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Dual

Definition: Dual

Dual

Adjective

1. Consisting of or involving two parts or components usually in pairs; "an egg with a double yolk"; "a double (binary) star"; "double doors"; "dual controls for pilot and copilot"; "duple (or double) time consists of two (or a multiple of two) beats to a measure".

2. Having more than one decidedly dissimilar aspects or qualities; "a double (or dual) role for an actor"; "the office of a clergyman is twofold; public preaching and private influence"- R.W.Emerson; "every episode has its double and treble meaning"-Frederick Harrison.

3. A grammatical number category referring to two items or units (as opposed to one item (singular) or more than one item (plural)); "ancient Greek had the dual form but it has merged with the plural form in modern Greek".

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.
 

Date "dual" was first used in popular English literature: sometime before 1790. (references)

Etymology: Dual \Du"al\, adjective. [Latin expression dualis, from duo two. See Two.]. (references)

 

Specialty Definition: Dual

DomainDefinition

Computing

Dual Every field of mathematics has a different meaning of dual. Loosely, where there is some binary symmetry of a theory, the image of what you look at normally under this symmetry is referred to as the dual of your normal things. In linear algebra for example, for any vector space V, over a field, F, the vector space of linear maps from V to F is known as the dual of V. It can be shown that if V is finite-dimensional, V and its dual are isomorphic (though no isomorphism between them is any more natural than any other). There is a natural embedding of any vector space in the dual of its dual: V -> V'': v -> (V': w -> wv : F) (x' is normally written as x with a horizontal bar above it). I.e. v'' is the linear map, from V' to F, which maps any w to the scalar obtained by applying w to v. In short, this double-dual mapping simply exchanges the roles of function and argument. It is conventional, when talking about vectors in V, to refer to the members of V' as covectors. (1997-03-16). Source: The Free On-line Dictionary of Computing.

Math

The dual of a planar graph, G, is a graph with a vertex for each region in G and an edge between vertices for each pair of adjacent regions. The new edge crosses the edge in G which is the boundary between the adjacent regions. (references)

Source: compiled by the editor from various references; see credits.

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Specialty Definition: Bra-ket notation

(From Wikipedia, the free Encyclopedia)

Bra-ket notation is the standard notation used for describing quantum mechanical states. It was invented by Paul Dirac. It is so called because the inner product of two states is denoted by a bracket, ⟨φ|ψ⟩, consisting of a left part, ⟨φ|, called the bra, and a right part, |ψ⟩, called the ket.

In quantum mechanics, the state of a physical system is identified with a vector in a Hilbert space, H. Each vector is called a ket, and written as

where ψ is an arbitrary label for the ket. Each element of the dual space of H (i.e. each continuous linear function from H to the complex numbers C) is known as a bra, and written as

where φ is an arbitrary label for the bra. Applying the bra ⟨φ| to the ket |ψ⟩ results in a complex number, called a bra-ket, which we write as

Every ket |ψ⟩ has a dual bra, written as ⟨ψ|, a continuous linear function on H defined as follows:

where the right hand side ( , ) denotes the inner product given on the Hilbert space. The notation is justified by the Riesz representation theorem, which states that every bra in the dual space arises from one and only one ket in this fashion.

The bra-ket operation has the following properties:

If A : H -> H is a linear operator, we can apply A to the ket |ψ⟩ to obtain the ket (A|ψ⟩). The operator also acts on bras: applying the operator A to the bra ⟨φ| results in the bra (⟨φ|A), defined as a linear functional on H by the rule

This expression is commonly written as

A convenient way to define linear operators on H is given by the outer product: if ⟨φ| is a bra and |ψ⟩ is a ket, the outer product |φ⟩ ⟨ψ| denotes the operator which maps the ket |ρ⟩ to the ket |φ⟩ ⟨ψ|ρ⟩ (here the scalar ⟨ψ|ρ⟩ is written to the right of the vector |φ⟩). One use of the outer product is to construct projection operators. Given a ket |ψ⟩ of norm 1, the orthogonal projection onto the subspace spanned by |ψ⟩ is

Two Hilbert spaces V and W may form a third space V × W by a tensor product. If |ψ⟩ is a ket in V and |φ⟩ is a ket in W, the tensor product of the two kets is a ket in V × W. This is written variously as

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Bra-ket notation."

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Dual

(From Wikipedia, the free Encyclopedia)

This article should be merged with Duality

Dual can be used to connotate something being both at the same instant (i.e,. being twofold), such as in duality. The duality of a phenonomen is characterized by the fact that some properties can be explained best by one model and others by another model. (see wave-particle duality)

In some languages, in addition to the singular and plural there is also a dual, which is used when exactly two people or things are meant. The plural in these languages is used only for groups greater than two. This is known as the dual grammatical number.

The word dual is used in mathematics, as in dual space, dual polyhedron and dual numbers, for example. See Duality.

Dual is a brand name for Hifi equipment, mostly know for vinyl record players.

Dual, in electronics, refers to two devices or circuits that have mathematical descriptions that are identical except that voltages in one correspond to currents in the other, and vice versa. For example:

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Dual (category theory)

(From Wikipedia, the free Encyclopedia)

In category theory, an abstract branch of mathematics, the dual of a category is the category formed by reversing all the morphisms of . That is, we take to be the category with objects those of , but with the morphisms from X to Y in being the morphisms from Y to X in . The dual of a dual of a category is itself.

It is also often called the opposite category. Examples come from reversing the direction of inequalities in a partial order. In logic, this then looks like a very general description of negation (that is, proofs run in the opposite direction). Inverse limits and direct limits are interchanged. One way in which the concept is used is to remove the distinction between covariant and contravariant functors: a contravariant functor to is equally a functor to the opposite of .

In some cases one can identify the opposite category: for example the category of affine schemes is the opposite of the category of commutative rings. The Pontryagin duality restricts to the duality between the category of compact Hausdorff abelian topological groups and that of (discrete) abelian groups. The category of Stone spaces and continuous functions is the opposite of the category of Boolean algebras and homomorphisms.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Dual (category theory)."

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Dual grammatical number

(From Wikipedia, the free Encyclopedia)

Dual is the grammatical number used for two referents.

Relatively few languages have the dual number. Most have no number or only singular and plural.

In some languages, in addition to the singular and plural there is also a dual, which is used when exactly two people or things are meant. The plural in these languages is used only for groups greater than two.

Slovenian uses the dual number in full, as does Inuktitut. Sorbian, the Slavic language of a very small minority in Germany, also uses the dual number. The Greek language used in the Homeric texts, the Iliad and Odyssey, has some use of the dual. Among living languages, modern standard Arabic uses dual number. Hebrew has some forms of dual, largely for parts of the body and things that come in pairs, such as `aynayim (eyes), shinayim (teeth, even all 32), and mishqafayim (eyeglasses). Akkadian had a dual number, though its use was confined to standard phrases like "two hands", "two eyes", and "two arms". Sanskrit also possesses a dual number, with specific (although fewer) inflections for verbs and nouns.

See also Grammatical number.

Languages with dual include:

Grammar | Language | Linguistics

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Dual grammatical number."

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Dual polyhedron

(From Wikipedia, the free Encyclopedia)

Polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the others. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another with equivalent edges. So the regular polyhedra - the Platonic solids and Kepler-Poinsot polyhedra - are arranged into dual pairs.

Duality is defined in terms of polar reciprocation about a given sphere. Here, each vertex is associated with a face plane so that the ray from the center to the vertex is perpendicular to the plane, and the product of the distances from the center to each is equal to the square of the radius. In coordinates, for reciprocation about the sphere x2 + y2 + z2 = r2, the vertex (x0, y0, z0) is associated with the plane x0x + y0y + z0z = r2.

The vertices of the dual, then, are the reciprocals of the face planes of the original, and the faces of the dual lie in the reciprocals of the vertices of the original. Also, any two adjacent vertices define an edge, and these will reciprocate to two adjacent faces which intersect to define an edge of the dual. This can be generalized to n-dimensional space, so we can talk about dual polytopes. Then the vertices of one correspond to the (n-1)-dimensional elements of the other, and the j points that define a (j-1)-dimensional element will correspond to j hyperplanes that intersect to give a (n-j)-dimensional element. The dual of a honeycomb can be defined similarly.

Notice that the dual of a polyhedron will depend on what sphere we reciprocate with respect to, the resulting forms being distortions of one another. The center of the sphere is sufficient to define the dual up to similarity. If multiple symmetry axes are present, they will necessarily intersect at a single point, and this is usually taken to be the center. Failing that a circumscribed sphere, inscribed sphere, or midsphere (one with all edges as tangents) can be used. It can be shown that all polyhedra can be distorted into a canonical form where a midsphere exists and in fact the points where the edges touch it average out to give the center of the circle, and this form is unique up to congruencies.

If a polyhedron has an element passing through the center of the sphere, it will have an infinite dual. It is worth noting that the vertices and edges of a convex polyhedron can be projected to form a graph on the sphere, and the corresponding graph formed by the dual of this polyhedron is its dual graph.

The concept of duality here is also related to that in projective geometry, where lines and edges are interchanged, and is in fact a particular version of the same.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Dual polyhedron."

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Dual space

(From Wikipedia, the free Encyclopedia)

In mathematics, the existence of a 'dual' vector space reflects in an abstract way the relationship between row vectors (1xn) and column vectors (nx1). The construction can also take place for infinite-dimensional spaces and gives rise to important ways of looking at measures, distributions and Hilbert space. The use of the dual space in some fashion is thus characteristic of functional analysis. It is also inherent in the Fourier transform.

Algebraic Dual Space

Given any vector space V over some field F, we define the dual space V* to be the set of all linear functionals on F, i.e., scalar-valued linear transformations on V (in this context, a "scalar" is a member of the base-field F). V* itself becomes a vector space over F under the following definition of addition and scalar multiplication:

(φ + ψ)(x) = φ(x) + ψ(x)
(aφ) (x) = a φ(x)
for all φ, ψ in V*, a in F and x in V. In the language of tensors, elements of V are sometimes called contravariant vectors, and elements of V*, covariant vectors or one-forms.

Examples

If the dimension of V is finite, then V* has the same dimension as V; if {e1,...,en} is a basis for V, then the associated dual basis {e1,...,en} of V* is given by

Concretely, if we intepret Rn as space of columns of n real numbers, its dual space is typically written as the space of rows of n real numbers. Such a row acts on Rn as a linear functional by ordinary matrix multiplication.

If V consists of the space of geometrical vectorss (arrows) in the plane, then the elements of the dual V* can be intuitively represented as collections of parallel lines. Such a collection of lines can be applied to a vector to yield a number in the following way: one counts how many of the lines the vector crosses.

If V is infinite-dimensional, then the above construction of ei does not produce a basis for V* and the dimension of V* is greater than that of V. Consider for instance the space R(ω), whose elements are those sequences of real numbers which have only finitely many non-zero entries. The dual of this space is Rω, the space of all sequences of real numbers. Such a sequence (an) is applied to an element (xn) of R(ω) to give the number ∑nanxn.

Transpose of a linear map

If f: V -> W is a linear map, we may define its transpose tf : W* -> V* by
tf (φ) = φ o f    for every φ in W*.
The assignment f |-> tf produces an injective homomorphism between the space of linear operators from V to W and the space of linear operators from W* to V*; this homomorphism is an isomorphism iff W is finite-dimensional. If the linear map f is represented by the matrix A with respect to two bases of V and W, then tf is represented by the transposed matrix tA with respect to the dual bases of W* and V*. If g: W -> X is another linear map, we have t(g o f) = tf o tg. In the language of category theory, taking the dual of vector spaces and the transpose of linear maps is therefore a contravariant functor from the category of vector spaces over F to itself.

Bilinear products and dual spaces

As we saw above, if V is finite-dimensional, then V is isomorphic to V*, but the isomorphism is not natural and depends on the basis of V we started out with. In fact, any isomorphism Φ from V to V* defines a unique non-degenerate bilinear product on V by

= (Φ(v))(w)

and conversely every such non-degenerate bilinear product on a finite-dimensional space gives rise to an isomorphism from V to V*.

Injection into the double-dual

There is a natural homomorphism Ψ from V into the double dual V**, defined by (Ψ(v))(φ) = φ(v) for all v in V, φ in V*. This map Ψ is always injective; it is an isomorphism if and only if V is finite-dimensional.

Continuous Dual Space

When dealing with a normed vector space V (e.g., a Banach space or a Hilbert space), one typically is only interested in the continuous linear functionals from the space into the base field. These form a normed vector space, called the continuous dual of V, sometimes just called the dual of V. It is denoted by V '. The norm ||φ|| of a continuous linear functional on V is defined by

||φ|| = sup { |φ(x)| : ||x|| ≤ 1 }
This turns the continuous dual into a normed vector space, indeed into a Banach space.

One may also talk about the continuous dual of an arbitrary topological vector space. This is however much harder to deal with since it will in general not be a normed vector space in any natural way.

Examples

For any finite-dimensional normed vector space or topological vector space, such as Euclidean n-space, the continuous dual and the algebraic dual coincide.

Let 1 < p < ∞ be a real number and consider the Banach space l p of all sequences space of sequences a = (an) for which

is finite. Define the number q by 1/p + 1/q = 1. Then the continuous dual of l p is naturally identified with l q: given an element φ ∈ (l p)', the corresponding element of l q is the sequence (φ(en)) where en denotes the sequence whose nth term is 1 and all others are zero. Conversely, given an element a = (an) ∈ l q, the corresponding continuous linear functional φ on l p is defined by φ(a) = ∑n an bn for all a = (an) ∈ l p (see Hölder's inequality).

In a similar manner, the continuous dual of l 1 is naturally identified with l ∞. Furthermore, the continuous duals of the Banach spaces c (consisting of all convergent sequences, with the supremums norm) and c0 (the sequences converging to zero) are both naturally identified with l 1.

Further properties

If V is a Hilbert space, then its continuous dual is a Hilbert space which is anti-isomorphic to V. This is the content of the Riesz representation theorem, and gives rise to the bra-ket notation used by physicists in the mathematical formulation of quantum mechanics.

In analogy with the case of the algebraic double dual, there is always a naturally defined injective continuous linear operator Ψ : V → V '' from V into its continuous double dual V ''. This map is in fact an isometry, meaning ||Ψ(x)|| = ||x|| for all x in V. Spaces for which the map Ψ is a bijection are called reflexive.

The continuous dual can be used to define a new topology on V, called the weak topology.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Dual space."

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Duality (physics)

(From Wikipedia, the free Encyclopedia)

In modern physics, duality most often refers to the paradigm underlying quantum mechanics, according to which matter can exhibit properties associated with wave physics as well as classical particle mechanics.

Because these two sets of phenomena are mutually exclusive in classical physics, but nevertheless are both needed in order to describe the possible behaviors of matter, one speaks of the wave-particle duality.

This duality also implies that light and electromagnetic radiation, which in classical physics are considered to be wave phenomena, can exhibit properties of matter: light has to be described as a wave in order to explain interference effects, whereas the photoelectric effect is usually explained by invoking the particle nature of light (although it can be shown to be fully explainable by treating light as a wave as well).

Dual descriptions of a physical system may have overlapping ranges of validity. In such regions of overlap, two dual theories will not give contradictory predictions.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Duality (physics)."

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Synonyms: Dual

Synonyms: double (adj), duple (adj), threefold (adj), treble (adj), twofold (adj). (additional references)

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Synonyms within Context: Dual

ContextSynonyms within Context (source: adapted from Roget's Thesaurus).

Accompaniment

Adjective: two, twin; dual, dualistic, double; binary, binomial; twin, biparous; dyadic; conduplicate; duplex; biduous, binate, diphyletic, dispermic, unijugate; tete-a-tete.

Source: adapted from Roget's Thesaurus.

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Crosswords: Dual

English words defined with "dual": divided highway, double, dual carriageway ♦ number ♦ Sulphur base ♦ threefold, treble, twofold. (references)
Specialty definitions using "dual": audio mode ♦ BW-755C ♦ call processing manager, complete inference system, consolidated period ♦ DBRI, Delaunay triangulation, digital number identification sequence, DIL, DIMM, Distributed Queue Dual Bus, DQDB, DTMF, dual index note, Dual In-Line, Dual In-line Memory Module, Dual In-Line Package, dual linear program, dual ported, Dual Tone Multi Frequency, DUAL-HOSE CEMENTER, dual-thrust motor ♦ Fiber Distributed Data Interface, Fibre Channel-Arbitrated Loop, FORMING CHUCK ♦ greatest lower bound ♦ HOME ENERGY ASSISTANCE PROGRAM, hose cementer, hose finisher ♦ Integrated Coverage Measurement ♦ least upper bound ♦ Mozilla ♦ no-break power system ♦ PDP-7, Pentium II, Pentium III, pole-peeler helper, POLE-PEELING-MACHINE-OPERATOR HELPER, pole-shaver helper, Post-Enumeration Survey ♦ self-priming centrifugal pump, Single Inline Pin Package, sixteen-pin case, soaking pit, soaking pit furnace, Socket 8, structured notes ♦ T1 tone detector-1 board, T1TD board, tensor product, touch-code ♦ uninterruptible power system ♦ V.24, video random access memory, Voronoi diagram. (references)
Non-English Usage: "Dual" is also a word in the following languages with English translations in parentheses.

Albanian (dual), German (dual), Portuguese (dual), Romanian (dual), Scottish (a lock of hair, braid, due, hereditary right, hereditary right or disposition, lock of hair, plait, plait or fold, ringlet), Spanish (dual).

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Modern Usage: Dual

DomainUsage

Screenplays

And so, unknown even to her closest friends, Rick Mason and Cindy Lee, she became a dual person: Andrea Thomas, teacher; and Isis, dedicated foe of evil, defender of the weak, champion of truth and justice (Isis; writing credit: Kathleen Barnes; Russell Bates)

Movie/TV Titles

Fong Sze Yu's Bloody Battle with the Net of Dual Forces (1959)

Dual Alibi (1946)

Dual! Paralle lunlun monogatari (1999)

Dual Flying Kicks (1982)

Source: compiled by the editor from various references; see credits.

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Commercial Usage: Dual

DomainTitle

Books

  • Gilbert and Sullivan: A Dual Biography (reference)

    (more book examples)

  

Theater & Movies

  • Armitage - Dual Matrix (Special Edition) (reference)

  • Dual - Trouble Adventure - Student Housing (Vol. 2) (reference)

    (more DVD examples; more video examples)

  

Music

  

High Tech

  

Consumer Goods

  • Sound N Lights With Dual Receivers (reference)

  • Bosch 4412 12" Dual Bevel Slide Miter Saw (reference)

  • Hitachi C10FSK 10" Dual Slide Compound Miter Saw with Free 10" x 72-Tooth Carbide Blade, a $69.99 Value (reference)

    (more baby examples; more wireless phone examples; more garden examples; more kitchen examples; more tool examples)

Source: compiled by the editor from various references; see credits.

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Image Slideshow: Dual

Photos:
Dual

More pictures...

Illustrations:
Dual

More pictures...

Computer Images:
Dual

More pictures...

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Photo Album: Dual

ThumbnailDescription & CreditThumbnailDescription & Credit

A Douglas SBD-3 "Dauntless" scout bomber (Bureau # 4542), of USS Enterprise's Bombing Squadron Six (VB-6), is parked on board USS Yorktown (CV-5) after landing at about 1140 hrs on 4 June 1942. This plane, damaged during the attack on the Japanese aircraft carrier Kaga that morning, landed on Yorktown as it was low on fuel. It was later lost with the carrier. Its crew included Ensign George H. Goldsmith, pilot, and Radioman 1st Class James W. Patterson, Jr. Note damage to the horizontal tail and dual stripes painted on the fin. Credit: NAVY.

Is this another case of dual personality?. Credit: Library of Congress.

Science and research. Mineral prospecting. Electrical prospecting for metallic minerals may be carried on by using the dual coil radiometer to measure the electro-magnetic field of the earth, as it may be influenced by the presence of an ore body. Student. Credit: Library of Congress.

Marion Hills, rehabilitation client, and dual purpose cattle purchased with rehabilitation loan. Center County, Iowa. Credit: Library of Congress.

Source: pictures compiled by the editor from various references; see picture credits.

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Digital Photo Gallery: Dual
 

"Dual dell notebook 1" by Balázs Kovács
Commentary: "My two DELL notebooks - Latitude C610 and C640."		"Engine" by Persist Persist
Commentary: "An antique truck engine. Straight six. Dual carbs. Taken October, 2002."

Source: photographs selected by the editor, with permission from the photographers.

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Non-Fiction Usage: Dual

SubjectTopicQuote

Health

Another option is 2 weeks of dual therapy. (references)

Dual Diagnosis (1993). Focuses on the problem of mental illness in drug-abusing and drug-addicted populations, and examines various approaches useful for treating dual-diagnosed clients. (references)

Measuring the exact amount of a person's body fat is not easy. The most accurate measures are to weigh a person underwater or to use an X-ray test called Dual Energy X-ray Absorptiometry (DEXA). (references)

Business

Dual voltage can be imported into the Kingdom. (references)

Genesis' major power station is a 1000MW dual fired station at Huntly. (references)

The remaining 29% (or 1,477 practices) were dual or multiple practitioner practices. (references)

Civil Liberties

Albania

Citizens born in the country who emigrate may hold dual citizenship. (references)

Kazakhstan

Citizens have the right to change their citizenship, but are not permitted to hold dual citizenship. (references)

Yugoslavia

To address this problem, in February the Government amended the 1997 Citizenship Law to allow dual citizenship. (references)

Economic History

Latvia

Neither country allows for dual citizenship. (references)

Botswana

Dual listings are permitted on the Botswana Stock Exchange. (references)

The Holy See

The rest have missions located outside Italy with dual accreditation. (references)

Human Rights

United Arab Emirates

There is a dual system of Shari'a and civil courts. (references)

Russia

He was charged with divulging state secrets, the unlawful transfer of dual use technologies, and for smuggling contraband. (references)

Poland

Provincial courts have a dual responsibility, handling appeals from regional courts while enjoying original jurisdiction for the most serious types of offenses. (references)

Minorities

Moldova

In August 2000, a law permitting dual citizenship went into effect. (references)

Tajikistan

An agreement ratified by the Russian Duma in December 1996 allows for dual Russian and Tajik citizenship. (references)

Moldova

According to this law, dual citizenship can be obtained through birth, marriage, on the basis of a bilateral agreement (although no such agreements are in effect), or if it is provided by an international accord to which the country is a party. (references)

Political Economy

Vietnam

The Prime Minister hosted a meeting in early 1999, which led to changes in the dual pricing structure. (references)

POLAND

Import Licenses: Licenses are required for strategic goods on Wassenaar dual use and munitions lists, as well as for fuel and tobacco. (references)

Armenia

A special presidential commission is preparing constitutional amendments providing for, inter alia, a stronger parliament and dual citizenship. (references)

Political Rights

Egypt

A number of court rulings declaring election results invalid went unimplemented, but one deputy (Rami Lakah) lost his seat in Cairo based on a court decision declaring him ineligible because he held dual citizenship. (references)

Trade

Taiwan

Dual labeling in metric and non-metric units is permitted. (references)

Portugal

For dual use products a certificate of delivery may also be required. (references)

Travel

Syria

Dual national males are subject to Syrian military duty laws. (references)

Egypt

Dual Egyptian-American nationals may enter and leave Egypt on their U.S. passport. (references)

Colombia

It is strongly recommended that all product literature be in Spanish or dual language. (references)

Worker Rights

Guyana

Historically, the two major political parties have wielded significant influence over the leadership of several unions, and trade union officials often served in dual roles as party officials. (references)

Source: compiled by the editor from ICON Group International, Inc.; see credits.

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Usage Frequency: Dual

"Dual" is generally used as an adjective (general or positive) -- approximately 98.02% of the time. "Dual" is used about 1,161 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)
Parts of SpeechPercentUsage per
100 Million Words		Rank in English
Adjective (general or positive)98.02%1,1386,725
Noun (proper)1.98%2372,767
                    Total100.00%1,161N/A

Source: compiled by the editor from several corpora; see credits.

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Usage in Company Names: Dual

CountryName
USA

Dual Holding Company

 (more examples...)

Source: compiled by the editor from Icon Group International, Inc.

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Expressions: Dual

Expressions using "dual": distributed Queue Dual Bus ♦ dual amplification ♦ Dual Auroral Radar Network ♦ dual band ♦ dual boot ♦ dual carriage way ♦ dual carriageway ♦ dual carriageway road ♦ dual control ♦ dual cycle ♦ Dual energy X-ray absortiometry ♦ dual exchange rate mechanism ♦ dual firing circuit ♦ dual gear ♦ dual glazing ♦ dual hand ♦ dual inline package switch ♦ dual instruction time ♦ dual mandate ♦ dual nationality ♦ dual orifice atomizer ♦ dual personality ♦ dual polarised aerial ♦ dual polarised antenna ♦ dual polarized antenna ♦ dual ported ♦ dual purpose ♦ dual recognition ♦ dual residence ♦ dual scan display ♦ dual sound in syncs ♦ dual spin ♦ dual stage regulator ♦ dual Tone Multi Frequency ♦ dual wheels. Additional references.

Hyphenated Usage

Beginning with "dual": DUAL-607, dual-action, dual-arc, dual-architecture, dual-attached, dual-beam, dual-board, dual-burn, dual-bus, dual-capable, dual-career, dual-carriage, dual-carriageway, dual-cassette, dual-chamber, dual-channel, dual-channel system, dual-chip, dual-coding, dual-command, dual-cone, dual-containment, dual-control, dual-cost, dual-cpu, dual-currency, dual-density, dual-detector, dual-earner, dual-edged, dual-element, Dual-Energy, dual-flush, dual-frequency, dual-fuel, dual-function, dual-gold, dual-homed, dual-income, dual-income family, dual-inline, dual-in-line, dual-insurance, dual-key, dual-labour, dual-lane, dual-launch, dual-level, dual-mode, dual-note, dual-operating, dual-organism, dual-period, dual-pointer, dual-polarised, dual-polarized, dual-ported, dual-practitioners, dual-presenter, dual-presidency, dual-price, dual-process, dual-processor, dual-purpose, dual-purpose card, dual-resident, dual-role, dual-roled, dual-route, dual-simplex, dual-source, dual-stack, dual-standard, dual-subject, dual-surface, dual-system, dual-tandem wheel undercarriage, dual-task, dual-temperature, dual-tone, dual-use, dual-voltage, dual-water-supply, dual-wavelength, dual-wired, dual-worker, dual-xxxx.

Ending with "dual": appointed-dual, arbitrators-dual, self-dual, you-dual.

Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: Dual

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.
 
ExpressionFrequency
per Day		ExpressionFrequency
per Day

dual hub speed switching

312

dual monitor video card

51

dual opteron server

296

dual fuel range

51

dual boot

223

dual exhaust system

51

dual

196

dual purpose motorcycle

50

dual citizenship

184

adventure dual parallel trouble

50

dual opteron

157

dual channel memory

46

dual exhaust

153

anime dual

45

dual monitor

149

medicus dual 2000

41

back cat dual exhaust n1 pexi series system

141

dual cpu motherboard

40

boot create dual

107

boot dual xp

40

dual processor motherboard

101

dual athlon

37

dual processor

94

citizenship dual india

36

dual diagnosis

90

dual diagnosis treatment

36

dual channel ddr

87

armitage dual matrix

33

dual sport motorcycle

79

minolta dimage scan dual iii

32

dual deck vcr

73

dual alarm clock

32

dual sport

64

boot dual window xp

32

dual monitor wallpaper

63

dual cpu

32

dual lite

62

dual time watch

31

dual hearts

56

dual motherboard

29
Source: compiled by the editor from various references; see credits.

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Modern Translation: Dual

Language Translations for "dual"; alternative meanings/domain in parentheses.

Albanian

  

dyjar, dyfish (di-, double, doubly, duplex, twofold), dual, i dyfishtë (double, double-headed, duple, duplex, duplicate, twofold). (various references)

   

Arabic 

  

‏مزدوج (binary, double, geminate, paired, twin), ‏مثنى, ‏زوج إثنان (couple), ‏عمل في وظيفتين, ‏ثنائي (bi-, bilateral, binary, duet, duo, duple, pair, twofold, twosome). (various references)

   

Bulgarian 

  

двойствен (ambivalent, amphibious, double-natured), двоен (binary, double, duplex, duplicate, geminate, twin, two ply, twofold). (various references)

   

Catalan

  

doble (double). (various references)

   

Chinese 

  

双重. (various references)

   

Czech

  

dvojí (duplicate). (various references)

   

Danish

  

dobbelt (double). (various references)

   

Dutch

  

tweevoudig (double), tweeledig (double), duplex (double), dubbel (double). (various references)

   

Esperanto

  

duobla (double). (various references)

   

Faeroese

  

dupultur (double). (various references)

   

Farsi 

  

دولا (Double, Geminate), دوتاءی (Binary, Couplement, Duplex), دوجنبه ای (Ambivalent). (various references)

   

Finnish

  

kaksinainen (twofold), kahtalainen (two sorts of .). (various references)

   

French

  

double (duple, duplex, duplicate). (various references)

   

Frisian

  

dûbeld (double), dûbel (double). (various references)

   

German

  

doppelt (double, doubly, duplex, duplicative, redoubled, twice, twin, twofold), zweifach (double, doubly, duplex, twice, twofold, twofoldly). (various references)

   

Greek 

  

διπλόσ (double, duple, duplex), διπλός (double, geminate), δυϊκός. (various references)

   

Hawaiian

  

dyfish (double). (various references)

   

Hebrew 

  

זוגי (double, duplicate), כפול (double, duple, duplicate, folded, multiplied, two fold). (various references)

   

Hungarian

  

dupla (clump, double, duplex), kettõs (bi-, binary, double, duplex, geminate, twin, twofold, twosome), kettős (double, duet, duplex, twin). (various references)

   

Indonesian

  

rangkap (double, geminate). (various references)

   

Italian

  

doppio (double, doubles, duplex, in duplicate, twice the amount, two faced, twofold, understudy). (various references)

   

Japanese Kanji 

  

二元的 , デモ隊 (demonstrator, Du Pont de Nemours, dual coat, dual system, dualism, duel, duet, duetto, duo, duplicate, duty-free, duty-free shop). (various references)

   

Japanese Katakana 

  

デュアル , にげんてき. (various references)

   

Korean 

  

이중 (Dup, Duplication). (various references)

   

Manx

  

dooblit (bipartite, double, duplex, twofold, two-way, two-way as cock etc), daagh. (various references)

   

Norwegian

  

dobbel. (various references)

   

Papiamen

  

dòbel (double). (various references)

   

Pig Latin

  

ualday.(various references)

   

Polish

  

podwójny (double). (various references)

   

Portuguese

  

duplo (double, dupery, duplicate, geminate, twofold). (various references)

   

Romanian

  

dublu (double, doubly, duplex, duplicate, twice, twofold), dual, compus din douã pãrţi. (various references)

   

Russian 

  

двойной (binary, double, double-bedded, duple, duplex, duplicate, twin, two ply, twofold, two-ply). (various references)

   

Serbo-Croatian

  

dvostruk (double, duplex, duplicate, twin, twofold). (various references)

   

Spanish

  

doble (ambidextrous, disingenuous, double, duplex, knell, ringer, stand in, twofold), dual. (various references)

   

Sranan

  

dobru (double). (various references)

   

Swedish

  

dubbel (double, doubles, duplicate, two ply, twofold). (various references)

   

Thai

  

ประกอบด้วยสองส่วน. (various references)

   

Turkish

  

ikili (binary, bipartite, double, duo-, duple, duplex, two), iki (ambi-, amphi-, bi-, brace, couple, duo-, dyad, twain, two, two-), çift (ambi-, amphi-, bi-, binary, brace, conjugate, couple, dipl-, diplo, double, duet, duple, duplicate, dyad, even, geminate, pair, twin, yoke). (various references)

   

Ukrainian

  

подвійний (bifold, bigeminal, binary, double, duplex, duplicate, twain, twin, two ply, twofold), двоїстий (double-natured). (various references)

   

Vietnamese 

  

lưỡng, kép (actor, compound, histrion), hai (deuce, double, duplex, two). (various references)

   

Welsh

  

deuol. (various references)

Source: compiled by the editor from various translation references.

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Derivations & Misspellings: Dual

Derivations

Words beginning with "dual": dualism, dualisms, dualist, dualistic, dualistically, dualists, dualities, duality, dualize, dualized, dualizes, dualizing, dually, duals. (additional references)

Words ending with "dual": decidual, dividual, gradual, individual, interindividual, nonindividual, residual, subdual, superindividual. (additional references)

Words containing "dual": gradualism, gradualisms, gradualist, gradualists, gradually, gradualness, gradualnesses, graduals, individualise, individualised, individualises, individualising, individualism, individualisms, individualist, individualistic, individualistically, individualists, individualities, individuality, individualization, individualizations, individualize, individualized, individualizes, individualizing, individually, individuals, residually, residuals, subduals. (additional references)


Misspellings

"Dual" is suggested in spellcheckers for the following: daal, dalf, Dalj, dall, dalq, dau, dauc, daug, daup, daux, dauz, dayal, Dduallt, deall, Deuel, Deuil, Diawl, diumal, Djalo, doak, doal, doil, douay, doul, Doula, Doulab, dozl, draal, dral, druel, druil, Dsubl, Duala, dualy, Duao, duar, duas, duat, duax, duay, Dubal, dubl, Dudai, duell, dufa, duga, Dugal, duil, duix, Dujac, dul, dula, dulay, dule, dulm, duma, dunav, dupal, dural, dusa, Duul, duval, dyal, eual, oual, rual, tual, ual, udag, Udale, Udl, wual. (additional references)

Source: compiled by the editor, based on several corpora (additional references).

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Rhyming with "Dual"

# of Phoneme MatchesPronunciationWord(s) rhyming with "dual" (pronounced duw"ul or duw"l)
4d uw" u lduel.
3-uw" u laccrual, crewel, cruel, fuel, gruel, jewel, nonaccrual, refuel, renewal.
2-uw" lBoule, Buhl, cool, drool, fool, spool, stool, supercool, joule, misrule, mule, pool, preschool, retool, rule, school, tool, uncool, Yule.

Source: compiled by the editor (additional references); see credits.

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Anagrams: Dual

Scrabble® Enable2K-Verified Anagrams

Direct Anagrams: auld, laud.

Words within the letters "a-d-l-u"

-1 letter: dal, lad.

-2 letters: ad, al, la.

 Words containing the letters "a-d-l-u"
 

+1 letter: adult, almud, aloud, cauld, duals, ducal, dulia, dural, fauld, lauds, ulnad, yauld.

 

+2 letters: adults, aidful, allude, almude, almuds, aludel, audial, audile, aulder, belaud, caudal, caudle, caulds, cedula, dually, ductal, dulias, faulds, feudal, hauled, landau, lauded, lauder, lurdan, mauled, radula, suldan, tuladi, unclad, unlade, unlaid, unlead, unload, upland, upload, valued, wauled.

 

+3 letters: abluted, acaudal, adulate, adultly, aliunde, alluded, alludes, allured, almudes, alodium, aludels, applaud, audible, audibly, audiles, auldest, avulsed, baulked, belauds, busload, calqued, caudles, caul