In the Canon law Catholic Church Canon Law of the Catholic Church , a canonicalimpediment is a legal ... CanonicalImpediment Category Canon law Catholic Church Category Sacraments Catholic Church Category ... Orders . Some canonical impediments can be Dispensation Catholic Church dispensed by the competent ... different criteria. ref Note In the following, canonical references to the 1983 Code of Canon Law are denoted by CIC , canonical references to the 1917 Code of Canon Law are denoted by 1917 CIC , and canonical ... only in relation to certain other parties permanent or temporary , according to the duration of the impediment .... This is an ecclesiastical impediment, and so does not apply to a marriage between two non Catholics ... impediment. Note that, in general, individual bishops do not have this authority cf. CIC c ... and antecedent to the marriage. The impotence can either be absolute or relative. This impediment ... , Beal, et al., p. 1286. ref The reason behind this impediment is explained in the Summa Theologica ..., CCEO c. 803 ref . A marriage between a Catholic and a non baptized person is invalid, unless this impediment ... marriage. Ecclesiastical, Citation needed date April 2007 temporary. Impediment of Crime Crimen ref .... Adoption ref CIC c. 1094, CCEO c. 812. See also CathEncy wstitle Canonical Adoption ref . The parties ... the laws and rites of the Catholic Church. Coercion . This impediment exists if one of the parties is pressured by any circumstances to enter into marriage. In order for the impediment to cease, the situation ..., is an impediment . ref name Can. 1041, 1 Apostasy, heresy or schism . Previous rejection of the faith which was public and notorious is an impediment. ref Can. 1041, 2 ref Attempted marriage ... or murder is an impediment. This could include driving a woman to the abortion clinic or paying for her .... The act of mutilation must be performed graviter et dolose in order for it to be an impediment cutting ... ref Political office or other positions that a priest is not permitted to occupy. This impediment disappears ... more details
The Impediment of Crime or crimen is, in the Canon law Catholic Church canon law of the Roman Catholic Church , a Annulment Annulment in the Catholic Church diriment impediment to marriage arising from certain circumstance involving homicide and adultery an impediment such that it prevents the marriage bond from being formed. Under the Decretal s of Pope Gregory IX , the requirements were that either the adulterous pair should promise marriage after the death of the spouse, or that they should attempt marriage while the spouse was still living. While both partners had to be aware that they are committing adultery, affected ignorance , ignorance from refusal to investigate what they are doing, does not remove it. Under the 1983 code of Canon law adultery is no longer an impidement to marriage. But it is still an impidement if you murdered your spouse in order to be able to remarry. If the pair who wish to marry co operated to kill the spouse of one of them, in order that they might be free to marry, the impediment is invoked, even if they had not committed adultery. Likewise, if one of an adulterous pair killed a spouse of either partner in order to marry, the impediment is invoked. Only the pope may dispense this impediment. There are no instances in which any pope has done so. External links http www.newadvent.org cathen 04489a.htm Catholic Encyclopedia Impediment of Crime Canon Law stub Category Canon law Catholic Church ... more details
For the free software company Canonical Ltd For the meta tag Canonical meta tag Wiktionarypar canonicalCanonical is an adjective derived from wikt canon canon . Canon comes from the greek word kanon ... meanings. Basic, canonic, canonical reduced to the simplest and most significant form possible without loss of generality, e.g., a basic story line a canonical syllable pattern. Arts Literature ... body of international church law. It is analogous to the English system of statute law. Canonical ... 142 ref refers to scriptures and other canonical texts , while another ref Bechert & Gombrich ... into canonical, commentarial and pseudo canonical. Canonization is the process by which a person becomes recognized as a saint . Science Biology In the molecular life sciences, canonical is used to refer ... known as the canonical Wnt pathway. In this pathway, the secreted signalling protein Wnt regulates ..., which acts as a transcriptional activator. Mutations in components of the canonical Wnt pathway ... the usual or standard state or manner of something for example, the canonical way to organize a file ... graph . ref cite web url http catb.org esr jargon html C canonical.html title Canonical publisher catb.org ... XML content to a canonical form, to take into account changes that can invalidate a signature over that data from JWSDP 1.6 . In enterprise application integration , the Canonical Model is a design pattern ... the canonical format , canonical document type or canonical data model . Instead of writing translators ... to write a translator between each format and the canonical format. OASIS organization Organization ... that is based on a canonical data model. Some people have been known to use the noun canonicality others use canonicity . In fields other than computer science, canonicity is this word s canonical form. In computer science, a canonical name record or CNAME record is a type of Domain Name System DNS record, a canonical number the old designation for a MAC address on routers and servers. Mathematics ... more details
orphan date February 2010 Infobox Person name Speech Impediment Man image alt caption birth name birth date birth date and age mf yes 1960 10 15 birth place Garden Grove , California , United States death date Death date and age YYYY MM DD YYYY MM DD death place body discovered death cause resting place resting place coordinates coord LAT LONG display inline,title residence nationality ethnicity citizenship other names known for The Howard Stern Show 1996 2004 education alma mater employer occupation years active home town salary networth height weight title term predecessor successor party opponents boards religion spouse partner children parents relations callsign awards signature website http www.myspace.com speechimpedimentman Official MySpace footnotes box width Life and Times of Speech Impediment Man Jeff Speech Impediment Man SIM Pines is a comedian who was born in Garden Grove, CA, on October 15, 1960. His Speech Impediment comes from when he was little, when he was age 2 he was involved in a car accidnet in which his forehead hit the dashboard. He is most known for being on The Howard Stern Show from 1996 2004. He first met Howard February 1996 at a book signing in Westwood, CA. It is also widely known that Tera Patrick is his fantasy woman, however Lisa Sparxxx or Jenna Jameson come in a close Second. After his run on The Howard Stern Show. he moved to Nashville, TN in 2007, and still does Comedy shows around the US from time to time. His most recent show was on September 25. 2009, at The Grove in Anaheim, CA. with The Killers of Comedy. References See Wikipedia Footnotes on how to create references using ref ref tags which will then appear here automatically Reflist All of this information was confirmed by Speech Impediment Man himself on September 23. 2009 at 8 48 PM. External links http www.myspace.com Official Myspace http www.howardstern.com Howard Stern Show Yahoo directory News and Media Radio Programs Howard Stern Show Wack Pack The Wack Pack http www.howardstern.com ... more details
Canonical model may refer to Canonical Model , a design pattern Canonical ring in mathematics Kripke semantics Canonical models Canonical Kripke models in modal logic Relative canonical model in mathematics disambiguation ... more details
Canonical Transformation may refer to Symplectomorphism , a mathematical treatment Canonical transformation , a physics treatment disambiguation ... more details
Out of date date November 2010 Canonical age in Canon law Catholic Church Roman Catholic canon law is an age one must reach, counting from birth, when one becomes capable of incurring certain obligations, enjoying special privileges, embracing special states of life, holding office or dignity, or receiving the sacraments. Each of these human acts requires a development of mind, body, or spirit appropriate to its free and voluntary acceptance and an adequate knowledge of, and capacity for, the duties and obligations attached. The ages prescribed by canon law differ, as do the privileges, offices, and dignities to which they apply. Sacraments Baptism can be validly administered regardless of age. For confession , the canonical age is seven, the Age of reason canon law age of reason , when a child is nominally supposed to be capable of mortal sin and being bound by the law of annual confession. Christians should receive Holy Communion when they have attained the age of discretion. There is much controversy as to what that age is precisely. Children in danger of death, capable of committing and confessing to mortal sin, and of distinguishing heavenly from ordinary food, when desirous of receiving Holy Communion, must not be denied it, although they may not have achieved the minimum age prescribed. Extreme unction is to be administered to a child of seven years or younger, who is capable of sin. Children of seven years are bound by the laws of abstinence and of hearing Mass. They can also be sponsors in the conferring of baptism and confirmation but the Roman Ritual says that it is more ... are held as sponsalia, inducing thereby impediment of public decorum . Priesthood, Orders, and Clerical ... day of the year in which the canonical age is to be reached is sufficiently timely for the reception .... External links http www.newadvent.org cathen 01206c.htm Catholic Encyclopedia Canonical Age of historical value only Catholic DEFAULTSORT Canonical Age Category Canon law Catholic Church de Kanonisches ... more details
Canonical domain may refer to CNAME record , loosely called a canonical domain name One of the simply connected Riemann surface s see uniformization theorem disambig ... more details
Orphan date February 2009 In Canon Law Canonical Acts are the documents which prove an ecclesiastical procedure. ref CathEncy wstitle Canonical Acts ref References reflist RC stub Category Canon law ... more details
Canonical faculties , in the canon law of the Roman Catholic Church , are ecclesiastical rights conferred on a subordinate, by a superior who enjoys jurisdiction in the external forum. These rights then allow the subordinate to act, in the external or internal forum, validly or lawfully, or at least safely. Classification They may be classified by the object to which they relate jurisdiction is granted to absolve from sins and ecclesiastical censures, to dispense in vows, in irregularities relating to the reception of orders, in matrimonial impediments permission or licence is given to do something which would be otherwise forbidden, as the reading of prohibited books, saying two Masses on the same day ordaining clerics under the prescribed age to avoid worry and qualms of conscience a precautionary dispensation or permission is granted to proceed in certain cases in relation to which the opinions of theologians may not appear sufficiently well founded, as for instance, a matrimonial dispensation may be conceded as a precaution, when it is not certain that an impediment exists, or permission to anticipate at 2 p.m. the recitation of the Divine Office is granted to a person who is unwilling to accept the opinion that anticipation at that hour is lawful. Secondly, faculties, by reason of their source, are Apostolic, episcopal, or regular. Faculties are styled Apostolic or papal when they proceed from the pope directly, or through the ordinary channels of the Sacred Roman Congregations. They are episcopal , if the power or privilege conferred proceeds from a diocesan bishop , by virtue of his own power or ordinary jurisdiction, as for instance, the faculties of the diocese, to hear confessions, say Mass, preach, etc., granted to priests who labour in the diocese for the salvation of souls. Faculties are regular when they proceed from superiors of the regular clergy by reason of their ordinary jurisdiction, or by virtue of extraordinary powers or privileges conceded to them ... more details
orphan date August 2010 A Canonical Inquisition is an official enquiry in the Roman Catholic Church conducted according to Canon Law . ref CathEncy wstitle Canonical Inquisition ref References reflist RC stub Category Canon law Category Inquiry Category Roman Catholic Church ... more details
In mathematics , the canonical bundle of a non singular algebraic variety math V math of dimension math ... sheaf . The canonical class is the divisor class of a Cartier divisor K on V giving rise to the canonical bundle &mdash it is an equivalence class for linear equivalence on V , and any divisor in it may be called a canonical divisor . An anticanonical divisor is any divisor &minus K with K canonical. The anticanonical bundle is the corresponding inverse bundle sup &minus 1 sup . The adjunction ... and that D is a smooth divisor on X . The adjunction formula relates the canonical bundles of X and D . It is a natural isomorphism math omega D i omega X otimes mathcal O D . math In terms of canonical ... On a singular variety math X math , there are several ways to define the canonical divisor. If the variety is normal, it is smooth in codimension one. In particular, we can define canonical divisor on the smooth ... by math K X math that is referred to as the canonical divisor on math X. math Alternately, again .... Canonical maps If the canonical class is effective, then it determines a rational map from V into projective space. This map is called the canonical map . The rational map determined by the n th multiple of the canonical class is the n canonical map . The n canonical map sends V into a projective space of dimension one less than the dimension of the global sections of the n th multiple of the canonical class. n canonical maps may have base points, meaning that they are not defined everywhere ... if they have zero dimensional fibers, they need not be local analytic isomorphisms. Canonical curves The best studied case is that of curves. Here, the canonical bundle is the same as the holomorphic cotangent bundle . A global section of the canonical bundle is therefore the same as an everywhere ... of the first kind . The degree of the canonical class is 2 g &minus 2 for a curve of genus g . ref Springer title canonical class id C c020120 ref Low genus Suppose that C is a smooth algebraic curve ... more details
In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context In a coordinate space, and more generally in a free module, it refers to the standard basis defined by the Kronecker delta In a polynomial ring, it refers to its standard basis given by the monomial s, math X i i math . For finite extension fields, it means the polynomial basis . In representation theory, Lusztig s canonical basis and closely related Kashiwara s crystal basis in quantum groups and their representations See also CanonicalCanonical form Normal form disambiguation Polynomial basis Normal basis Change of bases mathdab Category Linear algebra Category Abstract algebra fr Base canonique pl Baza kanoniczna pt Base can nica ... more details
Infobox company company name Canonical Group Limited ref cite web url http wck2.companieshouse.gov.uk 9997671e24728571142fd0f173c68da2 compdetails title Canonical Group Limited quote Company No. 06870835 publisher Companies House accessdate 2010 01 07 ref company logo File Canonical logo.svg 200px official ... , Edubuntu , Launchpad website Launchpad , Bazaar vcs Bazaar , Canonical Landscape Landscape ... 2010 04 28 ref num employees 350 ref name staff offices cite web url http www.canonical.com about canonical title Canonical About Canonical publisher Canonical Ltd. accessdate 2010 07 26 quote We now ... top priorities title Ubuntu Canonical s New CEO Discusses Top Priorities publisher TheVarGuy accessdate 2010 03 05 quote 3. On Canonical s Size and Financial Performance Canonical now has about 320 employees.. ref subsid Canonical UK Limited formerly Fieldwave Ltd. UK seems to be about tax technicalities ... MRS. VD ... M R S Mark Richard Shuttleworth Canonical UK Ltd. formerly Fieldwave Ltd. Canonical Ltd ... CANONICAL , filed 2004 09 29. ref is a private company founded and funded by South Africa n entrepreneur ... projects. Canonical is registered in the Isle of Man and employs staff around the world. Its main ... , USA and Taipei , Taiwan . ref cite web publisher Canonical Ltd url http blog.canonical.com ?p ... date 2008 08 19 accessdate 2008 09 19 quote In the OEM Services team at Canonical, primarily based in Lexington ... to their hardware ref Projects created or maintained by CanonicalCanonical Ltd. has created and continues ... system Ubuntu is the main Canonical product The Ubuntu family of Linux distribution s Ubuntu .... Fluxbuntu is NOT a Canonical project. Fluxbuntu , which offers the lightweight Fluxbox window manager ... improved specifically for educational or thin client environments. Ubuntu Studio is NOT a Canonical ... variant of Ubuntu consisting entirely of free software. Lubuntu is NOT a Canonical project. Ubuntu ... news storm python orm open sourced Canonical Releases Storm as Open Source Ubuntu Bot generated title ... more details
Canonical XML is a profile or subset of XML . Any XML document can be converted to Canonical XML, thus normalizing away specific kinds of minor differences while remaining an XML document. Because those specific differences are generally not considered to be meaningful , converting to Canonical XML is a good way to determine whether two XML documents are logically the same document despite differences of detail. For example, XML permits whitespace to occur at various points within start tags, and attributes to be specified in any order. Such differences are seldom if ever used to convey meaning, and so these forms are generally considered equivalent < p class a secure 1 < p secure 1 class a In converting an arbitrary XML document to Canonical XML, attributes are encoded in a normative order alphabetical by name , and with normative spacing and quoting. Thus, the second form above would be converted to the first. Canonical XML specifies a number of other details, some of which are the UTF 8 encoding is used line ends are represented using the character 0x0A whitespace in attribute values is normalized entity references are expanded CDATA marked sections are not used empty elements are encoded as start end pairs, not using the special empty element syntax default attributes are made explicit superfluous namespace declarations are deleted Converting a document to Canonical XML ... XML documents have the same canonical form, then the two documents are logically equivalent within ... with which Canonical XML is associated. For example, a steganography system could conceal information ... numeric character references, and so on. Obviously converting such a file to Canonical XML would ... for certain purposes. Such contexts are beyond the scope of Canonical XML. See also XML Signature External links http www.w3.org TR xml c14n W3C Recommendation, Canonical XML Version 1.0, 15 March ... standards ja Canonical XML sv Canonical XML zh Canonical XML ... more details
Confusing date December 2006 In statistics , canonical analysis from Gk. bar, measuring rod , ruler belongs to the family of regression methods for data analysis. Regression analysis quantifies a relationship between a predictor variable and a criterion variable by the coefficient of correlation r , coefficient of determination r , and the standard regression coefficient . Multiple regression analysis expresses a relationship between a set of predictor variables and a single criterion variable ... partial regression weights sub 1 sub , sub 2 sub , etc. Canonical variate analysis captures a relationship between a set of predictor variables and a set of criterion variables by the canonical correlation s sub 1 sub , sub 2 sub , ..., and by the sets of canonical weights C and D. Canonical analysis Canonical analysis belongs to a group of methods which involve solving the characteristic ... into a different, simpler and more meaningful structure increases the interpretability of the canonical weights C and D. In this the canonical analysis differs from Harold Hotelling s 1936 canonical variate analysis also called the canonical correlation analysis , designed to obtain maximum canonical correlations between the predictor and criterion canonical variates. The difference between the canonical variate analysis and canonical analysis is analogous to the difference between the principal ... and eigenvectors . Canonical analysis simple Canonical analysis is a multivariate technique .... The purpose of Canonical analysis is then to find the relationship between X and Y, i.e. ...., which are most highly correlated. This combination is known as the first canonical variates which ... called a canonical function . The next canonical function, U sub 2 sub and V sub 2 sub are then restricted ... in canonical analysis. Educational and Psychological Measurement, 36, 725 730. http www.visualstatistics.net ..., & Webb, J.M. 1995 K fold crossvalidation in canonical analysis. Multivariate Behavioral Research ... more details
Unreferenced stub auto yes date December 2009 dicdef Orphan date December 2009 A canonical sequence is a sequence of DNA , RNA , or amino acid s that reflects the most common choice of base chemistry base or amino acid at each position. See also Homology biology DEFAULTSORT Canonical Sequence Category Genetics Genetics stub ... more details
Canonical Model is a design pattern used to communicate between different data formats. A form of Enterprise Application Integration , it is intended to reduce costs and standardize on agreed data definitions associated with integrating business systems. A Canonical Model is any model that is canonical in nature, i.e. a model which is in the simplest form possible based on a standard, common view within a given context. Often the term Canonical Model is used interchangeably with Canonical Data Model, an enterprise design pattern which provides common data naming, definition and values within a generalized data framework. Adoption of a comprehensive enterprise integration strategy often entails a move to a message based integration methodology. A typical migration from point to point interfacing to message based integration begins with a decision on the middleware to be used to transport messages between endpoints. Often this decision results in the adoption of an Enterprise Service Bus ESB or Enterprise Application Integration EAI solution. Most organizations also adopt a set of standards for message structure and content message payload . The desire for consistent message payload results in the construction of an enterprise or business domain Canonical Model or adoption of an XML ..., Thomas Erl , Prentice Hall, 2005 ref . The goal of the Canonical Model is to provide a dictionary ... system interoperability. A Canonical Data Model allows developers and business users to discuss the integration ... internal formats, such as account , payer , and contact . Defining a Canonical Data Model is often ... data integrity. See also Canonical Schema pattern Enterprise Application Integration Enterprise ... http blogs.forrester.com mike gilpin 10 03 15 field first annual canonical model management forum Forrester Research http blogs.msdn.com b nickmalik archive 2007 06 12 canonical model canonical schema and event driven soa.aspx Canonical Model, Canonical Schema, and Event Driven SOA Categories Category ... more details
is the result of a Development of the Jewish Bible canon developmental process , canonical criticism focuses on the final form of the text. Canonical criticism , sometimes called canon criticism or the canonical ... on the origins, structure and history of the text, canonical criticism looks at the meaning the text ... 180px Brevard Childs , who pioneered the canonical approach. Canonical criticism involves paying ... John N. Oswalt, Canonical Criticism A Review From A Conservative Viewpoint, Journal of the Evangelical ... concentrating authority in the canonical text, and not in the people or events out of which ... of the tradition have sought to hide their own footprints in order to focus attention on the canonical text itself and not on the process. ref Brevard S. Childs, The Canonical Shape of the Prophetic Literature, Interpretation 32 1978 p. 53. ref However, Childs refuses to speak of canonical ... method . ref name Introduction82 Origins Bible related Canonical criticism is a relatively new approach ... set out his canonical approach in his Biblical Theology in Crisis 1970 and applied it in Introduction to the Old Testament as Scripture 1979 . The phrase canonical criticism was first used by James .... ref Childs, Canonical Shape, p. 54. ref blockquote Canonical criticism arose as a reaction to other ... Testament , 90. ref Sanders argues that canonical criticism is biblical criticism s self critical ... extent. ref James A. Sanders, Canon and Community A Guide to Canonical Criticism Fortress, 1984 , p ... communities of today blockquote Canonical criticism might be seen in metaphor as the beadle bedelos ... canonical criticism and the New Criticism of T. S. Eliot and others. Both schools of thought ... Testament , 144. ref Criticism The canonical approach has been criticised by scholars from both ... Conservative scholars, on the other hand, object to the way canonical criticism bypasses vexed questions relating to the historical validation of revelation. ref Oswalt, Canonical Criticism, 325. ref ... more details
Canonical provision is a term of the canon law of the Roman Catholic Church , signifying regular induction into a benefice . Analysis It comprises three distinct acts the designation of the person, canonical institution , and installation. In various ways a person may be designated to fill a vacant benefice by election, postulation, presentation, or recommendation, resignation made in one s favour, or approved exchange. In all cases confirmation by the proper ecclesiastical superior of the selection made is required, while letters of appointment, as a rule, must be presented. Reception of administration by a chapter without such letters brings excommunication reserved to the pope, together with privation of the fruits of the benefice and the nominee loses ipso facto all right to the prelacy. Ordinarily greater benefices are conferred by the pope minor benefices by the bishop, who as a rule has the power of appointing to all benefices in his diocese. The pope, however, owing to the fullness of his jurisdiction, may appoint to any benefice whatsoever. History These extraordinary provisions became common in the eleventh and subsequent centuries, and met at times with stern opposition. In 1351 an English statute Statute of Provisors was enacted, designed to prevent the pope from exercising this prerogative. Similar enactments were made in 1390 and in later years. At present only in certain defined circumstances does the Pope make use of this right. The bishop s power is further restricted at times to confirming an election or postulation or to approving candidates presented by one who enjoys the right of presentation by privilege, custom, or prescription.on Canonical institution main Canonical institution Canonical institution or collation is the concession of a vacant benefice ... necessary. An ecclesiastical benefice cannot be lawfully obtained without canonical institution ... wstitle Canonical Provision Category Canon law ... more details
In mathematics and classical mechanics , canonical coordinates are particular sets of coordinates on the phase space , or equivalently, on the cotangent manifold of a manifold . Canonical coordinates arise naturally in physics in the study of Hamiltonian mechanics . As Hamiltonian mechanics is generalized by symplectic geometry and canonical transformation s are generalized by contact transformation s, so the 19th century definition of canonical coordinates in classical mechanics may be generalized to a more abstract 20th century definition in terms of cotangent bundles. This article defines the canonical coordinates as they appear in classical mechanics . A closely related concept also appears in quantum mechanics see the Stone von Neumann theorem and canonical commutation relation s for details. Definition, in classical mechanics In classical mechanics , canonical coordinates are coordinates math q i , math and math p i , math in phase space that are used in the Hamiltonian mechanics Hamiltonian formalism. The canonical coordinates satisfy the fundamental Poisson bracket relations math q i, q j 0 qquad p i, p j 0 qquad q i, p j delta ij math Canonical coordinates can be obtained from the generalized coordinates of the Lagrangian mechanics Lagrangian formalism by a Legendre transformation , or from another set of canonical coordinates by a canonical transformation . Definition, on cotangent bundles Canonical coordinates are defined as a special set of coordinates on the cotangent bundle of a manifold . They are usually written as a set of math q i,p j math or math x i,p j math ... definition of canonical coordinates is any set of coordinates on the cotangent bundle that allow the canonical .... A change of coordinates that preserves this form is a canonical transformation these are a special ... math T Q math these coordinates are called the canonical coordinates . Generalized coordinates In Lagrangian ... on the cotangent bundle, then the generalized coordinates are related to the canonical coordinates ... more details
Canonical order may refer to in the context of sorting , a standard order theory order , typically a total order , obeying certain rules, e.g. lexicographic order for string computer science strings a monastic order of regular canon http www.aedificium.org Glossary.html See also Canonicalization dab ... more details
Unreferenced date March 2009 In mathematics , a canonical connection of a holomorphic vector bundle with a Hermitian structure , is the unique metric connection D, such that the part which increases the anti holomorphic type D annihilates holomorphic sections. Category Complex manifolds geometry stub ... more details
In mathematics, canonical singularities appear as singularities of the canonical model of a projective variety , and terminal singularities are special cases that appear as singularities of Minimal model program minimal models . They were introduced by harvtxt Reid 1979 . Terminal singularities are important in the minimal model program because smooth minimal models do not always exist, and thus one must allow certain singularities, namely the terminal singularities. Definition Suppose that Y is a normal variety such that its canonical class K sub Y sub is Q Cartier, and let f X &rarr Y be a resolution of the singularities of Y . Then math displaystyle K X f K Y sum i a iE i math where the sum .... Then the singularities of Y are called terminal if a sub i sub 0 for all i canonical if a sub i sub &ge 0 for all i log terminal if a sub i sub &minus 1 for all i log canonical if a sub i sub &ge &minus 1 for all i . Properties The singularities of a projective variety V are canonical if the variety is normal variety normal , some power of the canonical line bundle of the non singular ... resolution of its singularities. V has canonical singularities if and only if it is a relative canonical model . The singularities of a projective variety V are terminal if the variety is normal variety normal , some power of the canonical line bundle of the non singular part of V extends ... and were classified by harvtxt Mori 1985 . Two dimensional canonical singularities are the same as du ... canonical singularities have been classified by harvtxt Kawamata 1988 . Pairs More generally one ... divisors with rational coefficients. The pair is called terminal if Discrep X ,&Delta 0 canonical if Discrep ... purely log terminal if Discrep X ,&Delta &minus 1 lc log canonical if Discrep X ,&Delta &ge &minus ... location Alphen aan den Rijn id MathSciNet id 605348 year 1980 chapter Canonical 3 folds pages ... to canonical singularities pages 345 414 Category Singularity theory Category algebraic geometry ... more details
refimprove date December 2007 Generally, in mathematics , a canonical form often called normal form or standard form of an object is a standard way of presenting that object. Canonical form can also mean a differential form that is defined in a natural canonical way Differential forms see below . Finding a canonical form is called canonization . In some branches of computer science the term canonicalization ... . A canonical form is given by designating some objects of S to be in canonical form , such that every object under consideration is equivalent to exactly one object in canonical form. In other words, the canonical forms in S represent the equivalence classes, once and only once. To test whether two objects are equivalent, it then suffices to test their canonical forms for equality. A canonical form ... a distinguished canonical representative. In practical terms, one wants to be able to recognize the canonical forms. There is also a practical, algorithmic question to consider how to pass from a given object s in S to its canonical form s ? Canonical forms are generally used to make operating with equivalence classes more effective. For example in modular arithmetic , the canonical form for a residue ... . A canonical form may simply be a convention, or a deep theorem. For example, polynomials are conventionally ... of Jordan canonical form for a matrix is a deep theorem. Examples Note in this section, up to some equivalence relation E means that the canonical form is not unique in general, but that if one object has two different canonical forms, they are E equivalent. Linear algebra class wikitable Objects ... form Conjunctive normal form Disjunctive normal form Algebraic normal form Canonical form Boolean ... form of a bifurcation Graph theory main Graph canonization Differential forms Canonical differential form s include the canonical one form and canonical symplectic form , important in the study of Hamiltonian mechanics and symplectic manifold s. See also Canonical class Normalization Standardization ... more details
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