Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types — conditional GOTO, unconditional GOTO, assignment, HALT.

A canonical " dot-com " company's business model relied on harnessing network effects by operating at a sustained net loss to build market share ( or mind share ).

The Arrow-Debreu model has canonical presentations in Gérard Debreu's Theory of Value ( 1959 ) and in Arrow and Hahn's " General Competitive Analysis " ( 1971 ).

For any normal modal logic L, a Kripke model ( called the canonical model ) can be constructed, which validates precisely the theorems of L, by an adaptation of the standard technique of using maximal consistent sets as models.

The canonical model of L is a Kripke model, where W is the set of all L-MCS, and the relations R and are as follows:

Properties of the canonical model of K immediately imply completeness of K with respect to the class of all Kripke frames.

This argument does not work for arbitrary L, because there is no guarantee that the underlying frame of the canonical model satisfies the frame conditions of L.

* for any normal modal logic L which contains X, the underlying frame of the canonical model of L satisfies P.

Refinements and extensions of the canonical model construction often work, using tools such as filtration or unravelling.

Indeed, based on the canonical anatomofunctional model of basal ganglia, nigrostriatal dopamine is able to modulate the motor loop by acting on dopaminergic receptors located on striatal GABAergic medium spiny neurons.

For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called horn topologies, so called because of the shape of the pseudosphere, a canonical model of hyperbolic geometry.

Scott circulated the incomplete monograph amongst colleagues, introducing a number of important techniques in the semantics of model theory, most importantly presenting a refinement of canonical model that became standard, and introducing the technique of constructing models through filtrations, both of which are core concepts in modern Kripke semantics ( Blackburn, de Rijke, and Venema, 2001 ).

* The logit in logistic regression is a special case of a link function in a generalized linear model: it is the canonical link function for the binomial distribution.

The " canonical data model " is applied to integration technologies as a definition for specific data passed between the systems of an enterprise.

1 – 12 ( Copenhagen, 1853 ), was the model for Child ’ s resulting canonical five-volume edition of some 305 English and Scottish ballads and their numerous variants.

On the other hand, if 0 < sup >#</ sup > does not exist, then the constructible universe L is the core model — that is, the canonical inner model that approximates the large cardinal structure of the universe considered.

This combined time scale is published monthly in Circular T, and is the canonical TAI.

Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired ( as is often the case in category theory ).

The term apocrypha is used with various meanings, including " hidden ", " esoteric ", " spurious ", " of questionable authenticity ", ancient Chinese " revealed texts and objects " and " Christian texts that are not canonical ".

The can be used in Applesoft BASIC as a shortcut for " PRINT ", though spelling out the word is not only acceptable but canonical — Applesoft converted "?

Due to recorded predictions of the destruction of the temple, the Gospel of Mark is believed by many critical scholars to have been composed around or shortly after the fall of Jerusalem due to prophecies assumed to be ex post facto regarding the destruction of the temple, and both traditional and critical scholarly consensus maintains that it was the first written of the four canonical gospels.

The words, " Today I have begotten you ," are omitted from the canonical Gospel of Mark, however, and it is therefore generally believed to have less adoptionist tendencies than the Gospel of the Hebrews.

The canonical example for accumulator use is summing a list of numbers.

The canonical age for the ordination of a deacon was 25 ; Bede's early ordination may mean that his abilities were considered exceptional, but it is also possible that the minimum age requirement was often disregarded.

The Catholic Church does recognise as valid ( though illicit ) ordinations done by breakaway Catholic, Old Catholic or Oriental bishops, and groups descended from them ; it also regards as both valid and licit those ordinations done by bishops of the Eastern churches, so long as those receiving the ordination conform to other canonical requirements ( for example, is an adult male ) and an orthodox rite of episcopal ordination, expressing the proper functions and sacramental status of a bishop, is used ; this has given rise to the phenomenon of episcopi vagantes ( for example, clergy of the Independent Catholic groups which claim apostolic succession, though this claim is rejected by both Orthodoxy and Catholicism ).

While " there is an intentional editorial unity with a cohesive purpose and message in the canonical form of the book ," Job contains many separate elements, some of which may have had an independent existence prior to being incorporated into the present text.

Additionally, Elihu's first spoken words are a confession of his youthful status, being much younger than the three canonical friends, including a claim to be speaking because he cannot bear to remain silent ; it has been suggested that this interesting statement may have been symbolic of a " younger " ( that is to say, later and interpolating ) writer, who has written Elihu's sermon to respond to what he views as morally and theologically scandalous statements being made within the book of Job, and creating the literary device of Elihu to provide what seemed to be a faith-based response to further refute heresy and provide a counter-argument, a need partially provided by God's ambiguous and unspecific response to Job at the end of the book.

The canonical Book of Obadiah is an oracle concerning the divine judgment of Edom and the restoration of Israel.

The only canonical information we have comes from the book that is named for him.

The book of Habakkuk is accepted as canonical by adherents of the Jewish and Christian faiths.

Then is already an angle variable, and the canonical momentum conjugate is L, the angular momentum.

While unique sources, such as M, L, or Semitic first editions, are interesting for form-critical purposes, they are quite peripheral to the " synoptic problem " as to how the canonical gospels are interrelated.

More precisely: the canonical map h: L → U ( L ) is always injective.

The Lost Princess of Oz is the eleventh canonical Oz book written by L. Frank Baum.

With the canonical framing the above phase is the exponential of 2πi /( k + N ) times the linking number of L with itself.

In issue one of the Angel: After the Fall comic series ( which is the canonical continuation of the Angel series ), Gunn and a group he has assumed leadership of storm a stadium and kill Kr ' ph, one of the demon lords of L. A., who has taken up residence there.

In the canonical comic book continuation Angel: After the Fall, Lorne is wandering the streets of L. A. when the entire town is sent into hell.

If L is a Lie algebra over a field K, there is a canonical K-linear map h from L into the universal enveloping algebra U ( L ).

Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.

However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Legendre canonical forms ( i. e. the elliptic integrals of the first, second and third kind ).

The canonical example of a ligand-binding protein is haemoglobin, which transports oxygen from the lungs to other organs and tissues in all vertebrates and has close homologs in every biological kingdom.

Hence, no canonical source has given any family names to any Vulcan characters, and indeed, every one of the personal names previously mentioned are all officially described as being only Latin-alphabetical and English-phonetic approximations of the real ones.

" More precisely, a member of the Jacobson radical must project under the canonical homomorphism to the zero of every " right division ring " ( each non-zero element of which has a right inverse ) internal to the ring in question.

The resulting astronomical Easter dates in the Julian calendar used in Sweden from 1740 to 1752 occurred on the same Sunday as the Julian Easter every three years, but were earlier than the earliest canonical limit for Easter of March 22 in 1742, 1744 and 1750.

: there exist morphisms, called the canonical projections or projection morphisms, such that for every object and pair of morphisms there exists a unique morphism such that the following diagram commutes:

If R is a ring and S is a subset, consider all R-algebras A, so that, under the canonical homomorphism R → A, every element of S is mapped to a unit.

Although NGBC gives exhaustive background stories to every character, it is not a canonical continuation to any of their original games ( neither is SVC Chaos ).

Perhaps his primary importance to the historian of Syriac literature lies in the zeal with which he strove to replace the Diatessaron or Gospel Harmony of Tatian with the four canonical Gospels, ordering that a copy of the latter should be placed in every church.

For example, the Künneth standard conjecture, which states the existence of algebraic cycles π < sup > i </ sup > ⊂ X × X inducing the canonical projectors H < sup >∗</ sup >( X ) ↠ H < sup > i </ sup >( X ) ↣ H < sup >∗</ sup >( X ) ( for any Weil cohomology H ) implies that every pure motive M decomposes in graded pieces of weight n: M = ⊕ Gr < sub > n </ sub > M.

But it turns out that ( if A is " nice " enough ) there is one canonical way of doing so, given by the right derived functors of F. For every i ≥ 1, there is a functor R < sup > i </ sup > F: A → B, and the above sequence continues like so: 0 → F ( A ) → F ( B ) → F ( C ) → R < sup > 1 </ sup > F ( A ) → R < sup > 1 </ sup > F ( B ) → R < sup > 1 </ sup > F ( C ) → R < sup > 2 </ sup > F ( A ) → R < sup > 2 </ sup > F ( B ) → ....

The choice of Q and P is completely arbitrary, but not every choice leads to a canonical transformation.

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.

A canonical form thus provides a classification theorem and more, in that it not just classifies every class, but gives a distinguished ( canonical ) representative.

Metal Gear 2 serves as a follow-up to the original Metal Gear, ignoring the events of Snake's Revenge ( which was unreleased in Japan ), and every canonical Metal Gear title released afterward acknowledge only the events of Metal Gear 2, relegating Snake's Revenge to an apocryphal status.

The minimal model program proposed that the canonical ring of every smooth or mildly singular projective variety was finitely generated.

F-Script is based on a pure object paradigm ( every entity manipulated within the language is an object ), its base syntax and concepts being identical to those of Smalltalk ( the canonical example of the category ) with specific extensions to support array programming as in the APL programming language.