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## Some Related Sentences

Duality and theorem
The Principle of Plane Duality says that dualizing any theorem in a self-dual projective plane C produces another theorem valid in C.
This result is an application of Poincaré Duality together with the Universal coefficient theorem which gives an identification and.

Duality and definition
: From the point of view of the definition, this is an expression of the Poincaré Duality isomorphism where is the quotient of the field of fractions of by, considered as a-module, and where is the conjugate-module to ie: as an abelian group it is identical to but the covering transformation acts by.

Duality and category
Duality is the observation that σ is true for some category C if and only if σ < sup > op </ sup > is true for C < sup > op </ sup >.
Duality theorems of Tannaka and Krein describe the converse passage from the category Π ( G ) back to the group G, allowing one to recover the group from its category of representations.

Duality and theory
* Duality in field theory and statistical systems, Robert Savit, Rev.
** Duality ( order theory ), a concept regarding binary relations
This formulation of Poincaré Duality has become quite popular as it provides a means to define Poincaré Duality for any generalized homology theories provided one has a Thom Isomorphism for that homology theory.
* Duality ( order theory )
* Duality principle ( optimization theory )
* Duality principle in functional analysis, used in the large sieve method of analytic number theory
A treatment of this theory, Residues and Duality ( 1966 ) by Robin Hartshorne, became an accessible reference.

Duality and has
According to Giddens there is a " Duality of structure " by which social practice, which is the principal unit of investigation, has both a structural and an agency-component.
Ra has sold 80, 000 copies of Duality.

Duality and dual
Miguel Leon-Portilla interprets the name " Ometeotl " as " Lord of the Duality " and argues that Ometeotl was the supreme creator deity of the Aztecs, and that the Aztecs envisioned this deity as a mystical entity with a dual nature akin to the European concept of the trinity.
Duality of polytopes and order-theoretic duality are both involutions: the dual polytope of the dual polytope of any polytope is the original polytope, and reversing all order-relations twice returns to the original order.

Duality and which
Duality ( opposition ) that creates the energy ( or libido ) of the psyche, which Jung asserts expresses itself only through symbols: " It is the energy that manifests itself in the life process and is perceived subjectively as striving and desire.
" After the Red Dwarf crew finds the wreck it is brought aboard and repaired in order to utilise its Duality Jump engine, which could get the crew back to Earth within three months.

Duality and is
Duality with pluralism is considered a logical fallacy.
Duality is also sometimes called reciprocity or polarity.
Duality is most commonly defined in terms of polar reciprocation about a concentric sphere.
Xiuhtecuhtli is a manifestation of Ometecuhtli, the Lord of Duality, and according to the Florentine Codex Xiuhtecuhtli was considered to be mother and father of the Gods, who dwelled in the turquoise enclosure in the center of earth.
** The interview was also sampled in Konkhra's track " Religion is a Whore " and The Faceless's " Planetary Duality.
Duality, as such, is the assertion that truth is invariant under this operation on statements.
If the Star Goddess is the great Unity, than the Twins can be seen as representing all Duality.
Duality in the projective plane is a special case of duality for projective spaces, transformations of PG ( n, K ) ( also denoted by KP < sup > n </ sup >) with K a field, that interchange objects of dimension r with objects of dimension n-1-r ( = codimension r + 1 ).
The fact that this is an isomorphism of chain complexes is a proof of Poincaré Duality.
Poincaré Duality is closely related to the Thom Isomorphism Theorem, as we will explain here.
The Lotus Sutra's parable of the Burning House implies that all talk of Duality or Non-Duality by Buddhas and Bodhisattvas is merely Skillful Means ( Sanskrit upaya kausala ) meant to lead the deluded to a much higher truth.
Formally, this is captured by the Duality Principle for ordered sets:

Duality and by
* Duality ( film ), a Star Wars fan film by Dave Macomber and Mark Thomas
* Duality ( Lisa Gerrard & Pieter Bourke album ), a 1998 album by Lisa Gerrard and Pieter Bourke
* Duality ( song ), a 2004 single & Grammy-nominated song by metal band Slipknot
* Duality ( Ra album ), a 2005 album by the rock band Ra
* Duality, a large format audio mixing console by Solid State Logic
* Blackadder: " The Black Seal " ( 1983 ), " Chains " ( 1986 ), " Duel and Duality " ( 1987 ) — Along with " Goodbyeee " ( 1989 ), the final episodes of the Blackadder series took a liberty that many series would be unable to take, by killing off the major characters ( apart from in Blackadder the Third when only Prince George died ).
* K3 Surfaces and String Duality, by Paul Aspinwall
*" Xenochrist ", a song on the album Planetary Duality by The Faceless
* Quantum Principal Bundles and Tannaka – Krein Duality by Mico Durdevic

Duality and ".
* Nave, R., " Wave-Particle Duality ".
* B. R. Greene and M. R. Plesser, " Duality in Calabi-Yau Moduli Space ".

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