In mathematics , a homothety or homothecy or dilation is a Transformation mathematics transformation of an affine space determined by a point S called its center and a nonzero number called its ratio , which sends math M mapsto S lambda overrightarrow SM , math in other words it fixes S , and sends any M to another point N such that the segment SN is on the same line as SM , but scaled by a factor . ref J. Hadamard, Lessons in Plane Geometry, p. 145 ref In Euclidean geometry homotheties are the Similarity geometry similarities that fix a point and either preserve if nowrap > 0 or reverse if nowrap < 0 the direction of all vectors. Together with the Translation geometry translations , all homotheties of an affine or Euclidean space form a group, the group of homothety translations . These are precisely the affine transformation s with the property that the image of every line L is a line parallel geometry parallel to L . In Euclidean geometry, a homothety of ratio multiplies distances between points are by and all areas by sup 2 sup . The first number is called the ratio of magnification or dilation factor or scale factor or similitude ratio . Such a transformation can be called an enlargement if the scale factor exceeds 1. See also Scaling geometry a similar notion in vector spaces Homothetic center , the center of a homothetictransformation taking one of a pair of shapes into the other The Hadwiger conjecture combinatorial geometry Hadwiger conjecture on the number of strictly smaller homothetic copies of a convex body that may be needed to cover it Homothetic function economics , a function of the form U f y in which f is a homogeneous function and U is a monotonic function monotonically increasing function . External links http www.cut the knot.org Curriculum Geometry Homothety.shtml Homothety , interactive applet from Cut the Knot . Reflist Category Geometry Category Functions and mappings Category Linear operators ar az Homotetiya ca ... more details
unreferenced date May 2010 Homothetic preferences is a subset of preferences used in economics when analyzing the demand for Consumption economics consumption of various goods and services . In mathematics, a function of two or more arguments is homothetic if all ratios of its first partial derivatives depend only on the ratios of the arguments, not their levels see homothetictransformation . In economics, a model with competitive consumers or producers optimizing subject to homothetic utility or production functions, will imply that ratios of goods demanded depend only on relative prices, not on income or scale. Intratemporally homothetic preferences This assumption on individual preferences assures that decision makers with different incomes but facing the same prices will demand goods in the same proportions. Intertemporally homothetic preferences Models of modern macroeconomics and public finance often assume the constant relative risk aversion form for within period utility also called the power utility power or isoelastic form . The reason is that, in combination with additivity over time, this gives homothetic intertemporal preferences and this homotheticity is of considerable analytic convenience for example, it allows for the analysis of steady states in growth models . These assumptions imply that the elasticity of intertemporal substitution , and its inverse, risk aversion fluctuation risk aversion , are constant rich and poor decision makers are equally averse to proportional fluctuations in consumption. This may have significant implications, for example when evaluating the Welfare cost of business cycles costs of business cycles or evaluating a policy change in a dynamic general equilibrium model with heterogeneous agents. economics stub DEFAULTSORT Homothetic Preferences Category Utility Category Decision theory ... more details
geometry Homothetictransformation Radical axis , power center geometry radical center Apollonius ...Image Homothetic transformation.svg thumb right Figure 1 The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center. In geometry , a homothetic center also called a center of similarity or a center of similitude ... homothetic center S . The angles at corresponding points are the same and have the same sense ... If two geometric figures possess a homothetic center, they are Similarity geometry similar to one ... scaling. The homothetic center and the two figures need not lie in the same plane they can be related by a 3D projection projection from the homothetic center. Homothetic centers may be external .... Circles Image Circles homothetic centers.svg thumb right 300px Figure 3 Two circles have both types of homothetic centers, internal I and external E . The radii of the circles r sub 1 sub and r sub 2 sub are proportional to the distance d from each homothetic center. The points A sub 1 sub and A sub ... similar to one another and mirror symmetric. Hence, any pair of circles has both types of homothetic centers, internal and external their two homothetic centers lie on the line joining the centers ..., the internal and external homothetic centers may be found as follows. Two radii are drawn in the two ... and A sub 2 sub in Figure 3 intersects the line of centers at the external homothetic center. Conversely ... homothetic center. As a limiting case of this construction, a line tangent to both circles, where the circles fall on opposite sides, passes through the internal homothetic center, as illustrated by the line ... given circle, where the circles fall on the same side, passes through the external homothetic center ... given circles. In general, a ray emanating from a homothetic center will intersect each of its ... sub in Figure 3. Points which are collinear with respect to the homothetic center but are not homologous ... more details
wiktionarypar transformationTransformation may refer to TOCright 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 Metamorphosis , the biological process of changing physical form after birth or hatching Malignant 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 Transformation law , a concept in copyright law Transformation patent law Transformation Tal Wilkenfeld album , and album by, bassist, Tal Wilkenfeld Transformation music Transformation , a song by Nona Hendryx Transformation warfare Transformation of culture Transformation design , a design process Transformation fetish 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 See also Transform disambiguation Transformation Story Archive Transformation recruitment disambig cs Transformace de Transformation es Transformaci n fr Transformation nl Transformatie pl Transformacja pt Transforma o ru sk Transform cia sv Transformation ... 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 business stub ... more details
Infobox Television episode Title The Transformation Series Fringe TV series Fringe Image Deleted image removed File Fringe The Road Not Taken.jpg 250px Caption An episode of spontaneous combustion Season 1 Episode 13 Airdate February 3, 2009 Production 3T7662 Story Zack Whedon br J. R. Orci Director ... Ability The Transformation is the thirteenth List of Fringe episodes episode of the Fringe season ... after Hicks transformation restarts, depriving Olivia of the necessary information. Conrad makes ... The Transformation was written by Zack Whedon and J.R. Orci . ref name latimes ref name avclub ... 2010, The Transformation had an early screening at the November 2009 Paley Center for Media ... Pinkner replied that the huge porcupine man on the airplane from The Transformation was more shocking ... The Transformation aired, actor Joshua Jackson considered it his favorite episode. ref cite web ... 2011 02 18 ref Reception Ratings The Transformation was watched by 12.78 million viewers in the United ... 2009 02 fringe transfor.html title Fringe Transformation publisher Los Angeles Times first ... 950916p1.html title Fringe The Transformation Review publisher IGN first Ramsey last Isler date 2009 ... a transformation in the interpersonal dynamics of the show? If this dud of an episode serves a larger ... away . ref cite web url http open.salon.com blog josie kafka 2009 12 21 fringe the transformation 113 title Fringe The Transformation 1.13 publisher Open Salon .com first Josie last Kafka date 2009 12 ... t say that The Transformation broke any new ground. If anything, it recapitulated pretty much every ... cite web url http www.avclub.com articles the transformation,23392 title The Transformation publisher ... 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, The Category Fringe ... more details
A homothetic vector field sometimes homothetic collineation or homothety is a projective vector field which satisfies the condition math mathcal L X g ab 2c g ab math where c is a real constant. Homothetic vector fields find application in the study of gravitational singularity singularities in general relativity. See also Affine vector field Curvature collineation Killing vector field Matter collineation Spacetime symmetries relativity stub Category Mathematical methods in general relativity ... more details
found in any triangle. Another transformation introduced to young students is the homothetictransformation dilation . However, the inversive geometry reflection in a circle reflection in a circle transformation ... quarter turn. Such results show that transformation geometry includes non commutative processes. An entertaining ... school transformation geometry, is usually reserved for college students. Experiments with concrete ... with complex number s, hypercomplex number s, or matrix mathematics matrices to express transformation geometry. Such transformation geometry lessons present an alternate view that contrasts with classical ... , translated by Michael B.P. Slater, Academic Press . George E. Martin 1982 Transformation Geometry ... more details
matrix for an affine transformation Affine geometry Homothetictransformation Similarity transformation ... fractal that exhibits affine self similarity In geometry , an affine transformation or affine map ..., two affine space s consists of a linear transformation followed by a translation geometry translation math x mapsto A x b. math In the finite dimensional case each affine transformation is given by a matrix ... transformation in Euclidean space is one that preserves The Line geometry collinearity relation between points i.e., the points which lie on a line continue to be collinear after the transformation Ratios ... math p 2 p 1 p 3 p 2 math is preserved In general, an affine transformation is composed of linear ... is called affine transformation matrix , or projective transformation matrix as it can also be used to perform Projective transformation s . This representation exhibits the set of all Inverse function ... at 0,0, ... 0, 1 . A translation within the original space by means of a linear transformation of the higher dimensional space is then possible specifically, a shear transformation . The coordinates ... in computer graphics . Properties An affine transformation is invertible if and only if A is invertible ... then the transformation preserves area these also form a subgroup. Combining both conditions we have ... equal to 1 for all b the transformation has exactly one Fixed point mathematics fixed point there is a b for which the transformation has exactly one fixed point affine transformations with matrix A can be written as a linear transformation with some point as origin If there is a fixed point, we can take that as the origin, and the affine transformation reduces to a linear transformation. This may make it easier to classify and understand the transformation. For example, describing a transformation ... behavior of the transformation than describing it as a combination of a translation and a rotation. However, this depends on application and context. Describing such a transformation for an object ... more details
Bilinear transformation can refer to Bilinear operator M bius transformation disambig de Bilineare Transformation Long comment to avoid being listed on short pages ... more details
Canonical Transformation may refer to Symplectomorphism , a mathematical treatment Canonical transformation , a physics treatment disambiguation ... more details
The Great Transformation may refer to The Great Transformation book , a book by Karl Polanyi on the rise of the market economy in England The Great Transformation Norway , a period of social change in Norway in the mid to late 19th century Disambig ... more details
In mathematics , a congruent transformation or congruence transformation is Another term for an isometry see congruence geometry . A Transformation mathematics transformation of the form A P sup T sup AP , where A and P are square matrices, P is invertible matrix invertible , and P sup T sup denotes the transpose of P see Congruence relation Linear algebra congruence in linear algebra . disambig Category mathematical disambiguation ... more details
Orphan date February 2009 Transformation efficiency is the efficiency by which cells can take up extracellular DNA and express genes encoded by it. This is based on the competence biology competence of the cells. It can be calculated by dividing the number of successful transformants by the amount of DNA used during a transformation genetics transformation procedure. Transformants are cells which have taken up DNA foreign, artificial or modified and which can express genes on the introduced DNA. Factors affecting transformation efficiency A study done in E. coli found that transformation efficiency declines linearly with increasing plasmid size, and that there is a similar transformation efficiency for relaxed and DNA supercoil supercoiled plasmids. This study also found that individual cells were capable of taking up many DNA molecules, and that the presence of multiple plasmids did not significantly affect the occurrence of successful transformation events. ref cite journal author Hanahan D title Studies on the transformation of Escherichia coli with plasmids journal J Mol Bio volume 166 issue 4 pages 557 580 year 1983 pmid 6345791 doi 10.1016 S0022 2836 83 80284 8 ref See also Transformation genetics References references External links http www.sciencegateway.org tools transform.htm Bacteria Transformation Efficiency Calculator Category Genetics ... more details
Refimprove date April 2009 A model transformation in Model driven engineering takes as input a model conforming to a given Metamodeling metamodel and produces as output another model conforming to a given metamodel. Overview If the source and target metamodels are identical, the transformation is called endogeneous . If they are different the transformation is called exogeneous . If the level of abstraction does not change, the transformation is called horizontal . If the level of abstraction does change, the transformation is called vertical . These two distinctions are orthogonal . A model transformation may also have several source models and several target models. One of the characteristics of a model transformation is that it is also a model, i.e. it conforms to a given metamodel. This facilitates the definition of Higher Order Transformation s HOTs ref See Massimo Tisi et. al. On the Use of Higher Order Model Transformations. Lecture Notes in Computer Science, 2009, Volume 5562 2009, 18 33, DOI 10.1007 978 3 642 02674 4 3 ref , i.e. transformations taking other transformations as input and or transformations producing other transformations as output. Several model transformation language s in short MTL are presently available ref See Model Transformation Language Available transformation languages list of available transformation languages ref See also Model driven engineering MDE Model driven architecture MDA Domain specific language DSL Model transformation language Refinement Transformation disambiguation Program transformation Data transformation Graph transformation References Reflist Further reading Model Driven Architecture Applying MDA to Enterprise Computing ..., K, and Helsen, S Classification of Model Transformation Approaches. In Proceedings of the OOPSLA ... site MDA and Model Transformation http www.model transformation.org site access DEFAULTSORT Model Transformation Category Systems engineering Category Unified Modeling Language de Modelltransformation ... more details
A Procrustes transformation is a geometric transformation that involves only translation , rotation , uniform scaling , or a Function composition combination of these Linear transformation transformations . Hence, it may change the size, but not the shape of a geometric object. Named after the mythical Greek robber, Procrustes , who made his victims fit his bed either by stretching their limbs or cutting them off. See also Procrustes analysis Orthogonal Procrustes problem Affine transformation , which also allows for Shear matrix shear . External links http www.fon.hum.uva.nl praat manual Procrustes transform.html Procrustes transformation Category Euclidean symmetries Geometry stub ... more details
Data transformation A transformation language is a computer language designed to transform some input text in a certain formal language into a modified output text that meets some specific goal. Program transformation systems such as Stratego XT , TXL programming language TXL , DMS Software Reengineering Toolkit DMS , and ASF SDF Meta Environment ASF SDF all have transformation languages as a major component. The transformation languages for these systems are driven by declarative descriptions of the structure of the input text typically a grammar , allowing them to be applied to wide variety of formal languages and documents. Macro computer science Macro languages are a kind of transformation languages to transform a meta language into specific higher programming language like Java programming language Java , C , Fortran In the model driven engineering technical space, there are model transformation language s MTLs , that take as input models conforming to a given metamodel and produce as output models conforming to a different metamodel. An example of such a language is the QVT Object Management Group OMG standard. There are also low level languages such as the Lx family ref http lx.mii.lu.lv ref implemented by the Bootstrapping compilers bootstrapping method . The L0 language may be considered as assembler for transformation languages. There is also a high level graphical language built on upon Lx called MOLA. ref http mola.mii.lu.lv ref There are a number of XML transformation language s. These include XSLT , XQuery , Streaming Transformations for XML STX , FXT , XDuce , CDuce ... data migration data transformation metadata model transformation refinement contrast valign top Languages and typical transforms ATLAS Transformation Language ATL AWK tabular data transforms ... www.program transformation.org The Program transformation Wiki Computer language compu lang stub DEFAULTSORT Transformation Language Category Transformation languages Category Programming language classification ... more details
In mathematics, a rigid transformation or a Euclidean transformation is a transformation from a Euclidean space to itself that preserves distances between every pair of points isometry . In particular, any object will have the same shape and size before and after a rigid transformation. Rigid tranformations include rotation mathematics rotations , translation mathematics translations , or their combination sometimes called roto translations . Sometimes reflection mathematics reflections are excluded from the definition of a rigid transformation by imposing that the transformation also preserve the orientation mathematics handedness of figures in the Euclidean space. To avoid ambiguity, this smaller class of transformations is known as proper rigid transformations. In general, any proper rigid transformation can be decomposed as a rotation followed by a translation. Any rigid transformation can be decomposed as an improper rotation followed by a translation or as a sequence of reflections . The set of all proper rigid transformations is a group mathematics group called the Euclidean group . All rigid transformations are affine transformations . Rigid transformations which involve a translation are not linear transformation s. Not all transformations are rigid transformations. An example is a shear mathematics shear , which changes two axes in different ways, or a similarity transformation , which preserves angles but not lengths. In mechanics , proper rigid transformations are used to represent the Displacement vector linear and angular displacement of Rigid body rigid bodies . Formal definition A rigid transformation is formally defined as a transformation that, when acting ... &minus 1 sup i.e., R is an orthogonal transformation , and t is a vector giving the translation of the origin. A proper rigid transformation has, in addition, determinant det R 1 which means that R is a rotation mathematics rotation an orientation preserving orthogonal transformation . References citation ... more details
In algebra , a transformation semigroup or composition semigroup is a collection of function mathematics ... the identity function , it is a transformation or composition monoid . This is the semigroup anologue of a permutation group . A transformation semigroup of a set has a tautological semigroup ... semigroup can be realized as a transformation semigroup of some set. Transformation semigroups and monoids A transformation semigroup is a pair X , S , where X is a set and S is a semigroup of transformations of X . Here a transformation of X is just a function from X to itself, not necessarily ... closed under composition of functions . If S includes the identity transformation of X , then it is called a transformation monoid . Obviously any transformation semigroup S determines a transformation monoid M by taking the union of S with the identity transformation. A transformation monoid whose elements are invertible is a permutation group . The set of all transformations of X is a transformation monoid called the full transformation monoid or semigroup of X . It is also called the symmetric semigroup of X and is denoted by T sub X sub . Thus a transformation semigroup or monoid is just a subsemigroup or submonoid of the full transformation monoid of X . The full transformation monoid is a regular semigroup . If X , S is a transformation semigroup then X can be made into a semigroup action of S by evaluation math s cdot x s x text for s in S, x in X. math This is a monoid action if S is a transformation monoid. The characteristic feature of transformation semigroups, as actions, is that they are effective ... if a semigroup S acts on a set X by T s , x s &bull x then we can define, for s S , a transformation ... if and only if X , T is effective, in which case the image of this map is a transformation semigroup ... group . This theorem generalizes straightforwardly to monoids any monoid M is a transformation ... set of the monoid corresponding to S to realise S as a transformation semigroup of X . In particular ... more details
Power transformation may refer to Energy transformation Power transform disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
Unreferenced date August 2008 The Art of Transformation ISBN 9781933966007 is a 2006 book by former United States House of Representatives U.S. House Speaker of the United States House of Representatives Speaker Newt Gingrich and Nancy Desmond. nonfiction book stub DEFAULTSORT Art of Transformation Category 2006 books ... more details
Unreferenced date December 2009 In chemistry a chemical transformation shows the conversion chemistry conversion of a substrate biochemistry substrate to a product omitting the reagent s and catalyst s or underlying reaction mechanism as opposed to a chemical reaction . The phrase Chemical transformation is used in a more general sense when reaction specifics are not relevant or not available. The IUPAC Nomenclature for Transformations is based on this type of transformations. DEFAULTSORT Chemical Transformation Category Chemical processes Category Chemical reactions ... more details
In mathematics, a unitary transformation may be informally defined as a transformation mathematics transformation that respects the inner product the inner product of two vectors before the transformation is equal to their inner product after the transformation. More precisely, a unitary transformation is an isomorphism between two Hilbert space s. In other words, a unitary transformation is a bijective function math U H 1 to H 2 , math where math H 1 math and math H 2 math are Hilbert spaces, such that math langle Ux, Uy rangle langle x, y rangle math for all math x math and math y math in math H 1 math . A unitary transformation is an isometry , as one can see by setting math x y math in this formula. In the case when math H 1 math and math H 2 math are the same space, a unitary transformation is an automorphism of that Hilbert space, and then it is also called a unitary operator . A closely related notion is that of antiunitary transformation , which is a bijective function math U H 1 to H 2 , math between two complex number complex Hilbert spaces such that math langle Ux, Uy rangle overline langle x, y rangle langle y, x rangle math for all math x math and math y math in math H 1 math , where the horizontal bar represents the complex conjugate . See also Time reversal antiunitary Unitary group Unitary operator Unitary matrix Wigner s Theorem Mathanalysis stub Category Linear algebra Category Functional analysis fr Transformation unitaire pl Transformacja unitarna ru uk ... more details
dablink In genetics, Transformation genetics transformation is also used to describe the incorporation of foreign DNA by bacteria. Malignant transformation is the process by which cells acquire the properties of cancer . This may occur as a primary process in normal tissue, or secondarily as malignant degeneration of a previously existing benign tumor . There are many causes of primary malignant transformation, or tumorigenesis . The underlying commonality is genetic mutation either by inheritance or more commonly by acquiring mutations in one s DNA over time. Although malignant transformation may occur because of changes within the cell, it can be induced by inorganic toxic substances such as cadmium or arsenite and organics such as tobacco specific nitrosamines . It is also thought that some malignant transformations are due to viruses such as the Epstein Barr virus, although this is currently restricted to just a few cancer types. A more common cancer associated with viral infection is cervical cancer , which has been linked to the human papilloma virus . Malignant transformation of cells in a benign tumor may be detected by pathology pathologic examination of tissues. Often the clinical signs and symptoms are suggestive of a malignant tumor. The physician, during the medical history examination, can find that there have been changes in size or patient sensation and, upon direct examination, that there has been a change in the lesion itself. Risk assessment s can be done and are known for certain types of benign tumor which are known to undergo malignant transformation. One of the better known examples of this phenomenon is the progression of a nevus to melanoma . References ... s Ulcer. J. Bum Care and Rehab., 12, 3 1991. See also Teratoma Teratoma with malignant transformation Richter s transformation in blood cancers DEFAULTSORT Malignant Transformation Category Oncology Oncology stub de Maligne Transformation ru ur ... more details
Unreferenced stub auto yes date December 2009 Viral transformation most commonly refers to the virus induced malignant transformation of an animal cell biology cell in a body or cell culture . In molecular biology , the term may also refer to the transfection of DNA into a host cell using a viral vector . Virus induced malignant transformation See also Malignant transformation Viral transformation can impose characteristically determinable features upon a cell. Typical phenotype phenotypic changes include high saturation density, anchorage independent growth, loss of contact inhibition, loss of orientated growth, immortalisation, disruption of the cell s cytoskeleton . Epidemiological studies suggest that malignant transformation of cells by viruses occurs via multiple steps. This involves initiation, promotion and progression events. Viruses act along with other factors to transform cells. The persistence of at least part of the viral genome within the cell is required for cell transformation. This is accompanied by the continual expression from a number of viral gene s. These genes interfere with a cell s signal transduction signaling pathway causing the observed phenotypic changes of the cell. The end result is a transformed cell showing increased cell division, which is favorable to the virus. Transformation using viral vectors The term transformation genetics transformation is also used for the introduction of foreign DNA into cells, which can be achieved using a viral vector to transfer the DNA. This process is also referred to as transfection or transduction genetics transduction , respectively. Genetic engineering DEFAULTSORT Viral Transformation Category Molecular biology Category Virology Category Microbiology Molecular cell biology stub ... more details
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