Unreferenced stub auto yes date December 2009 In theoretical physics , the minimalmodels are a very concrete well defined type of rational conformal field theory . The individual minimalmodels are parameterized by two integers p,q that are moreover related for the unitary minimalmodels. The first element of the sequence of the minimalmodels is the critical behavior of the Ising model , followed by the tricritical Ising model . There also exist supersymmetric minimalmodels. DEFAULTSORT MinimalModels Category Conformal field theory Category Exactly solvable models Phys stub ... more details
wiktionary minimal minimalistic Minimal may refer to Minimal element , an element of a subset Minimal music , a style of music Minimal techno , a minimalist sub genre of techno Minimalism , an art movement Minimalism computing , the application of minimalist philosophies and principles in hardware and software design and usage Minimal song Minimal song , a song by Pet Shop Boys Minimally invasive procedure See also Maximal disambiguation disambig cs Minimal de Minimal es M nimo fr Minimal pl Minimal ... more details
For the Australian alternative rock band Models band Refimprove date August 2010 Infobox musical artist See Wikipedia WikiProject Musicians name The Models image caption image size Only for images narrower than 220 pixels background group or band alias Models origin Harrow, London , England instrument genre Punk rock Punk occupation years active c. 1977&ndash c. 1978 label Step Forward associated acts Siouxsie and the Banshees , Rema Rema , Adam Ant , Adam and the Ants , Mass English band Mass , The Wolfgang Press website current members past members Cliff Fox br Marco Pirroni br Mick Allen br Terry Day notable instruments The Models credited also as Models was a short lived punk band formed in Harrow, London , England . It consisted in Cliff Fox on vocals and guitar, Marco Pirroni on guitar, Mick Allen on bass and Terry Day on drums. Pirroni and Allen befriended while attending art school in Harrow. When punk emerged in 1976, the first formed Siouxsie and the Banshees , playing guitar, although for brief time. Shortly after that, he and Allen formed a band called The Beastly Cads, who later changed their name to The Models. ref http www.punk77.co.uk groups models marco pirroni interview2006.htm Punk77.co.uk ref The band only released one single Freeze and recorded four songs in the Peel Sessions, before dissolving. Later, Pirroni and Allen formed Rema Rema , a post punk band. Pirroni later reteamed up with Terry Day, who since then was named Terry Lee Miall, in Adam and the Ants , beginning to work alongside that band s singer and frontman, Adam Ant . Allen went on to other projects, the longest running being The Wolfgang Press on the influential British record label 4AD ... Geniuser. References Reflist External links http www.punk77.co.uk groups models.htm PUNK77 The Models ... Lee Miall formerly Terry Day interview DEFAULTSORT Models, The Category English punk rock groups es The Models ... more details
. Physical models of area minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film , which is a minimal surface whose boundary is the wire frame. Examples Classical examples of minimal surfaces include the plane geometry plane , which is a trivial mathematics trivial case catenoid s minimal surfaces made by rotating a catenary once around its ... 28, 2004 Online journal with several published models of minimal surfaces cite web author Stewart ...dablink For minimal surfaces in algebraic geometry see Minimal model birational geometry . Image Verrill minimal surface.jpg thumb right Verrill surface Verrill Minimal Surface Image Verrill minimal surface.jpg 200px right thumb Verrill minimal surface generated using MATLAB. Image Povr inska napetost milnica.jpg thumb Minimal surface In mathematics , a minimal surface is a surface with a mean curvature ... surface Recent work in minimal surfaces has identified new completely embedded minimal surfaces, that is minimal surfaces which do not intersect. In particular Costa s minimal surface was first described .... Minimal surfaces have become an area of intense mathematical and scientific study over the past ... nanotechnology applications. In the art world, minimal surfaces have been extensively ..., possibly at infinity , one can define its mean curvature , and a minimal surface is one for which the mean curvature vanishes. The term minimal surface is because these surfaces originally arose as surfaces ... boundary, but the term is used more generally. Minimal surfaces are the critical points .... The definition of minimal surfaces can be generalized extended to cover constant mean curvature surface ... Wiener process Brownian motion on a minimal surface leads to probabilistic proofs of several theorems on minimal surfaces. ref R. Neel 2008 http arxiv.org abs 0805.0556 arXiv , http dx.doi.org 10.1016 ... Bilinear interpolation References cite book author Robert Osserman title A Survey of Minimal ... more details
In mathematics , the term minimal prime is used in distinct ways Minimal prime commutative algebra describes the usage in commutative algebra Minimal prime recreational mathematics describes the usage in recreational number theory disambig ... more details
disambig Minimal polynomial may refer to Minimal polynomial linear algebra Minimal polynomial of a square matrix A , the monic polynomial p x of least degree such that p A 0. Minimal polynomial field theory Minimal polynomial of an algebraic element over a field F , the monic polynomial p x over F of least degree such that p 0. fr Polyn me minimal ru ... more details
In theoretical physics, the term minimal model usually refers to a special class of conformal field theory conformal field theories that generalize the Ising model, or to some closely related representations of the Virasoro algebra . It is a simple CFT model with finite primary fields and hence is completely solvable. In birational geometry, a Minimal model birational geometry minimal model of an algebraic variety is one for which the canonical line bundle is numerically effective, in particular as much has been blown down as possible. It can also mean the N ron minimal model of an abelian variety or elliptic curve. In algebraic topology, the Sullivan minimal model of a differential graded algebra is used in rational homotopy theory . In endocrinology and diabetology, the term minimal model denotes a mathematical model of metabolic control of glucose homeostasis via insulin. In set theory, the minimal model set theory minimal model of ZFC is part of the Constructible universe. mathdab ... more details
In the branch of abstract algebra known as ring theory , a minimal right ideal of a ring mathematics ring R is a nonzero right ideal which contains no other nonzero right ideal. Likewise a minimal left ideal is a nonzero left ideal of R containing no other nonzero left ideals of R , and a minimal ideal ... Said another way, minimal right ideals are minimal element s of the poset of nonzero right ideals ... may admit the zero ideal, and so zero could potentially be a minimal element in that poset. This is the case for the poset of prime ideal s of a ring, which may include the zero ideal as a minimal prime ideal . Definition The definition of a minimal right ideal N of a module R is equivalent to the following ... simple right R module. Minimal right ideals are the duality mathematics dual notion to the idea of maximal ideal maximal right ideals . Properties Many standard facts on minimal ideals can be found .... In contrast, there is no guarantee that minimal right, left, or two sided ideals exist in a ring ... structure defined in terms of the minimal right ideals of R . Rings for which every right ideal contains a minimal right ideal are exactly the rings with an essential right socle. Any right Artinian ring or right Kasch ring has a minimal right ideal. domain ring theory Domains which are not division ring s have no minimal right ideals. In rings with unity, minimal right ideals are necessarily principal ideal principal right ideals , because for any nonzero x in a minimal right ideal N , the set xR is a nonzero right ideal of R inside N , and so xR N . Brauer s lemma Any minimal right ideal ... element of R . harv Lam 2001 loc p.162 If N sub 1 sub and N sub 2 sub are nonisomorphic minimal right ... minimal ideals of a ring R , then N sub 1 sub N sub 2 sub 0 . A simple ring with a minimal right ideal is a semisimple ring . In a semiprime ring , there exists a minimal right ideal if and only if there exists a minimal left ideal. harv Lam 2001 loc p.174 Generalization A nonzero submodule ... more details
Minimal logic , or minimal calculus , is a Mathematical logic symbolic logic system originally developed by Ingebrigt Johansson . It is a variant of intuitionistic logic that rejects not only the classical logic classical law of excluded middle as intuitionistic logic does , but also the principle of explosion ex falso quodlibet . Just like intuitionistic logic, minimal logic can be formulated in a language using , , , logical implication implication , logical conjunction conjunction , logical disjunction disjunction and falsum as the basic logical connective connectives , treating A as an abbreviation for A . In this language it is axiomatized by the positive fragment i.e., formulas using only , , of intuitionistic logic, with no additional axioms or rules about . Thus minimal logic is a subsystem of intuitionistic logic, and it is strictly weaker as it does not derive the ex falso quodlibet principle math neg A,A vdash B math however, it derives its special case math neg A,A vdash neg B math . Adding the ex falso axiom math neg A to A to B math to minimal logic results in intuitionistic logic, and adding the double negation law math neg neg A to A math to minimal logic results in classical logic. Minimal logic is closely related to simply typed lambda calculus via the Curry Howard isomorphism , ie. the typing derivation s of simply typed lambda terms are isomorphic to natural deduction proofs in minimal logic. References Ingebrigt Johansson Johansson, Ingebrigt , 1936, http www.numdam.org numdam bin item?id CM 1937 4 119 0 Der Minimalkalkul, ein reduzierter intuitionistischer Formalismus . Compositio Mathematica 4 , 119 136. Logic mathlogic stub Category Non classical logic Category Constructivism mathematics Category Systems of formal logic fr Logique minimale uk ... more details
In control theory , given any transfer function , any state space controls state space model that is both controllability controllable and observability observable and has the same input output behaviour as the transfer function is said to be a minimal realization of the transfer function . The realization is called minimal because it describes the system with the minimum number of states. The minimum number of state variables required to describe a system equals the order of the differential equation more state variables than the minimum can be defined. For example, a second order system can be defined by two minimal realization or more state variables. math stub Category Control theory pl Model minimalny ... more details
ref aesthetic that exploits the use of repetition, and understated development. Minimal techno is thought ... Funk , Billboard Books, 1999, pp. 199 200 . ref although what is currently referred to as minimal ... journalist Philip Sherburne argues that minimal techno uses two specific stylistic approaches skeletalism ... minimal techno, only the core elements are included with embellishments used only for the sake of variation ... are layered over time, but with little variation in sonic elements. Today the influence of minimal ... Culture , New York Continuum, 2006, pp. 324 325 . ref Regardless of the style, minimal Techno corkscrews ... in House and Techno, in Audio Culture , New York Continuum, 2006, p. 322 . ref The minimal techno producer ... of Electronic Funk , Billboard Books, 1999. ref The minimal techno sound that emerged at this time ... hosted at http www.spannered.org spannered.org ref The average tempo of a minimal techno track is between ... tempo. In the early minimal techno scene most tracks were constructed around a Roland TR 808 or Roland TR 909 drum machine . Both are still often used on today s minimal techno tracks. In contrast to minimal house , minimal techno is less afrocentric and focusses more on middle frequencies ... name cox Philip Sherburne also proposes what the origins of Minimal techno might be. Sherburne states that, like most contemporary electronic dance music, minimal techno has its roots in the landmark works of pioneers such as Kraftwerk and Detroit Techno s Derrick May and Juan Atkins . Minimal techno ... Continuum, 2006, pp. 321 322 . ref By 1994, according to Sherburne, the term minimal was in use to describe ... Los Angeles based writer Daniel Chamberlin, attributes the origin of minimal techno to the German ... 09 18 music party arty Party Arty Minimal techno producers live up to their avant garde heritage ... Sherburne has suggested that the noted similarities between minimal forms of dance music and minimalist ... explain why certain stylistic features of minimal techno sound similar to works of Reich s that employ ... more details
Citations missing date September 2008 Infobox Single Name Minimal Cover PetShopBoys Minimal.JPG Border yes Artist Pet Shop Boys from Album Fundamental Pet Shop Boys album Fundamental B side In private ... single I m with Stupid Pet Shop Boys song I m with Stupid br 2006 This single Minimal br 2006 Next single Numb Pet Shop Boys song Numb br 2006 Minimal is a song by United Kingdom British synthpop musical ... Pet Shop Boys song I m with Stupid was chosen instead. Track listings CD Parlophone CDR6708 UK Minimal radio edit 3 40 In private 7 inch mix 4 13 CD Parlophone CDRS6708 UK Minimal radio edit 3 40 Minimal DJ Tocadisco Tocadisco s Sunday at Space Remix 8 04 Minimal M Factor Remix 8 49 Minimal U MYX software DVD Parlophone DVDR6708 UK Minimal Telex band Telex Hell mix 6 19 Blue on blue 3 15 No time for tears 7 inch mix 3 39 Minimal video Clear 7 Minimal radio edit 3 40 In private 7 inch mix 4 13 Promos CD Parlophone CDRDJ6708 UK Minimal radio edit 3 27 released June 2006 CD Parlophone 00946 371144 2 1 UK Minimal radio edit 3 40 Minimal Tocadisco s Sunday at Space Remix 8 04 Minimal M Factor Remix 8 49 Minimal M Factor dub 7 44 Minimal Tiga musician Tiga s M I N I M A L remix 5 38 Minimal Tiga s M I N I M A L dub 5 38 Minimal Superchumbo s Light and Shade dub 8 28 Minimal Telex Hell remix 6 19 Minimal Telex Heaven remix 4 29 In private Tomcraft 7 mix 3 51 Remix promo 12 Parlophone MINIMAL001 UK Minimal Tiga s M I N I M A L remix 5 38 Minimal Tiga s M I N I M A L dub 5 38 Minimal Telex Hell remix 6 19 Minimal Telex Heaven remix 4 29 Remix promo Deleted image removed Image U MYX Pet Shop Boys.PNG right thumb 250px The U MYX interface for Minimal . deletable image caption 1 Saturday, 3 November 2007 Another remix of Minimal by Lobe appears on the limited edition bonus CD of Fundamental , Fundamentalism . The Tiga remix was included on the Japanese release. Another remix of Minimal ... Songs written by Neil Tennant Category Songs written by Chris Lowe ru Minimal ... more details
reference, a FACT Magazine article penned by the Minimal Wave label founder. A greater number of less interested sources would be preferable. Minimal Wave is a contentiously named ref name gabriele cite web url http www.popmatters.com pm review 126314 various artists the minimal wave tapes volume one title Various Artists The Minimal Wave Tapes Volume One review last Gabriele first Timothy date ... Wave music New Wave , so called minimal electronic or synthesizer music, Synthpunk , Synthpop ... url http www.factmag.com 2010 01 26 20 best minimal wave title 20 best Minimal Wave magazine FACT magazine last Vasicka first Veronica date 26 January 2010 accessdate 2010 06 18 ref Although much Minimal ... include Minimalist music Minimalism in pop music minimal musical structures, ref name Vasicka ... can t speculate about it here without sources to cite. Veronica Vasicka, founder of the Minimal ... of Dutch magazines from the early 80s, and they kept using the terms minimal electronics , new ... this music, and I thought minimal wave could be it. When I registered the website, I was able to register ... one of the label s compilations, wrote Minimal Wave as a synecdoche of a broader scene has been a term ... publicity piece for the same compilation, she wrote The Minimal Wave genre actually formed only ... Wave 1978 1985 , mainly from North America, Europe and Japan. This music is sometimes referred to as Minimal Electronic, Minimal Synth, Cold Wave, New Wave, Techno pop, or Synthpop, depending on the particular ... culture Minimal Wave Records References reflist External links http www.minimalwave.org Minimal Wave Records MySpace minimalwave Minimal Wave Records http www.tinymixtapes.com Label Profiling Minimal Wave Minimal Wave, Crate digging For Obscure Gems To Reissue Tiny Mix Tapes , September, 2008. http anthemmagazine.com story 1234 Eye On 09 Minimal Wave , by Nik Mercer, January 16, 2009. http ... of Minimal Wave From North America 81 87 , by Franklin Bruno of the Boston Phoenix , April 1, 2008 ... more details
Unreferenced date December 2009 In mathematics , the method of considering a minimal counterexample or minimal criminal combines the ideas of inductive proof and proof by contradiction . Abstractly, in trying to prove a proposition P , one assumes that it is false, and that therefore there is at least one counterexample . With respect to some idea of size, which may need to be chosen skillfully, one assumes that there is such a counterexample C that is minimal . We expect that C is something quite hypothetical since we are trying to prove P , but it may be possible to argue that if C existed, it would have some definite properties. From those we then try to get a contradiction. If the form of the contradiction is that we can derive a further counterexample D , and that D is smaller than C in the sense of the working hypothesis of minimality, then this technique is traditionally called infinite descent . There may however be more complicated ways to argue. For example, the minimal counterexample method has been much used in the classification of finite simple groups . The Feit Thompson theorem , that infinite simple groups that are not cyclic group s have even order, was based on the hypothesis of some, and therefore some minimal, simple group G of odd order. Every proper subgroup of G can be assumed a solvable group , meaning that much theory of such subgroups could be applied. The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well ordering of some kind. The usual ordering on the natural number s is clearly possible, by the most usual formulation of mathematical induction but the scope of the method is well ordered induction of any kind. Fundamental theorem of arithmetic Euclid s proof Euclid s proof of the fundamental theorem of arithmetic is a simple proof using a minimal counterexample. Category Mathematical proofs ... more details
with a semantic relation, for example equivalence. Among all possible mappings, the minimal ... in the minimal set in time linear in the size of the input graphs, and ii none of the mapping elements in the minimal set can be dropped without losing property i . The main advantage of minimal mappings is that they are the minimal amount of information that needs to be dealt with. Notice that this is a rather ... and m the size of the two input ontologies. In particular, minimal mappings become crucial with large ..., potentially millions of them, are unmanageable. Minimal mappings provide clear usability advantages ... prone. Look at http eprints.biblio.unitn.it archive 00001525 01 078.pdf for a formal definition of minimal and, dually, redundant mappings, evidence of the fact that the set of minimal mappings always ... more details
In physics , minimal coupling refers to a coupling between field theory physics fields which involves only the charge physics charge distribution and not higher multipole moments of the charge distribution. This minimal coupling is in contrast to, for example, Pauli coupling , which includes the magnetic moment of an electron directly in the Lagrangian . In electrodynamics , minimal coupling is adequate to account for all electromagnetic interactions. Higher moments of particles are consequences of minimal coupling and non zero spin physics spin . Mathematically, minimal coupling is achieved by subtracting the charge math q math times the four potential math A mu math from the four momentum math p mu math in the Lagrangian or Hamiltonian math p mu p mu q A mu math Taken almost verbatim from Doughty s Lagrangian Interaction, pg. 456 ref name Doughty cite book last Doughty first Noel title Lagrangian Interaction url http www.amazon.com Lagrangian Interaction Introduction Relativistic Electrodynamics dp 0201416255 ref sr 1 1?ie UTF8&qid 1313027348&sr 8 1 publisher Westview Press year 1990 isbn 0201416255 ref See the Hamiltonian mechanics Charged particle in an electromagnetic field Hamiltonian mechanics article for a full derivation and examples. See also Gauge covariant derivative Hamiltonian mechanics Lagrangian mechanics References Reflist DEFAULTSORT Minimal coupling Category Gauge theories Category Particle physics Category Hamiltonian mechanics Category Lagrangian mechanics Category Quantum field theory Physics stub de Minimale Kopplung ... more details
In nuclear strategy , minimal deterrence also called minimum deterrence is an application of deterrence theory in which a state possesses no more nuclear weapons than is necessary to deter an adversary from attacking. ref Kristensen, Norris and Oelrich 2009, 21 ref Pure minimal deterrence is a doctrine of no first use , holding that the only mission of nuclear weapons is to deter a nuclear adversary by making the cost of a first strike unacceptably high. ref Kristensen, Norris and Oelrich 2009, 21 ref To present a credible deterrent, there must be the assurance that any attack would trigger a retaliatory strike. ref Lieber and Press 2006, 37 ref In other words, minimal deterrence requires rejecting a counterforce strategy in favor of pursuing survivable force that can be used in a countervalue ... strike capabilities during the Cold War , the People s Republic of China pursued a doctrine of minimal ... they term Minimum Credible Deterrence . ref Feickert and Kronstadt 2003, 9 ref Minimal deterrence .... For example, the United States nuclear force exceeds the requirements of minimal deterrence, and is structured ..., precision strike, and missile defense . ref Blair 2009, 23 ref One disadvantage of minimal ... is no longer credible. ref Stout 2010 ref A minimal deterrence strategy must also account for the nuclear .... ref Freedman 2003, 195 ref Additionally, a minimal deterrence capability may embolden a state when ... States. ref McVadon 2005, 6 ref Finally, while pursuing minimal deterrence during arms negotiations ... once minimal deterrence is reached because they will increase a state s vulnerability and provide ... to Minimal Deterrence A New Nuclear Policy on the Path Toward Eliminating Nuclear Weapons . http www.fas.org ... Nalebuff, Barry . Minimal Nuclear Deterrence. Journal of Conflict Resolution 32, no. 3 September ... www.au.af.mil au aunews archive 2010 0507 Articles0507 Stout0507.htm Minimal Deterrence Makes Minimal ... August 1, 2010. DEFAULTSORT Minimal Deterrence Category Nuclear strategies ... more details
Infobox musical artist name Minimal Compact image Minimal compact.jpg caption Minimal Compact s reunion gig, Tel Aviv image size background group or band alias origin Amsterdam , Brussels , Tel Aviv, Israel instrument genre New wave music New Wave , alternative rock , post punk , experimental rock years ... Minimal Compact was an Israel i rock music rock band associated with the post punk and indie rock movement ..., Minimal Compact played a small role in the European rock scene. Malka Spigel bass, vocals , Samy Birnbach ... had hit upon something worthy of development and their first, self titled, mini album Minimal Compact ... , It Takes a Lifetime . With this release Minimal Compact had become a real band with the addition of the native Amsterdammer Max Franken on drums. Now Minimal could play live, this was to prove a strong element in their career. As Minimal began to tour more extensively they went from strength to strength ... line up became complete with the addition of guitarist vocalist Rami Fortis a long time Minimal cohort ... became live favorites. By this time Minimal had become established in Brussels and were at the hub of the local ... up Minimal Compact recorded a 12 Immigrants Songs featuring a Led Zeppelin cover with Israeli ... tours were cancelled because the US immigration authorities refused to grant them visas. Minimal ... the 60th birthday of Samy Birnbach . On November 12, 2011, it was announced that Minimal Compact ... Rami Fortis guitars, vocals Discography albums and EPs Albums 1981 Minimal Compact Crammed Discs ... Discs 1987 The Figure One Cuts Crammed Discs 1988 Minimal Compact Live Crammed Discs 2003 Returning ... http www.swimhq.com artists Minimal Biog.html Biography at swim website External links Sutton, Michael Allmusic class artist id p19355 biography pure url yes Minimal Compact Biography , allmusic.com, Macrovision Corporation Sheridan, David http www.trouserpress.com entry.php?a minimal compact Minimal Compact , TrouserPress Category Israeli musical groups Category New Wave groups fr Minimal Compact ... more details
Orphan date October 2008 Minimal decency is an ethical requirement according to the moral philosophy of Immanuel Kant . It refers to the minimum requirement of kindness obliged by Kantian ethics those actions which go beyond the call of duty are considered http plato.stanford.edu entries supererogation supererogation . People need not engage in supererogation in order to be responsible moral agent moral agents . The distinction between minimal decency an ethical obligation and supererogation helps moral agents understand and protect their own and each other s http www.quodlibet.net kant.shtml rational autonomy . Category Kantianism philo stub ... more details
No footnotes date December 2010 Infobox musical artist name Minimal Man image caption background group or band origin San Francisco , California , United States genre industrial music Industrial br Post punk br Experimental rock Experimental br Gothic Rock years active 1979 1988 label Subterranean Records br LTM Recordings LTM br CD Presents website http www.myspace.com minimalmanpatrickmiller Myspace fan page Minimal Man was an United States American industrial music industrial and experimental rock project, formed in 1979 in San Francisco , California . The group was founded and led by Patrick Miller, a visual and sound artist who moved to San Francisco in the late 1970s. The band often changed members featuring at different times members of bands such as Tuxedomoon , Factrix and others active in the then thriving San Francisco experimental post punk and industrial scenes. Their cover version cover of The Shroud Of featured one of Miller s signature mask head paintings. Minimal Man remained active in San Francisco recording on the Subterranean Records label till the mid 1980s, after which Miller relocated to Europe, often working with compatriots Tuxedomoon who had made a similar move previously. The Minimal Man output ceased after the 1980s, and Miller returned to Los Angeles , where he worked as a set dresser. Miller died at his home in Eagle Rock, California , on December 14, 2003. ref Sisario, B. http www.nytimes.com 2004 01 08 arts patrick miller 51 avant garde leader of antimusic band.html Patrick Miller, 51, Avant Garde Leader Of Antimusic Band , The New York Times ... 2006 08 minimal man.html Underground Music Library Article on Minimal Man Patrick Miller http www.myspace.com minimalmanpatrickmiller Myspace fan page http www.last.fm music Minimal Man Last.fm page http www.discogs.com artist Minimal Man 2 Discography at Discogs.com http www.ltmrecordings.com mmanbio.html Minimal Man biography at LTM Category Musical groups from California Category American ... more details
In mathematics , in particular in differential geometry , the minimal volume is a number that describes one aspect of a Riemannian manifold s topology . This invariant was introduced by Mikhail Gromov mathematician Mikhail Gromov . Definition Consider a closed manifold closed orientability orientable connected space connected smooth manifold math M n math with a smooth Riemannian metric math g math , and define math Vol it M,g math to be the volume of a manifold math M math with the metric math g math . Let math K g math represent the sectional curvature . The minimal volume of math M math is a smooth invariant defined as math MinVol M inf g Vol M,g K g leq 1 math that is, the infimum of the volume of math M math over all metrics with bounded sectional curvature. Clearly, any manifold math M math may be given an arbitrarily small volume by selecting a Riemannian metric math g math and scaling it down to math lambda g math , as math Vol M, lambda g lambda n 2 Vol M, g math . For a meaningful definition of minimal volume, it is thus necessary to prevent such scaling. The inclusion of bounds on sectional curvature suffices, as math textstyle K lambda g frac 1 lambda K g math . If math MinVol M 0 math , then math M n math can be collapsed to a manifold of lower dimension and thus one with math n math dimensional volume zero by a series of appropriate metrics this manifold may be considered the Gromov Hausdorff convergence Hausdorff limit of the related sequence, and the bounds on sectional curvature ensure that this convergence takes place in a topologically meaningful fashion. Related topological invariants The minimal volume invariant is connected to other topological invariants in a fundamental way via Chern Weil theory , there are many topological invariants which can be described ... es and Pontryagin class es are bounded above by the minimal volume. Properties Gromov has conjectured that every closed Simply connected space simply connected odd dimensional manifold has zero minimal ... more details
unreferenced date November 2010 In phonology , minimal pairs are pairs of word s or phrases in a particular language , which differ in only one phonological element, such as a Phone phonetics phone , phoneme , toneme or chroneme and have distinct meanings. They are used to demonstrate that two phones ... in fact represent distinct phonemes IPA and IPA . An example for English consonants is the minimal ..., so that a particular minimal pair in one Accent linguistics accent is a pair of homophone ... IPA p and no minimal pair can be found to distinguish them, but the word bin shows that the phone ... table shows a minimal set in French distinguishing vowels, some or all of which may sound alike to an Anglophone ... Differentiating consonants A minimal triplet of consonants in French is class wikitable word IPA meaning ... bathtub Because IPA tn is not a single phoneme in French, this shows a minimal pair between the presence ... have many minimal pairs differing only in stress Dutch language Dutch has several stress indicated ... IPA p t never Greek IPA p t when Minimal pairs may differ superficially in more than ... and similar pairs appear superficially not to be minimal pairs for stress because they differ in vowel ... in stress, such pairs are considered minimal pairs. The case is similar in Russian language Russian , e.g. torture, pain and flour . External links Commons category Minimal pairs http billposer.org Software minpair.html Software that generates a list of minimal pairs from ... 9 resources&Itemid 117 Minimal Pairs etc from Caroline Bowen http www.speech language therapy.com ... from Caroline Bowen http myweb.tiscali.co.uk wordscape wordlist index.html Complete list of minimal ... com content&view article&id 134 mp2&catid 9 resources&Itemid 108 Word Lists Minimal Pairs from Caroline ... 9 resources&Itemid 108 Maximal Oppositions Minimal Pairs from Caroline Bowen References reflist DEFAULTSORT Minimal Pair Category Phonology als Minimalpaar ar ca Parell m nim cs Minim ln ... more details
About a musical style other uses Minimalism disambiguation Infobox music genre name Minimal music color .... ref fusiongenres Repetitive music regional scenes local scenes other topics Minimal music is a style ... , and Philip Glass . ref name Mertens Mertens, W. 1983 , American Minimal Music , Kahn & Averill ... called minimal music ibid p.8 . ref ref The term minimal music is generally used to describe a style ... and phase shifting. Minimal compositions that rely heavily on process techniques that follow strict ... John Adams emerged to become publicly associated with American minimal music. In Europe, the music ... G recki , Arvo P rt , and John Tavener exhibits minimalist traits. It is unclear where the term minimal ... The word minimal was perhaps first used in relation to music in 1968 by Michael Nyman, who deduced a recipe for the successful minimal music happening from the entertainment presented by Charlotte Moorman ..., any music that works with limited or minimal materials pieces that use only a few notes ... all, to a greater or lesser degree, indebted to John Cage as examples of minimal art , ref Rose 1965, 58, 65, 69. ref but did not specifically use the expression minimal music . The most prominent minimalist ... style was in full swing. Minimalism in pop music Minimal music has also had some influence on developments ... Underground had a connection with the New York down town scene from which minimal music emerged ... date accessdate 2010 11 08 ref Following the minimal electronic music of Brian Eno and the krautrock ... trance , minimal techno and Ambient music ambient . Citation needed date June 2011 Well known artists ... date October 2011 Sherburne 2006 suggests that the noted similarities between minimal forms of dance ... may explain why certain stylistic features of minimal techno and other forms of electronic dance music sound similar to minimal art music . ref Sherburne, Philip. Digital Discipline Minimalism in House ... an awareness of the American minimal tradition is the British Ambient music Ambient act The Orb ... more details
refimprove date December 2010 The Munich Models is a modeling agency in Munich , Germany . It was established in 1992 by Susanne Maushake . History The company was founded in 1992 by Susanne Maushake in Munich. The agency only represents female models for editorial and commercial modelling. Currently, Munich Models is responsible for the individual career management of more than 500 female models. ref http www.munich models.de index.php3?navi about us&sprache ger ref Notable models past and present Multicol Kim Alexis Alina Vacariu Almudena Fernandez Ana Beatriz Barros Beri Smither Candice Swanepoel Daniela Urzi Denisa Dvorakova Dewi Driegen Emina Cunmulaj Emma Booth actress Emma Booth Ingrid Seynhaeve Jennifer Hof Juliana Martins Julie Henderson Kate Elson Kemp Muhl Lena Gercke Malgosia Bela Michaela Kocianova Naomi Campbell Natasha Vojnovic Raica Oliveira Susan Eldridge Tatiana Usova Tatjana Patitz Valeria Mazza Vanessa Hessler Yfke Sturm Notes and references reflist External links http www.munich models.de index.php3 Munich Models http models.com agency Munich Modelsmodels Models.com http www.fashionmodeldirectory.com agencies munich models Fashion Model Databased Talent agencies Category Model agencies Category Companies established in 1992 Category Companies based in Munich ... more details
File WesternAston.jpg thumb 250px right Western Models LeMans race winner for 1957 driven by Carroll Shelby. This model is accurate down to asymmetrical grille pieces. Western Models Limited were a brand ..., England on the Cornwall peninsula. Models were either in kit or built form. The company ceased production of cars about 2007 to focus solely on contemporary aircraft models. History A First in White Metal Western Models Limited was one of the first companies anywhere to produce high quality hand built models for collectors, usually in white metal Johnson 1998, p. 246 . Small Wheels was a line name also used by Western Models. Models were introduced annually but production runs were often limited, so collectability was insured. By about the year 2000, more than 70 different models had been made, with a new line of aircraft as well Johnson 1998, p. 246 247 . Western Models was started by entrepreneur ... 2005 . Manufacturer for Danhausen Western Models was often commissioned to produce vehicles for Danhausen ... Miniatures of New Jersey Western Models 2011 Olson 2006, pp. 116 117 . Models could be purchased ..., but Western Models gained a reputation for exceptional detail, quality parts and ease of assembly. The first Western Models vehicle was a Mercedes Benz 540K made for Danhausen in November of 1973 Company History 1998 2011 . Danhausen attempted purchase of Western Models, but Stephens did not sell and Danhausen purchased AMR Models instead Minichamps 2011 . Through the 1980s and 1990s, hand built white metal Western Models similar to Brooklin Models gained a reputation for high quality and precision detailing and casting, where models are produced in the hundreds or a few thousand and not mass produced in the hundreds of thousands or millions Western Models 2011 . Models Produced ... a pair of engineer s calipers. The company specialized in 1 43, but did special models in a variety ..., with over 30 different models produced over the years Oxley 2005 . Though some boxes were black, packaging ... more details
Encyclopedia
top
