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Что (кто) такое well-ordered sets - определение

SPECIAL CASE OF DISCRETE OPTIMIZATION

Special Ordered Sets

Найдено результатов: 965

well-ordered set

TOTAL ORDER SUCH THAT EVERY NONEMPTY SUBSET OF THE DOMAIN HAS A LEAST ELEMENT

Well-ordered set; Well-ordered; Well-ordering; Well ordered; Well ordering; Well-ordering property; Wellorder; Wellordering; Well ordered set; Wellordered; Well ordering theory; Well ordering property; Well-Ordering; Well-Ordered; Well-orderable set; Well order

<mathematics> A set with a total ordering and no infinite descending chains. A total ordering "<=" satisfies x <= x x <= y <= z => x <= z x <= y <= x => x = y for all x, y: x <= y or y <= x In addition, if a set W is well-ordered then all non-empty subsets A of W have a least element, i.e. there exists x in A such that for all y in A, x <= y. Ordinals are isomorphism classes of well-ordered sets, just as integers are isomorphism classes of finite sets. (1995-04-19)

Well-quasi-ordering

$'''Pic.3:''' Hasse diagram of <math>\N^2</math> with componentwise order$

PREORDER IN WHICH EVERY INFINITE SEQUENCE HAS AN INCREASING OR EQUIVALENT PAIR OF CONSECUTIVE VALUES

Well partial order; WQO; Well quasi ordering; Wellquasiorder; Well-quasi-order; Well quasi order; Wqo; Well-quasi order; Well-partial-order

In mathematics, specifically order theory, a well-quasi-ordering or wqo is a quasi-ordering such that any infinite sequence of elements x_0, x_1, x_2, \ldots from X contains an increasing pair x_i\le x_j with i.

https://en.wikipedia.org/wiki/Well-quasi-ordering

All's Well That Ends Well

PLAY BY SHAKESPEARE

All's Well that Ends Well; All's well that ends well; Capilet; Parolles; All's well that ends well (proverb); Alls Well That Ends Well; All's Well That End's Well; All's Well, that Ends Well

All's Well That Ends Well is a play by William Shakespeare, published in the First Folio in 1623, where it is listed among the comedies. There is a debate regarding the dating of the composition of the play, with possible dates ranging from 1598 to 1608.

https://en.wikipedia.org/wiki/All's_Well_That_Ends_Well

Partially ordered group

GROUP WITH A COMPATIBLE PARTIAL ORDER

Lattice ordered group; Positive element (ordered group); Partially ordered monoid; Orderable group; Ordered group; Lattice-ordered group; Partially-ordered group; Integrally closed ordered group; Integrally closed partially ordered group; Integrally closed (partially ordered group); Positive cone of a partially ordered group

In abstract algebra, a partially ordered group is a group (G, +) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a + g ≤ b + g and g + a ≤ g + b.

https://en.wikipedia.org/wiki/Partially_ordered_group

partially ordered set

$'''Fig.2''' [[Commutative diagram]] about the connections between strict/non-strict relations and their duals, via the operations of reflexive closure (''cls''), irreflexive kernel (''ker''), and converse relation (''cnv''). Each relation is depicted by its [[logical matrix]] for the poset whose [[Hasse diagram]] is depicted in the center. For example <math>3 \not\leq 4</math> so row 3, column 4 of the bottom left matrix is empty.$

SET ORDERED BY A TRANSITIVE, ANTISYMMETRIC, AND REFLEXIVE BINARY RELATION

PartialOrderedSet; PartialOrder; Partial order; Poset; Partial ordering relation; Partial ordering; Partially ordered; Strict order; Partially ordered sets; Ordered n-tuple; Strict partial ordering; Strict partial order; Poset category; Ordered collection; Non-strict order; Ordered set; Strict ordering; Interval (partial order); Ordinal sum; Partial Order; Partially-ordered set

A set with a partial ordering.

partial ordering

$'''Fig.2''' [[Commutative diagram]] about the connections between strict/non-strict relations and their duals, via the operations of reflexive closure (''cls''), irreflexive kernel (''ker''), and converse relation (''cnv''). Each relation is depicted by its [[logical matrix]] for the poset whose [[Hasse diagram]] is depicted in the center. For example <math>3 \not\leq 4</math> so row 3, column 4 of the bottom left matrix is empty.$

SET ORDERED BY A TRANSITIVE, ANTISYMMETRIC, AND REFLEXIVE BINARY RELATION

PartialOrderedSet; PartialOrder; Partial order; Poset; Partial ordering relation; Partial ordering; Partially ordered; Strict order; Partially ordered sets; Ordered n-tuple; Strict partial ordering; Strict partial order; Poset category; Ordered collection; Non-strict order; Ordered set; Strict ordering; Interval (partial order); Ordinal sum; Partial Order; Partially-ordered set

A relation R is a partial ordering if it is a pre-order (i.e. it is reflexive (x R x) and transitive (x R y R z => x R z)) and it is also antisymmetric (x R y R x => x = y). The ordering is partial, rather than total, because there may exist elements x and y for which neither x R y nor y R x. In domain theory, if D is a set of values including the undefined value (bottom) then we can define a partial ordering relation <= on D by x <= y if x = bottom or x = y. The constructed set D x D contains the very undefined element, (bottom, bottom) and the not so undefined elements, (x, bottom) and (bottom, x). The partial ordering on D x D is then (x1,y1) <= (x2,y2) if x1 <= x2 and y1 <= y2. The partial ordering on D -> D is defined by f <= g if f(x) <= g(x) for all x in D. (No f x is more defined than g x.) A lattice is a partial ordering where all finite subsets have a least upper bound and a greatest lower bound. ("<=" is written in LaTeX as sqsubseteq). (1995-02-03)

Special ordered set

In discrete optimization, a special ordered set (SOS) is an ordered set of variables, used as an additional way to specify integrality conditions in an optimization model. Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as in ordinary mixed integer programming.

https://en.wikipedia.org/wiki/Special_ordered_set

poset

$'''Fig.2''' [[Commutative diagram]] about the connections between strict/non-strict relations and their duals, via the operations of reflexive closure (''cls''), irreflexive kernel (''ker''), and converse relation (''cnv''). Each relation is depicted by its [[logical matrix]] for the poset whose [[Hasse diagram]] is depicted in the center. For example <math>3 \not\leq 4</math> so row 3, column 4 of the bottom left matrix is empty.$

SET ORDERED BY A TRANSITIVE, ANTISYMMETRIC, AND REFLEXIVE BINARY RELATION

PartialOrderedSet; PartialOrder; Partial order; Poset; Partial ordering relation; Partial ordering; Partially ordered; Strict order; Partially ordered sets; Ordered n-tuple; Strict partial ordering; Strict partial order; Poset category; Ordered collection; Non-strict order; Ordered set; Strict ordering; Interval (partial order); Ordinal sum; Partial Order; Partially-ordered set

partially ordered set

WELL

EXCAVATION OR STRUCTURE CREATED IN THE GROUND TO ACCESS GROUNDWATER

Well water; Shallow well; Monitoring wells; Groundwater well; Village pump; Well-digger; Well digger; Well digging; Water wells; Monitoring well; Monitoring Wells; Willage pump; Village Pump; Well (water); Shallow wells; Well water contamination; User:Crouch, Swale/Well; Water well

Whole Earth #&39;Lectronic Net (Reference: network)

well

EXCAVATION OR STRUCTURE CREATED IN THE GROUND TO ACCESS GROUNDWATER

Well water; Shallow well; Monitoring wells; Groundwater well; Village pump; Well-digger; Well digger; Well digging; Water wells; Monitoring well; Monitoring Wells; Willage pump; Village Pump; Well (water); Shallow wells; Well water contamination; User:Crouch, Swale/Well; Water well

well¹

¦ adverb (better, best)

1. in a good or satisfactory way.

in a condition of prosperity or comfort.

archaic luckily; opportunely: hail fellow, well met.

2. in a thorough manner.

to a great extent or degree; very much.

Brit. informal very; extremely: he was well out of order.

3. very probably; in all likelihood.

without difficulty.

with good reason.

¦ adjective (better, best)

1. in good health; free or recovered from illness.

in a satisfactory state or position.

2. sensible; advisable.

¦ exclamation used to express surprise, anger, resignation, etc., or when pausing in speech.

Phrases

as well

1. in addition; too.

2. (as well or just as well) with equal reason or an equally good result.

sensible, appropriate, or desirable.

be well out of Brit. informal be fortunate to be no longer involved in.

be well up on (or in) know a great deal about.

leave (or let) well (N. Amer. enough) alone refrain from interfering with or trying to improve something.

very well used to express agreement or understanding.

well and truly completely.

Derivatives

wellness noun

Origin

OE wel(l), of Gmc origin; prob. related to the verb will¹.

Usage

The adverb well is often used in combination with past participles to form adjectival compounds. The general stylistic principle for hyphenation is that if the adjectival compound is placed attributively (i.e. before the noun), it should be hyphenated (a well-intentioned remark) but that if it is placed predicatively (i.e. standing alone after the verb), it should not be hyphenated (her remarks were well intentioned). In this dictionary, the unhyphenated form is generally the only one given.

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well²

¦ noun

1. a shaft sunk into the ground to obtain water, oil, or gas.

a depression made to hold liquid.

2. a plentiful source or supply: a deep well of sympathy.

3. an enclosed space in the middle of a building, giving room for stairs or a lift or allowing light or ventilation.

4. Brit. the place in a law court where the clerks and ushers sit.

5. Physics a region of minimum potential.

6. archaic a water spring or fountain.

¦ verb (often well up) (of a liquid) rise up to the surface and spill or be about to spill.

?(of an emotion) develop and become more intense.

Origin

OE wella, of Gmc origin.

Википедия

Special ordered set

In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an optimization model. Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as in ordinary mixed integer programming. Knowing that a variable is part of a set and that it is ordered gives the branch and bound algorithm a more intelligent way to face the optimization problem, helping to speed up the search procedure. The members of a special ordered set individually may be continuous or discrete variables in any combination. However, even when all the members are themselves continuous, a model containing one or more special ordered sets becomes a discrete optimization problem requiring a mixed integer optimizer for its solution.

The ‘only’ benefit of using Special Ordered Sets compared with using only constraints is that the search procedure will generally be noticeably faster. As per J.A. Tomlin, Special Order Sets provide a powerful means of modeling nonconvex functions and discrete requirements, though there has been a tendency to think of them only in terms of multiple-choice zero-one programming.

https://en.wikipedia.org/wiki/Special ordered set