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Topic: Canonical form

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	Canonical - Wikipedia, the free encyclopedia
		This word is used by theologians and canon lawyers to refer to the canons of the Eastern Orthodox and Roman Catholic churches, adopted by ecumenical councils.
		Canonical can also mean "part of the canon", i.e., one of the books comprising the biblical canon, as opposed to apocryphal books.
		Canonical variables are essential in the Hamiltonian formulation of physics, which is particularly important in quantum mechanics.
	en.wikipedia.org /wiki/Canonical (578 words)

	Canonical XML (Site not responding. Last check: 2007-11-07)
		This is done by comparing the canonical form of the original document before application processing with the canonical form of the document result of the application processing.
		The canonical form of an XML document may not be completely operational within the application context, though the circumstances under which this occurs are unusual.
		The canonical form of an XML document subset may not be well-formed XML.
	www.w3.org /TR/xml-c14n (6401 words)

	Canonical form (Boolean algebra) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		This is a special form of (Click link for more info and facts about conjunctive normal form) conjunctive normal form, qv.
		All logical functions are expressible in a canonical form, either a "sum of minterms" or "product of maxterms" form.
		This, apart from being able to express complicated logical functions in a straightforward and simple algebraic form, allows for greater analysis into the simplification of these functions, which is of great importance in the minimization of digital circuits.
	www.absoluteastronomy.com /encyclopedia/C/Ca/Canonical_form_(Boolean_algebra)1.htm (732 words)

	PlanetMath: p-adic canonical form (Site not responding. Last check: 2007-11-07)
		Those integers ending in a ``0'' are non-units of the ring, and they apparently form the only maximal ideal in the ring (which thus is a local ring).
		All 2-adic non-zero integers are of the form
		This is version 59 of p-adic canonical form, born on 2004-03-02, modified 2005-01-26.
	planetmath.org /encyclopedia/PAdicCanonicalForm.html (411 words)

	The Canonical Form of Marriage
		It is the canon law's insistence that the canonical form must still be observed when Catholics marry persons not of their faith (or indeed of no faith at all) that is the source of tension, providing the rationale for this paper.
		As well, with the abolition of canonical form the validity of a marriage would be judged much more on the basis of true facts: that is, whether or not the couple have come together and are living together with marital affection.
		Canon law says that: "If there are grave difficulties in the way of observing the canonical form, the local bishop of the Catholic party has the right to dispense from it in individual cases", although when that happens some public form of celebration is required.
	www.interchurchfamilies.org /resource/marriage/can-marr.shtm (2804 words)

	Introducing XML canonical form
		The W3C defines canonical XML (see Resources), which is a normalized lexical form for XML where all of the allowed variations have been removed, and strict rules are imposed to allow consistent byte-by-byte comparison.
		Character data in canonical form is basically as literal as possible: Character entities are resolved to the raw Unicode (which is then serialized as UTF-8); CDATA sections are replaced with their raw content; and more changes along these lines.
		Canonical XML Version 1.0 is a W3C Recommendation (March 2001), as is Exclusive XML Canonicalization Version 1.0 (July 2002).
	www-128.ibm.com /developerworks/xml/library/x-c14n (1912 words)

	SEMINAR IN MATHEMATICAL STATISTICS AND PROBABILITY
		This paper develops a canonical form in the state space representation of stochastic processes with a general configuration of roots on the unit circle.
		The canonical form is constructed so as to clearly reveal the integration and cointegration properties of the underlying stochastic process.
		The developed canonical form and the corresponding parametrization are shown to be continuous for fixed integration structure.
	www.math.ku.dk /cal/events/1264.htm (215 words)

	PlanetMath: Jordan canonical form theorem (Site not responding. Last check: 2007-11-07)
		A Jordan block or Jordan matrix is a matrix of the form
		"Jordan canonical form theorem" is owned by vypertd.
		This is version 3 of Jordan canonical form theorem, born on 2002-08-26, modified 2002-08-27.
	planetmath.org /encyclopedia/JordanCanonicalForm.html (117 words)

	canonical
		The canon of a given author is the complete body of authentic works by that author (this usage is familiar to Sherlock Holmes fans as well as to literary scholars).
		The establishment of a canon of scriptures within Christianity was meant to define a standard or a rule for the religion.
		Alongside this usage was the promulgation of ‘canons’ (‘rules’) for the government of the Catholic Church.
	catb.org /~esr/jargon/html/C/canonical.html (427 words)

	UAX #15: Unicode Normalization
		Canonical equivalence is a basic equivalency between characters or sequences of characters.
		Normalization Form C uses canonical composite characters where possible, and maintains the distinction between characters that are compatibility equivalents.
		Canonical decomposition is the process of taking a string, recursively replacing composite characters using the Unicode canonical decomposition mappings (including the algorithmic Hangul canonical decomposition mappings, see Annex 10: Hangul), and putting the result in canonical order.
	www.unicode.org /reports/tr15 (7195 words)

	Canonical Polyhedra
		This canonical form is a possibly distorted version of the given polyhedron in which the vertices are positioned in space to satisfy the following properties:
		One application of this is that given a new irregular-looking polyhedron, one can find its canonical form and look at it to see if it is the same as a previously familiar canonical form.
		I used it to produce the canonical forms above (and many others, for testing purposes.) The algorithm inputs a polyhedron (or maps a graph around the unit sphere to create a set of vertices and edges) and then iteratively modifies it to improve its conformance with the three conditions at the top of this page.
	www.georgehart.com /virtual-polyhedra/canonical.html (1072 words)

	RFC 3076 (rfc3076) - Canonical XML Version 1.0 (Site not responding. Last check: 2007-11-07)
		For example, in a digital signature application, the canonical form can be substituted for the original document without changing the digest calculation.
		Note: In the canonical form, the value of the attribute named attr in the element norm begins with a space, a single quote, then four spaces before the first character reference.
		The expression is true for e1 and its implicit namespace nodes, and it is true if the element identified by E3 is in the ancestor-or-self path of the context node (such that ancestor- or-self stays the same size under union with the element identified by E3).
	www.faqs.org /rfcs/rfc3076.html (5964 words)

	Mistaken Area of US 'Canonical Form' (Monograph) (Site not responding. Last check: 2007-11-07)
		The canonical form principle is common in the field of pure sociology, or, in other words, in the field of academic training, it is, after all, regarded as an important method for the development of sociology and a way for cultivating students' comprehensive ability (not knowledge).
		However, when people use the canonical form to present a policy, or seek a basis for a policy, if they oversimplify the reality and try their utmost to pursue an ordinary theory established on a fairly hypothetical basis, then, they will achieve just the opposite result-generating danger.
		With respect to the "canonical form of civilization conflict", according to this form, epochal "civilization" after the Cold War is most important in the world politics, the United States has to face the "threat" posed to it by Russia, China as well as the Islamic world.
	english.peopledaily.com.cn /english/200007/18/eng20000718_45760.html (760 words)

	Canonical XML
		Although two XML documents are equivalent (aside from limitations given in this section) if their canonical forms are identical, it is not a goal of this work to establish a method such that two XML documents are equivalent if and only if their canonical forms are identical.
		However, the XML processor used to prepare the XPath data model input is REQUIRED to use Unicode Normalization Form C [NFC, NFC-Corrigendum] when converting an XML document to the UCS character domain from any encoding that is not UCS-based (currently, UCS-based encodings include UTF-8, UTF-16, UTF-16BE, and UTF-16LE, UCS-2, and UCS-4).
		However, since the canonical form may be subjected to further XML processing, most XPath node-sets provided for canonicalization will be designed to produce a canonical form that is a well-formed XML document or external general parsed entity.
	www.w3.org /TR/2001/REC-xml-c14n-20010315 (6401 words)

	Improve XML transport performance, Part 1
		It's generally possible to reconstruct the original document from the encoded form, losing only information that XML deems irrelevant because it will be ignored by any XML processor (such as the number of spaces between attributes, the type of quote character used around an attribute value, and the order of attributes).
		It seems reasonable to say that a technique for representing XML data is an XML encoding if and only if the canonical form of an input document to an encoding is always the same as the canonical form of the reconstructed document.
		It's not generally possible to convert the data representations to and from standard XML text form with current implementations, so you'd also need to write some form of custom converter to take standard text XML documents and convert them into a form where the encoding could be used.
	www.ibm.com /developerworks/xml/library/x-trans1.html (2592 words)

	Zvon - RFC 2469 [A Caution On The Canonical Ordering Of Link-Layer Addresses] - Canonical Form
		Canonical form (also known as "LSB format" and "Ethernet format") is the name given to the format of a LAN adapter address as it should be presented to the user according to the 802 LAN standard.
		This puts the group address indicator (i.e., the bit that defines whether an address is unicast or multicast) in the least significant bit of the first byte.
		Likewise, addresses in canonical form that are handed to adaptors (e.g., to set an address, to specify a destination address in a link-layer header, etc.) may need to be bit-swapped in order for the adaptor to process the request as expected.
	www.zvon.org /tmRFC/RFC2469/Output/chapter2.html (287 words)

	Canonical Form (Site not responding. Last check: 2007-11-07)
		The canonical form of a fax number is the fully qualified number that uniquely identifies the destination.
		The Canonical Form is a field in the Dialing Rules database.
		Typically, a canonical form can be specified by providing both the country and area code of the fax number.
	www.faximum.com /manual.d/client.server.d/manage.13.html (136 words)

	Bug ID: 4075873 need to set "canonical form mode" for stream used by MarshalledObject
		In order for MarshalledObject.equals method to operate correctly, the marshalled object's representation needs to be in a canonical form to be used as a base for comparison.
		If the object is marshalled to a representation that is not in a canonical form, the blocking factor may vary between implementations and the "equals" method cannot be used to correctly determine whether two MarshalledObjects are equivalent.
		Ann Wollrath (9/3/97): Before marshaling the object to the underlying MarshalOutputStream, the canonical form mode is set to true.
	bugs.sun.com /bugdatabase/view_bug.do?bug_id=4075873 (177 words)

	Calculating Canonical Polyhedra
		However, it is possible to construct a topologically equivalent polyhedron which is in canonical form, shown at right.
		The connection between the canonical form and duality is that it follows from the theorem that the dual to the canonical polyhedron also has the above three properties, i.e., it is also in canonical form.
		To see this, imagine the circle where the face plane intersects the unit sphere; it is inscribed in the face and the dual edges lie on a cone tangent to the sphere at that circle.
	www.georgehart.com /canonical/canonical-supplement.html (1005 words)

	Canonical form -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Canonical form -- Facts, Info, and Encyclopedia article
		Generally, in (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, a canonical form is a function that is written in the most standard, conventional, and logical way.
		, although the two forms are essentially equivalent.
	www.absoluteastronomy.com /encyclopedia/c/ca/canonical_form.htm (129 words)

	A Canonical Form for Circuit Diagrams - Fisler (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: A canonical form for circuit diagrams with a designated start state is presented.
		The form is based upon finite automata minimization and Shannon's canonical form for boolean expressions.
		This canonical form will be used to prove a set of inference rules on circuit diagrams logically complete in a companion paper.
	citeseer.lcs.mit.edu /fisler95canonical.html (471 words)

	CANONICAL FORM (Site not responding. Last check: 2007-11-07)
		(Math.), the simples or most symmetrical form to which all functions of the same class can be reduced without lose of generality.
		English words defined with "CANONICAL FORM": basic ♦ canonic, canonical.
		Specialty definitions using "CANONICAL FORM": Canonical Encoding Rules ♦ floating-point ♦ resolution by refutation.
	www.websters-online-dictionary.org /Ca/Canonical+form.html (210 words)

	C.1 Conversion to Canonical Form (Site not responding. Last check: 2007-11-07)
		RFC 1521 requires that an Internet mail entity be converted to canonical form prior to being transferred, as described in Appendix G of RFC 1521 [5].
		Where it is possible, a proxy or gateway from HTTP to a strict RFC 1521 environment should translate all line breaks within the text media types described in Section 3.6.1 of this document to the RFC 1521 canonical form of CRLF.
		Note, however, that this may be complicated by the presence of a Content-Encoding and by the fact that HTTP allows the use of some character sets which do not use octets 13 and 10 to represent CR and LF, as is the case for some multi-byte character sets.
	www.freesoft.org /CIE/RFC/1945/80.htm (186 words)

	PlanetMath: (Site not responding. Last check: 2007-11-07)
		2-adic fractional number (in p-adic canonical form) owned by pahio
		2-adic integer (in p-adic canonical form) owned by pahio
		2-adic valuation (in p-adic canonical form) owned by pahio
	planetmath.org /encyclopedia/2 (36 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		Date: 04/29/98 at 00:56:41 From: Lisa Russo Subject: Jordan Canonical Form I need help in finding the Jordan Canonical Form of a matrix.
		For example, find the Jordan Canonical Form of: A = [(3 1 2),(0 3 0),(0 0 3)] I approached the problem by finding [lambda I-A].
		Date: 04/29/98 at 11:21:32 From: Doctor Rob Subject: Re: Jordan Canonical Form First you need to find the elementary divisors of A. They will be divisors of the minimal polynomial.
	mathforum.org /library/drmath/view/51981.html (484 words)

	ipedia.com: Canonical form (Boolean algebra) Article (Site not responding. Last check: 2007-11-07)
		In a Boolean algebra, a Boolean function that is composed of standard logical operators can be expressed in a canonical form using the dual concepts of a minterms and maxterms.
		We firstly begin with defining a minterm as a logical expression of n variables consisting of only the logical and operator and complements.
		In general, one assigns each minterm (ensuring the variables are written in the same order, usually alphabetic), an index based on the order of its complements, for example, associating the number 6 with a b c', and writes the minterm expression as m
	www.ipedia.com /canonical_form__boolean_algebra_.html (685 words)

	Kronecker Canonical Form
		In addition to Jordan blocks for finite and infinite eigenvalues, the Kronecker form contains singular blocks corresponding to minimal indices of a singular pencil (see below).
		This fact is utilized in algorithms for computing canonical structure of matrix pencils.
		We end this introductory description by briefly pointing to the relationship between structure information of the KCF and the GUPTRI form (8.28).
	www.cs.utk.edu /~dongarra/etemplates/node309.html (344 words)

	It's time to face a simple question: WHY is canonical form simple
		Simple sentences in 'canonical form' - that is, in each language's most typical main-clause surface word order for subject (S), object (O), and main verb (V) - are easier for its speakers and hearers to produce and understand, whether they are aphasic or unimpaired, children or adults, native speakers or second language learners.
		Apparent dependence on Agent-first canonical form may therefore really be dependence on active voice verb morphology, plus the expectation that the mapping of noun positions onto semantics will follow the pattern of the individual verb’s most frequent semantic frame.
		I propose that resolving this very simple question by proper studies is the most urgent aphasiological issue for the first decade of the new millenium.
	www.colorado.edu /linguistics/faculty/lmenn/B-L2000rev1.htm (1072 words)

	A Simple Jordan Canonical Form Algorithm
		This document is intended for anyone who has been exposed to a second course in linear algebra and who has been mystified by the usual lengthy treatments of the Jordan canonical form and who simply wants an algorithm which can be implemented by an exact arithmetic matrix calculator such as my CMAT.
		are called the Segre characteristic for the eigenvalue c and form a "vertical" partition of the algebraic multiplicity a.
		and are called the Weyr characteristic for the eigenvalue c and form a "horizontal" partition of a.
	www.numbertheory.org /jordan.html (421 words)

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