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Nitrous oxide

Nitrous oxide (dinitrogen oxide or dinitrogen monoxide), commonly known as laughing gas, nitrous, nitro, or nos, is a chemical compound, an oxide of nitrogen with the formula. At room temperature, it is a colourless non-flammable gas, and has a slightly sweet scent and taste. At elevated temperatures, nitrous oxide is a powerful oxidiser similar to molecular oxygen.

Nitrous oxide has significant medical uses, especially in surgery and dentistry, for its anaesthetic and pain-reducing effects. Its colloquial name, "laughing gas", coined by Humphry Davy, is due to the euphoric effects upon inhaling it, a property that has led to its recreational use as a dissociative anaesthetic. It is on the World Health Organization's List of Essential Medicines. It is also used as an oxidiser in rocket propellants, and in motor racing to increase the power output of engines.

Nitrous oxide's atmospheric concentration reached 333 parts per billion (ppb) in 2020, increasing at a rate of about 1 ppb annually. It is a major scavenger of stratospheric ozone, with an impact comparable to that of CFCs. About 40% of human-caused emissions are from agriculture. Nitrogen is added to the soil via animal urine and dung, and synthetic fertilisers: micro-organisms then release it in nitrous oxide. Being the third most important greenhouse gas, nitrous oxide substantially contributes to global warming. Reduction of emissions is a popular topic in the politics of climate change.

Nitrous oxide is used as a propellant, and has a variety of applications from rocketry to making whipped cream. It is used as a recreational drug for its potential to induce a brief "high". When used chronically, nitrous oxide has the potential to cause neurological damage through inactivation of vitamin B12.

Rocket motors
Nitrous oxide may be used as an oxidiser in a rocket motor. It has advantages over other oxidisers in that it is much less toxic, and because of its stability at room temperature, it is also easier to store and relatively safe to carry on a flight. As a secondary benefit, it may be decomposed readily to form breathing air. Its high density and low storage pressure (when maintained at low temperatures) enable it to be highly competitive with stored high-pressure gas systems.

In a 1914 patent, American rocket pioneer Robert Goddard suggested nitrous oxide and gasoline as possible propellants for a liquid-fuelled rocket. Nitrous oxide has been the oxidiser of choice in several hybrid rocket designs (using solid fuel with a liquid or gaseous oxidiser). The combination of nitrous oxide with hydroxyl-terminated polybutadiene fuel has been used by SpaceShipOne and others. It also is notably used in amateur and high power rocketry with various plastics as the fuel.

Nitrous oxide also may be used in a monopropellant rocket. In the presence of a heated catalyst, will decompose exothermically into nitrogen and oxygen, at a temperature of approximately 1070 F. Because of the large heat release, the catalytic action rapidly becomes secondary, as thermal autodecomposition becomes dominant. In a vacuum thruster, this may provide a monopropellant specific impulse (I) of as much as 180 s. While noticeably less than the I available from hydrazine thrusters (monopropellant or bipropellant with dinitrogen tetroxide), the decreased toxicity makes nitrous oxide an option worth investigating.

Nitrous oxide is said to deflagrate at approximately 600 C at a pressure of 309 psi (21 atmospheres). At 600 psi, for example, the required ignition energy is only 6 joules, whereas at 130 psi a 2,500-joule ignition energy input is insufficient.

Internal combustion engine
In vehicle racing, nitrous oxide (often called "nitrous") allows the engine to burn more fuel by providing more oxygen during combustion. The increase in oxygen allows an increase in the injection of fuel, allowing the engine to produce more engine power. The gas is not flammable at a low pressure/temperature, but it delivers more oxygen than atmospheric air by breaking down at elevated temperatures, about 570 degrees F (~300C). Therefore, it often is mixed with another fuel that is easier to deflagrate. Nitrous oxide is a strong oxidising agent, roughly equivalent to hydrogen peroxide, and much stronger than oxygen gas.

Nitrous oxide is stored as a compressed liquid; the evaporation and expansion of liquid nitrous oxide in the intake manifold causes a large drop in intake charge temperature, resulting in a denser charge, further allowing more air/fuel mixture to enter the cylinder. Sometimes nitrous oxide is injected into (or prior to) the intake manifold, whereas other systems directly inject, right before the cylinder (direct port injection) to increase power.

The technique was used during World War II by Luftwaffe aircraft with the GM-1 system to boost the power output of aircraft engines. Originally meant to provide the Luftwaffe standard aircraft with superior high-altitude performance, technological considerations limited its use to extremely high altitudes. Accordingly, it was only used by specialised planes such as high-altitude reconnaissance aircraft, high-speed bombers and high-altitude interceptor aircraft. It sometimes could be found on Luftwaffe aircraft also fitted with another engine-boost system, MW 50, a form of water injection for aviation engines that used methanol for its boost capabilities.

One of the major problems of using nitrous oxide in a reciprocating engine is that it can produce enough power to damage or destroy the engine. Very large power increases are possible, and if the mechanical structure of the engine is not properly reinforced, the engine may be severely damaged or destroyed during this type of operation. It is important with nitrous oxide augmentation of petrol engines to maintain proper operating temperatures and fuel levels to prevent "pre-ignition", or "detonation" (sometimes referred to as "knock"). Most problems that are associated with nitrous oxide do not come from mechanical failure due to the power increases. Since nitrous oxide allows a much denser charge into the cylinder, it dramatically increases cylinder pressures. The increased pressure and temperature can cause problems such as melting the pistons or valves. It also may crack or warp the piston or cylinder head and cause pre-ignition due to uneven heating.

Automotive-grade liquid nitrous oxide differs slightly from medical-grade nitrous oxide. A small amount of sulfur dioxide is added to prevent substance abuse.

Aerosol propellant
The gas is approved for use as a food additive (E number: E942), specifically as an aerosol spray propellant. Its most common uses in this context are in aerosol whipped cream canisters and cooking sprays.

The gas is extremely soluble in fatty compounds. In aerosol whipped cream, it is dissolved in the fatty cream until it leaves the can, when it becomes gaseous and thus creates foam. Used in this way, it produces whipped cream which is four times the volume of the liquid, whereas whipping air into cream only produces twice the volume. If air were used as a propellant, oxygen would accelerate rancidification of the butterfat, but nitrous oxide inhibits such degradation. Carbon dioxide cannot be used for whipped cream because it is acidic in water, which would curdle the cream and give it a seltzer-like "sparkling" sensation.

The whipped cream produced with nitrous oxide is unstable, and will return to a more liquid state within half an hour to one hour. Thus, the method is not suitable for decorating food that will not be served immediately.

In December 2016, some manufacturers reported a shortage of aerosol whipped creams in the United States due to an explosion at the Air Liquide nitrous oxide facility in Florida in late August. With a major facility offline, the disruption caused a shortage resulting in the company diverting the supply of nitrous oxide to medical customers rather than to food manufacturing. The shortage came during the Christmas and holiday season when canned whipped cream use is normally at its highest.

Similarly, cooking spray, which is made from various types of oils combined with lecithin (an emulsifier), may use nitrous oxide as a propellant. Other propellants used in cooking spray include food-grade alcohol and propane.

Medicine

Nitrous oxide has been used in dentistry and surgery, as an anaesthetic and analgesic, since 1844. In the early days, the gas was administered through simple inhalers consisting of a breathing bag made of rubber cloth. Today, the gas is administered in hospitals by means of an automated relative analgesia machine, with an anaesthetic vaporiser and a medical ventilator, that delivers a precisely dosed and breath-actuated flow of nitrous oxide mixed with oxygen in a 2:1 ratio.

Nitrous oxide is a weak general anaesthetic, and so is generally not used alone in general anaesthesia, but used as a carrier gas (mixed with oxygen) for more powerful general anaesthetic drugs such as sevoflurane or desflurane. It has a minimum alveolar concentration of 105% and a blood/gas partition coefficient of 0.46. The use of nitrous oxide in anaesthesia can increase the risk of postoperative nausea and vomiting.

Dentists use a simpler machine which only delivers an / mixture for the patient to inhale while conscious but must still be a recognised purpose designed dedicated relative analgesic flowmeter with a minimum 30% of oxygen at all times and a maximum upper limit of 70% nitrous oxide. The patient is kept conscious throughout the procedure, and retains adequate mental faculties to respond to questions and instructions from the dentist.

Inhalation of nitrous oxide is used frequently to relieve pain associated with childbirth, trauma, oral surgery and acute coronary syndrome (including heart attacks). Its use during labour has been shown to be a safe and effective aid for birthing women. Its use for acute coronary syndrome is of unknown benefit.

In Canada and the UK, Entonox and Nitronox are used commonly by ambulance crews (including unregistered practitioners) as rapid and highly effective analgesic gas.

Fifty per cent nitrous oxide can be considered for use by trained non-professional first aid responders in prehospital settings, given the relative ease and safety of administering 50% nitrous oxide as an analgesic. The rapid reversibility of its effect would also prevent it from precluding diagnosis.

Recreational use

Recreational inhalation of nitrous oxide, with the purpose of causing euphoria and/or slight hallucinations, began as a phenomenon for the British upper class in 1799, known as "laughing gas parties".

Starting in the 19th century, the widespread availability of the gas for medical and culinary purposes allowed for recreational use to expand greatly globally. In the UK as of 2014, nitrous oxide was estimated to be used by almost half a million young people at nightspots, festivals and parties.

Widespread recreational use of the drug throughout the UK was featured in the 2017 Vice documentary Inside The Laughing Gas Black Market, in which journalist Matt Shea met with dealers of the drug who stole it from hospitals.

A significant issue cited in London's press is the effect of nitrous oxide canister littering, which is highly visible and causes significant complaints from communities.

Prior to 8 November 2023, nitrous oxide was subject to the Psychoactive Substances Act 2016 in the UK. It was already illegal to produce, supply, import or export nitrous oxide for recreational use. However, the UK government updated the law on 8 November 2023 to include possession of nitrous oxide by classifying it as a Class C drug under the Misuse of Drugs Act 1971.

While casual use of nitrous oxide is understood by most recreational users to be a route to a "safe high", many are unaware that excessive consumption has the potential to cause neurological harm which, if left untreated, can result in permanent neurological damage. In Australia, recreation use became a public health concern following a rise in reported cases of neurotoxicity and a rise in emergency room admissions, and in (the state of) South Australia legislation was passed in 2020 to restrict canister sales.

Safety
Nitrous oxide is a significant occupational hazard for surgeons, dentists and nurses. Because nitrous oxide is minimally metabolised in humans (with a rate of 0.004%), it retains its potency when exhaled into the room by the patient, and can pose an intoxicating and prolonged exposure hazard to the clinic staff if the room is poorly ventilated. Where nitrous oxide is administered, a continuous-flow fresh-air ventilation system or scavenger system is used to prevent a waste-gas buildup.

The National Institute for Occupational Safety and Health recommends that workers' exposure to nitrous oxide should be controlled during the administration of anaesthetic gas in medical, dental and veterinary operators. It set a recommended exposure limit (REL) of 25 ppm (46 mg/m3) to escaped anaesthetic.

Mental and manual impairment
Exposure to nitrous oxide causes short-term decreases in mental performance, audiovisual ability and manual dexterity. These effects coupled with the induced spatial and temporal disorientation could result in physical harm to the user from environmental hazards.

Neurotoxicity and neuroprotection
Nitrous oxide is neurotoxic and there is evidence that medium or long-term habitual consumption of significant quantities can cause neurological harm with the potential for permanent damage if left untreated.

Like other NMDA receptor antagonists, it has been suggested that produces neurotoxicity in the form of Olney's lesions in rodents upon prolonged (several hour) exposure. It has been argued that, because is rapidly expelled from the body under normal circumstances, it is less likely to be neurotoxic than other NMDAR antagonists. Indeed, in rodents, short-term exposure results in only mild injury that is rapidly reversible, and neuronal death occurs only after constant and sustained exposure. Nitrous oxide also may cause neurotoxicity after extended exposure because of hypoxia. This is especially true of non-medical formulations such as whipped-cream chargers (also known as "whippets" or "nangs"), which never contain oxygen, since oxygen makes cream rancid.

In heavy (≥400 g or ≥200 L of gas in one session) or frequent (regular, i.e., daily or weekly) users reported to poison control centers, signs of peripheral neuropathy have been noted: the presence of ataxia (gait abnormalities) or paresthesia (perception of abnormal sensations, e.g. tingling, numbness, prickling, mostly in the extremities). These are considered an early sign of neurological damage and indicates chronic toxicity.

Nitrous oxide at 75% by volume reduces ischemia-induced neuronal death induced by occlusion of the middle cerebral artery in rodents, and decreases NMDA-induced Ca2+ influx in neuronal cell cultures, a critical event involved in excitotoxicity.

DNA damage
Occupational exposure to ambient nitrous oxide has been associated with DNA damage, due to interruptions in DNA synthesis. This correlation is dose-dependent and does not appear to extend to casual recreational use; however, further research is needed to confirm the duration and quantity of exposure needed to cause damage.

Oxygen deprivation
If pure nitrous oxide is inhaled without oxygen, oxygen deprivation can occur, resulting in low blood pressure, fainting, and even heart attacks. This can occur if the user inhales large quantities continuously, as with a strap-on mask connected to a gas canister. It can also happen if the user engages in excessive breath-holding or uses any other inhalation system that cuts off a supply of fresh air.

Vitamin B deficiency
Long-term exposure to nitrous oxide may cause vitamin B deficiency. This can cause serious neurotoxicity if the user has preexisting vitamin B deficiency. It inactivates the cobalamin form of vitamin B by oxidation. Symptoms of vitamin B deficiency, including sensory neuropathy, myelopathy and encephalopathy, may occur within days or weeks of exposure to nitrous oxide anaesthesia in people with subclinical vitamin B deficiency.

Symptoms are treated with high doses of vitamin B, but recovery can be slow and incomplete.

People with normal vitamin B levels have stores to make the effects of nitrous oxide insignificant, unless exposure is repeated and prolonged (nitrous oxide abuse). Vitamin B levels should be checked in people with risk factors for vitamin B deficiency prior to using nitrous oxide anaesthesia.

Prenatal development
Several experimental studies in rats indicate that chronic exposure of pregnant females to nitrous oxide may have adverse effects on the developing fetus.

Chemical/physical risks
At room temperature (20 C) the saturated vapour pressure is 50.525 bar, rising up to 72.45 bar at 36.4 C—the critical temperature. The pressure curve is thus unusually sensitive to temperature.

As with many strong oxidisers, contamination of parts with fuels have been implicated in rocketry accidents, where small quantities of nitrous/fuel mixtures explode due to "water hammer"-like effects (sometimes called "dieseling"—heating due to adiabatic compression of gases can reach decomposition temperatures). Some common building materials such as stainless steel and aluminium can act as fuels with strong oxidisers such as nitrous oxide, as can contaminants that may ignite due to adiabatic compression.

There also have been incidents where nitrous oxide decomposition in plumbing has led to the explosion of large tanks.

Mechanism of action
The pharmacological mechanism of action of in medicine is not fully known. However, it has been shown to directly modulate a broad range of ligand-gated ion channels, and this likely plays a major role in many of its effects. It moderately blocks NMDAR and β-subunit-containing nACh channels, weakly inhibits AMPA, kainate, GABA and 5-HT receptors, and slightly potentiates GABA and glycine receptors. It also has been shown to activate two-pore-domain channels. While affects quite a few ion channels, its anaesthetic, hallucinogenic and euphoriant effects are likely caused predominantly, or fully, via inhibition of NMDA receptor-mediated currents. In addition to its effects on ion channels, may act to imitate nitric oxide (NO) in the central nervous system, and this may be related to its analgesic and anxiolytic properties. Nitrous oxide is 30 to 40 times more soluble than nitrogen.

The effects of inhaling sub-anaesthetic doses of nitrous oxide have been known to vary, based on several factors, including settings and individual differences; however, from his discussion, Jay (2008) suggests that it has been reliably known to induce the following states and sensations: A minority of users also will present with uncontrolled vocalisations and muscular spasms. These effects generally disappear minutes after removal of the nitrous oxide source.
 * Intoxication
 * Euphoria/dysphoria
 * Spatial disorientation
 * Temporal disorientation
 * Reduced pain sensitivity

Anxiolytic effect
In behavioural tests of anxiety, a low dose of is an effective anxiolytic, and this anti-anxiety effect is associated with enhanced activity of GABA receptors, as it is partially reversed by benzodiazepine receptor antagonists. Mirroring this, animals that have developed tolerance to the anxiolytic effects of benzodiazepines are partially tolerant to. Indeed, in humans given 30%, benzodiazepine receptor antagonists reduced the subjective reports of feeling "high", but did not alter psychomotor performance, in human clinical studies.

Analgesic effect
The analgesic effects of are linked to the interaction between the endogenous opioid system and the descending noradrenergic system. When animals are given morphine chronically, they develop tolerance to its pain-killing effects, and this also renders the animals tolerant to the analgesic effects of. Administration of antibodies that bind and block the activity of some endogenous opioids (not β-endorphin) also block the antinociceptive effects of. Drugs that inhibit the breakdown of endogenous opioids also potentiate the antinociceptive effects of. Several experiments have shown that opioid receptor antagonists applied directly to the brain block the antinociceptive effects of, but these drugs have no effect when injected into the spinal cord.

Apart from an indirect action, nitrous oxide, like morphine also interacts directly with the endogenous opioid system by binding at opioid receptor binding sites.

Conversely, α-adrenoceptor antagonists block the pain-reducing effects of when given directly to the spinal cord, but not when applied directly to the brain. Indeed, α-adrenoceptor knockout mice or animals depleted in norepinephrine are nearly completely resistant to the antinociceptive effects of. Apparently -induced release of endogenous opioids causes disinhibition of brainstem noradrenergic neurons, which release norepinephrine into the spinal cord and inhibit pain signalling. Exactly how causes the release of endogenous opioid peptides remains uncertain.

Properties and reactions
Nitrous oxide is a colourless gas with a faint, sweet odour.

Nitrous oxide supports combustion by releasing the dipolar bonded oxygen radical, and can thus relight a glowing splint.

is inert at room temperature and has few reactions. At elevated temperatures, its reactivity increases. For example, nitrous oxide reacts with at 187 C to give :
 * 2 NaNH2 + N2O -> NaN3 + NaOH + NH3

The above reaction is the route adopted by the commercial chemical industry to produce azide salts, which are used as detonators.

History
The gas was first synthesised in 1772 by English natural philosopher and chemist Joseph Priestley who called it dephlogisticated nitrous air (see phlogiston theory) or inflammable nitrous air. Priestley published his discovery in the book Experiments and Observations on Different Kinds of Air (1775), where he described how to produce the preparation of "nitrous air diminished", by heating iron filings dampened with nitric acid.

Early use
The first important use of nitrous oxide was made possible by Thomas Beddoes and James Watt, who worked together to publish the book Considerations on the Medical Use and on the Production of Factitious Airs (1794). This book was important for two reasons. First, James Watt had invented a novel machine to produce "factitious airs" (including nitrous oxide) and a novel "breathing apparatus" to inhale the gas. Second, the book also presented the new medical theories by Thomas Beddoes, that tuberculosis and other lung diseases could be treated by inhalation of "Factitious Airs".

The machine to produce "Factitious Airs" had three parts: a furnace to burn the needed material, a vessel with water where the produced gas passed through in a spiral pipe (for impurities to be "washed off"), and finally the gas cylinder with a gasometer where the gas produced, "air", could be tapped into portable air bags (made of airtight oily silk). The breathing apparatus consisted of one of the portable air bags connected with a tube to a mouthpiece. With this new equipment being engineered and produced by 1794, the way was paved for clinical trials, which began in 1798 when Thomas Beddoes established the "Pneumatic Institution for Relieving Diseases by Medical Airs" in Hotwells (Bristol). In the basement of the building, a large-scale machine was producing the gases under the supervision of a young Humphry Davy, who was encouraged to experiment with new gases for patients to inhale. The first important work of Davy was examination of the nitrous oxide, and the publication of his results in the book: Researches, Chemical and Philosophical (1800). In that publication, Davy notes the analgesic effect of nitrous oxide at page 465 and its potential to be used for surgical operations at page 556. Davy coined the name "laughing gas" for nitrous oxide.

Despite Davy's discovery that inhalation of nitrous oxide could relieve a conscious person from pain, another 44 years elapsed before doctors attempted to use it for anaesthesia. The use of nitrous oxide as a recreational drug at "laughing gas parties", primarily arranged for the British upper class, became an immediate success beginning in 1799. While the effects of the gas generally make the user appear stuporous, dreamy and sedated, some people also "get the giggles" in a state of euphoria, and frequently erupt in laughter.

One of the earliest commercial producers in the U.S. was George Poe, cousin of the poet Edgar Allan Poe, who also was the first to liquefy the gas.

Anaesthetic use
The first time nitrous oxide was used as an anaesthetic drug in the treatment of a patient was when dentist Horace Wells, with assistance by Gardner Quincy Colton and John Mankey Riggs, demonstrated insensitivity to pain from a dental extraction on 11 December 1844. In the following weeks, Wells treated the first 12 to 15 patients with nitrous oxide in Hartford, Connecticut, and, according to his own record, only failed in two cases. In spite of these convincing results having been reported by Wells to the medical society in Boston in December 1844, this new method was not immediately adopted by other dentists. The reason for this was most likely that Wells, in January 1845 at his first public demonstration to the medical faculty in Boston, had been partly unsuccessful, leaving his colleagues doubtful regarding its efficacy and safety. The method did not come into general use until 1863, when Gardner Quincy Colton successfully started to use it in all his "Colton Dental Association" clinics, that he had just established in New Haven and New York City. Over the following three years, Colton and his associates successfully administered nitrous oxide to more than 25,000 patients. Today, nitrous oxide is used in dentistry as an anxiolytic, as an adjunct to local anaesthetic.

Nitrous oxide was not found to be a strong enough anaesthetic for use in major surgery in hospital settings, however. Instead, diethyl ether, being a stronger and more potent anaesthetic, was demonstrated and accepted for use in October 1846, along with chloroform in 1847. When Joseph Thomas Clover invented the "gas-ether inhaler" in 1876, however, it became a common practice at hospitals to initiate all anaesthetic treatments with a mild flow of nitrous oxide, and then gradually increase the anaesthesia with the stronger ether or chloroform. Clover's gas-ether inhaler was designed to supply the patient with nitrous oxide and ether at the same time, with the exact mixture being controlled by the operator of the device. It remained in use by many hospitals until the 1930s. Although hospitals today use a more advanced anaesthetic machine, these machines still use the same principle launched with Clover's gas-ether inhaler, to initiate the anaesthesia with nitrous oxide, before the administration of a more powerful anaesthetic.

As a patent medicine
Colton's popularisation of nitrous oxide led to its adoption by a number of less than reputable quacksalvers, who touted it as a cure for consumption, scrofula, catarrh and other diseases of the blood, throat and lungs. Nitrous oxide treatment was administered and licensed as a patent medicine by the likes of C. L. Blood and Jerome Harris in Boston and Charles E. Barney of Chicago.

Production
Reviewing various methods of producing nitrous oxide is published.

Industrial methods
Nitrous oxide is prepared on an industrial scale by carefully heating ammonium nitrate at about 250 °C, which decomposes into nitrous oxide and water vapour.
 * NH4NO3 -> 2 H2O + N2O

The addition of various phosphate salts favours formation of a purer gas at slightly lower temperatures. This reaction may be difficult to control, resulting in detonation.

Laboratory methods
The decomposition of ammonium nitrate is also a common laboratory method for preparing the gas. Equivalently, it can be obtained by heating a mixture of sodium nitrate and ammonium sulfate:
 * 2 NaNO3 + (NH4)2SO4 -> Na2SO4 + 2 N2O + 4 H2O

Another method involves the reaction of urea, nitric acid and sulfuric acid:
 * 2 (NH2)2CO + 2 HNO3 + H2SO4 -> 2 N2O + 2 CO2 + (NH4)2SO4 + 2 H2O

Direct oxidation of ammonia with a manganese dioxide-bismuth oxide catalyst has been reported: cf. Ostwald process.
 * 2 NH3 + 2 O2 -> N2O + 3 H2O

Hydroxylammonium chloride reacts with sodium nitrite to give nitrous oxide. If the nitrite is added to the hydroxylamine solution, the only remaining by-product is salt water. If the hydroxylamine solution is added to the nitrite solution (nitrite is in excess), however, then toxic higher oxides of nitrogen also are formed:
 * NH3OHCl + NaNO2 -> N2O + NaCl + 2 H2O

Treating with  and HCl also has been demonstrated:
 * 2 HNO3 + 8 HCl + 4 SnCl2 -> 5 H2O + 4 SnCl4 + N2O

Hyponitrous acid decomposes to NO and water with a half-life of 16 days at 25 °C at pH 1–3.
 * H2N2O2 -> H2O + N2O

Atmospheric occurrence
Nitrous oxide is a minor component of Earth's atmosphere and is an active part of the planetary nitrogen cycle. Based on analysis of air samples gathered from sites around the world, its concentration surpassed 330 ppb in 2017. The growth rate of about 1 ppb per year has also accelerated during recent decades. Nitrous oxide's atmospheric abundance has grown more than 20% from a base level of about 270 ppb in year 1750. Important atmospheric properties of are summarized in the following table:

In 2022 the IPCC reported that: "The human perturbation of the natural nitrogen cycle through the use of synthetic fertilizers and manure, as well as nitrogen deposition resulting from land-based agriculture and fossil fuel burning has been the largest driver of the increase in atmospheric N2O of 31.0 ± 0.5 ppb (10%) between 1980 and 2019."

Emissions by source
17.0 (12.2 to 23.5) million tonnes total annual average nitrogen in was emitted in 2007–2016. About 40% of emissions are from humans and the rest are part of the natural nitrogen cycle. The emitted each year by humans has a greenhouse effect equivalent to about 3 billion tonnes of carbon dioxide: for comparison humans emitted 37 billion tonnes of actual carbon dioxide in 2019, and methane equivalent to 9 billion tonnes of carbon dioxide.

Most of the emitted into the atmosphere, from natural and anthropogenic sources, is produced by microorganisms such as denitrifying bacteria and fungi in soils and oceans. Soils under natural vegetation are an important source of nitrous oxide, accounting for 60% of all naturally produced emissions. Other natural sources include the oceans (35%) and atmospheric chemical reactions (5%). Wetlands can also be emitters of nitrous oxide. Emissions from thawing permafrost may be significant, but as of 2022 this is not certain.

The main components of anthropogenic emissions are fertilised agricultural soils and livestock manure (42%), runoff and leaching of fertilisers (25%), biomass burning (10%), fossil fuel combustion and industrial processes (10%), biological degradation of other nitrogen-containing atmospheric emissions (9%) and human sewage (5%). Agriculture enhances nitrous oxide production through soil cultivation, the use of nitrogen fertilisers and animal waste handling. These activities stimulate naturally occurring bacteria to produce more nitrous oxide. Nitrous oxide emissions from soil can be challenging to measure as they vary markedly over time and space, and the majority of a year's emissions may occur when conditions are favorable during "hot moments" and/or at favorable locations known as "hotspots".

Among industrial emissions, the production of nitric acid and adipic acid are the largest sources of nitrous oxide emissions. The adipic acid emissions specifically arise from the degradation of the nitrolic acid intermediate derived from the nitration of cyclohexanone.

Biological processes
Natural processes that generate nitrous oxide may be classified as nitrification and denitrification. Specifically, they include:

 * aerobic autotrophic nitrification, the stepwise oxidation of ammonia to nitrite  and to nitrate
 * anaerobic heterotrophic denitrification, the stepwise reduction of to, nitric oxide (NO),  and ultimately , where facultative anaerobe bacteria use  as an electron acceptor in the respiration of organic material in the condition of insufficient oxygen
 * nitrifier denitrification, which is carried out by autotrophic -oxidising bacteria and the pathway whereby ammonia is oxidised to nitrite, followed by the reduction of  to nitric oxide (NO),  and molecular nitrogen
 * heterotrophic nitrification
 * aerobic denitrification by the same heterotrophic nitrifiers
 * fungal denitrification
 * non-biological chemodenitrification

These processes are affected by soil chemical and physical properties such as the availability of mineral nitrogen and organic matter, acidity and soil type, as well as climate-related factors such as soil temperature and water content.

The emission of the gas to the atmosphere is limited greatly by its consumption inside the cells, by a process catalysed by the enzyme nitrous oxide reductase.

Environmental impact
Global accounting of sources and sinks over the decade ending 2016 indicates that about 40% of the average 17 TgN/yr (teragrams, or million metric tons, of nitrogen per year) of emissions originated from human activity, and shows that emissions growth chiefly came from expanding agriculture.

Greenhouse effect

Nitrous oxide has significant global warming potential as a greenhouse gas. On a per-molecule basis, considered over a 100-year period, nitrous oxide has 265 times the atmospheric heat-trapping ability of carbon dioxide. However, because of its low concentration (less than 1/1,000 of that of ), its contribution to the greenhouse effect is less than one third that of carbon dioxide, and also less than methane. On the other hand, since about 40% of the entering the atmosphere is the result of human activity, control of nitrous oxide is part of efforts to curb greenhouse gas emissions.

Most human caused nitrous oxide released into the atmosphere is a greenhouse gas emission from agriculture, when farmers add nitrogen-based fertilizers onto the fields, and through the breakdown of animal manure. Reduction of emissions can be a hot topic in the politics of climate change.

Nitrous oxide is also released as a by-product of burning fossil fuel, though the amount released depends on which fuel was used. It is also emitted through the manufacture of nitric acid, which is used in the synthesis of nitrogen fertilizers. The production of adipic acid, a precursor to nylon and other synthetic clothing fibres, also releases nitrous oxide.

A rise in atmospheric nitrous oxide concentrations has been implicated as a possible contributor to the extremely intense global warming during the Cenomanian-Turonian boundary event.

Ozone layer depletion
Nitrous oxide has also been implicated in thinning the ozone layer. A 2009 study suggested that emission was the single most important ozone-depleting emission and it was expected to remain the largest throughout the 21st century.

India
Transfer of nitrous oxide from bulk cylinders to smaller, more transportable E-type, 1,590-litre-capacity tanks is legal when the intended use of the gas is for medical anaesthesia.

New Zealand
The Ministry of Health has warned that nitrous oxide is a prescription medicine, and its sale or possession without a prescription is an offense under the Medicines Act. This statement would seemingly prohibit all non-medicinal uses of nitrous oxide, although it is implied that only recreational use will be targeted legally.

UK
In August 2015, the Council of the London Borough of Lambeth (UK) banned the use of the drug for recreational purposes, making offenders liable to an on-the-spot fine of up to £1,000.

In September 2023, the Government announced that nitrous oxide would be made illegal by the end of the year, with possession potentially carrying up to a two-year prison sentence or an unlimited fine.

US
Possession of nitrous oxide is legal under federal law and is not subject to DEA purview. It is, however, regulated by the Food and Drug Administration under the Food Drug and Cosmetics Act; prosecution is possible under its "misbranding" clauses, prohibiting the sale or distribution of nitrous oxide for the purpose of human consumption. Many states have laws regulating the possession, sale and distribution of nitrous oxide. Such laws usually ban distribution to minors or limit the amount of nitrous oxide that may be sold without special license. For example, in the state of California, possession for recreational use is prohibited and qualifies as a misdemeanor.

title: Nitrous oxide


text:
Alliant RQ-6 Outrider

The Alliant RQ-6 Outrider unmanned aerial vehicle (UAV) was designed to provide near-real-time reconnaissance, surveillance, and target acquisition information to United States Marine Corps air/ground task forces, United States Army brigades, and deployed United States Navy units that was small enough for an entire system to be contained on two Humvees and trailer and transported on a single C-130 Hercules cargo aircraft.

The project began in 1996 and was canceled in 1999.

The "R" is the Department of Defense designation for reconnaissance; "Q" means unmanned aircraft system. The "6" refers to its being the sixth of a series of purpose-built unmanned aircraft systems.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Alliant RQ-6 Outrider


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Kannada

Kannada ( ಕನ್ನಡ, ), formerly also known as Canarese, is a Dravidian language spoken predominantly by the people of Karnataka in southwestern India, with minorities in all neighbouring states. It has around 44 million native speakers, and is additionally a second or third language for around 15 million non-native speakers in Karnataka.

Kannada was the court language of a number of dynasties and empires of South, Central India and Deccan Plateau, namely the Kadamba dynasty, Western Ganga dynasty, Nolamba dynasty, Chalukya dynasty, Rashtrakuta Empire, Western Chalukya Empire Yadava Dynasty or Seunas, Kingdom of Mysore, Nayakas of Keladi, Hoysala dynasty and the Vijayanagara Empire. The official and administrative language of the state of Karnataka, it also has scheduled status in India and has been included among the country's designated classical languages.

The Kannada language is written using the Kannada script, which evolved from the 5th-century Kadamba script. Kannada is attested epigraphically for about one and a half millennia and literary Old Kannada flourished in the 6th-century Ganga dynasty and during the 9th-century Rashtrakuta Empire. Kannada has an unbroken literary history of over a thousand years. Kannada literature has been presented with 8 Jnanapith awards, the most for any Dravidian language and the second highest for any Indian language. In July 2011, a center for the study of classical Kannada was established as part of the Central Institute of Indian Languages in Mysore to facilitate research related to the language.

Geographic distribution
Kannada had 43.5 million native speakers in India at the time of the 2011 census. It is the main language of the state of Karnataka, where it is spoken natively by million people, or about two thirds of the state's population. There are native Kannada speakers in the neighbouring states of Tamil Nadu ( speakers), Maharashtra, Andhra Pradesh/Telangana , Kerala and Goa. It is also spoken as a second and third language by over 12.9 million non-native speakers in Karnataka.

Kannadigas form Tamil Nadu's third biggest linguistic group; their population is roughly 1.23 million, which is 2.2% of Tamil Nadu's total population.

The Malayalam spoken by people of Lakshadweep has many Kannada words.

In the United States, there were 35,900 speakers in 2006–2008, a number that had risen to 48,600 by the time of the 2015 census. There are speakers in Canada (according to the 2016 census), 9,700 in Australia (2016 census), 22,000 in Singapore (2018 estimate), and 59,000 in Malaysia (2021 estimate).

Development
Kannada is a Southern Dravidian language and according to Sanford B. Steever, its history can be conventionally divided into three stages: Old Kannada (Haḷegannaḍa) from 450 to 1200 AD, Middle Kannada (Naḍugannaḍa) from 1200 to 1700 and Modern Kannada (Hosagannaḍa) from 1700 to the present. Kannada was influenced to a considerable degree by Sanskrit and Prakrit. The scholar Iravatham Mahadevan indicated that Kannada was already a language of rich spoken tradition earlier than the 3rd century BC and based on the native Kannada words found in Prakrit inscriptions of that period, Kannada must have been spoken by a broad and stable population. The scholar K. V. Narayana claims that many tribal languages which are now designated as Kannada dialects could be nearer to the earlier form of the language, with lesser influence from other languages.

Sanskrit and Prakrit influence
The sources of influence on literary Kannada grammar appear to be three-fold: Pāṇini's grammar, non-Pāṇinian schools of Sanskrit grammar, particularly Katantra and Sakatayana schools, and Prakrit grammar. Literary Prakrit seems to have prevailed in Karnataka since ancient times. The vernacular Prakrit speaking people may have come into contact with Kannada speakers, thus influencing their language, even before Kannada was used for administrative or liturgical purposes. Kannada phonetics, morphology, vocabulary, grammar and syntax show significant influence from these languages.

Some naturalised (tadbhava) words of Prakrit origin in Kannada are: baṇṇa (colour) derived from vaṇṇa, huṇṇime (full moon) from puṇṇivā. Examples of naturalised Sanskrit words in Kannada are: varṇa (colour), pūrṇime, and rāya from rāja (king).

Kannada also has borrowed (Tatsama) words such as dina (day), kōpa (anger), sūrya (sun), mukha (face), nimiṣa (minute).

Early traces

The earliest Kannada inscriptions are from the middle of the 5th century AD, but there are a number of earlier texts that may have been influenced by the ancestor language of Old Kannada.

Iravatam Mahadevan, a Brahmin, author of a work on early Tamil epigraphy, argued that oral traditions in Kannada and Telugu existed much before written documents were produced. Although the rock inscriptions of Ashoka were written in Prakrit, the spoken language in those regions was Kannada as the case may be. He can be quoted as follows: "If proof were needed to show that Kannada was the spoken language of the region during the early period, one needs only to study the large number of Kannada personal names and place names in the early Prakrit inscriptions on stone and copper in Upper South India [...] Kannada was spoken by relatively large and well-settled populations, living in well-organised states ruled by able dynasties like the Satavahanas, with a high degree of civilisation [...] There is, therefore, no reason to believe that these languages had less rich or less expressive oral traditions than Tamil had towards the end of its pre-literate period."

The Ashoka rock edict found at Brahmagiri (dated to 250 BC) has been suggested to contain words (Isila, meaning to throw, viz. an arrow, etc.) in identifiable Kannada.

In some 3rd–1st century BC Tamil inscriptions, words of Kannada influence such as Naliyura, kavuDi and posil were found. In a 3rd-century AD Tamil inscription there is usage of oppanappa vIran. Here the honorific appa to a person's name is an influence from Kannada. Another word of Kannada origin is taayviru and is found in a 4th-century AD Tamil inscription. S. Settar studied the sittanavAsal inscription of first century AD as also the inscriptions at tirupparamkunram, adakala and neDanUpatti. The later inscriptions were studied in detail by Iravatham Mahadevan also. Mahadevan argues that the words erumi, kavuDi, poshil and tAyiyar have their origin in Kannada because Tamil cognates are not available. Settar adds the words nADu and iLayar to this list. Mahadevan feels that some grammatical categories found in these inscriptions are also unique to Kannada rather than Tamil. Both these scholars attribute these influences to the movements and spread of Jainas in these regions. These inscriptions belong to the period between the first century BC and fourth century AD. These are some examples that are proof of the early usage of a few Kannada origin words in early Tamil inscriptions before the common era and in the early centuries of the common era.

Pliny the Elder, a Roman historian, wrote about pirates between Muziris and Nitrias (Netravati River), called Nitran by Ptolemy. He also mentions Barace (Barcelore), referring to the modern port city of Mangaluru, upon its mouth. Many of these are Kannada origin names of places and rivers of the Karnataka coast of 1st century AD.

The Greek geographer Ptolemy (150 AD) mentions places such as Badiamaioi (Badami), Inde (Indi), Kalligeris (Kalkeri), Modogoulla (Mudagal), Petrigala (Pattadakal), Hippokoura (Huvina Hipparagi), Nagarouris (Nagur), Tabaso (Tavasi), Tiripangalida (Gadahinglai), Soubouttou or Sabatha (Savadi), Banaouase (Banavasi), Thogorum (Tagara), Biathana (Paithan), Sirimalaga (Malkhed), Aloe (Ellapur) and Pasage (Palasige). He mentions a Satavahana king Sire Polemaios, who is identified with Sri Pulumayi (or Pulumavi), whose name is derived from the Kannada word for Puli, meaning tiger. Some scholars indicate that the name Pulumayi is actually Kannada's 'Puli Maiyi ' or ' One with the body of a tiger ' indicating native Kannada origin for the Satavahanas. Pai identifies all the 10 cities mentioned by Ptolemy (100–170 AD) as lying between the river Benda (or Binda) or Bhima river in the north and Banaouasei (Banavasi) in the south, viz. Nagarouris (Nagur), Tabaso (Tavasi), Inde (Indi), Tiripangalida (Gadhinglaj), Hippokoura (Huvina Hipparagi), Soubouttou (Savadi), Sirimalaga (Malkhed), Kalligeris (Kalkeri), Modogoulla (Mudgal) and Petirgala (Pattadakal), as being located in Northern Karnataka which signify the existence of Kannada place names (and the language and culture) in the southern Kuntala region during the reign of Vasishtiputra Pulumayi (c. 85-125 AD, i.e., late 1st century – early 2nd century AD) who was ruling from Paithan in the north and his son, prince Vilivaya-kura or Pulumayi Kumara was ruling from Huvina Hipparagi in present Karnataka in the south.

An early ancestor of Kannada (or a related language) may have been spoken by Indian traders in Roman-era Egypt and it may account for the Indian-language passages in the ancient Greek play known as the Charition mime.

Epigraphy
The earliest examples of a full-length Kannada language stone inscription (śilāśāsana) containing Brahmi characters with characteristics attributed to those of proto-Kannada in Haḷe Kannaḍa (lit Old Kannada) script can be found in the Halmidi inscription, usually dated c. 450 AD, indicating that Kannada had become an administrative language at that time. The Halmidi inscription provides invaluable information about the history and culture of Karnataka. A set of five copper plate inscriptions discovered in Mudiyanur, though in the Sanskrit language, is in the Pre-Old Kannada script older than the Halmidi edict date of 450 AD, as per palaeographers.

Followed by B. L. Rice, leading epigrapher and historian, K. R. Narasimhan following a detailed study and comparison, declared that the plates belong to the 4th century, i.e., 338 AD. The Kannada Lion balustrade inscription excavated at the Pranaveshwara temple complex at Talagunda near Shiralakoppa of Shivamogga district, dated to 370 AD is now considered the earliest Kannada inscriptions replacing the Halmidi inscription of 450 AD. The 5th century poetic Tamatekallu inscription of Chitradurga and the Siragunda inscription from Chikkamagaluru Taluk of 500 AD are further examples. Recent reports indicate that the Old Kannada Gunabhushitana Nishadi inscription discovered on the Chandragiri hill, Shravanabelagola, is older than Halmidi inscription by about fifty to hundred years and may belong to the period AD 350–400.

The noted archaeologist and art historian S. Shettar is of the opinion that an inscription of the Western Ganga King Kongunivarma Madhava (c. 350–370) found at Tagarthi (Tyagarthi) in Shikaripura taluk of Shimoga district is of 350 AD and is also older than the Halmidi inscription.

Current estimates of the total number of existing epigraphs written in Kannada range from 25,000 by the scholar Sheldon Pollock to over 30,000 by Amaresh Datta of the Sahitya Akademi. Prior to the Halmidi inscription, there is an abundance of inscriptions containing Kannada words, phrases and sentences, proving its antiquity. The 543 AD Badami cliff inscription of Pulakesi I is an example of a Sanskrit inscription in old Kannada script.

Kannada inscriptions are discovered in Andhra Pradesh and Telangana, Maharashtra, Tamil Nadu Madhya Pradesh and Gujarat in addition to Karnataka. This indicates the spread of the influence of the language over the ages, especially during the rule of large Kannada empires.

The earliest copper plates inscribed in Old Kannada script and language, dated to the early 8th century AD, are associated with Alupa King Aluvarasa II from Belmannu (the Dakshina Kannada district), and display the double crested fish, his royal emblem. The oldest well-preserved palm leaf manuscript in Old Kannada is that of Dhavala. It dates to around the 9th century and is preserved in the Jain Bhandar, Mudbidri, Dakshina Kannada district. The manuscript contains 1478 leaves written using ink.

Coins
Some early Kadamba Dynasty coins bearing the Kannada inscription Vira and Skandha were found in Satara collectorate. A gold coin bearing three inscriptions of Sri and an abbreviated inscription of king Bhagiratha's name called bhagi (c. 390–420 AD) in old Kannada exists. A Kadamba copper coin dated to the 5th century AD with the inscription Srimanaragi in Kannada script was discovered in Banavasi, Uttara Kannada district. Coins with Kannada legends have been discovered spanning the rule of the Western Ganga Dynasty, the Badami Chalukyas, the Alupas, the Western Chalukyas, the Rashtrakutas, the Hoysalas, the Vijayanagar Empire, the Kadamba Dynasty of Banavasi, the Keladi Nayakas and the Mysore Kingdom, the Badami Chalukya coins being a recent discovery. The coins of the Kadambas of Goa are unique in that they have alternate inscription of the king's name in Kannada and Devanagari in triplicate, a few coins of the Kadambas of Hangal are also available.

Old Kannada
The oldest known existing record of Kannada poetry in Tripadi metre is the Kappe Arabhatta record of 7th century AD. Kavirajamarga by King Nripatunga Amoghavarsha I (850 AD) is the earliest existing literary work in Kannada. It is a writing on literary criticism and poetics meant to standardise various written Kannada dialects used in literature in previous centuries. The book makes reference to Kannada works by early writers such as King Durvinita of the 6th century and Ravikirti, the author of the Aihole record of 636 AD. Since the earliest available Kannada work is one on grammar and a guide of sorts to unify existing variants of Kannada grammar and literary styles, it can be safely assumed that literature in Kannada must have started several centuries earlier. An early extant prose work, the Vaḍḍārādhane (ವಡ್ಡಾರಾಧನೆ) by Shivakotiacharya of 900 AD provides an elaborate description of the life of Bhadrabahu of Shravanabelagola.

Some of the early writers of prose and verse mentioned in the Kavirajamarga, numbering 8–10, stating these are but a few of many, but whose works are lost, are Vimala or Vimalachandra (c. 777), Udaya, Nagarjuna, Jayabandhu, Durvinita (6th century), and poets including Kaviswara, Srivijaya, Pandita, Chandra, Ravi Kirti (c. 634) and Lokapala. For fragmentary information on these writers, we can refer the work Karnataka Kavi Charite. Ancient indigenous Kannada literary compositions of (folk) poetry like the Chattana and Bedande which preferred to use the Desi metre are said to have survived at least until the date of the Kavirajamarga in 850 AD and had their roots in the early Kannada folk literature. These Kannada verse-compositions might have been representative of folk songs containing influence of Sanskrit and Prakrit metrical patterns to some extent. "Kavirajamarga" also discusses earlier composition forms peculiar to Kannada, the "gadyakatha", a mixture of prose and poetry, the "chattana" and the "bedande", poems of several stanzas that were meant to be sung with the optional use of a musical instrument. Amoghavarsha Nripatunga compares the puratana-kavigal (old Kannada poets) who wrote the great Chattana poems in Kannada to the likes of the great Sanskrit poets like Gunasuri, Narayana, Bharavi, Kalidasa, Magha, etc. This Old Kannada work, Kavirajamarga, itself in turn refers to a Palagannada (Old Kannada) of much ancient times, which is nothing but the Pre-Old Kannada and also warns aspiring Kannada writers to avoid its archaisms, as per R. S. Hukkerikar. Regarding earlier poems in Kannada, the author of "Kavirajamarga" states that old Kannada is appropriate in ancient poems but insipid in contemporaneous works as per R. Narasimhacharya. Gunanandi (900 AD), quoted by the grammarian Bhattakalanka and always addressed as Bhagawan (the adorable), was the author of a logic, grammar and sahitya. Durvinita (529–579 AD), the Ganga king, was the pupil of the author of Sabdavatara, i.e., Devanandi Pujyapada. Durvinita is said to have written a commentary on the difficult 15th sarga of Bharavi's Kiratarjuniya in Kannada. Early Kannada writers regularly mention three poets as of especial eminence among their predecessors – Samanta-bhadra, Kavi Parameshthi and Pujyapada. Since later Kannada poets so uniformly name these three as eminent poets, it is probable that they wrote in Kannada also. Samantabhadra is placed in 2nd century AD by Jain tradition. Old Kannada commentaries on some of his works exist. He was said to have born in Utkalikagrama and while performing penance in Manuvakahalli, he was attacked by a disease called Bhasmaka. Pujyapada also called Devanandi, was the preceptor of Ganga king Durvinita and belonged to the late 5th to early 6th century AD. Kaviparameshthi probably lived in the 4th century AD. He may possibly be the same as the Kaviswara referred to in the Kavirajamarga, and the Kaviparameswara praised by Chavunda Raya (978 AD) and his spiritual teacher, Nemichandra (10th century AD), all the names possibly being only epithets.

Kannada works from earlier centuries mentioned in the Kavirajamarga are not yet traced. Some ancient Kannada texts now considered extinct but referenced in later centuries are Prabhrita (650 AD) by Syamakundacharya, Chudamani (Crest Jewel—650 AD or earlier) by Srivaradhadeva, also known as Tumbuluracharya, which is a work of 96,000 verse-measures and a commentary on logic (Tatwartha-mahashastra). Other sources date Chudamani to the 6th century or earlier. An inscription of 1128 AD quotes a couplet by the famous Sanskrit poet Dandin (active 680–720 AD), highly praising Srivaradhadeva, for his Kannada work Chudamani, as having "produced Saraswati (i.e., learning and eloquence) from the tip of his tongue, as Siva produced the Ganges from the tip of his top-knot." Bhattakalanka (1604 CE), the great Kannada grammarian, refers to Srivaradhadeva's Chudamani as the greatest work in Kannada, and as incontestable proof of the scholarly character and value of Kannada literature. This makes Srivaradhadeva's time earlier than the 6th–7th century AD. Other writers, whose works are not extant now but titles of which are known from independent references such as Indranandi's "Srutavatara", Devachandra's "Rajavalikathe", Bhattakalanka's "Sabdanusasana" of 1604, writings of Jayakirthi are Syamakundacharya (650), who authored the "Prabhrita", and Srivaradhadeva (also called Tumubuluracharya, 650 or earlier), who wrote the "Chudamani" ("Crest Jewel"), a 96,000-verse commentary on logic. The Karnateshwara Katha, a eulogy for King Pulakesi II, is said to have belonged to the 7th century; the Gajastaka, a lost "ashtaka" (eight line verse) composition and a work on elephant management by King Shivamara II, belonged to the 8th century, this served as the basis for 2 popular folk songs Ovanige and Onakevadu, which were sung either while pounding corn or to entice wild elephants into a pit ("Ovam"). The Chandraprabha-purana by Sri Vijaya, a court poet of emperor Amoghavarsha I, is ascribed to the early 9th century. His writing has been mentioned by Vijayanagara poets Mangarasa III and Doddiah (also spelt Doddayya, c. 1550 AD) and praised by Durgasimha (c. 1025 AD). During the 9th century period, the Digambara Jain poet Asaga (or Asoka) authored, among other writings, "Karnata Kumarasambhava Kavya" and "Varadamana Charitra". His works have been praised by later poets, although none of his works are available today. "Gunagankiyam", the earliest known prosody in Kannada, was referenced in a Tamil work dated to 10th century or earlier ("Yapparungalakkarigai" by Amritasagara). Gunanandi, an expert in logic, Kannada grammar and prose, flourished in the 9th century AD. Around 900 AD, Gunavarma I wrote "Sudraka" and "Harivamsa" (also known as "Neminatha Purana"). In "Sudraka" he compared his patron, Ganga king Ereganga Neetimarga II (c. 907–921 AD), to a noted king called Sudraka. Jinachandra, who is referred to by Sri Ponna (c. 950 AD) as the author of "Pujyapada Charita", had earned the honorific "modern Samantha Bhadra". Tamil Buddhist commentators of the 10th century AD (in the commentary on Neminatham, a Tamil grammatical work) make references that show that Kannada literature must have flourished as early as the BC 4th century.

Around the beginning of the 9th century, Old Kannada was spoken from Kaveri to Godavari. The Kannada spoken between the rivers Varada and Malaprabha was the pure well of Kannada undefiled.

The late classical period gave birth to several genres of Kannada literature, with new forms of composition coming into use, including Ragale (a form of blank verse) and meters like Sangatya and Shatpadi. The works of this period are based on Jain and Hindu principles. Two of the early writers of this period are Harihara and Raghavanka, trailblazers in their own right. Harihara established the Ragale form of composition while Raghavanka popularised the Shatpadi (six-lined stanza) meter. A famous Jaina writer of the same period is Janna, who expressed Jain religious teachings through his works.

The Vachana Sahitya tradition of the 12th century is purely native and unique in world literature, and the sum of contributions by all sections of society. Vachanas were pithy poems on that period's social, religious and economic conditions. More importantly, they held a mirror to the seed of social revolution, which caused a radical re-examination of the ideas of caste, creed and religion. Some of the important writers of Vachana literature include Basavanna, Allama Prabhu and Akka Mahadevi.

Emperor Nripatunga Amoghavarsha I of 850 AD recognised that the Sanskrit style of Kannada literature was Margi (formal or written form of language) and Desi (folk or spoken form of language) style was popular and made his people aware of the strength and beauty of their native language Kannada. In 1112 AD, Jain poet Nayasena of Mulugunda, Dharwad district, in his Champu work Dharmamrita (ಧರ್ಮಾಮೃತ), a book on morals, warns writers from mixing Kannada with Sanskrit by comparing it with mixing of clarified butter and oil. He has written it using very limited Sanskrit words which fit with idiomatic Kannada. In 1235 AD, Jain poet Andayya, wrote Kabbigara Kava- ಕಬ್ಬಿಗರ ಕಾವ (Poet's Defender), also called Sobagina Suggi (Harvest of Beauty) or Madana-Vijaya and Kavana-Gella (Cupid's Conquest), a Champu work in pure Kannada using only indigenous (desya) Kannada words and the derived form of Sanskrit words – tadbhavas, without the admixture of Sanskrit words. He succeeded in his challenge and proved wrong those who had advocated that it was impossible to write a work in Kannada without using Sanskrit words. Andayya may be considered as a protector of Kannada poets who were ridiculed by Sanskrit advocates. Thus Kannada is the only Dravidian language which is not only capable of using only native Kannada words and grammar in its literature (like Tamil), but also use Sanskrit grammar and vocabulary (like Telugu, Malayalam, Tulu, etc.) The Champu style of literature of mixing poetry with prose owes its origins to the Kannada language which was later incorporated by poets into Sanskrit and other Indian languages.

Middle Kannada
During the period between the 15th and 18th centuries, Hinduism had a great influence on Middle Kannada (Naḍugannaḍa- ನಡುಗನ್ನಡ) language and literature. Kumara Vyasa, who wrote the Karṇāṭa Bhārata Kathāman̄jari (ಕರ್ಣಾಟ ಭಾರತ ಕಥಾಮಂಜರಿ), was arguably the most influential Kannada writer of this period. His work, entirely composed in the native Bhamini Shatpadi (hexa-meter), is a sublime adaptation of the first ten books of the Mahabharata. During this period, the Sanskritic influence is present in most abstract, religious, scientific and rhetorical terms. During this period, several Hindi and Marathi words came into Kannada, chiefly relating to feudalism and militia.

Hindu saints of the Vaishnava sect such as Kanakadasa, Purandaradasa, Naraharitirtha, Vyasatirtha, Sripadaraya, Vadirajatirtha, Vijaya Dasa, Gopala Dasa, Jagannatha Dasa, Prasanna Venkatadasa produced devotional poems in this period. Kanakadasa's Rāmadhānya Charite (ರಾಮಧಾನ್ಯ ಚರಿತೆ) is a rare work, concerning with the issue of class struggle. This period saw the advent of Haridasa Sahitya (lit Dasa literature) which made rich contributions to Bhakti literature and sowed the seeds of Carnatic music. Purandara Dasa is widely considered the Father of Carnatic music.

Modern Kannada
The Kannada works produced from the 19th century make a gradual transition and are classified as Hosagannaḍa or Modern Kannada. Most notable among the modernists was the poet Nandalike Muddana whose writing may be described as the "Dawn of Modern Kannada", though generally, linguists treat Indira Bai or Saddharma Vijayavu by Gulvadi Venkata Raya as the first literary works in Modern Kannada. The first modern movable type printing of "Canarese" appears to be the Canarese Grammar of Carey printed at Serampore in 1817, and the "Bible in Canarese" of John Hands in 1820. The first novel printed was John Bunyan's Pilgrim's Progress, along with other texts including Canarese Proverbs, The History of Little Henry and his Bearer by Mary Martha Sherwood, Christian Gottlob Barth's Bible Stories and "a Canarese hymn book."

Modern Kannada in the 20th century has been influenced by many movements, notably Navodaya, Navya, Navyottara, Dalita and Bandaya. Contemporary Kannada literature has been highly successful in reaching people of all classes in society. Further, Kannada has produced a number of prolific and renowned poets and writers such as Kuvempu, Bendre, and V K Gokak. Works of Kannada literature have received eight Jnanpith awards, the highest number awarded to any Indian language.

Dialects
There is also a considerable difference between the spoken and written forms of the language. Spoken Kannada tends to vary from region to region. The written form is more or less consistent throughout Karnataka. The Ethnologue reports "about 20 dialects" of Kannada. Among them are Kundagannada (spoken exclusively in Kundapura, Brahmavara, Bynduru and Hebri), Nador-Kannada (spoken by Nadavaru), Havigannada (spoken mainly by Havyaka Brahmins), Are Bhashe (spoken by Gowda community mainly in Madikeri and Sullia region of Dakshina Kannada), Malenadu Kannada (Sakaleshpur, Coorg, Shimoga, Chikmagalur), Sholaga, Gulbarga Kannada, Dharawad Kannada etc. All of these dialects are influenced by their regional and cultural background. The one million Komarpants in and around Goa speak their own dialect of Kannada, known as Halegannada. They are settled throughout Goa state, throughout Uttara Kannada district and Khanapur taluk of Belagavi district, Karnataka. The Halakki Vokkaligas of Uttara Kannada and Shimoga districts of Karnataka speak in their own dialect of Kannada called Halakki Kannada or Achchagannada. Their population estimate is about 75,000.

Ethnologue also classifies a group of four languages related to Kannada, which are, besides Kannada proper, Badaga, Holiya, Kurumba and Urali. The Golars or Golkars are a nomadic herdsmen tribe present in Nagpur, Chanda, Bhandara, Seoni and Balaghat districts of Maharashtra and Madhya Pradesh speak the Golari dialect of Kannada which is identical to the Holiya dialect spoken by their tribal offshoot Holiyas present in Seoni, Nagpur and Bhandara of Madhya Pradesh and Maharashtra. There were around 3,600 speakers of this dialect as per the 1901 census. Matthew A. Sherring describes the Golars and Holars as a pastoral tribe from the Godavari banks established in the districts around Nagpur, in the stony tracts of Ambagarh, forests around Ramplee and Sahangadhee. Along the banks of the Wainganga, they dwell in the Chakurhaitee and Keenee subdivisions. The Kurumvars of Chanda district of Maharashtra, a wild pastoral tribe, 2,200 in number as per the 1901 census, spoke a Kannada dialect called Kurumvari. The Kurumbas or Kurubas, a nomadic shepherd tribe were spread across the Nilgiris, Coimbatore, Salem, North and South Arcots, Trichinopoly, Tanjore and Pudukottai of Tamil Nadu, Cuddapah and Anantapur of Andhra Pradesh, Malabar and Cochin of Kerala and South Canara and Coorg of Karnataka and spoke the Kurumba Kannada dialect. The Kurumba and Kurumvari dialect (both closely related with each other) speakers were estimated to be around 11,400 in total as per the 1901 census. There were about 34,250 Badaga speakers as per the 1901 census.

Nasik district of Maharashtra has a distinct tribe called 'Hatkar Kaanadi' people who speak a Kannada (Kaanadi) dialect with lot of old Kannada words. Per Chidananda Murthy, they are the native people of Nasik from ancient times, which shows that North Maharashtra's Nasik area had Kannada population 1000 years ago. Kannada speakers formed 0.12% of Nasik district's population as per 1961 census.

Writing system
The language uses forty-nine phonemic letters, divided into three groups: swaragalu (vowels – thirteen letters); vyanjanagalu (consonants – thirty-four letters); and yogavaahakagalu (neither vowel nor consonant – two letters: anusvara ಂ and visarga ಃ). The character set is almost identical to that of other Indian languages. The Kannada script is almost entirely phonetic, but for the sound of a "half n" (which becomes a half m). The number of written symbols, however, is far more than the forty-nine characters in the alphabet, because different characters can be combined to form compound characters (ottakshara). Each written symbol in the Kannada script corresponds with one syllable, as opposed to one phoneme in languages like English—the Kannada script is syllabic.

Dictionary
Kannada–Kannada dictionary has existed in Kannada along with ancient works of Kannada grammar. The oldest available Kannada dictionary was composed by the poet 'Ranna' called 'Ranna Kanda' (ರನ್ನ ಕಂದ) in 996 AD. Other dictionaries are 'Abhidhana Vastukosha' (ಅಭಿದಾನ ವಾಸ್ತುಕೋಶ) by Nagavarma (1045 AD), 'Amarakoshada Teeku' (ಅಮರಕೋಶದ ತೀಕು) by Vittala (1300), 'Abhinavaabhidaana' (ಅಭಿನವಾಭಿದಾನ) by Abhinava Mangaraja (1398 AD) and many more. A Kannada–English dictionary consisting of more than 70,000 words was composed by Ferdinand Kittel.

G. Venkatasubbaiah edited the first modern Kannada–Kannada dictionary, a 9,000-page, 8-volume series published by the Kannada Sahitya Parishat. He also wrote a Kannada–English dictionary and a kliṣtapadakōśa (ಕ್ಲಿಷ್ಟಪಾದಕೋಶ), a dictionary of difficult words.

Consonants

 * Most consonants can be geminated.
 * Aspirated consonants very rarely occur in native vocabulary only in a few numerals like the number 9 and 80, which can be written with a /bʱ/, as in "ಒಂಭತ್ತು", ಎಂಭತ್ತು. However, it is usually written with a /b/, as in "ಒಂಬತ್ತು", ಎಂಬತ್ತು.
 * The aspiration of consonants depends entirely on the speaker and many do not do it in non-formal situations.
 * The alveolar trill /r/ may be pronounced as an alveolar tap [ɾ].
 * The voiceless retroflex sibilant /ʂ/ is commonly pronounced as a /ʃ/ except in consonant clusters with retroflex consonants.
 * There are also the consonants /f, z/ which occur in recent English and Perso-Arabic loans but they may be replaced by the consonants /pʰ, dʒ/ respectively by speakers.

Additionally, Kannada included the following phonemes, which dropped out of common usage in the 12th and 18th century respectively:
 * // ಱ (ṟ), the alveolar trill.
 * // ೞ (ḻ), the retroflex central approximant.

Old Kannada had an archaic phoneme /ɻ/ under retroflexes in early inscriptions which merged with /ɭ/ and it maintained the contrast between /r/ (< PD ∗ṯ) and /ɾ/ from (< PD ∗r). Both merged in Medieval Kannada.

In old Kannada at around 10th-14th century, most of the initial /p/ debuccalized into a /h/ e.g. OlKn. pattu, MdKn. hattu "ten".

Historically, the Tamil-Malayalam languages and, independently, Telugu, phonemically palatalized /k/ before a front vowel; Kannada never developed such phonemic palatalization (c.f. Kn. ಕಿವಿ, Ta. செவி , Te. చెవి "ear"); however, phonetically, Kannada speakers frequently palatalize velar consonants before front vowels, for example, realizing ಕಿವಿ  "ear" as  and ಗಿಳಿ  "parrot" as.

Vowels

 * and are phonetically central .  may be as open as   or higher.
 * The vowels /i iː e eː/ may be preceded by /j/ and the vowels /u uː o oː/ may be preceded by /ʋ/ when they are in an initial position.
 * The short vowels /a i u e o/, when in an initial or a medial position tend to be pronounced as [ɐ ɪ ʊ ɛ ɔ]. In a final position, this phenomenon occurs less frequently.
 * /æː/ occurs in English loans but can be switched with /aː/ or /ja:/.

At around the 8th century, Kannada raised the vowels e, o to i, u when before a short consonant and a high vowel, before written literature emerged in the language, e.g. Kn. kivi, Ta. cevi, Te. cevi "ear".

Grammar
The canonical word order of Kannada is SOV (subject–object–verb), typical of Indian languages. Kannada is a highly inflected language with three genders (masculine, feminine, and neuter or common) and two numbers (singular and plural). It is inflected for gender, number and tense, among other things. The most authoritative known book on old Kannada grammar is Shabdhamanidarpana by Keshiraja. The first available Kannada book, a treatise on poetics, rhetoric and basic grammar is the Kavirajamarga from 850 AD.

The most influential account of Kannada grammar is Keshiraja's Shabdamanidarpana (c. 1260 AD). The earlier grammatical works include portions of Kavirajamarga (a treatise on alańkāra) of the 9th century, and Kavyavalokana and Karnatakabhashabhushana (both authored by Nagavarma II in the first half of the 12th century).

Compound bases
Compound bases, called samāsa in Kannada, are a set of two or more words compounded together. There are several types of compound bases, based on the rules followed for compounding. The types of compound bases or samāsas: tatpurusha, karmadhāraya, dvigu, bahuvreehi, anshi, dvandva, kriya and gamaka samāsa. Examples: taṅgāḷi, hemmara, kannusanne.

Pronouns
In many ways the third-person pronouns are more like demonstratives than like the other pronouns. They are pluralised like nouns and the first- and second-person pronouns have different ways to distinguish number.

Sample text
The given sample text is Article 1 from the United Nations Universal Declaration of Human Rights.

English
All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.

Kannada
ಎಲ್ಲಾ ಮಾನವರು ಸ್ವತಂತ್ರರಾಗಿಯೇ ಹುಟ್ಟಿದ್ದಾರೆ ಹಾಗು ಘನತೆ ಮತ್ತು ಅಧಿಕಾರಗಳಲ್ಲಿ ಸಮಾನರಾಗಿದ್ದಾರೆ. ತಿಳಿವು ಮತ್ತು ಅಂತಃಕರಣಗಳನ್ನು ಪಡೆದವರಾದ್ದರಿಂದ, ಅವರು ಒಬ್ಬರಿಗೊಬ್ಬರು ಸಹೋದರ ಭಾವದಿಂದ ನಡೆದುಕೊಳ್ಳಬೇಕು.

Romanisation (ISO 15919)
Ellā mānavaru svatantrarāgiyē huṭṭiddāre hāgu ghanate mattu adhikāragaḷalli samānarāgiddāre. Tiḷivu mattu antaḥkaraṇagaḷannu paḍedavarāddarinda avaru obbarigobbaru sahōdara bhāvadinda naḍedukoḷḷabēku.

title: Kannada


text:
Latin square

In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3×3 Latin square is

The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3. Euler began the general theory of Latin squares.

History
The Korean mathematician Choi Seok-jeong was the first to publish an example of Latin squares of order nine, in order to construct a magic square in 1700, predating Leonhard Euler by 67 years.

Reduced form
A Latin square is said to be reduced (also, normalized or in standard form) if both its first row and its first column are in their natural order. For example, the Latin square above is not reduced because its first column is A, C, B rather than A, B, C.

Any Latin square can be reduced by permuting (that is, reordering) the rows and columns. Here switching the above matrix's second and third rows yields the following square:

This Latin square is reduced; both its first row and its first column are alphabetically ordered A, B, C.

Orthogonal array representation
If each entry of an n × n Latin square is written as a triple (r,c,s), where r is the row, c is the column, and s is the symbol, we obtain a set of n2 triples called the orthogonal array representation of the square. For example, the orthogonal array representation of the Latin square

is

 * { (1, 1, 1), (1, 2, 2), (1, 3, 3), (2, 1, 2), (2, 2, 3), (2, 3, 1), (3, 1, 3), (3, 2, 1), (3, 3, 2) },

where for example the triple (2, 3, 1) means that in row 2 and column 3 there is the symbol 1. Orthogonal arrays are usually written in array form where the triples are the rows, such as:

The definition of a Latin square can be written in terms of orthogonal arrays:
 * A Latin square is a set of n2 triples (r, c, s), where 1 ≤ r, c, s ≤ n, such that all ordered pairs (r, c) are distinct, all ordered pairs (r, s) are distinct, and all ordered pairs (c, s) are distinct.

This means that the n2 ordered pairs (r, c) are all the pairs (i, j) with   1 ≤ i, j ≤ n, once each. The same is true of the ordered pairs (r, s) and the ordered pairs (c, s).

The orthogonal array representation shows that rows, columns and symbols play rather similar roles, as will be made clear below.

Equivalence classes of Latin squares
Many operations on a Latin square produce another Latin square (for example, turning it upside down).

If we permute the rows, permute the columns, or permute the names of the symbols of a Latin square, we obtain a new Latin square said to be isotopic to the first. Isotopism is an equivalence relation, so the set of all Latin squares is divided into subsets, called isotopy classes, such that two squares in the same class are isotopic and two squares in different classes are not isotopic.

Another type of operation is easiest to explain using the orthogonal array representation of the Latin square. If we systematically and consistently reorder the three items in each triple (that is, permute the three columns in the array form), another orthogonal array (and, thus, another Latin square) is obtained. For example, we can replace each triple (r,c,s) by (c,r,s) which corresponds to transposing the square (reflecting about its main diagonal), or we could replace each triple (r,c,s) by (c,s,r), which is a more complicated operation. Altogether there are 6 possibilities including "do nothing", giving us 6 Latin squares called the conjugates (also parastrophes) of the original square.

Finally, we can combine these two equivalence operations: two Latin squares are said to be paratopic, also main class isotopic, if one of them is isotopic to a conjugate of the other. This is again an equivalence relation, with the equivalence classes called main classes, species, or paratopy classes. Each main class contains up to six isotopy classes.

Number of $n × n$ Latin squares
There is no known easily computable formula for the number $L_{n}$ of $n × n$ Latin squares with symbols $1, 2, ..., n$. The most accurate upper and lower bounds known for large $n$ are far apart. One classic result is that $$ \prod_{k=1}^n \left(k!\right)^{n/k}\geq L_n\geq\frac{\left(n!\right)^{2n}}{n^{n^2}}.$$

A simple and explicit formula for the number of Latin squares was published in 1992, but it is still not easily computable due to the exponential increase in the number of terms. This formula for the number $L_{n}$ of $n × n$ Latin squares is $$ L_n = n! \sum_{A \in B_n}^{} (-1)^{\sigma_0 (A)} \binom{\operatorname{per} A}{n},$$ where $B_{n}$ is the set of all $n × n$ {0, 1}-matrices, $σ_{0}(A)$ is the number of zero entries in matrix $A$, and $per(A)$ is the permanent of matrix $A$.

The table below contains all known exact values. It can be seen that the numbers grow exceedingly quickly. For each $n$, the number of Latin squares altogether is $n! (n − 1)!$ times the number of reduced Latin squares.

For each $n$, each isotopy class contains up to $(n!)^{3}$ Latin squares (the exact number varies), while each main class  contains either 1, 2, 3 or 6 isotopy classes.

The number of structurally distinct Latin squares (i.e. the squares cannot be made identical by means of rotation, reflection, and/or permutation of the symbols) for $n$ = 1 up to 7 is 1, 1, 1, 12, 192, 145164, 1524901344 respectively.

Examples
We give one example of a Latin square from each main class up to order five.

$$ \begin{bmatrix} 1 \end{bmatrix} \quad \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix} \quad \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{bmatrix} $$

$$ \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 1 & 4 & 3 \\ 3 & 4 & 1 & 2 \\ 4 & 3 & 2 & 1 \end{bmatrix} \quad \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 4 & 1 & 3 \\ 3 & 1 & 4 & 2 \\ 4 & 3 & 2 & 1 \end{bmatrix} $$

$$ \begin{bmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 3 & 5 & 1 & 4 \\ 3 & 5 & 4 & 2 & 1 \\ 4 & 1 & 2 & 5 & 3 \\ 5 & 4 & 1 & 3 & 2 \end{bmatrix} \quad \begin{bmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 4 & 1 & 5 & 3 \\ 3 & 5 & 4 & 2 & 1 \\ 4 & 1 & 5 & 3 & 2 \\ 5 & 3 & 2 & 1 & 4 \end{bmatrix} $$

They present, respectively, the multiplication tables of the following groups:
 * {0} – the trivial 1-element group
 * $$\mathbb{Z}_2$$ – the binary group
 * $$\mathbb{Z}_3$$ – cyclic group of order 3
 * $$\mathbb{Z}_2 \times \mathbb{Z}_2$$ – the Klein four-group
 * $$\mathbb{Z}_4$$ – cyclic group of order 4
 * $$\mathbb{Z}_5$$ – cyclic group of order 5
 * the last one is an example of a quasigroup, or rather a loop, which is not associative.

Transversals and rainbow matchings
A transversal in a Latin square is a choice of n cells, where each row contains one cell, each column contains one cell, and there is one cell containing each symbol.

One can consider a Latin square as a complete bipartite graph in which the rows are vertices of one part, the columns are vertices of the other part, each cell is an edge (between its row and its column), and the symbols are colors. The rules of the Latin squares imply that this is a proper edge coloring. With this definition, a Latin transversal is a matching in which each edge has a different color; such a matching is called a rainbow matching.

Therefore, many results on Latin squares/rectangles are contained in papers with the term "rainbow matching" in their title, and vice versa.

Some Latin squares have no transversal. For example, when n is even, an n-by-n Latin square in which the value of cell i,j is (i+j) mod n has no transversal. Here are two examples:$$ \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix} \quad \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \\ 3 & 4 & 1 & 2 \\ 4 & 1 & 2 & 3 \end{bmatrix} $$In 1967, H. J. Ryser conjectured that, when n is odd, every n-by-n Latin square has a transversal.

In 1975, S. K. Stein and Brualdi conjectured that, when n is even, every n-by-n Latin square has a partial transversal of size n−1.

A more general conjecture of Stein is that a transversal of size n−1 exists not only in Latin squares but also in any n-by-n array of n symbols, as long as each symbol appears exactly n times.

Some weaker versions of these conjectures have been proved:

 * Every n-by-n Latin square has a partial transversal of size 2n/3.
 * Every n-by-n Latin square has a partial transversal of size n − sqrt(n).
 * Every n-by-n Latin square has a partial transversal of size n − 11 log$n$(n).
 * Every n-by-n Latin square has a partial transversal of size n − O(log n/loglog n).
 * Every large enough n-by-n Latin square has a partial transversal of size n −1. (Preprint)

Algorithms
For small squares it is possible to generate permutations and test whether the Latin square property is met. For larger squares, Jacobson and Matthews' algorithm allows sampling from a uniform distribution over the space of n × n Latin squares.

Statistics and mathematics

 * In the design of experiments, Latin squares are a special case of row-column designs for two blocking factors.
 * In algebra, Latin squares are related to generalizations of groups; in particular, Latin squares are characterized as being the multiplication tables (Cayley tables) of quasigroups. A binary operation whose table of values forms a Latin square is said to obey the Latin square property.

Error correcting codes
Sets of Latin squares that are orthogonal to each other have found an application as error correcting codes in situations where communication is disturbed by more types of noise than simple white noise, such as when attempting to transmit broadband Internet over powerlines.

Firstly, the message is sent by using several frequencies, or channels, a common method that makes the signal less vulnerable to noise at any one specific frequency. A letter in the message to be sent is encoded by sending a series of signals at different frequencies at successive time intervals. In the example below, the letters A to L are encoded by sending signals at four different frequencies, in four time slots. The letter C, for instance, is encoded by first sending at frequency 3, then 4, 1 and 2.

$$ \begin{matrix} A\\ B\\ C\\ D\\ \end{matrix}

\begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 1 & 4 & 3 \\ 3 & 4 & 1 & 2 \\ 4 & 3 & 2 & 1 \\ \end{bmatrix} \quad

\begin{matrix} E\\ F\\ G\\ H\\ \end{matrix}

\begin{bmatrix} 1 & 3 & 4 & 2\\ 2 & 4 & 3 & 1\\ 3 & 1 & 2 & 4\\ 4 & 2 & 1 & 3\\ \end{bmatrix} \quad \begin{matrix} I\\ J\\ K\\ L\\ \end{matrix}

\begin{bmatrix} 1 & 4 & 2 & 3\\ 2 & 3 & 1 & 4\\ 3 & 2 & 4 & 1\\ 4 & 1 & 3 & 2\\ \end{bmatrix} $$

The encoding of the twelve letters are formed from three Latin squares that are orthogonal to each other. Now imagine that there's added noise in channels 1 and 2 during the whole transmission. The letter A would then be picked up as: $$\begin{matrix}12 & 12 & 123 & 124\end{matrix}$$

In other words, in the first slot we receive signals from both frequency 1 and frequency 2; while the third slot has signals from frequencies 1, 2 and 3. Because of the noise, we can no longer tell if the first two slots were 1,1 or 1,2 or  2,1  or  2,2. But the 1,2 case is the only one that yields a sequence matching a letter in the above table, the letter A. Similarly, we may imagine a burst of static over all frequencies in the third slot: $$\begin{matrix}1 & 2 & 1234 & 4\end{matrix}$$

Again, we are able to infer from the table of encodings that it must have been the letter A being transmitted. The number of errors this code can spot is one less than the number of time slots. It has also been proven that if the number of frequencies is a prime or a power of a prime, the orthogonal Latin squares produce error detecting codes that are as efficient as possible.

Mathematical puzzles
The problem of determining if a partially filled square can be completed to form a Latin square is NP-complete.

The popular Sudoku puzzles are a special case of Latin squares; any solution to a Sudoku puzzle is a Latin square. Sudoku imposes the additional restriction that nine particular 3×3 adjacent subsquares must also contain the digits 1–9 (in the standard version). See also Mathematics of Sudoku.

The more recent KenKen and Strimko puzzles are also examples of Latin squares.

Board games
Latin squares have been used as the basis for several board games, notably the popular abstract strategy game Kamisado.

Agronomic research
Latin squares are used in the design of agronomic research experiments to minimise experimental errors.

Heraldry
The Latin square also figures in the arms of the Statistical Society of Canada, being specifically mentioned in its blazon. Also, it appears in the logo of the International Biometric Society.

Generalizations

 * A Latin rectangle is a generalization of a Latin square in which there are n columns and n possible values, but the number of rows may be smaller than n. Each value still appears at most once in each row and column.
 * A Graeco-Latin square is a pair of two Latin squares such that, when one is laid on top of the other, each ordered pair of symbols appears exactly once.
 * A Latin hypercube is a generalization of a Latin square from two dimensions to multiple dimensions.

title: Latin square


text:
Overhand

Overhand may refer to:

 * Overhand (boxing), a looping punch
 * Overhand knot
 * Overhand throwing motion
 * Overhand grip

title: Overhand


text:
Mariner 9

Mariner 9 (Mariner Mars '71 / Mariner-I) was a robotic spacecraft that contributed greatly to the exploration of Mars and was part of the NASA Mariner program. Mariner 9 was launched toward Mars on May 30, 1971, from LC-36B at Cape Canaveral Air Force Station, Florida, and reached the planet on November 14 of the same year, becoming the first spacecraft to orbit another planet – only narrowly beating the Soviet probes Mars 2 (launched May 19) and Mars 3 (launched May 28), which both arrived at Mars only weeks later.

After the occurrence of dust storms on the planet for several months following its arrival, the orbiter managed to send back clear pictures of the surface. Mariner 9 successfully returned 7,329 images over the course of its mission, which concluded in October 1972.

Objectives

Mariner 9 was designed to continue the atmospheric studies begun by Mariner 6 and 7, and to map over 70% of the Martian surface from the lowest altitude (1500 km) and at the highest resolutions (from 1 kilometer to 100 meters (1,100 to 110 yards) per pixel) of any Mars mission up to that point. An infrared radiometer was included to detect heat sources in search of evidence of volcanic activity. It was to study temporal changes in the Martian atmosphere and surface. Mars' two moons were also to be analyzed. Mariner 9 more than met its objectives.

Under original plans, a dual mission was to be flown like Mariners 6–7, however the launch failure of Mariner 8 ruined this scheme and forced NASA planners to fall back on a simpler one-probe mission. NASA still held out hope that another Mariner probe and Atlas-Centaur could be readied before the 1971 Mars launch window closed. A few logistical problems emerged, including the lack of an available Centaur payload shroud of the correct configuration for the Mariner probes, however there was a shroud in NASA's inventory which could be modified. Convair also had an available Centaur stage on hand and could have an Atlas readied in time, but the idea was ultimately abandoned for lack of funding.

Mariner 9 was mated to Atlas-Centaur AC-23 on May 9 with investigation into Mariner 8's failure ongoing. The malfunction was traced to a problem in the Centaur's pitch control servoamplifier and because it was not clear if the spacecraft itself had been responsible, RFI testing was conducted on Mariner 9 to ensure the probe was not releasing interference that could cause problems with the Centaur's electronics. All testing came back negative and on May 22, a tested and verified rate gyro package arrived from Convair and was installed in the Centaur.

Liftoff took place on May 30 at 22:23:04 UT. All launch vehicle systems performed normally and the Mariner separated from the Centaur at 13 minutes and 18 seconds after launch.

Instruments

 * 1) Ultraviolet Spectrometer (UVS)
 * 2) Infrared Interferometer Spectrometer (IRIS)
 * 3) Celestial Mechanics (not a separate instrument; it relied upon tracking measurements including range, range rate, and Doppler)
 * 4) S-Band Occultation (not a separate instrument; experiment observed the attenuation of the communication signal as the orbiting satellite passed out of view)
 * 5) Infrared Radiometer (IRR)
 * 6) Visual Imaging System – in a lower orbit, half that of Mariner 6 and Mariner 7 flyby missions, and with a vastly improved imaging system, Mariner 9 achieved a resolution of 320 ft per pixel, whereas previous Martian probes had achieved only approximately 2600 ft per pixel.

Spacecraft and subsystems
The power for the spacecraft was provided by a total of 14,742 solar cells, being distributed between 4 solar panels, which in total resulted in 7.7 meters of solar panels being present in the spacecraft. The solar panels produced a 500 watts in the orbit of Mars, the energy was stored in a 20 amp-hr nickel-cadmium battery.

Propulsion was provided by the RS-2101a engine, which could produce 1340 N thrust, and in total could have 5 restarts. The engine was fueled by monomethyl hydrazine and nitrogen tetroxide. For atittude control, the spacecraft contained 2 sets of 6 nitrogen jets on the tip of the solar panels. Attitude knowledge was provided by a Sun sensor, a Canopus star tracker, gyroscopes, an inertial reference unit, and an accelerometer. The thermal control was achieved by the use of louvers on the eight sides of the frame and thermal blankets.

Achievements

Mariner 9 was the first spacecraft to orbit another planet. It carried an instrument payload similar to Mariners 6 and 7, but because of the need for a larger propulsion system to control the spacecraft in Martian orbit, it weighed more than Mariners 6 and 7 combined (Mariner 6 and Mariner 7 weighed 413 kilograms while Mariner 9 weighed 997.9 kilograms). When Mariner 9 arrived at Mars on November 14, 1971, planetary scientists were surprised to find the atmosphere was thick with "a planet-wide robe of dust, the largest storm ever observed." The surface was totally obscured. Mariner 9's computer was thus reprogrammed from Earth to delay imaging of the surface for a couple of months until the dust settled. The main surface imaging did not get underway until mid-January 1972. However, surface-obscured images did contribute to the collection of Mars science, including understanding of the existence of several huge high-altitude volcanoes of the Tharsis Bulge that gradually became visible as the dust storm abated. This unexpected situation made a strong case for the desirability of studying a planet from orbit rather than merely flying past. It also highlighted the importance of flexible mission software. The Soviet Union's Mars 2 and Mars 3 probes, which arrived during the same dust storm, were unable to adapt to the unexpected conditions, which severely limited the amount of data that they were able to collect.

After 349 days in orbit, Mariner 9 had transmitted 7,329 images, covering 85% of Mars' surface, whereas previous flyby missions had returned less than one thousand images covering only a small portion of the planetary surface. The images revealed river beds, craters, massive extinct volcanoes (such as Olympus Mons, the largest known volcano in the Solar System; Mariner 9 led directly to its reclassification from Nix Olympica), canyons (including the Valles Marineris, a system of canyons over about 2500 mi long), evidence of wind and water erosion and deposition, weather fronts, fogs, and more. Mars' small moons, Phobos and Deimos, were also photographed.

The findings from the Mariner 9 mission underpinned the later Viking program.

The enormous Valles Marineris canyon system is named after Mariner 9 in honor of its achievements.

After depleting its supply of attitude control gas, the spacecraft was turned off on October 27, 1972.

Construction
The ultraviolet spectrometer (UVS) aboard Mariner 9 was constructed by the Laboratory for Atmospheric and Space Physics at the University of Colorado, Boulder, Colorado. The ultraviolet spectrometer team was led by Professor Charles Barth.

The Infrared Interferometer Spectrometer (IRIS) team was led by Dr. Rudolf A. Hanel from NASA Goddard Spaceflight Center (GSFC). The IRIS instrument was built by Texas Instruments, Dallas, Texas.

The Infrared Radiometer (IRR) team was led by Professor Gerald Neugebauer from the California Institute of Technology (Caltech).

Error-correction codes achievements
To control for errors in the reception of the grayscale image data sent by Mariner 9 (caused by a low signal-to-noise ratio), the data had to be encoded before transmission using a so-called forward error-correcting code (FEC). Without FEC, noise would have made up roughly a quarter of a received image, while the FEC encoded the data in a redundant way which allowed for the reconstruction of most of the sent image data at reception.

Since the flown hardware was constrained with regards to weight, power consumption, storage, and computing power, some considerations had to be put into choosing an FEC, and it was decided to use a Hadamard code for Mariner 9. Each image pixel was represented as a six-bit binary value, which had 64 possible grayscale levels. Because of limitations of the transmitter, the maximum useful data length was about 30 bits. Instead of using a repetition code, a [32, 6, 16] Hadamard code was used, which is also a 1st-order Reed-Muller code. Errors of up to seven bits per each 32-bit word could be corrected using this scheme. Compared to a five-repetition code, the error correcting properties of this Hadamard code were much better, yet its data rate was comparable. The efficient decoding algorithm was an important factor in the decision to use this code. The circuitry used was called the "Green Machine", which employed the fast Fourier transform, increasing the decoding speed by a factor of three.

Present location
As of February 2022, Mariner 9's location is unknown; it is either still in orbit, or has already burned up in the Martian atmosphere or crashed into the surface of Mars.

NASA has provided multiple dates for when Mariner 9 could enter the Martian atmosphere. In 2011, NASA predicted that Mariner 9 would burn up or crash into Mars around 2022. However, a 2018 revision to the Mariner 9 mission page by NASA expected Mariner 9 would crash into Mars "sometime around 2020". At the time of the mission, Mariner 9 was left in an orbit that would not decay for at least 50 years, which placed the earliest date of atmospheric entry to October 2022. By August 2023, it is likely that Mariner 9 entered the Martian atmosphere and either burned up or impacted the surface.

title: Mariner 9