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Dual

'''Dual''' is a term used across various fields to denote something consisting of two parts, elements, or aspects. It can refer to paired or twofold meanings in general concepts, such as philosophical dualism, which posits the division of reality into two fundamental principles like mind and body. In mathematics and science, duality describes symmetrical relationships between structures, such as in projective geometry or particle-wave interpretations in physics. The grammatical dual is a linguistic number category for exactly two entities, used in languages like Sanskrit and Slovene. In technology, dual often describes configurations with two components, like dual-core processors. Additionally, "dual" appears in numerous acronyms (e.g., Dual In-line Package in electronics) and titles in media and entertainment, such as films or albums. This article outlines these and other uses of the term.

General Concepts

Paired or Twofold Meanings

In everyday usage, "dual" functions as an adjective denoting something composed of two parts, elements, or aspects, often implying a twofold or paired quality.^[1] This can describe entities with inherent duality, such as a person's dual nature—referring to conflicting traits like kindness and ruthlessness—or a professional's dual role, where one individual fulfills two distinct functions, like serving as both advisor and executor in an organization.^[2] The term emphasizes complementarity or contrast between the two components, distinguishing it from mere duplication.^[3] Specific applications of "dual" appear in various practical contexts. A dual carriageway is a roadway divided into two separate lanes or sets of lanes for traffic traveling in opposite directions, separated by a central barrier or reservation to enhance safety and traffic flow. Dual citizenship, also known as dual nationality, refers to the legal status of an individual recognized as a citizen by two countries simultaneously, granting rights and obligations in both, such as voting or taxation duties.^[4] Similarly, dual pricing involves setting different prices for the same product or service based on factors like customer location, market, or payment method—for instance, charging higher rates in international markets due to economic differences or offering cash discounts to offset credit card fees.^[5] The word "dual" originates from the Latin dualis, meaning "containing two" or "relating to two," derived from duo ("two").^[6] It entered English in the early 17th century, initially applied to paired or twofold items in grammatical and descriptive senses before broadening to general usage.^[1]

Philosophical Dualism

Philosophical dualism is the doctrine that reality is fundamentally divided into two irreducible categories, most prominently the mind and the body, positing that mental phenomena cannot be fully explained by physical processes alone. This view contrasts with monism, which asserts a single underlying substance or principle for all existence. In its classic form, dualism maintains that the mind operates independently of the material world, allowing for phenomena like consciousness and free will that transcend physical causation.^[7] The historical roots of dualism trace back to ancient philosophy, particularly Plato's theory of Forms in works like the Phaedo, where he distinguished the immortal, immaterial soul from the corruptible body, arguing that the soul pre-exists and survives independently through recollection and affinity arguments. This Platonic framework influenced later thinkers, evolving into more systematic forms during the medieval period via figures like Augustine and Aquinas, who integrated it with Christian theology to affirm the soul as an immaterial substance. The doctrine reached its modern articulation with René Descartes in the 17th century, who in his Discourse on the Method (1637) popularized interactive dualism by proposing that mind and body interact causally, with the mind as a non-extended thinking substance and the body as extended matter, a distinction he elaborated in his Meditations on First Philosophy (1641).^[7]^[8]^[9] Key variants of dualism include substance dualism, which holds that mind and body are separate, ontologically distinct substances capable of independent existence, as Descartes argued through the indivisibility of thought versus the divisibility of extension. Property dualism, a more contemporary refinement, rejects separate substances but asserts that mental properties—such as qualia or intentionality—are inherently non-physical and irreducible to physical properties of the brain, even if supervenient upon them, as defended by philosophers like David Chalmers. These variants address challenges like the mind-body interaction problem by varying degrees of separation between mental and physical realms.^[7]^[9] Dualism has faced significant criticisms from monists, notably Baruch Spinoza, who in his Ethics (1677) rejected Cartesian dualism in favor of substance monism, arguing that there is only one infinite substance—God or Nature—with thought and extension as parallel attributes rather than distinct realms, thereby resolving interaction issues through a unified ontology. Modern critiques extend this by highlighting violations of physical laws like conservation of energy and the evolutionary implausibility of non-physical minds, as noted by materialists like Paul Churchland, though dualism persists in philosophy of mind debates over consciousness.^[10]^[7]

Mathematics and Science

Duality Principles

In mathematics, duality refers to a correspondence between two distinct but related structures, such that operations or properties in one structure correspond inversely or in a complementary manner to those in the other.^[11] This principle manifests in various domains, enabling the translation of problems from one framework to its dual, often simplifying analysis or revealing hidden symmetries.^[12] A central concept in linear algebra is the dual space of a vector space V over a field K, denoted V^*, which consists of all linear functionals from V to K.^[11] These functionals act as linear maps \phi: V \to K, and V^* itself forms a vector space under pointwise addition and scalar multiplication.^[12] In optimization, the dual cone of a cone K \subseteq V is defined as K^* = \{\ell \in V^* \mid \ell(v) \geq 0 \ \forall v \in K\}, providing a framework for handling constraints and objectives through complementary slackness.^[13] For a basis \{v_i\} of V, the dual basis \{f_i\} in V^* satisfies f_i(v_j) = \delta_{ij}, where \delta_{ij} is the Kronecker delta (equal to 1 if i = j and 0 otherwise).^[11] This pairing extends to the duality bracket \langle v^*, v \rangle = \sum_i v^*_i v^i, where v^* has contravariant components v^*_i and v has covariant components v^i, encapsulating the bilinear form that defines the correspondence.^[12]

Applications in Physics

One of the most prominent applications of duality in physics is wave-particle duality, a cornerstone of quantum mechanics that reveals how entities like photons and electrons behave as both particles and waves depending on the experimental context. This concept emerged from observations challenging classical distinctions, such as Thomas Young's double-slit experiment in 1801, which demonstrated interference fringes when light passed through two narrow slits, providing strong evidence for light's wave nature. Extending this to matter, Clinton Davisson and Lester Germer conducted experiments in 1927 showing that electrons diffracted off a nickel crystal lattice produced patterns consistent with wave interference, confirming that subatomic particles exhibit wave properties under suitable conditions. These findings underscored the inadequacy of purely classical models and paved the way for quantum theory. The theoretical underpinning for wave-particle duality in matter was Louis de Broglie's 1924 hypothesis, which posited that any particle with momentum p possesses a associated de Broglie wavelength \lambda = \frac{h}{p}, where h is Planck's constant. This relation predicted observable wave effects for particles, later verified experimentally and integrated into the Schrödinger equation for quantum wave functions. In broader physical contexts, duality manifests in phenomena like dual superconductivity, where the vacuum of quantum chromodynamics (QCD) acts as a dual superconductor, confining quarks via a mechanism analogous to the Meissner effect; here, color magnetic monopoles condense to expel chromoelectric fields, forming flux tubes between quarks. Similarly, in string theory, T-duality establishes an equivalence between closed string theories compactified on circles of radius R and $1/R, revealing that physical predictions remain unchanged under this inversion of spatial scales, thus unifying seemingly distinct theoretical descriptions. Recent advancements as of 2025 have leveraged holographic duality through the AdS/CFT correspondence to probe black hole physics, particularly by mapping anti-de Sitter (AdS) black hole geometries to conformal field theories (CFTs) on the boundary. For instance, studies of fractional-order phase transitions in CFTs dual to charged AdS black holes, such as Reissner-Nordström-AdS solutions, have revealed novel critical behaviors and thermodynamic properties, offering insights into black hole evaporation and information paradoxes without direct gravitational computations.^[14] These holographic approaches highlight duality's role in bridging quantum field theories with gravitational phenomena, enabling simulations of extreme conditions inaccessible to classical methods.

Linguistics

Grammatical Dual

The grammatical dual is an inflectional category used in certain languages to denote exactly two entities or referents, distinguishing it from the singular (for one) and the plural (for more than two). This category applies across parts of speech, including nouns, pronouns, adjectives, and verbs, which take specific dual forms to agree in number. In such systems, the dual emphasizes paired or binary groupings, often reflecting conceptual or natural pairs like eyes, hands, or two individuals. The dual number traces its origins to Proto-Indo-European (PIE), the reconstructed ancestor of the Indo-European language family, dated approximately to 4500–2500 BCE, where it functioned as one of three grammatical numbers alongside singular and plural. PIE dual forms were marked by specific endings, such as *-h₁(e) for nominative dual in neuter nouns, and this category was fully integrated into the language's morphology for expressing duality in subjects, objects, and predicates. The dual persisted in early daughter languages, including Vedic Sanskrit and Ancient Greek, where it remained productive for denoting pairs, and left traces in Old English, particularly in personal pronouns like wit (we two) and git (you two).^[15]^[16] A representative example of dual inflection appears in Sanskrit, an ancient Indo-European language where the category was robust. The noun puruṣa (man) in the singular nominative is ekaḥ puruṣaḥ (one man), but in the dual nominative, it becomes dva puruṣau (two men), with the verb also agreeing in dual form, such as gacchataḥ (they two go). This contrasts with plural puruṣāḥ (men) and highlights how dual endings like -au replace singular markers to specify exactly two referents. Similar patterns occur in verbs and pronouns, ensuring syntactic harmony for dual subjects.^[17] Over time, the dual number declined in most Indo-European branches due to phonological mergers and simplification of inflectional paradigms, leading to its merger with the plural in languages like Latin, Modern Greek, and English by the medieval period. Today, it survives as a fully productive category only in two Slavic languages: Slovenian, where it inflects nouns, verbs, and adjectives for pairs (e.g., midve knjige for two books), and Sorbian (both Upper and Lower varieties), which retain dual forms influenced by animacy and gender but show signs of erosion in dialects. This retention in West Slavic languages underscores the dual's resilience in contexts emphasizing binary social or natural pairings.^[18]

Usage in Specific Languages

In Slovenian, the dual number remains fully productive across major parts of speech, including nouns, verbs, and adjectives, distinguishing it from many other Slavic languages where it has been lost or marginalized. This grammatical category obligatorily marks exactly two referents, with forms adjusting for case, gender, and agreement. For instance, the feminine noun hiša (house) inflects as ena hiša in the singular nominative, dve hiši in the dual nominative, and hiše in the plural nominative, demonstrating how numerals like dve (two) trigger dual agreement while higher cardinals select plural.^[19] Verbs and adjectives concord accordingly; a sentence like Dve hiši stojita tukaj (Two houses are standing here) features dual verb forms (stojita) and would adjust for other cases, such as genitive dveh hiš (of two houses). This system persists in standard Slovenian and many dialects, though colloquial usage may vary regionally.^[20] Arabic employs the dual number primarily for nouns and adjectives to denote exactly two entities, using specific suffixes that interact with the language's case system. The nominative dual adds the suffix -ān(i) to the singular stem, while the genitive and accusative cases use -ayni. This applies to both sound (regular) and broken (irregular) plurals, but is most straightforward with sound masculines and feminines. A classic example is the noun ʿayn (eye), which forms ʿaynān in the nominative dual to refer to a pair of eyes, as in ʿindī ʿaynān (I have two eyes). Adjectives agree in number and case, so kitaabān kabiirān (two big books) uses dual endings on both. The dual is obligatory with the numeral ithnāni (two) for masculines or ithnatāni for feminines, but optional otherwise, reflecting its utility for natural pairs like body parts or limbs.^[21]^[22] Fijian, an Austronesian language, distinguishes the dual number mainly in pronouns and possessive constructions, reflecting its inclusive/exclusive distinction and paucal (few) categories for small groups. Independent pronouns mark person, number, and inclusivity; for example, kemou denotes "you two" (second person dual), while keirau refers to "we two" (first person dual exclusive). These forms appear in subject or object positions, such as kemou lako (you two go) or keirau mai (we two come here), with verbs showing no number agreement but classifiers aiding possession. The dual is productive for exactly two referents, contrasting with trial/paucal for three or four and general plural for more, and is evident in dialects like Standard Fijian and Boumaa.^[23] In Kiowa, a Kiowa-Tanoan language spoken by Native American communities, the dual number is encoded through verb prefixes that indicate the number of actors, integrated into a complex agreement system sensitive to semantic roles like agent or patient. The prefix t- specifically marks dual actors, often for second or third person, as in constructions with intransitive verbs involving exactly two participants. For example, a second person dual actor form appears in phrases like t-bele (you two get down/off) or t-he:be (you two come in), where t- signals the dual without separate noun marking. This prefix operates within Kiowa's inverse system, prioritizing higher-ranked arguments (e.g., speech-act participants over third persons), and contrasts with singular or plural prefixes like ɂ- or inverse markers. The dual thus highlights paired actions in narratives and discourse.^[24]

Technology

Hardware Configurations

In hardware configurations, the term "dual" refers to designs incorporating two integrated or linked components to enhance performance, functionality, or versatility in consumer technology devices. These setups leverage parallelism or redundancy in physical hardware to address limitations in single-unit systems, such as processing power or connectivity options.^[25] Dual-core processors represent a foundational advancement in central processing units (CPUs), featuring two independent processing cores on a single chip to enable parallel task execution and improved multitasking efficiency. Intel introduced the first commercial dual-core desktop processor with the Pentium D series in 2005, specifically the Pentium Processor Extreme Edition 840 model, which operated at 3.2 GHz and marked the shift from single-core architectures in mainstream computing. This configuration allowed applications to distribute workloads across cores, reducing latency in operations like video encoding and gaming, though early models like the Pentium D 820 at 2.8 GHz did not support Hyper-Threading for additional virtual cores.^[25]^[26] Dual-SIM configurations in mobile phones integrate support for two subscriber identity module (SIM) cards within the device's hardware, permitting simultaneous use of multiple cellular networks without swapping cards. This feature gained prominence in the 2010s, particularly in emerging markets like India and Indonesia, where it facilitated cost savings for users managing personal and business lines or international travel. As of 2015, around 25% of Android users had dual-SIM phones, with adoption rising significantly in the following years, particularly in emerging markets. By 2024, dual-SIM configurations, including eSIM support, are standard in the majority of global smartphone shipments, exceeding 70% adoption in emerging markets.^[27]^[28]^[29]^[30] Dual-camera systems in smartphones employ two rear-facing lenses and sensors to capture depth information, enabling advanced photographic effects such as bokeh and portrait mode through hardware-based disparity analysis. Apple introduced a dual-camera system in its flagship iPhone 7 Plus in 2016, featuring a 12-megapixel wide-angle (28mm, f/1.8) lens alongside a telephoto (56mm, f/2.8) lens, which supported 2x optical zoom and computational depth mapping for simulated shallow depth-of-field. This hardware duo improved low-light performance and image processing by combining inputs from both sensors, influencing subsequent designs across the industry.^[31]^[32]^[33] Multi-GPU configurations, such as NVIDIA's Scalable Link Interface (SLI) and AMD's CrossFire, connect two or more graphics processing units (GPUs) via high-speed bridges or direct links to distribute rendering tasks for enhanced visual performance in gaming and professional applications. NVIDIA's SLI originated from 3dfx's 1998 Voodoo2 technology but was refined for modern GPUs starting with the GeForce 6 series in 2004, allowing near-linear scaling in frame rates for compatible titles. AMD's CrossFire, launched in 2005 with the Radeon X800 series, similarly enabled multi-board parallelism, though both technologies required specific motherboard slots and power supplies for physical integration.^[34]^[35] Hardware-enabled dual-boot systems rely on physical storage setups, such as multiple drives or partitioned disks, to support booting into different operating systems from firmware like UEFI. This configuration provides the foundational separation needed for stable multi-OS environments on a single machine.^[36]

Software and Systems

In software architectures and operating systems, dual-booting represents a foundational configuration that enables a single computer to select and load one of two distinct operating systems at startup, such as Microsoft Windows and a Linux distribution like Ubuntu, thereby accommodating diverse user requirements without needing separate hardware. This capability emerged prominently in the 1990s through multiboot bootloaders, with GRUB (GNU GRUB) serving as a key enabler since its initial development and release in 1995, allowing seamless detection and menu-based selection of multiple kernels and filesystems.^[37] Such setups rely on partitioning the storage drive and configuring the bootloader to chainload the chosen OS, a process that has become standard for interoperability in mixed environments. Security in software systems often incorporates dual-factor authentication (2FA), a verification method requiring two independent credentials from distinct categories—typically something the user knows (e.g., a password) and something the user has (e.g., a hardware token or authenticator app generating one-time codes)—to mitigate risks like credential theft. Standardization of 2FA protocols accelerated post-2005, exemplified by RFC 4226, which in December 2005 defined the HMAC-based one-time password (HOTP) algorithm for generating event-synchronized codes used in many implementations. This approach has since become integral to access controls in web applications, email services, and enterprise systems, reducing unauthorized access by over 99% in automated bot attacks according to deployment analyses.^[38] Networking protocols leverage dual-stack architectures to support coexistence of IPv4 and IPv6 during the internet's protocol transition, where devices maintain parallel protocol stacks to communicate with both legacy IPv4-only and modern IPv6-only networks without translation overhead. Defined in RFC 4213 by the IETF in October 2005, this mechanism provides complete implementations of both protocols on hosts and routers, enabling incremental adoption while preserving backward compatibility.^[39] Dual-stack has been widely adopted in enterprise and ISP infrastructures, facilitating over 45% global IPv6 deployment as of 2025 by allowing seamless traffic routing across mixed environments.^[40] In object-oriented design within programming languages, dual dispatch (or double dispatch) extends traditional single-dispatch polymorphism by resolving method calls based on the runtime types of two arguments, allowing flexible handling of interactions between disparate class hierarchies. This technique, which avoids rigid type hierarchies through mechanisms like virtual function tables invoked twice, is exemplified in the Visitor pattern for traversing complex object structures without modifying existing classes.^[41] As articulated in the influential "Design Patterns: Elements of Reusable Object-Oriented Software" by Gamma, Helm, Johnson, and Vlissides (1994), double dispatch promotes extensibility in scenarios like graphical user interfaces or compiler design, where operations must adapt to both the subject and the operator types.

Acronyms and Abbreviations

Common Acronym Expansions

In computing, a common acronym is DIP (Dual In-line Package), a type of integrated circuit packaging that features two parallel rows of electrical pins, originally developed by Fairchild Semiconductor engineers in 1964–1965 as a 14-lead ceramic package to accommodate increasing pin counts beyond metal can limits, and which became the dominant standard for through-hole mounting in the 1970s and 1980s due to its compatibility with automated assembly and circuit boards.^[42]^[43] Another computing-related term is the dual-access unit, referring to storage modules in early disc file systems that permitted simultaneous read/write access from multiple controllers, as seen in the SDS Model 9165-24 disc storage unit introduced in the late 1960s for mainframe systems.^[44] The term dual-use commonly describes goods, software, and technologies that have both civilian and military applications, with exports controlled under the Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies, a multilateral regime established in 1996 to promote transparency and responsibility in transfers among participating states.^[45] In processor architecture, Dual Independent Bus (DIB) denotes a design employing separate front-side and back-side buses for improved bandwidth—one connecting the CPU core to L2 cache and the other to main memory—first implemented by Intel in the Pentium Pro microprocessor in 1995 and extended to subsequent models like the Pentium II in the late 1990s.^[46] In education, Dual Enrollment (also known as dual credit) enables high school students to enroll in college-level courses for simultaneous credit toward both high school and postsecondary degrees, a practice that gained widespread adoption in the United States starting in the late 1970s and 1980s amid efforts to enhance college readiness and address curriculum gaps.^[47]^[48]

Specialized Technical Acronyms

In specialized technical fields such as medicine and engineering, the term "dual" frequently appears in acronyms denoting advanced diagnostic, therapeutic, or hybrid systems designed for precise functionality. These acronyms represent innovations that leverage duality in energy sources, modes of operation, or therapeutic agents to enhance efficacy and versatility.^[49] One prominent example in medical imaging is DXA, which stands for Dual-energy X-ray Absorptiometry, a non-invasive technique used to measure bone mineral density and assess osteoporosis risk. The method employs two X-ray beams at different energy levels to differentiate bone from soft tissue, providing accurate areal bone density measurements with low radiation exposure. Its origins trace back to the 1960s with precursor dual-photon absorptiometry techniques, but DXA as a distinct technology was developed in the mid-1980s and received FDA approval for clinical use in 1988, revolutionizing bone health diagnostics.^[50]^[49]^[51] In transportation engineering, DMV refers to Dual-mode Vehicle, a hybrid transport system capable of seamless operation on both roadways and railway tracks, addressing connectivity challenges in rural or integrated networks. These vehicles feature retractable rail wheels and specialized suspension to switch modes rapidly, typically within 15-30 seconds, without passenger disembarkation. Prototyped in Japan during the early 2000s through a Japan Railways Hokkaido project initiated in 2000, DMV systems have been implemented on routes like the Asa Coast Railway, carrying up to 21 passengers at speeds of 60 km/h on rails and 100 km/h on roads, promoting efficient public transit in geographically diverse areas.^[52]^[53] In cardiology, DAPT denotes Dual Antiplatelet Therapy, a regimen combining aspirin with a P2Y12 inhibitor (such as clopidogrel, prasugrel, or ticagrelor) to prevent thrombotic events in patients with acute coronary syndromes or following percutaneous coronary intervention. This approach reduces stent thrombosis and ischemic risks by inhibiting platelet aggregation through complementary mechanisms, with typical durations of 6-12 months post-procedure. The therapy gained prominence in the early 2000s following pivotal trials like CURE (2001), leading to ACC/AHA guideline endorsements starting with the 2004 update and subsequent revisions, including the 2025 guideline recommending 12 months of DAPT as the default for patients with acute coronary syndromes, with ticagrelor or prasugrel preferred over clopidogrel, and personalized durations based on bleeding and ischemic risks.^[54]^[55]^[56]^[57]

Media and Entertainment

Films and Television

In film and television, "Dual" has appeared as a title or key element in several notable productions exploring themes of duplication, identity, and conflict. The 2022 American satirical science fiction thriller Dual, written and directed by Riley Stearns, stars Karen Gillan in dual roles as Sarah and her clone. The plot centers on Sarah, who undergoes a cloning procedure after a terminal diagnosis but unexpectedly recovers, forcing her to prepare for a government-mandated duel to the death against her clone to resolve the duplication. The film premiered at the Sundance Film Festival in January 2022 and was released theatrically on April 15, 2022, by RLJE Films.^[58]^[59] Dual! Parallel Trouble Adventure is a 1999 Japanese anime television series produced by AIC and created by Masaki Kajishima, known for his work on the Tenchi Muyo! franchise. Spanning 24 episodes aired from April 8 to September 23, 1999, on TV Tokyo, the series follows high school student Kazuki Yotsuga, who uncovers a buried giant robot called the Duel Guardian and becomes entangled in a war between two parallel dimensions: the advanced "That World" and the more primitive "This World." The narrative blends mecha action, comedy, and harem elements, with Kazuki navigating alliances and romantic interests across the worlds.^[60] In the Star Trek: The Next Generation episode "Second Chances" (Season 6, Episode 24), which aired on May 24, 1993, a transporter malfunction during a mission on Nervala IV eight years earlier creates an exact duplicate of Commander William Riker, who has survived in isolation while the original continued his career. The Enterprise crew encounters the duplicate, Thomas Riker, leading to explorations of identity, choice, and interpersonal tensions, particularly with Counselor Deanna Troi, with whom the original Riker had a past relationship. Jonathan Frakes portrays both Rikers, highlighting their subtle differences in experience and demeanor.^[61]

Music and Literature

In music, "Dual" serves as the title for several notable albums and tracks across genres. The South Korean alternative rock band The Rose released their second full-length album, Dual, on September 22, 2023, featuring 11 tracks that blend indie rock with emotional ballads, including hits like "You're Beautiful" and "Back to Me," which explore themes of self-discovery and relationships.^[62] The album marked a significant evolution for the group, emphasizing dual vocal dynamics between members Woosung and Dojoon, and achieved over 72 million streams for its lead single on YouTube Music.^[63] Another prominent example is the 2022 album Dual by the collaborative project VA x BY, consisting of Dutch sound artist Albert van Abbe and raster-noton founder Olaf Bender (aka Byetone). This experimental electronic release, issued on the raster label, features abstract soundscapes derived from modular synthesis and field recordings, highlighting the duo's interplay between noise and minimalism across six tracks.^[64] The work exemplifies raster-noton's commitment to innovative sonic architecture, with van Abbe's contributions adding organic textures to Bender's precise digital frameworks. In the realm of instrumental and jazz fusion, Dual Identity (2010) by saxophonists Rudresh Mahanthappa and Steve Lehman stands out as a seminal recording. Produced on the Clean Feed label, the album comprises 11 original compositions that fuse alto saxophone lines with complex rhythms and electronics, drawing from bebop, South Indian carnatic music, and hip-hop influences; tracks like "The General" showcase their synchronized improvisation, earning acclaim for bridging contemporary jazz traditions.^[65] New Zealand electronic duo DUAL, formed in Auckland in the 2010s, has gained recognition for their psyche-dance sound, releasing a self-titled EP in 2017 on Banished Music. The EP, by Maurice Miller and Jamie Pyne, features tracks like "Two Hands Up" that incorporate pulsating synths and driving beats, reflecting the pair's collaborative live performances and visual aesthetics.^[66] Turning to literature, works titled "Dual" or variations thereof often explore themes of duality, identity, and multiplicity. Alix Ohlin's novel Dual Citizens (2019), published by House of Anansi Press, follows the complex bond between sisters Lark and Robin MacHale, navigating art, motherhood, and ambition across Montreal and New York; the narrative's dual perspectives illuminate intergenerational tensions and personal reinvention, earning a nomination for the Scotiabank Giller Prize.^[67] Matthew Minicucci's poetry collection Dual (2023), released by Acre Books, interrogates masculinity, violence, and cultural aggression through fragmented forms inspired by historical texts and contemporary events. Poems like those riffing on ancient epics juxtapose brutality with vulnerability, using dual voices to critique power structures; the book has been praised for its innovative structure and emotional depth in literary reviews.^[68] Earlier, J.C. Chillington's novel Dual Lives (1893), reprinted by the British Library, depicts the intertwined existences of characters grappling with moral and social dualities in late 19th-century Britain, blending romance with psychological introspection.^[69]

References

[1]
Duality Principle -- from Wolfram MathWorld
All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be ...
[2]
Duality - Encyclopedia of Mathematics
Feb 8, 2020 · Duality in the theory of topological vector spaces (by N.K. Nikol'skii). A dual pairing is a triplet {F, G ...
[3]
Dual basis - Encyclopedia of Mathematics
Feb 1, 2022 · Dual basis. From ... Occasionally the terminology conjugate module (conjugate space) is used instead of dual module (dual space).
[4]
Duality Theorem -- from Wolfram MathWorld
Dual pairs of linear programs are in "strong duality" if both are possible. The theorem was first conceived by John von Neumann.
[5]
Poincaré Duality -- from Wolfram MathWorld
Poincaré Duality. The Betti numbers of a compact orientable n -manifold satisfy the relation. b_i=b_(n-i). See also. Betti Number, Homology Intersection. Cite ...
[6]
https://www.etymonline.com/word/dual
[7]
DUAL Definition & Meaning - Dictionary.com
adjective composed or consisting of two people, items, parts, etc., together; twofold; double: dual ownership; dual controls on a plane.
[8]
DUAL | definition in the Cambridge English Dictionary
DUAL meaning: 1. with two parts, or combining two things: 2. two sets of controls in a vehicle, one for the…. Learn more.
[9]
Dual Nationality - Travel.gov - U.S. Department of State
The concept of dual nationality means that a person is a national of two countries at the same time. Each country has its own nationality laws based on its own ...
[10]
Dual Pricing: Definition, Purposes, Legality - Investopedia
Dual pricing is the practice of setting different prices in different markets for the same product or service. It happens more often than you might think.
[11]
Dual - Etymology, Origin & Meaning
Originating c.1600 from Latin dualis, meaning "relating to two," dual refers to grammar forms or anything composed of two parts, expressing the number two.
[12]
Dualism and Mind | Internet Encyclopedia of Philosophy
Dualists in the philosophy of mind emphasize the radical difference between mind and matter. They all deny that the mind is the same as the brain.Dualism · Platonic Dualism in the Phaedo · Descartes' Dualism · Property Dualism
[13]
The Project Gutenberg eBook of A Discourse on Method, by René ...
May 13, 2022 · Discourse on the method of rightly conducting the reason, and seeking truth in the sciences by René Descartes.Missing: dualism | Show results with:dualism
[14]
René Descartes: The Mind-Body Distinction
One of the deepest and most lasting legacies of Descartes' philosophy is his thesis that mind and body are really distinct—a thesis now called “mind-body ...
[15]
Descartes' dualism and its relation to Spinoza's metaphysics ...
Spinoza was one of the earliest and harshest critics of Descartes' dualism. As is so often the case, sharp disagreements rest on a very large base of shared ...
[16]
[PDF] Chapter 8 The Dual Space, Duality - UPenn CIS
Definition 8.1. Given a vector space E, the vector space Hom(E,K) of linear maps from E to K is called the dual space (or dual) of E. The space Hom(E,K) is.
[17]
[PDF] The Dual of a Vector Space - OSU Math
Sep 12, 2016 · To emphasize the duality between the two vector spaces, one takes advan- tage of Dirac's bra-ket notation, which he originally introduced into ...
[18]
[PDF] Cones and duality
Then −TC(v) and NC(v) are dual cones. Definition. The dual cone of a convex cone K ⊆ V is K∗ = {` ∈ V ∗ : `(v) ≥ 0 for all v ∈ K}. One can check that this is a ...
[19]
Dual origin.pdf - Academia.edu
The dual number in the Indo#European languages. The most ancient Indo#European languages (including Ancient Greek and Vedic) had three number categories ...
[20]
Old English Language Grammar by Cyril Babaev
Pronouns were the only part of speech in Old English which preserved the dual number in declension, but only this makes them more archaic than the rest parts of ...
[21]
Comparative analysis of Grammatical Number System in Russian ...
Jul 24, 2023 · This study provides a detailed comparison of the Grammatical Number systems in Russian and Sanskrit, two highly inflected languages from ...
[22]
The death of the dual, or how to count sheep in Slovenian - MORPH
Nov 14, 2017 · Proto-Indo-European made a distinction between dual and plural number in its nouns, adjectives, pronouns, and verbs, but most of the modern ...
[23]
Characteristics of early vocabulary and grammar development in ...
Aug 6, 2012 · ... dual number and continues to use it extensively (e.g. ena hiša 'one house', dve hiši 'two houses', tri hiše 'three houses'). In contrast to ...
[24]
(PDF) Use of dual in standard Slovene, colloquial ... - Academia.edu
In the colloquial language of Maribor, the dual is used for masculine and feminine nouns: dva (visoka) brata “two (tall) brothers” and dve (debeli) kravi “two ( ...
[25]
Arabic Case Marking with the Dual - Transparent Language Blog
Oct 31, 2009 · When the noun is used as an object, the case is accusative and the ending (ـَيْن) is used, e.g.. قرأت كتابين مفيدين. “I read (2) useful books.”.
[26]
Ahlan Grammar: Singular, Dual, and Plural in the Arabic Language
For the feminine dual, it indicates two females, For example: حقيبتان (two bags) in the nominative, and حقيبتَيْن (two bags) in the accusative and genitive.<|separator|>
[27]
[PDF] Say Bula! - The University of the South Pacific
We (two) are. O keirau. Kemudrau kei cei? | You and who else? (literally, you two with who?) and as the object of a verb: O raici keitou? | Do you see us ...
[28]
Dual Core Era Begins, PC Makers Start Selling Intel-Based PCs
Apr 18, 2005 · Intel's first dual-core processor-based platform includes the Intel® Pentium® Processor Extreme Edition 840 running at 3.2 GHz and the Intel® ...
[29]
Intel Pentium D 820 2.8 GHz Dual Core Review - PC Perspective
Jun 16, 2005 · The Pentium D processor line is based on the same core as the Pentium Extreme Edition, the Smithfield core.
[30]
One quarter of all Android users have dual-SIM phones - Quartz
25% of all Android users have phones with more than one SIM card slot. The numbers skew heavily to poor countries.<|control11|><|separator|>
[31]
Dual SIM smartphone usage - DeviceAtlas
Apr 9, 2019 · Dual SIM phones are most used in India and Indonesia. To see where dual SIM phones are most popular, we dived into DeviceAtlas statistics for Q4 ...
[32]
The rise of dual-SIM smartphones and eSIMs spell ... - Omdia - Informa
Dec 15, 2022 · Five years ago, in September 2017, 75% of global smartphones had single slots while 25% had dual slots. In September 2022, however, only 15% of ...
[33]
Portrait mode now available on iPhone 7 Plus with iOS 10.1 - Apple
Oct 24, 2016 · In addition to Portrait mode, the dual-camera system on iPhone 7 Plus offers optical zoom at two times and up to 10 times digital zoom for ...
[34]
The iPhone 7 Plus has two cameras that work as one - The Verge
Sep 7, 2016 · Apple is adding an extra layer of differentiation to its 2016 iPhone 7 Plus model with the introduction of a brand new dual-camera system.
[35]
Apple iPhone 7 Plus arrives with dual cameras - GSMArena.com news
Sep 7, 2016 · The new cameras on the iPhone 7 Plus are one "wide" angle 28mm and a "telephoto" 56mm unit. Both have 12MP sensors and the camera can combine the two ...
[36]
A Quick History of Multi-GPU Video Cards | PC Gamer
Jun 2, 2014 · It all started with the 3Dfx Voodoo2 and has continued on with modern cards like the Titan Z and R9 295X2.
[37]
From SLI to NVLink: The Evolution of Gaming and Multi-GPU ...
Sep 11, 2023 · While NVIDIA's SLI set the pace for multi-GPU configurations, it wasn't without competition. AMD's CrossFire was a direct rival, offering ...
[38]
https://www.paloaltonetworks.com/cyberpedia/what-is-the-evolution-of-multi-factor-authentication
[39]
GNU GRUB - GNU Project - Free Software Foundation (FSF)
GNU GRUB is a multiboot boot loader, the first software that runs when a computer starts, loading the OS kernel.Obtaining GRUB · GRUB FAQ · GRUB Legacy · GRUB Mailing Lists
[40]
What is the Evolution of Multifactor Authentication - Palo Alto Networks
Brief History of Multi-Factor Authentication · Password-Based Authentication (1970s-1980s): · Two-Factor Authentication (2FA) Emergence (1990s): · Software-Based ...
[41]
RFC 4213 - Basic Transition Mechanisms for IPv6 Hosts and Routers
RFC 4213 specifies IPv4 compatibility mechanisms for IPv6, including dual stack and configured tunneling, to ease the transition to IPv6.
[42]
Visitor and Double Dispatch - Refactoring.Guru
Even though the Visitor pattern is built on the double dispatch principle, that's not its primary purpose. Visitor lets you add “external” operations to a whole ...
[43]
Package is the First to Accommodate System Design Considerations
In 1965 Don Forbes, Rex Rice, and Bryant ("Buck") Rogers at Fairchild devised a 14-lead ceramic Dual-in-Line Package (DIP) with two rows of pins 100 mils apart ...Missing: Inline | Show results with:Inline
[44]
[PDF] Microcircuit Packaging
Dual-In-Line Package (DIP) created to provide more pins than a metal can while allowing through-hole assembly in conventional circuit boards. The DIP has leads ...Missing: 1970s | Show results with:1970s
[45]
[PDF] SDSMODEL 9164/9165 DISC FllE.ff1ASS lV1 Eril1 ORY SYSTEM
Two types of disc file storage modules are available: the. Model 9165-14 is a single-access unit with 32 discs; the. Model 9165-24 is a dual-access unit, also ...
[46]
About us - The Wassenaar Arrangement
Procedures for the Exchange of Information on Dual-Use Goods and Technology ... The Wassenaar Arrangement became operational in 1996, after the adoption of the ...
[47]
Intel's CEO Reveals New Bus Architecture To Be Implemented In ...
The Dual Independent Bus architecture was first implemented in the Pentium Pro processor and will continue with the Pentium II processor. The bus architecture ...Missing: 1990s | Show results with:1990s
[48]
[PDF] Dual Enrollment: Measuring Factors for Rural High School Student ...
However, due to an increased demand in the 1980s, many states began developing policies regarding dual enrollment (Andrews,. 2000; Girardi & Stein, 2001) ...Missing: history | Show results with:history
[49]
[PDF] Relationship Between Participation in a Dual Enrollment Program ...
Dec 20, 2021 · Dual enrollment, also known as concurrent enrollment, dual credit, or early college, began in the 1980s and grew in reputation throughout the ...
[50]
Dual-Energy X-Ray Absorptiometry - StatPearls - NCBI Bookshelf
Dual-energy x-ray absorptiometry (DEXA) has sustained a niche for measuring bone mineral density (BMD) since its approval by the Food and Drug Administration.
[51]
Evolution of the DXA scan - Irish Health Pro
WIth its origins in the 1960s, dual-energy x-ray absorptiometry has become central to the diagnosis, assessment and treatment of osteoporosis. Eimear Vize.
[52]
Bone Mineral Density: Clinical Relevance and Quantitative ...
Apr 1, 2021 · BMD measurement by dual-energy x-ray absorptiometry (DXA), since its approval by the U.S. Food and Drug Administration (FDA) in 1988, has ...
[53]
Japanese Dualmode Vehicle
Apr 29, 2007 · The prototype was developed from a JR Hokkaido project that was started in 2000. The 28-seat minibus has four highway wheels for roads and four ...
[54]
(PDF) Dual Mode Vehicle (DMV) Overview - ResearchGate
Aug 7, 2025 · The DMV is a microbus modiﬁed to. run in either direction on both road-. ways and railways—a dream vehicle. our predecessors once tried to de-.
[55]
2016 ACC/AHA Guideline Focused Update on Duration of Dual ...
Most contemporary studies of DAPT have compared either shorter (3 to 6 months) or longer (18 to 48 months) duration of therapy with 12 months of DAPT, which is ...
[56]
Demystifying the Contemporary Role of 12-Month Dual Antiplatelet ...
Jul 22, 2024 · In the DAPT (Dual Antiplatelet Therapy) trial, prolonged DAPT was superior to 12-month DAPT for the prevention of ischemic events.
[57]
A history of the development of dual antiplatelet therapy for coronary ...
In this review article, we provide a historical perspective on the development of DAPT, from the first major trials of DAPT all the way through to the use of ...
[58]
Dual (2022) - IMDb
Rating 5.8/10 (14,432) Dual: Directed by Riley Stearns. With Karen Gillan, Aaron Paul, Beulah Koale, Theo James. A woman opts for a cloning procedure after she receives a terminal ...Dual · Plot · Parents guide · Official Trailer
[59]
Dual movie review & film summary (2022) | Roger Ebert
Rating 2/4 · Review by Sheila O'MalleyApr 15, 2022 · Even with the excellent central performance by Karen Gillan, playing a “dual” role—herself and her own copy—”Dual” makes for a strangely tepid ...
[60]
Dual! Parallel Trouble Adventure (TV) - Anime News Network
Original creator: Masaki Kajishima. Original Character Design: Masaki Kajishima. Character Design: Atsushi Okuda. Art Director: Hiroshi Katō · Masaru Satō.
[61]
"Star Trek: The Next Generation" Second Chances (TV Episode 1993)
Rating 7.5/10 (3,255) Of course this episode belongs to Jonathan Frakes who delivers a great dual performance. We never do get to hear him on the trombone though. Related ...
[62]
DUAL - Album by The Rose - Apple Music
Listen to DUAL by The Rose on Apple Music. 2023. 11 Songs. Duration: 32 minutes ... The South Korean band melds hard-edged indie rock with soft romance.
[63]
DUAL - Album by The Rose - YouTube Music
DUAL ; 1. Dawn · 517K plays ; 2. You're Beautiful · 19M plays ; 3. Nauseous · 1.3M plays ; 4. Back To Me · 72M plays ; 5. Lifeline · 2.3M plays ...
[64]
Dual | VA x BY - raster - artistic platform - Bandcamp
Free deliveryDutch sound artist Albert van Abbe now joins the raster family, with an unexpected collaboration with founder Olaf Bender aka Byetone titled DUAL. Having spent ...
[65]
Dual Identity | Rudresh Mahanthappa & Steve Lehman - Clean Feed
Free deliveryDual Identity by Rudresh Mahanthappa & Steve Lehman, released 01 January 2010 1. The General 2. Foster Brothers 3. SMS 4. Post-Modern Pharaohs 5.
[66]
Dual: Self-titled EP - NZ Musician
Auckland's psyche-dance duo Dual make a crashing electric debut with this self-titled EP. Currently signed to local indie Banished Music they recorded it in ...
[67]
https://houseofanansi.com/products/dual-citizens
[68]
Dual | Acre Books
“Many ideas are at play in Matthew Minicucci's Dual, a poetry collection that examines masculinity, aggression, and violence while incorporating the semi- ...Missing: titled | Show results with:titled
[69]
Dual Lives. [A Novel.]: Chillington, J C - Books - Amazon.com
Title: Dual Lives. [A novel.]Publisher: British Library, Historical Print EditionsThe British Library is the national library of the United Kingdom.