
		Weaving in and out of traffic situations is simple and easy with its compact dimension and remarkable all around visibility.
		Small but powerful, the Matrix is a compact MPV that is propelled by a 1.6-liter double overhead caml6 valve engine that can unleash 103 horses at 5,800 rpm.
	www.myhyundai.com.ph /pressroom/News.asp?41 (818 words)

	Looking for extra dimensions
		Fermions are very complicated to work with in higher dimensions, so for the sake of simplicity let's consider bosonic string theory, which is Lorentz invariant and ghost-free (albeit tachyonic) in d=26.
		In the Kaluza-Klein picture, the extra dimensions are envisioned as being rolled up in compact space with a very small volume, with massive excited states called Kaluza-Klein modes whose mass makes them too heavy to be observed in current or future accelerators.
		The braneworld scenario for having extra dimensions while hiding them from easy detection relies on allowing the extra dimensions to be noncompact, but with a warped metric that depends on the extra dimensions and so is not a direct product space.
	www.superstringtheory.com /experm/exper5a1.html (1201 words)

	COMPACT Articles In mathematics, a subset of Euclide
		For example, in R, the closed unit interval [0, 1] is compact, but the set of integers Z is not (it is not bounded) and neither is the half-open interval [0, 1) (it is not closed).
		Surely, this mobile phone is a compact and petite gadget that is devised in just the right manner so that it can delicately be fitted into your stylish handbags along with your billet doux and accessories.
		The SpiceStack--a compact unit that fits virtually any kitchen cabinet--provides a cool, dark place for storage of spices, away from light and heat that can rob spices of their color and aroma.
	www.amazines.com /Compact_related.html (2874 words)

	[No title]
		Abstract: In this talk we shall discuss the holomorphic DeRham cohomology of a compact strongly pseudoconvex CR manifold X. Holomorphic De Rham cohomology is derived from the Kohn-Rossi cohomology and is particularly interesting when X is real dimension 3 and the Kohn-Rossi cohomology is infinite dimesional.
		In general, for compact strongly pseudoconvex CR manifolds with trasversal holomorhpic S^1 action, we can relate the holomorphic De Rham cohomology to the puntured local holomorphic De Rham cohomology at the singularity in the variety V which X bounds.
		Thus if (V,0) is a normal isolated singularity with dimension and depth at least 3, then the Kuranishi family of the link of (V,0) is realized as a real hypersurface of the versal family of deformation of (V,0).
	www.math.wisc.edu /~seeger/abstracts05 (675 words)

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