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IR

The real numbers, denoted \mathbb{R} or sometimes \mathbb{IR}, form the complete ordered field consisting of all rational numbers—fractions of integers—and irrational numbers that cannot be expressed as such ratios, such as \sqrt{2} and \pi.^[1]^[2] This structure satisfies the field axioms for addition and multiplication, including commutativity, associativity, distributivity, and the existence of identities and inverses (except zero for multiplication), alongside a total order compatible with the operations.^[3] The defining completeness property ensures that every nonempty subset bounded above has a least upper bound, enabling the rigorous treatment of limits, convergence, and continuity essential to mathematical analysis.^[1] The real numbers extend the rationals to fill gaps, such as those required for solving polynomial equations like x^2 - 2 = 0, and possess the Archimedean property that between any two positives there exists a rational.^[3] Rationals are dense in the reals, meaning every interval contains rationals, and vice versa for irrationals, underpinning the continuum's uncountable cardinality distinct from countable sets like integers.^[1] Historically, their axiomatic foundation was formalized by mathematicians like Dedekind and Peano, resolving foundational issues in calculus developed intuitively by Newton and Leibniz, though constructivist critiques question non-computable reals' "existence" without algorithmic definition.^[4] In applications, \mathbb{R} models continuous phenomena in physics and engineering, where discrete approximations suffice practically but the full continuum idealizes infinite precision.^[3]

Science and technology

Infrared radiation

Infrared radiation consists of electromagnetic waves with wavelengths ranging from approximately 780 nanometers to 1 millimeter, corresponding to frequencies between 300 gigahertz and 400 terahertz, positioning it between visible light and microwaves in the electromagnetic spectrum.^[5] This radiation is invisible to the human eye but is detectable as heat, as all objects with temperatures above absolute zero emit infrared radiation according to blackbody principles, with peak emission wavelength inversely proportional to temperature via Wien's displacement law.^[6] The term "infrared" derives from its position beyond the red end of the visible spectrum. British astronomer William Herschel discovered infrared radiation on March 11, 1800, while investigating the heating effects of sunlight dispersed through a prism; he observed that a thermometer placed beyond the red band registered the highest temperature, indicating the presence of unseen rays responsible for heat.^[7] Herschel's experiment demonstrated that these rays propagate in straight lines, reflect off surfaces, and can be refracted, mirroring optical properties of visible light while carrying thermal energy.^[8] Infrared radiation exhibits wave-particle duality, exerting radiation pressure and interacting with matter through absorption, emission, reflection, and transmission; it penetrates dense gases and dust with less scattering than visible light due to longer wavelengths, enabling applications in astronomy.^[6] Unlike ionizing radiation, non-ionizing infrared primarily induces thermal effects via molecular vibration excitation, though low-intensity near-infrared can trigger non-thermal photobiomodulation in biological tissues, enhancing cellular metabolism without significant heating.^[9] The infrared spectrum is subdivided into near-infrared (NIR, 0.78–3 μm), mid-infrared (MIR, 3–50 μm), and far-infrared (FIR, 50 μm–1 mm), with alternative classifications such as IR-A (780 nm–1.4 μm), IR-B (1.4–3 μm), and IR-C (3 μm–1 mm) used in contexts like optical safety standards.^[10] ^[6] These divisions reflect differing interactions: NIR overlaps with solar radiation and penetrates tissues shallowly, MIR enables molecular spectroscopy by exciting vibrational modes, and FIR dominates thermal emission from room-temperature objects.^[9] Natural sources include solar radiation, cosmic backgrounds, and terrestrial thermal emissions, while artificial sources encompass incandescent lamps, LEDs, lasers, and globar heaters; detection relies on bolometers, photodiodes, or thermal imagers converting infrared to electrical signals or visible images.^[5] ^[6] Applications span thermal imaging for non-contact thermography, night-vision systems exploiting human body emissions at around 10 μm, and remote controls using modulated NIR pulses.^[6] In spectroscopy, MIR absorption identifies chemical bonds, aiding material analysis; medically, controlled FIR exposure promotes wound healing and reduces inflammation via nitric oxide release, while NIR lasers enable precise tissue ablation in surgery.^[9] Industrial uses include drying processes and quality control via hyperspectral imaging, with military applications in missile guidance and surveillance.^[11]

Interventional radiology

Interventional radiology is a subspecialty of radiology focused on minimally invasive procedures guided by medical imaging to diagnose and treat a wide range of conditions, often serving as alternatives to open surgery. These procedures utilize real-time imaging modalities such as fluoroscopy, ultrasound, computed tomography (CT), or magnetic resonance imaging (MRI) to access targeted areas within the body via small incisions or needle punctures, enabling precise interventions on blood vessels, organs, and tissues.^[12]^[13] Interventional radiologists, who are board-certified radiologists with additional specialized training, interpret diagnostic images, perform the procedures, and manage post-procedure care, distinguishing the field from diagnostic radiology by its therapeutic emphasis.^[14] The origins of interventional radiology trace to advancements in vascular access techniques. In 1953, Swedish radiologist Sven-Ivar Seldinger introduced a percutaneous catheter insertion method using a guidewire, which revolutionized safe vascular entry without surgical cutdown and laid the foundation for catheter-based therapies.^[13] American radiologist Charles Dotter advanced the field in 1964 by performing the first percutaneous transluminal angioplasty on a patient's femoral artery, treating peripheral arterial disease by dilating a narrowed vessel with a catheter, marking the shift from diagnostic angiography to therapeutic intervention.^[15] The term "interventional radiology" was coined in the early 1960s by Dotter and colleagues, with formal recognition growing through milestones like the 1972 establishment of the Society of Cardiovascular Radiology (predecessor to the Society of Interventional Radiology, or SIR, founded in 1973) and the 1974 development of selective arterial thrombolysis for occlusions.^[16]^[17] By the 1980s, innovations such as catheter-delivered stents and embolization techniques expanded applications to oncology and beyond, with the field achieving independent medical specialty status in the United States in 2012.^[15] Common procedures in interventional radiology span vascular, non-vascular, and oncologic interventions. Vascular treatments include angioplasty and stenting to restore blood flow in narrowed arteries, embolization to block abnormal vessels (e.g., in uterine fibroids or gastrointestinal bleeding), and thrombolysis to dissolve clots in conditions like deep vein thrombosis or stroke.^[18]^[19] Non-vascular procedures encompass image-guided biopsies for tissue sampling, abscess or fluid drainage via percutaneous catheters, and ablation techniques such as radiofrequency or microwave ablation to destroy tumors by heating.^[18] Oncologic applications feature transarterial chemoembolization (TACE) for liver cancers, delivering chemotherapy directly to tumors while embolizing feeding vessels, and radioembolization using yttrium-90 microspheres.^[13] Other procedures include central venous access port placement for long-term chemotherapy and vertebral augmentation (e.g., kyphoplasty) for spinal compression fractures.^[19] These interventions offer distinct advantages over traditional surgery, including reduced tissue trauma due to small entry points (often 1-3 mm), lower rates of infection and bleeding, and minimal general anesthesia requirements, allowing many to be performed under local anesthesia or moderate sedation.^[12] Patients typically experience shorter hospital stays—frequently outpatient—and faster recovery, with studies showing complication rates under 5% for many procedures compared to 10-20% for equivalent surgeries.^[13] For instance, angioplasty for peripheral artery disease achieves patency rates of 70-90% at one year, often avoiding amputation.^[15] However, suitability depends on patient anatomy and disease complexity, with limitations in cases requiring direct visualization or extensive reconstruction.^[18] Training for interventional radiologists involves completion of a radiology residency followed by a 1-2 year fellowship accredited by the Accreditation Council for Graduate Medical Education (ACGME), emphasizing procedural skills, imaging interpretation, and patient management.^[20] Certification is provided by the American Board of Radiology, with over 8,000 members in the SIR, which establishes clinical practice guidelines and advocates for the specialty.^[21] Ongoing advancements, including robotic assistance and AI-enhanced imaging, continue to refine precision and expand indications, such as in neurointerventional treatments for aneurysms.^[13]

Information retrieval

Information retrieval (IR) is the activity of obtaining material, typically unstructured or semi-structured data such as documents, images, or multimedia, from a collection of resources that is relevant to an information need, usually specified by a query.^[22] This process involves indexing, searching, and ranking to return pertinent results efficiently, often using algorithms that match query terms to document content or metadata.^[23] IR systems power applications like web search engines, enterprise knowledge bases, and digital libraries, where the goal is to maximize retrieval of relevant items while minimizing irrelevant ones.^[24] The field emerged in the mid-20th century amid growing document collections in libraries and government archives, with early efforts focusing on automated text processing. In the 1960s, Gerard Salton at Cornell University developed the SMART (Salton's Magical Automatic Retriever of Text) system, a pioneering experimental platform for testing retrieval algorithms on corpora like the Cranfield collection, emphasizing automatic indexing and vector-based representations.^[25] SMART influenced subsequent advancements, including the vector space model, and demonstrated improvements over manual methods through evaluations on relevance metrics.^[26] Core IR techniques include document representation via term frequency-inverse document frequency (TF-IDF) weighting, which prioritizes terms rare across a corpus but frequent in specific documents. The Boolean model treats queries as logical expressions using operators like AND, OR, and NOT for exact matching, retrieving sets of documents that satisfy the conditions without inherent ranking.^[27] In contrast, the vector space model represents documents and queries as vectors in a high-dimensional space, computing similarity via cosine distance to rank results by proximity, enabling partial matches and graded relevance.^[28] Probabilistic models like BM25 refine ranking by estimating relevance probability, incorporating term saturation (diminishing returns for repeated terms) and collection statistics to outperform simpler TF-IDF in benchmarks such as TREC evaluations.^[29] Evaluation relies on metrics like precision (fraction of retrieved items that are relevant), recall (fraction of relevant items retrieved), and their harmonic mean F1-score, often assessed via test collections with ground-truth relevance judgments.^[25] Modern IR faces challenges in handling semantic ambiguity, where keyword matches fail to capture query intent, as in synonyms or context-dependent meanings; semantic search addresses this by leveraging embeddings from models like BERT to align latent meanings.^[30] Scalability with big data requires distributed indexing (e.g., inverted indexes), while biases in training data and computational demands pose ongoing issues, particularly in real-time enterprise or multilingual settings.^[31] Advances in neural IR integrate deep learning for end-to-end ranking, improving over traditional models on tasks like web search but demanding vast labeled data.^[32]

Other uses in science and technology

In computer architecture, IR designates the instruction register, a component of the central processing unit (CPU) control unit that temporarily holds the instruction fetched from memory for decoding and execution.^[33] This register captures the opcode and operand bits of the current instruction, enabling the processor to interpret and dispatch operations, as seen in von Neumann architectures where the instruction register interfaces with the program counter and decoder circuitry.^[34] In signal processing and systems engineering, IR stands for impulse response, which characterizes the output of a linear time-invariant (LTI) system to a brief input impulse, such as a Dirac delta function, revealing the system's dynamic behavior over time.^[35] The impulse response function, often denoted h(t) in continuous time or h in discrete time, underpins convolution operations for predicting system outputs to arbitrary inputs and is fundamental in applications like filter design, audio processing, and control theory.^[36] For instance, measuring an audio system's IR allows reconstruction of its frequency response via Fourier transform, aiding in equalization and simulation.^[35] In environmental toxicology and ecology, IR refers to ingestion rate, quantifying the amount of a substance or food consumed per unit time by an organism, often used in bioaccumulation models and risk assessments.^[37] This metric, typically expressed in mass per time (e.g., mg/kg/day), informs exposure pathways in food webs, as in studies of pollutant uptake in aquatic species where ingestion rate correlates with body size and contaminant concentration.^[37]

International relations

International relations (IR) is an academic discipline that examines the interactions among states and other actors in the global system, including non-state entities such as international organizations, multinational corporations, and transnational networks.^[38] It analyzes phenomena like diplomacy, conflict, trade, and cooperation, drawing on insights from political science, economics, history, and sociology to explain patterns of behavior in an environment characterized by the absence of a central authority.^[39] The field emphasizes empirical observation of state actions driven by material interests, such as security and economic gain, rather than assuming universal moral progress or inevitable harmony among nations.^[40] The discipline formalized in the aftermath of World War I, particularly in the United States and United Kingdom, as scholars sought to understand the causes of large-scale conflict and devise mechanisms to prevent recurrence.^[41] Institutions like the Woodrow Wilson School at Princeton University, established in 1930, reflected this impetus, training policymakers in foreign affairs amid the League of Nations' formation.^[40] Early IR focused on idealism, promoting collective security through international law and organizations, but the failure to avert World War II shifted emphasis toward more skeptical views of human nature and state motivations. By the mid-20th century, the field expanded with the Cold War, incorporating quantitative methods and game theory to model strategic interactions.^[40] Theoretical paradigms in IR provide frameworks for interpreting these dynamics, with realism positing that states, as primary actors in an anarchic system, prioritize survival through power maximization and balance-of-power strategies.^[38] Realist scholars like Hans Morgenthau argued in Politics Among Nations (1948) that foreign policy is rooted in national interest defined in terms of power, a view supported by historical patterns of alliance shifts and arms races, such as those preceding both world wars.^[42] In contrast, liberalism contends that interdependence via trade, democratic governance, and institutions fosters mutual gains and reduces conflict incentives; for instance, the post-1945 economic integration in Europe correlated with prolonged peace among major powers, though critics note this overlooks power asymmetries that undermine cooperation.^[38] Other approaches, like constructivism, highlight how shared ideas and identities shape interests, but empirical tests often favor realism's predictions in crises, such as the 2022 Russian invasion of Ukraine, where security dilemmas prevailed over institutional restraints.^[38] Central key concepts include anarchy, the condition where no overarching authority enforces rules, compelling states to rely on self-help for security.^[43] This interacts with sovereignty, the principle granting states exclusive authority over internal affairs and non-interference from others, codified in the 1648 Peace of Westphalia and upheld in treaties like the 1933 Montevideo Convention on statehood.^[44] Power, encompassing military, economic, and diplomatic capabilities, determines influence; for example, U.S. hegemony post-1945 enabled the Bretton Woods system, but relative decline—evidenced by China's GDP surpassing 60% of U.S. levels by 2023—alters global equilibria.^[43] Academic discourse on these concepts reveals tensions: while mainstream IR scholarship, often institutionally aligned with liberal paradigms, emphasizes norms and soft power, realist analyses better account for persistent great-power competition, as seen in data from the Correlates of War project documenting over 200 interstate conflicts since 1816.^[42] IR's analytical value lies in dissecting causal drivers of outcomes, such as how nuclear deterrence maintained bipolar stability from 1945 to 1991 despite ideological clashes.^[40] However, the field's Western-centric origins and prevalence of idealist assumptions in policy-oriented research have drawn critique for underestimating cultural divergences and non-state threats like terrorism, which spiked post-2001 with over 200,000 incidents globally per the Global Terrorism Database.^[39] Rigorous application requires cross-verifying theoretical claims against historical datasets, prioritizing observable state behaviors over normative prescriptions.^[41]

Industrial relations

Industrial relations encompasses the study of employment relationships, focusing on interactions among employers, employees, their representatives, and regulatory bodies to manage work-related conflicts and cooperation. It examines processes such as collective bargaining, grievance handling, and labor dispute resolution, drawing from disciplines including economics, sociology, and law.^[45]^[46] The primary actors include employees, who seek fair wages and conditions often through unions; employers, who prioritize operational efficiency and profitability; and governments, which enact laws to balance power dynamics and prevent market failures. Unions represent workers in negotiations, while employers' associations counterbalance through coordinated strategies. Empirical analyses indicate that government intervention, such as minimum wage laws or arbitration systems, influences bargaining outcomes but can distort labor markets if overly prescriptive.^[47]^[48] Theoretical frameworks interpret these dynamics differently. The unitary perspective views organizations as cohesive units where conflicts arise from miscommunication, advocating managerial leadership over union involvement. Pluralism acknowledges inherent conflicts from diverse stakeholder interests, promoting collective bargaining as a mechanism for compromise. Radical theory, rooted in Marxist analysis, posits structural antagonism under capitalism, with unions as tools for class struggle rather than mere mediators. These lenses guide policy but vary in empirical support; for instance, pluralist approaches align with systems where bargaining stabilizes relations, though radical predictions of inevitable collapse lack consistent evidence amid capitalist adaptations.^[49]^[50] Historically, industrial relations formalized during the 19th-century Industrial Revolution amid rising factory labor and disputes, evolving through milestones like the U.S. National Labor Relations Act of 1935, which protected union organizing. Post-World War II saw peak union influence, with U.S. membership nearing 35% by 1954, driven by wartime wage controls and economic growth. Subsequent declines followed globalization, deregulation, and shifts to service economies, reducing collective power.^[51]^[52]^[53] Key processes include collective bargaining agreements, which set wages and conditions via negotiation, and dispute resolution mechanisms like mediation or strikes. Strikes peaked in the U.S. at over 4,000 annually in the 1950s but fell to under 20 by 2023, reflecting lower union density. Governments mediate via agencies like the U.S. National Labor Relations Board, enforcing fair practices.^[54] Contemporary trends show declining union density, with U.S. membership at 9.9% in 2024, down from 20.1% in 1983, per Bureau of Labor Statistics data, amid right-to-work laws and gig economy growth. Globally, similar patterns hold in OECD nations, though sectors like public education retain higher rates.^[55]^[56] Empirically, unions raise member wages by 10-20% through bargaining premiums but correlate with 10-15% lower employment probabilities due to rigidities, per meta-analyses. Productivity effects are mixed: some studies find gains from reduced turnover, others losses from inflexibility hindering innovation. Establishment survival rates drop post-unionization, with payroll reductions offsetting wage hikes. These outcomes challenge pro-union narratives in academic literature, which often emphasize equity gains while underweighting disemployment costs evidenced in econometric models.^[57]^[58]^[59]^[60]

Business, finance, and organizations

Investor relations

Investor relations (IR) is a strategic management responsibility in publicly traded companies that integrates finance, communications, marketing, and securities law compliance to facilitate two-way information flow between the company and its investors, shareholders, analysts, and other stakeholders.^[61]^[62] The primary goal is to promote transparency, ensure compliance with disclosure requirements, and enable the company's securities to achieve valuation reflecting underlying fundamentals, thereby minimizing information asymmetry in capital markets.^[63] The formal practice of IR emerged in the United States during the mid-20th century amid rising public share ownership following World War II.^[64] General Electric coined the term "investor relations" in 1953 to describe systematic efforts to attract and inform individual investors through dedicated programs.^[65] By the late 1950s and 1960s, as institutional investing grew and regulatory frameworks like the U.S. Securities Exchange Act of 1934 evolved, companies established specialized IR departments to handle earnings communications and investor outreach.^[64] The National Investor Relations Institute (NIRI), founded in 1963, standardized professional practices and advocacy for the field.^[66] Core functions of IR include disseminating financial results via quarterly earnings releases, annual reports, and SEC filings such as Form 10-K and 10-Q; organizing investor days, roadshows, and analyst briefings; and monitoring peer valuations and shareholder composition to guide targeting of suitable investors.^[67]^[68] IR teams ensure adherence to regulations like Regulation Fair Disclosure (Reg FD, adopted by the SEC in 2000), which requires simultaneous public release of material nonpublic information to prevent selective disclosure.^[69] They also gather investor perceptions through surveys and meetings to relay feedback to executive management, influencing strategic decisions without compromising disclosure rules.^[66] In practice, effective IR emphasizes consistent messaging aligned with corporate strategy, proactive crisis communication, and use of digital tools for broader reach, such as webcasts and investor portals, to enhance accessibility and efficiency.^[70] While IR does not directly control stock prices, empirical evidence links robust practices to reduced volatility and improved liquidity, as informed investors respond more rationally to fundamentals than to rumors.^[63] Professional standards, as outlined by NIRI, prioritize ethical conduct, accuracy in projections, and avoidance of forward-looking statements that could mislead without safe harbor protections under the Private Securities Litigation Reform Act of 1995.^[66]

Inland Revenue

The Inland Revenue was a non-ministerial department of the United Kingdom government responsible for the assessment and collection of direct taxes, including income tax, corporation tax, capital gains tax, and inheritance tax.^[71] Established as the Board of Inland Revenue in 1849 through the merger of the Board of Stamps and Taxes with excise functions from the Board of Excise, it initially focused on inland duties before excise responsibilities transferred to the Board of Customs in 1909.^[72] The department's origins trace to the reintroduction of income tax in 1842 under Prime Minister Robert Peel to fund infrastructure and debt reduction, building on temporary wartime levies from 1799.^[72] By the 20th century, the Inland Revenue administered a broadening tax base, processing over 30 million self-assessment tax returns annually by the early 2000s and employing around 50,000 staff to enforce compliance through audits and investigations.^[73] Its operations emphasized direct taxation distinct from customs duties on imports, prioritizing efficiency in revenue yield, which averaged 35-40% of UK GDP in direct taxes during its later years.^[72] The department maintained headquarters in Somerset House, London, until relocating to Nottingham in the 1990s for cost savings.^[73] On 18 April 2005, the Inland Revenue merged with HM Customs and Excise to form HM Revenue and Customs (HMRC), driven by recommendations to streamline tax administration, reduce administrative burdens on taxpayers, and enhance counter-fraud measures across direct and indirect taxes.^[74] The merger integrated approximately 100,000 staff and aimed to boost collection efficiency, though early challenges included IT system incompatibilities and cultural clashes between the agencies.^[75] Post-merger, HMRC handles the former Inland Revenue's functions, collecting £800 billion in direct taxes annually as of 2023.^[76] The term "Inland Revenue" persists in other jurisdictions for analogous tax agencies, such as New Zealand's Inland Revenue Department, established in 1870 and responsible for income tax, goods and services tax (GST), and child support administration, collecting NZ$80 billion yearly.^[77] Similarly, Antigua and Barbuda's Inland Revenue Department manages property taxes and income assessments, while Trinidad and Tobago's Inland Revenue Division oversees corporation tax and value-added tax under the Ministry of Finance.^[78] These entities focus on domestic revenue mobilization, often modeled on British precedents but adapted to local fiscal needs.^[79]

Other business and finance uses

In finance, IR commonly denotes the information ratio, a risk-adjusted performance metric that evaluates a portfolio manager's ability to generate excess returns relative to a benchmark, normalized by the consistency of those excess returns.^[80] The ratio is calculated as the portfolio's average excess return over the benchmark divided by the tracking error, which measures the standard deviation of those excess returns; a higher IR indicates superior active management skill with lower volatility in outperformance.^[80] For instance, an IR above 0.5 is often considered strong, while values exceeding 1.0 suggest exceptional skill, though interpretations vary by market conditions and benchmark choice.^[81] Unlike the Sharpe ratio, which assesses total excess returns over the risk-free rate divided by total volatility, the information ratio specifically focuses on benchmark-relative performance and tracking error, making it particularly useful for evaluating active strategies in mutual funds or hedge funds.^[80] Introduced in quantitative finance literature, it aids investors in distinguishing skill from luck; empirical studies show that persistently high IRs correlate with long-term alpha generation, but short-term figures can mislead due to sampling variability.^[81] Portfolio managers target higher IRs by optimizing active bets while minimizing unintended deviations from the benchmark.^[82] IR may also refer to interest rate in certain economic and derivatives contexts, such as IR derivatives (e.g., swaps or options tied to benchmark rates like LIBOR or SOFR), where it denotes products hedging or speculating on rate movements.^[83] However, this usage is less standardized as a standalone acronym compared to investor relations, often appearing in specialized trading or risk management discussions rather than general business applications.^[84] Less common interpretations include interpretive rulings in regulatory finance, which provide agency guidance on financial rules without formal rulemaking.^[85]

Geography and places

Iran

Iran, officially the Islamic Republic of Iran, is a sovereign nation in southwestern Asia occupying the Iranian Plateau, with an area of 1,648,195 square kilometers, ranking it as the 17th-largest country by land area.^[86] Its capital and largest city is Tehran, home to approximately 12-15 million people in the greater metropolitan region.^[87] The country shares land borders totaling 5,894 kilometers with seven neighbors: Armenia, Azerbaijan, Afghanistan, Iraq, Pakistan, Turkey, and Turkmenistan; it also abuts the Caspian Sea to the north, the Persian Gulf and Gulf of Oman to the south.^[88]^[89] Geographically, Iran features diverse terrain dominated by mountain ranges such as the Zagros in the west and Alborz in the north, enclosing interior plateaus and two major salt deserts, Dasht-e Kavir and Dasht-e Lut, which are among the hottest and driest places on Earth. Fertile coastal plains are limited to the Caspian and Persian Gulf littorals, supporting agriculture amid predominantly arid conditions. The climate ranges from subtropical humid along northern and southern coasts to continental arid in the interior, with extreme temperature variations, seasonal dust storms, and low annual precipitation averaging under 250 millimeters outside highland areas.^[90]^[89] Iran's population stands at approximately 90.6 million as of 2023, with projections indicating growth to around 92 million by 2025, concentrated in urban centers amid a fertility rate decline.^[91]^[92] The nation traces its roots to ancient Persia, with modern statehood emerging after the 1979 Islamic Revolution, which replaced the monarchy with a theocratic republic under Ayatollah Ruhollah Khomeini; governance features a Supreme Leader—currently Ali Khamenei, in power since 1989—exercising control over key institutions, alongside an elected president, Masoud Pezeshkian, who assumed office in July 2024 following snap elections.^[93]^[94]

Other geographic uses

In Canada, "IR" is the standard abbreviation for Indian Reserve, a type of geographic designation referring to a tract of land set apart by the federal government for the exclusive use and benefit of a specific First Nations band or group of Indigenous peoples.^[95] These reserves are legally defined under the Indian Act of 1876 and subsequent amendments, comprising discrete parcels of Crown land with defined boundaries, often numbering in sequence (e.g., IR No. 1). As of the 2021 Census, Canada recognizes approximately 3,389 Indian reserves, though many are small or uninhabited, collectively spanning about 0.28% of the national land area or roughly 24,270 square kilometers. Indian Reserves are distributed across all provinces and territories except Prince Edward Island and Nunavut, with the highest concentrations in British Columbia (over 1,300) and Ontario (over 400). They vary widely in size, from tiny parcels under 1 hectare to larger ones exceeding 10,000 hectares, such as the Blood No. 148 Indian Reserve in Alberta, which covers 1,413 square kilometers and supports agricultural and resource-based economies. Governance occurs through band councils under federal oversight by Indigenous Services Canada, with reserves often featuring communities focused on traditional activities, though many residents commute to off-reserve urban areas for employment. Historically, reserves were established through treaties, surrenders, or administrative decisions between 1763 and the early 20th century, often resulting in fragmented land holdings due to colonial survey practices and negotiations. Population on reserves has declined as a proportion of the total Indigenous population, from about 45% in 1996 to 37% in 2021, reflecting urbanization trends driven by economic opportunities and infrastructure limitations on reserves. Challenges include jurisdictional disputes, as reserves fall under federal rather than provincial jurisdiction, affecting services like education and health.

Transportation and aviation

Instrument rating

An instrument rating is an aviation certification authorizing pilots to fly under instrument flight rules (IFR), which permit operations in instrument meteorological conditions (IMC) where visual references are insufficient, relying instead on aircraft instruments for attitude, navigation, and control.^[96] This rating extends beyond visual flight rules (VFR) limitations, enabling safer navigation through clouds, fog, or low visibility by following predefined instrument approach procedures and air traffic control clearances.^[97] In the United States, the Federal Aviation Administration (FAA) issues the rating as an add-on to existing pilot certificates, typically after a private pilot license is obtained.^[98] The foundational developments of instrument flying trace to the late 1920s, when aviation pioneers addressed the hazards of flying in poor weather without reliable instrumentation. On September 24, 1929, U.S. Army Air Corps Lieutenant James H. Doolittle completed the first documented "blind" instrument flight, taking off, navigating, and landing solely by reference to gyroscopic instruments in a hooded cockpit, demonstrating the feasibility of instrument-only operations.^[99] Concurrently, Edwin Link invented the Link Trainer in 1929, an early flight simulator that allowed pilots to practice instrument procedures on the ground, significantly reducing training risks and costs; by the 1930s, it was widely adopted for military and civilian instruction.^[100] Formal instrument ratings emerged as regulatory standards solidified post-World War II, with the FAA codifying requirements under 14 CFR Part 61 to standardize proficiency amid growing commercial aviation demands.^[101] To qualify for an instrument-airplane rating under FAA regulations (14 CFR § 61.65), applicants must hold at least a private pilot certificate with airplane category privileges, demonstrate English language proficiency, and complete ground and flight training from an authorized instructor or approved course.^[96] Aeronautical experience mandates include 50 hours of cross-country pilot-in-command time (with at least 10 hours in airplanes), 40 hours of actual or simulated instrument time (of which 15 hours must be with an instructor, including specific maneuvers like six instrument approaches and intercepting/ tracking courses), and preparation for the practical test.^[98]^[96] Training emphasizes skills such as attitude instrument flying, navigation using VOR, GPS, and ILS systems, recovery from unusual attitudes, and emergency procedures like partial panel operations without key instruments.^[97] Applicants must pass an FAA knowledge test covering topics like federal aviation regulations, weather theory, and instrument navigation, followed by a practical test evaluating risk management, aeronautical decision-making, and flight proficiency per the Instrument Rating Airman Certification Standards (ACS).^[101]^[102] Privileges conferred by the rating include filing and flying IFR flight plans in controlled airspace, executing precision and non-precision approaches, and holding patterns, subject to aircraft equipment and pilot currency.^[102] To maintain currency for IFR operations carrying passengers, pilots must perform and log six instrument approaches, holding procedures, and intercepting/tracking courses within the preceding six calendar months, using actual or simulated conditions. Limitations apply; for instance, the rating does not authorize takeoff or landing in zero visibility without additional qualifications, and operations remain governed by minimum equipment lists and alternate airport requirements.^[103] Internationally, equivalent ratings like the EASA Instrument Rating (IR) align closely but may impose additional modular or multi-crew requirements, reflecting harmonized ICAO standards.^[104]

Other transportation uses

In rail transport, IR denotes Indian Railways, the state-owned operator managing India's vast network of approximately 68,500 route kilometers as of 2023, serving as the primary mode of long-distance passenger and freight movement in the country.^[105] ^[106] This abbreviation appears extensively in official documents, station codes, and operational manuals issued by the Ministry of Railways.^[107] IR also refers to Irish Rail (Iarnród Éireann), the national railway operator in the Republic of Ireland, established in 1987 as a subsidiary of Córas Iompair Éireann and responsible for intercity, commuter, and regional passenger services across roughly 2,200 kilometers of track.^[108] ^[109] In maritime contexts, IR signifies Integrated Rating, a competency-based certification under the STCW Convention for entry-level seafarers, qualifying holders to assist in deck, engine room, or catering operations on vessels, typically requiring completion of approved training and six months of sea service.^[110] ^[111] This qualification supports crewing needs in international shipping, with programs standardized across jurisdictions like New Zealand and Australia.^[112]

Language and linguistics

Prefix ir-

The prefix ir- functions as a variant of the Latin prefix in-, denoting negation, opposition, or privation, and is specifically employed before base words or roots beginning with the consonant r to facilitate smoother pronunciation through assimilation.^[113] This assimilation process, where the nasal n in in- changes to r before an initial r, originated in Latin and persisted through Old French into Middle English, influencing many borrowed terms.^[114] In English, ir- imparts meanings such as "not," "without," or "opposite of," distinguishing it from the affirmative or locative uses of in- (e.g., "in" or "into").^[115] Etymologically, ir- traces to the Proto-Indo-European negative particle n-, combined with Latin in- ("not"), with assimilation variants like im-, il-, and ir- emerging by the classical Latin period to avoid awkward consonant clusters.^[116] This pattern parallels other negative prefixes in Indo-European languages, such as Greek a- or an-, but ir- entered English predominantly via Latin-derived vocabulary during the Norman Conquest and Renaissance scholarly borrowings.^[117] Unlike highly productive prefixes like un-, which is native Germanic and attaches freely to modern formations, ir- is largely bound to established Latinate words and is considered semi-productive or fossilized in contemporary usage.^[118] Common examples include irregular (not conforming to rules, from Latin irregularis, attested in English by the 14th century), irrelevant (not pertinent, from 18th-century legal and philosophical contexts), irresponsible (not answerable, emerging in the 17th century), and irreversible (not able to be reversed, recorded from 1640s). In rarer cases, ir- derives from in- in the sense of "in" or "towards," as in irrupt (to burst in, from Latin irrumpere, entering English in the 16th century), but such instances are outnumbered by negating forms and often require contextual distinction. Linguists note that ir- contributes to English's morphological complexity, aiding word recognition through predictable negation patterns in academic, scientific, and technical lexicon.^[119]

Other linguistic uses

In English phonology and orthography, the digraph "ir" commonly represents the r-controlled vowel sound /ɜːr/ (British English) or /ɝ/ (American English), as in words like bird, girl, third, and dirty. This grapheme is taught in phonics curricula as part of phase 5 letter-sound correspondences, where it contrasts with similar spellings such as "er" (her, fern) and "ur" (fur, turn) for the same phoneme, though usage lacks strict rules and relies on word-specific conventions.^[120]^[121] The sound arises from historical vowel shifts and rhotacization, with "ir" appearing in about 150 high-frequency words in primary reading lists.^[120] In linguistic glossing for interlinear morpheme-by-morphemes translations, "IR" abbreviates "irregular," applied to non-standard or suppletive forms within paradigms, such as an irregular locative (LOC.IR). This convention aids analysis of morphological anomalies across languages, distinct from standard abbreviations like IRR for irrealis mood.^[122]

Arts, media, and culture

Uses in entertainment

Infrared (IR) remote controls enable wireless operation of entertainment devices such as televisions, DVD players, and sound systems by transmitting signals in the infrared spectrum, typically within a range of 30-60 kHz modulated carrier waves.^[123] These devices, introduced commercially in the 1980s, rely on line-of-sight communication up to about 10 meters, powering consumer media consumption through simple commands for volume, channel selection, and playback control.^[124] IR technology facilitates motion capture in film and video game production, where infrared sensors track actors' movements for digital effects; for instance, IR emitters and cameras compute positions in real-time, contributing to visual effects in movies like those using six degrees of freedom (6DoF) tracking.^[125] In cinematography, IR-sensitive cameras capture wavelengths beyond visible light (approximately 700-1000 nm), producing surreal visuals such as ethereal landscapes or heat-based effects, as employed in sequences of films like Ad Astra (2019) for otherworldly atmospheres.^[126] In video games, IR head-tracking systems like TrackIR, utilizing infrared cameras and reflective headsets, allow players to control viewpoints by natural head movements, enhancing immersion in flight simulators and first-person shooters since the early 2000s with sub-millimeter accuracy and up to 100 Hz refresh rates.^[127] Nintendo's Switch console incorporates an IR camera in the Joy-Con controller for gesture-based inputs in titles such as 1-2-Switch (2017) and various Nintendo Labo kits (2018-2019), detecting finger positions or object outlines for interactive minigames.^[128] Earlier systems, like the Game Boy Color's IR port (1998-2003), supported multiplayer connectivity in over 20 games, including Tetris DX and Bomberman Quest, via infrared data association (IrDA) protocols for short-range, device-to-device links.^[129] Impulse responses (IRs) in audio engineering capture the acoustic characteristics of spaces or equipment, such as reverberation in concert halls, for convolution reverb plugins used in music production, film scoring, and live sound mixing; these digital files, derived from sine sweeps or noise bursts, enable realistic sound simulation in digital audio workstations (DAWs) like those processing Hollywood soundtracks.^[130] This technique, rooted in signal processing principles, preserves phase-accurate reflections, allowing producers to emulate environments without physical recording, as standardized in formats compatible with tools from companies like Fractal Audio since at least 2011.^[131]

Other cultural references

In literary genres, particularly romance fiction, "IR" denotes interracial romance, a subgenre featuring romantic narratives between characters of differing racial or ethnic backgrounds, often highlighting themes of cross-cultural relationships and societal challenges.^[132] This abbreviation is widely used in reader communities, book reviews, and online discussions to categorize titles, as seen in lists of romance tropes and fan recommendations.^[133] In art conservation and cultural heritage analysis, "IR" refers to infrared photography or reflectography, a non-destructive imaging technique that employs infrared wavelengths (typically 700–1000 nm) to reveal underdrawings, alterations, and hidden layers in paintings and artifacts invisible under visible light.^[134] Developed since the mid-20th century, it has been applied to works by masters like Rembrandt and Leonardo da Vinci, aiding authentication and restoration by distinguishing pigments with varying infrared transparency, such as carbon-based blacks that absorb IR versus lead whites that reflect it.^[135]^[136]

Miscellaneous uses

Military and defense

In military and defense contexts, IR refers to infrared radiation and technologies that detect or emit in the infrared spectrum (wavelengths from approximately 0.7 to 1,000 micrometers), enabling operations in low-visibility conditions by sensing heat signatures rather than visible light.^[137] These systems have been integral since World War II, with early experiments in infrared detectors like lead sulfide (PbS) photocells used for rudimentary night vision and fire control.^[138] By the Vietnam War, the U.S. military deployed infrared imaging for enhanced soldier visibility in darkness, marking a shift from passive observation to tactical advantage in nocturnal engagements.^[139] IR applications span surveillance, targeting, and protection. Electro-optical/infrared (EO/IR) sensors provide 24/7 detection, tracking, and identification of threats, such as aircraft or vehicles, by capturing thermal emissions from engines or exhaust—capabilities demonstrated in systems like Northrop Grumman's EO/IR suites for surface-to-space monitoring.^[140] In reconnaissance, uncooled IR imagers enable portable night-vision devices and unmanned aerial vehicle (UAV) payloads for persistent awareness without cryogenic cooling, reducing size, weight, and power demands for field deployment.^[141] Precision-guided munitions leverage IR seekers to home in on heat sources; the AIM-9 Sidewinder, operational since 1956, exemplifies short-range air-to-air missiles that lock onto target exhaust plumes, achieving high hit probabilities in beyond-visual-range scenarios.^[142] To counter IR-homing threats like man-portable air-defense systems (MANPADS), defenses include pyrotechnic flares that emit hotter signatures to seduce missiles away and advanced directional infrared countermeasures (DIRCM). DIRCM systems, such as the AN/AAQ-24, use modulated lasers to jam missile seekers by overwhelming their optical sensors, with rapid acquisition times under seconds against incoming threats.^[143] The U.S. Army's Common Infrared Countermeasures (CIRCM) program equips rotary- and fixed-wing aircraft with pod-mounted lasers compatible across platforms, addressing vulnerabilities from shoulder-fired IR missiles that account for significant aircraft losses in asymmetric conflicts.^[144] These technologies evolve with focal plane arrays and multispectral sensors to mitigate jamming and improve resolution against cooled seekers.^[137]

Additional abbreviations

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Ir- - Etymology & Meaning of the Prefix
Originating from Latin prefixes in- ("not") or in- ("in") before -r-, this word's meaning reflects the combined sense of negation or inclusion.
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ir-, prefix¹ meanings, etymology and more - Oxford English Dictionary
See meaning & use. Where does the prefix ir- come from? ir- is a borrowing from Latin. Etymons: Latin ir-. See etymology. Nearby entries. ipso facto, adv.1548 ...
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ir- - WordReference.com Dictionary of English
ir- · in; into; towards; within; on: infiltrate, immigrate · having an intensive or causative function: inflame, imperil.
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In- - Etymology & Meaning of the Prefix
in-(2) element meaning "into, in, on, upon" (also im-, il-, ir- by assimilation of -n- with following consonant), from Latin in- "in," from PIE root *en "in."
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etymology - Origins of negative prefixes like in-, un-, il-, ir-, dis-, a
Mar 9, 2011 · ir has origin from Latin, sometimes from Old French des-. a has origin from. Greek (when used in words like atypical); Old English, from the ...When do I use non-, ir-/i-, dis-, a-, or un - English Stack ExchangeWhy do so many prefixes mean "Not" - English Stack ExchangeMore results from english.stackexchange.comMissing: linguistics | Show results with:linguistics
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Word Root: ir- (Prefix) - Membean
The word part "ir-" is a prefix that means "not".
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Root Words, Suffixes, and Prefixes - Reading Rockets
Familiarity with Greek and Latin roots, as well as prefixes and suffixes, can help students understand the meaning of new words.
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Spelling word list: ir words | Activities, Games & Quizzes - Spellzone
This list includes words that use the letter combination ir to spell the /er/ sound. Ir words can be adjectives like dirty, adverbs like firmly, nouns like ...<|separator|>
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The ir sound | phonics | ir words - BBC Bitesize
Learn and practice the ir sound! Help the wizards to make ir words in this fun Phonics guide from BBC Bitesize.
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[PDF] The Leipzig Glossing Rules:
Several authors therefore use non-capitalized shortened abbreviations without a period. ... irrealis. LOC locative. M masculine. N neuter. N- non- (e.g. NSG ...
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Definition of IR remote control | PCMag
(InfraRed remote control) A handheld, wireless device used to operate audio, video and other electronic equipment within a room using light signals in the ...
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Infrared (IR): What Is It and How Does It Support AV Equipment?
Feb 11, 2025 · Infrared is an important component of audiovisual equipment that many people use every day. TV remotes, for example, rely on infrared signals to send commands.
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An Introduction to Infrared Cinematography - Filmmakers Academy
Infrared cinematography captures light beyond the visible spectrum, invisible to the naked eye, and is effectively heat, making the invisible visible.
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Infrared in cinema | Hidden Realms
Jan 13, 2021 · Infrared is used in cinema, such as in "At Eternity's Gate" for a short scene and in "Ad Astra" for a longer, other-worldly sequence.
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TrackIR: Home
Featuring a wide field of view, high frame rate, and 6DoF tracking technology, the TrackIR 5 dramatically increases situational awareness, adding depth to the ...
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I Played EVERY Nintendo Switch IR Camera Game... - YouTube
Sep 30, 2023 · " All clips and videos belong to their respective owners. I Played EVERY Nintendo Switch IR Camera Game... 580K views · 2 years ago ...more ...
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List of Game Boy Color games with IR support - Nintendo | Fandom
This is a list of Game Boy Color games that use the infrared (IR) port.
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Glossary of Terms - Sound - Theatrecrafts.com
(Sound) Abbreviated to IR. An Impulse Response is a digital recording of a burst of a full range of frequencies (known as an impulse) across the audible ...
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What's "IR" mean? - Fractal Audio Systems Forum
Aug 18, 2011 · It is Impulse Response, a way of capturing the response of a speaker cabinet for use with modellers.Missing: entertainment | Show results with:entertainment
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250+ Bookish Acronyms Every Reader Should Know (+ Slang ...
Aug 27, 2025 · IR: Interracial Romance. Love that crosses cultural and racial lines. OTP: One True Pairing. Your ultimate fictional couple. The ones you'll ...
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What does IR Stand For in texting? 11 meanings of IR
Incest Resources · — Injured Reserve · — Inter Racial · — Instant Replay · — Ivan Reitman · — InterRegio · — Inherited Runner · — Imperium ...
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Infrared Photography (IR) - Cultural Heritage Science Open Source
Infrared photography (IR) is used to detect underdrawing. IR is part of the Technical Photography documentation and it is used for the examination of many ...
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Infrared Reflectography in Art Conservation & History - IRINFO.org
May 1, 2019 · Infrared thermography (IR) covers the spectrum of 3 to 14 nm and gathers information from a painting by exposing it to an infrared source and ...
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IR Reflectography - ColourLex
IR Reflectography is an older imaging method suited for the investigation of works of art. Viewing a painting illuminated by visible light only allows us to ...
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The History, Trends, and Future of Infrared Technology - DSIAC
Nov 2, 2019 · This article provides a brief history of IR sensors and systems, as well as current trends and future projections for this important technology.
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[PDF] History of infrared detectors | Antoni Rogalski
This paper overviews the history of infrared detector materials starting with Herschel's experiment with thermometer on. February 11th, 1800.
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[PDF] What is infrared? - Association of American Universities (AAU)
The US military uses infrared imaging technology, or Night Vision, to enable soldiers to see better in darkness. It was used extensively in Vietnam and.<|control11|><|separator|>
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Electro-Optical and Infrared Sensors (EO/IR) | Northrop Grumman
From surface to space, Northrop Grumman's electro-optical/infrared (EO/IR) sensors harness the power of light to give warfighters a 24/7 view of the ...
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Uncooled infrared imaging | Military Aerospace
May 1, 2025 · Many military and commercial applications rely on IR imaging technology. These include night vision, biochemical detection, and remote sensing, ...
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In the Crosshairs - Understanding How IR Missiles Work
May 31, 2023 · The AIM-4 Falcon was the first IR guided missile to enter service. The AIM-4 Falcon was the first IR-guided ...
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AN/AAQ-24(V) DIRCM (Directional Infrared Countermeasure)
A Directional Infrared Countermeasures (DIRCM) system is required to defeat the latest and future advanced IR threats, and has a lower life cycle cost compared ...
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CIRCM – Common Infrared Countermeasures - Northrop Grumman
A lightweight, highly reliable infrared countermeasure system that is compatible with rotary wing, tiltrotor and small fixed wing aircraft.
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ir - abbreviation: ir - all meanings - Woxikon.com
Abbreviation ir ; IR, Intelligence Requirement, Military abbreviations ; IR, Internal Replenishment, Military abbreviations.
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IR Medical Abbreviation Meaning - All Acronyms
IR in Medical commonly refers to Infrared, a type of electromagnetic radiation with wavelengths longer than those of visible light, often utilized in various ...Missing: excluding | Show results with:excluding
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https://radiopaedia.org/articles/medical-abbreviations-and-acronyms-i-1?lang=us

IR