An ω-complete domain is complete in the sense that every directed subset has a least upper bound.

Every domain D can be embedded in an ω-complete domain completion ( called the ω-completion or simply the completion of D ) that is, in a precise sense, the smallest ω-complete domain containing D. The isolated elements of completion are precisely the isolated elements of D, but in general completion contains limit points that are not found in D. completion is uniquely determined up to isomorphism.

If all chains have a supremum, the order is called chain complete ( sometimes also " omega-complete ", written ω-complete ).

So why not use ω-complete domains only, as is traditional?

It is ω-complete when every increasing sequence of elements ( a type of countable chain ) has a least upper bound ; the same notion can be extended to other cardinalities of chains.

The traditional definition requires also that D be ω-complete, so that ω-continuous functions from D to D will have fixed points.

In mathematics, directed-complete partial orders and ω-complete partial orders ( abbreviated to dcpo, ωcpo or sometimes just cpo ) are special classes of partially ordered sets, characterized by particular completeness properties.

His sailing vessel is guided by fate to the shores of his own country at a time when Sibylla's domain is overrun by the armies of one of her rejected suitors.

In this domain the simple fact of coexistence in the same local, national, and world community is enough to guarantee that we cannot refrain from having some effect, large or small, upon Gentile-Jewish relations.

The difference is important, for although the older law of nations did cover relationships among sovereigns, this was by no means its exclusive domain.

Its domain is the powerset of A ( with the empty set removed ), and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets.

This exon encodes a portion of the mature TNF domain, as well as the leader sequence which is a highly conserved region necessary for proper intracellular processing.

The protein is organized with 6 transmembrane segments, then the C1 cytoplasmic domain, then another 6 membrane segments, and then a second cytoplasmic domain called C2.

In Mycobacterium tuberculosis, the AC-III polypeptide is only half as long, comprising one 6-transmembrane domain followed by a cytoplasmic domain, but two of these form a functional homodimer that resembles the mammalian architecture.

Abbadie gave his domain the name Abbadia, which is the name still used in Basque.

The castle was classified as a protected historical monument by France in 1984 and most of the domain now belongs to the Coastal Protection Agency and is managed by the city of Hendaye.

It is often used in signal processing for analyzing functions or series of values, such as time domain signals.

Active Directory ( AD ) is a directory service created by Microsoft for Windows domain networks.

For example, when a user logs into a computer that is part of a Windows domain, Active Directory checks the submitted password and determines whether the user is a system administrator or normal user.

A tree is a collection of one or more domains and domain trees in a contiguous namespace, linked in a transitive trust hierarchy.

If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.

A binary relation is the special case of an n-ary relation R ⊆ A < sub > 1 </ sub > × … × A < sub > n </ sub >, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain A < sub > j </ sub > of the relation.

The sets X and Y are called the domain ( or the set of departure ) and codomain ( or the set of destination ), respectively, of the relation, and G is called its graph.

This article also includes text from the Encyclopedia Biblica, another publication which has fallen into the public domain.

Bézier curves are also used in the time domain, particularly in animation and interface design, e. g., a Bézier curve can be used to specify the velocity over time of an object such as an icon moving from A to B, rather than simply moving at a fixed number of pixels per step.

As noted in the introduction, Bézout's identity works not only in the ring of integers, but also in any other principal ideal domain ( PID ).

A version also exists for the BBC Micro on public domain though never officially released.

In addition, works published before 1964 that did not have their copyrights renewed 28 years after first publication year also are in the public domain, except that books originally published outside the US by non-Americans are exempt from this requirement, if they are still under copyright in their home country ( see How Can I Tell Whether a Copyright Was Renewed for more details ).

The study of haptic ( tactile ), olfactory, and gustatory stimuli also fall into the domain of perception.

In order to apply professional standards, increase the level of practice, and possibly protect the public ( though this is also the domain of licensure ), a professional organization might establish a certification.

Time domain algorithms such as LPC also often have low latencies, hence their popularity in speech coding for telephony.

A DNS name server is a server that stores the DNS records for a domain name, such as address ( A ) records, name server ( NS ) records, and mail exchanger ( MX ) records ( see also list of DNS record types ); a DNS name server responds with answers to queries against its database.

For example, the domain names < tt > www. example. com </ tt > and < tt > example. com </ tt > are also hostnames, whereas the < tt > com </ tt > domain is not.

Typically, such caching DNS servers, also called DNS caches, also implement the recursive algorithm necessary to resolve a given name starting with the DNS root through to the authoritative name servers of the queried domain.

Filtering, particularly in non-realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain.

Frequency domain analysis is also called spectrum-or spectral analysis.

* A congruence relation is an equivalence relation whose domain X is also the underlying set for an algebraic structure, and which respects the additional structure.

The elimination of the collision domain for these connections also means that all the link's bandwidth can be used by the two devices on that segment and that segment length is not limited by the need for correct collision detection.

An expert (, also called cognoscente ) is someone widely recognized as a reliable source of technique or skill whose faculty for judging or deciding rightly, justly, or wisely is accorded authority and status by their peers or the public in a specific well-distinguished domain.

The filter response can also be completely characterized in the frequency domain by its transfer function, which is the Fourier transform of the impulse response h. Typical filter design goals are to realize a particular frequency response, that is, the magnitude of the transfer function ; the importance of the phase of the transfer function varies according to the application, inasmuch as the shape of a waveform can be distorted to a greater or lesser extent in the process of achieving a desired ( amplitude ) response in the frequency domain.

Expert witnesses may also deliver expert evidence about facts from the domain of their expertise.

The psychomotor domain deals with the development of motor skills, movement and coordination and has 7 categories, that also goes from simplest to complex.

In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.

An arbitrary PID has much the same " structural properties " of a Euclidean domain ( or, indeed, even of the ring of integers ), but knowing an explicit algorithm for Euclidean division, and thus also for greatest common divisor computation, gives a concreteness which is useful for algorithmic applications.