self similarity In geometry , an affinetransformation or affine map ref Citation last1 Berger first1 ... transformations, as are their combinations. An affinetransformation is equivalent to a linear transformation ..., this can be decomposed as an affinetransformation math mathcal A , to , mathcal B math that sends ... is called affinetransformation matrix , or projective transformation matrix as it can also be used ... in computer graphics and computer vision . Properties An affinetransformation is invertible if and only ... the transformation has exactly one fixed point affine transformations with matrix A can be written as a linear ..., and the affinetransformation reduces to a linear transformation. This may make it easier ..., eigenvector, and eigenspace Multiplicity multiplicity 2, but geometric multiplicity 1 Affinetransformation of the plane To visualise the general affinetransformation of the Euclidean plane , take labelled parallelogram s ABCD and A B C D . Whatever the choices of points, there is an affinetransformation ... case where ABCD has zero area , there is a unique such affinetransformation T . Drawing out a whole ..., for example, by the cross product of vectors . Examples of affine transformations Affinetransformation over a finite field The following equation expresses an affinetransformation in Galois ... vector math begin bmatrix 1 1 0 0 0 1 1 0 end bmatrix . math For instance, the affinetransformation ... 6 sup y sup 5 sup y sup 3 sup y sup 2 sup 1 11101101 ED . Affinetransformation in plane geometry File Geometric affinetransformation example.png thumb A simple affinetransformation on the real plane ... matrix Affine transformations The transformation matrix for an affinetransformationAffine ... is affinetransformation in 1D 3D projection Flat geometry Notes refimprove date April 2012 Reflist ... 94732 9 External links cite web url http www.haberdar.org AffineTransformation Example.htm title AffineTransformation Example publisher Hakan Haberdar, University of Houston accessdate March 2012 ... more details
wiktionarypar affineAffine may refer to Prospective editors please keep this list alphabetical Affine cipher , a special case of the more general substitution cipher Affine combination , a certain kind of constrained linear combination Affine connection , a connection on the tangent bundle of a differentiable manifold Affine geometry , a geometry not involving any notions of origin, length or angle Affine differential geometry , a geometry that studies differential invariants under the action of the special affine group Affine group , the group of all invertible affine transformations from any affine space over a field K into itself Affine representation , a continuous group homomorphism whose values are automorphisms of an affine space Affine scheme , the spectrum of prime ideals of a commutative ring Affine Soci t , A French Commercial real estate company. Affine space , an abstract structure that generalises the affine geometric properties of Euclidean space Affinetransformation , a linear transformation followed by a translation between two vector spaces, or equivalently, a transformation that preserves all affine combinations See also Affinity disambiguation disambig Category Mathematical disambiguation fr Affine pt Afim ... more details
wiktionarypar transformationTransformation may refer to Mathematics Transformation function Transformation combinatorics Integral transform Data transformation statistics Transformation matrix Natural science Phase transformation , a physical transition from one medium to another Chemical transformation ... transformation , the process of cells becoming cancerous Transformation genetics , genetic alteration of a cell by DNA uptake Transformation optics , generalized optical devices Computing Data transformation Model transformation Program transformation XML transformationTransformation of text Fiction Transformation novel Transformation novel , by Carol Berg Shapeshifting , a type of transformation common in mythology and folklore Henshin , a type of transformation common in anime, manga and tokusatsu Transformation , an alternate title for The Marble Faun , a novel by Nathaniel Hawthorne Other uses Maturity Transformation MT use borrow cheap e.g. short term money to invest at a more lucrative ... . Cf. Carry trade Interest rates carry trade on rates Transformation law , a concept in copyright law Transformation patent law Transformation Tal Wilkenfeld album Transformation Alex Skolnick Trio album Transformation music Transformation , a song by Nona Hendryx Transformation warfare Transformation of culture Transformation design , a design process Transformation playing card Transformation problem , a concept in economics Transformational grammar Spiritual transformation , a psychological and New Age concept Business Transformation , an idea in strategic management Business Network Transformation , a concept used in thinking about markets Transformation of precious metal s see Synthesis of precious metals Transformational festival See also Transform disambiguation Transformation Story Archive disambig ca Transformaci cs Transformace de Transformation et Transformatsioon es Transformaci n fr Transformation hu Transzform ci egy rtelm s t lap nl Transformatie pl Transformacja pt ... more details
In mathematics , an affine combination of vectors x sub 1 sub , ..., x sub n sub is a vector math sum i 1 n alpha i cdot x i alpha 1 x 1 alpha 2 x 2 cdots alpha n x n , math called a linear combination of x sub 1 sub , ..., x sub n sub , in which the sum of the coefficients is 1, thus math sum i 1 n alpha i 1. math Here the vectors are elements of a given vector space V over a field mathematics field K , and the coefficients math alpha i math are scalar mathematics scalars in K . This concept is important, for example, in Euclidean geometry . The act of taking an affine combination commutes with any affinetransformation T in the sense that math T sum i 1 n alpha i cdot x i sum i 1 n alpha i cdot Tx i math In particular, any affine combination of the fixed point mathematics fixed point s of a given affinetransformation math T math is also a fixed point of math T math , so the set of fixed points of math T math forms an affine subspace in 3D a line or a plane, and the trivial cases, a point or the whole space . When a stochastic matrix , A, acts on a column vector, B, the result is a column vector whose entries are affine combinations of B with coefficients from the rows in A. See also Related combinations details Linear combination Affine, conical, and convex combinations Convex combination Conical combination Linear combination Affine geometry Affine space Affine geometry Affine hull References Citation last1 Gallier first1 Jean title Geometric Methods and Applications publisher Springer Verlag location Berlin, New York isbn 978 0 387 95044 0 year 2001 . See chapter 2 . Category Affine geometry he hu Affin kombin ci nl Affiene combinatie pl Kombinacja afiniczna pt Combina o afim vi T h p afin ... more details
refimprove date June 2008 IT Transformation is the wholesale changing of an organization s technology systems. It is a term that typically applies more to large, complex organisations than smaller entities. Significant business change typically takes place in parallel with technology change. Because of the growing popularity of SOA Service oriented architecture and Open Systems, most transformation projects today include some form of these technologies. Due to the ongoing obsolescence of systems deployed in the late sixties and seventies, this is an emerging field. Check IT Transformation with SOA ref http itransform.abstraction.com ref for a more detailed discussion in this emerging field. A lot of companies are involved using this business model. References reflist Category Business planning Category Information technology management business stub ... more details
Infobox Television episode Title The Transformation Series Fringe TV series Fringe Image Caption Season 1 Episode 13 Airdate February 3, 2009 Production 3T7662 Writer Zack Whedon br J. R. Orci Director Brad Anderson director Brad Anderson Guests Michael Cerveris as The List of Fringe characters September The Observer Observer Neal Huff as Marshall Bowman Felix Solis as Daniel Hicks Armando Riesco as Gavin ... Ability The Transformation is the 13th List of Fringe episodes episode of the Fringe season 1 .... They successfully make contact, but the sellers become suspicious after Hicks transformation ... to his consciousness, which has finally left her own. Production The Transformation was co written ... 2009, The Transformation had an early screening at the November 2008 Paley Center for Media PaleyFest ... Jeff Pinkner replied that the huge porcupine man on the airplane from The Transformation was more ... the point The Transformation aired, actor Joshua Jackson considered it his favorite episode. ref cite ... date 2009 02 20 accessdate 2011 06 25 ref Reception Ratings The Transformation was watched by 12.78 ... http latimesblogs.latimes.com showtracker 2009 02 fringe transfor.html title Fringe Transformation ... url http tv.ign.com articles 950 950916p1.html title Fringe The Transformation Review publisher IGN ... that the John Scott resolution signals a transformation in the interpersonal dynamics of the show? If this dud ... 12 21 fringe the transformation 113 title Fringe The Transformation 1.13 publisher Open Salon .com first ... director Brad Anderson. I wouldn t say that The Transformation broke any new ground. If anything, it recapitulated ... title The Transformation publisher A.V. Club first Noel last Murray date 2009 02 03 accessdate 2011 02 17 ref References reflist 2 External links Wikiquote Fringe The Transformation .5B1.13.5D The Transformation http www.fox.com fringe recaps season 1 episode 13 The Transformation at Fox Broadcasting Company Fox IMDb episode 1248541 Tv.com episode 1250199 Fringe Fringe episodes DEFAULTSORT Transformation ... more details
math u x v, math the archetype of an affinetransformation of x . Ternary fields are also characterized ... chapter of From affine to Euclidean geometry . Affine transformations main Affinetransformation ... orthogonality . ref Coxeter 1942 178 ref In this viewpoint, an affinetransformation geometry is a group ...In mathematics affine geometry is the study of geometric properties which remain unchanged by affinetransformation s, i.e. non singular linear transformation s and Translation geometry translations . The name affine geometry, like projective geometry and Euclidean geometry , follows naturally from the Erlangen program of Felix Klein . Affine geometry is a form of geometry featuring the unique parallel ... postulates are ignored . First identified by Euler , many affine properties are familiar from Euclidean ... by parallel projection from one Plane mathematics plane to another are affine. In effect, affine geometry is a generalization of Euclidean geometry characterized by slant and scale distortions. Projective geometry is more general than affine since it can be derived from projective space ... of Klein s Erlangen program , the underlying symmetry in affine geometry is the group mathematics ... transformation s of a vector space together with the translation geometry translation s by a vector. Affine geometry can be developed on the basis of linear algebra . One can define an affine ... as obtaining the affine space from its associated vector space by forgetting the origin zero vector . History In 1748 Euler introduced the term affine ref cite web title Earliest Known Uses of Some ... see chapter XVII . In 1827 August M bius wrote on affine geometry in his Der barycentrische Calcul , chapter 3. Only after Felix Klein s Erlangen program was affine geometry recognized for being ... Systems of axioms Several axiomatic approaches to affine geometry have been put forward Pappus law As affine geometry deals with parallel lines, one of the properties of parallels noted by Pappus of Alexandria ... more details
n math , with Covering space Monodromy action monodromy acting by affinetransformation s. This equivalence ...Other uses Affine manifold disambiguation In differential geometry , an affine manifold is a manifold equipped with a flat connection flat , torsion tensor torsion free affine connection connection . Equivalently ... with an atlas called the affine structure with all transition functions between chart s affine that is, have ... to both, with transitions from both atlases to a smaller atlas being affine. A manifold having a distinguished affine structure is called an affine manifold and the charts which are affinely related to those of the affine structure are called affine charts . In each affine coordinate domain the coordinate ... parts, so there is a unique connection associated with an affine structure. Note there is a link between linear connection mathematics connection also called affine connection and a web differential geometry web . Formal definition An affine manifold math M , math is a real manifold with charts ... math i, j , , math where math rm Aff Bbb R n math denotes the Lie group of affine transformations. An affine manifold is called complete if its universal covering is homeomorphism to math Bbb R n math . In the case of a compact affine manifold math M math , let math G math be the fundamental group ... affine manifold comes with a developing map math D colon tilde M to Bbb R n math , and a homomorphism ... complete flat affine manifold is called an affine crystallographic group . Classification of affine ... group contains an abelian subgroup of finite index. Important longstanding conjectures Geometry of affine ... affine manifold is complete if and only if it has constant volume. ref Hirsch M. and Thurston ... affine manifolds, Topology 3 1964 , 131 139. ref ref Fried D. and Goldman W., Three dimensional affine crystallographic groups , Adv. Math. 47 1983 , 1 49. ref stating that any affine crystallographic ... part of a properly discontinuous group of affine transformations, J. Differential Geom., 60 ... more details
transformation is a function that preserves all linear combination s an affinetransformation is a function ... of affine space, and conversely any affine linear transformation extends uniquely to a projective ... is that M bius transformation s transformations of the projective line, or Riemann sphere are affine ... one may then projectivize, but this requires a choice. See also affine geometry affinetransformation ...distinguish affinity space In mathematics , an affine space is a geometric structure mathematics structure that generalizes the affine geometry affine properties of Euclidean space . In an affine space ... set of an inhomogeneous linear equation is either empty or an affine space but note that a single point is also an affine space, over a zero dimensional vector space . Informal descriptions The following ... definition an affine space is what is left of a vector space after you ve forgotten which point is the origin or, in the words of the French mathematician Marcel Berger , An affine space is nothing ... from different origins. While Alice knows the linear structure , both Alice and Bob know the affine structure i.e. the values of affine combination s, defined as linear combinations in which the sum of the coefficients is 1. An underlying set with an affine structure is an affine space. Definition An affine space ref cite book author Berger, Marcel chapter Affine spaces title Problems in Geometry ..., an affine space is a principal homogeneous space over the additive group of a vector space. cn date April 2012 Explicitly, an affine space is a point set math scriptstyle A math together with a map math ... Tarrida, Agusti R. chapter Affine spaces title Affine Maps, Euclidean Motions and Quadrics publisher ... . The vector space math scriptstyle V math is said to underlie the affine space math scriptstyle ... A math into a vector space. Conversely, any vector space, math scriptstyle V math , is an affine ..., only such affine combinations of points have meaning. By noting that one can define subtraction of points ... more details
Projection linear algebra projection P . Affine involutions If A represents a linear involution, then x A x b b is an affinetransformationaffine involution. One can check that any affine involution in fact has this form. Geometrically this means that any affine involution can be obtained by taking oblique reflections against any number from 0 through n hyperplanes going through a point b . Affine involutions can be categorized by the dimension of the affine space of Fixed point mathematics ... above , i.e., the dimension of the eigenspace for eigenvalue 1. The affine involutions in 3D are the identity ... 1 is orthogonal to every eigenvector with eigenvalue 1, such an affine involution is an isometry .... unref date December 2007 DEFAULTSORT Affine Involution Category Affine geometry ... more details
under a special affine group special affinetransformation an affinetransformation that preserves area . The curves of constant equi affine curvature k are precisely all non singular conic section ... . math By applying a suitable special affinetransformation, we can arrange that C sub sub 0 ... affinetransformation. In fact, a slightly stronger statement holds Given any continuous function ... affinetransformation. This is analogous to the fundamental theorem of curves in the classical ... x partial y, quad X 2 y partial x, quad H x partial x y partial y. math An affinetransformation not only ...This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection . Special affine curvature , also known as the equi affine curvature or affine ... point contact with the curve at the point. In the same way, the special affine curvature of a curve at a point P is the special affine curvature of its hyperosculating conic , which is the unique conic ... 1,P 2,P 3,P 4 to P. math In some contexts, the affine curvature refers to a differential invariant of the affine group general affine group , which may readily obtained from the special affine curvature k by k sup 3 2 sup d k d s , where s is the special affine arc length. Where the general affine group is not used, the special affine curvature k is sometimes also called the affine curvature harv Shirokov 2001b . Formal definition Special affine arclength To define the special affine curvature, it is necessary first to define the special affine arclength also called the equi affine arclength . Consider an affine plane curve math beta t math . Choose co ordinates for the affine plane such that the area ... invariant of the special affine group, and gives the signed area of the parallelogram spanned by the velocity ... undergoes then a transformation of the following sort, by the chain rule math begin align ... 2 end bmatrix , ,dt. math This integral is called the special affine arclength , and a curve carrying ... more details
In mathematics , the affine group or general affine group of any affine space over a field mathematics field K is the group mathematics group of all invertible affinetransformation s from the space into itself. It is a Lie group if K is the real or complex field or quaternions . Relation to general linear group Construction from general linear group Concretely, given a vector space V, it has an underlying affine space A obtained by forgetting the origin, with V acting by translations, and the affine group of A can be described concretely as the semidirect product of V by GL V , the general linear group of V math operatorname Aff A V rtimes operatorname GL V math The action of GL V on V is the natural ... Given the affine group of an affine space A , the Group action Orbits and stabilizers stabilizer ... space math A,p math recall that if one fixes a point, an affine space becomes a vector space. All ... 1 to V to V rtimes operatorname GL V to operatorname GL V to 1 math . In the case that the affine ... space is the original GL V . Matrix representation Representing the affine group as a semidirect ... operatorname GL V oplus K math , with V embedded as the affine plane math v,1 v in V math , namely the stabilizer of this affine plane the above matrix formulation is the transpose of the realization ... ones. Each of these two classes of matrices is closed under matrix multiplication. Other affine ... an affine group, sometimes denoted math operatorname Aff G math analogously as math operatorname ... over R . ref an associated affine group math V rtimes rho G math one can say that the affine group ... sequence math 1 to V to V rtimes rho G to G to 1. math Special affine group main Special affine group The subset of all invertible affine transformations preserving a fixed volume form, or in terms of the semi ... as the special affine group . Poincar group main Poincar group The Poincar group is the affine .... Category Affine geometry Category Group theory Category Lie groups fr Groupe affine nl Affiene groep ... more details
In affine geometry , a branch of mathematics , an affine frame in an affine space A consists of a choice P of origin of A along with a basis of a vector space basis of the space of vectors based at P . Category Affine geometry geometry stub ca Marc af fr Rep re affine ... more details
Affine algebra may refer to affine Lie algebra , a type of Kac Moody algebras the Lie algebra of the affine group finitely generated algebra disambig ... more details
are always given by affinetransformation s from one tangent plane to another. This notion of parallel transport of tangent vectors, by affine transformations, along a curve has a characteristic feature ... defined by rolling does not fix this origin it is affinetransformationaffine rather than linear the linear ... to satisfy several properties for any two points x , y on C , parallel transport is an affinetransformation ...File Parallel transport sphere.svg right thumb An affine connection on the sphere rolls the affine tangent ... the development . In the branch of mathematics called differential geometry , an affine connection ... with values in a fixed vector space. The notion of an affine connection has its roots ... the idea is that a choice of affine connection makes a manifold look infinitesimally like Euclidean space not just smoothly, but as an affine space . On any manifold of positive dimension there are infinitely many affine connections. If the manifold is further endowed with a Riemannian metric then there is a natural choice of affine connection, called the Levi Civita connection . The choice of an affine ... definition of an affine connection as a covariant derivative or linear connection vector bundle connection on the tangent bundle . A choice of affine connection is also equivalent to a notion of parallel ... yields another description of an affine connection, either as a Cartan connection for the affine group ... of an affine connection are its torsion of connection torsion and its curvature . The torsion measures how closely the Lie derivative Lie bracket of vector fields can be recovered from the affine connection. Affine connections may also be used to define affine geodesics on a manifold, generalizing ... tangent vectors at nearby points cannot be compared in a well defined way. The notion of an affine ... plane at that point, which is an affine subspace of Euclidean space. Differential geometers in the 19th ... affine. In the point of view of Cartan connections, however, the affine subspaces of Euclidean space ... more details
Affine logic is a substructural logic whose proof theory rejects the structural rule of Idempotency of entailment contraction . It can also be characterized as linear logic with weakening . The name affine logic is associated with linear logic , to which it differs by allowing the weakening rule. Jean Yves Girard introduced the name as part of the geometry of interaction semantics of linear logic, which characterises linear logic in terms of linear algebra here he alludes to affinetransformation s on vector spaces. ref Jean Yves Girard , 1997. http www.seas.upenn.edu sweirich types archive 1997 98 msg00134.html Affine . Message to the TYPES mailing list. ref The logic predated linear logic. V. N. Grishin used this logic in 1974, ref Grishin, 1974, and later, Grishin, 1981. ref after observing that Russell s paradox cannot be derived in a set theory without contraction, even with an unbounded comprehension axiom . ref Cf. Frederic Fitch s demonstrably consistent set theory ref Likewise, the logic formed the basis of a decidable subtheory of predicate logic , called Direct logic Ketonen & Wehrauch, 1984 Ketonen & Bellin, 1989 . Affine logic can be embedded into linear logic by rewriting the affine arrow math A rightarrow B math as the linear arrow math A circ B otimes top math . Whereas full linear logic i.e. propositional linear logic with multiplicatives, additives and exponentials is undecidable, full affine logic is decidable. Affine logic forms the foundation of ludics . Notes references References V.N. Grishin, 1974. A nonstandard logic and its application to set theory, Russian . Studies in Formalized Languages and Nonclassical Logics Russian , 135 171. Izdat, Nauka, Moskow. . V.N. Grishin, 1981. Predicate and set theoretic calculi based on logic without contraction rules, Russian . Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya 45 1 47 68. 239. Math. USSR Izv., 18, no.1, Moscow. Ketonen and Weyhrauch, 1984, A decidable fragment of predicate calculus. Theoretical ... more details
italic title Unreferenced date March 2007 Taxobox name Sphagnum affine regnum Plant ae divisio Moss Bryophyta classis Sphagnopsida subclassis Sphagnidae ordo Sphagnales familia Sphagnaceae genus Sphagnum species S. affine binomial Sphagnum affine Sphagnum affine is a species of peat moss or sphagnum moss which is exploited to make commercial peat products. This moss has a yellowish coloring. DEFAULTSORT Sphagnum Affine Category Sphagnum Affine Bryophyte stub de Sphagnum affine es Sphagnum affine fr Sphagnum affine it Sphagnum affine fi Rannikkorahkasammal ... more details
of transformation used in affine ciphers is used in linear congruential generator s, a type of pseudorandom ...The affine cipher is a type of monoalphabetic substitution cipher , wherein each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted ... In the affine cipher the letters of an alphabet of size math m math are first mapped to the integers ... m & x mod m . end align math Weaknesses Since the affine cipher is still a monoalphabetic substitution cipher, it inherits the weaknesses of that class of ciphers. The Caesar cipher is the Affine cipher ... non trivial affine ciphers, not counting the 26 trivial Caesar ciphers. This number comes from the fact ... for the same reason that the affine cipher is not secure. Examples In these two examples, one ... Handouts affine.pdf ref the plaintext to be encrypted is AFFINE CIPHER using the table mentioned .... The table below shows the completed table for encrypting a message in the Affine cipher. class ... table for an affine cipher. a must be coprime to m 26. def affine a, b for i in range 26 print chr i 65 chr a i b 26 65 An example call affine 5, 8 source Or in Java programming language Java source lang Java public void Affine int a, int b for int num 0 num 26 num System.out.println char A num char A a num b 26 Affine 5,8 source Or in Pascal programming language Pascal source lang pascal Procedure Affine a,b Integer begin for num 0 to 25 do WriteLn Chr num 65 , , Chr a num b mod 26 65 end begin Affine 5,8 end. source See also Affine function s Atbash Atbash code Caesar cipher ROT13 Topics in cryptography Perl interface to http search.cpan.org manwar Crypt Affine 0.02 Affine cipher References Reflist Cryptography navbox classical DEFAULTSORT Affine Cipher Category Classical ciphers de Affine Chiffre es Cifrado af n fr Chiffre affine hu Affin rejtjel pl Szyfr afiniczny pt Cifra afim ru vi M t m Affine zh ... more details
In mathematics , the affine hull of a set mathematics set S in Euclidean space R sup n sup is the smallest affine set containing S , or equivalently, the intersection set theory intersection of all affine sets containing S . Here, an affine set may be defined as the translation mathematics translation of a vector subspace . The affine hull aff S of S is the set of all affine combination s of elements of S , that is, math operatorname aff S left sum i 1 k alpha i x i Bigg x i in S, , alpha i in mathbb R , , i 1,2, dots, k , sum i 1 k alpha i 1 k 1, 2, dots right . math Examples The affine hull of a set of two different points is the line through them. The affine hull of a set of three points not on one line is the plane going through them. The affine hull of a set of four points not in a plane in R sup 3 sup is the entire space R sup 3 sup . Properties math mathrm aff mathrm aff S mathrm aff S math math mathrm aff S math is a closed set Related sets If instead of an affine combination one uses a convex combination , that is one requires in the formula above that all math alpha i math be non negative, one obtains the convex hull of S , which cannot be larger than the affine hull of S as more restrictions are involved. The notion of conical combination gives rise to the notion of the conical hull If however one puts no restrictions at all on the numbers math alpha i math , instead of an affine combination one has a linear combination , and the resulting set is the linear span of S , which contains the affine hull of S . References R.J. Webster, Convexity , Oxford University Press, 1994. ISBN 0 19 853147 8. Category Affine geometry Category Closure operators de Affine H lle fr Sous espace affine engendr vi Bao afin ... more details
In mathematics , an affine plane may refer to The Euclidean plane Affine plane incidence geometry , an abstract system of points and lines such that every pair of points has a line containing both of them A two dimensional affine space , an origin free generalization of a vector space The plane with two complex Cartesian coordinates , called the affine plane in algebraic geometry to emphasize the difference between it and its projective completion mathdab ... more details
In mathematics, and especially differential geometry , an affine sphere is a hypersurface for which the Affine differential geometry The affine normal line affine normal s all intersect in a single point. ref name spring cite web url http eom.springer.de a a011110.htm publisher Springer Online References title Affine Sphere author E. V. Shikin ref The term affine sphere is used because they play an analogous role in affine differential geometry to that of ordinary spheres in Euclidean differential geometry. An affine sphere is called improper if all of the affine normals are constant. ref name spring In that case, the intersection point mentioned above lies on the hyperplane at infinity . Affine spheres have been the subject of much investigation, with many hundreds of research article s devoted to their study. ref cite web url http scholar.google.co.uk scholar?hl en&q 22affine sphere 22&btnG Search&as sdt 1 2C5&as ylo &as vis 0 title Google Scholar Search publisher Google Inc ref Examples All quadric s are affine spheres the quadrics that are also improper affine spheres are the paraboloid s. ref cite book last1 Buchin first1 S. title Affine differential geometry year 1983 publisher Sci. Press and Gordon & Breach location language isbn 0 677 31060 9 ref If is a smooth function on the plane and the determinant of the Hessian matrix is 1 then the graph of in three space is an improper affine sphere. ref cite journal last1 Ishikawa first1 G. last2 Machida first2 Y. year 2005 title Singularities of improper affine spheres and surfaces of constant Gaussian curvature arxiv math 0502154 ref References reflist DEFAULTSORT Affine sphere Category Differential geometry differential geometry stub ... more details
italic title Taxobox name Fusarium affine regnum Fungi phylum Ascomycota classis Sordariomycetes subclassis Hypocreomycetidae ordo Hypocreales familia Nectriaceae genus Fusarium species F. affine binomial Fusarium affine binomial authority Fautrey & Lambotte Fusarium affine is a fungus fungal plant pathogen. External links http www.speciesfungorum.org Names Names.asp Index Fungorum http nt.ars grin.gov fungaldatabases USDA ARS Fungal Database DEFAULTSORT Fusarium Affine Category Fusarium affine Category Plant pathogens and diseases Hypocreales stub plant disease stub ... more details
Italic title Taxobox name Bulbophyllum affine image regnum Plantae unranked divisio Angiosperms unranked classis Monocots ordo Asparagales familia Orchidaceae subfamilia Epidendroideae genus Bulbophyllum species Bulbophyllum affine binomial binomial authority synonyms Bulbophyllum affine is a species of orchid in the genus Bulbophyllum . References http bulbophyllum checklist.bulbophyllum.at The Bulbophyllum Checklist http www.orchidspecies.com indexbulb.htm The Internet Orchid Species Photo Encyclopedia DEFAULTSORT Bulbophyllum affine Category Bulbophyllum affine Bulbophyllum stub az Bulbophyllum affine vi C u di p g n ... more details
Italic title Taxobox name Eulithidium affine image image caption regnum Animal ia phylum Mollusca classis Gastropoda unranked superfamilia clade Vetigastropoda superfamilia Phasianelloidea familia Phasianellidae subfamilia genus Eulithidium species E. affine binomial Eulithidium affine binomial authority C. B. Adams, 1850 synonyms ref synonyms Eulithidium affine is a species of sea snail , a marine gastropod mollusk in the family biology family Phasianellidae . ref name WoRMS WRMS species 419483 Eulithidium affine C. B. Adams, 1850 19 April 2010 ref Description Empty section date April 2010 Distribution Empty section date April 2010 References reflist External links Use dmy dates date January 2011 DEFAULTSORT Eulithidium Affine Category Phasianellidae Phasianellidae stub vi Eulithidium affine ... more details
italic title Taxobox name Agonum affine image regnum Animal ia phylum Arthropod a classis Insect a ordo Beetle Coleoptera familia Carabidae genus Agonum species A. affine binomial Agonum affine binomial authority William Forsell Kirby Kirby , 1837 synonyms Agonum carbo small LeConte, 1850 small Agonum affine is a species of ground beetle s in the Carabidae family. It is found in the United States . ref http carabidae.pro carabidae affine kirby 1837.html Carabidae of the World ref References Reflist carabidae stub Category Animals described in 1837 Category Carabidae ... more details
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