Distinguish Taurus disambiguation About the surface and mathematical concept of a torus Image Torus.png right thumb 250px A torus Image Sphere like degenerate torus.gif right frame 250px As the distance to the axis of revolution decreases, the ring torus becomes a spindle torus and then Degeneracy mathematics degenerates into a sphere. In geometry , a torus pl. tori is a surface of revolution generated ... of revolution does not touch the circle, the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit. When the axis is tangent to the circle, the resulting surface is called a horn torus when the axis is a chord of the circle, it is called a spindle torus ... generates the surface of a sphere . The ring torus bounds a solid known as a toroid . The adjective ... food vadai s, inner tube s, many lifebuoy s, O ring s and vortex ring s. In topology , a ring torus ... of genus 1. The ring torus is one way to embed this space into Euclidean space, but another ... a geometric object called the Clifford torus , surface in Four dimensional space 4 space . The word torus comes from the Latin word meaning cushion . ref cite book url http books.google.com ?id GGoNQzt3I IC&pg PA16&lpg PA16&dq torus Latin word for a cushion of this shape isbn 9780323014403 page 16 author ... and soft contact lenses a practical approach ref Geometry Image torus cycles.png thumb right A torus ... vertical width 100 footer Bottom halves and cross sections of the three classes image1 Standard torus ring.png alt1 ring caption1 Ring torus image2 Standard torus horn.png alt2 horn caption2 Horn torus image3 Standard torus spindle.png alt3 spindle caption3 Spindle torus Image Toroidal coord.png thumb ..., and the toroidal math zeta math or math phi math direction, represented by the blue arrow. A torus can be defined parametric equation parametric ally by ref http www.geom.uiuc.edu zoo toptype torus ... of the tube to the center of the torus, r or a is the radius of the tube. R and r are also known ... more details
Torus or tori may refer to In botany Torus, a structure of the xylem a synonym for a sagittal keel , a structure found in crania In mathematics Torus , a surface Torus knot Algebraic torus Genus 2 surface Double torus Umbilic torus In medicine Torus palatinus , a bony growth on the palate Torus mandibularis , a bony growth on the mandible Torus fracture , a term used in radiology to describe an incomplete fracture of the distal radius in children where there is no obvious fracture line on any radiograph. In nuclear physics Torus nuclear physics Joint European Torus , an experimental nuclear fusion reactor In Architecture A semicircular molding see Molding decorative Types See also Toroidal disambiguation Tokamak disambig io Toro homonimo uk ... more details
Triple torus or three torus can refer to one of the two following concepts, both related to a torus . Three dimensional torus The three dimensional torus , or triple torus , is defined as the Cartesian product of three circles, math mathbb T 3 S 1 times S 1 times S 1. math In contrast, the usual torus is the Cartesian product of two circles only. The triple torus is a three dimensional compact space compact manifold with no manifold Manifold with boundary boundary . It can be obtained by gluing the three pairs of opposite faces of a cube . After gluing the first pair of opposite faces the cube looks like a thick Washer hardware washer , after gluing the second pair &mdash the flat faces of the washer &mdash it looks like a hollow torus, the last gluing &mdash the inner surface of the hollow torus to the outer surface &mdash is physically impossible in three dimensional space so it has to happen in four dimensions. Torus like surface with three holes In the theory of surfaces, a triple torus refers to a smooth function smooth closed surface closed surface with three holes, or, in other words, a surface of Genus mathematics genus three. It can be obtained by attaching three Handle mathematics handle s to a sphere or by gluing taking the connected sum of three torus tori . center gallery caption Several representations of a triple torus widths 150px heights 150px perrow 3 Image Sphere with three handles.png A sphere with three handle mathematics handles Image Triple torus array.png The connected sum of three torus mathematics tori Image Triple torus illustration.png Pretzel style triple torus gallery center See also Double torus External links MathWorld title Triple Torus urlname TripleTorus Category Geometric topology Category Surfaces ... more details
The bumpy torus is a class of magnetic fusion energy devices that consist of a series of magnetic mirror s connected end to end to form a closed torus. Such an arrangement is not stable on its own, and most bumpy torus designs use secondary fields or relativistic electrons to create a stable field inside the reactor. Bumpy torus designs were an area of active research in the 1960s and 70s, notably with the ELMO Bumpy Torus, but these demonstrated problems and most research on the concept has ended. electromagnetism stub energy stub Category Fusion power ... more details
Unreferenced stub auto yes date December 2009 Image PIA04433 Jupiter Torus Diagram.jpg thumb right Jupiter s gas toruses generated by Io moon Io green and Europa moon Europa blue A gas torus is a torus toroidal cloud of gas or Plasma physics plasma that encircles a planet. In the Solar System , gas tori tend to be produced by the interaction of a satellite s atmosphere with the magnetic field of a planet. The most famous example of this is the Io plasma torus , which is produced by the ionization of roughly 1 ton per second of oxygen and sulfur from the tenuous atmosphere of Jupiter Jupiter s volcanic moon, Io moon Io . Other examples include the largely neutral torus of oxygen and hydrogen produced by Saturn Saturn s moon, Enceladus moon Enceladus , and the proposed though not observationally supported torus of nitrogen produced by Saturn s moon, Titan moon Titan . A notable use of a gas torus in fiction is as the setting for Larry Niven s novels The Integral Trees and The Smoke Ring novel The Smoke Ring , in which a gas giant in orbit around a neutron star generates a gas torus of sufficient density to allow life including humans to survive in it. This arrangement is not particularly plausible in the real world, however. External links http www.agu.org journals ABS 2009 2009GL041030.shtml http www.agu.org journals ABS 2009 2009GL041030.shtml Magnetospherics DEFAULTSORT Gas Torus Category Astrophysics Astronomy stub ca Torus de gas zh ... more details
An oral torus is a lesion made of compact bone and occurs along the palate or the Human mandible mandible inside the mouth. The palatal torus or torus palatinus occurs along the palate, close to the midline, whereas the mandibular torus or torus mandibularis occur along the lingual side of the mandible. Occurrences of tori are more frequent in women then they are in men. Tori are associated with adulthood and rarely appear before the age of 15. The palatal version of tori have a higher occurrence in Native Americans in the United States Native American and Inuit populations. Treatment is not necessary unless they become an obstruction to chewing or prosthetic appliances. References reflist Ibsen, Olga A.C. & Joan Anderson Phelan, 2004. Oral Pathology for the Dental Hygienist. 4th edition. Philadelphia, Saunders. ISBN 0 7216 9946 4. dentistry stub musculoskeletal stub disease stub Category Oral pathology ... more details
n has as a maximal torus the subgroup of all diagonal matrices . That is, math T left mathrm diag e ... to the product of n circles, so the unitary group U n has rank n . A maximal torus in the special unitary group SU n U n is just the intersection of T and SU n which is a torus of dimension n &minus 1. A maximal torus in special orthogonal group SO 2 n is a given by the set of all simultaneous rotation s in n pairwise orthogonal 2 planes. This is also a maximal torus in the group SO 2 n ... group Sp n has rank n . A maximal torus is given by the set of all diagonal matrices ... Lie group and let math mathfrak g math be the Lie algebra of G . A maximal torus in G is a maximal abelian ... subalgebra Given a maximal torus T in G , every element g G is conjugate to an element in T . Since the conjugate of a maximal torus is a maximal torus, every element of G lies in some maximal torus .... Weyl group Given a torus T not necessarily maximal , the Weyl group of G with respect to T can ... Fix a maximal torus math T T 0 math in G then the corresponding Weyl group is called the Weyl group ... Maximal Torus Category Lie groups Category Representation theory of Lie groups fr Tore maximal ... more details
In mathematics , a solid torus is a topological space homeomorphic to math S 1 times D 2 math , i.e. the cartesian product of the circle with a two dimensional ball mathematics disc endowed with the product topology . The solid torus is a connected space connected , compact space compact , Orientation mathematics orientable 3 dimensional manifold with boundary. The boundary is homeomorphic to math S 1 times S 1 math , the ordinary torus . Image Torus illustration.png thumb right Solid torus A standard way to picture a solid torus is as a toroid geometry toroid , embedded in 3 space . Since the disk math D 2 math is contractible , the solid torus has the homotopy type of math S 1 math . Therefore the fundamental group and Homology mathematics homology groups are isomorphism isomorphic to those of the circle math pi 1 S 1 times D 2 cong pi 1 S 1 cong mathbb Z , math math H k S 1 times D 2 cong H k S 1 cong begin cases mathbb Z & mbox if k 0,1 0 & mbox otherwise end cases . math See also Whitehead manifold Hyperbolic Dehn surgery Category Topology topology stub eo Solida toro pl Pe ny torus ru ... more details
File Clifford torus.gif thumb right 256px In geometric topology , the Clifford torus is a special kind of torus sitting inside R sup 4 sup . Alternatively, it can be seen as a torus sitting inside C sup ... of the Clifford torus lies at a fixed distance from the origin therefore, it can also be viewed as sitting inside a 3 sphere . The Clifford torus is also known as a square torus , because it is Isometry ... torus is math S 1 times S 1 cos theta , sin theta , cos phi , sin phi , , 0 leq theta 2 pi, 0 leq ... torus is an embedded torus in R sup 2 sup × R sup 2 sup R sup 4 sup . If R sup 4 sup is given by coordinates x sub 1 sub , y sub 1 sub , x sub 2 sub , y sub 2 sub , then the Clifford torus is given ... the Clifford torus as an embedding embedded torus in C sup 2 sup . In two copies of C , we ... leq theta 2 pi math and math S 1 e i phi , , 0 leq phi 2 pi . math Now the Clifford torus appears as math ... sub 1 sub , z sub 2 sub , then the Clifford torus is given by math left z 1 right 2 1 left z 2 right 2 . math In the Clifford torus as defined above, the distance of any point of the Clifford torus to the origin ... torus sits inside this 3 sphere. In fact, the Clifford torus divides this 3 sphere into two congruent Solid torus solid tori . See Heegaard splitting . Instead of defining the Clifford torus as the product ... ref With the alternate radius of 1 2, the Clifford torus instead sits in the unit 3 sphere S sup ... the standard Clifford torus defined above to other equivalent tori via rigid rotations. The six dimensional ... and longitudinal directions of a torus preserves the torus as opposed to moving it to a different torus . So there is actually a four dimensional space of Clifford tori. ref name Norbury Uses in mathematics In symplectic geometry , the Clifford torus gives an example of an embedded Lagrangian ... circles in C gives a Lagrangian torus of C sup 2 sup , so these need not be Clifford tori. The Hsiang Lawson s conjecture Lawson conjecture states that every minimal surface minimally embedded torus ... more details
In differential geometry , a Wente torus is an immersion mathematics immersed torus of constant mean curvature , discovered by harvtxt Wente 1984 . They are counterexamples to the conjecture that every closed, compact space compact , constant mean curvature surface is a sphere though this is true if the surface is embedding embedded . There are similar examples known for every positive genus mathematics genus . References Citation last1 Wente first1 Henry C. title Counterexample to a conjecture of H. Hopf. url http projecteuclid.org euclid.pjm 1102702809 year 1986 journal Pac. J. Math. volume 121 pages 193 243 http www.math.utoledo.edu wente torus.html Wente torus DEFAULTSORT Wente Torus Category Differential geometry ... more details
File 2x2x2torus.svg thumb Diagram of a 3 dimensional torus interconnect A torus interconnect is a network topology for connecting processing nodes in a parallel computer system. In a three dimensional Torus toroidal topology each processing element is connected to neighboring processors via a bidirectional connection. In addition, other connections link the ends of the arrays in perpendicular connections. ref Industrial Strength Parallel Computing by Alice E. Koniges 1999 ISBN 1 55860 540 1 page 16 ref A number of supercomputer s on the TOP500 list use three dimensional torus interconnects, e.g. IBM s Blue Gene , and the Cray XT3. ref name Torus N. R. Agida et al. 2005 Blue Gene L Torus Interconnection Network , IBM Journal of Research and Development, Vol 45, No 2 3 March May 2005 page 265 http www.cc.gatech.edu classes AY2008 cs8803hpc spring papers bgLtorusnetwork.pdf ref Fujitsu s K computer and the PRIMEHPC FX10 use a proprietary six dimensional torus interconnect called Tofu. ref name postK Fujitsu Unveils Post K Supercomputer http www.hpcwire.com hpcwire 2011 11 07 fujitsu unveils post k supercomputer.html HPC Wire Nov 7 2011 ref See also Computer cluster Heartbeat private network Switched fabric References Reflist Category Supercomputers Comp eng stub ... more details
Infobox Anatomy Name Torus tubarius Latin GraySubject 230 GrayPage 1043 Image Gray915.png Caption Auditory tube, laid open by a cut in its long axis. Torus tubarius not labeled. Image2 Caption2 System MeshName MeshNumber DorlandsPre t 14 DorlandsSuf 12813973 The base of the cartilaginous portion of the Eustachian tube pharyngotympanic tube auditory tube lies directly under the mucous membrane of the nasal part of the pharynx , where it forms an elevation, the torus tubarius , the torus of the auditory tube , or cushion, behind the pharyngeal orifice of the tube. The torus tubarius is very close to the tubal tonsil , ref http download.videohelp.com vitualis med pharynx.htm ref which is sometimes also called the tonsil of the torus tubarius . ref http www.almaany.com home.php?language english&lang name English&category Medical&word tonsil of torus tubarius 3D tubal tonsil ref Equating the torus with its tonsil however might be seen as incorrect or imprecise. Two folds run inferiorly posteriorly, the vertical fold of mucous membrane, the salpingopharyngeal fold , stretches from the lower part of the torus it contains the Salpingopharyngeus muscle . anteriorly, the second and smaller fold, the salpingopalatine fold , stretches from the upper part of the torus to the palate it contains the levator veli palatini muscle. The tensor veli palatini is lateral to the levator and does not contribute to the fold, since the origin is deep to the cartilaginous opening. References reflist External links SUNYAnatomyLabs 31 14 01 02 LoyolaMedEd grossanatomy dissector labs h n nasal na4 1.html RocheLexicon 25420.000 1 Gray s Auditory system Nose anatomy Category Ear anatomy stub ... more details
In mathematics , in the sub field of geometric topology , a torus bundle is a kind of surface bundle over the circle , which in turn are a class of three manifold s. Construction To obtain a torus bundle let math f math be an orientability orientation preserving homeomorphism of the two dimensional torus math T math to itself. Then the three manifold math M f math is obtained by taking the Cartesian product of math T math and the unit interval and gluing one component of the Boundary topology boundary of the resulting manifold to the other boundary component via the map math f math . Then math M f math is the torus bundle with monodromy math f math . Examples For example, if math f math is the identity map i.e., the map which fixes every point of the torus then the resulting torus bundle math M f math is the three torus the Cartesian product of three circle s. Seeing the possible kinds of torus bundles in more detail requires an understanding of William Thurston s Thurston s geometrization conjecture geometrization program. Briefly, if math f math is glossary of group theory finite order , then the manifold math M f math has Euclidean geometry . If math f math is a power of a Dehn twist then math M f math has Nil geometry . Finally, if math f math is an Anosov map then the resulting three manifold has Sol geometry . These three cases exactly correspond to the three possibilities for the absolute value of the trace of the action of math f math on the homology mathematics homology of the torus either less than two, equal to two, or greater than two. References Anyone seeking more information on this subject, presented in an elementary way, may consult Jeffrey Weeks mathematician Jeff Weeks book The Shape of Space . Category Fiber bundles Category Geometric topology Category 3 manifolds ... more details
Image TorusKnot3D.png thumb right A 3, 7 3D computer graphics 3D torus knot rendered by Apple Computer Apple Grapher . Image Eurelea.png thumb right EureleA Award showing a 2,3 torus knot. In knot theory , a torus knot is a special kind of knot mathematics knot that lies on the surface of an unknotted torus in R sup 3 sup . Similarly, a torus link is a link knot theory link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integer s p and q . A torus ... divisor gcd p, q . A torus knot is unknot trivial if and only if either p or q is equal to 1 or 1. The simplest nontrivial example is the 2,3 torus knot, also known as the trefoil knot . Image Trefoil knot left.svg thumb right the 2, 3 torus knot, also known as the left handed trefoil knot Geometrical representation A torus knot can be rendered geometrically in multiple ways which are topologically ... and its figures is the following. The p , q torus knot winds q times around a circle in the interior of the torus, and p times around its axis of rotational symmetry. If p and q are not relatively prime, then we have a torus link with more than one component. The direction in which the strands of the knot wrap around the torus is also subject to differing conventions. The most common is to have ... , q torus knot can be given by the parametrization math x r math math cos p phi math math y r math math ... on the surface of the torus given by math r 2 2 z 2 1 math in cylindrical coordinates . Other ... for the 2,3 and 3,8 torus knots can be obtained by taking math r cos q phi 4 math , and in the case of the 2,3 torus knot by furthermore subtracting respectively math 3 cos p q phi math and math ... of a 3, 8 torus knot. A torus knot is unknot trivial if and only if iff either p or q is equal to 1 or 1. ref name murasugi ref name kawauchi Each torus knot is prime knot prime and chirality mathematics chiral . The p , q torus knot is equivalent to the q , p torus knot. ref name livingston ... more details
Image Stanford torus external view by Don Davis AC76 0525.jpg thumb right Exterior view of a Stanford torus. Bottom center is the non rotating primary solar mirror, which reflects sunlight onto the angled ring of secondary mirrors around the hub. Painting by Donald E. Davis Image Stanford torus under construction.jpg thumb right External view of a Stanford torus with some of the radiation shielding chevron mirrors removed to show interior space File Stanford Torus Cutaway view.jpeg thumb right Cutaway view of a Stanford torus Image Internal view of the Stanford torus.jpg thumb right Interior of a Stanford torus, painted by Donald E. Davis The Stanford torus is a proposed design ref cite news ... ibid. NASA Study, pg 1, The Overall System , pg 60, Summary ref The Stanford Torus was proposed during ... proposed his Island One or Bernal sphere as an alternative to the torus. ref Gerard K. O Neil, The High Frontier , William Morrow & Co., 1977, p149 ref Stanford torus refers only to this particular version ... Poto nik . ref Hermann Poto nik The Problem of Space Travel 1929 ref It consists of a torus ... ref Sunlight is provided to the interior of the torus by a system of mirror s. The ring is connected ... space of the torus itself is used as living space, and is large enough that a natural environment can be simulated the torus appears similar to a long, narrow, straight glacial valley whose ends curve ... stage of a Stanford Torus Space station in collaboration with U.S. scientists. ref name asarov interview ... structures that more closely resemble the Stanford Torus idea The novels of the Gaea Trilogy by John ... Torus. In the anime series Mobile Suit Gundam Wing , most of the many Space Colony Gundam space colonies in Earth orbit are based on the Stanford torus. The anime series Mobile Suit Gundam ... of a Stanford Torus. In the anime series Planetes , the main action also takes place in a Stanford torus type space station around Earth. Hideo Kojima s PlayStation 2 video game Zone of the Enders ... more details
Infobox Disease Name Torus mandibularis aka TUSKS Image Torus cropped.jpg Caption Left mandibular torus as visualized in an intraoral mirror DiseasesDB ICD10 ICD10 K 10 0 k 00 ICD9 ICDO OMIM Torus mandibularis pl. tori mandibular or mandibular torus pl. mandibular tori in English is a bone bony exostosis growth in the Human mandible mandible along the surface nearest to the tongue . Mandibular tori are usually present near the premolar s and above the location of the mylohyoid muscle s attachment to the mandible. ref name neville21 Neville, B.W., D. Damm, C. Allen, J. Bouquot. Oral & Maxillofacial Pathology . Second edition. 2002. Page 21. ISBN 0 7216 9003 3. ref In 90 of cases, there is a torus on both the left and right sides, making this finding an overwhelmingly Symmetry biology Bilateral symmetry bilateral condition. The prevalence of mandibular tori ranges from 5 40 . It is less common than bony growths occurring on the palate , known as torus palatinus . Mandibular tori are more common in Asian and Inuit populations, and slightly more common in male s. In the United States, the prevalence is 7 10 of the population. It is believed that mandibular tori are caused by several factors. ref name neville21 Neville, B.W., D. Damm, C. Allen, J. Bouquot. Oral & Maxillofacial Pathology . Second edition. 2002. Page 21. ISBN 0 7216 9003 3. ref They are more common in early adult life and are associated with bruxism . The size of the tori may fluctuate throughout life, and in some cases the tori can be large enough to touch each other in the midline of mouth. Consequently, it is believed ... of dentures . If removal of the tori is needed, torus removal surgery surgery can be done ... Photoclinic December 1, 2008, Torus mandibularis http www.maxillofacialcenter.com BondBook bone exostosis.html Thomas Bond s Book Palatal & Mandibular Torus, & Exostosis Dentofacial anomalies and jaw disease Category Jaw disorders es Torus mandibularis ... more details
Image Umbilic Torus.png thumb right Umbilic Torus The umbilic torus is a single edged 3 dimensional figure created by Helaman Ferguson as a mathematical artwork. Ferguson created a 27 inch 69 centimeters bronze sculpture, Umbilic Torus , and it is his most widely known piece of art. The lone edge goes three times around the ring before returning to the starting point. A cross section geometry cross section of the surface taken from an umbilic torus corresponds with a hypocycloid . The torus is defined by the following set of parametric equations . math x sin u left 7 cos left u over 3 2v right 2 cos left u over3 v right right math math y cos u left 7 cos left u over 3 2v right 2 cos left u over 3 v right right math math z sin left u over 3 2v right 2 sin left u over 3 v right math math mbox for pi le u le pi, quad pi le v le pi , math In 2010, it was announced that James Harris Simons Jim Simons had commissioned an Umbilic Torus sculpture to be constructed outside the Math and Physics buildings at Stony Brook University , in proximity to the Simons Center for Geometry and Physics . The torus will be made out of cast bronze, and will be mounted on a stainless steel column. The total weight of the sculpture will be 65 tonnes, and will have a height of convert 28 ft m . The torus will have a diameter of convert 24 ft m , the same diameter as the granite base. Various mathematical equations will be inscribed on the base. Installation should be complete by Summer of 2012. See also Torus M bius strip Mathematics and art References Larson, Roland E., et al. Calculus . Ed. Charles Hartford. 6th ed. Boston Houghton Mifflin Company, 1998. Helaman Ferguson, Two Theorems, Two Sculptures, Two Posters , American Mathematical Monthly, Volume 97, Number 7,August September 1990, pages 589 610. External links http www.helasculpt.com gallery umbilictorus4inch Umbilic Torus Category Sculptures Category Mathematics and culture ... more details
Refimprove date May 2009 Infobox disease Name Torus palatinus Image 06 06 06palataltori.jpg Caption An example of palatal torus. DiseasesDB ICD10 ICD10 K 10 0 k 00 ICD9 ICDO OMIM MedlinePlus eMedicineSubj eMedicineTopic MeshID Torus palatinus pl. tori palatinus palatinus torus pl. palatal tori in English is a bone bony protrusion on the palate . Palatal tori are usually present on the midline of the hard palate. ref name neville20 Neville, B.W., D. Damm, C. Allen, J. Bouquot. Oral & Maxillofacial Pathology . Second edition. 2002. Page 20. ISBN 0 7216 9003 3. ref Most palatal tori are less than 2 cm in diameter, but their size can change throughout life. Prevalence of palatal tori ranges from 9 60 and are more common than bony growths occurring on the Human mandible mandible , known as Torus Mandibularis torus mandibularis . Palatal tori are more common in Asian and Inuit populations, and twice more common in female s. In the United States, the prevalence is 20 35 of the population with similar findings between blacks and whites. Although some research suggest palatal tori to be an autosomal dominant trait, it is generally believed that palatal tori are caused by several factors. ref name neville20 They are more common in early adult life and can increase in size. In some older people, the size of the tori may decrease due to bone resorption. It is believed that mandibular torus tori of the lower jaw are the result of local stresses and not solely on Genetics genetic influences. Sometimes, the tori are categorized by their appearance. ref name neville20 Arising as a broad base and a smooth surface, flat tori are located on the midline of the palate and extend symmetrically to either side. Spindle tori have a ridge located at their midline. Nodular tori have multiple ... may complicate the fabrication of dentures . If removal of the tori is needed, Torus removal surgery ... bone exostosis.html Thomas Bond s Book Palatal & Mandibular Torus, & Exostosis DEFAULTSORT Torus ... more details
In mathematics , an algebraic torus is a type of commutative affine algebraic group . These groups were named by analogy with the theory of tori in Lie group theory see maximal torus . The theory of tori ... but no deformations. Definition Given a base Scheme mathematics scheme S , an algebraic torus over ... particularly important case is when S is the spectrum of a field K , making a torus over S an algebraic ... the Rank mathematics rank dn date July 2011 of the torus, and it is a locally constant function on S . If a torus is isomorphic to a product of multiplicative groups G sub m sub S , the torus is said ... admits a non split torus given by Weil restriction restriction of scalars over a separable extension ... that is not a torus. Weights Over a separably closed field, a torus T admits two primary invariants ... G sub m sub T . These are both free abelian groups whose rank is that of the torus, and they have ..., and the automorphism group of a torus is a general linear group over Z . The quasi ... a field K is not separably closed, the weight and coweight lattices of a torus over K are defined ... a finite separable field extension L K and a torus T over L , we have a Galois module isomorphism math ... groupoids of the base with respect the fpqc topology. If the torus is locally trivializable with respect ..., an etale sheaf gives rise to a quasi isotrivial torus, and if S is locally noetherian and normal more generally, Unibranch local ring geometrically unibranched , the torus is isotrivial. As a partial converse, a theorem of Grothendieck asserts that any torus of finite type is quasi isotrivial, i.e., split by an etale surjection. Given a rank n torus T over S , a twisted form is a torus over ..., it is a torus of the same rank. Isomorphism classes of twisted forms of a split torus are parametrized ... a constant sheaf. In particular, twisted forms of a split torus T over a field K are parametrized ... torus whose real points form the Lie group of nonzero complex numbers. Restriction of scalars ... more details
Image Pinched torus.jpg thumb A Pinched Torus In mathematics , and especially topology and differential geometry , a pinched torus or croissant surface is a kind of two dimensional surface . It gets its name from its resemblance to a torus that has been pinched at a single point. A pinched torus is an example of an orientable surface orientable , compact surface compact 2 dimensional pseudomanifold . ref cite journal last1 Brasselet first1 J. P. year 1996 title Intersection of Algebraic Cycles journal Journal of Mathematical Sciences publisher Springer New York volume 82 issue 5 pages 3625 3632 url http www.springerlink.com content ju28j2wqm174hx10 ref Parametrisation A pinched torus is easily parametrisable. Let us write nowrap 1 g x , y 2 sin x 2 .cos y . An example of such a parametrisation which was used to plot the picture is given by nowrap 1 0,2&pi sup 2 sup R sup 3 sup where math f x,y left g x,y cos x , g x,y sin x , sin left frac x 2 right sin y right math Topology Topologically, the pinched torus is homotopy equivalent to the Wedge sum wedge of a sphere and a circle. ref name TOP Citation first Allen last Hatcher title Algebraic Topology publisher Cambridge University Press year 2001 ISBN 0521795400 ref ref name TOP0 cite web url http www.math.cornell.edu hatcher AT ATch0.pdf title Chapter 0 Algebraic Topology author Allen Hatcher accessdate August 6, 2010 ref It is homeomorphic to a sphere with two distinct points being quotient space identified . ref name TOP ref name TOP0 Homology Let P denote the pinched torus. The homology group s of P over the integer s can be calculated. They are given by math H 0 P, Z cong Z, H 1 P, Z cong Z, text and H 2 P, Z cong Z. math Cohomology The cohomology group s of P over the integer s can be calculated. They are given by math H 0 P, Z cong Z, H 1 P, Z cong Z, text and H 2 P, Z cong Z. math References reflist Category Surfaces ... more details
Infobox Basketball club name br KK Torus logo KKTorus basketball logo.png imagesize 100px leagues Macedonian Premier League basketball Macedonian First League founded 1999 history arena Boris Trajkovski Arena br capacity 10,000 location Skopje , Republic of Macedonia Macedonia colors Blue and Yellow br color box blue color box yellow president Vojo Petrov coach Marjan Srbinovski championships 0 website h body 0000FF h pattern b h shorts 0000FF h pattern s a body FFFF00 a pattern b a shorts FFFF00 a pattern s KK Torus lang mk is a basketball club based in Skopje , Republic of Macedonia . They currently play in the Macedonian Premier League basketball Macedonian First League and the 2011 12 BIBL season Balkan League . History The club was founded on 25 May 1999. Name KK Torus, KK Torus SC Boris Trajkovski Honours League Achievements Macedonian Cup Finalist 2010 ref cite web url http www.eurobasket.com team.asp?Cntry FYR 20Macedonia&Team 8436&Page 5 title KK Torus Skopje basketball team History first last ref br Macedonian Cup Semifinals 2011, 2012 Macedonian League Semifinals 2010, 2011 Current squad style border 5px solid 000000 cellspacing 3 align center bgcolor CCCCCC colspan 5 KK Torus br big align right flagicon USA Bryan Harrison align right flagicon USA Justin Reynolds align right flagicon Macedonia Dimitar Karadzovski align right flagicon Macedonia Bojan Trajkovski align right flagicon Macedonia Aleksandar Kojcevski align right flagicon USA Jeremiah Boswell align right flagicon Macedonia Pero Blazevski align right flagicon Macedonia Ivica Dimcevski align right flagicon Macedonia Jovan Markovski align right flagicon USA Phil Turner align right flagicon USA Karon Bradley align right flagicon Macedonia Goran Markovski align right flagicon Macedonia Vladimir Dikovski Technical staff ref http www.balkanleague.net en team.php?id 26 ref class wikitable ...?Cntry FYR 20MACEDONIA&Team 8436&Page 1 Team info from Eurobasket Skopje DEFAULTSORT KK Torus ... more details
unreferenced date November 2008 Image Torus games logo.png thumb 130px right Torus Games company logo. Torus Games Pty. Ltd. is a video games developer founded in 1994, and is subsequently one of the oldest and most consistently stable game development studios in Australia . Torus has released over 60 titles, spanning almost every gaming platform, including but not limited to the Xbox 360 , Personal Computer PC , Nintendo Wii , Xbox , PlayStation 2 , Nintendo DS , Sony PSP , GameCube , Nokia N Gage , Game Boy Advance , Game Boy Color , Game Boy , Sega Saturn , Leapster and Leapster2 . Torus Games has a single, scalable cross platform game engine that currently actively supports the Xbox 360 , PlayStation 3 , Personal Computer PC , Nintendo Wii , iPhone iPad iPod Touch , Nintendo 3DS , Nintendo DS and PlayStation 2 , and support for next generation hardware is in development, including the PlayStation Vita . The Torus game engine uniquely runs on consoles, hand helds including those without floating point support and mobile phones, and their unified asset pipeline allows Torus to deliver the same game from the same common code base across all hardware platforms. Torus Games is located in Bayswater, Victoria Bayswater , Victoria Australia . Torus is a family business, with the managing director being Bill McIntosh. Torus is most commonly known for their family action adventure games, having predominantly released titles of that genre in recent years. Their latest release is Scooby ... to Scooby Doo First Frights . Torus has several games actively in development, spanning all current hardware generations. Torus Games began developing their first game in 1994, a Game Boy and Game Gear game based on the film Stargate film Stargate , published by Acclaim Entertainment . Torus is a current ... Nascar 2007 External links http www.torusgames.com Official Torus Games website Category Video game ... videogame company stub ca Torus Games pt Torus Games ... more details
In mathematics , a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense i.e. the cartesian product of some number N circle s . Here N must be the even number 2 n , where n is the complex dimension of M . All such complex structures can be obtained as follows take a lattice group lattice in C sup n sup considered as real vector space then the quotient group C sup n sup &Lambda is a compact space compact complex manifold. All complex tori, up to isomorphism, are obtained in this way. For n 1 this is the classical period lattice construction of elliptic curve s. For n 1 Bernhard Riemann found necessary and sufficient conditions for a complex torus to be an algebraic variety those that are varieties can be embedded into complex projective space , and are the abelian varieties . The actual projective embeddings are complicated see equations defining abelian varieties when n 1, and are really coextensive with the theory of theta function s of several complex variable s with fixed modulus . There is nothing as simple as the cubic curve description for n 1. Computer algebra can handle cases for small n reasonably well. By Chow s theorem , no complex torus other than the abelian varieties can fit into projective space. References Citation last1 Birkenhake first1 Christina last2 Lange first2 Herbert title Complex tori publisher Birkh user Boston location Boston, MA series Progress in Mathematics isbn 978 0 8176 4103 0 mr 1713785 year 1999 volume 177 Category Complex manifolds Category Complex surfaces Category Abelian varieties ... more details
In mathematics , the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f . Take the cartesian product of X with a closed interval I , and glue the boundary components together by the static homeomorphism math M f frac I times X 1,x sim 0,f x math The result is a fiber bundle whose base is a circle and whose fiber is the original space X . If X is a manifold , M sub f sub will be a manifold of dimension one higher, and it is said to fiber bundle fiber over the circle . Mapping tori of surface homeomorphisms play a key role in the theory of 3 manifold s and have been intensely studied. If S is a closed surface of surface Classification of closed surfaces genus g 2 and if f is a self homeomorphism of S , the mapping torus M sub f sub is a Closed manifold closed 3 manifold that fiber bundle fibers over the circle with fiber S . A deep result of William Thurston Thurston states that in this case the 3 manifold M sub f sub is a hyperbolic manifold hyperbolic if and only if f is a pseudo Anosov map pseudo Anosov homeomorphism of S ref W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces , Bulletin of the American Mathematical Society , vol. 19 1988 , pp. 417&ndash 431 ref . References reflist Category General topology Category Geometric topology Category Homeomorphisms fr Tore d application ... more details
Use Australian English date April 2012 Orphan date February 2009 BLP sources date May 2008 Torus Tammer born 1969 is an Australia n film maker . Career Tammer was born in Melbourne, Australia ref name News.com cite news url http www.news.com.au entertainment story 0,23663,19987137 5007181,00.html title Red hot and smoking date 2 August 2006 publisher News Limited accessdate 2009 10 13 ref and moved to Los Angeles in 1992 and began working odd jobs on low budget films. During this period, he met film producers Mike Erwin and Max Kirishima . Erwin and Kirishima hired Tammer to work for their production company, Den Pictures . While at Den, Tammer worked on the development of a remake of the classic cult film Easy Rider the rights to which Den Pictures owned . With the encouragement of Erwin and Kirishima, Tammer began developing two pet projects Golgo 13 and Preacher . Both projects were adaptations of comic books Golgo 13 AKA The Professional by the legendary Japanese comic book artist Takao Saito and Preacher which at the time, was a cutting edge new series for Vertigo DC comics created by Garth Ennis. Both projects never made it through the development phase and Tammer embarked on a solo career. In 1995, Tammer worked in development for Valerie Kearns and screenwriter James V. Hart at the now defunct HBI Pictures . After a short stint, Tammer in 1996 decided to begin his own independent project so he wrote and subsequently directed Lone Greasers . It was here that he met close friend and future producing partner Daniel Dubiecki . Dubiecki produced Lone Greasers which showcased an ensemble cast of veteran character actors including former X front man John Doe, Peter Dobson and Mariah O brien. Tammer continued writing and directing until 1999 at which point, he decided to focus ... date August 2010 Persondata Metadata see Wikipedia Persondata . NAME Tammer, Torus ALTERNATIVE NAMES ..., Torus Category Australian film producers Category 1969 births Category Living people ... more details
Encyclopedia
top
